Centrifugal steam turbine isentropic efficiency test and cfd optimization method

Abstract

The application belongs to the technical field of thermal turbines, and discloses a centripetal steam turbine isentropic efficiency test and CFD optimization method. First, the centripetal steam turbine prototype is operated under the set working condition, and multiple types of operation parameters are synchronously collected, effective samples are screened by a steady state criterion to construct a test benchmark; then, a complete three-dimensional fluid calculation domain is established, compressible flow control equations are solved, and a coupling SST k-omega turbulence model and real water vapor properties are used to complete flow heat exchange solution and decouple total pressure loss; finally, flow field parameters are extracted to analyze loss mechanism, the model is calibrated through closed-loop iteration comparison of CFD and test results under each working condition, and structure targeted optimization is realized. The application focuses on suppressing four types of dominant losses, and can keep isentropic efficiency at 0.72-0.82 and total pressure loss at 2.0%-2.5% in the flow range of 0.45-0.65 kg / s. The simulation and test normalized RMSE consistency index reaches 0.97 or above, which can improve the reliability of wide working condition performance prediction and shorten the iteration time.

Description

Technical Field

[0001] This invention relates to the field of thermal turbine technology, and in particular to an entropy efficiency test and CFD optimization method for centripetal steam turbines. Background Technology

[0002] The current scale of industrial waste heat and pressure resources is enormous. The recoverable waste energy resources in key industries such as steel, chemicals, and building materials alone amount to hundreds of millions of tons of standard coal. Market demand for waste heat power generation and waste pressure utilization continues to grow. By 2025, the annual output value of my country's energy-saving service industry was approaching 600 billion yuan, and its clean energy investment scale continues to lead the world. Performance improvement of efficient waste heat and energy conversion equipment has become a key support for industrial upgrading. As the core equipment for medium- and low-temperature waste heat and saturated steam waste pressure recovery power generation, the isentropic efficiency and wide operating condition performance of the centripetal steam turbine directly determine the energy conversion efficiency of the waste heat recovery system. Existing centripetal steam turbine optimization technologies are mainly based on a combination of one-dimensional mean-linear aerodynamic design, empirical loss model correction, and three-dimensional CFD numerical simulation. First, the core geometric parameters and preliminary performance boundaries of the turbine are quickly determined using one-dimensional methods. Then, three-dimensional CFD tools are used to analyze the internal flow field structure and local flow characteristics. Finally, the performance at the design point is verified through physical bench tests. Existing research mainly uses air, natural gas, supercritical carbon dioxide, etc. as the main working fluids, focusing on improving the output power and single-point isentropic efficiency under rated operating conditions, forming a relatively mature single-condition turbine design and verification system.

[0003] However, existing technologies still have three significant shortcomings in the optimization of centripetal steam turbines: First, the fit between the actual physical properties of steam and the phase change mechanism is insufficient. The core loss model and physical property assumptions are mainly constructed for dry working gases such as air, natural gas, and supercritical carbon dioxide, which do not fully adapt to the non-equilibrium condensation, latent heat release, and wet steam two-phase flow coupling characteristics during the transonic expansion of steam. This leads to a systematic deviation between the performance prediction under steam conditions and the actual operation, and it is impossible to quantitatively assess the risks of local supercooling and droplet erosion. Second, the decoupling of the total pressure loss components cannot directly support targeted structural optimization. The existing optimization logic is guided by the single-point isentropic efficiency and output power under rated operating conditions, and the optimization process only uses empirical trial and error to adjust the macroscopic efficiency trend. First, it is impossible to quantify the contribution of different loss sources to the overall performance, making it difficult to establish the correspondence between "flow field structure change - local loss formation - macroscopic efficiency decline". This leads to blind optimization direction and low iteration efficiency, making it difficult to simultaneously take into account the performance stability across the entire operating range. Second, the pure simulation boundary is disconnected from the real experimental boundary, resulting in insufficient reliability of wide-condition prediction. Three-dimensional CFD simulation generally adopts idealized boundary conditions and only conducts single-point bench tests after the design is finalized. The experimental data is not involved in the iterative calibration of the simulation model throughout the process, which causes the simulation results to be disconnected from the real physical process. Under the actual operating conditions of wide speed, variable flow rate, and variable pressure ratio, the prediction accuracy is insufficient, and it is impossible to provide a quantifiable and reproducible reliable basis for engineering structure optimization. Summary of the Invention

[0004] The purpose of this invention is to provide a method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines, thereby solving the above-mentioned technical problems.

[0005] To achieve the above objectives, this invention provides a method for experimental and CFD optimization of entropy efficiency in centripetal steam turbines, comprising the following steps: S1. Run the centripetal turbine prototype under the conditions of set inlet total temperature, inlet total pressure, outlet back pressure, mass flow rate and speed. Obtain the temperature, pressure, flow rate, speed and output power data at the turbine inlet and outlet through experimental measurement, and calculate the isentropic efficiency and total pressure loss. S2. Establish the energy conversion relationship in the expansion stage of the Brayton cycle, and use the Euler turbine equation to describe the rotor's work mechanism; S3. Key thermodynamic, aerodynamic and mechanical parameters during turbine operation are collected synchronously, and effective samples are screened using steady-state criteria to construct an experimental sample library. S4. Based on the actual geometric structure of the test prototype, establish a three-dimensional fluid computational domain, divide the computational domain into meshes, and map the test conditions into numerical model boundary conditions. S5. Solve the mass, momentum, and energy conservation equations for compressible flow in a three-dimensional computational domain, and couple them together. SST k-ωTurbulence model is used to solve for flow heat transfer; S6. Extract the temperature field, pressure field, total pressure field, velocity field, Mach number distribution, vorticity field, turbulent kinetic energy distribution, and wall shear stress distribution inside the turbine. Calculate the vorticity vector, viscous dissipation rate, and the proportion of each component loss in the total pressure loss. Establish the correspondence between flow field structure changes, local loss formation, and macroscopic efficiency reduction to determine the dominant loss source. Compare the CFD prediction results with the experimental results for each operating condition. When the error exceeds the threshold, correct the parameters and re-execute the CFD solution until the convergence requirement is met, thus achieving targeted structural optimization.

[0006] Preferably, S1 converts the measured raw operating data such as temperature, pressure, and flow rate into quantitative indicators that can evaluate turbine performance, including calculating the experimental isentropic efficiency, total pressure loss, and actual outlet enthalpy under wet steam conditions. The experimental isentropic efficiency is used to characterize the turbine's energy conversion capability, and its calculation formula is as follows: ; in, To test isentropic efficiency, Total enthalpy at the entrance. This represents the total enthalpy of actual exports. The total enthalpy at the ideal isentropic outlet under the same inlet entropy and outlet pressure; Total pressure loss characterizes the irreversible loss of mechanical energy during the flow of the working fluid, and includes absolute total pressure loss and total pressure loss coefficient; among which, absolute total pressure loss characterizes the total pressure difference between the turbine inlet and outlet: ; in, For total pressure loss, For the total pressure at the turbine inlet, Total turbine outlet pressure; The total pressure loss coefficient is used to characterize the degree of total pressure loss in a normalized form, facilitating cross-sectional comparisons between different inlet pressures, mass flow rates, and rotational speeds. The calculation formula is as follows: ; In the formula, This is the total pressure loss coefficient; The actual enthalpy of the steam outlet is used to characterize the thermal state of the turbine outlet under wet steam conditions. The calculation formula is as follows: ; in, This represents the actual enthalpy value at the steam outlet. For saturated water enthalpy, For latent heat of vaporization, The outlet dryness is determined by the following methods: in experimental scenarios, it is calculated by back-calculating based on the outlet temperature and pressure combined with the actual physical properties of water vapor, or by converting it from the measured data of outlet steam condensation; in CFD simulation scenarios, it is calculated by a coupled wet steam non-equilibrium phase change model.

[0007] Preferably, in S2, the physical mechanism of centripetal steam turbine expansion work based on the Brayton cycle is constructed, clarifying the conversion relationship between the enthalpy drop of the working fluid and the rotor shaft work, as well as the turbine expansion intensity. This includes calculating the actual specific work per unit mass of working fluid, the Euler turbine specific work, and the turbine expansion pressure ratio. Specific formulas include: The formula for calculating the actual work done per unit mass of working fluid is: ; in, The actual work done by a unit mass of working fluid in the turbine; Total enthalpy at turbine inlet; Total enthalpy at turbine outlet; The formula for calculating the work done by an Euler turbine is: ; in, Work done by the Euler turbine; , These are the rotor inlet and outlet circumferential velocities, respectively. , These are the circumferential components of the absolute velocity of the working fluid at the rotor inlet and outlet, respectively. The formula for calculating the turbine expansion pressure ratio is: ; in, This refers to the turbine expansion pressure ratio; Total pressure at the turbine inlet; The total pressure at the turbine outlet.

[0008] Preferably, S3 employs high-frequency multi-channel synchronous sampling technology to synchronously collect key parameters during turbine operation, including inlet total pressure, inlet total temperature, outlet back pressure, outlet temperature, mass flow rate, rotational speed, output power, wall temperature, and steam condensation rate, under a unified time reference. The collected raw operating data is used to calculate the working fluid mass flow rate, effective output power, and perform steady-state verification. Valid test samples are obtained through steady-state criterion screening. The performance parameters, operating condition labels, and timestamps of the valid samples are associated and stored to construct a test sample library. Specific calculation formulas include: The working fluid mass flow rate is calculated based on the cross-sectional parameters to determine the steam flow rate in the pipeline. The calculation formula is as follows: ; in, For the working fluid mass flow rate; The density of the inlet working fluid; To measure the effective area of ​​the cross-section; The average velocity of the working fluid across the cross section; The effective output power, based on the power generation and torque testing scenarios, is calculated using the following formula: Power generation scenario: ; Torque test scenario: ; in, For effective output power; This refers to the voltage at the generator terminal. This refers to the current at the generator end; For generator efficiency; This refers to the shaft end torque; The angular velocity of the shaft; The formula for determining steady state of data is: ; in, For the first in the steady-state window Each sample value; This represents the average value of the parameters within the sampling window. This represents the total number of sampling points; This is the preset steady-state allowable fluctuation threshold.

[0009] Preferably, in S4, a three-dimensional fluid computational domain is established based on the turbine's geometric parameters, the computational domain is divided into partitioned meshes, and the experimental conditions are mapped to the boundary conditions of the numerical model. Turbine geometry parameters include volute cross-sectional dimensions, flow channel curvature, throat area, outlet diffuser continuity, angle and cross-sectional transition shape, guide vane outlet angle, rotor inlet relative flow angle, blade tip radial clearance, blade profile, and turbine hub diameter; a complete three-dimensional fluid computational domain is established, including the volute, guide vanes, rotor, blade tip radial clearance, outlet diffuser, and exhaust section. During mesh generation, local refinement is applied to the leading edge, trailing edge, tip clearance, endwall boundary layer, and high-pressure gradient regions of the blade. The formula for calculating the dimensionless wall distance is: ; in, The distance is a dimensionless wall distance; This is the normal distance from the center of the first-layer mesh to the wall. The kinematic viscosity of the working fluid; Let be the friction speed, and , This refers to the wall shear stress. The density of the working fluid; The inlet total pressure, inlet total temperature, mass flow rate, rotational speed, outlet back pressure, and wall thermal boundary obtained from the experiment are simultaneously mapped to the boundary conditions of the CFD model. The experimental-simulation boundary condition mapping relationship is then as follows: ; in, To measure boundary parameters in the experiment, These are the boundary parameters of the simulation model; ω is the rotor angular velocity.

[0010] Preferably, in S5, the mass conservation equation, momentum conservation equation, and energy conservation equation for compressible flow are solved simultaneously within the three-dimensional fluid computational domain to complete the coupled solution of flow and heat transfer. Specifically, the mass conservation equation formula is as follows: ; in, For the working fluid density, For time, The working fluid velocity vector; The equation for the conservation of momentum is: ; in, For fluid pressure, It is the viscous stress tensor; The energy conservation equation is used to couple the heat transfer effect and the viscous dissipation effect in the flow process, and the formula is: ; in, The specific heat capacity of the working fluid at constant pressure For the working fluid temperature, The thermal conductivity of the working fluid is This is a viscous dissipation term; The solution process couples the actual physical property model of water vapor with k-ω or SST k-ω The working fluid properties are dynamically updated using a realistic water vapor property function in response to local pressure and temperature. A turbulence model is used to describe the rotating turbulent flow characteristics inside the turbine. After solving, the total pressure loss inside the turbine is decoupled based on the flow field calculation results, decomposing the macroscopic total pressure loss into the sum of local losses from multiple sources. The update formula for the water vapor property model is as follows: ; In the formula, Dynamic viscosity; It is a specific heat at constant pressure; Enthalpy; These are the actual physical property functions of water vapor; For local static pressure, Localized static temperature; k-ω or SST k-ω Turbulent flow is described by solving the turbulent kinetic energy transport equation and the specific dissipation rate transport equation, where the turbulent kinetic energy transport equation is: ; The specific dissipation rate transport equation is: ; in, For turbulent kinetic energy, For specific dissipation rate, For turbulent kinetic energy generation, For turbulent viscosity, , , , , All are constants of the turbulence model; After solving, a one-dimensional link is established between the volute, guide vanes, nozzle, rotor impeller, and outlet diffuser section. The internal turbine losses are then divided into outlet loss, tip clearance loss, nozzle loss, incident loss, channel loss, trailing edge loss, and impeller friction loss as the main losses. Among these, outlet loss, tip clearance loss, nozzle loss, and incident loss are the dominant losses affecting isentropic efficiency and total pressure loss, while channel loss, trailing edge loss, and impeller friction loss are considered auxiliary losses. The corresponding decomposition formulas are as follows: ; in, To reduce the total enthalpy loss inside the turbine, Losses due to exports; This is due to tip clearance loss; For nozzle loss; For incident loss; This is due to channel loss; For trailing edge loss; This is the loss due to friction of the wheel.

[0011] Preferably, in S6, based on the flow heat transfer solution obtained in S5, multi-dimensional flow field parameters inside the turbine are extracted and flow field-loss-efficiency correlation mechanism analysis is carried out. The correspondence between flow field structure change, local loss formation and macro efficiency decrease is established, and the dominant loss source and corresponding structural optimization direction under each working condition are obtained. Multi-dimensional flow field parameters inside the turbine are extracted, including temperature field, pressure field, total pressure field, velocity field, Mach number distribution, vorticity field, turbulent kinetic energy distribution, and wall shear stress distribution. Regarding the pressure field, the locations of total pressure attenuation at the volute outlet, guide vane throat, rotor inlet, blade tip clearance, and outlet diffuser section are identified to determine the concentrated areas of total pressure loss. Regarding the temperature field, the correlation between expansion cooling, wall heat transfer, local temperature rise, and steam condensation risk is analyzed, and the wet steam state in the low-temperature, low-pressure region is identified for the working fluid. Regarding the vorticity field, the structures of blade leading-edge impact vortices, endwall secondary vortices, blade tip leakage vortices, wake vortices, and outlet vortices are identified to analyze their impact on channel blockage, energy dissipation, and efficiency reduction. Based on the above analysis, the proportion of various losses under different geometric structures and different working conditions is ranked to determine the dominant loss sources.

[0012] Preferably, in S6, the correspondence between the flow field structure and local losses is established by calculating the vorticity vector, viscous dissipation rate, proportion of single-type losses, and thermal conductivity heat flux density; the vorticity vector is used to characterize the rotation intensity of fluid micro-elements and the vortex system structure, and the calculation formula is: ; in, The vorticity vector. For spatial differential operators, The working fluid velocity vector; Viscous dissipation rate is used to quantify the degree of energy dissipation in a flow process. The calculation formula is as follows: ; in, For viscous dissipation rate, It is the viscous stress tensor; Let be the velocity gradient tensor; where For tensor double dot product operation, it means multiplying and summing the corresponding components of two second-order tensors, which is used to characterize the internal friction energy dissipation effect generated by the coupling of viscous stress and fluid velocity gradient. The percentage of single-type losses is used to identify the dominant loss source affecting efficiency, and the calculation formula is as follows: ; in, For the first The proportion of this type of loss in the total pressure loss. For the first Localized total pressure loss; This is to reduce the total pressure loss inside the turbine. Thermal conductivity and heat flux density are used to analyze the heat transfer and temperature field evolution of walls. The calculation formula is as follows: ; in, For thermal conductivity heat flux density, Thermal conductivity, For temperature gradient.

[0013] Preferably, in S6, the isentropic efficiency, total pressure loss, outlet temperature, outlet pressure, mass flow rate and output power are compared under each operating condition, the error between simulation and experiment is calculated and the parameters are corrected. The isentropic efficiency error determination formula is used to limit the range of efficiency deviation between simulation and experiment. The formula is as follows: ; in, This represents the relative error of isentropic efficiency. For CFD prediction of isentropic efficiency, To test isentropic efficiency; The preset isentropic efficiency allowable error threshold; The relative error of total pressure loss is used to quantify the simulation deviation of total pressure loss, and the calculation formula is as follows: ; in, This represents the relative error of the total pressure loss. For CFD prediction of total pressure loss, The total pressure loss was measured in the experiment; A comprehensive error objective function is constructed to integrate multiple types of index errors. Parameters are iteratively corrected based on the error gradient. The correction formula is as follows: ; in, These are the corrected parameters. To correct the parameters before, To correct the step size, The objective function is the comprehensive error. Furthermore, the formula for calculating the comprehensive error objective function is: ; in, , , , , , These are the weighting coefficients. For CFD prediction of isentropic efficiency, To test the isentropic efficiency; For CFD prediction of total pressure loss, The total pressure loss was measured in the experiment; For CFD prediction of outlet temperature, To test and measure the outlet temperature; For CFD prediction of mass flow rate, To test and measure the mass flow rate; For CFD prediction of output power, To test and measure the output power; For CFD prediction of export dryness, The outlet dryness was measured in the experiment.

[0014] Preferably, the centripetal steam turbine isentropic thermal efficiency test and optimization system based on the above method includes: a gas source supply component, a pretreatment and parameter measurement component, a centripetal turbine test piece, a power generation and load component, and a parameter acquisition component electrically connected to each component, connected in sequence. The gas supply component includes a gas compressor and a gas storage tank connected in sequence, which are used to generate compressed water vapor working fluid and reduce pressure pulsation, and output a stable water vapor test working fluid. The pretreatment and parameter measurement components include a valve control unit, a filter dryer, a flow meter, and a pressure transmitter connected in sequence. These components are used to achieve manual safety isolation, gas path opening and closing, operating condition adjustment, working fluid purification, and to collect the water vapor working fluid flow rate and inlet pressure parameters entering the centripetal turbine test specimen. The input end of the centripetal turbine test piece is connected to the pretreatment and parameter measurement components, and the output shaft is connected to the power generation and load components via a speed and torque sensor, which is used to convert the pressure energy and kinetic energy of the water vapor working fluid into the mechanical energy output by the rotor shaft. The power generation and load components include a generator and an adjustable electrical load connected by a drive, used to convert mechanical energy into electrical energy and simulate different electrical load conditions; The parameter acquisition component includes a speed and torque sensor, an ammeter, and a voltmeter. The speed and torque sensor is connected in series with the transmission shaft between the turbine test piece and the generator. The ammeter is connected in series with the generator circuit between the generator and the adjustable electrical load. The voltmeter is connected in parallel across the adjustable electrical load. The mechanical parameters of the transmission shaft and the electrical parameters of the generator circuit are collected synchronously, respectively.

[0015] Therefore, the present invention employs the above-mentioned centripetal steam turbine entropy efficiency test and CFD optimization method, which has the following beneficial effects: 1. By decomposing the total pressure loss inside the turbine into multiple quantifiable local losses, such as angle of attack loss, secondary flow loss in the channel, radial clearance leakage loss at the blade tip, disc friction loss, outlet residual velocity / wake loss, nozzle loss, and additional loss due to water vapor phase change, the dominant dissipation sources under various operating conditions are accurately identified. This transforms the optimization method from traditional empirical trial-and-error based on macroscopic efficiency to targeted structural adjustments targeting the root causes of various losses. Experiments and simulations have verified that the total pressure loss inside the turbine can be reduced by approximately 2% after optimization. Within the mass flow rate range of 0.45–0.65 kg / s, the entropy efficiency of the turbine is stably maintained at 0.72–0.82, achieving the dual effects of improved energy conversion efficiency and low total pressure loss operation across the entire operating range.

[0016] 2. In the CFD solution process, a realistic steam property model is coupled with the non-equilibrium phase change mechanism of wet steam. Based on local static pressure and static temperature, the density, dynamic viscosity, isobaric specific heat capacity, thermal conductivity, and specific enthalpy of the working fluid are dynamically updated. This accurately analyzes the abrupt changes in properties, latent heat release, and local non-equilibrium condensation effects during the transonic expansion of steam. This completely overcomes the shortcomings of traditional loss models and property assumptions for dry gases such as air and supercritical carbon dioxide in adapting to steam conditions. Compared with traditional simulation models based on ideal gas assumptions, the systematic deviation of performance prediction under steam conditions is significantly reduced. While achieving high isentropic efficiency, the total pressure loss is stably maintained at approximately 1.0%–2.5%, and less than 3% throughout the process. These results demonstrate that this invention can achieve a synergistic effect of high isentropic efficiency and low total pressure loss under high-quality flow conditions.

[0017] 3. A closed-loop calibration process involving the entire experimental data process was established. By comparing the core performance indicators of simulation and experiment under each working condition and iteratively correcting the model parameters, a high degree of consistency between experimental and simulation results was achieved. This solved the problem of large prediction deviations under wide working conditions in the traditional single-point verification mode, and significantly improved the reliability of performance prediction under variable speed, variable flow, and variable pressure ratio conditions, so that simulation results can directly guide the optimization of engineering structures.

[0018] 4. By synchronously acquiring key thermodynamic, aerodynamic, and electrical parameters of turbine operation through multiple channels and filtering out transient fluctuation data using a steady-state window, a highly reliable experimental sample library was constructed. This provided a unified and reliable physical benchmark for CFD model boundary setting, error calibration, and optimization effect verification, ensuring the reproducibility and engineering applicability of the entire optimization process.

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0020] Figure 1 This invention provides an overall technical roadmap for an entropy efficiency test and CFD optimization method for centripetal steam turbines. Figure 2 This invention provides a flowchart of the centripetal steam turbine geometric parameter control and step-by-step CFD optimization method in the entropy efficiency test and CFD optimization of centripetal steam turbines. Figure 3 This invention provides a CFD mechanism calculation optimization process and a decoupling flowchart for turbine total pressure loss in a centripetal steam turbine isotropic efficiency test and CFD optimization method. Figure 4 A schematic diagram of the connection structure of a centripetal turbine test bench for a centripetal steam turbine entropy efficiency optimization system provided by the present invention. Figure 5 This invention provides a schematic diagram of the key experimental component structure of a centripetal steam turbine for optimizing entropy-thermal efficiency in a centripetal steam turbine. Figure 5 (a) is a side view of the turbine volute. Figure 5 (b) is a cross-sectional view of the turbine volute; Figure 5 (c) is the assembly drawing of the turbine engine; Figure 6 A comparison of experimental and simulation results of the evolution of the entropy efficiency and total pressure loss of a centripetal steam turbine as a function of operating conditions in an isentropic thermal efficiency optimization system provided by this invention. Figure 7 The invention provides a three-dimensional simulation result of the total pressure of a centripetal steam turbine under different flow rates, based on an entropy efficiency test and CFD optimization method. Figure 7 (a) is a simulation diagram of the total pressure distribution under the condition of low mass flow rate (0.45 kg / s). Figure 7 (b) is a simulation diagram of total pressure distribution under high-quality flow (0.60 kg / s) conditions; Figure 8 The invention provides a three-dimensional simulation result of the total temperature of a centripetal steam turbine under different flow rates, based on an entropy efficiency test and CFD optimization method. Figure 8 (a) is a simulation diagram of the total temperature distribution under low mass flow rate (0.45 kg / s) conditions. Figure 8 (b) is a simulation diagram of the total temperature distribution under high-quality flow (0.60 kg / s) conditions.

[0021] Figure Labels 1-Gas compressor; 2-Gas tank; 3-Stop valve; 4-Solenoid control valve; 5-Filter dryer; 6-Flow meter; 7-Pressure transmitter; 8-Centrifugal turbine test piece; 9-Generator; 10-Adjustable electrical load; 11-Speed ​​and torque sensor; 12-Ammeter; 13-Voltmeter. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0023] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0024] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0025] Based on the above analysis, this invention is designed. (See appendix.) Figures 1-8 A centripetal steam turbine entropy efficiency test and CFD optimization method includes the following steps: S1. Run the centripetal turbine prototype under the conditions of set inlet total temperature, inlet total pressure, outlet back pressure, mass flow rate and speed. Obtain the temperature, pressure, flow rate, speed and output power data at the turbine inlet and outlet through experimental measurement, and calculate the isentropic efficiency and total pressure loss. S1 transforms the measured raw operating data, such as temperature, pressure, and flow rate, into quantitative indicators that can evaluate turbine performance, including calculating the experimental isentropic efficiency, total pressure loss, and actual outlet enthalpy under wet steam conditions. The experimental isentropic efficiency characterizes the turbine's energy conversion capability, and its calculation formula is as follows: ; in, To test isentropic efficiency, Total enthalpy at the entrance. This represents the total enthalpy of actual exports. The total enthalpy at the ideal isentropic outlet under the same inlet entropy and outlet pressure; Total pressure loss characterizes the irreversible loss of mechanical energy during the flow of the working fluid, and includes absolute total pressure loss and total pressure loss coefficient; among which, absolute total pressure loss characterizes the total pressure difference between the turbine inlet and outlet, and is calculated using the following formula: ; in, For total pressure loss, For the total pressure at the turbine inlet, Total turbine outlet pressure; The total pressure loss coefficient is used to characterize the degree of total pressure loss in a normalized form, facilitating cross-sectional comparisons between different inlet pressures, mass flow rates, and rotational speeds. The calculation formula is as follows: ; In the formula, This is the total pressure loss coefficient; The actual enthalpy of the steam outlet is used to characterize the thermal state of the turbine outlet under wet steam conditions. The calculation formula is as follows: ; in, This represents the actual enthalpy value at the steam outlet. For saturated water enthalpy, For latent heat of vaporization, The outlet dryness is determined by the following methods: in experimental scenarios, it is calculated by back-calculating based on the outlet temperature and pressure combined with the actual physical properties of water vapor, or by converting it from the measured data of outlet steam condensation; in CFD simulation scenarios, it is calculated by a coupled wet steam non-equilibrium phase change model.

[0026] S2. Establish the energy conversion relationship in the expansion stage of the Brayton cycle, and use the Euler turbine equation to describe the rotor's work mechanism; S2 establishes the physical mechanism of centripetal steam turbine expansion work based on the Brayton cycle, clarifying the conversion relationship between working fluid enthalpy drop and rotor shaft work, as well as the turbine expansion intensity. This includes calculating the actual specific work per unit mass of working fluid, the Euler turbine specific work, and the turbine expansion pressure ratio. Specific formulas include: The formula for calculating the actual work done per unit mass of working fluid is: ; in, The actual work done by a unit mass of working fluid in the turbine; Total enthalpy at turbine inlet; Total enthalpy at turbine outlet; The formula for calculating the work done by an Euler turbine is: ; in, Work done by the Euler turbine; , These are the rotor inlet and outlet circumferential velocities, respectively. , These are the circumferential components of the absolute velocity of the working fluid at the rotor inlet and outlet, respectively. The formula for calculating the turbine expansion pressure ratio is: ; in, This refers to the turbine expansion pressure ratio; Total pressure at the turbine inlet; The total pressure at the turbine outlet.

[0027] S3. Key thermodynamic, aerodynamic and mechanical parameters during turbine operation are collected synchronously, and effective samples are screened using steady-state criteria to construct an experimental sample library. S3 employs high-frequency multi-channel synchronous sampling technology to synchronously acquire key parameters during turbine operation, including inlet total pressure, inlet total temperature, outlet back pressure, outlet temperature, mass flow rate, rotational speed, output power, wall temperature, and steam condensation rate, under a unified time reference. The acquired raw operating data is used to calculate the working fluid mass flow rate, effective output power, and perform steady-state verification. Valid test samples are selected based on steady-state criteria, and their performance parameters, operating condition labels, and timestamps are associated and stored to construct a test sample library. Specific calculation formulas include: The working fluid mass flow rate is calculated based on the cross-sectional parameters to determine the steam flow rate in the pipeline. The calculation formula is as follows: ; in, For the working fluid mass flow rate; The density of the inlet working fluid; To measure the effective area of ​​the cross-section; The average velocity of the working fluid across the cross section; The effective output power, based on the power generation and torque testing scenarios, is calculated using the following formula: Power generation scenario: ; Torque test scenario: ; in, For effective output power; This refers to the voltage at the generator terminal. This refers to the current at the generator end; For generator efficiency; This refers to the shaft end torque; The angular velocity of the shaft; The formula for determining steady state of data is: ; in, For the first in the steady-state window Each sample value; This represents the average value of the parameters within the sampling window. This represents the total number of sampling points; This is the preset steady-state allowable fluctuation threshold.

[0028] For each set of valid operating conditions, the system records the average value, variance, fluctuation amplitude, and operating condition label, and stores the measured parameters in association with geometric parameters, valve opening, load state, and test timestamp. This sample library is used to calculate the actual isentropic efficiency and total pressure loss, and to provide real boundary conditions for the CFD model and a reference for subsequent experimental verification.

[0029] S4. Based on the actual geometric structure of the test prototype, establish a three-dimensional fluid computational domain, divide the computational domain into meshes, and map the test conditions into numerical model boundary conditions. In S4, a three-dimensional fluid computational domain is established based on the turbine's geometric parameters. The computational domain is divided into partitioned meshes, and the experimental conditions are mapped to the boundary conditions of the numerical model. Turbine geometry parameters include volute cross-sectional dimensions, flow channel curvature, throat area, outlet diffuser continuity, angle and cross-sectional transition shape, guide vane outlet angle, rotor inlet relative flow angle, blade tip radial clearance, blade profile, and turbine hub diameter; a complete three-dimensional fluid computational domain is established, including the volute, guide vanes, rotor, blade tip radial clearance, outlet diffuser, and exhaust section. During geometric modeling, ensure that the leading edge, trailing edge, endwall, tip radial clearance, and flow channel bending area of ​​the blade are consistent with the experimental prototype to avoid deviation between simulation results and experimental results due to geometric simplification; During mesh generation, local refinement is applied to the leading edge, trailing edge, tip clearance, endwall boundary layer, and high-pressure gradient regions of the blade. For the main flow channel, structured or hybrid meshes can be used. The formula for calculating the dimensionless wall distance is: ; in, The distance is a dimensionless wall distance; This is the normal distance from the center of the first-layer mesh to the wall. The kinematic viscosity of the working fluid; Let be the friction speed, and , This refers to the wall shear stress. The density of the working fluid; The inlet total pressure, inlet total temperature, mass flow rate, rotational speed, outlet back pressure, and wall thermal boundary obtained from the experiment are simultaneously mapped to the boundary conditions of the CFD model. The experimental-simulation boundary condition mapping relationship is then as follows: ; in, To measure boundary parameters in the experiment, These are the boundary parameters of the simulation model; ω is the rotor angular velocity.

[0030] S5. Solve the mass, momentum, and energy conservation equations for compressible flow in a three-dimensional computational domain, and couple them together. k-ω or SST k-ω To solve for flow heat transfer; In S5, the mass conservation equation, momentum conservation equation, and energy conservation equation for compressible flow are solved simultaneously within the three-dimensional fluid computational domain to complete the coupled solution of flow and heat transfer. Specifically, the mass conservation equation formula is as follows: ; in, For the working fluid density, For time, The working fluid velocity vector; The equation for the conservation of momentum is: ; in, For fluid pressure, It is the viscous stress tensor; The energy conservation equation is used to couple the heat transfer effect and the viscous dissipation effect in the flow process, and the formula is: ; in, The specific heat capacity of the working fluid at constant pressure For the working fluid temperature, The thermal conductivity of the working fluid is This is a viscous dissipation term; The solution process couples the actual physical property model of water vapor with k-ω or SST k-ω The working fluid properties are dynamically updated using a realistic water vapor property function in response to local pressure and temperature. A turbulence model is used to describe the rotating turbulent flow characteristics inside the turbine. After solving, the total pressure loss inside the turbine is decoupled based on the flow field calculation results, decomposing the macroscopic total pressure loss into the sum of local losses from multiple sources. The update formula for the water vapor property model is as follows: ; In the formula, Dynamic viscosity; It is a specific heat at constant pressure; Enthalpy; These are the actual physical property functions of water vapor; For local static pressure, Localized static temperature; k-ω or SST k-ω Turbulent flow is described by solving the turbulent kinetic energy transport equation and the specific dissipation rate transport equation, where the turbulent kinetic energy transport equation is: ; The specific dissipation rate transport equation is: ; in, For turbulent kinetic energy, For specific dissipation rate, For turbulent kinetic energy generation, For turbulent viscosity, , , , , All are constants of the turbulence model; For steam working fluid, the IAPWS-IF97 real steam property library and wet steam phase change source terms can be further coupled to update parameters such as density, specific heat, viscosity, and thermal conductivity as temperature and pressure change. After solving, a one-dimensional link is established between the volute, guide vanes, nozzle, rotor impeller, and outlet diffuser section. The internal turbine losses are then divided into outlet loss, tip clearance loss, nozzle loss, incident loss, channel loss, trailing edge loss, and impeller friction loss as the main losses. Among these, outlet loss, tip clearance loss, nozzle loss, and incident loss are the dominant losses affecting isentropic efficiency and total pressure loss, while channel loss, trailing edge loss, and impeller friction loss are considered auxiliary losses. The corresponding decomposition formulas are as follows: ; in, To reduce the total enthalpy loss inside the turbine, Export losses; This is due to tip clearance loss; For nozzle loss; For incident loss; This is due to channel loss; For trailing edge loss; This is the loss due to friction of the wheel.

[0031] Specifically, the expansion formulas for the four main types of losses—exit loss, tip clearance loss, channel loss, and incident loss—are as follows: The exit loss characterizes the residual velocity loss resulting from the failure to effectively recover the remaining kinetic energy at the exit diffuser or subsequent flow channels. The calculation formula is as follows: ; in, For export losses, The average absolute velocity at the turbine exit section; Tip clearance loss is used to characterize the leakage loss caused by the pressure difference across the blade tip driving the leakage flow and mixing with the mainstream. The calculation formula is as follows: ; in, For tip clearance loss, This is the tip leakage correction factor. This is the radial clearance at the blade tip. For Ye Gao, The pressure difference across the blade tip. The density of the working fluid; Channel loss is used to characterize the flow dissipation generated during impeller wall friction, endwall secondary flow, and mainstream bends. The calculation formula is as follows: ; in, For channel loss, The coefficient of frictional resistance of the wall surface. The equivalent length of the leaf passage. The hydraulic diameter of the impeller. This is the secondary flow loss coefficient. The average relative velocity of the blade passage; Incident loss is used to characterize the leading-edge impact and local separation loss caused by the mismatch between the rotor inlet flow direction and the blade inlet metal angle. The calculation formula is: ; in, For incident loss, The relative velocity at the rotor inlet. This is the actual relative flow angle at the rotor inlet. The inlet metal angle of the blade; The proportion of the above four types of dominant losses to the total losses is determined by the following formula: ; in, The proportion of losses in four main categories; when When the loss is ≥85%, the main focus is on the outlet loss, tip clearance loss, channel loss and incident loss, and the structural optimization is prioritized around the outlet diffuser section, tip radial clearance, flow passage structure and rotor inlet angle.

[0032] Different loss terms correspond to different structural regions and flow mechanisms: angle of attack loss is mainly related to the mismatch between the inlet airflow angle and the blade mounting angle; channel loss is mainly caused by wall friction and secondary flow; tip clearance leakage loss is driven by the pressure difference on both sides of the rotor blade tip; residual velocity loss reflects that the outlet kinetic energy is not fully recovered.

[0033] S6. Extract the temperature field, pressure field, total pressure field, velocity field, Mach number distribution, vorticity field, turbulent kinetic energy distribution, and wall shear stress distribution inside the turbine. Calculate the vorticity vector, viscous dissipation rate, and the proportion of each component loss in the total pressure loss. Establish the correspondence between flow field structure changes, local loss formation, and macroscopic efficiency reduction to determine the dominant loss source. Compare the CFD prediction results with the experimental results for each operating condition. When the error exceeds the threshold, correct the parameters and re-execute the CFD solution until the convergence requirement is met, thus achieving targeted structural optimization.

[0034] In S6, based on the flow heat transfer solution obtained in S5, multi-dimensional flow field parameters inside the turbine are extracted and flow field-loss-efficiency correlation mechanism analysis is carried out. The correspondence between flow field structure change, local loss formation and macro efficiency decrease is established, and the dominant loss source and corresponding structural optimization direction under each working condition are obtained. Multi-dimensional flow field parameters inside the turbine are extracted, including temperature field, pressure field, total pressure field, velocity field, Mach number distribution, vorticity field, turbulent kinetic energy distribution, and wall shear stress distribution. Regarding the pressure field, the locations of total pressure attenuation at the volute outlet, guide vane throat, rotor inlet, blade tip clearance, and outlet diffuser section are identified to determine the concentrated areas of total pressure loss. Regarding the temperature field, the correlation between expansion cooling, wall heat transfer, local temperature rise, and steam condensation risk is analyzed, and the wet steam state in the low-temperature, low-pressure region is identified for the working fluid. Regarding the vorticity field, the structures of blade leading-edge impact vortices, endwall secondary vortices, blade tip leakage vortices, wake vortices, and outlet vortices are identified to analyze their impact on channel blockage, energy dissipation, and efficiency reduction. Based on the above analysis, the proportion of various losses under different geometries and operating conditions is ranked to identify the dominant loss sources. This result guides subsequent structural adjustments, such as reducing tip clearance, optimizing guide vane exit angle, smoothing bend curvature, improving diffuser structure, or adjusting exit flow direction.

[0035] In S6, the correspondence between the flow field structure and local losses is established by calculating the vorticity vector, viscous dissipation rate, proportion of single-type losses, and thermal conductivity heat flux density. The vorticity vector is used to characterize the rotation intensity of fluid micro-elements and the vortex structure, and its calculation formula is as follows: ; in, The vorticity vector. For spatial differential operators, The working fluid velocity vector; Viscous dissipation rate is used to quantify the degree of energy dissipation in a flow process. The calculation formula is as follows: ; in, For viscous dissipation rate, It is the viscous stress tensor; Let be the velocity gradient tensor; where For tensor double dot product operation, it means multiplying and summing the corresponding components of two second-order tensors, which is used to characterize the internal friction energy dissipation effect generated by the coupling of viscous stress and fluid velocity gradient. The percentage of single-type losses is used to identify the dominant loss source affecting efficiency, and the calculation formula is as follows: ; in, For the first The proportion of this type of loss in the total pressure loss. For the first Localized total pressure loss; This is to reduce the total pressure loss inside the turbine. Thermal conductivity and heat flux density are used to analyze the heat transfer and temperature field evolution of walls. The calculation formula is as follows: ; in, For thermal conductivity heat flux density, Thermal conductivity, For temperature gradient.

[0036] In S6, the isentropic efficiency, total pressure loss, outlet temperature, outlet pressure, mass flow rate and output power are compared for each operating condition. The error between simulation and experiment is calculated and the parameters are corrected. The isentropic efficiency error determination formula is used to limit the range of efficiency deviation between simulation and experiment. The formula is as follows: ; in, This represents the relative error of isentropic efficiency. For CFD prediction of isentropic efficiency, To test isentropic efficiency; The preset isentropic efficiency allowable error threshold; The relative error of total pressure loss is used to quantify the simulation deviation of total pressure loss, and the calculation formula is as follows: ; in, This represents the relative error of the total pressure loss. For CFD prediction of total pressure loss, The total pressure loss was measured in the experiment; The normalized RMSE consistency index is used to comprehensively evaluate the degree of agreement between CFD simulation results and experimental results under a wide range of operating conditions. Its calculation formula is as follows: ; ; in, For multi-condition root mean square error, For normalization Consistency indicators To verify the number of working conditions, For the first CFD prediction values ​​under various operating conditions For the corresponding experimental values, and These are the maximum and minimum values ​​of the corresponding index in the test sample, respectively; when When the value is ≥0.97, the CFD simulation results are considered to have a high degree of consistency with the experimental results, and this index is used as the basis for evaluating model iteration convergence and prediction reliability.

[0037] A comprehensive error objective function is constructed to integrate multiple types of index errors. Parameters are iteratively corrected based on the error gradient. The correction formula is as follows: ; in, These are the corrected parameters. To correct the parameters before, To correct the step size, The objective function is the comprehensive error. Furthermore, the formula for calculating the comprehensive error objective function is: ; in, , , , , , These are the weighting coefficients. For CFD prediction of isentropic efficiency, To test the isentropic efficiency; For CFD prediction of total pressure loss, The total pressure loss was measured in the experiment; For CFD prediction of outlet temperature, To test and measure the outlet temperature; For CFD prediction of mass flow rate, To test and measure the mass flow rate; For CFD prediction of output power, To test and measure the output power; For CFD prediction of export dryness, The test measures the outlet dryness. If the error is mainly manifested in the overall efficiency being too high or too low, the loss model, wall roughness, leakage gap, or power generation efficiency conversion parameters should be corrected first. If the error is concentrated in a specific pressure ratio or speed range, the inlet boundary, outlet back pressure, or rotation domain settings should be corrected. If the error mainly occurs in the prediction of steam outlet temperature or dryness, the steam properties, thermal boundary, or condensation model parameters should be corrected.

[0038] The experimental and optimization system for the entropy-dependent thermal efficiency of a centripetal steam turbine based on the above method is described in [reference needed]. Figure 4 As shown, it includes: a gas supply component, a pretreatment and parameter measurement component, a centripetal turbine test specimen, a power generation and load component, and a parameter acquisition component electrically connected to each component, connected in sequence. The gas supply assembly includes a gas compressor 1 and a gas storage tank 2 connected in sequence. The gas compressor 1 serves as the gas supply end of the test bench, used to generate compressed water vapor working fluid with a set pressure and flow rate. The compressed water vapor working fluid first enters the gas storage tank 2, which is used to reduce pressure pulsation at the outlet of the gas compressor 1 and to stabilize and buffer the compressed water vapor working fluid, making the airflow into the subsequent pipeline more stable. The pretreatment and parameter measurement components include a valve control unit, a filter dryer 5, a flow meter 6 and a pressure transmitter 7 connected in sequence, used to realize the opening and closing of the gas path and the adjustment of the operating conditions, the purification of the working fluid, and to collect the working fluid flow rate and inlet pressure parameters entering the centripetal turbine test piece. The valve control unit includes a shut-off valve 3 and a solenoid control valve 4 connected in sequence. The inlet of the shut-off valve 3 is connected to the outlet of the gas storage tank 2, and is used to realize the manual opening and closing of the gas pipeline and safety isolation. The solenoid control valve 4 is used to realize the on / off of the gas path, the opening degree adjustment, and the switching control of different test conditions. The filter dryer 5 is used to remove particulate impurities, oil mist and moisture from the compressed water vapor to prevent impurities from entering the centripetal turbine test piece 8 and causing wear or blockage to the impeller, bearings and internal flow channels. The flow meter 6 is used to measure the gas flow rate before entering the centripetal turbine test piece 8 in real time. The pressure transmitter 7 is used to monitor the pressure status before the inlet of the centripetal turbine test piece 8 in real time. The input end of the centripetal turbine test piece 8 is connected to the pretreatment and parameter measurement assembly, and the output end is connected to the power generation and load assembly for converting the pressure energy and kinetic energy of the working fluid into the mechanical energy output by the rotor shaft. The specific structure of the centripetal turbine test specimen 8 is as follows: Figure 5 As shown, it includes a turbine volute, a volute cross-section flow channel, a turbine hub, and a rotor assembly. The turbine volute is used to uniformly distribute the inlet gas circumferentially to the rotor inlet region, reducing inlet flow unevenness and localized impacts. The volute cross-section flow channel forms a continuous circumferential guide channel, ensuring a relatively stable circumferential velocity component of the working fluid before it enters the rotor. The turbine hub, located at the center, supports the rotor and connects to the shaft. The rotor assembly receives the high-speed working fluid and completes energy conversion.

[0039] The power generation and load assembly includes a generator 9 and an adjustable electrical load 10 connected by a drive, used to convert mechanical energy into electrical energy and simulate different electrical load conditions. The output shaft of the centripetal turbine test specimen 8 is connected to the input shaft of the generator 9 via a coupling. The generator 9 is used to convert the mechanical energy output by the turbine into electrical energy output. The adjustable electrical load 10 is electrically connected to the output end of the generator 9 to simulate the power generation output state under different power load conditions and to realize the load test of the generator output end.

[0040] The parameter acquisition components include a speed and torque sensor 11, an ammeter 12, and a voltmeter 13, which synchronously acquire the mechanical parameters of the transmission shaft system and the electrical parameters of the generator circuit, respectively.

[0041] A speed and torque sensor 11 is connected in series at the coupling between the centripetal turbine test piece 8 and the generator 9 to measure the speed and torque parameters of the transmission shaft system in real time. An ammeter 12 is connected in series in the power supply circuit between the generator 9 and the adjustable electrical load 10 to measure the output current of the generator 9 in real time. A voltmeter 13 is connected in parallel across the adjustable electrical load 10 to measure the voltage across the load in real time. The parameter acquisition unit uses high-frequency multi-channel synchronous sampling technology to synchronously acquire mechanical and electrical parameters for calculating turbine output power, isentropic efficiency, and total voltage drop.

[0042] Data collected synchronously by flow meter 6, pressure transmitter 7, speed and torque sensor 11, ammeter 12, and voltmeter 13 can be used to obtain the operating status of the centripetal turbine test piece 8 under different inlet pressures, different intake flow rates, different speeds, and different loads. This data can be further used to calculate output power, energy conversion efficiency, isentropic efficiency, and total pressure loss, and serve as the experimental basis for subsequent CFD simulation boundary setting, model verification, and structural optimization.

[0043] thus, Figure 4 The test bench shown forms a continuous test chain of "gas source compression - gas storage and pressure stabilization - valve adjustment - filtration and drying - inlet measurement - turbine expansion and work - shaft end speed and torque measurement - power generation loading - electrical parameter acquisition - performance calculation and analysis".

[0044] Embodiment 1 of the present invention: The CFD simulation process is as follows: Figure 2 As shown, the core geometric parameters and structural optimization process are based on the geometry of the prototype, with the volute, guide vanes, rotor impeller, blade tip clearance, flow channel bends, throat area, and outlet diffuser section as the main structural objects.

[0045] First, a three-dimensional fluid computational domain model is performed. Based on the actual geometric structure of the centripetal turbine test specimen, a complete three-dimensional fluid computational domain including the volute, guide vanes, rotor, blade tip clearance, outlet diffuser section, and exhaust section is established. During geometric modeling, it is ensured that the leading edge, trailing edge, endwall, rotor blade tip radial clearance, and flow channel bending area are consistent with the test prototype to avoid deviation between simulation results and experimental results due to geometric simplification.

[0046] Subsequently, mesh generation was performed. A structured mesh was used for the main channel, while local meshing was applied to the leading edge, trailing edge, tip clearance, endwall boundary layer, and high pressure gradient regions to capture the boundary layer, leakage flow, and vortex structure. The near-wall mesh controlled the dimensionless wall distance. satisfy SST k-ω The calculation requirements must be met to ensure the reliability of calculations for wall shear stress, friction loss, and heat exchange.

[0047] In terms of solver setup, a three-dimensional CFD solver is used, coupled with the mass conservation, momentum conservation, and energy conservation equations for compressible flow, and simultaneously coupled... SST k-ω and IAPWS-IF A database of 97 water vapor real-world properties is used to analyze the pressure, temperature, density, velocity, vorticity, and local latent heat release processes during the transonic expansion of water vapor. For the wet steam flow region, a non-equilibrium phase transition model is introduced. Strict convergence criteria are set during the solution process: the root mean square residual of the energy conservation equation must strictly converge to 10. -6 The momentum / continuity equation residuals converge to 10 on the order of magnitude. -5 The order of magnitude is such that the overall inlet and outlet mass flow imbalance rate is less than 0.1%, ensuring the absolute stability of the numerical solution.

[0048] Loss decomposition and targeted optimization logic as follows Figure 3 As shown, the initial loss screening is first completed based on a one-dimensional link, and then the refined total pressure loss decoupling is completed through three-dimensional flow field calculation: First, a one-dimensional link is established between the volute, guide vane, nozzle, rotor impeller and outlet diffuser section, and the internal turbine losses are divided into seven basic losses: incident loss (corresponding to the angle of attack loss in three-dimensional decoupling), nozzle loss, channel loss (corresponding to the secondary flow loss in three-dimensional decoupling), tip clearance loss (corresponding to the tip radial clearance leakage loss in three-dimensional decoupling), outlet loss (corresponding to the outlet residual velocity / wake loss in three-dimensional decoupling), trailing edge loss and impeller friction loss. Among them, incident loss, nozzle loss, tip clearance loss and outlet loss are the dominant losses affecting isentropic efficiency and total pressure loss, while channel loss, trailing edge loss and impeller friction loss are auxiliary losses participating in the comprehensive evaluation. In the three-dimensional flow field refined decoupling stage, the additional loss of water vapor phase change is added on the basis of the above, and finally a complete total pressure loss sub-system is formed. The proportion of each type of loss in the total loss is quantitatively ranked. When the proportion of a certain sub-loss is the highest, the corresponding structural region is determined as the priority optimization object.

[0049] Embodiment 2 of the present invention: See Figures 6-8 As shown, this verifies that the proposed method has the technical advantages of high isentropic efficiency, low total pressure loss, and good consistency between simulation and experiment.

[0050] like Figure 6As shown, the simulation prediction curves and the experimental measured points are highly consistent. The relative errors of the isentropic efficiency, total pressure loss, and outlet temperature are ≤1.5%, ≤2%, and ≤1%, respectively, all meeting the residual verification thresholds set by this method. This fully verifies the predictive reliability of the experimental-simulation closed-loop calibration model. When the mass flow rate increases from approximately 0.45 kg / s to approximately 0.65 kg / s, the isentropic efficiency of the turbine remains at a high level, showing a trend of first increasing and then slightly decreasing: when the mass flow rate is approximately 0.45 kg / s, the isentropic efficiency is approximately 0.72; when the mass flow rate increases to around 0.50 kg / s, 0.55 kg / s, and 0.60 kg / s, the isentropic efficiency increases to approximately 0.77, 0.79, and 0.82, respectively, reaching a peak around 0.60 kg / s; when the mass flow rate continues to increase to around 0.65 kg / s, the isentropic efficiency decreases slightly but remains in the range of 0.78–0.80. Meanwhile, the total pressure loss inside the turbine remained stable at a low level with increasing mass flow rate, increasing only slightly and staying within a reasonable range of 2.0% to 2.5%. The condensation rate was approximately 2.0% at low flow rates, and no sudden increase in condensation occurred in the medium-to-high flow rate range, indicating no significant additional losses caused by unbalanced over-condensation. Furthermore, when the results of the above multiple indicators were comprehensively verified using the normalized RMSE consistency index, the RMSE consistency index reached over 0.97, further demonstrating a good agreement between the simulation and experimental results.

[0051] like Figure 7 As shown, under the low mass flow rate of 0.45 kg / s, the total pressure distribution in the rotor passage is mainly composed of high and low value regions, with relatively small local high total pressure regions, indicating that the pressure energy input and main flow of the working fluid after entering the passage are relatively limited. Under the high mass flow rate of 0.60 kg / s, a more obvious dark-colored high total pressure region appears near the passage inlet and some pressure surfaces, and a relatively continuous total pressure gradient is formed along the passage direction. This indicates that under the high flow rate condition, the pressure energy and momentum carried by the inlet working fluid are more sufficient, which can provide a stronger driving force for the rotor to expand and do work. There is no large-scale turbulent low-pressure backflow region or obvious pressure fault, and the total pressure loss is controlled at a low level.

[0052] like Figure 8 As shown, under the low mass flow rate of 0.45 kg / s, the total temperature distribution inside the blade passage is generally low, mainly concentrated around 490–510 K; under the high mass flow rate of 0.60 kg / s, the total temperature distribution inside the blade passage is in the range of approximately 510–525 K, and the distribution along the flow passage is relatively continuous. This indicates that the thermodynamic state of the working fluid is more stable under high flow rate conditions, and no abnormally low temperature zone or large-area uneven cooling zone appears during the expansion process, which is beneficial to reducing the risk of local supercooling and water vapor condensation.

[0053] This embodiment addresses the waste heat and pressure energy recovery scenario of gas turbines. Through the aforementioned method, it achieves high isentropic efficiency, low total pressure loss, and reliable prediction over a wide range of operating conditions for centripetal steam turbines. It can accurately locate the core structural optimization objects such as blade tip radial clearance, guide vane outlet angle / attack angle, rotor inlet relative flow angle, flow channel curvature, outlet diffuser continuity, and throat area. This provides a quantifiable, verifiable, and iterative engineering optimization method for the design of centripetal steam turbines in gas turbine waste heat and pressure energy recovery equipment.

[0054] In summary, this invention constructs a test-simulation closed-loop optimization system with full participation of experimental data, coupling the real physical properties of water vapor with the phase change mechanism. It decomposes the total pressure loss inside the turbine into traceable component losses and establishes the correlation between the flow field structure and the formation of losses. This achieves precise structural targeted optimization starting from the root cause of the losses. At the same time, through multi-index error comparison and model iteration correction under different operating conditions, it significantly improves the reliability of performance prediction under variable speed, variable flow rate, and variable pressure ratio conditions. While effectively improving the isentropic efficiency of the turbine under all operating conditions, it precisely controls the total pressure loss and wet steam loss. This provides a quantifiable, verifiable, and engineering-promotable optimization method for centripetal steam turbines used for waste heat and pressure energy recovery from gas turbines.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for experimental and CFD optimization of entropy efficiency in centripetal steam turbines, characterized in that, Includes the following steps: S1. Run the centripetal turbine prototype under the conditions of set inlet total temperature, inlet total pressure, outlet back pressure, mass flow rate and speed. Obtain the temperature, pressure, flow rate, speed and output power data at the turbine inlet and outlet through experimental measurement, and calculate the isentropic efficiency and total pressure loss. S1 transforms the measured raw operating data, including temperature, pressure, and flow rate, into quantitative indicators for evaluating turbine performance. This includes calculating the experimental isentropic efficiency, total pressure loss, and the actual enthalpy at the outlet under wet steam conditions. The actual enthalpy at the steam outlet characterizes the turbine's thermal state under wet steam conditions, and its calculation formula is as follows: ； in, This represents the actual enthalpy value at the steam outlet. For saturated water enthalpy, For latent heat of vaporization, The outlet dryness is obtained in the following ways: in the test scenario, it is calculated by back-calculating based on the outlet temperature and outlet pressure combined with the actual physical properties of water vapor, or by converting it from the measured data of outlet steam condensation; in the CFD simulation scenario, it is calculated by a coupled wet steam non-equilibrium phase change model. S2. Establish the energy conversion relationship in the expansion stage of the Brayton cycle, and use the Euler turbine equation to describe the rotor's work mechanism; S3. Key thermodynamic, aerodynamic and mechanical parameters during turbine operation are collected synchronously, and effective samples are screened using steady-state criteria to construct an experimental sample library. S4. Based on the actual geometric structure of the test prototype, establish a three-dimensional fluid computational domain, divide the computational domain into meshes, and map the test conditions into numerical model boundary conditions. S5. Solve the mass, momentum, and energy conservation equations for compressible flow in a three-dimensional computational domain, and couple them together. SST k-ω A turbulent flow model is used to solve for flow heat transfer, and the solution process couples the actual water vapor property model with... k-ω or SST k- ω The working fluid properties are dynamically updated by using the real physical property function of water vapor with local pressure and temperature, and the rotating turbulent flow characteristics inside the turbine are described by the turbulence model. S6. Extract the temperature field, pressure field, total pressure field, velocity field, Mach number distribution, vorticity field, turbulent kinetic energy distribution, and wall shear stress distribution inside the turbine. Calculate the vorticity vector, viscous dissipation rate, and the proportion of each component loss in the total pressure loss. Establish the correspondence between flow field structure changes, local loss formation, and macroscopic efficiency reduction to determine the dominant loss source. Compare the CFD prediction results with the experimental results for each operating condition. When the error exceeds the threshold, correct the parameters and re-execute the CFD solution until the convergence requirement is met, thus achieving targeted structural optimization.

2. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to claim 1, characterized in that: Experimental isentropic efficiency is used to characterize the energy conversion capability of a turbine, and the calculation formula is as follows: ； in, To test isentropic efficiency, Total enthalpy at the entrance. This represents the total enthalpy of actual exports. The total enthalpy at the ideal isentropic outlet under the same inlet entropy and outlet pressure; Total pressure loss characterizes the irreversible loss of mechanical energy during the flow of the working fluid, and includes absolute total pressure loss and total pressure loss coefficient; among which, absolute total pressure loss characterizes the total pressure difference between the turbine inlet and outlet, and is calculated using the following formula: ； in, For total pressure loss, For the total pressure at the turbine inlet, Total turbine outlet pressure; The total pressure loss coefficient is used to characterize the degree of total pressure loss in a normalized form, facilitating cross-sectional comparisons between different inlet pressures, mass flow rates, and rotational speeds. The calculation formula is as follows: ； In the formula, This is the total pressure loss coefficient.

3. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to claim 2, characterized in that: S2 establishes the physical mechanism of centripetal steam turbine expansion work based on the Brayton cycle, clarifying the conversion relationship between working fluid enthalpy drop and rotor shaft work, as well as the turbine expansion intensity. This includes calculating the actual specific work per unit mass of working fluid, the Euler turbine specific work, and the turbine expansion pressure ratio. Specific formulas include: The formula for calculating the actual work done per unit mass of working fluid is: ； in, The actual work done by a unit mass of working fluid in the turbine; Total enthalpy at turbine inlet; Total enthalpy at turbine outlet; The formula for calculating the work done by an Euler turbine is: ； in, Work done by the Euler turbine; , These are the rotor inlet and outlet circumferential velocities, respectively. , These are the circumferential components of the absolute velocity of the working fluid at the rotor inlet and outlet, respectively. The formula for calculating the turbine expansion pressure ratio is: ； in, This refers to the turbine expansion pressure ratio; Total pressure at the turbine inlet; The total pressure at the turbine outlet.

4. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to claim 3, characterized in that: The S3 employs high-frequency multi-channel synchronous sampling technology to synchronously collect key parameters during turbine operation, including inlet total pressure, inlet total temperature, outlet back pressure, outlet temperature, mass flow rate, rotational speed, output power, wall temperature, and steam condensation rate, under a unified time reference. The collected raw operating data is used to calculate the working fluid mass flow rate, calculate the effective output power, and perform steady-state verification. Valid test samples are obtained through steady-state criterion screening. The performance parameters, operating condition labels, and timestamps of the valid samples are associated and stored to construct a test sample library. The specific calculation formulas include: The working fluid mass flow rate is calculated based on the cross-sectional parameters to determine the steam flow rate in the pipeline. The calculation formula is as follows: ； in, For the working fluid mass flow rate; The density of the inlet working fluid; To measure the effective area of ​​the cross-section; The average velocity of the working fluid across the cross section; The effective output power, based on the power generation and torque testing scenarios, is calculated using the following formula: Power generation scenario: ； Torque test scenario: ； in, For effective output power; This refers to the voltage at the generator terminal. This refers to the current at the generator end. For generator efficiency; This refers to the shaft end torque; The angular velocity of the shaft; The formula for determining steady state of data is: ； in, For the first in the steady-state window Each sample value; This represents the average value of the parameters within the sampling window. This represents the total number of sampling points; This is the preset steady-state allowable fluctuation threshold.

5. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to claim 4, characterized in that: In S4, a three-dimensional fluid computational domain is established based on the turbine's geometric parameters. The computational domain is divided into partitioned meshes, and the experimental conditions are mapped to the boundary conditions of the numerical model. Turbine geometry parameters include volute cross-sectional dimensions, flow channel curvature, throat area, outlet diffuser continuity, angle and cross-sectional transition shape, guide vane outlet angle, rotor inlet relative flow angle, blade tip radial clearance, blade profile, and turbine hub diameter; a complete three-dimensional fluid computational domain is established, including the volute, guide vanes, rotor, blade tip radial clearance, outlet diffuser, and exhaust section. During mesh generation, local refinement is applied to the leading edge, trailing edge, tip clearance, endwall boundary layer, and high-pressure gradient regions of the blade. The formula for calculating the dimensionless wall distance is: ； in, The distance is a dimensionless wall distance; This is the normal distance from the center of the first-layer mesh to the wall. The kinematic viscosity of the working fluid; Let be the friction speed, and , This refers to the wall shear stress. The density of the working fluid; The inlet total pressure, inlet total temperature, mass flow rate, rotational speed, outlet back pressure, and wall thermal boundary obtained from the experiment are simultaneously mapped to the boundary conditions of the CFD model. The experimental-simulation boundary condition mapping relationship is then as follows: ； in, To measure boundary parameters in the experiment, These are the boundary parameters of the simulation model; ω is the rotor angular velocity.

6. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to claim 5, characterized in that: In S5, the mass conservation equation, momentum conservation equation, and energy conservation equation for compressible flow are solved simultaneously within the three-dimensional fluid computational domain to complete the coupled solution of flow and heat transfer. Specifically, the mass conservation equation formula is as follows: ； in, For the working fluid density, For time, The working fluid velocity vector; The equation for the conservation of momentum is: ； in, For fluid pressure, It is the viscous stress tensor; The energy conservation equation is used to couple the heat transfer effect and the viscous dissipation effect in the flow process, and the formula is: ； in, The specific heat capacity of the working fluid at constant pressure For the working fluid temperature, The thermal conductivity of the working fluid is This is a viscous dissipation term; After the solution is completed, the total pressure loss inside the turbine is decoupled based on the flow field calculation results, and the macroscopic total pressure loss is decomposed into the sum of local losses from multiple sources. Among them, the update relationship formula of the physical property parameters of the water vapor real property model is: ； In the formula, Dynamic viscosity; It is a specific heat at constant pressure; Enthalpy; These are the actual physical property functions of water vapor; For local static pressure, Localized static temperature; k-ω or SST k-ω Turbulent flow is described by solving the turbulent kinetic energy transport equation and the specific dissipation rate transport equation, where the turbulent kinetic energy transport equation is: ； The specific dissipation rate transport equation is: ； in, For turbulent kinetic energy, For specific dissipation rate, For turbulent kinetic energy generation, For turbulent viscosity, , , , , All are constants of the turbulence model; After solving, a one-dimensional link is established between the volute, guide vanes, nozzle, rotor impeller, and outlet diffuser section. The internal turbine losses are then divided into outlet loss, tip clearance loss, nozzle loss, incident loss, channel loss, trailing edge loss, and impeller friction loss as the main losses. Among these, outlet loss, tip clearance loss, nozzle loss, and incident loss are the dominant losses affecting isentropic efficiency and total pressure loss, while channel loss, trailing edge loss, and impeller friction loss are considered auxiliary losses. The corresponding decomposition formulas are as follows: ； in, To reduce the total enthalpy loss inside the turbine, Losses due to exports; This is due to tip clearance loss; For nozzle loss; For incident loss; This is due to channel loss; For trailing edge loss; This refers to the loss due to friction of the wheel.

7. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to claim 6, characterized in that: In S6, based on the flow heat transfer solution obtained in S5, multi-dimensional flow field parameters inside the turbine are extracted and flow field-loss-efficiency correlation mechanism analysis is carried out. The correspondence between flow field structure change, local loss formation and macro efficiency decrease is established, and the dominant loss source and corresponding structural optimization direction under each working condition are obtained. Multi-dimensional flow field parameters inside the turbine are extracted, including temperature field, pressure field, total pressure field, velocity field, Mach number distribution, vorticity field, turbulent kinetic energy distribution, and wall shear stress distribution. Regarding the pressure field, the locations of total pressure attenuation at the volute outlet, guide vane throat, rotor inlet, blade tip clearance, and outlet diffuser section are identified to determine the concentrated areas of total pressure loss. Regarding the temperature field, the correlation between expansion cooling, wall heat transfer, local temperature rise, and steam condensation risk is analyzed, and the wet steam state in the low-temperature, low-pressure region is identified for the working fluid. Regarding the vorticity field, the structures of blade leading-edge impact vortices, endwall secondary vortices, blade tip leakage vortices, wake vortices, and outlet vortices are identified to analyze their impact on channel blockage, energy dissipation, and efficiency reduction. Based on the above analysis, the proportion of various losses under different geometric structures and different working conditions is ranked to determine the dominant loss sources.

8. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to claim 7, characterized in that: In S6, the correspondence between the flow field structure and local losses is established by calculating the vorticity vector, viscous dissipation rate, proportion of single-type losses, and thermal conductivity heat flux density. The vorticity vector is used to characterize the rotation intensity of fluid micro-elements and the vortex structure, and its calculation formula is as follows: ； in, The vorticity vector. For spatial differential operators, The working fluid velocity vector; Viscous dissipation rate is used to quantify the degree of energy dissipation in a flow process. The calculation formula is as follows: ； in, For viscous dissipation rate, It is the viscous stress tensor; Let be the velocity gradient tensor; where For tensor double dot product operation, it means multiplying and summing the corresponding components of two second-order tensors, which is used to characterize the internal friction energy dissipation effect generated by the coupling of viscous stress and fluid velocity gradient. The percentage of single-type losses is used to identify the dominant loss source affecting efficiency, and the calculation formula is as follows: ； in, For the first The proportion of this type of loss in the total pressure loss. For the first Localized total pressure loss; This is to reduce the total pressure loss inside the turbine. Thermal conductivity and heat flux density are used to analyze the heat transfer and temperature field evolution of walls. The calculation formula is as follows: ； in, For thermal conductivity heat flux density, Thermal conductivity, For temperature gradient.

9. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to claim 8, characterized in that: In S6, the isentropic efficiency, total pressure loss, outlet temperature, outlet pressure, mass flow rate and output power are compared for each operating condition. The error between simulation and experiment is calculated and the parameters are corrected. The isentropic efficiency error determination formula is used to limit the range of efficiency deviation between simulation and experiment. The formula is as follows: ； in, This represents the relative error of isentropic efficiency. For CFD prediction of isentropic efficiency, To test isentropic efficiency; The preset isentropic efficiency allowable error threshold; The relative error of total pressure loss is used to quantify the simulation deviation of total pressure loss, and the calculation formula is as follows: ； in, This represents the relative error of the total pressure loss. For CFD prediction of total pressure loss, The total pressure loss was measured in the experiment; A comprehensive error objective function is constructed to integrate multiple types of index errors. Parameters are iteratively corrected based on the error gradient. The correction formula is as follows: ； in, These are the corrected parameters. To correct the parameters before, To correct the step size, The objective function is the comprehensive error. Furthermore, the formula for calculating the comprehensive error objective function is: ； in, , , , , , These are the weighting coefficients. For CFD prediction of isentropic efficiency, To test the isentropic efficiency; For CFD prediction of total pressure loss, The total pressure loss was measured in the experiment; For CFD prediction of outlet temperature, To test and measure the outlet temperature; For CFD prediction of mass flow rate, To test and measure the mass flow rate; For CFD prediction of output power, To test and measure the output power; For CFD prediction of export dryness, The outlet dryness was measured in the experiment.

10. The method for experimental and CFD optimization of entropy efficiency of centripetal steam turbines according to any one of claims 1-9, characterized in that: The centripetal steam turbine isotropic thermal efficiency test and optimization system based on the above method includes: a gas source supply component, a pretreatment and parameter measurement component, a centripetal turbine test piece, a power generation and load component, and a parameter acquisition component electrically connected to each component, connected in sequence. The gas supply component includes a gas compressor and a gas storage tank connected in sequence, which are used to generate compressed water vapor working fluid and reduce pressure pulsation, and output a stable water vapor test working fluid. The pretreatment and parameter measurement components include a valve control unit, a filter dryer, a flow meter, and a pressure transmitter connected in sequence. These components are used to achieve manual safety isolation, gas path opening and closing, operating condition adjustment, working fluid purification, and to collect the water vapor working fluid flow rate and inlet pressure parameters entering the centripetal turbine test specimen. The input end of the centripetal turbine test piece is connected to the pretreatment and parameter measurement components, and the output shaft is connected to the power generation and load components via a speed and torque sensor, which is used to convert the pressure energy and kinetic energy of the water vapor working fluid into the mechanical energy output by the rotor shaft. The power generation and load components include a generator and an adjustable electrical load connected by a drive, used to convert mechanical energy into electrical energy and simulate different electrical load conditions; The parameter acquisition component includes a speed and torque sensor, an ammeter, and a voltmeter. The speed and torque sensor is connected in series with the transmission shaft between the turbine test piece and the generator. The ammeter is connected in series with the generator circuit between the generator and the adjustable electrical load. The voltmeter is connected in parallel across the adjustable electrical load. The mechanical parameters of the transmission shaft and the electrical parameters of the generator circuit are collected synchronously, respectively.

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