A kind of therrmodynamic system parameter optimization method
Technical field
The present invention relates to the energy, Power Machinery Engineering field, therrmodynamic system method for optimally designing parameters is specifically provided.
Background technology
Therrmodynamic system is the device for absorbing the external leaving momentum of heat of high temperature heat source and used heat being discharged to low-temperature heat source, hot
Power apparatus is also referred to as heat engine, is mainly filled including high-temperature heat-exchanging, expanding machine, cryogenic heat exchanger, liquid circulation pump, thermal device inside
Working medium, carry out thermodynamic cycle of the working medium in heat engine are marked with, highly pressurised liquid working medium is evaporated in high-temperature heat-exchanging, absorbs thermal source
Heat, become high steam, by expanding machine to extraneous output work, drive engine power generation, low pressure working fluid gas passes through low temperature
Heat exchanger condenses, and becomes liquid, then by liquid circulation pump, after liquid working substance adherence pressure, be sent into high-temperature heat-exchanging heat absorption
Evaporation, a thermodynamic cycle is completed, does not stop circulation work so.Current steam power plant, substantially using this circulation.Therrmodynamic system
Thermal parameter, the main heat source temperature including high temperature, low temperature, the mean temperature difference and heat transfer flow velocity of high and low temperature heat exchanger
Rate, power output, the thermal efficiency of evaluation system performance.Current thermodynamic argument, by the first law of thermodynamics, i.e. energy is kept
Permanent equation, there is provided the equilibrium relation of the heat absorption of circulation, heat release and output work, there is provided Carnot Engine efficiencyThe respectively temperature of high temperature and low-temperature heat source, Carnot Engine are high and low temperature heat exchangers without heat transfer
The high temperature of the efficiency of the temperature difference, i.e. cycle fluid is equal with the temperature of high temperature heat source, the low temperature of working medium and the temperature phase of low-temperature heat source
Deng this needs heat exchanger heat exchange area infinitely great or working medium has endless heat-exchange time with thermal source, and actual heat engine is to accomplish
's.Actual heat engine does not allow equilibration time endless, and its heat absorption and heat release and circulation must all be completed in finite time, that
, what the peak power output of heat engine and efficiency of frontier be again in finite time, 1975, Canadian scholar Curzon
Consider this problem first with Ahlborn, within reversible Carnot cycle models, be derived with finite rate and limited cycle
The efficiency of heat engine boundary in cycle, i.e., it is famousEfficiency, the Carnot Engine efficiency in Maximum Power Output are.Hereafter, the Chen Lingen in China【15】, Yan Zijun, Chen Jincan【16】Deng large quantities of scholars with various countries,
Numerous studies have been carried out to limited thermodynamic analysis method, have expanded the achievement in research of interior Reversible model.But scholar's use at present
Finite time analytic approach, it is respectively to a time quantum, such as energy stream to each link of circulation in Introduction Time variable
It is by the high-temperature heat-exchanging used time, it is by the cryogenic heat exchanger used time, the working medium in expanding machine and liquid circulation pump is ignored
After energy-exchange time, cycle period is fixedFor, on this basis, utilize the heat transfer equation of two heat exchangers, energy side
Journey, solve Maximum Power Output when Carnot Engine efficiency be;But because its variable is more, derive
Power, the high temperature of efficiency and cycle fluid, the relation of low temperature be implicit function relation, it is difficult to it is apparent to be applied to actual therrmodynamic system
Optimum design of engineering structure.Document(Chen Jincan, Yan Zijun, several important marks in the feature of theory of finite-time thermodynamics and development
Will, Xiamen University's journal (natural science edition), 2001, Vo l. 40, No. 2,232-240)What so evaluation was present has thermal relief
Force analysis:" because limited thermodynamic analysis method introduces time variable, the irreversible procedure of investigation is more complicated than reversible process to be obtained
More, especially Evolution is even more complicated various, increases therrmodynamic system performance evaluation difficulty, at present also only to institute's Solve problems
Largely simplified, be only possible to obtain some analytic solutions, and solution's expression complexity is difficult to be received by engineering circles, so limitation
Its application." as, while inside irreversible and finite heat capacity it is outer can not inversion model with engineering physical condition similar in have
The achievement of thermal relief force analysis is also relative to be lacked;
In addition, the design parameter of heat exchanger simply ensures energy Balancing relization in systems in therrmodynamic system, for high and low
Warm heat exchanger performance matching lacks the theoretical direction of system function optimization;
The efficiency of actual therrmodynamic system can only obtain according to the system of completion and experiment, be passive type, lack actively optimization and set
Meter guiding theory and prediction become the ability of operating mode.
Bibliography
[ 1 ] Curzon F L, Ahlborn B. Efficiency of a Carnot engine at maximum
power output [J ]. Am. J. Phys. , 1975, 43(1): 22- 24.
[ 2 ] Bejan A. Entropy Generation Through Heat and Fluid Flow. New York:
Wiley, 1982
[ 3 ] Chen Lingen, Sun Fengrui, Chen Wenzhen, finite-time thermodynamics new development, magazine, 1992.15 (4):249-
253
[ 4 ] Chen Jincan, Yan Zijun, several important symbols in the feature of theory of finite-time thermodynamics and development, Xiamen are big
Journal (natural science edition), 2001, Vo l. 40, No. 2,232-240
[ 5 ] Prigogine I. Structure, Dissipation et al Communication
Presented of the First International Conference / Theoretical physics and
Biology . Amsterdam: North-Holland pub, 1969
[ 6 ] the new method Engineering Thermophysics journals of a kind of heat exchanger optimization designs of Chen Zeshao journey Wen Longhu Peng, 2013.
[ 7 ] Hesselgreaves J E. Rationalisation of second law analysis of heat
exchangers.Inter J Heat Mass Trans, 2000, 43: 4189—4204
[ 8 ] Guo Jiangfeng, Cheng Lin, Xu Ming fieldDissipation number and its application Science Bulletins, 2009,54: 2998~
3002
[ 9 ]《Mathematics handbook》Write group, mathematics handbook, People's Education Publishing House(Beijing), 1979.11,232-235
[ 10 ] Yan Zijun, the relation between the optimum efficiency and power of Carnot Engine, Engineering Thermophysics journal, 1985. 6
(1):1-5
[ 11 ] Zhao Dongxu, Yu Min, Chen Lichao, Yang Mo, the optimization of finite time actual steam power cycle thermal performance,
Shanghai University of Science and Technology's journal, 2010,32 (4):329-333
Xu Z M, Yang S R, Chen Z Q. A modified entropy generation number for
heat exchanger. J Therm Sci, 1996, 5: 257—263。
The content of the invention
In order to overcome existing thermodynamic argument effective percentage concept and the defects of without rate of heat transfer and existing finite time heating power
Analytic approach can not provide the rate of heat transfer of actual therrmodynamic system and the deficiency of the clear explicit function relation of thermodynamic system efficiency, Yi Jire
Physical field lacks the effective ways of therrmodynamic system parameter optimization, and the present invention proposes a kind of therrmodynamic system parameter optimization method, can
To establish the power of therrmodynamic system, efficiency and high and low temperature thermal source, high temperature, the low temperature of cycle fluid, heat transfer coefficient of heat exchanger it is clear
Clear relation, and optimum efficiency selection principle is provided and improves the heat exchanger matching process of power output, obtain therrmodynamic system high
Efficiency has high power output simultaneously.
To realize above-mentioned target, the present invention is using following technical schemes:
A kind of therrmodynamic system parameter optimization method, described therrmodynamic system are to be operated in temperature to beHigh temperature heat source and temperature
Spend and beLow-temperature heat source between heat engine, heat engine includes high-temperature heat-exchanging, expanding machine, cryogenic heat exchanger, liquid circulation pump,
And the duplex matter system being sequentially composed in series, highly pressurised liquid working medium absorbs high temperature heat source in high-temperature heat-exchanging during thermodynamic cycle
Heat be changed into high steam, external leaving momentum while be changed into low-pressure low-temperature steam when passing through expanding machine, then change by low temperature
Used heat being discharged to low-temperature heat source during hot device and condensing into liquid, low temperature and low pressure liquid working medium is pressurizeed by liquid circulation pump, then defeated
Enter to high-temperature heat-exchanging and absorb heat, so move in circles;The overall heat-transfer coefficient of high and low temperature heat exchanger is designated as respectivelyWith, it is total to pass
Hot coefficient is heat transfer coefficientWith heat exchange areaProduct;The ratio of the overall heat-transfer coefficient of cryogenic heat exchanger and high-temperature heat-exchanging,
It is designated as,, referred to as overall heat-transfer coefficient ratio;When working medium circulation reaches stable state by high-temperature heat-exchanging suction
Rate of heat flow, referred to as heat absorption rate, are designated as;The rate of heat flow discharged by cryogenic heat exchanger, referred to as heat liberation rate, heat release rate, are designated as;Working medium
The net power output that the power output of expansion process expanding machine deducts the power of liquid circulation pump consumption is designated as, referred to as export
Power;The average eguivalent thermal temperature of high-temperature heat-exchanging working medium evaporation endothermic process, is designated as, referred to as equivalent endothermic temperature;
Cryogenic heat exchanger working medium condenses the average eguivalent thermal temperature of exothermic process, is designated as, referred to as equivalent exothermic temperature;Heating power system
The power output of systemWith heat absorption rateRatio be defined as efficiency, be designated as;The maximal efficiency of therrmodynamic system is Carnot Engine
Efficiency, it is designated as, now, the power output of actual therrmodynamic system is 0;In equivalent endothermic temperatureWith
Equivalent exothermic temperatureCombination when changing, power output and the efficiency of therrmodynamic system are continually changing, remember that therrmodynamic system goes out
Existing peak power output is , efficiency corresponding with peak power output is,;
It is characterized in that:A kind of therrmodynamic system parameter optimization method, it is using two step optimum seeking methods selection optimum efficiency,
Optimum output powerWith optimal overall heat-transfer coefficient ratio;The first step, select optimum efficiency;Second step, with unit
The minimum principle of power output cost, cooperate with optimum choice optimum output powerWith optimal overall heat-transfer coefficient ratio, i.e.
In optimum efficiencyOn the premise of keeping fixed, by increasing overall heat-transfer coefficient ratio, power output is reached satisfied defeated
Go out power, and makeIncrease increase heat exchanger area and the Income Maximum of manufacturing cost;
The first step of two described step optimum seeking methods, first, determines the optimum efficiency of therrmodynamic systemScope be betweenBetween, i.e.,;Secondly, with the maximal efficiency of therrmodynamic systemWith the efficiency of peak power outputWeight equation (1) optimum efficiency is calculated by preferred weight factor, optimum efficiency weight equation is
(1)
In formula,For maximal efficiencyWeight factor,Between 0.25-0.75;Again, recommend to use equal weight side
Formula (2) calculates optimum efficiency, i.e.,,
(2)
The second step of two described step optimum seeking methods, first, establish and correspond to the optimum efficiency that equal weight equation determines
Power outputWith overall heat-transfer coefficient ratioFunctional relation, obtain formula (3),
(3)
In formula,;WhenOptimum efficiency when power output, be designated as, calculating formula is formula (4),
(4)
Any overall heat-transfer coefficient ratio during optimum efficiencyPower outputWithRatio, be designated as
, the referred to as contrast delivery efficiency of optimum efficiency,WithRelational expression be formula (5),
(5)
Secondly, with the minimum principle of unit capacity equipment cost of therrmodynamic system, overall heat-transfer coefficient ratio is selected;Institute
The equipment cost for the therrmodynamic system stated is by high-temperature heat-exchanging, cryogenic heat exchanger, expanding machine, liquid circulation pump and other auxiliary equipments
Cost structure;WithAnd optimum efficiencyWhen high-temperature heat-exchanging costFor the cost unit of benchmark, noteWhen high-temperature heat-exchanging, cryogenic heat exchanger, expanding machine, the cost coefficient of liquid circulation pump and other auxiliary equipments be respectively 1,
A, b, c and d,When, high-temperature heat-exchangingConstant, its cost is also constant, and the coefficient of high-temperature heat-exchanging is still 1, and is neglected
Slightly the cost coefficient of liquid circulation pump and other auxiliary equipments withChange;The dimensionless equipment cost of therrmodynamic system, is designated as,;The unit capacity equipment of described therrmodynamic system into
This, is designated as, it is defined as dimensionless equipment costWith the contrast delivery efficiency of optimum efficiencyRatio, its count
Formula is formula (6)
(6)
According to unit capacity equipment costEquation (6) is to overall heat-transfer coefficient ratioExtreme value is sought, makes extreme value equation etc.
In 0, referring to formula(7)
(7)
Optimal overall heat-transfer coefficient ratio is tried to achieve, is designated as, calculating formula is formula (8)
(8)
Optimal overall heat-transfer coefficient ratioScope be, lacking a, b, c and d number of concrete engineering
During value, the overall heat-transfer coefficient ratio of recommendationTo keep optimum efficiencyUnder the conditions of, power outputWithWhen
The peak power output of therrmodynamic systemEqualValue, i.e.,, derived optimal overall heat-transfer coefficient
RatioMathematic formula be formula (9)
(9)
Again, ask for corresponding to the optimum efficiency that equal weight method determinesAnd optimum output powerOther optimal heat
Force parameter, these parameters are respectively:
Best equivalence exothermic temperature, is designated as, calculating formula (10) is:
(10)
Best equivalence endothermic temperatureCalculating formula be:, formula (11);
Optimal heat absorption rateCalculating formula be:, formula (12);
The optimal overall heat-transfer coefficient of high-temperature heat-exchangingCalculating formula is:, formula
(13);
The optimal overall heat-transfer coefficient of cryogenic heat exchangerCalculating formula is:, formula (14);
Optimal heat liberation rate, heat release rateCalculating formula be:, formula (15).
A kind of described therrmodynamic system parameter optimization method, it is characterised in that:Described equivalent endothermic temperature, it is in height
The difference of the specific enthalpy of warm heat exchanger heat transfer process working mediumWith the difference of specific entropyQuotient, i.e.,, footnote a, b represent rising, only for process respectively;Described equivalent exothermic temperatureIt is in high temperature
The specific enthalpy difference of heat exchanger heat transfer process working mediumWith specific entropy differenceQuotient, i.e.,。
A kind of described therrmodynamic system parameter optimization method, it is characterised in that:Described high temperature heat source temperature, when thermal source is
During with high temperature gas flow heat supply, high temperature heat source temperatureIt is that the high temperature gas flow of thermal source exists for high temperature heat source equivalent temperature
The difference of the specific enthalpy of high-temperature heat-exchanging heat transfer processWith the difference of specific entropyQuotient, i.e.,, footnote a, b represent rising, only for process respectively;Described low-temperature heat source temperature, when
When low-temperature heat source is the absorption of fluids used heat with surrounding air stream or current, low-temperature heat source temperatureFor equivalent low-temperature thermal source temperature
Degree, be low-temperature heat source fluid cryogenic heat exchanger heat transfer process specific enthalpy differenceWith the difference of specific entropyQuotient, i.e.,。
A kind of innovative point of therrmodynamic system parameter optimization method of the present invention:
(1) according to the efficiency of peak power outputWith Carnot Engine maximal efficiencyTwo efficiency equal weights it is former
Then, the optimum efficiency of therrmodynamic system is recommended, and by increasing overall heat-transfer coefficient ratio, therrmodynamic system is being kept best effective
It can be obtained while rateValue do not adjust before peak power output, or bigger power output;And propose unit output
Power apparatus cost minimization principle, establish the meter for the optimal overall heat-transfer coefficient ratio for determining cryogenic heat exchanger and high-temperature heat-exchanging
Formula, rationale is provided for the optimization design of therrmodynamic system;
(2) The present invention gives the calculating formula of whole thermal parameters of therrmodynamic system optimal design;
(3) the equivalent endothermic temperature of working medium proposed by the present inventionWith the equivalent exothermic temperature of working medium, and equivalent thermal source
Temperature, actual therrmodynamic system cycle analysis is used interior reversible cycle heat engine model treatment, be interior reversible cycle heat engine mould
The important step that type finite time analytic approach is combined with the actual therrmodynamic system of engineering, this link are that another Shen is diverted from one use to another in digestion
Please patent of invention " a kind of heating power transform analysis method of equal value " achievement in research;
The method of the present invention, has important guiding effect to the optimization design of actual therrmodynamic system.
Brief description of the drawings
Below in conjunction with the accompanying drawings and embodiment the invention will be further described
The interior reversible cycle heat engine thermodynamic analysis model of Fig. 1 embodiment of the present inventionFigure;
The selection optimum efficiency of Fig. 2 embodiment of the present inventionDiagram method explanation figure;
Fig. 3 embodiment of the present invention with unit capacity cost minimization principle pairOptimization illustrate figure.
Embodiment
Fig. 1 show a kind of temperature-hot-fluid of the embodiment physical model of therrmodynamic system parameter optimization methodFigure, figure
In, the temperature of high and low temperature thermal sourceIt is known parameters, the equivalent endothermic temperature of endothermic process, heat release in working medium circulation
The equivalent exothermic temperature of process is respectively, the power output of power cycle is during system stable state, heat absorption rate is
, heat liberation rate, heat release rate is;High-temperature heat-exchanging, the heat exchange area of cryogenic heat exchanger and the overall heat-transfer coefficient of heat transfer coefficient product are respectively.Based on the physical characteristics of heat engine stationary state operation, reduced form finite time analytic approach directly uses the energy flow rate side of stationary state
Journey group is analyzed:
Can flow rate equation
(16)
High-temperature heat-exchanging heat transfer flow rate equation
(17)
Cryogenic heat exchanger heat transfer flow rate equation
(18)
The characteristics of interior reversible heat engine model equation
(19)
Interior reversible heat engine effectiveness formula
(20)
Using 5 equations of formula (16) ~ (20), with equivalent exothermic temperatureOr equivalent endothermic temperature is intermediate variable, is asked
Solve power, efficiencyMathematic(al) representation be respectively
(21)
(22)。
Fig. 2 is a kind of therrmodynamic system parameter optimization method embodiment of the present inventionWithFigure, left ordinate are
, right ordinate is, bottom abscissa is, pushing up abscissa is, as the preferred efficient point of equal weight method due toWithFor
From reduced parameter, benchmark is respective maximal efficiency and peak power output, is normalized processing method;To difference
The dimensionless power output of value does normalized can illustrate the physical significance of equal weight method in a width figure;In Fig. 3, O points
For the optimum efficiency recommended of the present invention, the graphing method of equal weight method be byCross origin 45 ° of skew lines with from contrast
Power outputThe intersection point of curve is obtained, and equal weight method mathematical expression is calculated by formula (2), and optimum efficiency is
(2a)
Seen by Fig. 3, the power output of best efficiency point is the 0.8230 of peak power output, and optimum efficiency is also for most
The 0.8230 of big efficiency, both are taken into account importance.
Fig. 3 is a kind of being set with the unit capacity of therrmodynamic system for therrmodynamic system parameter optimization method embodiment of the invention
The minimum principle of standby cost, selects overall heat-transfer coefficient ratioOptimization explanation figure;The longitudinal axisRepresent unit capacity equipment into
This,Definition be
(6)
Wherein,For therrmodynamic system dimensionless equipment cost, the cost of high-temperature heat-exchangingFor benchmark
Cost unit, noteWhen high-temperature heat-exchanging, cryogenic heat exchanger, expanding machine, the cost of liquid circulation pump and other auxiliary equipments
Coefficient is respectively 1, a, b, c and d;The contrast delivery efficiency of the optimum efficiency defined for formula (5);The transverse axis coordinate representation of figure
Overall heat-transfer coefficient ratio;(1), the cost coefficient of (2) two recessed parabolical equipment are respectively in figure:(1) a=1、b=1、
c+ d=1;(2) a=1、b=0.8、c+ d=1;(1) the unit capacity cost minimization point of curve is tried to achieve optimal;(2) the unit capacity cost minimization point of curve is tried to achieve optimal, and with power outputWhen therrmodynamic system peak power outputEqualValue, i.e.,, it is derived most
Good overall heat-transfer coefficient ratioMathematic formula be the value coincidence obtained of formula (9),
(9)
Wherein,;
。