CN112360810A - Impeller inlet design method of supercritical carbon dioxide centrifugal compressor - Google Patents

Impeller inlet design method of supercritical carbon dioxide centrifugal compressor Download PDF

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CN112360810A
CN112360810A CN202011138696.6A CN202011138696A CN112360810A CN 112360810 A CN112360810 A CN 112360810A CN 202011138696 A CN202011138696 A CN 202011138696A CN 112360810 A CN112360810 A CN 112360810A
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impeller inlet
impeller
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CN112360810B (en
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李孝检
刘正先
赵祎佳
谢兴奥
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Tianjin University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/26—Rotors specially for elastic fluids
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    • F04D29/284—Rotors specially for elastic fluids for centrifugal or helico-centrifugal pumps for radial-flow or helico-centrifugal pumps for compressors
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/26—Rotors specially for elastic fluids
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Abstract

The invention discloses a design method for an impeller inlet of a supercritical carbon dioxide centrifugal compressor, and aims to provide a design method which can limit the condensation phenomenon of the impeller inlet, keep geometric compactness and has high thermodynamic cycle efficiency. The method comprises the following steps: setting total temperature of an impeller inlet, total pressure of the impeller inlet, a target flow function, machine Mach number and a pre-rotation inlet angle; calculating to obtain total enthalpy of an inlet of the impeller; determining impeller inlet total entropy, impeller inlet static entropy, acceptable acceleration margin empirical coefficient and steam fraction value; calculating the maximum expansion Mach number, and determining the acceptable expansion Mach number according to the obtained maximum expansion Mach number; determining the absolute Mach number of an impeller inlet according to the obtained acceptable expansion Mach number; calculating static parameters of the impeller inlet under the actual condition according to the obtained absolute mach number of the impeller inlet; calculating the average isentropic index, calculating the relative axial airflow angle of the optimal impeller inlet wheel cover, calculating the relative Mach number of the impeller inlet wheel cover, and calculating the shape coefficient of the impeller inlet.

Description

Impeller inlet design method of supercritical carbon dioxide centrifugal compressor
Technical Field
The invention relates to the technical field of centrifugal compressor design, in particular to a design method of an impeller inlet of a supercritical carbon dioxide centrifugal compressor.
Background
Supercritical carbon dioxide (SCO)2) Has excellent thermodynamic characteristics, such as large specific heat capacity and isothermal compressibility, and small viscosity. Compared with superheated steam, with SCO2Energy systems that are fluid working fluids typically require less compression work and have higher cycle efficiencies. In addition, SCO2Is very high, and thus SCO is compared to a conventional rankine cycle2The brayton cycle has a more compact structure. Furthermore, CO2The critical temperature (304.13K) of the SCO is far lower than that of other common fluid working media, so that the SCO2The brayton thermodynamic cycle is easier to implement. Due to the advantages, SCO2Brayton cycle is widely used in nuclear power systems, waste heat recovery systems, solar power systems, geothermal systems, and the like.
The centrifugal compressor being SCO2One of the key components of the brayton cycle. As the compressor inlet fluid approaches its critical point, the cycle compression work will be further reduced and the cycle efficiency will be further increased. However, CO around the critical point2The thermodynamic property of the gas compressor shows strong nonlinearity, and the change rule of the physical property parameter obviously deviates from a complete gas state equation, so that the compressor design method based on the complete gas assumption is completely ineffective. On the other hand, if SCO2The inlet gross parameters of the compressor are very close to the critical point and the design of the impeller inlet becomes very difficult. The acceleration of the fluid working medium not only occurs in the process from the total parameter state of the impeller inlet to the static parameter state; but also the fluid acceleration is present in the vicinity of the blade leading edge due to the geometrical curvature of the suction surface of the blade leading edge. Due to the acceleration process of the two aspects, the thermodynamic state of the fluid working medium is likely to cross a working medium saturation line, so that the condensation phenomenon (two-phase flow) occurs at the inlet of the impeller. The condensation of the working fluid near the impeller inlet can reduce the flow stability of the compressor and lead to large aerodynamic losses.
At SCO2In the design practice of the compressor, the total impeller inlet parameter should be close to the critical point to achieve higher cycle efficiency. On the other hand, to avoid the impeller inlet condensation, the flow acceleration near the impeller inlet should be limited. This means that for a given mass flow the cross-sectional area of the impeller inlet becomes relatively large, so that the compactness of the compressor is reduced. Heretofore, the existing design methods have not been able to solve the above-mentioned contradictions well. It is necessary to develop a new design method for the impeller inlet to achieve the comprehensive effects of limiting the condensation phenomenon of the impeller inlet, ensuring the compactness of the compressor structure and not losing the cycle efficiency.
Disclosure of Invention
The invention aims to provide a method for designing an impeller inlet of a supercritical carbon dioxide compressor, which can limit the condensation phenomenon of the impeller inlet, keep the geometric compactness of the compressor and simultaneously enable the whole thermodynamic cycle to have higher cycle efficiency, aiming at the technical defects in the prior art.
The technical scheme adopted for realizing the purpose of the invention is as follows:
a design method for an impeller inlet of a supercritical carbon dioxide centrifugal compressor comprises the following steps:
(1) given total impeller inlet temperature Tt1Total pressure p at the inlet of the impellert1Target flow function phi and machine Mach number Mu2And a pre-swirl inlet angle alpha1(ii) a According to the total temperature T of the inlet of the impellert1And total inlet pressure pt1Obtaining total enthalpy h of an impeller inlet by utilizing a thermal power and transport characteristic database REFPROPt1；
(2) Determining impeller inlet total entropy St1Impeller inlet static entropy S1Acceptable acceleration margin empirical coefficient lambda and steam fraction Q value:
i) according to the total temperature T of the impeller inlett1And total pressure p at the impeller inlett1Obtaining the total entropy S of the impeller inlet by using a thermal and transport characteristic database REFPROPt1；
II) static entropy S of impeller inlet1Equal to the impeller inlet assemblyEntropy St1；
III) the method for determining the acceptable acceleration margin empirical coefficient lambda comprises the following steps: comparison of reference pressure prefAnd critical pressure pcrIf reference pressure pref> critical pressure pcrIf yes, the empirical factor λ of the acceleration margin is acceptable to be 0.3, otherwise λ is 0.5;
iv) calculating the steam fraction Q: comparison of reference pressure prefAnd critical pressure pcrIf reference pressure pref> critical pressure pcrIf the steam fraction Q is 0, otherwise Q is 1;
the reference pressure prefAccording to static entropy S of impeller inlet1And assuming that the critical temperature T is reached by isentropic expansioncrObtaining by using a thermal and transport characteristic database REFPROP;
(3) calculating the maximum expansion Mach number
Figure BDA0002737581380000031
According to the obtained maximum expansion Mach number
Figure BDA0002737581380000032
Determining acceptable expansion Mach number
Figure BDA0002737581380000033
According to the obtained acceptable expansion Mach number
Figure BDA0002737581380000034
Determining impeller inlet absolute mach number Mc1；
(4) According to the obtained absolute Mach number M of the impeller inletc1Calculating static parameters of an impeller inlet under the actual condition; the method comprises the following steps:
(I) setting initial static temperature T of an impeller inlet under actual conditions1,g；
(II) initial static temperature T of impeller inlet according to actual conditions1,gAnd static entropy S of impeller inlet1Obtaining initial static temperature T of an impeller inlet under actual conditions by utilizing a thermal and transport characteristic database REFPROP1,gCorresponding impeller inlet local acoustic velocity a1,g；
(III) according to the initial static temperature T of the impeller inlet under the actual condition1,gAnd static entropy of import S1Obtaining initial static temperature T of an impeller inlet under actual conditions by utilizing a thermal and transport characteristic database REFPROP1,gCorresponding static enthalpy h of impeller inlet1,g；
(IV) calculating the initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet absolute velocity c1,gThe calculation formula is as follows:
Figure BDA0002737581380000035
(V) calculating the initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet absolute Mach number Mc1,gThe calculation formula is as follows: mc1,g＝c1,g/a1,g；
(VI) determining the absolute Mach number M of the impeller inletc1And (V) calculating the initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet absolute Mach number Mc1,gWhether the relative error of (a) is less than 1%;
(VII) if the relative error is more than or equal to 1%, returning to the step (I), and resetting the initial static temperature T of the impeller inlet under the actual condition by adopting a dichotomy1,gAnd (5) repeating the steps (I) to (VI) until the absolute Mach number M of the impeller inletc1And (V) calculating the initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet absolute Mach number Mc1,gIs less than 1%, and then the next step is carried out;
(VIII) if the relative error is less than 1%, determining iteration convergence, and determining the initial static temperature T of the impeller inlet under the actual condition1,gStatic temperature T of impeller inlet in practical situation1(ii) a The initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet local acoustic velocity a1,gLocal sound velocity a at impeller inlet as actual condition1The initial static temperature T of the impeller inlet under the actual condition1,gCorresponding static enthalpy h of impeller inlet1,gAsStatic enthalpy h at impeller inlet in practical situation1The initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet absolute velocity c1,gAs actual impeller inlet absolute velocity c1Carrying out the next calculation;
(IX) impeller inlet static temperature T according to actual conditions1And static entropy S of impeller inlet1Obtaining impeller inlet static pressure p under actual condition by using thermal power and transport characteristic database REFPROP1And impeller inlet density rho under actual conditions1；
(5) Calculating the mean isentropic index
Figure BDA0002737581380000041
The calculation formula is as follows:
Figure BDA0002737581380000042
wherein: gamma rayt1Specific heat ratio, gamma, corresponding to the total parameter1Specific heat ratio, κ, for static parameterT,t1The isothermal compressibility factor, κ, corresponding to the overall parameterT,1The isothermal compression coefficient corresponding to the static parameter;
(6) calculating the optimal relative axial airflow angle beta of the impeller inlet wheel cover1sThe calculation formula is as follows:
Figure BDA0002737581380000043
(7) calculating relative Mach number M of impeller inlet wheel coverw1The calculation formula is as follows:
Figure BDA0002737581380000044
(8) calculating the shape coefficient k of the impeller inlet, wherein the calculation formula is as follows:
Figure BDA0002737581380000051
step (3) of calculating the maximum expansion Mach number
Figure BDA0002737581380000052
The method comprises the following steps:
i) setting initial static temperature T 'of an impeller inlet under the condition of maximum expansion'1,g；
II) initial static temperature T 'of an impeller inlet under the condition of maximum expansion'1,gAnd obtaining corresponding entropy S 'by utilizing the steam fraction Q through a thermal power and transport characteristic database REFPROP'1,g；
III) determining the static entropy S of the impeller inlet1And the initial static temperature T 'of the inlet of the impeller under the condition of maximum expansion calculated in the step II)'1,gCorresponding entropy S'1,gWhether the relative error of (a) is less than 1%;
IV) if the relative error is more than or equal to 1%, returning to the step I), and resetting the initial static temperature T 'of the inlet of the impeller under the condition of maximum expansion by adopting a dichotomy'1,gRepeating the steps I) to III) until the relative error is less than 1%, and carrying out the next step;
v) judging iteration convergence if the relative error is less than 1%, and judging the initial static temperature T 'of an impeller inlet under the condition of maximum expansion'1,gImpeller Inlet static temperature T 'as maximum expansion'1Carrying out the next calculation;
VI) impeller Inlet static temperature T 'according to maximum expansion'1And obtaining the static enthalpy h 'of the impeller inlet under the condition of maximum expansion by utilizing the steam fraction Q through a thermodynamic and transport characteristic database REFPROP'1And local sound velocity a 'at impeller inlet'1；
VII) calculating the Absolute impeller Inlet velocity c 'at maximum expansion'1The calculation formula is as follows:
Figure BDA0002737581380000053
VIII) calculation of the maximum expansion Mach number
Figure BDA0002737581380000054
The calculation formula is as follows:
Figure BDA0002737581380000055
step (3) of calculating the Mach number of the acceptable expansion
Figure BDA0002737581380000056
The calculation formula of (2) is as follows:
Figure BDA0002737581380000057
wherein: λ is an acceptable acceleration margin empirical coefficient,
Figure BDA0002737581380000058
is the maximum expansion mach number; step (3) calculating the absolute Mach number M of the impeller inletc1The calculation formula is as follows:
Figure BDA0002737581380000059
wherein: sigma is a safety factor which is set as the standard,
Figure BDA00027375813800000510
at an acceptable expansion mach number.
The safety factor sigma is 0.92.
Step (5) calculating average isentropic index
Figure BDA0002737581380000061
In the calculation formula (2), the specific heat ratio gamma corresponding to the total parametert1According to the total temperature T of the inlet of the impellert1And total pressure p at the impeller inlett1Obtained by using a thermal and transport characteristics database REFPROP.
Step (5) calculating average isentropic index
Figure BDA0002737581380000062
In the calculation formula (2), the specific heat ratio gamma corresponding to the static parameter1According to the static temperature T of the impeller inlet under the actual condition1And impeller inlet static pressure p under actual conditions1Obtained by using a thermal and transport characteristic database REFPROP。
Step (5) calculating average isentropic index
Figure BDA0002737581380000063
In the calculation formula (D), the isothermal compression coefficient kappa corresponding to the total parameterT,t1According to the given total temperature T of the impeller inlett1And total pressure p at the impeller inlett1And obtaining the data by utilizing a thermal and transport characteristic database REFPROP.
Step (5) calculating average isentropic index
Figure BDA0002737581380000064
In the calculation formula (D), the isothermal compression coefficient kappa corresponding to the static parameterT,1According to the static temperature T of the impeller inlet under the actual condition1And impeller inlet static pressure p under actual conditions1Obtained by using a thermal and transport characteristics database REFPROP.
Compared with the prior art, the invention has the beneficial effects that:
1) the design method of the invention calculates the corresponding reference pressure aiming at the given total inlet parameters, and assigns different empirical coefficients of acceptable acceleration margin according to the relative magnitude of the reference pressure and the critical pressure. The method can effectively limit the condensation phenomenon of the inlet area of the impeller under the condition of any given total inlet parameter, so that the total inlet parameter of the impeller can be closer to the critical point of the fluid working medium, and the cycle efficiency is improved.
2) The method of the invention obtains the optimal relative axial airflow angle of the impeller inlet shroud through the relation designed by the actual maximum gas circulation capacity, and under the same circulation capacity, the relative Mach number of the front edge of the impeller blade is minimum, the aerodynamic loss is minimum, and the geometric structure of the impeller inlet is more compact.
3) The design method of the invention can limit the condensation phenomenon of the impeller inlet, can keep the geometric compactness of the compressor, and simultaneously ensures that the whole thermodynamic cycle has higher cycle efficiency.
Detailed Description
The present invention will be described in detail with reference to specific examples.
The impeller inlet design method of the supercritical carbon dioxide centrifugal compressor comprises the following steps:
(1) given total impeller inlet temperature Tt1Total pressure p at the inlet of the impellert1Target flow function phi and machine Mach number Mu2And a pre-swirl inlet angle alpha1(ii) a According to the total temperature T of the inlet of the impellert1And total inlet pressure pt1Obtaining total enthalpy h of an impeller inlet by utilizing a thermal power and transport characteristic database REFPROPt1；
(2) Determining impeller inlet total entropy St1Impeller inlet static entropy S1Acceptable acceleration margin empirical coefficient lambda and steam fraction Q value:
according to the total temperature T of the inlet of the impellert1And total pressure p at the impeller inlett1Obtaining the total entropy S of the impeller inlet by using a thermal and transport characteristic database REFPROPt1；
(II) static entropy S of impeller inlet1Is equal to the total entropy S of the impeller inlett1；
(III) according to the static entropy S of the impeller inlet1And assuming a critical temperature T reached by isentropic expansioncrObtaining the reference pressure p by using a thermal and transport characteristics database REFPROPref(ii) a Critical temperature TcrTo disclose a constant, Tcr＝304.1282K；
(IV) calculating an acceptable acceleration margin empirical coefficient lambda: comparison of reference pressure prefAnd critical pressure pcrIf reference pressure pref> critical pressure pcrIf yes, the empirical factor λ of the acceleration margin is acceptable to be 0.3, otherwise λ is 0.5; wherein the critical pressure pcrTo disclose a constant, is pcr＝7.3773Mpa；
(v) calculating the steam fraction Q: comparison of reference pressure prefAnd critical pressure pcrIf reference pressure pref> critical pressure pcrIf so, the steam fraction Q is 0, otherwise Q is 1.
(3) Calculating the maximum expansion Mach number
Figure BDA0002737581380000071
I) setting initial static temperature T 'of an impeller inlet under the condition of maximum expansion'1,g；
II) initial static temperature T 'of an impeller inlet under the condition of maximum expansion'1,gAnd obtaining corresponding entropy S 'by utilizing the steam fraction Q through a thermal power and transport characteristic database REFPROP'1,g；
III) determination of the static entropy S of the intake1And the initial static temperature T 'of the inlet of the impeller under the condition of maximum expansion calculated in the step II)'1,gCorresponding entropy S'1,gIf the relative error is less than 1%, returning to the step I), resetting the initial static temperature of the impeller inlet under the maximum expansion condition by adopting a dichotomy, and repeating the steps I) to III) until the relative error is less than 1%; judging iteration convergence if the relative error is less than 1%, and judging the initial static temperature T 'of the impeller inlet under the condition of maximum expansion'1,gImpeller Inlet static temperature T 'as maximum expansion'1I.e. T'1＝T′1,gCarrying out the next calculation;
IVV) impeller Inlet static temperature T 'according to maximum expansion'1And obtaining the static enthalpy h 'of the impeller inlet under the condition of maximum expansion by utilizing the steam fraction Q through a thermodynamic and transport characteristic database REFPROP'1；
V) impeller inlet static temperature T 'according to maximum expansion condition'1And obtaining the local sound velocity a 'of the impeller inlet under the condition of maximum expansion by utilizing the steam fraction Q through a thermal and transport characteristic database REFPROP'1；
VI) calculating the impeller Inlet Absolute velocity at maximum expansion c'1The calculation formula is as follows:
Figure BDA0002737581380000081
wherein h ist1Is total enthalpy of impeller inlet, h'1The static enthalpy of the impeller inlet under the maximum expansion condition;
VII) calculation of maximum expansion Mach number
Figure BDA0002737581380000082
The calculation formula is as follows:
Figure BDA0002737581380000083
wherein c'1Impeller Inlet absolute velocity at maximum expansion, a'1Is the local speed of sound at the impeller inlet at maximum expansion.
(4) Calculating an acceptable expansion Mach number
Figure BDA0002737581380000084
The calculation formula is as follows:
Figure BDA0002737581380000085
where lambda is an acceptable acceleration margin empirical coefficient,
Figure BDA0002737581380000086
is the maximum expansion mach number;
(5) calculating the absolute Mach number M of the impeller inletc1The calculation formula is as follows:
Figure BDA0002737581380000087
where σ is a safety factor, σ is recommended to be 0.92,
Figure BDA0002737581380000088
at an acceptable expansion mach number;
(6) according to the absolute Mach number M of the impeller inletc1And calculating static parameters of an impeller inlet under the actual condition:
i) setting initial static temperature T of an impeller inlet under actual conditions1,g；
II) initial static temperature T of the impeller inlet according to actual conditions1,gAnd static entropy S of impeller inlet1Obtaining initial static temperature T of an impeller inlet under actual conditions by utilizing a thermal and transport characteristic database REFPROP1,gCorresponding impeller inlet local acoustic velocity a1,g；
III) initial static temperature T of the impeller inlet according to actual conditions1,gAnd static entropy S of impeller inlet1Using thermal and transport characteristicsObtaining the initial static temperature T of the impeller inlet under the actual condition by the database REFPROP1,gCorresponding static enthalpy h of impeller inlet1,g；
IV) calculating the initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet absolute velocity c1,gThe calculation formula is as follows:
Figure BDA0002737581380000091
wherein h ist1Is the total enthalpy of the impeller inlet, h1,gIs the initial static temperature T of the inlet of the impeller under the actual condition1,gThe corresponding impeller inlet static enthalpy;
v) calculating the initial static temperature T of the inlet of the impeller under the actual condition1,gCorresponding impeller inlet absolute Mach number Mc1,gThe calculation formula is as follows: mc1,g＝c1,g/a1,g；
VI) judging the absolute Mach number M of the impeller inletc1And V) calculating to obtain the initial static temperature T of the impeller inlet under the actual condition1,gCorresponding inlet absolute mach number Mc1,gIf the relative error is less than 1%, returning to the step I), resetting the initial static temperature of the impeller inlet under the actual condition by adopting a dichotomy, and repeating the steps I) to V) until the relative error is less than 1%; if the relative error is less than 1%, determining iteration convergence, and determining the initial static temperature T of the impeller inlet under the actual condition1,gStatic temperature T of impeller inlet in practical situation1(ii) a The initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet local acoustic velocity a1,gLocal sound velocity a at impeller inlet as actual condition1The initial static temperature T of the impeller inlet under the actual condition1,gCorresponding static enthalpy h of impeller inlet1,gStatic enthalpy h at the impeller inlet as a practical matter1The initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet absolute velocity c1,gAs actual impeller inlet absolute velocity c1Namely: t is1＝T1,g，a1＝a1,g，h1＝h1,g，c1＝c1,gAnd carrying out the next calculation.
VII) impeller inlet static temperature T according to actual conditions1And static entropy S of impeller inlet1Obtaining the static pressure p of the impeller inlet under the actual condition by utilizing a thermal power and transport characteristic database REFPROP1；
VIII) according to the static temperature T of the inlet of the impeller under actual conditions1And static entropy S of impeller inlet1Obtaining the inlet density rho under the actual condition by utilizing a thermal and transport characteristic database REFPROP1。
(7) Calculating the mean isentropic index
Figure BDA0002737581380000101
I) according to a given total temperature T of the impeller inlett1And total pressure p at the impeller inlett1Obtaining specific heat ratio gamma corresponding to total parameters of an impeller inlet by utilizing a thermal power and transport characteristic database REFPROPt1；
II) impeller inlet static temperature T according to actual conditions1And impeller inlet static pressure p under actual conditions1Obtaining specific heat ratio gamma corresponding to static parameters of an impeller inlet by utilizing a thermal power and transport characteristic database REFPROP1；
III) according to a given total impeller inlet temperature Tt1And total pressure p at the impeller inlett1Obtaining an isothermal compression coefficient kappa corresponding to the total parameters of the impeller inlet by utilizing a thermal and transport characteristic database REFPROPT,t1；
IV) impeller inlet static temperature T according to actual conditions1And impeller inlet static pressure p under actual conditions1Obtaining an isothermal compression coefficient kappa corresponding to static parameters of an impeller inlet by utilizing a thermal and transport characteristic database REFPROPT,1；
V) calculating average isentropic index
Figure BDA0002737581380000102
The calculation formula is as follows:
Figure BDA0002737581380000103
wherein: gamma rayt1Specific heat ratio, gamma, corresponding to the total parameter1Specific heat ratio, κ, for static parameterT,t1The isothermal compressibility factor, κ, corresponding to the overall parameterT,1The isothermal compression coefficient corresponding to the static parameter;
(8) obtaining the optimal impeller inlet shroud relative axial airflow angle beta by a relation designed by the actual maximum gas circulation capacity and adopting an implicit form iterative calculation method1sThe calculation formula is as follows:
Figure BDA0002737581380000104
wherein: alpha is alpha1For pre-swirl of the air angle, Mc1The absolute mach number of the impeller inlet,
Figure BDA0002737581380000105
is an average isentropic index;
(9) calculating relative Mach number M of impeller inlet wheel coverw1The calculation formula is as follows:
Figure BDA0002737581380000106
wherein: alpha is alpha1For pre-swirl of the air angle, Mc1Impeller inlet absolute mach number, beta1sThe relative axial airflow angle of the impeller inlet wheel cover is the optimal;
(10) calculating the shape coefficient k of the impeller inlet, wherein the calculation formula is as follows:
Figure BDA0002737581380000111
wherein: alpha is alpha1For pre-swirl of the air angle, Mc1Impeller inlet absolute mach number, beta1sFor optimum impeller inlet shroud relative axial airflow angle,
Figure BDA0002737581380000112
is an average isentropic index, Mu2Machine mach number.
To this end, all key geometric, aerodynamic and flow parameters of the impeller inlet have been derived, including: impeller inlet total temperature Tt1Total pressure p at the inlet of the impellert1Target flow function phi, machine Mach number Mu2Prerotation inlet angle alpha1Total entropy S of impeller inlett1Static entropy S of impeller inlet1Mach number of maximum expansion
Figure BDA0002737581380000113
Acceptable expansion mach number
Figure BDA0002737581380000114
And in practice all relevant parameters: impeller inlet absolute mach number Mc1Impeller inlet static temperature T1Local speed of sound a at impeller inlet1Absolute speed of impeller inlet c1Static enthalpy at impeller inlet h1Static pressure p at the inlet of the impeller1Impeller inlet density ρ1(ii) a Mean isentropic index
Figure BDA0002737581380000115
Optimum impeller inlet shroud relative axial airflow angle beta1sRelative mach number M of inlet shroud of impellerw1Impeller inlet shape factor k.
Example (b): the description will be given by taking the design of an impeller inlet of a supercritical carbon dioxide compressor of a certain Brayton thermodynamic cycle as an example:
(1) setting total temperature T of impeller inlet of supercritical carbon dioxide compressort1310K, total pressure p at the impeller inlett18MPa, target flow function phi 0.0118 and machine Mach number Mu20.8799, pre-swirl inlet angle α10 deg; according to total inlet temperature Tt1And total inlet pressure pt1Obtaining total enthalpy h of inlet by using thermal and transport characteristic database REFPROPt1＝381.94kJ/kg；
(2) Determining impeller inlet total entropy St1Impeller inlet static entropy S1Acceptable acceleration margin empirical factorλ and steam fraction Q value:
i) according to the total temperature T of the impeller inlett1And total pressure p at the impeller inlett1Obtaining total entropy S of impeller inlet by using thermodynamic and transport characteristic database REFPROPt11.5905kJ/(kg K), impeller inlet static entropy S1Equal to the total entropy S of the impeller inlett1I.e. S1＝St1＝1.5905kJ/(kg·K)；
II) according to the static entropy S of the impeller inlet1And assuming a critical temperature T reached by isentropic expansioncrObtaining the reference pressure p by using a thermal and transport characteristic database REFPROPref7.2628 MPa; wherein the critical temperature TcrTo disclose a constant, Tcr＝304.1282K；
III) calculating an acceptable acceleration margin empirical coefficient lambda: comparison of reference pressure pref7.2628MPa and critical pressure pcr7.3773MPa, p in this exampleref＜pcrIf so, the acceptable acceleration margin empirical coefficient λ is 0.5; wherein the critical pressure pcrTo disclose constants, pcr＝7.3773Mpa；
Iv) calculating the steam fraction Q: comparison of reference pressure prefAnd critical pressure pcrIn this embodiment, pref＜pcrIf the steam fraction Q is 1;
(3) calculating the maximum expansion Mach number
Figure BDA0002737581380000121
I) setting initial static temperature T 'of an impeller inlet under the condition of maximum expansion'1,g＝260.3641K；
II) initial inlet static temperature T 'according to maximum expansion condition'1,gAnd steam fraction Q, obtaining corresponding entropy S 'by utilizing a thermal power and transport characteristic database REFPROP'1,g＝1.9126kJ/(kg·K)；
III) determining the static entropy S of the impeller inlet1And the initial static temperature T 'of the inlet of the impeller under the condition of maximum expansion calculated in the step II)'1,gCorresponding entropy S'1,gWhether the relative error of (2) is less than 1%, the relative error of the present embodimentIf the difference is more than 1%, returning to the step I), resetting the initial static temperature of the impeller inlet under the maximum expansion condition by adopting a dichotomy, and recalculating the initial static temperature T 'of the impeller inlet under the maximum expansion condition'1,gCorresponding entropy S'1,g(ii) a Until the static entropy S of the impeller inlet1And the initial static temperature T 'of the inlet of the impeller under the condition of maximum expansion calculated in the step II)'1,gCorresponding entropy S'1,gIs less than 1%. Judging iteration convergence if the relative error is less than 1%, and enabling the static temperature of the impeller inlet under the condition of maximum expansion to be equal to the initial static temperature of the impeller inlet under the condition of maximum expansion, namely T'1＝T′1,gCarrying out the next calculation; in this embodiment, the finally obtained static temperature of the impeller inlet and the initial static temperature of the impeller inlet under the maximum expansion condition are: t'1＝T′1,g＝301.5763K。
IV) according to the inlet static temperature T 'at maximum expansion'1And obtaining the static enthalpy h 'of the impeller inlet under the condition of maximum expansion by utilizing the steam fraction Q through a thermodynamic and transport characteristic database REFPROP'1＝378.61kJ/kg；
V) inlet static temperature T 'according to maximum expansion'1And obtaining the local sound velocity a 'of the impeller inlet under the condition of maximum expansion by utilizing the steam fraction Q through a thermal and transport characteristic database REFPROP'1＝180.6456m/s；
VI) using a calculation formula
Figure BDA0002737581380000131
Calculating impeller Inlet Absolute velocity at maximum expansion c'181.5459m/s, wherein ht1Is total enthalpy of impeller inlet, h'1The static enthalpy of the impeller inlet under the maximum expansion condition;
VII) using a calculation formula
Figure BDA0002737581380000139
Calculating the maximum expansion Mach number
Figure BDA0002737581380000132
Wherein c'1At maximum expansionImpeller Inlet absolute velocity of a'1The local sound velocity of the impeller inlet under the maximum expansion condition;
(4) using a formula of calculation
Figure BDA0002737581380000133
Calculating an acceptable expansion Mach number
Figure BDA0002737581380000134
Wherein: λ is an acceptable acceleration margin empirical coefficient, λ is 0.5,
Figure BDA0002737581380000135
is the maximum expansion mach number;
(5) using a formula of calculation
Figure BDA0002737581380000136
Calculating the absolute Mach number M of the impeller inletc10.2077, where σ is a safety factor, 0.92 is recommended;
Figure BDA0002737581380000137
at an acceptable expansion mach number;
(6) according to the absolute Mach number M of the impeller inletc1And calculating static parameters of an impeller inlet under the actual condition:
i) setting initial static temperature T of an impeller inlet under actual conditions1,g＝304.1282K；
II) initial static temperature T of the impeller inlet according to actual conditions1,gAnd static entropy of import S1Obtaining the local sound velocity a of the impeller inlet under the actual condition by utilizing a thermal and transport characteristic database REFPROP1,g＝184.9274m/s；
III) initial static temperature T of the impeller inlet according to actual conditions1,gAnd static entropy of import S1Obtaining static enthalpy h of an impeller inlet under actual conditions by utilizing a thermal power and transport characteristic database REFPROP1,g＝379.62kJ/kg；
IV) using a calculation formula
Figure BDA0002737581380000138
Calculating the absolute speed c of the impeller inlet under the actual condition1,g68.1447m/s, wherein ht1Is the total enthalpy of the impeller inlet, h1,gThe static enthalpy of the impeller inlet under the actual condition;
v) using the formula Mc1,g＝c1,g/a1,gCalculating the absolute Mach number M of the impeller inlet under the actual conditionc1,g0.3685 wherein c1,gIs the actual absolute speed of the impeller inlet, a1,gThe local sound velocity of the impeller inlet under the actual condition;
VI) judging the absolute Mach number M of the impeller inletc1And V) calculating to obtain the initial static temperature T of the impeller inlet under the actual condition1,gCorresponding impeller inlet absolute Mach number Mc1,gWhether the relative error is less than 1%, in the embodiment, the relative error is greater than 1%, the step I) is returned, the initial static temperature of the impeller inlet under the actual condition is reset by adopting a dichotomy, and the steps I) to V) are repeated until the relative error is less than 1%. If the relative error is less than 1%, determining iteration convergence, and determining the static temperature T of the impeller inlet under the actual condition1＝T1,gThe local sound velocity a at the impeller inlet under actual conditions1＝a1,gStatic enthalpy h at the impeller inlet in practical conditions1＝h1,gActual impeller inlet absolute velocity c1＝c1,gCarrying out the next calculation;
and (3) final iteration results: inlet static temperature T in practical conditions1308.0205K, the inlet local sound velocity a in practice1191.0433m/s, inlet static enthalpy h in practical cases1381.15kJ/kg, actual inlet absolute velocity c1＝39.6706m/s；
VII) inlet static temperature T according to actual conditions1And static entropy of import S1Obtaining inlet static pressure p under actual condition by using thermal power and transport characteristic database REFPROP1＝7.7448MPa；
VIII) inlet static temperature T according to actual conditions1And static entropy of import S1Obtaining actual conditions by using a thermal and transport characteristic database REFPROPInlet density p of1＝320.8368kg/m3；
(7) Calculating the mean isentropic index
Figure BDA0002737581380000141
I) according to the total temperature T of the impeller inlett1And total pressure p at the impeller inlett1Obtaining specific heat ratio gamma corresponding to total parameters of an impeller inlet by utilizing a thermal power and transport characteristic database REFPROPt1＝8.3366；
II) according to the static temperature T of the inlet of the impeller1And impeller inlet static pressure p1Obtaining specific heat ratio gamma corresponding to static parameters of an impeller inlet by utilizing a thermal power and transport characteristic database REFPROP1＝9.1544；
III) according to the total temperature T of the impeller inlett1And total pressure p at the impeller inlett1Obtaining an isothermal compression coefficient kappa corresponding to the total parameters of the impeller inlet by utilizing a thermal and transport characteristic database REFPROPT,t1＝6.7399×10-4(1/kPa)；
IV) according to the static temperature T of the impeller inlet1And impeller inlet static pressure p1Obtaining an isothermal compression coefficient kappa corresponding to static parameters of an impeller inlet by utilizing a thermal and transport characteristic database REFPROPT,1＝7.8177×10-4(1/kPa)；
V) calculating average isentropic index
Figure BDA0002737581380000142
The calculation formula is as follows:
Figure BDA0002737581380000151
calculated mean isentropic index of
Figure BDA0002737581380000152
(8) Calculating the inlet parameters of the impeller: calculating the optimal impeller inlet shroud relative axial airflow angle beta by adopting an implicit form iterative calculation method1sThe calculation formula is as follows:
Figure BDA0002737581380000153
wherein: alpha is alpha1For pre-swirl of the air angle, Mc1The absolute mach number of the impeller inlet,
Figure BDA0002737581380000154
is an average isentropic index; optimum impeller inlet shroud relative axial airflow angle beta1s＝55.8034deg。
(9) Calculating relative Mach number M of impeller inlet wheel coverw1The calculation formula is as follows:
Figure BDA0002737581380000155
wherein: alpha is alpha1For pre-swirl of the air angle, Mc1Impeller inlet absolute mach number, beta1sThe relative axial airflow angle of the impeller inlet wheel cover is the optimal; relative mach number M of impeller inlet shroudw1＝0.3696。
(10) Calculating the shape coefficient k of the impeller inlet, wherein the calculation formula is as follows:
Figure BDA0002737581380000156
the impeller inlet shape factor k is calculated to be 0.6220.
To this end, all key geometric, aerodynamic and flow parameters of the impeller inlet have been derived, including: impeller inlet total temperature Tt1Total pressure p at the inlet of the impellert1Target flow function phi, machine Mach number Mu2Prerotation inlet angle alpha1Total entropy S of impeller inlett1Static entropy S of impeller inlet1Mach number of maximum expansion
Figure BDA0002737581380000157
Acceptable expansion mach number
Figure BDA0002737581380000158
And in practice all relevant parameters: impeller inlet absolute mach number Mc1Impeller inlet static temperature T1Local speed of sound a at impeller inlet1Absolute speed of impeller inlet c1Static enthalpy at impeller inlet h1Static pressure p at the inlet of the impeller1Impeller inlet density ρ1(ii) a Mean isentropic index
Figure BDA0002737581380000159
Optimum impeller inlet shroud relative axial airflow angle beta1sRelative mach number M of inlet shroud of impellerw1Impeller inlet shape factor k.
The application of the impeller inlet parameters obtained in the above embodiment to the supercritical carbon dioxide compressor is proved by experiments that: the condensation phenomenon at the inlet of the impeller can be limited, the geometric compactness of the compressor can be kept, and meanwhile, the whole thermodynamic cycle has higher cycle efficiency.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (8)

1.一种超临界二氧化碳离心压缩机的叶轮进口设计方法，其特征在于，包括下述步骤：1. an impeller inlet design method of a supercritical carbon dioxide centrifugal compressor, is characterized in that, comprises the following steps: (1)给定叶轮进口总温Tt1、叶轮进口总压pt1、目标流量函数Φ、机器马赫数Mu2及预旋进气角α1；根据叶轮进口总温Tt1及进口总压pt1利用热力与输运特性数据库REFPROP得到叶轮进口总焓ht1；(1) Given the total impeller inlet temperature T t1 , the impeller inlet total pressure p t1 , the target flow function Φ, the machine Mach number M u2 and the pre-rotation inlet angle α 1 ; according to the impeller inlet total temperature T t1 and the total inlet pressure p t1 obtains the impeller inlet total enthalpy h t1 by using the thermal and transport characteristic database REFPROP; (2)确定叶轮进口总熵St1、叶轮进口静熵S1、可接受加速裕度经验系数λ及蒸汽分数Q值：(2) Determine the total impeller inlet entropy S t1 , the impeller inlet static entropy S 1 , the acceptable acceleration margin empirical coefficient λ and the steam fraction Q value: Ⅰ)根据叶轮进口总温Tt1及叶轮进口总压pt1利用热力与输运特性数据库REFPROP得到所述叶轮进口总熵St1；1) According to the total temperature T t1 at the inlet of the impeller and the total pressure p t1 at the inlet of the impeller, the total entropy S t1 at the inlet of the impeller is obtained by using the thermal and transport characteristic database REFPROP; Ⅱ)所述叶轮进口静熵S1等于所述叶轮进口总熵St1；II) The static entropy S 1 of the impeller inlet is equal to the total entropy S t1 of the impeller inlet; Ⅲ)所述可接受加速裕度经验系数λ的确定方法为：对比参考压力pref与临界压力pcr，如果参考压力pref＞临界压力pcr，则可接受加速裕度经验系数λ＝0.3，否则λ＝0.5；III) The method for determining the acceptable acceleration margin empirical coefficient λ is: comparing the reference pressure pref with the critical pressure p cr , if the reference pressure pref > critical pressure p cr , the acceptable acceleration margin empirical coefficient λ=0.3 , otherwise λ=0.5; Ⅳ)计算蒸汽分数Q：对比参考压力pref与临界压力pcr，如果参考压力pref＞临界压力pcr，则蒸汽分数Q＝0，否则Q＝1；Ⅳ) Calculate the steam fraction Q: compare the reference pressure pref with the critical pressure p cr , if the reference pressure pre ref > the critical pressure p cr , then the steam fraction Q=0, otherwise Q=1; 所述参考压力pref根据叶轮进口静熵S1及假设通过等熵膨胀达到临界温度Tcr利用热力与输运特性数据库REFPROP获得；The reference pressure pre is obtained according to the static entropy S 1 of the impeller inlet and the assumption that the critical temperature T cr is reached by isentropic expansion using the thermal and transport characteristics database REFPROP ; (3)计算最大膨胀马赫数
Figure FDA0002737581370000011
根据所得最大膨胀马赫数
Figure FDA0002737581370000012
确定可接受膨胀马赫数
Figure FDA0002737581370000013
根据所得可接受膨胀马赫数
Figure FDA0002737581370000014
确定叶轮进口绝对马赫数Mc1；(3) Calculate the maximum expansion Mach number
Figure FDA0002737581370000011
According to the obtained maximum expansion Mach number
Figure FDA0002737581370000012
Determining the Acceptable Dilation Mach Number
Figure FDA0002737581370000013
According to the resulting acceptable expansion Mach number
Figure FDA0002737581370000014
Determine the absolute Mach number M c1 of the impeller inlet; (4)根据所得叶轮进口绝对马赫数Mc1计算实际情况下的叶轮进口静参数；包括下述步骤：(4) Calculate the static parameters of the impeller inlet under the actual situation according to the obtained absolute Mach number M c1 of the impeller inlet; including the following steps: (Ⅰ)设定实际情况下的叶轮进口初始静温T1,g；(I) Set the initial static temperature T 1,g of the impeller inlet under actual conditions; (Ⅱ)根据实际情况下的叶轮进口初始静温T1,g及叶轮进口静熵S1利用热力与输运特性数据库REFPROP得到实际情况下的叶轮进口初始静温T1,g对应的叶轮进口当地声速a1,g；(II) According to the initial static temperature T 1,g of the impeller inlet and the static entropy S 1 of the impeller inlet under the actual situation, the impeller inlet corresponding to the initial static temperature T 1,g of the impeller inlet under the actual situation is obtained by using the thermal and transport characteristic database REFPROP local speed of sound a 1,g ; (Ⅲ)根据实际情况下的叶轮进口初始静温T1,g及进口静熵S1利用热力与输运特性数据库REFPROP得到实际情况下的叶轮进口初始静温T1,g对应的叶轮进口静焓h1,g；(III) According to the initial static temperature T 1,g of the impeller inlet and the static entropy S 1 of the impeller under the actual situation, the impeller inlet static temperature corresponding to the initial static temperature T 1,g of the impeller inlet under the actual situation is obtained by using the thermal and transport characteristic database REFPROP enthalpy h 1,g ; (Ⅳ)计算实际情况下的叶轮进口初始静温T1,g对应的叶轮进口绝对速度c1,g，计算公式为：
Figure FDA0002737581370000021
(IV) Calculate the absolute velocity c 1,g of the impeller inlet corresponding to the initial static temperature T 1,g of the impeller inlet under the actual situation, and the calculation formula is:
Figure FDA0002737581370000021
 (Ⅴ)计算实际情况下的叶轮进口初始静温T1,g对应的叶轮进口绝对马赫数Mc1,g，计算公式为：Mc1,g＝c1,g/a1,g；(V) Calculate the absolute Mach number M c1,g of the impeller inlet corresponding to the initial static temperature T 1,g of the impeller inlet under the actual situation, and the calculation formula is: M c1,g =c 1,g /a 1,g ; (Ⅵ)判断叶轮进口绝对马赫数Mc1与步骤(Ⅴ)计算得到的实际情况下的叶轮进口初始静温T1,g对应的叶轮进口绝对马赫数Mc1,g的相对误差是否小于1％；(Ⅵ) Judging whether the relative error between the absolute Mach number M c1 of the impeller inlet and the initial static temperature T 1,g of the impeller inlet under the actual situation calculated in step (Ⅴ) is less than 1%. ; (Ⅶ)如果相对误差大于或等于1％，返回步骤(Ⅰ)，采用二分法重新设定实际情况下的叶轮进口初始静温T1,g，重复步骤(Ⅰ)至步骤(Ⅵ)，直至叶轮进口绝对马赫数Mc1与步骤(Ⅴ)计算得到的实际情况下的叶轮进口初始静温T1,g对应的叶轮进口绝对马赫数Mc1,g的相对误差小于1％，之后执行下一步；(VII) If the relative error is greater than or equal to 1%, return to step (I), use the dichotomy method to reset the initial static temperature T 1,g at the impeller inlet under actual conditions, and repeat steps (I) to (VI) until The relative error between the absolute Mach number M c1 of the impeller inlet and the initial static temperature T 1,g of the impeller inlet under the actual situation calculated by the step (V) is less than 1%, and then the next step is performed. ; (Ⅷ)如果相对误差小于1％则判定为迭代收敛，则将实际情况下的叶轮进口初始静温T1,g作为实际情况下的叶轮进口静温T1；将实际情况下的叶轮进口初始静温T1,g对应的叶轮进口当地声速a1,g作为实际情况下的叶轮进口当地声速a1，将实际情况下的叶轮进口初始静温T1,g对应的叶轮进口静焓h1,g作为实际情况下的叶轮进口静焓h1，将实际情况下的叶轮进口初始静温T1,g对应的叶轮进口绝对速度c1,g作为实际情况下的叶轮进口绝对速度c1，进行下一步计算；(Ⅷ) If the relative error is less than 1%, it is determined as iterative convergence, and the initial static temperature T 1,g of the impeller inlet under the actual situation is taken as the impeller inlet static temperature T 1 under the actual situation; The local sound velocity a 1,g at the impeller inlet corresponding to the static temperature T 1,g is taken as the local sound velocity a 1 at the impeller inlet under the actual situation, and the impeller inlet static enthalpy h 1 corresponding to the initial static temperature T 1,g of the impeller inlet under the actual situation ,g is taken as the impeller inlet static enthalpy h 1 under the actual situation, and the impeller inlet absolute velocity c 1 ,g corresponding to the impeller inlet initial static temperature T 1,g under the actual situation is taken as the impeller inlet absolute velocity c 1 under the actual situation, Carry out the next calculation; (Ⅸ)根据实际情况下的叶轮进口静温T1及叶轮进口静熵S1利用热力与输运特性数据库REFPROP得到实际情况下的叶轮进口静压p1及实际情况下的叶轮进口密度ρ1；(Ⅸ) According to the impeller inlet static temperature T 1 and the impeller inlet static entropy S 1 under the actual situation, use the thermal and transport characteristic database REFPROP to obtain the impeller inlet static pressure p 1 and the impeller inlet density ρ 1 under the actual situation ; (5)计算平均等熵指数
Figure FDA0002737581370000031
计算公式为：(5) Calculate the average isentropic index
Figure FDA0002737581370000031
The calculation formula is:
Figure FDA0002737581370000032
Figure FDA0002737581370000032
 其中：γt1为总参数对应的比热比，γ1为静参数对应的比热比，κT,t1为总参数对应的等温压缩系数，κT,1为静参数对应的等温压缩系数；Among them: γ t1 is the specific heat ratio corresponding to the total parameters, γ 1 is the specific heat ratio corresponding to the static parameters, κ T,t1 is the isothermal compressibility corresponding to the total parameters, κ T,1 is the isothermal compressibility corresponding to the static parameters; (6)计算最佳叶轮进口轮盖相对轴向气流角β1s，计算公式为：(6) Calculate the relative axial airflow angle β 1s of the optimal impeller inlet cover, and the calculation formula is:
Figure FDA0002737581370000033
Figure FDA0002737581370000033
 (7)计算叶轮进口轮盖相对马赫数Mw1，计算公式为：(7) Calculate the relative Mach number M w1 of the impeller inlet cover, and the calculation formula is:
Figure FDA0002737581370000034
Figure FDA0002737581370000034
 (8)计算叶轮进口形状系数k，计算公式为：(8) Calculate the shape coefficient k of the impeller inlet, and the calculation formula is:
Figure FDA0002737581370000035
Figure FDA0002737581370000035
 2.根据权利要求1所述的超临界二氧化碳离心压缩机的叶轮进口设计方法，其特征在于，步骤(3)计算最大膨胀马赫数
Figure FDA0002737581370000036
包括下述步骤：2. the impeller inlet design method of supercritical carbon dioxide centrifugal compressor according to claim 1, is characterized in that, step (3) calculates maximum expansion Mach number
Figure FDA0002737581370000036
Include the following steps: Ⅰ)设定最大膨胀情况下的叶轮进口初始静温T′1,g；Ⅰ) Set the initial static temperature T′ 1,g of the impeller inlet under the condition of maximum expansion; Ⅱ)根据最大膨胀情况下的叶轮进口初始静温T′1,g及蒸汽分数Q利用热力与输运特性数据库REFPROP得到对应的熵S′1,g；Ⅱ) Obtain the corresponding entropy S′ 1,g according to the initial static temperature T′ 1,g and the steam fraction Q of the impeller inlet under the condition of maximum expansion by using the thermal and transport characteristic database REFPROP; Ⅲ)判断叶轮进口静熵S1与步骤Ⅱ)计算得到的最大膨胀情况下的叶轮进口初始静温T′1,g对应的熵S′1,g的相对误差是否小于1％；Ⅲ) Determine whether the relative error of the impeller inlet static entropy S 1 and the entropy S' 1 ,g corresponding to the initial static temperature T' 1,g of the impeller inlet under the condition of the maximum expansion calculated in step II) is less than 1%; Ⅳ)如果相对误差大于或等于1％，返回步骤Ⅰ)，采用二分法重新设定最大膨胀情况下的叶轮进口初始静温T′1,g，重复步骤Ⅰ)至步骤Ⅲ)，直至相对误差小于1％，进行下一步；IV) If the relative error is greater than or equal to 1%, go back to step I), use the dichotomy method to reset the initial static temperature T′ 1,g at the impeller inlet under the condition of maximum expansion, and repeat steps I) to step III) until the relative error less than 1%, proceed to the next step; Ⅴ)如果相对误差小于1％则判定为迭代收敛，则将最大膨胀情况下的叶轮进口初始静温T′1,g作为最大膨胀情况下的叶轮进口静温T1′，进行下一步计算；Ⅴ) If the relative error is less than 1%, it is determined as iterative convergence, and the initial static temperature T′ 1,g of the impeller inlet under the maximum expansion condition is taken as the impeller inlet static temperature T 1 ′ under the maximum expansion condition, and the next step is calculated; VI)根据最大膨胀情况下的叶轮进口静温T1′及蒸汽分数Q利用热力与输运特性数据库REFPROP得到最大膨胀情况下的叶轮进口静焓h′1及叶轮进口当地声速a′1；VI) According to the impeller inlet static temperature T 1 ′ and steam fraction Q under the condition of maximum expansion, use the thermal and transport characteristic database REFPROP to obtain the impeller inlet static enthalpy h′ 1 and the local sound velocity a′ 1 of the impeller inlet under the maximum expansion condition; VII)计算最大膨胀情况下的叶轮进口绝对速度c′1，计算公式为：
Figure FDA0002737581370000041
VII) Calculate the absolute velocity c′ 1 of the impeller inlet under the condition of maximum expansion, the calculation formula is:
Figure FDA0002737581370000041
 VIII)计算最大膨胀马赫数
Figure FDA0002737581370000042
计算公式为：
Figure FDA0002737581370000043
VIII) Calculate the maximum expansion Mach number
Figure FDA0002737581370000042
The calculation formula is:
Figure FDA0002737581370000043
 3.根据权利要求1所述的超临界二氧化碳离心压缩机的叶轮进口设计方法，其特征在于，步骤(3)计算可接受膨胀马赫数
Figure FDA0002737581370000044
的计算公式为：
Figure FDA0002737581370000045
其中：λ为可接受加速裕度经验系数，
Figure FDA0002737581370000046
为最大膨胀马赫数；步骤(3)计算叶轮进口绝对马赫数Mc1，计算公式为：
Figure FDA0002737581370000047
其中：σ为安全系数，
Figure FDA0002737581370000048
为可接受膨胀马赫数。3. the impeller inlet design method of supercritical carbon dioxide centrifugal compressor according to claim 1, is characterized in that, step (3) calculates acceptable expansion Mach number
Figure FDA0002737581370000044
The calculation formula is:
Figure FDA0002737581370000045
Where: λ is the empirical coefficient of acceptable acceleration margin,
Figure FDA0002737581370000046
is the maximum expansion Mach number; step (3) calculates the absolute Mach number M c1 at the impeller inlet, and the calculation formula is:
Figure FDA0002737581370000047
Where: σ is the safety factor,
Figure FDA0002737581370000048
is the acceptable expansion Mach number. 4.根据权利要求3所述的超临界二氧化碳离心压缩机的叶轮进口设计方法，其特征在于，所述安全系数σ＝0.92。4 . The impeller inlet design method of a supercritical carbon dioxide centrifugal compressor according to claim 3 , wherein the safety factor σ=0.92. 5 . 5.根据权利要求1所述的超临界二氧化碳离心压缩机的叶轮进口设计方法，其特征在于，步骤(5)计算平均等熵指数
Figure FDA0002737581370000049
的计算公式中，所述总参数对应的比热比γt1根据叶轮进口总温Tt1及叶轮进口总压pt1利用热力与输运特性数据库REFPROP得到。5. the impeller inlet design method of supercritical carbon dioxide centrifugal compressor according to claim 1, is characterized in that, step (5) calculates average isentropic index
Figure FDA0002737581370000049
In the calculation formula of , the specific heat ratio γ t1 corresponding to the total parameters is obtained according to the total impeller inlet temperature T t1 and the impeller inlet total pressure p t1 using the thermal and transport characteristics database REFPROP. 6.根据权利要求1所述的超临界二氧化碳离心压缩机的叶轮进口设计方法，其特征在于，步骤(5)计算平均等熵指数
Figure FDA00027375813700000410
的计算公式中，所述静参数对应的比热比γ1根据实际情况下的叶轮进口静温T1及实际情况下的叶轮进口静压p1利用热力与输运特性数据库REFPROP得到。6. the impeller inlet design method of supercritical carbon dioxide centrifugal compressor according to claim 1, is characterized in that, step (5) calculates average isentropic index
Figure FDA00027375813700000410
In the calculation formula of , the specific heat ratio γ 1 corresponding to the static parameter is obtained according to the impeller inlet static temperature T 1 under the actual situation and the impeller inlet static pressure p 1 under the actual situation using the thermal and transport characteristics database REFPROP. 7.根据权利要求1所述的超临界二氧化碳离心压缩机的叶轮进口设计方法，其特征在于，步骤(5)计算平均等熵指数
Figure FDA0002737581370000051
的计算公式中，所述总参数对应的等温压缩系数κT,t1根据给定的叶轮进口总温Tt1及叶轮进口总压pt1，利用热力与输运特性数据库REFPROP得到。7. the impeller inlet design method of supercritical carbon dioxide centrifugal compressor according to claim 1, is characterized in that, step (5) calculates average isentropic index
Figure FDA0002737581370000051
In the calculation formula of , the isothermal compression coefficient κ T,t1 corresponding to the total parameters is obtained according to the given impeller inlet total temperature T t1 and impeller inlet total pressure p t1 using the thermal and transport characteristics database REFPROP. 8.根据权利要求1所述的超临界二氧化碳离心压缩机的叶轮进口设计方法，其特征在于，步骤(5)计算平均等熵指数
Figure FDA0002737581370000052
的计算公式中，所述静参数对应的等温压缩系数κT,1根据实际情况下的叶轮进口静温T1及实际情况下的叶轮进口静压p1利用热力与输运特性数据库REFPROP得到。8. the impeller inlet design method of supercritical carbon dioxide centrifugal compressor according to claim 1, is characterized in that, step (5) calculates average isentropic index
Figure FDA0002737581370000052
In the calculation formula of , the isothermal compression coefficient κ T,1 corresponding to the static parameter is obtained according to the impeller inlet static temperature T 1 under the actual situation and the impeller inlet static pressure p 1 under the actual situation using the thermal and transport characteristics database REFPROP.
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