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
inlet
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mach number
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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. A design method for an impeller inlet of a supercritical carbon dioxide centrifugal compressor is characterized by comprising 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 an impellerInlet total pressure pt1Obtaining 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) 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 FDA0002737581370000011
According to the obtained maximum expansion Mach number
Figure FDA0002737581370000012
Determining acceptable expansion Mach number
Figure FDA0002737581370000013
According to the obtained acceptable expansion Mach number
Figure FDA0002737581370000014
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 FDA0002737581370000021
(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 Will be in actual conditionInitial static temperature T of impeller inlet1,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 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 FDA0002737581370000031
The calculation formula is as follows:
Figure FDA0002737581370000032
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 FDA0002737581370000033
(7) calculating relative Mach number M of impeller inlet wheel coverw1The calculation formula is as follows:
Figure FDA0002737581370000034
(8) calculating the shape coefficient k of the impeller inlet, wherein the calculation formula is as follows:
Figure FDA0002737581370000035
2. the method of claim 1, wherein the step (3) of calculating the maximum expansion Mach number
Figure FDA0002737581370000036
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 expansion1', performing the next calculation;
VI) impeller inlet static temperature T in accordance with the maximum expansion1' and the steam fraction Q obtains the impeller under the condition of maximum expansion by utilizing a thermal and transport characteristic database REFPROPStatic enthalpy of entry h'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 FDA0002737581370000041
VIII) calculation of the maximum expansion Mach number
Figure FDA0002737581370000042
The calculation formula is as follows:
Figure FDA0002737581370000043
3. the method of claim 1, wherein the step (3) of calculating the acceptable expansion Mach number
Figure FDA0002737581370000044
The calculation formula of (2) is as follows:
Figure FDA0002737581370000045
wherein: λ is an acceptable acceleration margin empirical coefficient,
Figure FDA0002737581370000046
is the maximum expansion mach number; step (3) calculating the absolute Mach number M of the impeller inletc1The calculation formula is as follows:
Figure FDA0002737581370000047
wherein: sigma is a safety factor which is set as the standard,
Figure FDA0002737581370000048
at an acceptable expansion mach number.
4. The method of designing an impeller inlet of a supercritical carbon dioxide centrifugal compressor according to claim 3, wherein the safety factor σ is 0.92.
5. The method of designing an impeller eye of a supercritical carbon dioxide centrifugal compressor as claimed in claim 1, wherein step (5) calculates an average isentropic index
Figure FDA0002737581370000049
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.
6. The method of designing an impeller eye of a supercritical carbon dioxide centrifugal compressor as claimed in claim 1, wherein step (5) calculates an average isentropic index
Figure FDA00027375813700000410
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 characteristics database REFPROP.
7. The method of designing an impeller eye of a supercritical carbon dioxide centrifugal compressor as claimed in claim 1, wherein step (5) calculates an average isentropic index
Figure FDA0002737581370000051
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.
8. The method for designing an impeller inlet of a supercritical carbon dioxide centrifugal compressor according to claim 1, wherein the method is characterized in thatCharacterized in that the average isentropic index is calculated in the step (5)
Figure FDA0002737581370000052
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.
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