THERMAL SYSTEM FOR THE GENERATION OF MECHANICAL ENERGY IN A SHAFT OF A TURBINE IN CLOSED CIRCUIT, WI

专利摘要:
Thermal system for the generation of mechanical energy in a shaft of a turbine in a closed circuit, with a compressor and with input of heat from an external source, and internal recovery of heat and mechanical energy, for the generation of electricity, according to a procedure, and procedure of selection of system operation status. The system includes flared mechanical recuperators to transform dynamic pressure into static pressure at the compressor or turbine outlet, and several cycles can be chained into one, with increased performance. Additionally, the system establishes vertical circulation of the fluids in the heat exchangers, and provides a procedure for selecting the thermodynamic state to operate the system, depending on the availability of energy and temperature of the external heat source, for which it includes an auxiliary fluid supply system, to inject or extract fluid from the closed circuit, depending on whether it is desired to increase or decrease power. (Machine-translation by Google Translate, not legally binding)
公开号:ES2779783A1
申请号:ES201930997
申请日:2019-06-13
公开日:2020-08-19
发明作者:Penalosa Jose Maria Martinez-Val
申请人:Universidad Politecnica de Madrid；
IPC主号:

专利说明:

[0001] THERMAL SYSTEM FOR THE GENERATION OF MECHANICAL ENERGY IN A SHAFT OF A TURBINE IN CLOSED CIRCUIT, WITH A COMPRESSOR AND WITH SUPPLY OF HEAT FROM AN EXTERNAL SOURCE, AND INTERNAL RECOVERY OF HEAT AND MECHANICAL ENERGY, FOR GENERATION OF ELECTRICITY, ACCORDING TO A PROCEDURE, ACCORDING TO A PROCEDURE, SELECTING THE STATE OF SYSTEM OPERATION
[0003] TECHNICAL SECTOR
[0004] The invention falls within the field of thermodynamic cycles that transform thermal energy into kinetic energy of the axis of rotation of its expanding machine or turbine, whose axis is coupled to the axis of an electric generator.
[0006] TECHNICAL PROBLEM TO BE SOLVED AND BACKGROUND OF THE INVENTION
[0007] The problem consists of making the most of the energy from an external heat source, devising a thermodynamic assembly that uses relatively conventional machines and equipment, but interconnected in a novel way, exploiting to the maximum the thermo-physical qualities of the real working fluid, through recovery internal thermal energy and mechanical energy, obtaining results that go beyond the state of the art.
[0009] Furthermore, the invention consists in devising the appropriate technical requirements of the thermodynamic system to set the upper and lower pressure values, between which the system works, and also devising the operating procedures to vary the power generated by the system, depending on the power available in the hot spot, and the cooling conditions of the cold spot.
[0010] From the theoretical point of view and analysis of proposals, the state of the art can be seen described in the previous applications of the inventor of the present application; Specifically, patent ES 2427648 B2 deals with a Brayton cycle with ambient cooling close to the critical isotherm, the second document, with Spanish patent application number P 201731263, which describes a cycle with a lower enthalpy point that has a temperature below of criticism, but his pressure is above critical pressure.
[0012] It is well known that the thermo-mechanical performance is limited to the Carnot performance, as a theoretical maximum. Additionally, they impact against performance, irreversibilities and friction of all kinds that may occur throughout the cycle, which is generally defined assuming reversible processes. However, given the impossibility of reducing irreversibilities to zero, it is very important that the proposed novelty includes the effects of irreversibilities, which will be pointed out when describing the invention.
[0013] An important part of the state of the art is the theoretical formulation of the Brayton cycle in its various specificities, which is briefly reviewed below:
[0015] For an open Brayton cycle, in which the air inlet to the compressor is at atmospheric pressure, and the same happens with the turbine exhaust, the ideal gas performance is
[0018] £ = 1 ~ ^ p
[0020] where p is the thermal exponent of an isentropic evolution, where r is the compression ratio. It is particularly applicable to isentropic compression initiated with pressure P0 and temperature T0; and reaching pressure P1 and temperature T1, the value of which is
[0024] where r is the compression ratio, equal to P1 / P0. For an ideal gas the value of p corresponds to (y-1) / y; where y is the adiabatic coefficient.
[0026] Properly speaking, the aforementioned performance is achieved in the best case of an open Brayton, which is when the compressor and turbine outlet temperatures reach the same value, so the Carnot ratio p (= Tm / T0 ) it is
[0031] Note that the subscripts of temperature are
[0033] 0 = compressor inlet (which is the minimum fluid in the cycle)
[0034] C = compressor outlet
[0036] t = turbine outlet
[0037] M = inlet into the turbine (which is the maximum fluid temperature in the cycle).
[0038] At first glance it is strange that the performance does not depend on the extreme temperature quotient, p, but in reality it does depend, by the last equation, so it can be rewritten
[0042] Vm
[0044] This performance is always worse than Carnot's (1-p-1).
[0046] It is very important to note that, in the open cycle, the performance increases as does the compression ratio.
[0048] This trend changes absolutely in a closed regenerative cycle, which in the ideal gas case is governed by
[0053] where WC is the specific work absorbed by the compressor shaft, and WT is that delivered by the turbine shaft.
[0058] And therefore, in the closed Brayton ideal cycle, with ideal gas we get to
[0060] rP
[0063] It is seen that the yield increases as p increases, and as r decreases . Furthermore, the limit of this yield, when r tends to 1, is precisely the Carnot yield; but properly speaking, that limit does not exist, as there would be no cycle, because the high and low isobars would coincide.
[0064] Note in this case that the Carnot quotient has a different expression than the previous one, since it includes the effect of the regenerative exchanger; which requires that the turbine outlet temperature be higher than that of the compressor outlet. The Carnot quotient is now decomposed into:
[0069] where m is the factor that characterizes the regeneration. In the equation it has been indicated that, in real cases, the exponents of expansion (P ') and compression (P) will be different, as well as the respective compression ratios, r and r', the latter being less than the first , for reasons of loss of charge in the circuit.
[0071] In the previous equation it is summarized that, in each half cycle, there are three phases: compression, regeneration and external heating, in the half cycle of rising enthalpy; and expansion, regeneration and external cooling in the downstream.
[0073] The cycle is closed through the entropy balance, taking into account that both compression and expansion are considered isentropic. This allows the balance to be formulated simply, as the entropy gained from the end of the compression to the beginning of the expansion, by the high isobar, is equal, in absolute value, to the entropy lost from the end of the expansion, up to the principle of compression, by the low isobar.
[0075] For each of the isobar phases, the entropy and enthalpy variation can be written in these terms, as a function of the specific heat Cp and the temperatures of the beginning and end of the phase, Txi and Txf.
[0080] r Txf
[0081] & Hx = I CP dT = Cx ( Txf - TXi)
[0084] From this, the temperature Tx that characterizes each phase can be defined, and corresponds to
[0085] T _ AHx _ cx -Txf - Txi) _ c
[0086] x ASx GxLn {Txf / Txi) % x X °
[0088] Where Tx0 is the temperature that would be characteristic in an ideal gas under these conditions, since Cp is constant in the ideal gas, and Cx = Gx.
[0090] The entropy balance can be written, using a and b as identifiers of the high and low pressure isobars; and corresponding the subscript r to the regenerative exchanger, the h to the hot source, and the f to the cold source:
[0092]
[0094] For its precise definition, it is necessary to identify the temperature Ta in which it ends
[0095] high pressure regeneration, and external heating begins. Said Ta must be less than the turbine outlet temperature Tt, being able to write
[0096] Tt = Ta + AT, where the AT value has been entered as the difference (practically constant) between the hot and cold fluid in the regenerative exchanger. For
[0097] the absolutely ideal case, which would require an exchanger of infinite length, and therefore impossible, said difference between both currents would be AT = 0.
[0099] The definitions are thus
[0101] ASra _ GraLn ( j-)
[0103] A Sh _ G hLn ( T- +
[0108] ASr rbb _ Gr rb4Ln ( T _t a _c 2 A ATT))
[0110] It is well known that when gases get very close to the biphasic bell
[0111] liquid-vapor, that is to say, at the saturation curve by beginning of condensation, the behavior of the real gas is quite far from ideal gas; and it moves further away when it approaches the critical point.
[0112] As a generalized equation of state, the Ideal Gas is used, including the so-called "compressibility factor", identified by "z", and that at each point is what makes it true
[0114] P -V = z - R - T
[0116] It is important to note that z is dimensionless, but not R (which is measured in kJ / (kgK)).
[0118] The compressibility factor z is equal to 1 when the substance behaves as an ideal gas.
[0120] There are a number of thermodynamic properties that are part of the state of the art, and help to formulate the invention. An indispensable property is the expression of the variation of enthalpy in an isentropic process:
[0124] Another useful parameter to characterize the equation of state is fp, called the "logarithmic factor of isobar dilation", and corresponds to
[0128] This logarithmic factor is 0 for ideal gases.
[0130] The change in specific enthalpy that occurs when passing from P0 to P1 along a given temperature isotherm, Ti; which is denoted by AHi obeys
[0134] where the mean value of V ( VTi) and fp ( fpi) have been used. The minus sign is due to the specific enthalpy decreasing when the pressure increases along an isotherm.
[0136] In turn, the logarithmic isobar expansion factor is used to generally calculate the thermal exponent of temperature evolution in a real isentropic compression or expansion, which has been denoted by p, which is, as shown below,
[0138] p = ^ L> (1 2 fp)
[0139] and which determines the aforementioned thermal evolution, which starts in a state characterized by the pressure P0 and the temperature T0 and evolves to the pressure Pi, then the final temperature Ti is
[0141] h
[0142] ^h © '
[0143] To obtain the equation of p, we start from the following Maxwell equation:
[0147] in which the following equalities apply
[0152] And combining both derivatives the previous value of p is obtained:
[0153] ^{P (/ OdT}} f ^{/ dLnT } _ R (} f ^{d L nz} ' ^}
[0154] T dp) s ~ dLÜp) s ~ Z cp [ d íñ T) P 1 = P
[0155] It is important to remember that general isentropic evolution, characterized by dS = 0, part of the definition of entropy
[0156] dT OP
[0157] dS = Cvv - _t - 2 ( - _{q ^ tj} ) _v vdV
[0158] The real equation of state is incorporated into this equation, with z giving
[0159] Q ^tdP v ^{R f (Oz >}
[0160] ^{= = 7} { ^t Q v ^{2 z} )
[0165] By pointing to a pressure P0 next to T0, you are choosing an isentropic one. When the high pressure P1 is chosen, having already set the maximum admissible temperature, TM, the high isentropic that closes the cycle will be obtained.
[0167] When considering the compression and regeneration processes, two enthalpic increases appear, which cannot be recovered in regeneration or thermal recovery:
[0168] - One, the increase in enthalpy CpAT, with AT being the difference between hot and cold temperatures in the regenerative exchanger.
[0169] - Two, the increase in enthalpy that occurs when going down the isotherm from P1, Tc to P0, Tc. This last drop is not part of the material cycle of the fluid, but it belongs to the regenerative heat transfer process, since it is its limit, due to the low enthalpy end.
[0171] This last value of enthalpy increase, previously called AHi, is the minimum that is lost in regeneration, for reasons of the equation of state. To this we must add the first point, and thus we can define the decompensated enthalpy, or not recovered, QA in the regenerative exchange, which can be expressed by
[0173] QA - í 1 Cpm ^ T
[0175] where Cpm is the average value of the specific heat in the regeneration low isobar. This non-recoverable quantity must be minimized, and since the first addition is equal to -VTífpí {P1 - P0), it is advisable to minimize f (which is equal to 0 for ideal gas). That is, a domain of the diagram of the gas used as the working fluid must be chosen, in which it behaves as an ideal gas. In that diagram, the value of Cp will be appreciably constant, not depending significantly on T or P.
[0177] This is a prescription that is already well known in the state of the art, but it is included here because the novelty of the invention is implemented with better results in this ideal gas domain.
[0179] If we take into account the specific work (specific enthalpy) of the WT turbine, the compressor, WC and the decompensated enthalpy QA the performance can be written as
[0182] £ - 11 Q ^to / W ^t
[0184] This equation includes, by QA, the effect of the impossibility of regenerating these facilities to 100%.
[0186] Along with this purely thermodynamic effect, two other sources of mechanical irreversibilities must be accounted for: those due to machines, turbine and compressor, which present interstitial flows and friction; and the effect of manometric head loss in all pipes.
[0188] These three sources of thermodynamic irreversibility, due to machines, due to the loss of manometric head, and due to the impossibility of recovering 100% of the regeneration heat, are fundamental facts that must be strictly taken into account when defining the real cycle; for if they are not considered properly, the proposed result could be an entelechy, not a constructable reality.
[0190] It is convenient to delve into the structure of the cycle performance equation, which with the equation of state of a real fluid, without including irreversibilities, could be written
[0194] Where it has been distinguished between the exponent p of the compression and the P 'of the expansion (which will be very close to that of the ideal gas, that is, R / Cp). In fact, if the gas behaves as an ideal throughout the cycle domain, both exponents will be equal and constant, given by:
[0198] being and
[0202] the ratio between specific heats, isobar and isocar. As a reference to the state of the art, it starts from a cyclical process that in its ideal definition or without irreversibilities, works between an isobar of lower pressure, or low isobar, which is at P0, and a high isobar, or higher pressure, P1 , existing
[0204] - A compression phase, in which a compressor draws in the fluid at its lowest specific enthalpy point of the entire cycle, at pressure P0 and temperature T0, and raises it in pressure throughout an isentropic evolution, in the case of ideal cycle, up to Pc, leaving the compressor with a temperature Tc, which is linked to T0 through its quotient (Tc / T0) is equal to rp, where r is the quotient of pressures (Pc / P0) and p is the thermal exponent of compression. (The effect of the various phase performances on the overall performance is included at the end of the cycle).
[0205] - It is followed by a heating phase in which two types of heat sources act successively, which are
[0207] ^or the working fluid itself, from another phase of the cycle, in which it is warmer, which is at the outlet of the turbine, thus carrying out a thermally regenerative phase, which in this heating phase reaches a temperature Ta that is below the turbine outlet temperature, Tt, by an amount called the upper terminal temperature difference, Dtst, whose value is between 0.001 K and the temperature difference between the turbine outlet and the outlet of the compressor, and as a reference of the invention the value of 20 K is taken.
[0209] ^o The external source of heat input to the working fluid, with which the fluid is heated up to TM, which is the maximum temperature that the working fluid reaches, selecting the source of said heat from the combustion of a fuel in a chamber of combustion outside the closed circuit of the working fluid, or another heat source such as solar thermal, transferring the heat generated, or captured, to the working fluid, through a heat exchanger called a heater.
[0210] - An expansion phase, from the point of maximum specific enthalpy of the cycle, in which the working fluid is at pressure PM and temperature TM, evolving, in the case of the ideal cycle, isentropically up to the pressure P0, leaving the turbine or expanding machine, where this phase is carried out, with temperature Tt; where Tt = TM / rp
[0211] - It is followed by a regenerative cooling phase, in which the cold fluid is the working fluid itself, in another phase of the cycle in which it is colder, which is at the compressor outlet. This heat transfer is carried out in a regenerative heat exchanger, cooling the fluid to a temperature Tb that is above the Compressor outlet temperature Tc, in an amount called lower terminal temperature difference, represented by Dtit, whose value is between 0.001 K and the temperature difference between the turbine outlet and the compressor outlet, and as a reference of the invention the value of 20 K is taken.
[0212] - And there is a last phase, which takes place in the external cooling sump, which cools the fluid to T0, which was the point taken as the start of the cycle.
[0214] Thus, in the cycle there are basically two types of phases, which are described in the thermodynamic diagram, with their very clear specificities:
[0216] - Isobar phases, which are those present in heating and cooling.
[0217] - Isentropic phases, which are those that govern pressure changes, and in which thermomechanical transformations take place (ideally).
[0219] The physical evolution of the fluid states throughout the cycle is defined by 5 variables, which must be known at each point, and which are: pressure (P), temperature (T), density (p), speed ( c) and straight section (S) of the fluid passage. In general, all ducts will be assumed to be circular cross section. If they are not, they can be treated as such, using the concept of Hydraulic Diameter.
[0221] The five equations necessary to determine evolution are as follows, perfectly defined. They are written in their integrated form, between the beginning of a phase, denoted by the subscript i, and its end, with the subscript e, in the absence of external circumstances that imply substantial modifications in the Balance Sheet Form:
[0223] - Equation of continuity, or mass balance (more exactly, of flow, or mass flow, in
[0224] w) Pic Yes w e fish
[0225] - Linear impulse balance, or pressures
[0227] 4 1 mPíC = pl MpeC
[0228] - Energy balance (per unit mass) in quasi-ideal gas conditions
[0231] - Equation of state of the fluid (ideal gas; if anything with a minor correction, through z
[0233] - = zRT
[0235] - Equation of the transformation of the fluid, essentially counting on the two already mentioned:
[0236] Isóbara: 4¿ = 4e
[0237] Isentropic: 4¿6) y = 4eVey
[0239] For these last transformations, which are essential to properly convert thermal energy into mechanical energy, it is very useful to take into account that the evolutions of P, T and p (or their inverse, the specific volume, V) are entangled, due to the equation of state and the equation with the adiabatic quotient Y- This is usually expressed by introducing the Mach number in the equations, as the quotient between the speed of the fluid at a given point, c, and the speed of sound at that point, cs, being defined the latter for
[0241] cs = VHRT
[0243] Keeping the previous nomenclature of the initial state i; and from the final or escape state, e, it is obtained that in the isentropic (ideal) transformations the following equations are satisfied:
[0245] T | {1 il ^ - ± M M2 2)) = T, e | 1 H_ —_ 1 M ^q 2 2 '
[0246] 2 ^"l) e V 2
[0247] ^{, y / (yD} (V ~ 1 2 y / (yD
[0248] 4) 'i ~~ 2 ~ Q)) _{= 4e | 1 "" 2 M)}
[0253] With these precedents taken from the state of the art and from general thermodynamic knowledge, the description of the invention is approached, which requires prior considerations on the mechanisms that generate thermal or mechanical losses, fundamentally those that come from friction, such as pressure loss manometric, or the entropy increase in fluid machines.
[0254] Furthermore, it is recalled that the thermal system of the state of the art is made up of the following physical components, concatenated in a closed circuit, which we call the main circuit:
[0256] - a compressor, with its blade plate and its static outlet diffuser, the blade plate being driven by an electric motor;
[0257] - a post compressor mechanical energy recuperator
[0258] - a regenerative heat exchanger, with a high pressure branch, which is connected to the previous recuperator, and which in the way selected to materialize the invention is constituted by a regular quadrangular bundle of tubes, inside a reinforced prismatic casing; the high pressure gas flowing inside the tubes, and the low pressure gas flowing outside them, inside the shell;
[0259] - a hot spot, which is an exchanger, in which heat is supplied from an external hot fluid, to the working fluid that moves in a closed circuit, at the end of its high pressure path;
[0260] - a gas expansion turbine, with two parts in which the two phases through which the fluid passes in the turbine occur: the crown of nozzles to create very high speed jets, without reaching the speed of sound; and the blades whose turning plate is connected to an axis of revolution, which is jointly connected to an electric generator;
[0261] - a post turbine mechanical energy recuperator;
[0262] - a cold source, consisting of an inlet manifold and an exchanger, in which heat is extracted from the working fluid, at the end of its low pressure path, to a cold outside fluid, such as air from the atmosphere or water from the hydrosphere, also having an outlet collector for the cooled working fluid, which leads to the inlet of the compressor.
[0264] It is prescribed that the working fluid behaves sufficiently as an ideal gas in the thermodynamic domain in which the cycle will unfold, meaning that the real values of the state variables do not differ from the ideal gas values by more than 5%.
[0266] As has been pointed out, there are two essential parameters in the description of the cycle, which are the pressure ratio, r, in each machine, compressor and turbine, and the adiabatic quotient, and, which is the quotient between the isobar and isochor specific heats. For simplification of writing, the coefficient p will be used, as already commented
[0270] It will be denoted with the compressor performance, which is measured by the ideal enthalpy increase in the compression isentropic, divided by the real increase, corresponding to the real outlet temperature, Tc which can be written
[0274] With this denomination, the specific real compression work, Wcr is expressed as a function of the theoretical one, Wc, always measured in joules per kilogram, as is the enthalpy, which is always specific, that is, per unit mass, and therefore expressed in J / kg. When these quantities are multiplied by the mass flow, in kg / s, the corresponding power is obtained.
[0276] For the compressor the expression
[0280] Similarly, the turbine performance, represented by qt, is defined as the real decrease in enthalpy, divided by the ideal decrease, and is expressed as a function of the real temperature at its outlet, Tt, with respect to that of the turbine inlet, TM, and the theoretical output, r "pTM,
[0284] The ideal cycle performance was defined as
[0288] where p is the Carnot quotient, TM / T0.
[0290] If in the previous definition, the theoretical specific tasks of the compressor and the turbine are replaced by the realistic ones, which include the performances of these machines, the following expression is obtained
[0291] Wcr r
[0292] £ r = 1 - 1¿ L = 1 --------- Wtr PRcRt
[0294] In this expression the other two efficiency loss effects are not considered: enthalpy not recovered in regeneration; and the defect produced by the loss of manometric head.
[0296] The first affects the entire equation, since it requires increasing the total heat input, QA. Its effect is therefore accounted for in the denominator of the yield equation, as already expressed
[0299] £ = T T q j w T
[0301] If the ratio QA / Wtr is called d, the negative effect on realistic performance, £ r, can be expressed as
[0305] As for the manometric head loss, the main effect will be the fact that the pressure ratio in the compressor (or compression ratio), including the effect of the post-compressor mechanical recuperator at its outlet, will be greater than the pressure ratio in the turbine, including the effect of the post-turbine mechanical recuperator at the turbine outlet, so that the fluid goes from the compressor to the turbine, and back.
[0307] If we identify the pressures P of the significant points by the subscripts of these points, the compression ratio can be equated to the product of the successive quotients between successive points, as the fluid circulates through the circuit that materializes the cycle. Calling rcr to the pressure ratio in the compressor, plus its recuperator, and rtr the same ratio, but in the turbine, including its recuperator at the outlet, we have
[0309] i p cr i 4 cr 14 M 14 tr
[0310] rcr = 4P0 = P ~ M4 ~ PPtr P W0 = Urtr
[0311] Where the parameter j, greater than 1, is
[0314] Pcr, which is the pressure at the outlet of the compressor recuperator, must be greater than PM, the pressure at the turbine inlet, in such an amount as to balance the loss of manometric head in the high or higher isobar. The same can be said of the low or lower isobar, from the output of the post-turbine mechanical recuperator (Ptr) to the inlet of the compressor (P0). The head losses take place, above all, in the high and low pressure branches of the regenerative exchanger.
[0316] For the final formulation of the realistic performance, the quotient must be taken into account
[0318] Wcr T0 {jP r P - 1)
[0319] wtr TMr ~ P (rp - 1) RcVt
[0320] where r now represents the pressure ratio in the turbine, and j is the specified parameter, as a product of the pressure ratios in each branch, ideally isobar, the numerator of each ratio being the pressure at the beginning of the branch, and the denominator being the pressure at the end of it.
[0321] From this, the equivalent performance for manometric head loss, Hj
[0325] Which allows to express definitively the complete realistic yield, £ r, by means of the following equation
[0329] In the previous equation, and in the one that precedes it, r represents the pressure ratio in the turbine, and its recuperator, being that of the compressor jr.
[0331] From this last equation it follows that to obtain a positive performance in the real cycle, the first parenthesis must be positive, and therefore it must be prescribed that the temperature ratio in the turbine (which is equal to r3) must be less than a certain coefficient that results from multiplying the Carnot quotient by the three thermo-mechanical performances: compressor, turbine and manometric pressure drop, which can be called modified Carnot coefficient:
[0333] r P <fflcVtVj
[0334] There must also be a lower bound, which in this case refers to the second parenthesis of the realistic performance equation, which refers to the other cause of loss of efficiency, which occurs in the non-total recovery of heat from regeneration. For this, a regeneration performance is defined, which is:
[0338] As the prescription has been established requiring that the gas be very close to ideal gas, the non-recovery of enthalpy in regeneration will be given by the difference in temperatures Dt between the hot and cold fluid,
[0340] = Dt
[0341] é T ^m ( 1 - r ~ P ) Rt
[0342] And the regeneration performance remains
[0346] For simplicity, it can be called
[0350] Realistic performance can therefore be formulated as
[0354] where
[0356] r ^P - one
[0357] R ^Y [r ^p - 1
[0359] The previous development is immediately summarized in a requirement on the Carnot quotient, and therefore, a requirement on the maximum temperature TM that the working fluid must reach
[0361] ^{_ Tm ^} R ^g one
[0362] P = TfT
[0363] T ⁰ R ^g - ^{r ^} R ^c R ^t R ^j
[0364] On the other hand, there is an additional restriction on r, which comes from the limitation that the velocity of the fluid does not reach, in any machine or conduit, the value speed of sound, as the sonic block would occur, causing flow limitations and significant irreversibilities.
[0366] In the turbine, the conversion of thermal to mechanical energy is carried out in two phases that are carried out in two different bodies: the nozzle (or nozzles, arranged circularly) in which the fluid loses pressure and temperature isentropically (in the ideal cycle ), reducing the pressure by a factor r, while greatly accelerating the flow of the working fluid; and the impeller or crown of blades, where a significant part of the kinetic energy of the fluid passes to kinetic energy of rotation of the impeller shaft, and of the electric generator coupled to it; and in all this evolution, the fluid cannot exceed the speed of sound at any point, because if Mach = 1 is reached, the sonic blockage would occur, which apart from slowing down the fluid, would cause great energy losses. The passage through the nozzles to produce the acceleration of the fluid, consuming thermal energy, is accompanied by a very large increase in the Mach number, from Mm, which is practically 0, to MX = 1 (in reality, somewhat lower, but they can Use the extreme values 0 and 1 for the theoretical formulation, in which the subscript X refers to the outlet of the nozzle and the entrance into the impeller or blade plate; from which it exits under conditions denoted by the exhaust subscript E , following these processes the equations that follow:
[0370] The previous relationships are fundamental in this system, and they particularly limit the pressure ratio in a single stage, which would correspond to PM / PX, which is a function of the adiabatic coefficient, ^and ; and it is immediately calculated that the upper limit of r in a single stage is 2.05 for Ar; 1,893 for N2, and 1,825 for CO2.
[0372] To design the coupling device between the outlet of the turbine impeller and the low pressure branch of the regenerative exchanger, the balances will be used already presented, which we repeat here to facilitate the exposition. In this case, i represents the turbine exhaust, and in the connection to the regenerative exchanger
[0374] - Flow continuity equation, or mass flow, m '
[0376] ^w) pjCjS; w ^e p ^e c ^e S ^e
[0377] Linear impulse balance, or pressures
[0379] P 1 MP) cf = P ^e + M Pe C
[0380] - Energy balance (per unit mass) in quasi-ideal gas conditions
[0385] - Fluid equation of state (ideal gas)
[0389] - Equation of the transformation of the fluid, in the aforementioned cases:
[0390] Isentropic: 4) 6) y = PeVj
[0392] The above equations are essential to correctly devise the performance specifications.
[0394] With regard to heat exchangers, and fundamentally regenerative, their basic selection is that they be tubes arranged in a square grid, within a reinforced prismatic shell.
[0396] The fundamental equation is the equality of the thermal power, according to the total enthalpy balance of any one of the two fluids, which in this case the one that is heated is chosen, and according to the thermo-transfer equation, that is:
[0398] Q = m'CpAT = UN2nRLST
[0399] Q = thermal power exchanged
[0401] m ’= flow or mass flow
[0403] Cp = specific heat at constant pressure
[0405] AT = temperature increase during heating in the exchanger
[0406] U = global heat transfer coefficient. For thin-walled tubes, with the same film coefficient inside and outside, h, the value of U = h / 2
[0407] N = total number of tubes, arranged in a quadrangular bundle nxn
[0409] R = radius of the tube (very thin-walled, although the modification is elementary if it is thick-walled)
[0411] L = length of tubes
[0413] 5T = temperature difference between the hot and cold branch in the regenerative exchanger, which is practically constant, since the exchanger works in a balanced way (the product m'Cp is the same value in both branches)
[0415] And also it should be noted that m 'can be written as
[0417] m = pcNnR2
[0419] where c is the speed. In fact, both the speed and the density will vary throughout the heating, but not m ', which will remain, under stationary conditions.
[0421] The essential question now is to relate U to the hydraulic regime. Two alternative approximations fit here (whose validity depends on the Reynolds number).
[0423] In the laminar regime, with low or very low Reynolds (below 2000) the Nusselt number can be considered constant, with a value between 4 and 5 (which would depend on the specific configuration of the heat transfer; therefore, it can be taken an average value, 4.5 in this estimate. The value of the film coefficient is therefore
[0427] Introducing U = h / 2 in the previous equality between values of Q, the fundamental equation of the geometric factor (L / R) in this regime can be found, and using the Prandtl number in addition to the Reynolds number, we arrive at
[0429] % AT Pr
[0430] R = sT4 ~ 5Re
[0432] This expression is not a physical law, but the semi-empirical result of applying an experimental correlation to a well-proven model of heat transmission. Results are most reliable when the Reynolds is below 1,000. On the contrary, as you approach 2,000, and enter the transition to turbulence, the precision worsens, although the behavior trend remains.
[0434] For fully developed turbulence situations, with Reynolds above 10,000, the Dittus Boelter correlation, well proven for general purposes, can be used, and for gases such as air and N2 (with Prandlt of about 0.7) it remains
[0435] g
[0436] h = 0.02 fie0'8 -
[0438] where k is the conductivity of the gas. With this correlation, the following relationship is reached for the form factor
[0442] The two equations give the same value when Re = 880; But that does not mean that above this value, the Dittus Boelter correlation is better, but rather that a transition zone is entered in which it is convenient to use its own correlation, although they all emerge from one constant Nusselt situation to another in which its value depends on the speed of the fluid, although this dependence never reaches direct line proportionality, but with powers of the speed lower than 1.
[0444] For a Reynolds of 880, L / R = 6,000 approximately, with a value of 50 in the quotient between increase and temperature difference. That means if the radius of the tubes is 0.4 cm; the length of the tube will be 24 m.
[0446] To make it possible to use shorter tubes, the laminar regime has to be used more notably, that is, with Reynolds on the order of 200 or less.
[0448] Note that in no regime, the length depends on the total power. This is distributed among as many tubes as necessary, but the measurements of each tube depend on the way in which the enthalpy transfer rate is related to the rate of heating or cooling of each branch.
[0450] In addition, the manometric pressure drop must be taken into account, which is made up of 3 factors:
[0452] - The dynamic pressure,% pc2.
[0453] - The form factor (L / 2R) which we have seen grows as the Reynolds number grows.
[0454] - The dimensionless adjustment factor, which for the pure laminar case is 64 / Reynolds; and for turbulent it can be adjusted by the general Blausius approximation, which is 0.32 / Re0.25.
[0456] The foregoing is valid when working with low or moderate pressures, due to the demands of the compressor and the turbine, as in the invention presented, in which the pressure of the low isobar is of the order of atmospheric, although said machines can use at higher pressures, as long as it is mechanically supported by both its fixed and rotating parts.
[0458] The biggest drawback of horizontal laminar flows is that they are susceptible to developing temperature stratification, which results in a deterioration in heat exchange performance; which is addressed in the invention proposal.
[0460] EXPLANATION OF THE INVENTION
[0462] The invention consists of a system that corresponds to an assembly of the closed circuit of the working fluid, which, in a first embodiment includes two novel devices for recovering the mechanical energy of the fluid, which are coupled, one, in the exhaust of the turbine and it is called a post turbine mechanical energy recuperator; and, the other, in the compressor exhaust, which is called post-compressor mechanical energy recuperator; entering, through this device, the flow from the compressor, into the high pressure branch of the cold source exchanger, with a speed that makes the flow laminar within said branch, taking 0.7 m as a reference speed / s; and entering the flow from the turbine into the low pressure branch, with a speed that makes the flow laminar within said branch, taking 1 m / s as a reference speed; each device consisting of a pipe with an increasing straight section, which goes from the outlet of the corresponding machine, compressor or turbine, to the intake manifold of the corresponding branch of the regenerative exchanger; being the straight section of fluid passage not only a control element to induce greater or lesser speed to the circulation of the fluid, but also to make the recovery of mechanical energy effective, transforming dynamic pressure into static pressure, and kinetic energy into enthalpy.
[0464] Ultimately, the system comprises the following physical components, concatenated in a closed circuit called the main circuit:
[0465] - a centrifugal compressor, equipped with a blade plate and a static outlet diffuser, the blade plate being driven by an electric motor;
[0466] - a post-compressor mechanical energy recuperator, shaped like a horn; which converts surplus kinetic energy into static pressure energy
[0467] - a regenerative heat exchanger, with a high pressure branch, which is connected to the previous mechanical energy recuperator; - a hot spot, which is an exchanger, in which heat is supplied from an external hot fluid, to the working fluid that moves in a closed circuit, at the end of its high pressure path;
[0468] - a centripetal gas expansion turbine, with two sub-stages: a crown of nozzles for creating very high speed jets, without reaching the speed of sound; and an impeller of blades, whose rotating frame is attached to an axis of revolution, which is integrally attached to an electric generator;
[0469] - a post-turbine mechanical energy recuperator, shaped like a horn, the end of which is smaller in section is connected to the turbine exhaust; its other end being attached to the casing of the regenerative exchanger;
[0470] - a cold source, which is an exchanger, in which heat is extracted from the working fluid, at the end of its low pressure path, to a cold outside fluid, selected from air from the atmosphere and water from the hydrosphere;
[0472] Furthermore, the invention refers to a method of generating electricity by means of the thermal system, the closed circuit of which is configured to operate according to the following thermodynamic phases:
[0473] - isobar acceleration of the gas by means of the rotating blade plate of the centrifugal compressor, driven by the shaft driven by the electric motor, with a speed multiplier in the event of rotation mismatch with the original performance;
[0474] - deceleration of the centrifuged gas, as it passes through the compressor diffuser, changing dynamic pressure to static, along an isentropic, which in reality, due to irreversibilities, will be inclined towards an increase in entropy, before its evacuation from the compressor diffuser;
[0475] - isentropic deceleration, carried out in a post-compressor mechanical recuperator in the shape of a horn connecting the evacuation from the compressor diffuser, and the high pressure branch of the regenerative exchanger, being in this horn where mechanical recovery is carried out, with a strong increase of the static pressure and where it adapts to the flow to acquire laminar regime; - isobar heating of the fluid flowing through the high pressure branch of the regenerative heat exchanger; until reaching a temperature that is Dt degrees lower than the outlet temperature of a post-turbine mechanical energy recuperator provided at the turbine outlet;
[0476] - isobar heating up to the highest temperature of the cycle, the heat coming from an external source;
[0477] - isentropic acceleration of the fluid emerging from heating in the hot spot; through the inlet nozzles in the centripetal turbine, always in subsonic regime, and with Mach close to 1 in the higher speed parts;
[0478] - isobar deceleration in the impeller of the expansion turbine, with transfer of mechanical energy to its shaft which is mechanically connected to the electric generator;
[0479] - isentropic deceleration in the post-turbine mechanical energy recovery device, the horn of which connects the turbine outlet with the low-pressure branch of the regenerative exchanger;
[0480] - isobaric cooling in the low pressure branch of the regenerative exchanger;
[0481] - isobaric cooling in the cold source, which comprises a heat exchanger, where the cold fluid, which cools the working fluid, comes from the environment.
[0483] To make the physics of this innovation understandable, it is necessary to expose the dependence of the overall performance of the system, with respect to the characteristics of each of the phases of the cycle; including, when necessary, the subdivision of some phase into two sub-phases or stages, for the better demonstrate the benefits obtained with the fundamental innovation, exposed in the foregoing.
[0485] As a complement to the innovation, it is prescribed that the working fluid behaves sufficiently as an ideal gas in the thermodynamic domain in which the cycle is going to unfold; and that is specified by requiring that the logarithmic isobar expansion factor, f, be less than unity throughout the entire cycle, the verification of this requirement at the point at the compressor outlet being sufficient.
[0487] As already stated, realistic performance can therefore be formulated as
[0491] where
[0493] r P - 1
[0496] It must be limited below the value of the performance of regeneration, ^r, and it linearly dependent sr. If we denote with ra this limit of, which will not be less than 0.50 so as not to leave the installation energy ruined, the lower bound that was sought for the pressure ratio, r, or the isentropic temperature ratio, rp, can be found.
[0498] It can be written
[0502] From which the minimum value requirement of the pressure ratio can be obtained
[0506] Likewise, a requirement is obtained for parameter 9 (which is greater than 1)
[0508] [<r
[0509] The better you want the thermal system to be, the higher r will be selected, and the lower will be 9 (but always above 1). To meet this requirement, the temperature difference between the exchange currents is reduced regenerative heat (below 20, which is the reference) or the product Tm Rt-
[0510] If instead of the 20 K reference, we use Dt to denote the temperature difference between the two streams in the regenerative exchanger, the last restriction can be written generally as
[0514] The parametric analysis that bases the specification of the cycle of this thermal system must also be used to limit or establish prescriptions to the relevant values, fundamentally the Carnot quotient, p.
[0516] From the realistic performance equation of the system, you can write
[0520] And since the pressure ratio, r, must be greater than unity, we have, for the (modified) Carnot quotient
[0524] Which immediately becomes a requirement on the Carnot quotient, and therefore, a requirement on the maximum temperature TM that the working fluid must reach
[0528] This specification on the maximum and minimum temperatures reached by the working fluid, complements the limitation on the pressure ratio in the turbine, which together is
[0532] where r is the minimum tolerable value for regeneration performance, and therefore a reference index of the required technical quality, which must be greater than 0.5 and less than 1; and in the invention, 0.98 is taken as a reference value, due to a compromise between the large volumes that are needed when this parameter tends asymptotically to 1, and the improvement experienced by the system's performance, when that value approaches 1.
[0534] The above shows that the pressure ratio, r, is limited to very low values. Take into account that a very high Carnot number, p, is 4 (in the case of a cold focus at 300 K, and a hot focus that takes the fluid up to 1,200 K); but the 3 above mentioned performances, turbine, compressor and loss of load must be affected; and assuming a yield for each one of them, of 0.85; 0.85; and 0.99; the result is that p is reduced to 2.86. If it is desired to have a cycle performance (not counting regeneration) of the order of 50%, the value of r3 must be half of the last value of p, that is, 1.43. If a diatomic is used as the gas, as is being assumed in some examples, the value of the pressure ratio is found to be 1.89. If it exceeds this value, the cycle performance declines. Lowering this value of r increases performance.
[0536] However, this value cannot be reduced indefinitely, because as indicated in the last equation, the regeneration performance depends strongly on r, and decreases when it falls, and hence the lower bound of r3 is constituted .
[0538] On the other hand, there is an additional restriction in r , which comes from the limitation that the speed of the fluid does not reach, in any machine or conduit, the value of the speed of sound, since the sonic block would occur, which would cause limitations of significant flow and irreversibilities; which will be seen in the Materialization of the Invention section.
[0540] This narrow constraint, imposed when analyzing the prescriptions that the cycle definition parameters must meet in order to obtain good performance, apparently represents a setback for this idea. But this setback will be overcome by a more in-depth analysis, showing the various characteristics that will be used in the innovations; and in particular, the recovery of mechanical energy.
[0542] To begin this extended analysis, it must be remembered that in the performance of thermal machines, as measured or tested, there are two forms of energy losses that must be considered properly and separately, although in the catalog specifications of these machines, the The given returns are generally joint, that is, as they have been presented in the explanation above. But an adequate explanation of the invention requires differentiating between two types of losses, in a machine of this type;
[0544] - Thermal losses in any part of the machine, due to friction between parts of it that have different speeds. These losses are not recoverable in any way, although they can be reduced, technologically, through a good lubrication system. On a well-designed and well-tested machine, this performance should be greater than 0.95.
[0545] - The kinetic losses in the exhaust, since it is impossible to transfer all the kinetic energy of the fluid to the axis of the rotating machine. This energy, per unit of time, can be 15 or 20% of the thermal power of the working fluid. For a turbine tested isolated, or inserted in a combined cycle, the performance that is measured includes the effect of these kinetic losses. For the invention, it is absolutely essential to give them a differentiated treatment from the previous ones, which raises the root of this substantial part of the invention, which is the mechanical energy recuperator at the compressor outlet; and the same device at the outlet of the turbine. This last device has its outlet at the beginning of the low pressure branch of the regenerative exchanger. As for the device at the compressor outlet, it connects it with the inlet of the high pressure branch of said regenerative exchanger.
[0547] As already described, in the case of the turbine, the conversion of thermal to mechanical energy is carried out, as is known, in two phases that are carried out in two different bodies, which successively conduct the fluid: the nozzle ( or nozzles, arranged circularly) in which the fluid loses pressure and temperature isentropically (in the ideal cycle), reducing the pressure by a factor r, while greatly accelerating the passage of the working fluid; and the impeller of blades, where a significant part of the kinetic energy of the fluid passes to kinetic energy of rotation of the axis of the impeller, and of the electrical generator coupled to it; and in all this evolution, the fluid cannot exceed the speed of sound at any point, because if Mach = 1 is reached, the sonic blockage would occur, which apart from slowing down the fluid, would cause great energy losses. The passage through the nozzles to produce the acceleration of the fluid, consuming thermal energy, is accompanied by a very large increase in the Mach number, from Mm, which is practically 0, to MX = 1 (in reality, somewhat lower, but the extreme values 0 and 1 can be used for the theoretical formulation, in which the subscript X refers to the output of the nozzle and entry into the impeller; from which it exits under conditions denoted by the exhaust subscript E, following these processes the equations that follow:
[0551] The above relationships are fundamental in this invention, and they particularly limit the pressure ratio in a single stage, which would correspond to PM / PX, which is a function of the adiabatic coefficient, and; and it is immediately calculated that the upper limit of r in a single stage is 2.05 for Ar; 1,893 for N2, and 1,825 for CO2.
[0553] Logically, the speed at the point denoted by X would be practically the sonic:
[0555] Kx - csx - p yPTX
[0557] The temperature of the intermediate point, X, will actually be higher than the TX given by the first of the equations of this group, due to the thermal losses in the nozzle, characterized by a performance £ txt that will be very close to 1, since the nozzles have a smooth shaping to adapt the straight section of the passage to the fluid conditions, especially measured through density, preventing the acceleration of the fluid from separating from the ideal. The actual temperature TXr will be
[0559] TXr - TM ~ £ tx t (TM ~ TX)
[0560] Which means that the Mach number will be somewhat less than 1, and can be approximated by
[0562] QXr - VTXTTXr
[0563] At the outlet of the turbine impeller, the speed cannot be zero (or very small) as it must precisely be commensurate with the inner triangle of speeds, radial, tangential and drag, to adequately evacuate the fluid.
[0565] The escape velocity cE is therefore related to the mechanical performance of the impeller, £ rm, since
[0567] kE (1 ^ rm) KXr
[0568] This speed must be modified downwards by the thermal losses in the impeller, which would be characterized by the complement of the isobaric efficiency of the impeller, £ rtt (in this we are admitting that the turbine is 100% action, and all the energy conversion Thermal to kinetic energy is carried out in the nozzles, and the impeller is isobarous; but it could be partially reactive, in which said conversion is carried out in part in the impeller itself; although the explanation requires a more complex algebra, but that does not help to the explanation of the invention itself). As for the real speed, cEr, it complies
[0570] KEr = £ rttcE
[0571] It is important that the speed cE is the one that produces the best results in the conversion of kinetic energy of the fluid to kinetic energy of rotation of the shaft, and how much it drags; but note that in all open cycle assemblies, the kinetic energy of the fluid in the exhaust is a loss.
[0573] In the assembly of the innovation presented here, this loss is not such, since it is recovered in the form of static pressure and enthalpy, which causes the inlet pressure to the compressor, once the fluid has circulated through the low pressure branch of the exchanger regenerative, and cold focus, is higher than required, if that mechanical energy is not recovered, as explained later. Thus, the specific work done by the compressor to reach a certain static outlet pressure will be less than originally proposed, when the kinetic energy of the exhaust was considered a loss (and it was, since it was not used).
[0575] To design the coupling device between the outlet of the turbine impeller and the low pressure branch of the regenerative exchanger, the balances already presented will be used, which we repeat here to facilitate the exposition. In this case, i represents the turbine exhaust, and e the connection to the regenerative exchanger.
[0577] - Flow continuity equation, or mass flow, m '
[0578] w) pjCjS; w e fish
[0579] Linear impulse balance, or pressures
[0581] 4) 1 M P) cf = P e M Pe C
[0582] - Energy balance (per unit mass) in quasi-ideal gas conditions
[0587] - Equation of state of the fluid (ideal gas; if anything with a minor correction, through z
[0589] - = zRT
[0591] - Equation of the transformation of the fluid, essentially counting on the two already mentioned:
[0592] Isentropic: 4) 6) y = 4e6ey
[0594] Take into account that T¡ = TEr and Te will be the one that corresponds to the slowdown process that occurs in the coupling device, in which the straight section of the duct expands until it achieves its objective, expressed in ce = 1 m / s.
[0596] This last piece of information is the consequence of the innovation of operating the regenerative exchanger in a laminar regime, which will provide a solution that occupies more volume than the turbulent options, although it will provide two great advantages, which are a very low dynamic pressure and a lower than turbulent, between the length of the exchanger tubes, and their diameter. This means that the pressure drop of the laminar option is very small, and therefore the index j is practically 1, being
[0598] ■ = _4l 4l
[0599] J 4m 40
[0601] where Pc is the pressure at the compressor outlet, PM the pressure at the turbine inlet, Pt the turbine outlet, and P0 at the compressor inlet, and therefore the equivalent performance for gage pressure drop, r is also very close to 1.
[0603] Once this final condition of the regenerative turbine-exchanger coupling device is defined, and the complete output conditions of the turbine impeller, TEry cEr, known, the output conditions of the coupling device are set. In particular
[0605] CpTEr - c Er = CpTe - 1
[0607] from which Te is obtained and therefore M Ery Me can be calculated , which facilitates the determination of the other values, Pe and pe, by means of
[0612] i / (y- i). i / (y-D
[0613] J l r (1 H—- MEr = Pe (1 y— - M i
[0615] The fundamental question is to accommodate the straight section of passage, S, from the initial SE to the final, Se.
[0617] pErcEr ^ E ^ e pê e
[0618] Note that it has already been used that the inlet velocity ce in the exchanger is equal to 1 m / s. Se is obtained from this equation, from which the device of the invention is designed.
[0620] Said device consists of a horn that starts from a small mouth, and multiplies the area of its straight section by a factor somewhat lower than the speed ratio between the input to the device and the output, which as a reference has been set at 1 m / s. A numerical example is given in the embodiment of the invention section.
[0622] The length of the device is related to the deceleration that is established, to gradually convert the dynamic pressure into static. Said deceleration corresponds in the case of a fluid to
[0626] where X is the length of the device, which in turn is the deceleration space. If you want this to be constant, to better distribute the efforts and avoid friction between currents very differently decelerated, it would reach
[0630] The detailed design has infinite solutions, but the fundamental requirement is that the horn opens with little inclination of its walls, and at the same time it is respected that the length X is in accordance with the usual dimensions in power energy systems, although the condition that the length does not depend on the total power, but on intensive variables, either the speed or the pressure.
[0632] In this sense, it is set as a condition that the increase in the internal radius of the device, divided by the increase in the length of the axis of the device, is not greater than 0.2 radian.
[0634] Another essential condition to be fulfilled by the device is that it be strongly insulated, thermally, since all heat loss must be counted as such in the thermal performance of the installation.
[0636] A final question to be clarified is the type of machines that satisfy the prescriptions of the invention, as well as their limitations, derived from the Physics of the processes involved. In particular, it has been noted that the pressure ratio is limited to a low value, approximately 2, although the limitation depends on the adiabatic quotient, y. In principle, the results are better the smaller it is and, assuming that the gases involved always behave as ideal; which is so much less true, the more complex the molecule is, since in this case more degrees of freedom appear in the oscillations of the atoms, which cause their specific heat, Cp, to vary considerably with temperature. The worst behavior of complex molecules, with respect to ideal gas, is also evidenced by the appearance of values of the parameter f other than 0, in areas of the thermodynamic diagram where monatomic molecules, such as argon, have null values of f, which shows that behave like ideal gases.
[0638] After these details, somewhat detailed, but important, on the working fluid, it is convenient to complete the definition of the system presented, noting that the type of turbine that can be selected for this invention, to meet the requirements The prescriptions made are centripetal, with entry through radially arranged nozzles, and exit through the area near the axis, and with a single stage.
[0640] And analogously, but inversely, the compressor that is selected in the invention as the reference choice is the one-stage centrifuge. The output of these compressors is carried out by means of a diffuser, in such a way that a part of the dynamic pressure becomes static in the machine itself; but in any case, a device must be interposed between the compressor outlet and the inlet on the high pressure branch, in all respects the same as the one explained in the connection of the turbine exhaust with the low pressure branch of the regenerative exchanger .
[0642] The invention remains to be explained with regard to heat exchangers, and fundamentally the regenerative one, whose basic selection is that of tubes arranged in a square grid, within a prismatic casing, which in the basic selection with respect to the working fluid , in said casing it will be at a pressure very similar, or equal, to the surrounding atmospheric one. The tubes, therefore, constitute a bundle that can undergo changes of direction or turns of the tubes, maintaining the parallelism between them, which is a great advantage when a large number of tubes have to be handled, on the order of 30 thin tubes ( of the order of 1 cm in diameter) per kW of thermal power transferred.
[0644] To adequately explain the selection of this innovation to work on both branches in a laminar regime, it is enough to recall the above that in this regime the highest cooling capacity is obtained for a given value of manometric head loss.
[0646] Additionally, auxiliary elements can be added to the system to promote variations in the work regime. Specifically, flow regulation valves are placed inside the recovery horns, and a relief valve must also be included, as well as a valve for supplying working fluid, gas, before entering the compressor; so a gas storage tank is also added.
[0648] The most important issue is that of staggered assembling the components of two or more cycles of this class, forming a single cycle, with the compressors in cascade and with intermediate cooling, which is done in branches of the cold source, from which the fluid passes to the compressor immediately higher in pressure, until reaching the compressor with the highest pressure, from which, through the horn of its recuperator, it is connected to the high pressure branch of the regenerative exchanger; and stacking the turbines also in cascade, each one followed by its post-turbine mechanical recuperator, which except in the case of the lower pressure turbine, are connected with intermediate superheatings, which are branches of the hot spot, after which the fluid expands to the subsequent lower level in pressure; the post turbine recuperator of the lower pressure turbine being connected to the low pressure branch of the regenerative exchanger.
[0650] Furthermore, the invention comprises an improvement that is made in the main circuit, and consists of selecting the configuration and position of each of the three exchangers, corresponding to the hot source, the cold source and the regenerative exchanger, so that the development of the fluids flows in a vertical direction, ascending that of the flows that are heated, and descending those that are cooled. As the basic configuration of the improvement, that of the tube and shell exchangers is selected, and the tubes are arranged in a vertical direction, as well as the shell.
[0652] In this case, the arrangement of the tubes that is selected is the regular quadrangular, as it is the one with the greatest flexibility to extract or introduce bundles of tubes into a receptacle, particularly the casing, where a set of nn tubes will be arranged inside. This involves the problem that the casing should, in principle, be prismatic in shape with a square straight section, which is not acceptable, as long as there is pressure inside. To solve this problem, the invention includes a method characterized in that the pressure wall of the casing is cylindrical, with a circular cross section, and inside a square-based prism is inscribed, inside which is the tube bundle, inside which The fluid circulates when it is at high pressure, and through the exterior of the tube bundle and in the square-based prism the flow of working fluid is channeled, when it circulates through the low-pressure branch; and between the outer face of the prism, and the pressure wall of the cylindrical housing, there are four volumes in the shape of a circular segment, which are filled with fluid under pressure through some holes in the walls of the prism, without these holes allowing the longitudinal movement of the fluid, in the four volumes indicated; since these volumes are closed at their ends, thus being useless for the exchange and extraction of heat.
[0653] The two mechanical recuperators, post turbine and post compressor, must have their straight inlet and outlet sections adjusted, fulfilling that, in the post turbine recuperator, that the straight section of the turbine exhaust coincides with the straight section of the inlet of flow in the post-turbine recuperator, and the straight section of the outlet, coincides with the straight section of the regenerative exchanger casing, although the working fluid cannot enter the four circular segments outside the prism, nor the tubes that constitute the high pressure branch of said exchanger, channeling the flow outside the tubes, inside the prism inscribed in the shell. Another improvement of the invention is that the post-turbine recuperator has a longitudinal straight section with an outer profile of the parabolic type, described by the equation
[0655] R (z) = 2mIGz
[0657] Where z is the coordinate along the virtual axis of the recuperator, which goes from ze at the input to zs at the output, with the radius Re in the first, and Rs in the latter, and where G is a constant that depends on the length of the recuperator, which also conditions its geometric opening, as well as the maximum slope of growth of the radius of the recuperator, as it advances along its axis; and the value of said G is determined by limiting said maximum opening slope, which is generally expressed as
[0661] this slope acquires its maximum for ze, and is set by design, taking into account that, in general, the greater the slope, the more turbulence is induced, and therefore, the greater losses; but setting a very low value of that slope for the beginning of the recuperator, in the input section, leads to very long recuperators.
[0663] ^{Calling this maximum slope m , which is the value of} #R ^{particularized} for ze, and knowing the values Re and Rs, which are conditioned by other elements of the system, such as the turbine outlet and the coupling with the exchanger casing. regenerative, from these two values and m, the three values that are needed to define the longitudinal profile of the recuperator can be determined, that is, G, ze and zs.
[0665] G = 2mRe
[0666] Z Re_
[0667] e 2 m
[0671] From which the length of the post-turbine recuperator is also obtained, which we denote by H
[0675] The post-compressor recuperator joins the compressor outlet to the tubes of the regenerative exchanger, which constitutes the boundary conditions that allow defining the shape of the recuperator, which is also of the parabolic type, as has been said, and obeys the same formulation geometric view for the post turbine recuperator, changing the meaning of the variables to the following definitions
[0677] Re = radius of the straight section of the compressor outlet manifold, which is the inlet in the post-compressor recuperator
[0679] Rs = radius of the straight section of the collector from which the regenerative exchanger tubes exit, which is the output of the post-compressor recuperator
[0680] ze = value of the coordinate of the virtual axis of revolution of the post-compressor recuperator, at its input,
[0682] zs = value of the coordinate of the virtual axis of revolution of the post-compressor recuperator, at the recuperator output,
[0684] ^{m = value of} #R ^{particularized for ze of the post compressor recuperator}
[0686] G = geometric parameter that characterizes the profile of the post-compressor recuperator, its value being
[0688] G = 2mRe
[0690] and being said profile
[0692] R (z) = ÍG z
[0694] which relates the radius of the straight section of the recuperator with the z coordinate of the virtual axis of revolution, also fulfilling
[0699] which provides the value of the length of the post compressor recuperator, H ,
[0700] What is it
[0702]
[0703] To select this form, we have followed Liouville's theorem, which
[0704] states that the emittance of any beam of particles, and in this case is
[0705] a beam of molecules of the working fluid, cannot decrease along the
[0706] time, but at a minimum, remain constant. The emittance is the integral, a
[0707] along a straight section of the beam, of a function that is the product of the
[0708] distance of the particle, or its associated volume, from the beam axis, multiplied by
[0709] the slope that the particle takes on its path, which is measured as
[0710] ( dr / dz). Applied this theorem to the globality of the flow included in the
[0711] mechanical recuperator, the parabolic shape that has been used from
[0712] departure.
[0714] An additional problem in recuperators is the high turbulence that can
[0715] triggered, as a result of such a sudden stop in a chamber
[0716] empty, although with a pressure gradient and collimation of very
[0717] matching. However, to avoid losses of mechanical energy, which
[0718] degenerate to thermal energy, post turbine and post compressor recuperators
[0719] include inside some longitudinal, flat spacers, developed
[0720] also in a radial direction, although without reaching the virtual axis, being subject
[0721] firmly to the wall of the recuperator. The central zone, around the virtual axis
[0722] of revolution of the recuperator, it is exempt from separators, because they would generate
[0723] Narrow channels of great friction when the fluid passes.
[0725] A variant of spacing is the warped spacer, which is screwed
[0726] partially around the virtual axis of the recuperator, and whose outer edge is
[0727] fixed on the inside face of the recuperator wall. This results in a guided
[0728] cyclonic type of the working fluid in its braking, which generally offers
[0729] very good flow stabilization conditions.
[0730] Regarding the selection of the thermodynamic state of work, it depends especially on the pressure levels chosen, which may depend on several conditions, such as the thermal power available in the external heat source of the hot bulb, and the range of temperatures at which said heat is supplied to the working fluid.
[0732] Said range of pressures will have an upper limit, due to the mechanical effects and resistance of materials, which the pressure changes entail; It is essential to point out that the innovation contains an instrument, simple to apply and very reliable, to vary the pressure levels in the operating state, and it is the variation of the total fluid content that is injected into the closed circuit of the invention.
[0734] For this, it is necessary to take into account what effects this content variation induces, which requires analyzing the fundamental equations of the relevant variables. In this it will be assumed that the working fluid behaves as an ideal gas, that is, that the product PV does not differ from RT by more than 5%, up or down.
[0736] It is also assumed that the temperature map of the working fluid does not change, although the power varies, or changes very little (less than 5% in the values of T, for an increase in power of 100%).
[0738] The specific work of a machine, compressor or expansion (turbine), does not change when changing P
[0742] However, the mass flow does change
[0744] cS
[0745] m = pcS = - P
[0747] since the straight section is the same, as the circuit is the same, and the speed map "c" cannot vary, if the temperature map does not, since the value of the Mach number at the various points must be respected , especially in the entrance and exit of the machines.
[0749] This means something very important, assuming that the performances of the machines and of the friction do not vary appreciably (less than 5%): the power of any machine, or the thermal power exchanged in a exchanger, in this system it depends linearly on the pressure. This means that, in case of wanting to increase power, of course it will be necessary to have it available in the hot bulb, but also the pressure will have to be increased, injecting additional fluid into the closed circuit, thanks to the charging system it has.
[0751] It should be noted that the Reynolds number also varies linearly with P, which has noteworthy effects. The Reynolds is
[0755] In the right-hand side of this Reynolds equation, everything remains constant except P.
[0757] The force exerted on the blades of the machines is also proportional to the pressure. This can be demonstrated taking into account that mechanical power is the product of force and speed; and the velocity map is maintained, as the temperature map is maintained. Therefore, force (or torque, if measured in geometry of revolution) is proportional to pressure. This causes the deformation of the blades to accentuate with pressure, and this is a fundamental criterion for setting the maximum operating pressure. Specifically, the pressure can be limited so that the deformation does not take the blade beyond the elastic field of stresses and deformations. For this, the movement of the blade tip is limited in such a way that the tensile stress on the embedded base of the blade does not reach the elastic limit, at operating temperature; which is formulated taking into account that a thin plate, with one-dimensional mechanical stresses, which is deformed with a radius of curvature Rc, and whose material has a Young's modulus E, and has a straight section with a moment of inertia I, is subjected in that area to a bending moment M which is
[0761] And in turn, the moment M, for a plate of one-dimensional behavior and constant cross section, is
[0763] to him
[0764] M = ~ a
[0766] where o is the maximum stress (which occurs on the face of the plate that is elongated) and "a" is the thickness of the plate. If in turn we express the height of the blade as a multiple of said thickness, A being the coefficient proportionality, that is
[0767] blade height = A a
[0769] and in such a case, which is sufficiently representative of blades in general, we have
[0773] that can be rewritten
[0775] 2nd to
[0778] The yield point is typically found for o / E values of 1/1000; which leads to find that the maximum permissible transverse displacement of the tip of a blade, which we denote with w, is
[0782] For example, for a blade of a medium power machine, with a = 2 mm; and 6 cm high (A = 30) the allowed displacement w is practically equal to the thickness.
[0784] The previous restriction is very difficult to put into practice, since the forces acting on the blades depend on the detailed map of internal speeds, which is really difficult to determine. In fact, although it is intended to maintain the velocity map, as directly linked to the temperature map, through the sonic velocity and the Mach number, the performance of any heat engine varies by varying the pressure, and the density at which works. (Remember that the passage of fluid through the machine is practically isobar; but the pressure of this isobar depends linearly on the fluid load in the closed circuit).
[0786] Thus, as a fundamental specification for the choice of the working pressure, and taking into account the equation of the thermo-mechanical performance of the system, the operating pressure must be chosen for which the product of the performance of the compressor and the turbine, reaches its maximum value, provided it is compatible with the permanence of the mechanical components in the elastic regime of resistance of materials, which is the one previously exposed of the deformation displacement of the blade tip with higher stresses.
[0788] The other performance to take into account is that associated with the pressure drop, whose characteristics depend on the fluid regime of the working gas.
[0790] In the case of the laminar regime (developed vertically, as stated), according to Darcy's expression,
[0794] Which does not depend on P, since this effect is canceled, which occurs through the Reynolds number.
[0796] In the turbulent regime, the Blausius equation can be used as representative
[0798] AP = 0.32 Re ~ 0.25- _D - R e— = 0.16LucD ~ 2Re0.75 = constant ■ P0.75 _{2 D 'I a-}
[0799] From it it follows that the pressure drop in turbulent regime increases with pressure, but less than linearly.
[0801] It can be seen that the option selected, with a laminar regime in the exchangers, not only produces less pressure drop, but that its value does not vary when the pressure varies.
[0803] It remains to be verified how the thermal power of the heat exchangers operating in a laminar regime is affected, in which the
[0804] Q = mCpAT = UN2nRLST
[0806] The member on the left varies linearly with P, through m ', and this forces the member on the right, in which all the parameters are constant, except 5T, which is forced to depend linearly of P. This means that, for example, if the thermal power to be exchanged doubles, the temperature difference between the hot and cold fluid, which is what 5T represents, doubles as well.
[0808] This prescription is valid for the hot bulb exchanger, for the cold bulb exchanger, and for the regenerative exchanger. In the hot spot, it is clear that there must be change of external conditions, which are not of the invention itself, since the hot bulb must generate greater thermal power, and do so at a slightly higher temperature.
[0810] In the cold focus, it must also have sufficient capacity to extract that increase in power to dissipate, which will be slightly more than double that extracted previously, if we continue with the example of duplication. The latter is due to the fact that in the regenerative exchanger, the doubling of 5T results in the doubling of Dt, which makes the regenerative performance vary.
[0814] since parameter 9 will vary, according to the equation
[0818] See that for TM = 1000K, for example, and a turbine efficiency of 0.9; the value of 9 is 1.022 with Dt = 20 K; and it goes to 1.044 when doubling this last parameter, Dt. This affects the regeneration performance, which in the base case, with air as fluid, and r = 1.7 gives a performance ng of 0.86; which decreases to 0.76 when the power is doubled. This strong decrease makes this an aspect of the system that must be taken into account. Remember that realistic performance corresponds to
[0823] The procedure by which the system can be adapted to the power available in the hot spot remains to be described. Precisely, some renewable energy sources, and in particular concentrated solar thermal energy, fluctuate considerably throughout a day, mainly due to interference from clouds, and it is pertinent to have a thermodynamic cycle that is fast and adaptable, to take advantage of the energy that is captured in all circumstances. This also applies to the recovery of waste heat emitted by heat engines.
[0825] To the system already described, a system for selecting the thermodynamic state of operation is added, which can vary the total content of working fluid in the main circuit, and which is succinctly called auxiliary fluid supply system, and consists of:
[0826] - a tank, outside the closed circuit, for storing the working fluid at low pressure;
[0827] - connected, through a conduit, to the working fluid inlet manifold at the cold source,
[0828] - said conduit provided with a valve that controls, or cuts off, the passage of working fluid from the circuit to the tank, or from the tank to the circuit, according to the relative pressures;
[0829] - said tank being in turn connected to a 3-way valve, which can put the tank in fluid connection with the outlet of a fluid supply compressor, which pressurizes the supplied fluid to the level that is requested;
[0830] - there is also an external high pressure storage tank, provided with an auxiliary heating element;
[0831] - and said high pressure tank communicates through a conduit, with the working fluid inlet collector in the hot spot, in which enthalpy is provided from the outside, through a heat exchanger, in which there is a difference logarithmic mean temperature of value 5Tlmfc defined by the inlet and outlet temperatures of the working fluid in said exchanger, respectively Tefc and Tsfc, and the inlet and outlet temperatures of the fluid outside the focus, which is the enthalpy source, called Teec and Tsec, defining itself
[0832] (Teec ~ Tsfc) ~ (Tsec ~ Tef c)
[0833] ST, Imfc
[0834] ~ n ((Teec ~ Tsfc) / (Tsec ~ Tefc))
[0835] - This conduit being provided with a valve that controls, or cuts, the flow of working fluid from the discharge branch of the main circuit to the tank, or from the tank to the branch, according to the relative pressures;
[0836] - and existing in this high pressure tank a pressure relief valve, which depending on the case can relieve the fluid in the open air, or in a closed space of appropriate dimensions;
[0837] - said high pressure tank being also connected to the 3-way valve that is at the outlet of the fluid supply compressor.
[0838] Regarding the procedure for selecting said operating state of the cycle, the guidelines to follow are:
[0839] - in the case of increasing the thermal power, said procedure comprises increasing the enthalpy contributed from the outside to the hot spot, represented by a positive value of the logarithmic derivative of the supplied enthalpy, Q, with respect to time, said derivative being defined by the function (1 / Q) (dQ / dt), which is accompanied by an identical value of the logarithmic derivative of the mean logarithmic temperature difference, 5Tlmfc with respect to time, defined by the inlet temperatures Tefc and outlet Tsfc of the fluid work in the exchanger that constitutes the hot spot, and by the inlet and outlet temperatures of the external fluid that contributes the enthalpy, the latter logarithmic derivative being defined by the function (1 / 5Tlmfc) (d5Tlmfc / dt) while keeping constant the temperatures Tefc and Tsfc of the working fluid, and producing a contribution of working fluid to the collector of the hot spot, in the closed circuit, in such a way that the mass flow or m'fc of input to the hot spot, present a value of its logarithmic derivative with respect to time, which is also equal to the value of the logarithmic derivative of the enthalpy Q with respect to time, expressed by the equation (1 / m'fc) • (dm'fc / dt) = (1 / Q) - (dQ / dt)
[0840] - where to maintain this equality, a fluid supply compressor is used, and a high pressure external tank, which when it does not have enough pressure, and in case of a lack of temperature in the stored working fluid, a heater is activated auxiliary included in said high pressure outdoor tank; Furthermore, the outlet pressure of the main circuit compressor is increased, increasing the power of its electric motor, in such a way that said outlet pressure of the main circuit compressor increases the thermal power managed by the thermal cycle with a value of its logarithmic derivative equal to that given for the mass flow m'fc.
[0841] - to reduce power, the procedure is simply the opposite, that is, with negative values of the logarithmic derivatives involved. To do this, the amount of working fluid must be extracted from the inlet collector to the hot spot, per unit of time, such that, divided by the mass flow at each moment, an absolute value equal to the absolute value of the derivative logarithmic of the enthalpy contributed from the outside, to the hot spot; and in case the pressure in the external high tank is excessive and does not allow the extraction of fluid, the pressure relief valve that has that tank opens. And the power of the electric motor of the thermodynamic cycle compressor is reduced to obtain an outlet pressure whose logarithmic (negative) derivative is equal to that of the mass flow m'fc. To fill the circuit from the idle shutdown condition, or increase the total fluid content in the main circuit and in its auxiliary elements, the external low tank is used, and fluid is injected through the conduit that connects it to the inlet. in the cold focus. If necessary, the fluid supply compressor is used, selecting the position of the 3-way valve at its outlet, to discharge to the low pressure tank.
[0843] EXPLANATION OF THE FIGURES
[0845] Figure 1 shows the lines of the processes and the main thermodynamic points of a conventional cycle, representative of the state of the art of closed gas cycles, with heat supplied from the outside, without incorporating the innovation presented here. A thermodynamic graph (enthalpy, log P) is used.
[0846] Figure 2 shows the process lines and the main thermodynamic points of a closed gas cycle, which incorporates the innovation presented here. A thermodynamic graph (enthalpy, log P) is used.
[0848] Figure 3 shows a diagram of an assembly to embody the invention.
[0849] Figure 4 represents a thermodynamic cycle of the invention, with staging of compression and expansion stages, with intermediate cooling between two successive compressions, and with reheating between two successive expansions. A thermodynamic graph (enthalpy, log P) is used.
[0851] Figure 5 shows a diagram of an assembly to materialize the invention in its cascade version of compressions and expansions, shown in Figure 4.
[0853] Figure 6 shows a diagram of an embodiment of the system of the invention comprising the main circuit and the auxiliary fluid supply system.
[0855] Figure 7 shows the lines of the processes and the main thermodynamic points of a closed gas cycle, which corresponds to the innovation of the previous figure, and includes numerical data of the mentioned points. A thermodynamic graph (temperature, log P) is used.
[0857] Figure 8 shows a geometric and functional arrangement of the components of the thermodynamic cycle that allows the fluids of the three exchangers to work in a laminar regime, with vertical flows.
[0859] Figure 9 presents the straight section of an exchanger, either regenerative, or with a hot focus, or a cold focus, with a tube and shell structure, with a regular quadrangular arrangement, including the volumes that are useless for heat transmission, but which maintain the same pressure as the working fluid inside the prism that houses the tube bundle.
[0861] Figure 10 is made up of two, 10a, which shows the longitudinal straight section of a post-turbine and post-compressor mechanical energy recuperator, and 10b, which shows the straight section perpendicular to the axis of revolution of the previous recuperators.
[0863] Figure 11 is analogous to 10, and includes two drawings, 11a and 11b, showing the same projections, but of a case with warped spacers in the recuperator.
[0865] To improve understanding of the explanation of the figures, the elements that make up the invention are listed below:
[0867] 1. Turbine (expansion).
[0868] 2. Turbine exhaust, which consists of a post-turbine mechanical energy recuperator, passing most of the dynamic pressure of the fluid to static pressure, and most of the residual kinetic energy of the expansion to enthalpy.
[0869] 3. Low pressure branch of the regenerative exchanger, with the fluid circulating through the casing, coming from the exhaust 2.
[0870] 4. Regenerative exchanger
[0871] 5. Output of the low pressure branch of the regenerative exchanger 6. Cold source or heat sink
[0872] 7. Inlet, to the heat sink, of the fluid that performs the cooling action of cold focus.
[0873] 8. Outlet of the working fluid from the heat sink, and connection to the compressor inlet
[0874] Conduit for loading and unloading the working fluid, controlling the total content of working fluid in the main circuit of the thermodynamic cycle.
[0875] Outside refrigerant outlet from heat sink
[0876] Main circuit compressor
[0877] Compressor outlet (11)
[0878] Compressor Drive Electric Motor (11)
[0879] Electric generator activated by the turbine shaft (1)
[0880] Branch made of a bundle of tubes, to pass the working fluid in the cold, high-pressure branch in the regenerative exchanger.
[0881] Exit of the high pressure branch of the regenerative exchanger and connection manifold with the hot bulb
[0882] Hot spot, which is a countercurrent exchanger with a very high temperature external fluid, which can come from various energy sources
[0883] Exit, from the hot spot, of the fluid at high pressure and at the highest temperature, for entry into the turbine
[0884] Inlet of the external fluid of very high temperature, in the hot spot Output of the outer fluid of the hot spot
[0885] Volute for conducting the hot gas from the turbine exhaust (1), the volute being passed through the bundle of tubes (15) Thermal insulation of the entire set of components
[0886] Motor-compressor shaft (11)
[0887] Turbine-generator shaft (14)
[0888] Post-compressor mechanical energy recuperator, consisting of a mechanical energy recovery horn in the compressor drive (11).
[0889] Valve (generally closed) for loading or unloading of working fluid at the outlet of the cold source. There is a valve 26b, with a similar function, but at the outlet of the hot bulb
[0890] Relief valve
[0891] Storage tank of working fluid for its transfer with the outlet of the cold source.
[0892] Thermodynamic point of minimum enthalpy and pressure in the cycle Thermodynamic point of maximum enthalpy and pressure of the cycle Thermodynamic point of turbine exhaust, in state of the art cycle
[0893] Thermodynamic outlet point of the high pressure branch of the regenerative exchanger.
[0894] Thermodynamic entry point to the high pressure branch of the regenerative exchanger, from the compressor outlet, in state of the art assembly
[0895] Thermodynamic outlet point of the low pressure branch of the regenerative exchanger, in assembly of the state of the art Thermodynamic outlet point of the compressor, according to ideal isentropic compression, in assembly of the invention. There is a homologous point 35b in the assembly of two cycles in cascade (figure 4) End point of the heating suffered, from point 35, by the compressed fluid, as a consequence of friction (in reality, this phase is embedded in the one that passes from 29 to 35, but they are painted consecutively to clarify the explanation). There is a homologous point 36b in the assembly of two cycles in cascade (figure 4)
[0896] End point of the isentropic mechanical recovery experienced by the working fluid before entering the high pressure branch of the regenerative exchanger. There is a homologous point 37b in the assembly of two cascaded cycles (figure 4).
[0897] End point of the ideal isentropic expansion of the gas in the turbine. There is a homologous point 38b in the assembly of two cycles in cascade (figure 4)
[0898] End point of the heating suffered, from point 38, by the compressed fluid, as a consequence of friction (in reality, this phase is embedded in the one that runs from 30 to 38, but they are painted consecutively to clarify the explanation). There is a homologous point 39b in the assembly of two cycles in cascade (figure 4)
[0899] End point of the isentropic mechanical recovery experienced by the working fluid from the expansion in the turbine, before entering the low-pressure branch of the regenerative exchanger. There is a homologous point 40b in the assembly of two cascaded cycles.
[0900] Thermodynamic outlet point of the low pressure branch of the regenerative exchanger, in the assembly of the invention
[0901] 42. Thermodynamic outlet point of the high pressure branch of the regenerative exchanger, in the assembly of the invention
[0902] 43. End point of intermediate cooling between two compressions, in cascade assembly
[0903] 44. End point of intermediate heating between two expansions, in cascade assembly
[0904] 45. Connector between successive stages, in cascade assembly, indicated as 45c if it is the compressor cascade, or as 45t, if it is in the turbine cascade.
[0906] In figure 5 there are several labels that have an a or a b as a suffix, after a figure. The latter preserves the meaning given in the previous table; and a means that it is from the high pressure stage, and b that it is from the low pressure stage.
[0907] In the diagrams of Figures 1, 2 and 4, there are several lines defined by a property: the abscissa axis is indicated by H, specific enthalpy; and the axis of ordinate by Log P, which means pressure, in logarithmic scale. The mark LPi in figure 1 indicates the line in which the pressure is constant and corresponds to the lower pressure. LPs is the high isobar.
[0909] On the other hand, in the diagram of figure 7 there are several lines defined by a property: the abscissa axis is indicated by T, temperature on a linear scale; and the axis of ordinate by Log P, which means pressure, in logarithmic scale. In this graph, temperatures are used because they are more intuitive and understandable than enthalpy; also happening that the enthalpy in an ideal gas is linearly proportional to the temperature, along an isobar transformation.
[0911] T0 is the temperature of the point of minimum enthalpy of the cycle (29), and TM that of maximum enthalpy (30).
[0913] LSc is the isentropic compression.
[0915] LSt is the isentropic expansion in the turbine.
[0917] Lri represents the conditions of the regenerative exchanger on the lower face (enthalpy or temperature) and Lrs the conditions of the upper face.
[0919] Obviously, the points of the thermodynamic diagrams correspond to points of the physical assembly of the main circuit, which are where the pressure and temperature conditions predicted in the diagram. In this sense, the points of the cycle in Figure 2 can be located in Figures 3 and 6. Specifically, the following correspondences are representative:
[0921] Point 29 = inlet manifold to compressor 8 of figures 3 and 6.
[0923] Line 36-37 = mechanical recuperator 25
[0925] Point 30 = outlet collector 18 of the hot spot, which is where the maximum temperature of the TM fluid is reached (which in turn is Tsfc)
[0927] Line 39-40 = mechanical recuperator 2
[0929] Point 41 = inlet manifold, 5, to cold bulb
[0931] Point 42 = inlet manifold, 16, to the hot spot, which is where you have the Tefc temperature
[0933] Other elements of relevance for the operation of the invention, in relation to the embodiment of figures 6 and 8, are:
[0935] 100. Valve to allow the transfer of working fluid from the low-pressure branch of the main circuit, before entering the cold source, to the external low-pressure storage tank (101), of said fluid; or vice versa from the tank to the branch, with the help of other elements that follow.
[0937] 101. External storage tank, at low pressure, of the working fluid, for its injection, or extraction, before entering the cold source.
[0939] 102. External storage tank, at high pressure, of the working fluid.
[0940] 103. Connection duct of the inlet manifold in the hot spot with the external high tank (102).
[0942] 104. Valve to allow the transfer of working fluid from the high pressure branch of the main circuit to the external high pressure storage tank (102), of said fluid; or vice versa from tank to branch.
[0944] 105. High external tank pressure relief valve and conduit (102) to send working fluid, surplus, to the outside, or to another storage tank.
[0946] 106. 3-way valve, to channel the fluid supplied by the fluid supply compressor (107) either to the outer low tank or to the high tank.
[0948] 107. Compressor for the auxiliary working fluid supply system.
[0949] 108. Supply conduit for working fluid, from a general external storage system, to the installation.
[0951] 109. High pressure outdoor tank auxiliary heater.
[0953] In addition, in figure 8 the following numerical labels are used, which are homologous to those in figure 6, but adding 1000, to identify that they correspond to the specific assembly of locating the exchangers with flows in a vertical direction (so they correspond to the fluid of job,).
[0955] 1001. Centripetal (expansion) turbine.
[0956] 1002. Post turbine mechanical energy recuperator.
[0957] 1003. Low pressure branch of the regenerative exchanger, with the fluid circulating through the casing
[0958] 1004. Regenerative exchanger
[0959] 1005. Outlet of the low pressure branch of the regenerative exchanger 1006. Cold source or heat sink
[0960] 1007. Inlet, to the heat sink, of the fluid that performs the cooling action of cold focus.
[0961] 1008. Outlet of the working fluid from the heat sink, and connection to the compressor inlet
[0962] 1009. (not used).
[0963] 1010. Heat sink exterior refrigerant outlet
[0964] 1011. Centrifugal compressor of the main circuit.
[0965] 1012. Compressor outlet.
[0966] 1013. (not used)
[0967] 1014. (not used)
[0968] 1015. Branch made of a bundle of tubes, for the passage of the working fluid in the cold, high pressure branch in the regenerative exchanger.
[0969] 1016. Outlet of the high pressure branch of the regenerative exchanger and connection manifold with the hot bulb
[0970] 1017. Hot spot, which is a countercurrent exchanger with an external fluid of very high temperature, which can come from various energy sources
[0971] 1018. Outlet, from the hot spot, of the fluid at high pressure and at the highest temperature, for entry into the turbine
[0972] 1019. Entry of the external fluid of very high temperature, in the hot spot
[0973] 1020. Outlet of the external fluid of the hot bulb
[0974] 1021. (not used)
[0975] 1022. (not used)
[0976] 1023. (not used)
[0977] 1024. (not used)
[0978] 1025. Post compressor mechanical recuperator (11)
[0979] 1026. Manifold from which the regenerative exchanger tubes exit
[0980] For Figures 9, 10 and 11, the following labels are used
[0982] 2001. Regenerative exchanger housing, cylindrical body.
[0984] 2002. Prismatic conduction of the working fluid, to maintain a regular quadrangular tube arrangement.
[0986] 2003. Stagnant working fluid volumes, with the same pressure as inside the prism, although without longitudinal fluid displacement.
[0988] 2004. Tubes inside which the high pressure fluid goes.
[0990] 2005. Spaces between tubes, which constitute the elementary cells for the passage of the fluid at low pressure.
[0992] 2006. Body of a mechanical recuperator, to convert kinetic energy of the flow into pressure energy.
[0994] 2007. Inlet in the recuperator.
[0996] 2008. Recovery outlet mouth.
[0998] 2009. Longitudinal flow separators.
[1000] 2010. Virtual axis of revolution of the recuperator.
[1002] 2011. Warped fluid flow separators.
[1004] MODE OF EMBODIMENT OF THE INVENTION
[1006] The system is materialized by appropriately integrating the two physical elements that compose it: the working fluid, and the thermo-mechanical equipment in which the processes that make up the cycle take place. Said equipment consists of a main circuit that includes:
[1008] - a compressor (11), with its blade plate and its static outlet diffuser, the blade plate being driven by an electric motor (13);
[1009] - a post-compressor mechanical energy recuperator (25), shaped like a horn;
[1010] - A regenerative heat exchanger (4), with a high-pressure branch, which is connected to the previous recuperator (25), the high-pressure gas flowing inside the tubes, and the low-pressure gas outside them, inside from the casing (3), said low pressure gas coming from the mechanical recuperator (2) connected to the outlet of the turbine (1);
[1011] - a hot spot, which is an exchanger (17), in which heat is supplied from an external hot fluid (19), to the working fluid that moves in a closed circuit, at the end of its high pressure path;
[1012] - a gas expansion turbine (1), with two internal sub-stages: the crown of nozzles for creating very high speed jets, without reaching the speed of sound; and the blades whose turning impeller is attached to an axis of revolution (24), which is integrally attached to an electric generator (14);
[1013] - a post-turbine mechanical energy recuperator (2), shaped like a horn, the end of which is smaller section, or mouth, is attached to the turbine exhaust (1); its other end being attached to the casing of the regenerative exchanger (4);
[1014] - a cold source, which is an exchanger (6), in which heat is extracted from the working fluid, at the end of its path at low pressure, to an external cold fluid (7,10), such as air from the atmosphere or water of the hydrosphere.
[1016] For the realization of the invention, a working fluid is selected from a pure substance or a mixture of substances, which behaves as an ideal gas in the thermodynamic domain in which the cycle develops. To do this, it is verified that its parameter fp is less than 1 at the compressor output point. In the selection, the chemical stability of the gas must also be taken into account, so that it does not decompose with successive increases in temperature.
[1018] The most immediate candidate gases can be monatomic, such as argon; diatomic, such as nitrogen; or triatomic, like CO2.
[1020] To value them, the ratio or quotient of temperatures, t, is used in an isentropic, which is
[1021] € = r P
[1023] This allows realistic performance to be expressed as
[1027] This expression is very important, since it explains that, to have the same performance with the same machine performance, etc., the fluids must have the same rp value, which means that the fluids that have a lower p value will need higher values of r. However, this is in contradiction to isentropic compressions and expansions, if you want to avoid sonic blocking, otherwise the performance of the machines will drop a lot. If PM is the maximum pressure, and PX that of the end of an expansion with fluid velocity equal to that of sound, theoretically, we have
[1031] And therefore, for a single isentropic jump, the maximum pressure ratio is rM which is equal to
[1035] This ratio is worth 2.05 for Ar, 1.893 for N2 and 1.825 for CO2.
[1037] The maximum temperature ratio that can occur in an expansion without sonic block is also very important, which is precisely (1+ ^y ) / 2; and respectively corresponds, for the three said fluids, to 1,333; 1.20 and 1.143. This last value is the ^t of the performance equation, which means that, equal to all the installation parameters (p, 0, and the performances q) the fluid with the lowest value of t, in this case CO2 , is the one with the best total return £ r. However, due to its high critical temperature (31 ° C), CO2 is the one that behaves the worst as an ideal gas, and its parameter 0 is almost double that of the values for Ar and N2.
[1039] Because it is in the middle of the two trends, high and low value of ^y , it will be the latter, N2, which is chosen to give concrete examples of values of T, P and performance of the proposed cycle.
[1041] Also note that £ performance is not everything. The specific work of the turbine, Wt, (J / kg) also matters since the real power, N, (J / s) given by the turbine on the shaft, is a function of the specific work and the flow m ' (kg / s):
[1043] a = m'Wt
[1045] And Wt can be approximated very well, as it is an ideal gas with specific heat at constant pressure, Cp, as a function of the inlet temperature TM and outlet temperature, TX of the turbine.
[1047] W = Cp {Tm - Tx)
[1049] Since TM = ^t Tx; CO2 is the one with the lowest specific work, and therefore, the one that needs the highest mass flow or expense (m ').
[1051] This expense is fixed once the system is in operating condition. An auxiliary circuit for charging and discharging the working fluid may be required, as envisaged in figure 3, but the nominal operating regime does not require injections or extractions of fluid. In this auxiliary circuit, the valves (26 and 26 b) and the tank (28) are conventional. It also has a relief valve (27).
[1053] To assess the proposed cycle, based on what exists in the state of the art, the parametric expression of engine performance can be written, such as:
[1057] where ^{t is} the ratio (theoretical or ideal) of temperatures in the turbine
[1062] And p ’is the Carnot quotient, modified by the mechanical performances
[1064] ¿= McRtRj
[1066] Being the parameter of thermal regeneration performance
[1070] It can be seen that the effect of the mechanical performances is equal to reducing the value of the maximum temperature of the working gas, in the same proportion, with respect to the minimum temperature of the gas, T0. This clearly indicates the importance of improving these returns.
[1071] To assess the proposed cycle, a compressor performance of the
[1072] 85% and that of the turbine 75% and the performance by loss of load can be
[1073] express in terms of r and j
[1075] ■ = Í L 4 l
[1078] where Pc is the pressure at the compressor outlet, PM the pressure at the
[1079] turbine, Pt at the turbine outlet, and P0 at the compressor inlet.
[1081] This performance can be estimated in advance, although it depends on the
[1082] operating properties of the system as a whole (as opposed to
[1083] compressor and turbine performances, which can be determined
[1084] experimentally before, with remarkable precision).
[1086] The value of qj as a function of j and r (for N2, as we have said) is given in
[1087] following table:
[1089] jr = 1.1 r = 1.2 r = 1.4 r = 1.6 r = 1.8 r = 2 1.001 0.9895 0.9944 0.9969 0.9977 0.9982 0.9984 1.01 0.9042 0.9469 0.9699 0.9778 0.9819 0.9844 1.015 0.8630 0.9225 0.9556 0.9672 0.9732 0.9768 1.02 0.8256 0.8995 0.9417 0 .9568 0.9646 0.9694 1.025 0.7914 0.8776 0.9283 0.9467 0.9562 0.9621 1.03 0.7600 0.8568 0.9153 0.9368 0.9480 0.9549 1.035 0 .7312 0.8371 0.9027 0.9271 0.9399 0.9479 1.04 0.7045 0.8183 0.8905 0.9177 0.9321 0.9410 1.045 0.6798 0.8004 0.8787 0, 9085 0.9243 0.9342 1.05 0.6568 0.7834 0.8672 0.8995 0.9167 0.9275 1.06 0.6154 0.7515 0.8452 0.8821 0.9020 0.9145 1 .07 0.5792 0.7222 0.8244 0.8655 0.8879 0.9020
[1091] In the immediately preceding table, it can be seen that the performance drops
[1092] a lot for low values of r, especially for high values of j. The board
[1093] indicates that you should not go below a value of 1.6 for r; it should not rise above 1,025
[1094] to J. The latter will require high-number heat exchangers
[1095] parallel ducts of short or moderate length, which is consistent with the
[1096] selection made of laminar flow for the exchangers, especially the
[1097] regenerative.
[1098] This means that despite what is already known, that the performance of the theoretical cycle increases as r decreases, it must be taken into account that the realistic part of the gas movement, which is specified in manometric head loss, presents the opposite behavior: its performance worsens when we lower r.
[1100] Something analogous happens with regeneration. A part of the enthalpy not recovered in this phase, which depends on the gas equation of state, decreases as r decreases; but the one corresponding to maintaining a difference Dt (20 K, as a reference) between the hot and cold currents of the regeneration, will be relatively more burdensome for the performance when r decreases, since the enthalpy decrease of the turbine also decreases. This can be seen in the following table, which presents the calculation of the regeneration performance, using N2 as the working gas.
[1102] r [= 1.01 [= 1.02 [= 1.025
[1103] 1.1 0.72892784 0.57347479 0.51821667
[1104] 1.2 0.8355474 0.71754522 0.6702186
[1105] 1.3 0.87847867 0.78329198 0.74303649
[1106] 1.4 0.90171591 0.82102247 0.78585966
[1107] 1.5 0.91631228 0.84555012 0.81411513
[1108] 1.6 0.92635042 0.86280518 0.83419342
[1109] 1.7 0.93368932 0.87562596 0.84922071
[1110] 1.8 0.93929704 0.88554201 0.86090757
[1112] Obviously the very low r's do not make practical sense, but they are not admissible either due to the very low performance results of the heat regeneration phase. As an informative complement, it should be noted that Dt is equal to the total thermal power to be regenerated, divided by the product of the heat transfer area by the global heat transfer coefficient through said area, and as a reference range of its value, it can be limited between 5 and 20 ° C.
[1114] It is necessary to point out that the realization of this invention requires consecutively arranging the elements or components of thermal engineering in which each phase of the cycle takes place, for whose understanding it is important to put it in accordance with figure 2, which associates each component, previously mentioned of the main circuit, to a certain evolution of the fluid, as indicated below:
[1115] - compressor (11) with its motor (13); thanks to the compressor, the fluid evolves through the isentropic LSc; At the end of this phase, a heating of internal origin is represented between points 35 and 36, since it is that of the irreversibilities during compression, which have been grouped in this way, to better demonstrate it, but the line of compression from point 29 to 36 directly;
[1116] - flared mechanical recuperator (25) at the compressor outlet (11) passing the fluid from point 36 to 37, thereby increasing the static pressure of the fluid, and reducing its speed, adjusting it to the laminar regime sought;
[1117] - High pressure branch, inside the quadrangular bundle tubes (15), which make up the main body of the regenerative exchanger (4); and from them emerges the fluid at point 42 of figure 2;
[1118] - constant section conduit that connects the outlet of the tube bundle (15) with the hot spot (17) in the high pressure branch;
[1119] - hot spot (17) which is essentially an exchanger where the hot fluid comes from an external heat source, entering through conduit 19 and exiting through 20, flowing countercurrent to the working fluid, which heats up to the point (30 ) of maximum enthalpy in the cycle;
[1120] - collector duct (18) inlet to the turbine (1)
[1121] - plus the turbine itself (1) that drives the electric generator (14);
[1122] the working fluid experiencing an isentropic expansion along the line LSt, arriving, as a final theoretical result at point 38, after which an isobar heating section is added in figure 2, up to point 39, said heat being the contributed by irreversibilities;
[1123] - Existing as a component after the turbine exhaust (1), the post-turbine mechanical recuperator (2), which corresponds to a flared connection in which the working fluid is mechanically recovered, which loses speed, and therefore dynamic pressure, and it gains static pressure, and leads the fluid to the entrance in the low pressure branch of the regenerative exchanger (4);
[1124] - the fluid exiting said downstream branch through the collector (5), which introduces it into the cold source (6)
[1125] - the cold source (6) being a countercurrent exchanger, cooled by a cold fluid that comes from an external low-temperature reservoir, and enters through the conduit (7) and exits through the (10)
[1126] - passing the working fluid from the cold source (6) to the compressor (11) through a conduit (8).
[1128] The materialization includes as an essential question to fix the levels of the relevant variables in the definition of the cycle, fulfilling the prescriptions already expressed; in particular, not reaching the sonic block, when accelerating in a nozzle crown, which forces the quotient between the upper pressure in the step, Psup and the lower pressure, Pinf, r, to comply
[1133] And in turn r must be greater than the value that provides a regeneration performance that is not less than the product of the performance, due to thermal irreversibilities, of the compressor and the turbine.
[1135] In the case to be adopted to assess the cycle, the yields in question are taken, both, turbine and compressor, of 0.95; which gives 0.914 as the regeneration performance limit; which requires, according to the table given above for this performance, that r be greater than 1.4 and that the temperature difference in the regenerative exchanger be less than 1% of the maximum absolute temperature that the fluid reaches, multiplied by the thermo-mechanical performance of the turbine, which includes the kinetic energy of the fluid at the outlet of the turbine as a loss.
[1137] To assess the proposed cycle, a thermo-mechanical efficiency of the compressor of 85% and that of the turbine of 75% will be assumed. Parameter 0, which measures the regeneration performance, can be estimated at 0.05 (a loss of 20 K in 400 K of regeneration) and the performance due to pressure loss can be assumed equal to 1, if the point is chosen well operating, as has been done, by imposing laminar flow on the exchangers, which entails a negligible dynamic pressure.
[1138] Figure 1 shows a cycle of the state of the art, which starts from the thermodynamic points of minimum and maximum enthalpy, which are points 29 and 30
[1140] The table below shows P and T for each marked point.
[1142]
[1145] The thermo-mechanical efficiency of this cycle can be expressed as the useful power (which is that of the turbine, minus that of the compressor) divided by the power supplied to the hot bulb.
[1147] The Cp is considered to be constant (and indeed it is, that of N2, in that domain, and its value can be rounded to 1,000 J / kgK).
[1149] The formulation of the aforementioned performance is therefore rewritten as a temperature difference, greater less less, of each phase, which produces
[1154] For the novel cycle of Figure 2, the temperatures of its extreme thermodynamic points, 29 and 30, are the same as before, but the values of the other points vary considerably, including the new points that appear in the recovery of mechanical energy after compression and expansion. In this case, it is necessary to differentiate, in the efficiencies assigned to the compressor and the turbine, what corresponds to thermal losses, which essentially will heat the emerging working fluid (without increasing its pressure), and mechanical losses, for high outlet velocity, which can be converted into pressure (and temperature, isentropic) increase in mechanical recuperators.
[1155] Specifically, for the compressor, with 0.85 performance, we assume that of the 0.15 losses, 0.05 are thermal and 0.10 mechanical; and in the turbine, with 0.75 performance, the losses are distributed between 0.05 thermal and 0.20 mechanical. As the mechanical losses recover, it will be seen that the pressure drop given in the compressor is less than that given in the turbine. In fact, the analysis of the cycle has to start with the turbine, because as it is the largest jump, it is where the limitation of not reaching the sonic block is applied. Thus, the r of the turbine is 1.85; and that of the compressor will come from the results of mechanical recoveries.
[1157] With the given value of r it follows that the exit T of the complete isentropic expansion is 1007 K (under an inlet temperature of 1200 K). From there, the effect of thermal irreversibility and post-turbine mechanical recovery is added; and in a self-consistent way, having assumed a compression performance, the values of the post compression points are found.
[1159] All of this is summarized in the following table. The warning is repeated that the drawing is not exactly to scale, as in that case there would be effects that would not be appreciated. From the point of view of precision, only tables are valid.
[1161]
[1162] The performance is obtained by the same formulation of the previous case, but now we have that the specific work of the turbine is 0.75 (1200-1007), which gives 145 kJ / kg.
[1164] That of the compressor is the total to rise from point 29 to 37, and therefore 47.5 kJ / kg.
[1166] In the hot spot, a specific enthalpy equal to Cp multiplied by the temperature difference between point 30 and point 42 (1200 -1034 = 166) must be transferred to the fluid. The performance remains:
[1168] ^e = 1451 ~ 6647.5 = 0.587
[1169] These data show that the system has very good characteristics to achieve efficiencies not common in the state of the art, thanks to the mechanical recovery that is carried out. This is accentuated if cascade cycles are used, such as the one shown in the thermodynamic diagram of figure 4. In this case, the starting point is the same extreme temperatures, at points 29 and 30, and the minimum pressure, 0.1 MPa it is reached at the end of the low turbine expansion; being the pressure jumps in each turbine of r = 1.85.
[1171] The cycle data, always with N2, are
[1173]
[1174]
[1177] The performance of the cascade of figure 5 is similar in formulation to the case of a single level, since both the work of the turbine and that of the compressor are doubled. However, the denominator is not doubled, because in the first heating in the hot spot, it goes from point 42 to 30, which represents Dt degrees Celsius more than in the second heating, which goes from point 40b to 44, so that in the case of the previous table we have
[1180] For a very high number of stages, the third and subsequent intermediate heating between two decreasing pressure turbines would have the same enthalpy increase as the second, which would bring the overall performance of said cycle with numerous steps closer to 97.5 divided times 150, which is 0.65.
[1181] The Carnot yield with the mentioned extreme temperatures would be 0.75.
[1183] Another essential question is the physical materialization of the various components, and the determination of their dimensions. In the case of heat exchangers, and especially the regenerative one, in which a high heat recovery performance is required, a transmission in laminar regime has been chosen, with fluid velocities of the order of 1 m / S and pipes of 1 cm in diameter, which even with the maximum density that will exist (of 1 kg / m3) and a representative viscosity (33 microPascalsecond) gives a Reynolds of 300, which provides an aspect ratio (L / R) in the 2800 exchanger tube, so the tube would have to be 14 m long (it can be in a U), all according to the equation
[1184] L AT Pr
[1185] - = --------- Re
[1187] In it, it has been considered that the quotient between the increase in temperature (between inlet and outlet; for example, 600 ° C) and the difference in temperature between the hot and cold fluid (20 ° C) is 30, and the Prandtl is worth 0.7.
[1189] If a well turbulent case had been chosen by design, with a velocity of 10 m / s and 10 cm in diameter, its Reynolds would have been 30,000, and according to the corresponding equation
[1193] it would have an L / R of 8200, so the length of the tube would be 41 m, which would be disproportionate, and very bad because it entails a lot of pressure drop. In fact, in the laminar case the pressure drop in the characteristic tube that has been exposed, is 150 Pa; while in the turbulent case it is 5,100, thirty-four times more. It should also be noted that the dynamic pressure of the turbulent case is 100 times higher than that of the laminar one.
[1195] Certainly the latter requires a greater number of tubes, since 78 cm3 / s circulate through those of the laminar case, and in the turbulent 0.078 m3 / s; e s say a thousand times more; and in output 78 mg / s and 78 g / s.
[1197] It should be remembered that in the simple novel cycle (single stage) the net specific work was 97.5 kJ / kg. If you wanted to have a net power of 1MW, you would need an expense of 10.25 kg / s; which would mean 130,000 tubes in the laminar case, and 130 in the turbulent one, which would fit in a network of 361x360 tubes, and 11x12, respectively, that would fit in a prism of 5x5 meters, and 14 meters long, in the first case, and 1.5X1.5, and 41 long in the second. In volume it would be 350 m3 in the laminar regenerative exchanger, and 92 in the turbulent one. Regarding the total masses of metal (steel, typically) used for the regenerative exchanger, the equation reached, where k is a constant
[1201] Which makes the steel mass of the laminar is 2.8 times greater than that of the turbulent case. This is expensive, but is more than compensated for by having a 34 times less pressure drop, which is very beneficial for system performance.
[1203] But the system also requires the correct coupling between the outputs of the machines, compressor and turbine, and the corresponding branch, of high or low pressure respectively, in the regenerative exchanger, which is done by means of post mechanical energy recovery horns. turbine and post compressor (going from kinetic energy, or dynamic pressure, to enthalpy, or static pressure).
[1205] In the turbine, which is the component where higher speeds are reached, in the inlet nozzle a speed close to 680 m / s will be reached; and at the exit the kinetic energy will represent 20% of the initial one, which will represent a Mach of 0.44 and therefore an exit speed of 300 m / s.
[1207] This value must be reduced in the horn to 1 m / s, in an isentropic deceleration, in which the initial and final density are related by
[1211] which implies an increase in density by a factor 1.1; taking into account that the value of the Mach number in section 2, which is the end of the horn and entry into the downstream branch of the regenerative exchanger, is negligible.
[1212] The fundamental equation to fulfill is the continuity of mass,
[1213] p1V1 $ 1 = p2V2 $ 2
[1214] With the assumed data, we arrive at S 2 = 275 S 1.
[1216] The straight section of the turbine outlet, S ¹ , will be a function of the conditions that occur in it, but a density of 0.4 kg / m3 can be assumed, and with the speed already mentioned and the mass flow rate of 10, 5 kg / s, an initial straight section at the horn of 0.0875 m2 is obtained, and the one at the end of the horn and entry into the branch would be 24 m2.
[1218] The ratio between the radii of both sections is 16.6. The tangent of the horn angle, supposedly made of constant aperture slope, would be
[1221] Where r = 2.75 m is the radius in section 2, and l is the length of the horn. For 10 ° of constant aperture (angle w) the length would be 14.75 m. These measures, considerably proportionate, are due to the improvement introduced in the invention, on the shape and geometric properties of the mechanical recuperators.
[1223] In the study of the regenerative exchanger, it was estimated that it would have a straight section of 5x5m, but the lower branch had not really been considered, outside the tubes, but rather something proportional to the upper branch had been estimated, where the 131,000 tubes have a straight section of 10.3 m2. Added to the 24 m2 to size the downstream branch, the regenerative exchanger would be a prism of 34.3 m2 of straight section, which is 5.8x5.8 meters, which does not appreciably vary the hypotheses of the calculation carried out, with the that the feasibility of the materialization is demonstrated.
[1225] An improvement of the embodiment of Figures 1 to 4 is described below, with the aid of Figures 6 to 11 in which an auxiliary system for supplying the working fluid connected to the main circuit is used.
[1227] In this case, the complete system of the invention is materialized by appropriately integrating the components identified above; some belonging to the main circuit, in which the thermodynamic cycle takes place, in a closed circuit with constant content of working fluid, once the operating power has been selected, and others belonging to the auxiliary system for loading or unloading, or fluid supply , in order to fix the fluid content at the desired value, which will first of all have implications for the pressure values of the main circuit.
[1229] In the descriptions made of the main circuit and the auxiliary system, the instrumentation has not been detailed, which is mainly for measuring temperature, pressure and flow, as it is conventional. Neither has any power variation system been detailed, particularly for the electric motors of the compressors, as they are standard elements.
[1231] It is also very important to point out that the realization of the invention can and should be guided by the optimization of performance, precisely following the guidelines derived from the theory that supports the invention. Of course, the use of machines, turbine and compressor, with better performance, entails the improvement of overall performance; and a higher value of the Carnot quotient (maximum T / minimum T of the fluid in the cycle) also improves the overall performance of the cycle; But what is involved here is the optimization of the overall performance, based on the free design parameters, and very notably, on the pressure ratio (r); since both the Carnot quotient and the machine performances will be given as design boundary conditions, but precisely the invention must incorporate a prescription to guide the optimization, as a function of "r", according to the values that we have of said terms.
[1233] Two tables are given below, useful for that purpose. The first gives the cycle efficiency, according to the Carnot quotient, assuming that the turbine and compressor efficiencies are 0.8.
[1235] Tmax / Tmin r = 1.2 r = 1.4 r = 1.6 r = 1.8
[1245] The second table gives the performance, according to the performance of the turbine and compressor machines (assumed equal) with a Carnot quotient of 2.5.
[1247] yield maq r = 1.2 r = 1.4 r = 1.6 r = 1.8
[1255] It is appreciated that for low values of the Carnot quotient or of the machine performances, it is advisable to choose low values of the pressure ratio, even decreasing to r = 1.2. However, this has the disadvantage of having to recycle a lot of heat through regeneration; and therefore, the regenerative exchanger is very bulky, and the pressure drop also increases, due to the increase in recirculated mass flow in regeneration.
[1257] This had already been exposed in an inequality derived from the performance of the cycle, which is
[1259] r <W rftlj
[1260] But if the Carnot quotient is very low, or the performance of the machines, or all of them, the total performance achieved is also very low, and it would be necessary to question the use of energy.
[1262] On the contrary, when these values increase, so does the total efficiency, and it is possible to increase the pressure ratio, r, almost to its upper limit, already mentioned, and that is 1.89 for N2.
[1264] Note also that when r descends, the machines rotate more slowly, since the linear speed decreases, and since the radius of gyration is the same, the angular velocity falls, according to the following illustrative table.
[1265] r T Mach
[1266] 1.4 1.102 0.7145
[1267] 1.6 1.145 0.853
[1268] 1.8 1.185 0.96
[1270] If the temperature map is maintained, the sonic speed is also maintained, and therefore the speeds, since the Mach numbers are maintained at each point of the circuit.
[1272] The first step in the design of this system is the configuration of the thermodynamic cycle, in which the values of the essential, intensive variables are set, such as pressure, P and temperature, T, plus the specific enthalpy, given in kJ / kg.
[1274] The real values of the power exchanged or transferred, in a given component (in kJ / s, that is, kW) is equal to the product of variation of the specific enthalpy (in kJ / kg) by the mass flow (in kg / s ) of working fluid.
[1275] In the table that follows, the values of P, T and specific enthalpy are given, and they correspond, with greater precision than that of the graph, to the cycle presented in figure 7.
[1277]
[1280] The configuration of the cycle allows to calculate its performance, and other intrinsic characteristics. For the calculation of the gross powers in each component, it is necessary to set the flow rate (kg / s) of working fluid, which is also essential to calculate the appropriate dimensions of the various equipment, and ensure that they meet the appropriate specifications. for example, of bounding the mechanical stresses that are induced in each solid component.
[1282] Regarding performance, it could be defined in different ways, but the most direct way is gross performance, as the unit minus the quotient of dividing the power transferred in the cold bulb, divided by the power absorbed by the hot bulb, which It is expressed with the enthalpies of the points involved in both phases:
[1287] Although it is a gross value, and friction in the axes and some other real contingency not easily reflected in equations should be discounted, since it is essentially phenomenological, the value obtained is very high, and this is due to two properties of the cycle, which result On it:
[1288] - The mechanical recovery of the kinetic energy from the turbine outlet, makes the compressor have to work with pressure levels much closer to each other than those of the turbine, thus reducing its power consumption (on the shaft, driven by an electric motor normally).
[1289] - Thermal regeneration, which allows the thermal power supply of the hot bulb at a very high temperature; and this results (as Carnot establishes) in the improvement of performance. But this has a cost, logically, and the regenerative heat exchanger, which also has not small dimensions (in fact, it is the largest and heaviest component of the entire installation that has to be assembled to materialize the invention. Note that the specific enthalpy transferred in the cold source is 48 kJ / kg; and that of the hot source, 113; while that transferred in the regenerative exchanger is 550 kJ / kg. That is, 4.87 times greater than the power of the hot bulb, and 8.46 times the net thermal power, of 65 kJ / kg.
[1291] It should also be noted that the net electrical power would have to be affected by the performance of the compressor motor and the turbine generator. If we admit a value of 0.97 for both, which is of the order of the current state of the art, the yield would be
[1295] And the net electrical power would be the product of 65 kJ / kg by the expense. For example, for a flow rate of 1.8 kg / s of working fluid circulation, the net electricity generation would be 108 kW.
[1297] Note that the closed circuit has been mounted with the minimum pressure level, since the lowest part manometrically is at 1 atmosphere (0.1 MPa). If the pressure is raised proportionally, without varying the temperature map, the power is increased proportionally, admitting that the components support thermal stresses (temperature gradients, expansions) and mechanical stress.
[1298] In fact, one of the difficulties in assembling the closed circuit is the sizing of the turbine and the compressor. With the pressure level chosen, which is the minimum, the devices that are usually used in turbochargers can be used to supercharge diesel engines, particularly marine ones; Although it is necessary to note an important difference: the overloaders act in an open circuit, since they throw the turbine exhaust into the atmosphere, and take from the atmosphere the air to be compressed and injected into the diesel cylinders; and yet in this invention, they work in a closed circuit. But the pressure ratio in both cases is practically the same, and they work with similar Mach numbers, at homologous points.
[1300] If we consider an expansion in the turbine of 1.7 pressure ratio, the Mach number of the exit of the inlet nozzle at the turbine blade plate will be 0.9. With a nozzle outlet temperature of 800 K, the velocity will be 522 m / s (which corresponds to 580 x 0.9). The density will be determined by pressure and temperature, and will be approximately 0.5 kg / m3, which will give a flux density of 260 kg / m2 s. In order to transfer the value of expenditure that it has assigned, of 1.8 kg / s, a straight section of 70 cm2 will be necessary, that is, a passage slightly less than 10 cm in diameter (very in line with the dimensions of the overloaders diesel; well known).
[1302] Other components that need to be dimensioned are the post-turbine and post-compressor mechanical recuperators, which have to couple very different flow conditions, from the inlet to the outlet. It has been pointed out that at the inlet nozzle in the turbine, the fluid is accelerated by isentropic expansion (or close to it) and reaches values of 0.9 Mach (but not higher, to avoid sonic blockage), and transfers to the axis a certain amount (for example, 60%) of its kinetic energy, leaving the rest (for example, 30%) with the kinetic energy of the exhaust (the other 10% going to heating of the fluid itself due to irreversibilities). The aforementioned 30% has to be recovered as static pressure, in the post-turbine recuperator.
[1304] For this, it must be taken into account that the Mach number squared, at the exit of the plate of blades, has to be 30% of the entrance, which was 0.81. This leads to an output Mach of approximately 0.5, with a sonic velocity of 580 m / s (corresponding to 806 K), which means that the fluid will go to 290 m / s at the inlet mouth of the post-turbine recuperator ( what is the thermodynamic point 39, in the previous table of the cycle). With the P and T conditions existing at this point, the density leaves 0.42 kg / m3, and the mass flow continuity equation leads to a straight input section of 148 cm2.
[1306] The thermodynamic connection between the inlet and outlet of the post-turbine recuperator will be based on the fact that the Mach of the outlet fluid will be negligible, so it can be written
[1308] Te (l ^ M |) = T S @ 1 1 ^ M |) = Ts (l 1 0)
[1312] that in the case under study, Me = 0.5, leads to Ps = 0.1186 MPa. In turn, the density that we find at the outlet is 0.47 kg / m3, since the outlet temperature rises to 840 K (actually to 845.5 K, due to the effects of irreversibility).
[1313] This outlet must be coupled to the downstream branch of the regenerative exchanger, the straight section of which will depend on the speed selected. For example, with 1 m / s, the output straight section would be 3.8 m2; which would obviously be cut in half if the speed were to double. They are numbers close to those that will be obtained below for the mentioned exchanger.
[1315] If a speed of 2 m / s is chosen, and therefore 1.9 m2 of section, the radius would go from 6.9 cm to 77.7 cm; which would require 4.4 m in length, if the value of 1 is taken as the maximum expansion slope of the post-turbine recuperator at its inlet.
[1317] Regarding heat exchangers, the one with the greatest demands is the regenerative exchanger, as has already been seen. Their analysis is very instructive, especially in light of the vertical mounting proposed in figure 8. This serves to underline the importance of thermal energy management in this invention, whose thermodynamic cycle includes a heat exchanger, volume and weight much higher than the rest of the installation as a whole.
[1319] Next, results of the design of the exchanger are given, to effect a thermal transfer of 1 MW, in round numbers, which would be the power necessary to operate a circuit like the one indicated in the table immediately preceding, where the values of the pressure, temperature and enthalpy, of the assembly were exposed to give an electrical generation of 108 kW.
[1321] The working fluid used is nitrogen, N2, of which it should be remembered that its Prandtl number always remains close to 0.7; and for the intended operating range, the conductivity is 0.045 W / mK, and the viscosity is 30 micropascals.
[1323] The configuration adopted is of shell and tubes, as already explained, and as shown in figure 8, schematically, and in figure 9.
[1325] As design variables, the flow rate per unit of straight section is used, which is the product of the density and the speed, inside the tubes, and the radius of the tubes. In this example, mean values of the relevant variables are used, since it is sufficient to demonstrate the idea, without the need to complicate it with detailed calculations.
[1327] It should be noted that, due to the relationships between variables, the heat transfer area, the total volume occupied by the tubes, and the power density within said tubes (which constitute the high pressure branch of the exchanger) only depends on the radius of said tubes. , but not the expense per unit of straight section.
[1329] On the contrary, the straight section of the tubes only depends on the flow rate per unit of straight section, but not on the radius.
[1331] The design windows that derive from all the information set out below, are the result of the improvement introduced in the invention, relative to the constitution and working regime of the exchangers,
[1333] In the block of tables that follow, they all have the same structure: the columns correspond to the indicated values of the diameter of the tubes, except for the first column, which indicates the cost per unit of straight section, for each row. And the first row indicates the diameter D of each column, all of this always using the SI unit system.
[1334] This first tab the ex p o n e v a lo re s of Reynolds' number for
[1335] cad a c a so (which corresponds to a matrix node):
[1337] Reynolds
[1338] kg / s-m2 0.002 0.004 0.006 0.008 0.01
[1341] The following table of this block gives the length (in m eters) of the
[1342] tu b o s of the regen erative exchanger (which in the m o n taje of the figure
[1343] 3, are above):
[1345] L laminar
[1346] rho * v # D = 0.002 0.004 0.006 0.008 0.01
[1349] Another variab fun dam in such is the number of your b o s that should have the
[1350] regen erative exchanger. (They are your b o s sim p le s, not a le te a d o s; and
[1351] c iertam en te can be searched with figuration is more common and
[1352] efficient, but the tu b o s s im p le s, in quadruple disposition, have
[1353] the advantage of o offer a very e lem ent explanation of following, in
[1354] as to the term-transfer, and clearly indicative of size, etc.).
[1356] No. of tubes
[1357] rho * v #
[1358] D = 0.002 0.004 0.006 0.008 0.01
[1359] 1 572956.4553 143239,114 63661.8284 35809.7785 22918.2582 2 286478.2277 71619.5569 31830.9142 17904.8892 11459.1291 3 190985.4851 47746.3713 21220.6095 11936.5928 7639.4194 4 143 239 , 1138 35809.7785 15915.4571 8952.44461 5729.56455 5 114591.2911 28647.8228 12732.3657 7161.95569 4583.65164
[1360] Apparently it is a very high number of tubes, but they are elements of very
[1361] easy machining, handling and assembly, including spacer grids for
[1362] geometry maintenance, including shapes and elbows to absorb
[1363] dilations (See figure 8).
[1364] Next, the tables corresponding to Total Straight Section of
[1365] step (inside the tubes, in m2), Total volume occupied by the tubes (in
[1366] m3), Power Density (in MW / m3) transferred, Transfer area (m2), and
[1367] Mass of tubes (kg).
[1369] Total straight section through pitch, 1 ° (within
[1370] tubes)
[1371] rho * v #
[1372] D = 0.002 0.004 0.006 0.008 0.01
[1375] Total volume of 1st LAMINAR
[1376] rho * v #
[1377] D = 0.002 0.004 0.006 0.008 0.01
[1380] LAMINAR Power density (MW / m3) rho * v #
[1381] D = 0.002 0.004 0.006 0.008 0.01
[1382] 1 1.072884245 0.26822106 0.11920936 0.06705527 0.04291537 2 1.072884245 0.26822106 0.11920936 0.06705527 0.04291537 3 1.072884245 0.26822106 0.11920936 0.06705527 0.04291537 4 1.072884245 0.2682236106 0.11920920936 0.06705527 0.04291537 5 1.072884245 0.26822106 0.11920936 0.06705527 0.04291537
[1384] Thermo-transfer area
[1385] rho * v #
[1386] D = 0.002 0.004 0.006 0.008 0.01
[1389] Mass (kg) of tubes
[1390] rho * v #
[1391] D = 0.002 0.004 0.006 0.008 0.01
[1392] 1 1454.02452 6397.70789 13086.2207 23264.3923 36350.613 2 1454.02452 6397.70789 13086.2207 23264.3923 36350.613
[1393] 3 1454.02452 6397.70789 13086.2207 23264.3923 36350.613
[1394] 4 1454.02452 6397.70789 13086.2207 23264.3923 36350.613
[1395] 5 1454.02452 6397.70789 13086.2207 23264.3923 36350.613
[1397] Once all the elements or components indicated in the foregoing are available, the procedure for selecting the thermodynamic state of operation of this system is very direct, and is based on adapting the total fluid content in the closed circuit, so that the map pressure corresponds to the barometric levels given. Actually, it is enough to essentially check the 3-point pressure (from the thermodynamic graph in figure 7: point 29, which is the inlet to the compressor, point 30, which is the inlet to the turbine, and point 39, which is the turbine outlet.
[1399] To increase or reduce the content of working fluid, there is an auxiliary fluid supply system, which allows transfers between the latter and the main circuit, in one direction or the opposite.
[1401] For what corresponds to absorbing in the system to the variations of thermal power, the fundamental thing is the fulfillment of the prescription that the indicated logarithmic derivatives are equal; which can be done manually, or automatically. There are no special requirements in this.
[1403] Finally, it should be noted that, in the procedure for selecting the thermodynamic state of operation of this thermal system, the following can be used as alternative or complementary modalities:
[1405] - increase the rotation speed of the compressor (11), to provide a greater mass flow, and a greater value of the pressure ratio, r; allowing the working fluid to extract more energy from the hot spot (17), provided it has it, and causing a greater pressure drop in the turbine (1), to increase its specific work, and the power generated in the shaft of the turbine; and
[1406] -decrease the rotation speed of the compressor, to provide a lower mass flow, and a lower value of the pressure ratio, r; allowing the working fluid to introduce energy into the hot spot (17), and cause a lower pressure drop in turbine 1, which decreases its specific work, and the power generated in the turbine shaft.

权利要求:
Claims (1)
[0001]
r e iv in d ic a tio n s
1 - Thermal system for the generation of mechanical energy in a shaft of a turbine in a closed circuit, with a compressor and with input of heat from an external source, and internal recovery of heat and mechanical energy, for the generation of electricity, characterized in that it comprises a main circuit equipped with the following physical components, concatenated in a closed circuit:
- a centrifugal compressor (11), equipped with a blade plate and a static outlet diffuser, the blade plate being driven by an electric motor (13);
- a post-compressor mechanical energy recuperator (25), shaped like a horn;
- a regenerative heat exchanger (4), with a high pressure branch, which is connected to the post-compressor mechanical energy recovery unit;
- a hot source (17), which is an exchanger, in which heat is supplied from an external hot fluid, to the working fluid that moves in a closed circuit, at the end of its high pressure path;
- a centripetal gas expansion turbine (1), with two sub-stages:
a crown of nozzles for creating very high speed jets, without reaching the speed of sound; and a blade impeller, whose rotating frame is attached to an axis of revolution (24), which is integrally attached to an electric generator (14);
- a post-turbine mechanical energy recuperator (2), in the shape of a horn, whose end with a smaller section is connected to the turbine exhaust (1); its other end being attached to the casing of the regenerative exchanger (4);
- a cold source (6), which is an exchanger, in which heat is extracted from the working fluid, at the end of its path at low pressure, to an external cold fluid, selected from air from the atmosphere and water from the hydrosphere;
2 - System, according to claim 1, characterized in that it comprises at least two compressors connected in cascade and with intermediate cooling, materialized by the interposition of branches of the cold focus, where after each intermediate cooling, the fluid to be sucked by the compressor passes immediately higher in pressure, up to the highest pressure compressor, from which, through the horn of its post-compressor mechanical recuperator, it is connected to the high pressure branch of the regenerative exchanger; and comprises at least two turbines connected in cascade, each one followed by its post-turbine mechanical recuperator, which except in the case of the lower pressure turbine, are connected with intermediate overheating, materialized through branches of the hot spot, and in each turbine fluid expands to the subsequent lower level in pressure; the post turbine recuperator of the lower pressure turbine being connected to the low pressure branch of the regenerative exchanger (4).
3 - System, according to claims 1 or 2, characterized in that the working fluid satisfies that the logarithmic factor of isobar expansion is less than the unit at the thermodynamic point of the compressor outlet, said factor fp being defined by

where z is the compressibility factor, equal to PV / (RT), where P is the pressure, V is the specific volume, T is the absolute temperature, and r is the ideal gas constant specified for the working fluid, in the units used in the three previous magnitudes.
4 - System, according to claims 1 or 2, characterized in that in a turbine step, the quotient r between the upper pressure, inlet, Psup and the lower pressure, Pinf, meets

where y is the quotient between the specific heat at constant pressure and the specific heat at constant volume, and in turn the pressure ratio r satisfies the requirement defined by

where r is a parameter, which represents the lowest value that is allowed for thermal regeneration performance, and where p is an exponent equal to

; and where 9 is a parameter defined by

where Dt is the temperature difference between the hot and cold stream of the heat exchanger where regeneration takes place, TM the temperature at the turbine inlet, and Rt the turbine performance.
5 - System according to claim 1, characterized in that the regenerative heat exchanger consists of a regular quadrangular bundle of tubes (15), inside a prismatic casing; through which high pressure gas flows inside the tubes, and low pressure gas outside them, inside the casing, in a regular quadrangular arrangement, with an equivalent hydraulic diameter equal to a value between one third and three times the internal diameter of the tubes.
6 - System, according to claim 4, characterized in that Dt is equal to the total thermal power to regenerate, divided by the product of the heat transfer area by the global heat transfer coefficient through said area, and is between 5 and 20 ° C.
7 - System, according to claim 1, characterized in that it has flow regulation valves inside the mechanical recovery horns, and a relief valve, as well as a valve for supplying working fluid, gas, before entering the compressor; and it also consists of a gas storage tank.
8 - System according to claim 1, characterized in that it comprises an auxiliary fluid supply system to set the total content of working fluid in the closed circuit of the main circuit, said auxiliary fluid supply system comprising:
- a low pressure working fluid storage tank, outside the closed circuit (101);
- connected, through a conduit (9), to the working fluid inlet manifold in the cold source (6),
- said conduit (9) being provided with a valve (100) to allow the passage of working fluid from the closed circuit to the low pressure tank (101), or from said tank to the closed circuit, depending on the pressure of the tank with respect to the pressure of said closed circuit in the cold source (6); and
- said low pressure tank being in turn connected to a 3-way valve (106), which according to a previously selected parameter allows the fluid connection of the low pressure tank with the outlet of a fluid supply compressor (107) of the auxiliary fluid supply system, to pressurize the supplied fluid (108) to a previously selected level;
- a high pressure storage tank, external to the closed circuit (102), provided with an auxiliary heating element (109);
- a conduit (103), which communicates said high pressure tank (102) with the working fluid inlet manifold (16) in the hot spot (17), in which enthalpy is provided from the outside (19), through a heat exchanger, in which there is a mean logarithmic temperature difference of 5Tlmfc value defined by the inlet and outlet temperatures, in said exchanger, of the working fluid, respectively Tefc and Tsfc, and the inlet temperatures (19 ) and outlet (20) of the external fluid, called Teec and Tsec, being this flow from the outside the one that contributes the enthalpy, defining
ST, (Teec ~ Tsfc) ^{~ (Tsec ~ Tef c)}
Im fc
~ n ((Teec ~ Tsfc) / (Tsec ~ Tefc))
- said conduit (103) being provided with a valve (104) that allows the passage of working fluid from the high-pressure branch of the closed circuit to the high-pressure tank, or from the high-pressure tank to the branch of the closed circuit, in function of the relative pressures between them; and
- a pressure relief valve (105), provided in the high pressure tank that makes it possible to reduce the pressure in said tank and that of the fluid in the hot spot (17);
where said high pressure tank is also connected to the 3-way valve (106) existing at the outlet of the fluid supply compressor (107).
9 - System, according to claim 8, characterized in that the three exchangers, corresponding to the hot focus, the cold focus and the regenerative exchanger, are configured so that the fluids flows in a vertical direction, upwards that of the heated flows , and descending those that cool down.
10 - System according to claim 9, characterized in that the exchangers are of the so-called tube and shell type, in which the tubes and shell are arranged vertically; where the tubes are arranged inside the casing according to a regular quadrangular configuration of nxn tubes, and where the pressure wall of the casing (2001) is cylindrical, with a circular cross section, and inside which, a square-based prism (2002), inside which are the bundle of tubes (2004), through which the fluid circulates when it is at high pressure, and through whose outside (2005) the bundle of tubes and inside the square-based prism, the working fluid flow is channeled, when it circulates through the low pressure branch; and where between the outer face of the prism and the pressure wall of the cylindrical housing, there are four volumes in the shape of a circular segment (2003), which are filled with fluid under pressure through some holes in the walls of the prism, leaving said volumes closed at their ends, being therefore useless for the exchange and extraction of heat.
11 - Thermal system for the generation of mechanical energy on a shaft, according to claim 10, characterized in that the post-turbine and post-compressor mechanical energy recuperators have their straight inlet (2007) and outlet (2008) sections adjusted, fulfilling that, In the post-turbine recuperator, the straight section of the exhaust coincides with the straight section of flow inlet in said post-turbine recuperator, and its straight outlet section, coincides with the straight section of the casing of the regenerative exchanger exchanger, where it channels the flow outside (2005) of the tubes (2004), and inside the prism (2002) inscribed in the casing (2001); and the post-turbine recuperator (2006) having a longitudinal straight section with an external profile of the parabolic type, described by the equation
^{R, z} - = ^{ÍG z}
where z is the coordinate along the virtual axis (2010) of the post-turbine recuperator, which goes from ze at the input to zs at the output, with the radius Re in the former, and Rs in the latter, and G being a constant which depends on the length of the post-turbine recuperator, whose G value is determined by limiting said maximum opening slope, which is expressed as

where the slope acquires its maximum for ze, and is set by design, taking into account that, the greater the slope, the more turbulence is induced, and therefore, the greater losses; and if a very low value of that slope is set for the beginning of the post-turbine recuperator, in the inlet section, it leads to very long post-turbine recuperators; Therefore, calling said maximum slope m , and knowing the Re and Rs values , which are conditioned by other elements of the system, such as the turbine output (1) and the coupling with the regenerative exchanger casing (4) From these two values and that of m , the three values that are needed to define the longitudinal profile of the post-turbine recuperator are determined, that is, G, ze and zs.
G = 2 m R e


and the length of the post-turbine recuperator is also obtained, which we denote by H

and, where the post-compressor recuperator goes from the compressor outlet to the collector from which the regenerative exchanger tubes come out, which constitute the boundary conditions that allow defining the shape of the post-compressor recuperator, which is also of the parabolic type, according to the same geometric formulation specified for the post turbine recuperator, changing the meaning of the variables to the following definitions
Re = radius of the straight section of the compressor outlet manifold, which is the inlet to the post-compressor recuperator (1025)
Rs = radius of the straight section of the collector (1026) from which the regenerative exchanger tubes exit, which is the output of the post-compressor recuperator
ze = value of the coordinate of the axis of revolution of the post-compressor recuperator, at its input,
zs = value of the coordinate of the axis of revolution of the post-compressor recuperator, at the recuperator output,
m = value of #R particularized for zedel post compressor recuperator
G = geometric parameter that characterizes the profile of the post-compressor recuperator, its value being
G = 2 m R e
and being said profile
R (z) = VGZ
which relates the radius of the straight section of the post compressor recuperator with the z coordinate of the axis of revolution, also fulfilling


which provides the value of the length of the post compressor recuperator, H , which is
p2 _ p2
H = zs - Ze _{Rs Re}
2mRe
12 - Thermal system for the generation of mechanical energy in a shaft, according to claim 11, characterized in that the post-turbine and post-compressor recuperators include in their interior some longitudinal, flat spacers, developed in a radial direction, without reaching the virtual axis, being subject firmly to the wall of the recuperator; and the central zone, around the virtual axis of revolution of the recuperator, is free of spacers.
13 - Thermal system for generating mechanical energy on an axis, according to claim 11, characterized in that the post-turbine and post-compressor recuperators include inside them some warped longitudinal spacers, which are partially screwed around the virtual axis of the recuperator, remaining fixed, by its outer edge, on the inner face of the recuperator wall.
14 - Procedure for generating electricity in a thermal system for generating mechanical energy on a shaft of a gas expansion turbine in a closed circuit, with a compressor and with input of heat from an external source and internal recovery of heat and mechanical energy, characterized in that the main circuit is configured to function according to the following thermodynamic phases:
- isobar acceleration of the gas by means of a plate of rotating blades of a centrifugal compressor (11), driven by a shaft driven by an electric motor, with a speed multiplier in the event of rotation mismatch with the original performance;
- deceleration of the centrifuged gas, as it passes through a compressor diffuser (11), passing dynamic pressure to static, along an isentropic that, due to irreversibilities, is inclined towards an increase in entropy, before its evacuation from the diffuser of the compressor;
- isentropic deceleration, carried out in a post-compressor mechanical energy recuperator (25) constituted by a connection horn between the evacuation from the compressor diffuser, and a high-pressure branch of a regenerative exchanger (4), being in this horn where mechanical recovery is carried out, with an increase in static pressure and where it also adapts to the flow to acquire a laminar regime;
- isobar heating of the fluid flowing through the high pressure branch of the regenerative heat exchanger (4); until reaching a temperature that is Dt degrees lower than the outlet temperature of a post-turbine mechanical energy recuperator (2), constituted by a horn provided at the turbine outlet;
- isobar heating up to the highest temperature of the cycle, the heat coming from an external source (18, 19);
- isentropic acceleration of the fluid emerging from heating in a hot spot (17); by means of the inlet nozzles in the centripetal turbine (1), always in subsonic regime, and with Mach close to 1 in the higher speed parts;
- isobar deceleration in the impeller of the expansion turbine, with transfer of mechanical energy to its shaft, which is mechanically connected to an electrical generator (14);
- isentropic deceleration in the post-turbine mechanical energy recovery device, (2) that connects the turbine outlet with a low-pressure branch of the regenerative exchanger;
- isobaric cooling in the low pressure branch of the regenerative exchanger (4);
- isobaric cooling in a cold focus, comprising a heat exchanger (6), where the cold fluid (7), which cools the working fluid, comes from the environment.
15 - Procedure for selecting the thermodynamic state of operation of a thermal system, according to claim 14, characterized in that it comprises establishing as the operating pressure of the closed circuit a value at which the maximum value of the product of the performance of the compressor is reached (11 ) and of the turbine (1), provided that said value is compatible with the permanence of the mechanical components in the elastic regime of resistance of the compressor and turbine materials.
16 - Procedure for selecting the thermodynamic state of operation, according to claim 15, characterized in that when the mechanical components of the turbine and compressor are blades embedded in the base and free at the tip, the maximum transverse displacement allowed at the tip of the blade, w , it is

where a is the thickness of the blade, and A is the length of the blade measured in terms of its thickness, which can be expressed as that length is Sometimes a.
17 - Procedure for selecting the thermodynamic state of operation, according to claim 15, characterized in that:
- to increase the thermal power, said procedure comprises increasing the enthalpy supplied from the outside to the exchanger of the hot spot (17), represented by a positive value of the logarithmic derivative of the supplied enthalpy, Q, with respect to time, said derivative being defined by the function (1 / Q) (dQ / dt), which is accompanied by an identical value of the logarithmic derivative of the mean logarithmic temperature difference, 5T ^lmfc with respect to time, defined by the inlet and outlet temperatures T ^efc T ^sfc of the working fluid in the heat exchanger of the hot spot (17), and by the inlet (19) and outlet (20) temperatures of the external fluid that contributes the enthalpy, the latter logarithmic derivative being defined by the function (1 / 5T ^LMFC) (D5T ^LMFC / dt) keeping the same constant time temperatures T ^efc and T ^sfc of the working fluid and producing a supply of working fluid to the collector of the exchanger the hot source (16), RT l so that the mass flow m ' ^fc entering the hot spot has a value of its logarithmic derivative with respect to time, which is also equal to the value of the logarithmic derivative of the enthalpy Q with respect to time, expressed by the equation
(1 / m ' ^fc ) • (dm' ^fc / dt) = (1 / Q) (dQ / dt)
where to maintain this equality, a fluid supply compressor (107) is used, and an external high pressure tank (102), which when it does not have enough pressure, and in case it lacks temperature in the stored working fluid , an auxiliary heater (109) included in said high pressure outdoor tank (102) is activated; and furthermore the outlet pressure of the compressor (11) is increased, increasing the power of its electric motor (13), in such a way that said outlet pressure of the compressor (11) increases the thermal power managed by the thermal cycle with a value of its logarithmic derivative equal to that given for the mass flow m '^fc; and
- to reduce power, the procedure is the opposite and comprises extracting from the inlet manifold (16) to the compressor of the hot spot (17), an amount of working fluid, per unit of time, such that, divided by the mass flow at each moment, of an absolute value equal to the absolute value of the logarithmic derivative of the enthalpy supplied from the outside, to the hot spot (17); where in case the pressure in the external high pressure tank (102) is excessive and does not allow the extraction of fluid, it comprises opening a pressure relief valve (105) provided in said high pressure tank; and reducing the power of the electric motor (13) of the compressor (11) to obtain a pressure at its outlet whose logarithmic (negative) derivative is equal to that of the mass flow m'fc, in such a way as to reduce the thermal power managed by the thermal cycle, with negative values of the logarithmic derivatives involved.
18 - Procedure for selecting the thermodynamic state of operation, according to claim 14, characterized in that it comprises a phase selected from:
- increase the rotation speed of the compressor (11), to provide a greater mass flow, and a greater value of the pressure ratio, r; allowing the working fluid to extract more energy from the hot bulb (17), provided it has it, and causing a greater pressure drop in the turbine (1), to increase its specific work, and the power generated in the shaft of the turbine; and
-decrease the rotation speed of the compressor, to provide a lower mass flow, and a lower value of the pressure ratio, r; allowing the working fluid to introduce energy to the hot spot (17), and cause a lower pressure drop in the turbine (1), which reduces its specific work, and the power generated in the turbine shaft.

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ES2713123B2|2019-11-06|

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