CN115640659B - Design method of transcritical carbon dioxide centrifugal compressor - Google Patents
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Abstract
The invention provides a design method of a transcritical carbon dioxide centrifugal compressor, which relates to the technical field of impeller machinery, wherein each physical property interval of transcritical carbon dioxide is equivalent to the physical property interval of an ideal working medium based on a fluid similarity theory, the design of the rated working condition and the variable working condition of the compressor is carried out according to the ideal working medium to obtain the performance curve of the ideal working medium centrifugal compressor, and the performance curve of the ideal working medium centrifugal compressor is contracted back to the performance curve of the transcritical carbon dioxide centrifugal compressor according to the fluid similarity theory. The design method of the transcritical carbon dioxide centrifugal compressor provided by the invention can effectively improve the success rate of the design of the transcritical carbon dioxide centrifugal compressor.
Description
Technical Field
The invention relates to the technical field of turbines, in particular to a design method of a transcritical carbon dioxide centrifugal compressor.
Background
The supercritical carbon dioxide thermodynamic cycle power generation technology is a novel common power technical scheme which is formed by comprehensively matching the physical properties of a working medium of supercritical carbon dioxide, a cycle process and equipment innovation based on the Brayton cycle principle by utilizing the physical properties of the working medium; the method is expected to be rapidly popularized and applied in the fields of nuclear energy, photo-thermal power plants, gas power plants, waste heat, biomass power generation and the like, brings technical and industrial changes in the fields, and simultaneously drives equipment manufacturing development in the energy field.
Research shows that in the supercritical carbon dioxide thermodynamic cycle system, when the thermodynamic cycle of carbon dioxide is in a transcritical state, namely when the inlet temperature of a compressor is reduced from 305K to 300K, the cycle efficiency is improved by more than 1.5%, the inlet temperature is reduced to 295K, and the cycle efficiency is improved by more than 2.7%. For large power systems, these substantial increases in efficiency can have a strong impact on the economics of the power plant.
For a transcritical carbon dioxide cycle power generation system, the core technology is a compressor design technology which can realize safety and stability and avoid cavitation. Common air compressors are divided into positive displacement compressors and speed compressors; the positive displacement compressor comprises a piston compressor and a reciprocating compressor, and is applied to a transcritical carbon dioxide refrigeration cycle in kilowatts to dozens of kilowatts at present, but is not applied to a carbon dioxide cycle with a larger power generation scale due to structural and size limitations; the speed type air compressors are divided into centrifugal air compressors and axial flow type air compressors, the centrifugal air compressors are usually used under the conditions of low flow and large enthalpy drop, hundreds of kilowatt-level to megawatt-level carbon dioxide circulating power generation systems disclosed by the current documents all adopt centrifugal air compressors, and the axial flow type air compressors are suitable for the conditions of high flow and low enthalpy drop and are suitable for carbon dioxide circulating power generation systems with larger power generation levels.
For a centrifugal compressor structure of a hundred kilowatt-level to megawatt-level carbon dioxide cycle power generation system, the rapid change of physical properties of a trans-critical carbon dioxide region can cause the conditions of large interpolation error, insufficient cavitation allowance of the compressor and the like in the traditional physical property interpolation design, so that the trans-critical carbon dioxide centrifugal compressor and the trans-critical carbon dioxide cycle design fail, and the search for a proper and accurate design method of the trans-critical carbon dioxide centrifugal compressor is urgent priority of trans-critical carbon dioxide cycle.
In view of the above, the inventor designs a design method of a transcritical carbon dioxide centrifugal compressor through repeated experiments according to production design experiences in the field and related fields for many years, so as to solve the problems in the prior art.
Disclosure of Invention
The invention aims to provide a design method of a transcritical carbon dioxide centrifugal compressor, which can effectively improve the success rate of the design of the transcritical carbon dioxide centrifugal compressor.
In order to achieve the purpose, the invention provides a design method of a transcritical carbon dioxide centrifugal compressor, wherein each physical property interval of the transcritical carbon dioxide is equivalent to the physical property interval of an ideal working medium based on a fluid similarity theory, the compressor is designed under a rated working condition and a variable working condition according to the ideal working medium to obtain a performance curve of the ideal working medium, and the performance curve of the ideal working medium centrifugal compressor is contracted to the performance curve of the transcritical carbon dioxide centrifugal compressor according to the fluid similarity theory.
The design method of the transcritical carbon dioxide centrifugal compressor is characterized in that at the inlet of the transcritical carbon dioxide centrifugal compressor, carbon dioxide is in a supercooled liquid state; at the outlet of the transcritical carbon dioxide centrifuge, the carbon dioxide is in a supercritical state.
The design method of the transcritical carbon dioxide centrifugal compressor is characterized in that the performance indexes of the transcritical carbon dioxide include pressure ratio, mass flow and isentropic efficiency.
The method for designing the transcritical carbon dioxide centrifugal compressor, wherein the step of scaling the performance curve of the ideal working medium centrifugal compressor back to the performance curve of the transcritical carbon dioxide centrifugal compressor according to the fluid similarity theory, comprises the following steps:
converting the pressure ratio of the transcritical carbon dioxide according to similar prandtl and equal isentropic pressure head coefficients;
converting the mass flow of the trans-critical carbon dioxide according to geometric similarity;
and obtaining the isentropic efficiency of the transcritical carbon dioxide according to an approximate empirical relation.
The method for designing the transcritical carbon dioxide centrifugal compressor comprises the following steps of similar Reynolds numbers, similar Plantt numbers, similar geometry and similar empirical relations.
The design method of the transcritical carbon dioxide centrifugal compressor, wherein the similar prandtl numbers require that the isentropic head coefficient and the specific speed of the transcritical carbon dioxide centrifugal compressor are equal.
The design method of the transcritical carbon dioxide centrifugal compressor is characterized in that the geometric similarity is ensured by a flow coefficient, a volume flow and a rotating speed phase.
The method for designing the transcritical carbon dioxide centrifugal compressor, as described above, wherein the designing of the operating conditions includes calculating various parameters of the transcritical carbon dioxide centrifugal compressor.
The method for designing the transcritical carbon dioxide centrifugal compressor, wherein the parameters include a compressor head coefficient and a specific rotation speed, a compressor inlet diameter, a compressor impeller outlet speed and a compressor impeller outlet diameter.
The design method of the transcritical carbon dioxide centrifugal compressor adopts a 2D mean line method for the rated working condition design and the variable working condition design of the compressor. Compared with the prior art, the invention has the following characteristics and advantages:
the design method of the transcritical carbon dioxide centrifugal compressor provided by the invention is characterized in that the physical property interval of transcritical carbon dioxide is equivalent to the physical property interval of an ideal working medium, the physical property of the ideal working medium does not change rapidly in thermal cycle, so that the problem of rapid change of the physical property of a transcritical carbon dioxide region is avoided, then the design of the rated working condition and the design of the variable working condition of the compressor are carried out according to the equivalent ideal working medium, and finally the performance curve of the equivalent ideal working medium centrifugal compressor is contracted back to the performance curve of the transcritical carbon dioxide centrifugal compressor according to the fluid similarity theory, so that the problems of inaccurate physical property interpolation and difficult design of the transcritical carbon dioxide centrifugal compressor caused by rapid change of the physical property of the carbon dioxide transcritical region are solved, and technical support and guidance are provided for the design of the transcritical carbon dioxide centrifugal compressor and the high-efficiency transcritical carbon dioxide cycle.
Drawings
The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way. In addition, the shapes, the proportional sizes, and the like of the respective members in the drawings are merely schematic for facilitating the understanding of the present invention, and do not specifically limit the shapes, the proportional sizes, and the like of the respective members of the present invention. Those skilled in the art, having the benefit of the teachings of this invention, may choose from the various possible shapes and proportional sizes to implement the invention as a matter of case.
Fig. 1 is a flow chart of a design method of a transcritical carbon dioxide centrifugal compressor provided by the invention;
FIG. 2 is a schematic diagram of a carbon dioxide transcritical cycle.
1 is an inlet of a gas compressor; 2 is the outlet of the compressor; 3 is a turbine inlet; 4 is a turbine outlet; 5 is the critical point of carbon dioxide.
Detailed Description
The details of the present invention can be more clearly understood in conjunction with the accompanying drawings and the description of the embodiments of the present invention. However, the specific embodiments of the present invention described herein are for the purpose of illustration only and are not to be construed as limiting the invention in any way. Any possible variations based on the present invention may be conceived by the skilled person in the light of the teachings of the present invention, and these should be considered to fall within the scope of the present invention.
As shown in figure 1, the invention provides a design method of a transcritical carbon dioxide centrifugal compressor, wherein each physical property interval of transcritical carbon dioxide is equivalent to the corresponding physical property interval of an ideal working medium based on a fluid similarity theory, the compressor is designed according to the rated working condition and the variable working condition of the ideal working medium, the performance curve of each ideal working medium centrifugal compressor is obtained, and the performance curve of the ideal working medium centrifugal compressor is contracted back to the performance curve of the transcritical carbon dioxide centrifugal compressor according to the fluid similarity theory.
The design method of the transcritical carbon dioxide centrifugal compressor provided by the invention is characterized in that the physical property interval of transcritical carbon dioxide is equivalent to the physical property interval of an ideal working medium, the physical property of the ideal working medium does not change rapidly in thermal cycle, so that the problem of rapid change of the physical property of a transcritical carbon dioxide region is avoided, then the design of the rated working condition and the design of the variable working condition of the compressor are carried out according to the equivalent ideal working medium, and finally the performance curve of the equivalent ideal working medium is contracted back to the performance curve of the transcritical carbon dioxide according to the fluid similarity theory, so that the problems of inaccurate physical property interpolation and difficult design of the transcritical carbon dioxide centrifugal compressor caused by rapid change of the physical property of the transcritical carbon dioxide region are solved, and technical support and guidance are provided for the design of the transcritical carbon dioxide centrifugal compressor and the high-efficiency transcritical carbon dioxide cycle.
The design method of the transcritical carbon dioxide centrifugal compressor provided by the invention can be used for designing the hundreds kilowatt-level to megawatt-level transcritical carbon dioxide centrifugal compressor, thereby providing technical support and guarantee for research and development of the hundreds kilowatt-level to megawatt-level transcritical carbon dioxide centrifugal compressor and the transcritical carbon dioxide circulation design.
In an alternative embodiment, at the inlet of the transcritical carbon dioxide centrifuge, the carbon dioxide is in a subcooled liquid state; at the outlet of the transcritical carbon dioxide centrifuge, the carbon dioxide is in a supercritical state.
As shown in fig. 2, the transcritical carbon dioxide circulation refers to a carbon dioxide circulation mode that the temperature and the pressure at the inlet of the compressor (at the position of point 1 in fig. 2) are lower than the critical point (at the position of point 5 in fig. 2), and compared with the supercritical carbon dioxide circulation, the reduction of the inlet temperature of the compressor of the transcritical carbon dioxide circulation is beneficial to improving the circulation efficiency, so that the system power generation amount is improved, and the method has considerable economic benefits.
The pressure at the critical point was 7.38MPa, and the temperature was 31.1 ℃.
In an alternative embodiment of the invention, the performance metrics for transcritical carbon dioxide include pressure ratio, mass flow rate, and isentropic efficiency.
The pressure ratio and the mass flow of the trans-critical carbon dioxide are equivalent to corresponding physical property intervals of an ideal working medium based on a fluid similarity theory, and the ideal working medium can be one or more.
In an alternative example of this embodiment, the fluid similarity theory includes Reynolds number similarity, plantt number similarity, geometric similarity, and approximate empirical relationships.
In an optional example of the present invention, the designing of the operating condition includes calculating various parameters of the compressor, and specifically includes: the coefficient and the specific speed of a pressure head of the compressor, the diameter of an inlet of the compressor, the speed of an outlet of an impeller of the compressor and the diameter of an outlet of the impeller of the compressor.
Specifically, the reynolds number is a substantially similar criterion that ensures similar fluid flow characteristics, defined as follows:
in the formula (I), the compound is shown in the specification,
is the fluid density; />
Is the fluid velocity; />
The diameter of the inlet of the compressor; />
Is the kinetic viscosity coefficient.
Physical parameters such as the specific heat coefficient of the carbon dioxide transcritical region at constant pressure are changed rapidly, so that the prandtl number for representing the heat exchange capacity of the fluid is required to be used as a similarity criterion, and the prandtl number is defined as follows:
in the formula (I), the compound is shown in the specification,
is the kinematic viscosity coefficient; />
Is the thermal diffusivity.
Further, the similar prandtl numbers require that the compressor head coefficient and the specific rotation speed are equal, and then the compressor head coefficient and the specific rotation speed are respectively defined as follows:
in the formula (I), the compound is shown in the specification,
the compressor head coefficient; />
The average compression coefficient of an inlet and an outlet of the compressor is obtained; />
Is the carbon dioxide gas constant; />
The total inlet temperature; />
Is the specific heat ratio; />
The pressure ratio of inlet and outlet; />
Is the rotor angular velocity; />
Is the inlet volumetric flow rate.
The geometric similarity is ensured by the flow coefficient, the volume flow and the rotating speed being equal. Wherein the flow coefficient is defined as follows:
in the formula (I), the compound is shown in the specification,
is the outlet speed of the impeller of the compressor>
Diameter of the compressor impeller outlet.
In the embodiment, the design method of the compressor in each equivalent ideal working medium is a 2D mean line method, namely, a compressor speed triangular graph under various loss models is considered to predict the variation condition change of the compressor.
In an alternative embodiment of the present invention, scaling the performance curve of the ideal working fluid back to the transcritical carbon dioxide performance curve comprises:
converting the pressure ratio of the transcritical carbon dioxide according to the similar prandtl and equal isentropic pressure head coefficients; specifically, the pressure ratio of the transcritical carbon dioxide centrifugal compressor is obtained according to the isentropic pressure head coefficient and after conversion as follows:
in the formula (I), the compound is shown in the specification,
，/>
，/>
，/>
，/>
the compressor inlet and outlet average compression coefficient, gas constant, inlet total temperature, specific heat ratio and inlet and outlet pressure ratio of equivalent ideal working medium are respectively.
And converting the mass flow of the transcritical carbon dioxide according to geometric similarity, wherein the converted mass flow of the transcritical carbon dioxide centrifugal compressor is as follows:
in the formula (I), the compound is shown in the specification,
、/>
、/>
the density of the carbon dioxide, the density of the equivalent ideal working medium and the mass flow of the equivalent ideal working medium are respectively.
Scaling to obtain the isentropic efficiency of transcritical carbon dioxide according to an approximate empirical relationship, which uses the empirical relationship as follows:
wherein n is the swelling index.
Meanwhile, under the rated working condition, the diameter ratio of the outlet of the impeller is solved as follows:
in the formula (I), the compound is shown in the specification,
is the inlet total enthalpy>
Is a slip factor.
Therefore, the expansion index n can be obtained according to the impeller outlet diameter ratio under the rated working condition of the compressor and the equation (7), so that a complete isentropic efficiency empirical relation is obtained.
In the invention, the inlet of the transcritical carbon dioxide centrifugal compressor is in a supercooled liquid state, and the outlet of the transcritical carbon dioxide centrifugal compressor is in a supercritical state. In addition, the transcritical carbon dioxide centrifugal compressor needs to experience a region with sharp change of physical properties in the operation process, so that in order to avoid gasification or cavitation in the operation process to cause surging or severe vibration, an inlet of the compressor is selected to be in a supercooled liquid state, so that carbon dioxide gas has enough allowance when being subjected to isentropic expansion to condensation pressure in regions such as the top of an impeller.
In an alternative embodiment of the invention, the transcritical carbon dioxide centrifugal compressor corresponds to a cycle power generation system with a rating of hundreds of kilowatts to megawatts.
The present invention is not limited to the above embodiments, and in particular, various features described in different embodiments can be arbitrarily combined with each other to form other embodiments, and the features are understood to be applicable to any embodiment except the explicitly opposite descriptions, and are not limited to the described embodiments.
Claims (8)
1. A design method of a transcritical carbon dioxide centrifugal compressor is characterized in that each physical property interval of the transcritical carbon dioxide is equivalent to a physical property interval of an ideal working medium based on a fluid similarity theory, the design of the rated working condition and the variable working condition of the compressor is carried out according to the ideal working medium to obtain a performance curve of the ideal working medium, and the performance curve of the ideal working medium centrifugal compressor is contracted back to the performance curve of the transcritical carbon dioxide centrifugal compressor according to the fluid similarity theory; wherein, the first and the second end of the pipe are connected with each other,
and converting the pressure ratio of the transcritical carbon dioxide according to similar prandtl and equal isentropic head coefficients, wherein the pressure ratio of the transcritical carbon dioxide centrifugal compressor is obtained according to the isentropic head coefficients and after conversion as follows:
in the formula (I), the compound is shown in the specification,
，/>
，/>
，/>
，/>
the average compression coefficient, the gas constant, the total inlet temperature, the specific heat ratio and the inlet-outlet pressure ratio of the compressor are equivalent ideal working media;
and converting the mass flow of the transcritical carbon dioxide according to geometric similarity, wherein the converted mass flow of the transcritical carbon dioxide centrifugal compressor is as follows:
in the formula (I), the compound is shown in the specification,
、/>
、/>
respectively the density of carbon dioxide, the density of an equivalent ideal working medium and the mass flow of the equivalent ideal working medium;
scaling to obtain the isentropic efficiency of transcritical carbon dioxide according to an approximate empirical relationship, which uses the empirical relationship as follows:
wherein n is the swelling index;
under the rated working condition, the diameter ratio of an outlet of the impeller is solved as follows:
in the formula (I), the compound is shown in the specification,
is inlet total enthalpy, is combined with>
Is a slip factor;
at the inlet of the transcritical carbon dioxide centrifuge, the carbon dioxide is in a subcooled liquid state; at the outlet of the transcritical carbon dioxide centrifuge, the carbon dioxide is in a supercritical state; the transcritical carbon dioxide circulation refers to a carbon dioxide circulation mode that the temperature and the pressure at the inlet of the compressor are lower than the critical point; the pressure at the critical point was 7.38MPa and the temperature was 31.1 ℃.
2. The method for designing a transcritical carbon dioxide centrifugal compressor as recited in claim 1, wherein the performance indicators of the transcritical carbon dioxide include pressure ratio, mass flow rate and isentropic efficiency.
3. The method of claim 1, wherein the flow similarity theory comprises Reynolds number similarity, plantt number similarity, geometric similarity, and approximate empirical relations.
4. The design method of the transcritical carbon dioxide centrifugal compressor as claimed in claim 3, wherein the similar prandtl numbers require that the isentropic head coefficient and the specific speed of the transcritical carbon dioxide centrifugal compressor are equal.
5. The method for designing a transcritical carbon dioxide centrifugal compressor as recited in claim 3, wherein said geometric similarity is ensured by flow coefficient, volumetric flow rate and rotational speed.
6. The method for designing the transcritical carbon dioxide centrifugal compressor according to claim 1, wherein the working condition design comprises calculation of parameters of the transcritical carbon dioxide centrifugal compressor.
7. The method of designing a transcritical carbon dioxide centrifugal compressor of claim 6, wherein said parameters include compressor head coefficient and specific speed, compressor inlet diameter, compressor impeller outlet speed, and compressor impeller outlet diameter.
8. The design method of the transcritical carbon dioxide centrifugal compressor as claimed in claim 1, wherein the compressor rated condition design and variable condition design adopt a 2D mean line method.
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| US20060059945A1 (en) * | 2004-09-13 | 2006-03-23 | Lalit Chordia | Method for single-phase supercritical carbon dioxide cooling |
| CN108061405A (en) * | 2018-01-23 | 2018-05-22 | 郑州云宇新能源技术有限公司 | Self cooled high-performance CO2Trans-critical cycle heat pump circulating system |
| CN112065521A (en) * | 2020-09-16 | 2020-12-11 | 天津大学 | Based on CO2Mixed working medium supercharging heat absorption transcritical circulation hot dry rock geothermal power generation model |
| CN113028668B (en) * | 2021-01-14 | 2021-12-28 | 西安交通大学 | Micro-channel near-isothermal compression type transcritical carbon dioxide circulating system and method |
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| WO2018062627A1 (en) * | 2016-09-29 | 2018-04-05 | 한국과학기술원 | Stirling engine using supercritical fluid |
| CN206816364U (en) * | 2017-06-28 | 2017-12-29 | 广汉天空动力机械有限责任公司 | A kind of gas turbine critical-cross carbon dioxide condensation cycle combined generating system |
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| CN215292607U (en) * | 2021-01-06 | 2021-12-24 | 华北电力大学 | Waste incineration power generation system integrated with supercritical carbon dioxide circulation |
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