CN111062124B - Similar modeling method for supercritical carbon dioxide compressor test - Google Patents
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- CURLTUGMZLYLDI-UHFFFAOYSA-N Carbon dioxide Chemical compound O=C=O CURLTUGMZLYLDI-UHFFFAOYSA-N 0.000 title claims abstract description 190
- 229910002092 carbon dioxide Inorganic materials 0.000 title claims abstract description 95
- 239000001569 carbon dioxide Substances 0.000 title claims abstract description 95
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Abstract
The invention relates to a similar modeling method for a supercritical carbon dioxide compressor test. Then, according to the flow similarity criterion among different working media, the main criterion numbers are ensured to be consistent, the operating parameters of the air working medium compressor such as the rotating speed, the inlet pressure, the inlet temperature and the flow are obtained, experimental research is carried out, and experimental data are obtained. And secondly, deducing performance parameters such as the pressure ratio, the isentropic efficiency, the stress load, the leakage flow and the like of the supercritical carbon dioxide compressor according to a performance conversion criterion. And finally, changing the operation condition, evaluating the comprehensive performance of the supercritical carbon dioxide compressor under different operation conditions, and verifying the variable condition performance of the supercritical carbon dioxide compressor. By adopting the modeling method, the complexity of the supercritical carbon dioxide compressor test system and the test stand building difficulty can be obviously reduced, the test cost is saved, and the product research and development period of the supercritical carbon dioxide compressor is shortened.
Description
Technical Field
The invention belongs to the field of impeller machinery, and particularly relates to a similar modeling method for a supercritical carbon dioxide compressor test.
Background
The supercritical carbon dioxide is used as the power cycle working medium, so that the advantages of high density, low viscosity and low surface tension of the supercritical carbon dioxide can be fully utilized, the size of a power cycle system is obviously reduced, and the cycle efficiency is improved. Supercritical carbon dioxide (SCO)2) The application of the brayton cycle in the aspects of new generation nuclear power, coal power, waste heat utilization and renewable energy utilization draws more and more attention. The compressor is one of the core components of the power cycle, the function of the compressor is to compress the low-pressure supercritical carbon dioxide working medium to a high-pressure state required by the heating of a heat source, and the power consumption and the efficiency of the compressor have great significance to the efficiency of the whole thermodynamic cycleThe influence of (c).
Although numerical simulation has been widely used in the design research of compressors, experimental research is still an indispensable loop in the design of compressors to the final production process in order to ensure the accuracy of the numerical simulation results. However, for the supercritical carbon dioxide compressor, many inconvenient factors exist in the experimental research process, such as the preparation and storage problems of working media in a supercritical state, the safety problems brought to the motor and the main shaft by high rotating speed, the problem of two-phase flow condensation caused by the approach of the inlet parameters of the compressor to the critical point, and the like. In addition, the development of experimental research under actual operation conditions greatly increases the test difficulty and the research and development period, and is not favorable for the rapid iterative update of products. In this context, similar modeling experiments are becoming increasingly favored by designers. Similarity means that for the same physical process, if the magnitudes of the physical quantities at the corresponding points and the corresponding moments are proportional and the corresponding directions of the vectors are consistent, the two physical phenomena are said to be similar, and the solutions of the problems also have similarity. According to the similar modeling method, the modeling test can be developed under the condition that the design working condition is difficult to meet, the design working condition parameters are reduced through flow similarity, and the performance research of the fluid machinery can be carried out by replacing an actual working medium with a simple working medium, so that the similar modeling test can greatly simplify a test system, improve the test capability and avoid some running conditions which are difficult to reach. For similar modeling tests of different working media, safe, easily available and cheap air is generally adopted to replace the working media. However, for the supercritical carbon dioxide working medium, the physical parameters of the supercritical carbon dioxide working medium are obviously different from that of air, how to organize the modeling test of the supercritical carbon dioxide compressor using the air working medium is a real and complex problem, and no similar modeling method which is systematically and directly used for guiding the test design of the supercritical carbon dioxide compressor exists in the currently disclosed data.
Disclosure of Invention
The invention aims to provide a similar modeling method for a supercritical carbon dioxide compressor test aiming at the complexity of the development of the supercritical carbon dioxide compressor test. According to the similarity principle, the strength and the pneumatic comprehensive performance of the supercritical carbon dioxide compressor are researched by using air as a substitute working medium, the complexity of a test system and the building difficulty of a test bed are obviously reduced, a similar modeling test flow of the supercritical carbon dioxide compressor is provided, the similar modeling test of the supercritical carbon dioxide compressor can be directly guided, and the test result is applied to the optimization design of the actual compressor blade.
The invention is realized by adopting the following technical scheme:
a similar modeling method for supercritical carbon dioxide compressor test comprises the following steps:
1) geometric similarity modeling
Obtaining structural parameters of a modeled compressor impeller through geometric similarity modeling according to an original supercritical carbon dioxide compressor model;
2) flow similarity modeling
Obtaining the flow parameters of an air working medium test through flow similarity modeling by utilizing the principle of flow similarity between a supercritical carbon dioxide working medium and an air working medium according to the compressor structure parameters and the supercritical carbon dioxide working medium flow parameters determined by geometric similarity modeling;
3) compressor performance conversion
Carrying out test research on the flow parameters of the air working medium determined according to the flow similarity modeling to obtain air working medium test data, and obtaining the performance parameters of the supercritical carbon dioxide compressor through the performance conversion process of the compressor;
4) evaluation of comprehensive Properties
And changing the modeling operation condition, evaluating the comprehensive performance of the compressor under different working conditions, and checking the strength and the pneumatic characteristic of the supercritical carbon dioxide compressor.
The invention is further improved in that, in the step 1), the test compressor and the design compressor have proportional geometric relationship in the geometric similarity modeling process; specifically, the section profile and the number of blades of the air compressor and the supercritical carbon dioxide compressor used in the test are kept consistent, and the chord length of the blades, the height of the blades, the thickness of the blades, the diameter of a wheel disc, the pitch of a blade cascade and the clearance of a blade top are all enlarged or reduced in equal proportion, and the following relation is specifically met:
na＝n0
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, m is a geometric similarity ratio, and D is a compressor geometric parameter.
The further improvement of the invention is that in the step 2), the average adiabatic index from the compression start point to the compression end point is adopted as the substitute of the adiabatic index for the drastic change of the supercritical carbon dioxide adiabatic index near the critical point in the flow similarity modeling process, and the definition formula is as follows:
wherein,
is the supercritical carbon dioxide average adiabatic index, P1Is the impeller inlet pressure, P2And k is the impeller exit pressure, and k is the adiabatic index.
The invention is further improved in that in the process of flow similarity modeling, the tangential Mach number, the Reynolds number, the product of the flow coefficient and the inlet Mach number are selected as similarity criteria, and the mass flow, the total inlet temperature, the total inlet pressure, the wheel disc diameter and the average adiabatic index are ensured to satisfy the following relations:
wherein μ is the dynamic viscosity, R is the gas constant, T1 *Is the total inlet temperature, P, of the compressor1 *Is the total pressure at the inlet of the compressor, N is the rotating speed, d is the diameter of the wheel disc,
k is the adiabatic index for mass flow.
The further improvement of the invention is that in the process of flow similarity modeling, the inlet and outlet speed triangles of the model test compressor are similar to the actual working conditions, namely:
α1,a＝α1,0,β1,a＝β1,0
α2,a＝α2,0,β2,a＝β2,0
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, α1Is the absolute speed angle, beta, of the stationary blade outlet1Is the relative velocity angle, alpha, of the stationary blade outlet2Is the absolute speed angle, beta, of the outlet of the movable blade2Is the absolute speed angle of the outlet of the movable blade.
The further improvement of the invention is that in the step 3), in the process of converting the performance of the compressor, performance parameters such as the pressure ratio, the isentropic efficiency, the stress load, the leakage flow and the like of the supercritical carbon dioxide compressor are obtained through a performance conversion criterion; the pressure ratio and the isentropic efficiency relation are as follows:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, pi*Is the total pressure ratio, k*Is the average adiabatic index of supercritical carbon dioxide, eta is the isentropic efficiency, k is the adiabatic index, Ma1The inlet Mach number;
the conversion relation among the axial stress of the fluid, the circumferential stress of the fluid and the centrifugal stress is as follows:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, σzFor distribution of axial stress on the impeller surface, σθFor circumferential stress distribution, σ, of the impeller surfacerDistribution of centrifugal stress to the impeller, ρfFor fluid density, U is the fluid characteristic velocity, ρsThe density of the impeller solid, N is the rotating speed, and m is the geometric similarity ratio;
the actual leakage flow conversion relation is as follows:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, mlFor leakage flow, ρfFor fluid density, U is the fluid characteristic velocity and m is the geometric similarity ratio.
The further improvement of the invention is that in the step 4), the operation condition of the compressor is changed in the process of evaluating the comprehensive performance, the strength and the pneumatic performance parameters of the supercritical carbon dioxide compressor in the variable condition state are obtained through the similar modeling test, and the strength characteristic of the compressor is checked, so that the maximum equivalent stress of the compressor meets sigmam＜σcWhere σ ismMaximum equivalent stress, σ, of the compressor impellercEvaluating the pressure for maximum stress allowed for the materialLeakage flow m of compressorlIsentropic efficiency eta, satisfying ml＜mcl，η＞ηcWherein m isclTo design to allow maximum leakage flow, ηcTo design efficiency values.
The invention has at least the following beneficial technical effects:
in the design and development process of the supercritical carbon dioxide compressor, experimental research is an essential loop in the process from the design of the compressor to the final production. However, many inconvenient factors, such as too high a rotation speed of the compressor, difficult to reach working conditions, too small a size of the impeller, etc., limit the development of prototype tests. The similar modeling method for the supercritical carbon dioxide compressor test can be used for guiding similar modeling design of the supercritical carbon dioxide compressor test, carrying out test research by using the air working medium and the model compressor, obtaining performance parameters of the designed supercritical carbon dioxide compressor through performance conversion, and analyzing the variable working condition characteristics of the compressor. The invention can obviously reduce the complexity of the test system and the difficulty of building the test bed, and save the test cost.
Furthermore, the air is used as the substitute working medium, so that the operating condition parameters of the compressor are reduced, the safety of the test system is improved, the test system is simplified, and the test cost is reduced.
Furthermore, the average adiabatic index from the compression starting point to the compression end point is adopted to replace the adiabatic index of the supercritical carbon dioxide, so that the precision of the similar modeling test is greatly improved.
In conclusion, the similar modeling method for the supercritical carbon dioxide compressor test provided by the invention can obtain the comprehensive performance of the supercritical carbon dioxide compressor under different working conditions by developing the air compressor test, thereby reducing the difficulty of test development, improving the operability of the test and shortening the test period.
Drawings
FIG. 1 is a system diagram of a similar modeling test method of a supercritical carbon dioxide compressor;
FIG. 2 is a diagram of a similar modeling method for a compressor; wherein fig. 2(a) is a supercritical carbon dioxide compressor model, and fig. 2(b) is a test compressor model;
FIG. 3 is a schematic view of a leakage flow;
FIG. 4 is a flow chart of the overall performance analysis of the supercritical carbon dioxide compressor.
Description of reference numerals:
the actual impeller 11, the model impeller 21, the impeller upper cover plate 22, the vaned diffuser 23 and the seal ring 24.
Detailed Description
The invention is further described below with reference to the following figures and examples.
Referring to fig. 1, fig. 1 is a flow chart of a supercritical carbon dioxide compressor test similarity modeling method, which includes four steps of geometric similarity modeling, flow similarity modeling, compressor performance conversion and comprehensive performance evaluation of a supercritical carbon dioxide-air compressor.
Specifically, the invention provides a similar modeling method for a supercritical carbon dioxide compressor test. Firstly, according to the geometric similarity criterion, the geometric parameters of the experimental model are obtained through geometric scaling. And then, according to the flow similarity criterion among different working media, ensuring the consistency of the main criterion numbers, obtaining the operating parameters of the air working medium compressor, such as the rotating speed, the inlet pressure, the inlet temperature, the flow and the like, developing experimental research and obtaining the experimental data of the air compressor. And secondly, deducing performance parameters such as the pressure ratio, the isentropic efficiency, the stress load, the leakage flow and the like of the supercritical carbon dioxide compressor according to a performance conversion criterion. And finally, evaluating the comprehensive performance of the supercritical carbon dioxide compressor under different operating conditions, verifying the variable-condition performance of the supercritical carbon dioxide compressor, and providing guidance for the design and optimization of the supercritical carbon dioxide compressor.
A similar modeling approach to the supercritical carbon dioxide compressor test is described below using a centrifugal compressor as an example:
referring to fig. 2, a test model geometric similarity modeling is first performed such that the test compressor has a proportional geometric relationship with the design compressor. Specifically, the section profile and the number of blades of the air compressor and the supercritical carbon dioxide compressor used in the test are kept consistent, and the chord length of the blades, the height of the blades, the thickness of the blades, the diameter of a wheel disc, the pitch of a blade cascade and the clearance of a blade top are all enlarged or reduced in equal proportion, and the following relation is specifically met:
na＝n0
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, m is a geometric similarity ratio, and D is a compressor geometric parameter.
After the structural parameters of the air compressor are obtained through the geometric similarity modeling, the flow similarity modeling of the supercritical carbon dioxide-air is carried out. To maximize cycle efficiency, the start of compression of a supercritical carbon dioxide compressor is often set near the critical point. Since the adiabatic index of supercritical carbon dioxide changes drastically around the critical point, in order to ensure the accuracy of the flow-like modeling result, the average adiabatic index from the start point to the end point of compression is used as a substitute for the adiabatic index, which is defined as follows:
wherein,
is the supercritical carbon dioxide average adiabatic index, P1Is the impeller inlet pressure, P2And k is the impeller exit pressure, and k is the adiabatic index.
And then selecting the product of the tangential Mach number, the Reynolds number, the flow coefficient and the inlet Mach number as a similarity criterion to ensure that the mass flow, the total inlet temperature, the total inlet pressure, the diameter of the wheel disc and the average adiabatic index satisfy the following relations:
wherein μ is the dynamic viscosity, R is the gas constant, T1 *Is the total inlet temperature, P, of the compressor1 *Is the total pressure at the inlet of the compressor, N is the rotating speed, d is the diameter of the wheel disc,
to mass flow rate, k*Is the supercritical carbon dioxide average adiabatic index. On the premise of meeting the similarity criterion of the formula, the inlet and outlet speed triangle of the model test impeller is similar to the actual working condition, namely:
α1,a＝α1,0,β1,a＝β1,0
α2,a＝α2,0,β2,a＝β2,0
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, α1Is the absolute speed angle, beta, of the stationary blade outlet1Is the relative velocity angle, alpha, of the stationary blade outlet2Is the absolute speed angle, beta, of the outlet of the movable blade2Is the absolute speed angle of the outlet of the movable blade.
According to the designed operating condition of the supercritical carbon dioxide compressor, the operating parameters such as the corresponding rotating speed, the inlet pressure, the inlet temperature, the flow and the like of the air compressor can be obtained through the flow similarity modeling process. And then, the pneumatic test research of the air compressor can be carried out, and the actual operation data of the air compressor can be obtained.
And then, according to the test data of the air compressor, performance parameters such as the pressure ratio, the isentropic efficiency, the stress load, the leakage flow and the like of the supercritical carbon dioxide compressor can be obtained through a performance conversion criterion. The pressure ratio and the isentropic efficiency relation are as follows:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, pi*Is the total pressure ratio, k*Is the average adiabatic index of supercritical carbon dioxide, eta is the isentropic efficiency, k is the adiabatic index, Ma1The inlet mach number.
For the supercritical carbon dioxide working medium, the high-density characteristic of the supercritical carbon dioxide working medium enables the compressor device to have a compact structure, and simultaneously brings a severe test to the strength requirement of the blade material, so that the investigation of the stress distribution of the supercritical carbon dioxide compressor has important value on the structural reliability and performance of the impeller. The impeller is mainly acted by axial force and circumferential force brought by fluid and centrifugal force caused by rotation in the working process, and corresponding stress is generated on the surface of the impeller under the action of the axial force and the circumferential force. According to the similarity principle, the stress conversion relation is as follows:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, σzFor distribution of axial stress on the impeller surface, σθFor circumferential stress distribution, σ, of the impeller surfacerIs the impeller receivesCentrifugal stress distribution, ρfFor fluid density, U is the fluid characteristic velocity, ρsThe density of the impeller solid, N is the rotation speed, and m is the geometric similarity ratio.
Referring to fig. 3, when the compressor impeller is in operation, part of the gas will leak from the gaps between the driven stator blades, and the leakage flow will cause the reduction of the actual circulation flow and bring adverse effects to the flow field structure. In the test, the air leakage amount at the position is obtained by arranging a flow sensor, and the actual leakage flow rate of the supercritical carbon dioxide compressor can be estimated according to the following conversion relation:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, mlFor leakage flow, ρfFor fluid density, U is the fluid characteristic velocity and m is the geometric similarity ratio.
Finally, referring to fig. 4, the comprehensive performance of the supercritical carbon dioxide compressor under different working conditions is evaluated. Changing the operation condition of the compressor, obtaining the strength and the pneumatic performance parameters of the supercritical carbon dioxide compressor under the variable condition state through the similar modeling test, and checking the strength characteristic of the compressor to ensure that the maximum equivalent stress of the compressor meets sigmam＜σcWhere σ ismMaximum equivalent stress, σ, of the compressor impellercEvaluating compressor leakage flow m for maximum stress allowed by the materiallIsentropic efficiency eta, satisfying ml＜mcl，η＞ηcWherein m isclTo design to allow maximum leakage flow, ηcTo design efficiency values. And quantifying the mutual relation among the structural parameters, the operation working conditions and the comprehensive performance of the supercritical carbon dioxide compressor, and summarizing the design conditions of the supercritical carbon dioxide compressor to provide basic data for the optimal design of the supercritical carbon dioxide compressor.
Claims (1)
1. A similar modeling method for a supercritical carbon dioxide compressor test is characterized by comprising the following steps:
1) geometric similarity modeling
Obtaining structural parameters of a modeled compressor impeller through geometric similarity modeling according to an original supercritical carbon dioxide compressor model; in the geometric similarity modeling process, the test compressor and the design compressor have a proportional geometric relationship; specifically, the section profile and the number of blades of the air compressor and the supercritical carbon dioxide compressor used in the test are kept consistent, and the chord length of the blades, the height of the blades, the thickness of the blades, the diameter of a wheel disc, the pitch of a blade cascade and the clearance of a blade top are all enlarged or reduced in equal proportion, and the following relation is specifically met:
na＝n0
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, m is a geometric similarity ratio, and D is a compressor geometric parameter;
2) flow similarity modeling
Obtaining the flow parameters of an air working medium test through flow similarity modeling by utilizing the principle of flow similarity between a supercritical carbon dioxide working medium and an air working medium according to the compressor structure parameters and the supercritical carbon dioxide working medium flow parameters determined by geometric similarity modeling; in the flow similarity modeling process, for the drastic change of the supercritical carbon dioxide adiabatic index near the critical point, the average adiabatic index from the compression starting point to the compression end point is used as a substitute for the adiabatic index, and the definition formula is as follows:
wherein,
is the average absolute value of supercritical carbon dioxideThermal index, P1Is the impeller inlet pressure, P2Is the impeller outlet pressure, and k is the adiabatic index;
in the flow similar modeling process, the product of tangential Mach number, Reynolds number, flow coefficient and inlet Mach number is selected as a similarity criterion, and the following relations of mass flow, total inlet temperature, total inlet pressure, wheel disc diameter and average adiabatic index are ensured:
wherein μ is dynamic viscosity, R is gas constant, T1 *Is the total inlet temperature, P, of the compressor1 *Is the total pressure at the inlet of the compressor, N is the rotating speed, d is the diameter of the wheel disc,
mass flow, k is the adiabatic index;
in the process of flow similarity modeling, the inlet and outlet speed triangle of the model test compressor keeps similar to the actual working condition, namely:
α1,a＝α1,0,β1,a＝β1,0
α2,a＝α2,0,β2,a＝β2,0
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, α1Is the absolute speed angle, beta, of the stationary blade outlet1Is the relative velocity angle, alpha, of the stationary blade outlet2Is the absolute speed angle, beta, of the outlet of the movable blade2To moveAn absolute speed angle of the leaf outlet;
3) compressor performance conversion
Carrying out test research on the flow parameters of the air working medium determined according to the flow similarity modeling to obtain air working medium test data, and obtaining the performance parameters of the supercritical carbon dioxide compressor through the performance conversion process of the compressor; in the process of converting the performance of the compressor, performance parameters such as the pressure ratio, the isentropic efficiency, the stress load, the leakage flow and the like of the supercritical carbon dioxide compressor are obtained according to performance conversion criteria; the pressure ratio and the isentropic efficiency relation are as follows:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, pi*The ratio of the total pressure is used as the ratio,
is the average adiabatic index of supercritical carbon dioxide, eta is the isentropic efficiency, k is the adiabatic index, Ma1The inlet Mach number;
the conversion relation among the fluid axial stress, the fluid circumferential stress and the centrifugal stress is as follows:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, σzFor distribution of axial stress on the impeller surface, σθFor circumferential stress distribution, σ, of the impeller surfacerDistribution of centrifugal stress to the impeller, ρfFor fluid density, U is the fluid characteristic velocity, ρsThe density of the impeller solid, N is the rotating speed, and m is the geometric similarity ratio;
the actual leakage flow conversion relation is as follows:
wherein subscript a represents an air compressor parameter, subscript 0 represents a supercritical carbon dioxide compressor parameter, mlFor leakage flow, ρfIs the fluid density, U is the fluid characteristic velocity, and m is the geometric similarity ratio;
4) evaluation of comprehensive Properties
Changing the modeling operation condition, evaluating the comprehensive performance of the compressor under different working conditions, and checking the strength and the pneumatic characteristic of the supercritical carbon dioxide compressor;
in the comprehensive performance evaluation process, the operation condition of the compressor is changed, the strength and the pneumatic performance parameters of the supercritical carbon dioxide compressor in the variable condition state are obtained through the similar modeling test, and the strength characteristic of the compressor is checked, so that the maximum equivalent stress of the compressor meets sigmam＜σcWhere σ ismMaximum equivalent stress, σ, of the compressor impellercEvaluating compressor leakage flow m for maximum stress allowed by the materiallIsentropic efficiency eta, satisfying ml＜mcl，η＞ηcWherein m isclTo design to allow maximum leakage flow, ηcTo design efficiency values.
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