CN113158356B - A Collaborative Optimization Design Method for Anti-cavitation Rectifier Cone of Cryogenic Liquid Expander - Google Patents

Abstract

The invention discloses a collaborative optimization design method for an anti-cavitation rectification cone of a low-temperature liquid expander. A rectifier cone is added to the impeller of the low-temperature liquid expander, and the three-dimensional geometry of the impeller and the rectifier cone of the low-temperature liquid expander is collaboratively optimized to control The vortex cavitation flow downstream of the impeller includes the following steps: numerical prediction of the two-phase vortex cavitation of the cryogenic liquid expander, analysis of the impeller-rectifier cone and vortex cavitation interference mechanism and identification of the best coupling method, rectifier cone-impeller coupling Establishment of parametric expression, extraction of geometrically sensitive parameters of expander impeller with rectifier cone, extraction of vortex cavitation feature quantity, construction of objective function for vortex cavitation suppression, and establishment of impeller-cone geometry collaborative optimization problem aiming at suppressing vortex cavitation Its adaptive solution, this method can effectively control the vortex cavitation flow, and improve the anti-cavitation performance of the cryogenic liquid expander.

Description

A Collaborative Optimization Design Method for Anti-cavitation Rectifier Cone of Cryogenic Liquid Expander

technical field

The invention belongs to the fields of low-temperature air separation and low-temperature liquefaction, and relates to a collaborative optimization design method of an anti-cavitation rectifying cone and an impeller of a low-temperature liquid expander.

Background technique

Cryogenic liquid expander is the key energy-saving equipment of large-scale air separation unit and liquefied natural gas unit. It is used to replace the throttle valve to reduce the vaporization rate, improve the extraction rate of air separation products and realize pressure energy recovery. The liquid cavitation induced by the vortex flow downstream of the impeller of the cryogenic liquid expander will cause impact and corrosion damage to the surface material of the blade, and will induce vibration of the unit, which seriously threatens the stable operation of the liquid expander and the main process cryogenic device. Therefore, it is of great significance to effectively control the cavitation flow in cryogenic liquid expanders.

For normal temperature hydraulic machinery, some anti-cavitation design methods have been published. For example, patent 201110202524.5 "A method for optimizing the impeller design of an anti-cavitation centrifugal pump", and patent 201510679202.8 "a method for hydraulic design of a highly anti-cavitation centrifugal impeller", both of which optimize the geometric shape of the impeller of the centrifugal pump to improve its anti-cavitation Performance; Patent No. 201110183162.X "Method for Inhibiting Cavitation on the Backside of Francis Turbine Blades", by drilling holes at the lowest point of pressure on the backside of blades, destroying the formation of cavitation and improving the anti-cavitation performance of water turbines.

However, unlike water pumps and turbines operating at room temperature, due to the significant thermodynamic benefits of cryogenic fluids, the internal cavitation mechanism of cryogenic hydraulic machinery is more complicated, and cavitation is induced by local pressure drop or a small temperature rise. According to domestic and foreign literature, there are few anti-cavitation methods involving low-temperature hydraulic machinery. For example, patent 201420342677.9 "A high-efficiency, anti-cavitation vertical multi-stage cryogenic pump" proposes a design method to improve the cavitation resistance of cryogenic centrifugal pumps through the design of spiral grooves; 201910014308 "A kind of cryogenic fluid-based "Numerical Prediction Method for Cavitation Flow in Turbine Pump Inducer Wheel" discloses a numerical prediction method for cavitation flow in a turbo pump inducer wheel based on a cavitation model. In the public information, for low-temperature liquid expanders, there are only patents 201810008748.4 "An effective control method for vortex cavitation flow in a low-temperature liquid expander", and 201810009053 "An optimized design for anti-cavitation of a two-phase low-temperature liquid expander Method", respectively, by optimizing the design of the impeller and adding inducer components, the anti-cavitation performance of the cryogenic liquid expander is improved.

Mechanism studies have found that the vortex flow originating from the trailing edge of the high-speed rotating impeller expands to the diffuser with the main flow, and the local low pressure induced by it and the local temperature rise caused by the corresponding flow loss are the main causes of cavitation downstream of the impeller. Furthermore, when the low-temperature liquid enters the diffuser from the impeller, it encounters a sudden expansion of the flow channel, and the further deterioration of the flow is another important cause of cavitation. Therefore, adding a rectifying cone at the outlet of the impeller can help reduce the loss caused by the sudden expansion of the flow channel and suppress the occurrence of cavitation, and has a simple structure and low cost. However, because the flow in the impeller and rectifying cone is coupled with each other and there is complex interference with the downstream flow, the matching of the shape of the three-dimensional impeller blades and rectifying cone, as well as the complex effects of collaborative deformation on the vortex cavitation flow must be considered in the design. The vortex cavitation flow is extremely sensitive to changes in the geometry of the impeller blade trailing edge and the straightening cone. In the design, the coordinated change and matching of the three-dimensional impeller and the straightening cone shape should be considered. It is necessary to continuously call and rely on time-consuming prediction numerical calculations to predict low temperature two-phase The flow greatly increases the complexity of the design problem, and the above reasons make it difficult to realize this active anti-cavitation method. At present, no public information on this aspect has been found.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art, and provide a collaborative optimization design method for the anti-cavitation rectification cone of the low-temperature liquid expander, which can effectively control the vortex cavitation flow, and improve the anti-cavitation of the low-temperature liquid expander. corrosion performance.

In order to achieve the above-mentioned purpose, the anti-cavitation rectifying cone collaborative optimization design method of the cryogenic liquid expander of the present invention includes adding a rectifying cone to the impeller of the cryogenic liquid expander, and performing a three-dimensional geometrical analysis on the impeller and the rectifying cone of the cryogenic liquid expander Collaborative optimization to control the vortex cavitation flow downstream of the impeller, specifically includes the following steps: sequentially perform numerical prediction of the two-phase vortex cavitation of the cryogenic liquid expander, analyze the interference mechanism of the impeller-rectifier cone and the vortex cavitation and determine the best coupling mode, Establishment of rectifier cone-impeller coupling parametric expression, extraction of geometrically sensitive parameters of expander impeller with rectifier cone, extraction of vortex cavitation feature quantity, construction of vortex cavitation suppression objective function, and impeller-rectifier cone geometry aimed at suppressing vortex cavitation Co-optimization problem establishment and its adaptive solution.

The numerical prediction of two-phase vortex cavitation in a cryogenic liquid expander specifically includes the following steps:

Establish a complete machine model including the volute, nozzle, impeller with rectifying cone and diffuser pipe flow channel, and then use the Rayleigh-Plesset cavitation model to simulate the internal cavitation flow of the low-temperature liquid expander based on the complete machine model, using turbulent flow The model and the variable wall function method describe the braided vortex flow of the liquid expander and the downstream of the impeller; at the same time, the thermophysical properties are expressed as a function of temperature and pressure and combined with the total energy equation to solve it, so as to consider the thermodynamic effect of low temperature fluid, real-time Changes in physical properties with pressure and temperature during the update calculation.

The specific operation process of the analysis of the interference mechanism of the impeller-rectifier cone and vortex cavitation and the identification of the optimal coupling mode is: according to the working condition parameters of the cryogenic liquid expander, the interference mechanism of the impeller-rectifier cone and vortex cavitation is analyzed, and the geometric shape of the rectifier cone is established Correlation relationship with vortex cavitation, and then determine the optimal rectifying cone form and impeller-cone rectifying coupling method that match the working conditions, and construct a parametric design scheme for the coupling of rectifying cone and three-dimensional impeller.

The specific process of extracting geometrically sensitive parameters of the expander impeller with rectifying cone is as follows:

By changing the geometric parameters of the meridian contour line and the coordinate parameters of the arc control points of the blade shape, the geometry of impellers and rectifier cones of different shapes can be simulated, and then the grid division and the numerical solution of the two-phase flow field are carried out, and then the variable sensitivity is carried out for the simulation results Analyze and obtain several geometric parameters of the meridian contour and control point parameters of the blade mid _- arc that are sensitive to the vortex _- cavitation flow. The angle α ₁ between the outer end surface and the radial surface, the rectifying cone angle β and the dimensionless diameter of the rectifying cone head D ₀ /D ₁ , the arc control point parameters of the blade shape include the three-dimensional blade tip and blade root blade shape The control point coordinate parameters of the arc.

The characterization of the vortex cavitation flow in the cryogenic liquid expander includes the following steps: Through the mechanism analysis of different forms of vortex-cavitation flow, the average gas volume fraction vfrac _ave on the suction surface of the impeller blade is extracted as the characterization of the cavitation degree at the impeller outlet The average vortex intensity λ _ave in the diffuser tube downstream of the impeller is used as the characterization of vortex flow, in which, the distribution of the gas volume fraction vfrac on the blade suction surface is predicted by two-phase numerical simulation, and the local vortex intensity λ is obtained by logarithmic simulation. The local velocity gradient The tensor is obtained by eigenvalue analysis.

The constructed vortex-cavitation suppression multi-objective optimization function is:

为对旋涡-空化流动敏感的叶轮及整流锥几何敏感参数，Refri_original和Refri分别为优化前后膨胀机所产制冷量。in,

are the geometrically sensitive parameters of the impeller and rectifier cone sensitive to the vortex-cavitation flow, and Refri _original and Refri are the cooling capacity produced by the expansion machine before and after optimization, respectively.

The efficient adaptive solution process of the impeller-cone geometry co-optimization problem aiming at suppressing vortex cavitation is:

对应的三维叶轮及整流锥几何，通过整机数值模拟获得流场信息，并计算旋涡-空化抑制多目标优化函数，得目标函数值

1) For the geometrically sensitive parameters of the expander impeller and the rectifying cone, the DOE experimental design is used to determine the variable combination of the NUM group within the range of the geometrically sensitive parameters of the expander impeller and the rectifying cone.

The corresponding three-dimensional impeller and rectifying cone geometry, the flow field information is obtained through the numerical simulation of the whole machine, and the vortex-cavitation suppression multi-objective optimization function is calculated to obtain the objective function value

及其对应的目标函数值

拟合各优化目标的初始代理模型；2) According to the parameters

and its corresponding objective function value

Fit an initial surrogate model for each optimization objective;

及预测标准差

的多目标采样策略，其中，m为优化目标的个数，通过最大化多目标改进期望矩阵的规范数

即

搜索最具潜力的候选设计，其中，搜索到的最具潜力的候选设计为：3) Construct while considering the predicted value of the model

and predicted standard deviation

The multi-objective sampling strategy of , where m is the number of optimization objectives, and the normative number of the expected matrix is improved by maximizing the multi-objective

which is

Search for the most potential candidate design, where the most potential candidate design found is:

Optimize the surrogate model and the global search by searching the most potential candidate design, where k is the number of non-dominated points of the multi-objective Pareto front obtained by non-dominated sorting from the NUM evaluated sample points ;

并以此构建的自适应采样-协同优化为特征的优化方式，并以此获得有潜力的候选设计，利用该候选设计、对应的两相数值模拟结果及多目标函数值对代理模型动态更新并对下一次迭代全局搜索，直至满足预定终止条件后输出优化后的叶轮及整流锥几何。4) Use co-evolutionary optimization algorithm to solve

And the adaptive sampling-co-optimization feature of this construction is used as an optimization method, and a potential candidate design is obtained, and the proxy model is dynamically updated and For the next iteration of the global search, the optimized geometry of the impeller and rectifier cone is output until the predetermined termination condition is met.

The present invention has the following beneficial effects:

The anti-cavitation rectification cone collaborative optimization design method of the cryogenic liquid expander described in the present invention, in specific operation, by adding a rectifier cone to the impeller of the cryogenic liquid expander, and synergizing the three-dimensional geometry of the cryogenic liquid expander impeller and the rectifier cone Optimization to effectively suppress the vortex cavitation flow downstream of the impeller, improve the anti-cavitation performance of the cryogenic liquid expander, avoid unit vibration, shutdown and air separation liquefaction plant shutdown, and effectively improve the performance and operational reliability of the cryogenic liquid expander.

Description of drawings

Fig. 1a is the schematic diagram of the complete machine model of liquid expander;

Figure 1b is a schematic diagram of a liquid expander with a rectifying cone impeller and a downstream diffuser;

Figure 2a is a schematic diagram of a liquid expander without a rectifying cone impeller;

Figure 2b is a schematic diagram of a complete liquid expander with a spherical rectifying cone;

Fig. 2c is a schematic diagram of a complete liquid expander with an ellipsoidal rectifying cone;

Figure 2d is a schematic diagram of a liquid expander with a spherical head and a tapered rectifying cone;

Figure 3a is a parametric schematic diagram of the meridian contour;

Figure 3b is a schematic diagram of a three-dimensional blade;

Figure 3c is a schematic diagram of a primitive leaf shape;

Figure 3d is a parametric schematic diagram of the arc in the blade;

Fig. 4 is a schematic diagram of an adaptive solution to a nonlinear optimization problem aiming at vortex-cavitation suppression.

detailed description

The present invention is described in further detail below in conjunction with accompanying drawing:

During the operation of the anti-cavitation rectifying cone cooperative optimization design method of the cryogenic liquid expander, a rectifying cone is added to the impeller of the cryogenic liquid expander, and the three-dimensional geometry of the cryogenic liquid expander impeller and the rectifying cone is collaboratively optimized, In order to control the vortex cavitation flow downstream of the impeller, it specifically includes the following steps: sequentially carry out the numerical prediction of the two-phase vortex cavitation of the cryogenic liquid expander, analyze the interference mechanism of the impeller-rectifier cone and vortex cavitation and determine the best coupling mode, rectifier cone- Establishment of parametric expression of impeller coupling, extraction of geometrically sensitive parameters of expander impeller with rectifier cone, extraction of vortex cavitation feature quantity, establishment of impeller-cone geometry co-optimization problem aiming at suppressing vortex cavitation and its adaptive solution.

Referring to Fig. 1a and Fig. 1b, the numerical prediction of two-phase vortex cavitation in a cryogenic liquid expander specifically includes the following steps:

Establish the whole machine model including volute, nozzle, impeller with rectifying cone and diffuser pipe flow channel to reflect the real flow in the expander, use ICEM and CFX-TURBOGRID to mesh the flow domain of each part, and then pass the interface Connect to form a whole machine grid.

The Rayleigh-Plesset (PR) cavitation model is used to describe the cavitation flow inside the cryogenic liquid expander. The cavitation model regards cavitation as a volume fraction governing equation of a two-phase three-component system, each component has the same velocity of the hypothetical mixed-phase mass, momentum and energy equations, and uses the PR equation to predict the gasification rate and vacuole formation and collapse.

Combining the k-ε model and the variable wall function method, the braided vortex flow in the whole liquid expander and downstream of the impeller is described. The dynamic and static rotor interface between the nozzle-impeller and the impeller-diffuser is processed by the Frozen Rotor model, which reduces calculation consumption on the basis of retaining the circumferential distribution characteristics of flow field parameters.

Express physical parameters including density, enthalpy, entropy, viscosity coefficient and saturated vapor pressure as binary functions of temperature and pressure and solve them in combination with the total energy equation to consider the thermodynamic effects of cryogenic fluids;

Use CEL (CFX Expression Language) language to compile the physical property interface file, and import CFX to solve it combined with the total energy equation, so as to realize the real-time update of physical property parameters with the change of local pressure and temperature during the calculation process. At the same time, in the iterative solution process of numerical simulation , to monitor the convergence of the temperature field solution in real time to ensure the solution accuracy of the temperature field.

Referring to Fig. 2a to Fig. 2d, the specific operation process of impeller-rectifier cone and vortex cavitation interference mechanism analysis and optimal coupling mode identification is as follows:

1) Complete a set of initial design for each of the three types of impeller outlet equal-diameter spherical rectifying cone, ellipsoidal rectifying cone and spherical head with tapered rectifying cone;

2) For the initial design of different types of rectifying cones, geometric modeling and grid division are carried out, and the numerical prediction method of the two-phase vortex cavitation of the cryogenic liquid expander is used to carry out the vortex cavitation flow downstream of the impeller without rectifying cones and different forms of rectifying cones Characteristic research, capturing the characteristics of the unbalanced velocity gradient in the circumferential direction of the impeller outlet and its coupling characteristics with the downstream sudden expansion area, and diagnosing the key geometric factors that lead to the significant deterioration of the downstream flow of the impeller;

3) Constantly change the geometric form and parameters of the blade, carry out geometric sensitivity research, obtain the correlation relationship between the geometry of the rectifier cone and the vortex cavitation in different forms and parameters, and on this basis, determine the best rectifier that matches the working conditions The parametric design scheme of the cone form and the coupling between the rectifying cone and the three-dimensional impeller.

Referring to Fig. 3a and Fig. 3b, the specific process of geometric parametric expression and sensitive parameter extraction of expander impeller with rectifying cone is as follows:

The three-dimensional impeller geometry is jointly defined by the two-dimensional contour line of the meridian contour and the three-dimensional twisted blade. The two-dimensional contour line of the meridian contour defines the disk line and the wheel cover line respectively through two parabolic curves 1-4 and 2-3, and the The smooth and connected straightening cone outline, taking the spherical head with a tapered straightening cone as an example, it uses a circular arc-shaped head + tangent segment to define the axisymmetric contour line with a taper; the three-dimensional twisted blade is due to the three-dimensional blade Both the pressure surface and the suction surface adopt ruled surfaces, which can be defined by the two-dimensional blade shape at the blade root (disk) and blade top (wheel cover). The middle arcs of the blades are parameterized using the Bezier curve shown in Figure 3d, and the coordinates of the control points of the Bezier curve are adjusted during the design process to achieve fine optimization of the three-dimensional blade. According to the above definition, the geometry of the impeller-cone rectifier can realize the collaborative deformation control of the geometry of the three-dimensional impeller and the rectifier cone by adjusting the geometric parameters of the meridian contour and the coordinates of the control points of the arc in the blade profile. Based on the above-mentioned geometric parameterization method, the self-owned program is used to quickly generate three-dimensional geometry files of the impeller including meridian contour lines and three-dimensional blades according to different geometric parameter control variables during the optimization process for numerical simulation.

The specific steps of sensitive parameter extraction are as follows: by changing the geometric parameters of the meridian contour line and the coordinate parameters of the arc control point of the blade shape, the geometry of impellers and rectifier cones of different shapes is obtained, and geometric modeling, grid division and flow field values are carried out. Simulation and analysis. Analyze the flow field data obtained after the simulation, and obtain the geometric parameters sensitive to the vortex-cavitation flow through variable sensitivity analysis, including the geometric parameters of the meridian surface, the geometric parameters of the straightening cone, and the three-dimensional blade tip and blade root profile The coordinate parameters of some control points of the middle arc, among which, the geometric parameters of the meridian surface include the inner diameter R ₁ of the impeller outlet, the outer diameter R ₂ of the impeller outlet, and the angle α ₁ between the outer end surface of the inducer and the radial surface, and the geometric parameters of the rectifier cone include The rectifier cone angle β and the dimensionless rectifier cone head diameter D ₀ /D ₁ , etc., the above-mentioned sensitive geometric parameters and coordinates are used as optimization variables, and the three-dimensional impeller and rectifier cone geometry are coordinated and fine-tuned in the optimization design to realize Effective control of vortex cavitation flow.

Based on the above-mentioned geometric parameterization method, the self-owned program is used to quickly generate three-dimensional geometric files including the impeller meridian surface profile, rectifying cone surface and three-dimensional blades according to different geometric parameter control variables during the optimization process. simulation.

The specific methods of extracting vortex cavitation feature quantity and constructing vortex cavitation suppression objective function are as follows:

The vortex-cavitation flow downstream of the impeller of the cryogenic liquid expander is highly coupled, and the mechanism analysis of different forms of vortex-cavitation flow is carried out through a large number of numerical simulations, and the average gas volume fraction vfrac _ave of the suction surface of the impeller blade is extracted as the degree of cavitation at the outlet of the impeller The characterization quantity, the average vortex intensity λ _ave in the diffuser downstream of the impeller is used as the characterization quantity of the vortex flow, and its specific connotation and calculation method are as follows:

vfrac为当地气体体积分数，dA为微元面积，Area_blade为叶片吸力面表面积。The characterization of cavitation flow at the impeller outlet and its calculation: the average gas volume fraction vfrac _ave on the suction surface of the impeller blade is used as the characterization of the cavitation degree at the impeller outlet. The cavitation intensity in the diffuser is positively correlated, vfrac _ave is the integral average of the gas volume fraction on the suction surface of the blade, and its calculation formula is:

vfrac is the local gas volume fraction, dA is the microelement area, and Area _blade is the surface area of the suction surface of the blade.

其中，dA为微元面积，Area_tube扩压管中间截面面积，λ_ci为当地漩涡强度，可通过对数值模拟得到的如下速度梯度张量D进行特征值分析得到，具体为：Vortex flow characterization and its calculation: The average vortex intensity _λave in the diffuser downstream of the impeller is used as the vortex flow characterization, which is defined as the area-weighted average of the vortex intensity λ on the axisymmetric middle section of the diffuser, namely

Among them, dA is the microelement area, the area of the middle section of the diffuser tube of the Area _tube , and _λci is the local vortex intensity, which can be obtained by analyzing the eigenvalues of the following velocity gradient tensor D obtained by numerical simulation, specifically:

Its eigenvalue λ satisfies:

λ ³ +Pλ ² +Qλ+R＝0

in,

Q＝(d ₂₂ d ₃₃ -d ₂₃ d ₃₂ )+(d ₁₁ d ₂₂ -d ₁₂ d ₂₁ )+(d ₃₃ d ₁₁ -d ₁₃ d ₃₁ )

R＝d ₁₁ (d ₂₃ d ₃₂ -d ₂₂ d ₃₃ )+d ₁₂ (d ₂₁ d ₃₃ -d ₃₁ d ₂₃ )+d ₁₃ (d ₃₁ d ₂₂ -d ₂₁ d ₃₂ )

set up:

When satisfied:

Then the tensor D has a real eigenvalue λ _r and a pair of conjugate complex eigenvalues λ _cr ±iλ _ci , where:

set up:

but:

Among them, λ _ci is the local eddy strength to be calculated.

In order to suppress the occurrence of vortex-cavitation at the same time, the following vortex-cavitation suppression optimization multi-objective function is constructed by integrating the cavitation degree vfrac _ave at the outlet of the impeller and the average vortex intensity λ _ave in the diffuser tube downstream of the impeller:

代表对旋涡-空化流动敏感的叶轮及整流锥几何敏感参数， Refri_original和Refri分别代表优化前后膨胀机所产制冷量，该目标函数用于同时最小化叶片吸力面气体体积分数以及叶轮下游扩压管内旋涡强度，约束条件则用于保证优化前后膨胀机制冷量不显著下降，以满足空分及低温流程所需。in,

Represents the geometrically sensitive parameters of the impeller and rectifier cone that are sensitive to vortex-cavitation flow, Refri _original and Refri respectively represent the cooling capacity produced by the expander before and after optimization, this objective function is used to minimize the gas volume fraction on the suction surface of the blade and the downstream expansion of the impeller The vortex strength in the compression tube and the constraint conditions are used to ensure that the cooling capacity of the expander does not decrease significantly before and after optimization, so as to meet the needs of air separation and low temperature processes.

The process of efficiently solving multi-objective complex non-linear optimization problems for the purpose of vortex-cavitation suppression is:

Combining the multi-objective adaptive sampling surrogate model method, the collaborative optimization algorithm, the geometric parameterization method of the impeller of the expander with a rectifying cone, and the numerical prediction method of the low-temperature two-phase vortex cavitation flow, the cavitation resistance of the low-temperature liquid expander as shown in Figure 4 is established. The collaborative optimization design platform of rectifier cone and impeller, its main functional modules and specific implementation are as follows:

Geometric parameterization module: Based on the geometric parametric expression method of the impeller of the rectifying cone, the automatic program is compiled, and the geometric files including the impeller meridian surface profile, the rectifying cone surface and the three-dimensional blade are quickly generated according to different geometric parameter variables. in numerical analysis.

以及

并完成目标函数计算。Automatic numerical prediction module of vortex cavitation flow: based on the numerical prediction method of low-temperature two-phase vortex cavitation flow of liquid expander, the whole process of numerical simulation is fully automatically completed by calling the CFD module through its own program. The specific process of the vortex cavitation flow automatic numerical prediction module is as follows: the first step is to enable the geometric parameterization module to obtain the three-dimensional geometric file of the candidate design; the second step is to import the geometric model into the grid software, and use the topology template technology Carry out automatic grid division; the third step is to set up the two-phase numerical simulation, including importing the grid, physical model, setting boundary conditions, cavitation model and turbulence model; the fourth step is to start the CFD solver in parallel through its own program Solving; the fifth step, after the calculation converges, the required flow field data can be found everywhere by calling the post-processing module; the sixth step, respectively calculate

as well as

And complete the calculation of the objective function.

对应的三维叶轮 及整流锥几何，通过旋涡空化流动自动数值预测模块获得其流场数据， 并计算特征量

以及

的数值。在此基础上， 计算M组变量组合多对应的目标函数值，将其几何参数及对应的目标函 数值储存进数据库模块，在NUM组控制变量

及对应目标函数值

的基础上拟合相对粗糙的初始代理模型，所述代理模型用 于在优化过程中预测未知变量组合对应的目标函数值、指导以抑制旋涡 空化为目标的优化过程。Proxy model initialization module: for the geometrically sensitive parameters of the expander impeller and rectifier cone, use DOE (Design of Experiment, experimental design method) to determine the geometric parameters of NUM groups of impeller and rectifier cone within its variation range, and for each set of geometric parameters

The corresponding three-dimensional impeller and rectifying cone geometry, the flow field data are obtained through the automatic numerical prediction module of vortex cavitation flow, and the characteristic quantities are calculated

as well as

value. On this basis, calculate the objective function values corresponding to the M group of variable combinations, store the geometric parameters and corresponding objective function values in the database module, and control variables in the NUM group

and the corresponding objective function value

Fitting a relatively rough initial surrogate model on the basis of , the surrogate model is used to predict the objective function value corresponding to the unknown variable combination in the optimization process, and guide the optimization process with the goal of suppressing vortex cavitation.

Adaptive sampling-cooperative optimization module: based on Kriging Surrogate Model, multi-objective improved expectation matrix method (Expected Improvement Matrix, EIM) and cooperative evolutionary algorithm (Cooperative Co-evolutionary Algorithm, CCEA) to establish a multi-objective self- Adaptive sampling-co-optimization is an optimization method module, which is suitable for solving nonlinear optimization problems that require time-consuming numerical simulation.

处的预 测值

及预测标准差

Among them, the Kriging surrogate model is responsible for establishing the correlation between the geometric variables in the sample database and their corresponding objective function values, which is used to predict the objective function value of the combination of unknown variables and guide the optimization process with the goal of suppressing vortex-cavitation. For the following multi-objective optimization function with m optimization objectives, the fitted kriging surrogate model can simultaneously provide the optimization variables

predicted value at

and predicted standard deviation

处，改进值

在

处的期望函数，即多目标改进期望矩阵 (Expected Improvement Matrix,EIM)定义为：For the known minimum value y _{i, min} in the sample library, 1≤i≤m, in the optimization variable

place, improved value

exist

The expectation function at , that is, the multi-objective improvement expectation matrix (Expected Improvement Matrix, EIM) is defined as:

及预测标准差

的多目标采样策略，该策略通过最大化如下多目标改 进期望矩阵(Expected Improvement Matrix,EIM)的规范数

即

搜索最具潜力的候选设计，以考虑代理模型的预测 最优值与预测不确定度，指出最优设计最可能存在的潜在区域以及模型 预测精度较差的区域。Build while taking model predictions into account

and predicted standard deviation

A multi-objective sampling strategy, which maximizes the normative number of the expected improvement matrix (Expected Improvement Matrix, EIM) by maximizing the following multi-objective

which is

The most potential candidate designs are searched to account for the predicted optimal value and prediction uncertainty of the surrogate model, pointing out the potential regions where the optimal design is most likely to exist and the regions where the model prediction accuracy is poor.

The candidate designs obtained from the search are used to improve model accuracy and global search, where k is the number of non-dominated points of the multi-objective Pareto front obtained by non-dominated sorting from NUM evaluated sample points.

及修正后的代理模型参数

即同时进行全局搜索以This auxiliary optimization problem is a high-dimensional nonlinear optimization problem, which is extremely difficult to solve. The present invention utilizes the co-evolutionary algorithm CCEA to solve it. Through variable correlation analysis, this method decomposes the multidimensional optimization problem into several easy-to-solve sub-problems to be solved collaboratively, and quickly obtains potential new design samples

and the modified proxy model parameters

i.e. simultaneously conduct a global search to

对应的三维叶轮及整流锥几何，调用旋涡空化流 动自动数值预测模块获得其流场数据并计算对应的目标函数值，新增样 本及其目标函数同时存入数据库，并进行下一步寻优。For newly acquired samples

For the corresponding three-dimensional impeller and rectifying cone geometry, the automatic numerical prediction module of vortex cavitation flow is called to obtain the flow field data and calculate the corresponding objective function value. The newly added samples and their objective functions are stored in the database at the same time, and the next step of optimization is carried out.

Carry out an iterative cycle according to the above steps, and continuously interact through the adaptive sampling-cooperative optimization module to continuously improve the accuracy of the proxy model and provide a better design until the predetermined optimization search termination criterion is met, and the optimized impeller and rectifier are output cone geometry.

The above description is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as above with preferred embodiments, it is not intended to limit the present invention. Anyone familiar with this field Those skilled in the art, without departing from the scope of the technical solution of the present invention, may use the method and technical content disclosed above to make some changes or modifications to equivalent embodiments with equivalent changes, but all without departing from the content of the technical solution of the present invention Any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention still belong to the scope of the technical solutions of the present invention.

Claims (5)

1. A collaborative optimization design method for anti-cavitation rectification cones of cryogenic liquid expanders, characterized in that a rectifier cone is added to the impeller of the cryogenic liquid expander, and the three-dimensional geometry of the impeller of the cryogenic liquid expander and the rectifier cones is collaboratively optimized, In order to control the vortex cavitation flow downstream of the impeller, it specifically includes the following steps: sequentially carry out the numerical prediction of the two-phase vortex cavitation of the cryogenic liquid expander, analyze the interference mechanism of the impeller-rectifier cone and vortex cavitation and determine the best coupling mode, and rectify the cone-impeller Establishment of coupling parameterization expression, extraction of geometrically sensitive parameters of expander impeller with rectifier cone, extraction of vortex cavitation feature quantity, construction of vortex cavitation suppression objective function, and establishment of impeller-rectifier cone geometry collaborative optimization problem aiming at suppressing vortex cavitation and its adaptive solution; The characterization of the vortex cavitation flow in a cryogenic liquid expander includes the following steps: By analyzing the mechanism of different forms of vortex-cavitation flow, the average gas volume fraction vfrac _ave of the suction surface of the impeller blade is extracted, and this is used as a characterization of the cavitation degree at the outlet of the impeller, and the average vortex intensity λ _ave in the diffuser tube downstream of the impeller As a characterization of vortex flow, the distribution of gas volume fraction vfrac on the blade suction surface is predicted by two-phase numerical simulation, and the local vortex intensity λ is obtained by eigenvalue analysis of the local velocity gradient tensor obtained by numerical simulation; It is characterized in that the constructed vortex-cavitation suppression multi-objective optimization function is:

in,

are the geometrically sensitive parameters of the impeller and rectifier cone sensitive to the vortex-cavitation flow, Refri _original and Refri are the cooling capacity produced by the expansion machine before and after optimization; The efficient adaptive solution process of the impeller-cone geometry co-optimization problem aiming at suppressing vortex cavitation is: 1) For the geometrically sensitive parameters of the expander impeller and the rectifying cone, the DOE experimental design is used to determine the variable combination of the NUM group within the range of the geometrically sensitive parameters of the expander impeller and the rectifying cone.

The corresponding three-dimensional impeller and rectifying cone geometry, the flow field information is obtained through the numerical simulation of the whole machine, and the vortex-cavitation suppression multi-objective optimization function is calculated to obtain the objective function value

2) According to the parameters

and its corresponding objective function value

Fit an initial surrogate model for each optimization objective; 3) Construct while considering the predicted value of the model

and predicted standard deviation

The multi-objective sampling strategy of , where m is the number of optimization objectives, and the normative number of the expected matrix is improved by maximizing the multi-objective

which is

Search for the most potential candidate design, where the most potential candidate design found is:

Optimize the surrogate model and the global search by searching the most potential candidate design, where k is the number of non-dominated points of the multi-objective Pareto front obtained by non-dominated sorting from the NUM evaluated sample points ; 4) Use co-evolutionary optimization algorithm to solve

And build an optimization method characterized by adaptive sampling-cooperative optimization to obtain a potential candidate design, use the corresponding two-phase numerical simulation results and multi-objective function values of the candidate design to dynamically update the proxy model and update the next iteration of the global Search until the predetermined termination condition is met, and output the optimized geometry of the impeller and rectifier cone. 2. The anti-cavitation rectification cone collaborative optimization design method of cryogenic liquid expander according to claim 1, characterized in that the numerical prediction of the two-phase vortex cavitation of cryogenic liquid expander specifically comprises the following steps: Establish the complete machine model including the volute, nozzle, impeller with rectifying cone and diffuser pipe flow channel, and then use the Rayleigh-Plesset cavitation model to describe the two-phase flow in the liquid expander according to the complete machine model. The turbulent flow model and the variable wall function method describe the braided vortex flow downstream of the impeller of the liquid expander; at the same time, the thermophysical properties are expressed as a function of temperature and pressure and combined with the total energy equation to solve it, so as to consider the thermodynamic effect of low temperature fluid and update the calculation in real time Variation of physical properties with pressure and temperature during the process. 3. The anti-cavitation rectification cone collaborative optimization design method of cryogenic liquid expander according to claim 1, characterized in that the specific operation process of analyzing the interference mechanism of impeller-rectifier cone and vortex cavitation and judging the best coupling mode is as follows: According to the working condition parameters of the cryogenic liquid expander, the interference mechanism of the impeller-rectifier cone and vortex cavitation is analyzed, and the correlation between the geometry of the rectifier cone and the vortex cavitation is established, and then the optimal form of the rectifier cone matching the working conditions is determined. And the optimal coupling method of the impeller-cone rectifier, and construct the parametric design scheme of the coupling between the rectifier cone and the three-dimensional impeller. 4. The anti-cavitation rectifying cone collaborative optimization design method of cryogenic liquid expander according to claim 1, characterized in that, based on the impeller-cone rectifying optimal coupling mode, construct the parametric expression of the rectifying cone-impeller coupling, that is, The geometry of the impeller with straightening cone is expressed by the two-dimensional contour line of the meridian plane and the three-dimensional twisted blade. The two-dimensional contour line of the meridian plane is described by the parameterized impeller cover line, the wheel disk line and the straightening cone outer contour line smoothly connected with it , the three-dimensional distorted blade uses spline curve control points to control the deformation of the three-dimensional blade tip and the middle arc of the blade root. 5. The cryogenic liquid expander anti-cavitation rectifying cone cooperative optimization design method according to claim 1, characterized in that the specific process of extracting geometrically sensitive parameters of the expander impeller with rectifying cone is: By changing the geometric parameters of the meridian contour line and the coordinate parameters of the arc control points of the blade shape, the geometry of impellers and rectifying cones of different shapes is obtained, and then the grid division and the numerical solution of the two-phase flow field are performed, and then the variable sensitivity analysis is carried out for the simulation results , obtain a number of geometric parameters of the meridian contour line and control point parameters of the airfoil mid-arc that are sensitive to vortex-cavitation flow, and use the geometrically sensitive parameters and coordinates as optimization variables, and perform three-dimensional impeller and rectifying cone geometry in the optimal design Collaborative fine-tuning.

Images