CN111859563A - Similar modeling method for supercritical carbon dioxide turbine test - Google Patents
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Abstract
The invention discloses a similar modeling method for a supercritical carbon dioxide turbine test, which comprises the following steps: firstly, scaling the supercritical carbon dioxide turbine at the same ratio according to a geometric similarity criterion to obtain geometric parameters of an air turbine model. Then, the similarity principle of flow is utilized to ensure that the main criterion number and the speed triangle are similar, the actual working condition of the supercritical carbon dioxide working medium is used as an input variable of the similarity criterion, the operation working condition parameters of the air working medium turbine such as the pressure ratio, the rotating speed and the inlet temperature are calculated, experimental research is carried out, and the air turbine test data and the performance parameters are obtained. And secondly, deducing performance parameters such as a non-dimensional speed field, turbine efficiency, stress load, leakage amount and the like of the supercritical carbon dioxide turbine according to a performance conversion criterion. And finally, evaluating the comprehensive performance of the supercritical carbon dioxide turbine under different boundary conditions, verifying the feasibility of stable and efficient operation of the supercritical carbon dioxide turbine, and providing guidance for the design and optimization of the supercritical carbon dioxide turbine.
Description
Technical Field
The invention belongs to the technical field of supercritical carbon dioxide turbines, and particularly relates to a similar modeling method for a supercritical carbon dioxide turbine test.
Background
Supercritical carbon dioxide (SCO)2) Brayton cycle with SCO2The novel power cycle of the cycle working medium has the characteristics of high efficiency, small volume, light weight, low noise and the like, and has great comprehensive advantages in the application of occasions with narrow space and low heat source temperature. The method is one of important directions for replacing the traditional boiler heating steam power generation technology and realizing the development of more efficient energy utilization and low cost. The supercritical carbon dioxide Brayton cycle power system mainly comprises a heat source, a compressor, a turbine, a heat regenerator, a precooler, a pipe valve system, a control system and auxiliary systems (gas supply, cooling, security and the like). The turbine has the function of converting internal energy of the high-temperature and high-pressure supercritical carbon dioxide working medium into mechanical energy required by rotation of a main shaft of the generator, and is a thermal-power conversion core component. The design and manufacturing level and performance of the turbine have a significant impact on the efficiency of the overall thermodynamic cycle.
Compared with numerical simulation, the development of experimental research is more accurate in the aspects of obtaining the key operating parameters of the turbine, evaluating the performance of the turbine and the like, and is an essential loop in the process of designing and putting into production of the turbine. However, for the supercritical carbon dioxide turbine, many inconvenient factors, such as safety problems brought by high rotating speed to the motor and the main shaft, requirements of high density of working media to material strength, safety problems caused by high pressure or leakage, and the like, limit development of turbine tests. In addition, the test of the real operation environment of the turbine consumes a great deal of time and resources, greatly increases the research and development period, and is not beneficial to the quick iterative update of products. Under the background, similar modeling tests are gradually favored by designers, and the modeling tests are carried out by a modeling method, so that a test system can be effectively simplified, the test capability is improved, some running conditions which are difficult to achieve are avoided, and the performance characteristics of special working media can be obtained by converting the test results of simple working media. 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 those of air, and how to organize the supercritical carbon dioxide turbine modeling test using the air working medium is a real and complex problem. The invention provides a similar modeling method for a supercritical carbon dioxide turbine test, which can be used for obtaining performance parameters of the supercritical carbon dioxide turbine by developing an air turbine test according to a similar modeling principle, directly guiding the design of the similar modeling test of the supercritical carbon dioxide turbine, reducing the test difficulty and shortening the research and development period of the supercritical carbon dioxide turbine.
Disclosure of Invention
The invention aims to provide a similar modeling method for a supercritical carbon dioxide turbine test aiming at the complexity of development of the supercritical carbon dioxide turbine test. According to the similarity principle, the strength and the pneumatic comprehensive performance of the supercritical carbon dioxide turbine are researched by taking air as a substitute working medium, the similar modeling test process of the supercritical carbon dioxide turbine is provided, the similar modeling test of the supercritical carbon dioxide turbine can be directly guided, and the test result is applied to the optimal design of the actual turbine blade.
The invention is realized by adopting the following technical scheme:
a method of modeling a supercritical carbon dioxide turbine test similarly, comprising:
1) scaling the supercritical carbon dioxide turbine in the same ratio according to a geometric similarity criterion to obtain geometric parameters of an air turbine model, and determining a geometric similarity ratio;
2) the method comprises the steps of utilizing a flowing similarity principle to ensure that main criteria are similar in number and speed triangles, taking actual working conditions and geometric similarity ratios of supercritical carbon dioxide working media as input variables of the similarity criteria, calculating pressure ratios, rotating speeds and inlet temperature operation working condition parameters of the air working media turbine, and then carrying out test research to obtain air turbine test data and performance parameters;
3) Taking air turbine test data and performance parameters as input variables, and deriving performance parameters of a dimensionless speed field, turbine efficiency, stress load and leakage amount of the supercritical carbon dioxide turbine according to a performance conversion criterion;
4) and evaluating the comprehensive performance of the supercritical carbon dioxide turbine under different boundary conditions, verifying the feasibility of stable and efficient operation of the supercritical carbon dioxide turbine, and providing guidance for the design and optimization of the supercritical carbon dioxide turbine.
The further improvement of the invention is that the specific implementation method of the step 1) is as follows:
firstly, modeling the geometric similarity of a test to ensure that the test turbine and a designed turbine have a proportional geometric relationship, wherein the air turbine and the supercritical carbon dioxide turbine used in the test have the same section profile and the same blade number, and the blade chord length, the blade height, the blade thickness, the wheel disc diameter, the blade cascade pitch and the blade top clearance parameters are amplified or reduced in equal proportion, and the geometric similarity specifically satisfies the following relational expression:
na＝n0
wherein subscript a represents air turbine parameters, subscript 0 represents supercritical carbon dioxide turbine parameters, g is a geometric similarity ratio, l is blade height, d is wheel disc diameter, b is blade thickness, t is blade grid pitch, s is blade chord length, and n is blade number.
The further improvement of the invention is that the specific implementation method of the step 2) is as follows:
adopting approximate modeling, and selecting a similarity criterion which dominates the flow influence as a similarity standard; selecting a flow coefficient, a Reynolds number, a speed ratio and a compression coefficient as similarity criteria, and ensuring the following dimensionless criterion numbers to be equal:
wherein ,
for mass flow, pinIs turbine inlet density, N is rotational speed, d is wheel disc diameter, U is impeller circumferential speed, mu is dynamic viscosity, Delta hkFor a variable enthalpy drop, VinIs the inlet volume flow, VoutIs the outlet volume flow;
simultaneously, the inlet and outlet airflow angle of the model test turbine is ensured to be consistent with the actual value, and the requirement of similarity of speed triangles is met, namely:
α1,a＝α1,0,β1,a＝β1,0
α2,a＝α2,0,β2,a＝β2,0
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine 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;
taking the actual working condition of the supercritical carbon dioxide working medium and the geometric similarity ratio g obtained in the step 1) as input variables of the similarity criterion, and then determining the pressure ratio, the rotating speed, the inlet temperature and the flow operation working condition parameters of the air working medium according to the following steps;
Firstly, the inlet pressure P of the air turbine is determinedin,aAnd estimating an inlet temperature T'in,aObtaining the air turbine outlet pressure P byout,a：
ρin,a,sin,a＝REF(T′in,a,Pin,a)
Pout,a＝REF(sin,a,ρout,a)
Wherein REF (. circle.) represents a REFPROP physical property table obtained by reference to predetermined parameters, and subscript a represents an air turbine parameter, T'inTo estimate the inlet temperature, pinIs inlet density, ρoutIs the exit density;
then, the actual inlet temperature T of the air turbine is estimated according to the Reynolds number similarity criterionin,a：
Tin,a＝REF(μin,a,Pin,a)
Wherein REF (. cndot.) represents the retrieval of a REFPROP physical property table according to given parameters, subscript a represents the air turbine parameter,. mu.inFor inlet kinematic viscosity, TinIs the inlet temperature;
the obtained inlet temperature Tin,aSubstitute for estimated inlet temperature T'in,aSubstituting the formula into the formula and recalculating until the two are equal;
subsequently, the air turbine speed and flow rate can be calculated by the following formula:
where subscript a represents the air turbine parameter, N is the rotational speed, d is the disk diameter, Δ hkFor a polytropic enthalpy drop, ρinThe density of the inlet is the density of the inlet,
is the mass flow rate.
The further improvement of the invention is that the specific implementation method of the step 3) is as follows:
taking the air turbine test data obtained in the step 2) as an input variable, and obtaining performance parameters of a supercritical carbon dioxide turbine speed field, turbine efficiency, stress load and leakage amount through a performance conversion criterion; wherein the velocity distribution relation is as follows:
Wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter,
is a velocity field, and U is the peripheral velocity of the impeller;
for turbine efficiency, the conversion relationship is as follows:
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter, η is turbine efficiency, k is adiabatic index, Ma1Is the inlet Mach number, pinIs inlet density, ρoutIs the exit density;
when the turbine works, the turbine is acted by various forces, and loads borne by the impeller are different under different conditions due to unsteady characteristics of flow and changes of working conditions, but the turbine is mainly acted by axial force, circumferential force and centrifugal force of fluid, and under the action of the axial force, the circumferential force and the centrifugal force, corresponding stress can be generated on the surface of the impeller; the conversion relation is as follows:
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter, σzFor distribution of axial stress on the impeller surface, σθIs leaf ofDistribution of circumferential stress of wheel surface, σrDistribution of centrifugal stress to the impeller, ρfFor fluid density, U is the impeller peripheral speed, ρsThe density of the impeller solid is shown, d is the diameter of a wheel disc, N is the rotating speed, and g is the geometric similarity ratio;
When a turbine impeller works, partial gas leaks from the gap of the driven stationary blade, the air leakage amount at the position is obtained by arranging a flow sensor in a test, the actual leakage amount of the supercritical carbon dioxide turbine is obtained by a conversion criterion, and the conversion relation is as follows:
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter,
for leakage flow, ρfFor fluid density, U is the fluid characteristic velocity and g is the geometric similarity ratio.
The further improvement of the invention is that the specific implementation method of the step 4) is as follows:
changing the operating condition of the turbine, obtaining the strength and the pneumatic performance parameters of the supercritical carbon dioxide turbine under the variable working condition state through the steps, and checking the strength characteristic of the turbine to ensure that the maximum equivalent stress of the turbine meets the requirement of sigmam＜σc, wherein σmFor maximum equivalent stress, σ, of the turbine wheelcEstimating turbine leakage for maximum allowable stress of material
Efficiency η of the turbine, satisfy
η＞ηc, wherein mclTo design the maximum allowable leakage, etacTo design efficiency values.
The invention has at least the following beneficial technical effects:
in the process of designing and developing the supercritical carbon dioxide turbine, in order to accurately obtain the performance parameters of the designed turbine, experimental research needs to be carried out on the designed turbine. However, the physical properties of the supercritical carbon dioxide working medium bring inconvenience to the development of tests, such as too high turbine rotation speed, difficult working condition achievement, too small impeller size and the like. The similar modeling method for the supercritical carbon dioxide turbine test can be used for carrying out similar modeling design on the supercritical carbon dioxide turbine test, carrying out similar modeling test by using the air turbine and providing a performance conversion criterion for converting a modeling test result into an operation performance parameter of the supercritical carbon dioxide turbine. Compared with a prototype test, the complexity of a similar modeling test system adopting the air turbine and the building difficulty of a test bed are both greatly reduced, the modeling method can greatly save the test cost, shorten the test period and further shorten the research and development period of the supercritical carbon dioxide turbine product. According to the similar modeling method for the supercritical carbon dioxide turbine test, air is used as a substitute test working medium, so that the limit of the severe operation condition of the supercritical carbon dioxide turbine is overcome, the test working medium preparation system is simplified, the test cost is reduced, and the test result under the wider operation condition can be obtained.
Furthermore, the similar modeling method for the supercritical carbon dioxide turbine test provided by the invention applies flow similarity conversion, can obviously reduce the turbine rotating speed in the modeling test and improve the safety of a rotor and a bearing by reasonably selecting modeling parameters.
In conclusion, the similar modeling method for the supercritical carbon dioxide turbine test provided by the invention can be used for developing the modeling test of the supercritical carbon dioxide turbine, obtaining the comprehensive performance parameters of the turbine under different working conditions and providing basic data for the optimal design of the supercritical carbon dioxide turbine. The method can provide basis and reference for the design of the supercritical carbon dioxide turbine test scheme, and has important engineering significance and wide application prospect.
Drawings
FIG. 1 is a system diagram of a supercritical turbine oxidation simulation modeling test method;
FIG. 2 is a diagram of a turbine modeling-like process; wherein (a) in fig. 2 is a supercritical carbon dioxide turbine model and (b) in fig. 2 is a test turbine model;
FIG. 3 is a schematic view of a leakage flow;
FIG. 4 is a flow chart of the overall performance analysis of a supercritical turbine.
In the figure: the impeller comprises an actual impeller A, an actual blade profile B, a model impeller A, a model blade profile B, a blade diffuser, a sealing ring and an impeller upper cover plate, wherein the actual impeller A is used as 11, the actual blade profile B is used as 12, the model blade profile B is used as 22, the blade diffuser is used as 23, the sealing ring is used as.
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 simulation modeling method for a supercritical carbon dioxide compressor test, and the method comprises four steps of geometric simulation modeling, flow simulation modeling, turbine performance conversion and comprehensive performance evaluation of a supercritical carbon dioxide-air turbine.
The invention provides a similar modeling method for a supercritical carbon dioxide turbine test. Firstly, scaling the supercritical carbon dioxide turbine at the same ratio according to a geometric similarity criterion to obtain geometric parameters of an air turbine model. Then, the similarity principle of flow is utilized to ensure that the main criterion number and the speed triangle are similar, the actual working condition of the supercritical carbon dioxide working medium is used as an input variable of the similarity criterion, the operation working condition parameters of the air working medium turbine such as the pressure ratio, the rotating speed and the inlet temperature are calculated, experimental research is carried out, and the air turbine test data and the performance parameters are obtained. And secondly, deducing performance parameters such as a non-dimensional speed field, turbine efficiency, stress load, leakage amount and the like of the supercritical carbon dioxide turbine according to a performance conversion criterion. And finally, evaluating the comprehensive performance of the supercritical carbon dioxide turbine under different boundary conditions, verifying the feasibility of stable and efficient operation of the supercritical carbon dioxide turbine, and providing guidance for the design and optimization of the supercritical carbon dioxide turbine.
A similar modeling approach to the supercritical carbon dioxide turbine test is described below for a radial inflow turbine:
referring to fig. 2, a test geometric similarity modeling is first performed such that the test turbine has a proportional geometric relationship with the design turbine, where 11 is the actual impeller a, 12 is the actual profile B, 21 is the model impeller a, and 22 is the model profile B. Specifically, the air turbine and the supercritical carbon dioxide turbine used in the test should have the same section profile and the same number of blades, and the parameters of the blade chord length, the blade height, the blade thickness, the wheel disc diameter, the blade cascade pitch and the blade tip clearance are enlarged or reduced in equal proportion, and specifically satisfy the following relation:
na＝n0
wherein subscript a represents air turbine parameters, subscript 0 represents supercritical carbon dioxide turbine parameters, g is a geometric similarity ratio, l is blade height, d is wheel disc diameter, b is blade thickness, t is blade grid pitch, s is blade chord length, and n is blade number.
Followed by flow similarity modelling. The modeling process grasps the primary similarity criterion condition, abandons the secondary similarity criterion condition, adopts approximate modeling, and selects the similarity criterion which dominates the flow influence as the similarity criterion. Selecting a flow coefficient, a Reynolds number, a speed ratio and a compression coefficient as similarity criteria, and ensuring the following dimensionless criterion numbers to be equal:
wherein ,
For mass flow, pinIs turbine inlet density, N is rotational speed, d is wheel disc diameter, U is impeller circumferential speed, mu is dynamic viscosity, Delta hkFor a variable enthalpy drop, VinIs the inlet volume flow, VoutIs the outlet volume flow.
Simultaneously, the inlet and outlet airflow angle of the model test turbine is ensured to be consistent with the actual value, and the requirement of similarity of speed triangles is met, namely:
α1,a＝α1,0,β1,a＝β1,0
α2,a＝α2,0,β2,a＝β2,0
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine 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 actual working condition and the geometric similarity ratio g of the supercritical carbon dioxide working medium are used as input variables of the similarity criterion, and then the operating working condition parameters such as the pressure ratio, the rotating speed, the inlet temperature, the flow and the like of the air working medium can be determined according to the following steps.
Firstly, the inlet pressure P of the air turbine is determinedin,aAnd estimating an inlet temperature T'in,aObtaining the air turbine outlet pressure P byout,a：
ρin,a,sin,a＝REF(T′in,a,Pin,a)
Pout,a＝REF(sin,a,ρout,a)
Wherein REF (. circle.) represents a REFPROP physical property table obtained by reference to predetermined parameters, and subscript a represents an air turbine parameter, T'inTo estimate importTemperature, pinIs inlet density, ρ outIs the outlet density.
Then, the actual inlet temperature T of the air turbine is estimated according to the Reynolds number similarity criterionin,a：
Tin,a＝REF(μin,a,Pin,a)
Wherein REF (. cndot.) represents the retrieval of a REFPROP physical property table according to given parameters, subscript a represents the air turbine parameter,. mu.inFor inlet kinematic viscosity, TinIs the inlet temperature.
The obtained inlet temperature Tin,aSubstitute for estimated inlet temperature T'in,aSubstituting the above formula to recalculate until the two are equal.
Subsequently, the air turbine speed and flow rate can be calculated by the following formula:
where subscript a represents the air turbine parameter, N is the rotational speed, d is the disk diameter, Δ hkFor a polytropic enthalpy drop, ρinThe density of the inlet is the density of the inlet,
is the mass flow rate.
And carrying out a similar modeling test according to the air turbine operation condition parameters obtained in the step to obtain actual operation data of the air turbine. The air turbine test data are used as input parameters, and performance parameters such as a supercritical carbon dioxide turbine speed field, turbine efficiency, stress load and leakage amount are obtained through a performance conversion criterion. Wherein the velocity distribution relation is as follows:
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter,
for the velocity field, U is the impeller peripheral velocity.
For turbine efficiency, the conversion relationship is as follows:
Wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter, η is turbine efficiency, k is adiabatic index, Ma1Is the inlet Mach number, pinIs inlet density, ρoutIs the outlet density.
The turbine is acted by various forces during working, and due to unsteady characteristics of flow and changes of working conditions, loads borne by the impeller are different under different conditions, but are mainly acted by fluid axial force, fluid circumferential force and centrifugal force, and under the action of the forces, corresponding stress can be generated on the surface of the impeller. The conversion relation is as follows:
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine 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 impeller peripheral speed, ρsThe density of the impeller solid, d is the diameter of the wheel disc, N is the rotating speed, and g is the geometric similarity ratio.
Referring to fig. 3, 21 is a model impeller, 23 is a vaned diffuser, 24 is a seal ring, and 25 is an impeller upper cover plate. When the turbine impeller works, part of gas leaks from a gap between the model impeller 21 and the vaned diffuser 23, and the high-temperature and high-pressure leakage flow threatens the safety of a bearing and a rotor and reduces the actual efficiency of the turbine. In the test, the air leakage amount at the position is obtained by arranging a flow sensor, and the actual leakage amount of the supercritical carbon dioxide turbine is obtained by a conversion criterion, wherein the conversion relation is as follows:
Wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter,
for leakage flow, ρfFor the fluid density, U is the impeller peripheral speed and g is the geometric similarity ratio.
Finally, referring to FIG. 4, the overall performance of the supercritical carbon dioxide turbine under different boundary conditions is evaluated. Changing the operating condition of the turbine, obtaining the supercritical carbon dioxide turbine strength and the pneumatic performance parameters under the variable condition state through the similar modeling test, and checking the strength characteristic of the turbine to ensure that the maximum equivalent stress of the turbine meets the requirement of sigmam＜σc, wherein σmFor maximum equivalent stress, σ, of the turbine wheelcEstimating turbine leakage for maximum allowable stress of material
Efficiency η of the turbine, satisfy
η＞ηc, wherein mclTo design the maximum allowable leakage, etacTo design efficiency values. Quantifying the correlation among the structural parameters, the operation conditions and the comprehensive performance of the supercritical carbon dioxide turbine and summarizing the supercritical carbon dioxide turbineThe design condition provides basic data for the optimal design of the supercritical carbon dioxide turbine.
Claims (5)
1. A method of modeling a supercritical carbon dioxide turbine test, comprising:
1) scaling the supercritical carbon dioxide turbine in the same ratio according to a geometric similarity criterion to obtain geometric parameters of an air turbine model, and determining a geometric similarity ratio;
2) The method comprises the steps of utilizing a flowing similarity principle to ensure that main criteria are similar in number and speed triangles, taking actual working conditions and geometric similarity ratios of supercritical carbon dioxide working media as input variables of the similarity criteria, calculating pressure ratios, rotating speeds and inlet temperature operation working condition parameters of the air working media turbine, and then carrying out test research to obtain air turbine test data and performance parameters;
3) taking air turbine test data and performance parameters as input variables, and deriving performance parameters of a dimensionless speed field, turbine efficiency, stress load and leakage amount of the supercritical carbon dioxide turbine according to a performance conversion criterion;
4) and evaluating the comprehensive performance of the supercritical carbon dioxide turbine under different boundary conditions, verifying the feasibility of stable and efficient operation of the supercritical carbon dioxide turbine, and providing guidance for the design and optimization of the supercritical carbon dioxide turbine.
2. The method for modeling the similarity of the supercritical carbon dioxide turbine test according to claim 1, wherein the step 1) is realized by the following steps:
firstly, modeling the geometric similarity of a test to ensure that the test turbine and a designed turbine have a proportional geometric relationship, wherein the air turbine and the supercritical carbon dioxide turbine used in the test have the same section profile and the same blade number, and the blade chord length, the blade height, the blade thickness, the wheel disc diameter, the blade cascade pitch and the blade top clearance parameters are amplified or reduced in equal proportion, and the geometric similarity specifically satisfies the following relational expression:
na＝n0
Wherein subscript a represents air turbine parameters, subscript 0 represents supercritical carbon dioxide turbine parameters, g is a geometric similarity ratio, l is blade height, d is wheel disc diameter, b is blade thickness, t is blade grid pitch, s is blade chord length, and n is blade number.
3. The method for modeling the similarity of the supercritical carbon dioxide turbine test according to claim 2, wherein the step 2) is realized by the following steps:
adopting approximate modeling, and selecting a similarity criterion which dominates the flow influence as a similarity standard; selecting a flow coefficient, a Reynolds number, a speed ratio and a compression coefficient as similarity criteria, and ensuring the following dimensionless criterion numbers to be equal:
wherein ,
for mass flow, pinIs turbine inlet density, N is rotational speed, d is wheel disc diameter, U is impeller circumferential speed, mu is dynamic viscosity, Delta hkFor a variable enthalpy drop, VinIs the inlet volume flow, VoutIs the outlet volume flow;
simultaneously, the inlet and outlet airflow angle of the model test turbine is ensured to be consistent with the actual value, and the requirement of similarity of speed triangles is met, namely:
α1,a＝α1,0,β1,a＝β1,0
α2,a＝α2,0,β2,a＝β2,0
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter, α1Is the absolute speed angle, beta, of the stationary blade outlet 1Is 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;
taking the actual working condition of the supercritical carbon dioxide working medium and the geometric similarity ratio g obtained in the step 1) as input variables of the similarity criterion, and then determining the pressure ratio, the rotating speed, the inlet temperature and the flow operation working condition parameters of the air working medium according to the following steps;
firstly, the inlet pressure P of the air turbine is determinedin,aAnd estimating an inlet temperature T'in,aObtaining the air turbine outlet pressure P byout,a：
ρin,a,sin,a＝REF(T′in,a,Pin,a)
Pout,a＝REF(sin,a,ρout,a)
Wherein REF (. circle.) represents the retrieval of a REFPROP physical property table according to given parameters, subscript a represents the air turbine parameter, Ti'nTo estimate the inlet temperature, pinIs inlet density, ρoutIs the exit density;
then, the actual inlet temperature T of the air turbine is estimated according to the Reynolds number similarity criterionin,a：
Tin,a＝REF(μin,a,Pin,a)
Wherein REF (. cndot.) represents the retrieval of a REFPROP physical property table according to given parameters, subscript a represents the air turbine parameter,. mu.inFor inlet kinematic viscosity, TinIs the inlet temperature;
the obtained inlet temperature Tin,aSubstitute for estimated inlet temperature T'in,aSubstituting the formula into the formula and recalculating until the two are equal;
subsequently, the air turbine speed and flow rate can be calculated by the following formula:
where subscript a represents the air turbine parameter, N is the rotational speed, d is the disk diameter, Δ h kFor a polytropic enthalpy drop, ρinThe density of the inlet is the density of the inlet,
is the mass flow rate.
4. The method for modeling the similarity of the supercritical carbon dioxide turbine test according to claim 3, wherein the step 3) is realized by the following steps:
taking the air turbine test data obtained in the step 2) as an input variable, and obtaining performance parameters of a supercritical carbon dioxide turbine speed field, turbine efficiency, stress load and leakage amount through a performance conversion criterion; wherein the velocity distribution relation is as follows:
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter,
is a velocity field, and U is the peripheral velocity of the impeller;
for turbine efficiency, the conversion relationship is as follows:
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter, η is turbine efficiency, k is adiabatic index, Ma1Is the inlet Mach number, pinIs inlet density, ρoutIs the exit density;
when the turbine works, the turbine is acted by various forces, and loads borne by the impeller are different under different conditions due to unsteady characteristics of flow and changes of working conditions, but the turbine is mainly acted by axial force, circumferential force and centrifugal force of fluid, and under the action of the axial force, the circumferential force and the centrifugal force, corresponding stress can be generated on the surface of the impeller; the conversion relation is as follows:
Wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine 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 impeller peripheral speed, ρsThe density of the impeller solid is shown, d is the diameter of a wheel disc, N is the rotating speed, and g is the geometric similarity ratio;
when a turbine impeller works, partial gas leaks from the gap of the driven stationary blade, the air leakage amount at the position is obtained by arranging a flow sensor in a test, the actual leakage amount of the supercritical carbon dioxide turbine is obtained by a conversion criterion, and the conversion relation is as follows:
wherein subscript a represents an air turbine parameter, subscript 0 represents a supercritical carbon dioxide turbine parameter,
for leakage flow, ρfFor fluid density, U is the fluid characteristic velocity and g is the geometric similarity ratio.
5. The method for modeling the similarity of the supercritical carbon dioxide turbine test according to claim 4, wherein the step 4) is realized by the following steps:
changing the operating condition of the turbine, obtaining the strength and the pneumatic performance parameters of the supercritical carbon dioxide turbine under the variable working condition state through the steps, and checking the strength characteristic of the turbine to ensure that the maximum equivalent stress of the turbine meets the requirement of sigma m＜σc, wherein σmFor maximum equivalent stress, σ, of the turbine wheelcEstimating turbine leakage for maximum allowable stress of material
Efficiency η of the turbine, satisfy
η＞ηc, wherein mclTo design the maximum allowable leakage, etacTo design efficiency values.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112989511A (en) * | 2021-02-09 | 2021-06-18 | 华中科技大学 | Boiler design method and system of supercritical carbon dioxide unit and storage medium |
| CN113342314A (en) * | 2021-05-28 | 2021-09-03 | 西安交通大学 | Supercritical carbon dioxide working medium axial flow type turbine design system and method |
| CN114896905A (en) * | 2022-05-12 | 2022-08-12 | 西安交通大学 | Similarity criterion determination method for different working medium spray droplet motion evaporation process |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106055792A (en) * | 2016-05-31 | 2016-10-26 | 哈尔滨工程大学 | Dynamic simulation method for matching of supercritical carbon dioxide gas compressor and turbine |
| US9752462B1 (en) * | 2016-03-03 | 2017-09-05 | Rolls-Royce Plc | Supercritical fluid heat engine |
| CN107131017A (en) * | 2017-04-27 | 2017-09-05 | 西安交通大学 | Circulation therrmodynamic system and control method based on supercritical carbon dioxide axial flow compressor Yu axial-flow turbine coaxial configuration |
| CN110069848A (en) * | 2019-04-18 | 2019-07-30 | 西安交通大学 | A kind of turbine blade is pneumatic-dehumidifying-cooling test modeling method |
| CN110118160A (en) * | 2018-02-06 | 2019-08-13 | 浙江大学 | Solar energy supercritical carbon dioxide Brayton Cycle system |
| CN110566297A (en) * | 2019-07-29 | 2019-12-13 | 中国船舶重工集团公司第七一九研究所 | Supercritical carbon dioxide Brayton cycle system |
| CN111062124A (en) * | 2019-12-05 | 2020-04-24 | 西安交通大学 | Similar modeling method for supercritical carbon dioxide compressor test |
-
2020
- 2020-07-10 CN CN202010664676.6A patent/CN111859563B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9752462B1 (en) * | 2016-03-03 | 2017-09-05 | Rolls-Royce Plc | Supercritical fluid heat engine |
| CN106055792A (en) * | 2016-05-31 | 2016-10-26 | 哈尔滨工程大学 | Dynamic simulation method for matching of supercritical carbon dioxide gas compressor and turbine |
| CN107131017A (en) * | 2017-04-27 | 2017-09-05 | 西安交通大学 | Circulation therrmodynamic system and control method based on supercritical carbon dioxide axial flow compressor Yu axial-flow turbine coaxial configuration |
| CN110118160A (en) * | 2018-02-06 | 2019-08-13 | 浙江大学 | Solar energy supercritical carbon dioxide Brayton Cycle system |
| CN110069848A (en) * | 2019-04-18 | 2019-07-30 | 西安交通大学 | A kind of turbine blade is pneumatic-dehumidifying-cooling test modeling method |
| CN110566297A (en) * | 2019-07-29 | 2019-12-13 | 中国船舶重工集团公司第七一九研究所 | Supercritical carbon dioxide Brayton cycle system |
| CN111062124A (en) * | 2019-12-05 | 2020-04-24 | 西安交通大学 | Similar modeling method for supercritical carbon dioxide compressor test |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112989511A (en) * | 2021-02-09 | 2021-06-18 | 华中科技大学 | Boiler design method and system of supercritical carbon dioxide unit and storage medium |
| CN112989511B (en) * | 2021-02-09 | 2024-04-19 | 华中科技大学 | Boiler design method, system and storage medium of supercritical carbon dioxide unit |
| CN113342314A (en) * | 2021-05-28 | 2021-09-03 | 西安交通大学 | Supercritical carbon dioxide working medium axial flow type turbine design system and method |
| CN113342314B (en) * | 2021-05-28 | 2023-08-18 | 西安交通大学 | Supercritical carbon dioxide working medium axial flow turbine design system and method |
| CN114896905A (en) * | 2022-05-12 | 2022-08-12 | 西安交通大学 | Similarity criterion determination method for different working medium spray droplet motion evaporation process |
| CN114896905B (en) * | 2022-05-12 | 2024-03-29 | 西安交通大学 | Similarity criterion determination method for different working medium spray droplet motion evaporation process |
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