CN113158356A - Collaborative optimization design method for anti-cavitation rectification cone of low-temperature liquid expansion machine - Google Patents

Collaborative optimization design method for anti-cavitation rectification cone of low-temperature liquid expansion machine Download PDF

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CN113158356A
CN113158356A CN202110130574.0A CN202110130574A CN113158356A CN 113158356 A CN113158356 A CN 113158356A CN 202110130574 A CN202110130574 A CN 202110130574A CN 113158356 A CN113158356 A CN 113158356A
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宋鹏
孙金菊
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Xian Jiaotong University
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Abstract

The invention discloses a collaborative optimization design method for an anti-cavitation rectification cone of a low-temperature liquid expansion machine, which is characterized in that a rectification cone is additionally arranged on an impeller of the low-temperature liquid expansion machine, and the three-dimensional geometric shapes of the impeller and the rectification cone of the low-temperature liquid expansion machine are collaboratively optimized to control the vortex cavitation flow at the downstream of the impeller, and specifically comprises the following steps: the method comprises the steps of sequentially carrying out numerical prediction of two-phase vortex cavitation of the low-temperature liquid expander, analysis of an impeller-rectifying cone and vortex cavitation interference mechanism and judgment of an optimal coupling mode, establishment of rectifying cone-impeller coupling parameterization expression, extraction of geometric sensitive parameters of the expander impeller with the rectifying cone, extraction of vortex cavitation characteristic quantity, establishment of a vortex cavitation inhibition objective function, establishment of an impeller-rectifying cone geometric collaborative optimization problem aiming at vortex cavitation inhibition and self-adaptive solution of the problem.

Description

Collaborative optimization design method for anti-cavitation rectification cone of low-temperature liquid expansion machine
Technical Field
The invention belongs to the fields of low-temperature air separation, low-temperature liquefaction and the like, and relates to a collaborative optimization design method of an anti-cavitation rectification cone and an impeller of a low-temperature liquid expansion machine.
Background
The low-temperature liquid expansion machine is a key energy-saving device of a large-scale air separation plant and a liquefied natural gas plant, and is used for replacing a throttle valve to reduce the vaporization rate, improve the extraction rate of air separation products and realize pressure energy recovery. Liquid cavitation induced by vortex flow at the downstream of an impeller of the low-temperature liquid expansion machine causes impact and corrosion damage to the surface material of the blade, can induce vibration of a machine set, and seriously threatens the stable operation of the liquid expansion machine and a main process low-temperature device. Therefore, the method has great significance for effectively controlling the cavitation flow of the low-temperature liquid expander.
For normal-temperature hydraulic machinery, some anti-cavitation design methods are disclosed. For example, patent 201110202524.5, "an optimal design method for anti-cavitation centrifugal pump impeller", and patent 201510679202.8, "a hydraulic design method for high anti-cavitation centrifugal impeller", all improve the anti-cavitation performance by optimally designing the geometric shape of the centrifugal pump impeller; patent 201110183162.X 'method for inhibiting cavitation on the back surface of a blade of a mixed flow water turbine', the cavitation resistance of the water turbine is improved by drilling the lowest point of the pressure on the back surface of the blade to destroy the formation of cavitation.
However, unlike water pumps, water turbines, etc. operating at normal temperature, cavitation occurs in cryogenic hydraulic machines in a more complex mechanism due to the significant thermodynamic benefits of the cryogenic fluid, which manifests as cavitation induced by either local pressure drop or a small temperature rise. As for domestic and foreign documents, the cavitation resistance method related to the low-temperature hydraulic machine is less. For example, patent 201420342677.9, "a high-efficiency, anti-cavitation vertical multi-stage cryogenic pump", proposes a design method for improving the anti-cavitation capability of a cryogenic centrifugal pump by the design of a spiral groove; 201910014308 'turbine pump inducer cavitation flow numerical prediction method based on low temperature fluid', discloses a turbine pump inducer cavitation flow numerical prediction method based on cavitation model. In the disclosure, only patents 201810008748.4 "an effective control method of vortex cavitation flow in a cryogenic liquid expander" and 201810009053 "an optimal design method of anti-cavitation of a two-phase cryogenic liquid expander" are disclosed for cryogenic liquid expanders, which respectively improve the anti-cavitation performance of the cryogenic liquid expander by performing optimal design on an impeller and adding an induction wheel component.
The mechanism research finds that the vortex flow originated from the trailing edge of the high-speed rotating impeller is expanded to the diffuser pipe along with the main flow, and the local temperature rise caused by the induced local low pressure and the corresponding flow loss is the main reason of cavitation at the downstream of the impeller. Further, when the cryogenic liquid enters the diffuser pipe from the impeller, the flow channel suddenly expands, and further deterioration of the flow is another important cause of cavitation. Therefore, the rectifying cone is additionally arranged at the outlet of the impeller, which is beneficial to reducing the loss caused by the sudden expansion of the flow passage and inhibiting the occurrence of cavitation, and the rectifying cone has simple structure and low cost. However, since the flows in the impeller and the rectifying cone are coupled with each other, there is a complex interference effect with the downstream flow, and the matching of the shapes of the three-dimensional impeller blade and the rectifying cone and the complex influence of the synergistic deformation on the vortex cavitation flow must be considered simultaneously in the design. The vortex cavitation flow is extremely sensitive to the change of the geometric shapes of the trailing edge of the impeller blade and the rectifying cone, the cooperative change and matching of the three-dimensional impeller and the rectifying cone are simultaneously considered in the design, time-consuming prediction numerical calculation is required to be continuously called to predict low-temperature two-phase flow, the complexity of the design problem is greatly increased, and the active anti-cavitation mode is difficult to realize due to the reasons. At present, no public data in the aspect is found at home and abroad.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a collaborative optimization design method for an anti-cavitation rectification cone of a low-temperature liquid expansion machine, which can effectively control vortex cavitation flow and improve the anti-cavitation performance of the low-temperature liquid expansion machine.
In order to achieve the above object, the method for collaborative optimization design of an anti-cavitation rectification cone of a cryogenic liquid expander comprises the steps of adding a rectification cone on an impeller of the cryogenic liquid expander, and carrying out collaborative optimization on three-dimensional geometric shapes of the impeller and the rectification cone of the cryogenic liquid expander so as to control vortex cavitation flow at the downstream of the impeller, and specifically comprises the following steps: the method comprises the steps of sequentially carrying out numerical prediction of two-phase vortex cavitation of the low-temperature liquid expander, analysis of an impeller-rectifying cone and vortex cavitation interference mechanism and judgment of an optimal coupling mode, establishing rectifying cone-impeller coupling parameterization expression, extracting geometric sensitive parameters of the expander impeller with the rectifying cone, extracting vortex cavitation characteristic quantity, establishing a vortex cavitation inhibition objective function, establishing an impeller-rectifying cone geometric collaborative optimization problem aiming at inhibiting vortex cavitation and solving the problem in a self-adaptive mode.
The numerical prediction of the two-phase vortex cavitation of the low-temperature liquid expander specifically comprises the following steps:
establishing a complete machine model comprising a volute, a nozzle, an impeller with a rectifying cone and a diffuser pipe runner, simulating internal cavitation flow of the low-temperature liquid expander by adopting a Rayleigh-Plesset cavitation model according to the complete machine model, and describing the braid-shaped vortex flow of the complete machine of the liquid expander and the downstream of the impeller by utilizing a turbulence model and a variable wall function method; meanwhile, the thermophysical property is expressed as a function of temperature and pressure and is solved by combining a total energy equation so as to consider the thermodynamic effect of the low-temperature fluid and update the change of the physical property along with the pressure and the temperature in the calculation process in real time.
The specific operation process of the interference mechanism analysis and the optimal coupling mode judgment of the impeller-fairing cone and the vortex cavitation comprises the following steps: and (3) analyzing an impeller-rectifying cone and vortex cavitation interference mechanism according to the working condition parameters of the low-temperature liquid expander, establishing a correlation relation between the geometric shape of the rectifying cone and the vortex cavitation, determining an optimal rectifying cone form matched with the working condition and an optimal impeller-rectifying cone coupling mode according to the correlation relation, and constructing a coupling parameterization design scheme of the rectifying cone and the three-dimensional impeller.
The specific process for extracting the geometric sensitive parameters of the expansion machine impeller with the rectifying cone comprises the following steps:
through changing meridian contour line geometric parameters and blade profile camber line control point coordinate parameters, the geometric parameters of impellers and rectifying cones in different shapes are obtained through simulation, then grid division and two-phase flow field numerical solution are carried out, and then variation is carried out on simulation resultsAnalyzing the volume sensitivity to obtain a plurality of meridian contour line geometric parameters and blade profile camber line control point parameters which are sensitive to vortex-cavitation flow, wherein the meridian contour line geometric parameters comprise the inner diameter R of an impeller outlet1Impeller outlet outer diameter R2The included angle alpha between the outer end surface of the inducer and the radial surface1Cone angle beta and dimensionless cone head diameter D0/D1The blade profile mean camber line control point parameters comprise control point coordinate parameters of the three-dimensional blade top and the blade root profile mean camber line.
The characterization expression of the vortex cavitation flow in the cryogenic liquid expander comprises the following steps: by analyzing the mechanism of vortex-cavitation flow in different forms, the average gas volume fraction vfrac of the suction surface of the impeller blade is extractedaveAs the characteristic quantity of cavitation degree at the outlet of the impeller, the average vortex strength lambda in the diffuser pipe at the downstream of the impelleraveThe distribution of the gas volume fraction vfrac of the blade suction surface is predicted by two-phase numerical simulation, and the local vortex intensity lambda is obtained by performing eigenvalue analysis on a local velocity gradient tensor obtained by numerical simulation.
The constructed vortex-cavitation inhibition multi-objective optimization function is as follows:
Figure RE-GDA0003104837840000051
Figure RE-GDA0003104837840000052
wherein the content of the first and second substances,
Figure RE-GDA0003104837840000053
refri, a geometric parameter of impeller and fairing cone sensitivity to vortex-cavitation floworiginalAnd Refri is the refrigeration capacity produced by the front and rear expanders respectively.
The efficient self-adaptive solving process of the geometric collaborative optimization problem of the impeller-fairing cone aiming at the inhibition of the vortex cavitation comprises the following steps:
1) aiming at the geometric sensitive parameters of the impeller and the rectifier cone of the expander, NUM variable combinations are determined in the variation range of the geometric sensitive parameters of the impeller and the rectifier cone of the expander by utilizing DOE experimental design, and aiming at the parameters in each variable combination
Figure RE-GDA00031048378400000511
Corresponding three-dimensional impeller and rectifying cone geometry, obtaining flow field information through numerical simulation of the whole machine, and calculating a vortex-cavitation inhibition multi-objective optimization function to obtain an objective function value
Figure RE-GDA0003104837840000054
2) According to the parameters
Figure RE-GDA0003104837840000055
And its corresponding objective function value
Figure RE-GDA0003104837840000056
Fitting an initial proxy model of each optimization target;
3) construction while taking model predictions into account
Figure RE-GDA0003104837840000057
And predicted standard deviation
Figure RE-GDA0003104837840000058
Wherein m is the number of optimization objectives, and the number of criteria for improving the expectation matrix by maximizing the multi-objectives
Figure RE-GDA0003104837840000059
Namely, it is
Figure RE-GDA00031048378400000510
Searching the most potential candidate design, wherein the searched most potential candidate design is as follows:
Figure RE-GDA0003104837840000061
Figure RE-GDA0003104837840000062
optimizing the agent model and the global search through the searched most potential candidate design, wherein k is the number of multi-target pareto frontier non-dominant points obtained through non-dominant sorting from NUM evaluated sample points;
4) solving using a coevolution optimization algorithm
Figure DEST_PATH_GDA0003104837840000063
And obtaining a potential candidate design by an optimization mode characterized by the constructed adaptive sampling-collaborative optimization, dynamically updating the proxy model by using the candidate design, a corresponding two-phase numerical simulation result and a multi-target function value, and carrying out next iterative global search until a preset termination condition is met and outputting the optimized impeller and fairing cone geometry.
The invention has the following beneficial effects:
in the collaborative optimization design method for the anti-cavitation rectification cone of the low-temperature liquid expansion machine, when the method is in specific operation, the rectification cone is additionally arranged on the impeller of the low-temperature liquid expansion machine, and the three-dimensional geometric shapes of the impeller and the rectification cone of the low-temperature liquid expansion machine are collaboratively optimized, so that the vortex cavitation flow at the downstream of the impeller is effectively inhibited, the anti-cavitation performance of the low-temperature liquid expansion machine is improved, the vibration, the halt of a machine set and the shutdown of an air separation liquefaction device are avoided, and the performance and the operation reliability of the low-temperature liquid expansion machine are effectively improved.
Drawings
FIG. 1a is a schematic view of a liquid expander complete model;
FIG. 1b is a schematic illustration of a liquid expander with a fairing cone impeller and a downstream diffuser tube;
FIG. 2a is a schematic view of a liquid expander without a fairing cone impeller;
FIG. 2b is a schematic view of a liquid expander with a spherical fairing cone;
FIG. 2c is a schematic view of a liquid expander with an ellipsoidal cone;
FIG. 2d is a schematic view of a liquid expander having a spherical head with a tapered cone;
FIG. 3a is a schematic view of a meridian profile parameterization;
FIG. 3b is a schematic view of a three-dimensional blade;
FIG. 3c is a schematic diagram of a primitive leaf profile;
FIG. 3d is a schematic parametric illustration of the camber line of the blade;
FIG. 4 is a schematic diagram of an adaptive solution of a nonlinear optimization problem targeting vortex-cavitation suppression.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
when the method for designing the cavitation-resistant rectification cone collaborative optimization of the low-temperature liquid expander is operated, the rectification cone is additionally arranged on the impeller of the low-temperature liquid expander, and the three-dimensional geometric shapes of the impeller and the rectification cone of the low-temperature liquid expander are collaboratively optimized to control the vortex cavitation flow at the downstream of the impeller, and the method specifically comprises the following steps: the method comprises the steps of sequentially carrying out numerical prediction of two-phase vortex cavitation of the low-temperature liquid expander, analysis of an impeller-rectifying cone and vortex cavitation interference mechanism and judgment of an optimal coupling mode, establishing rectifying cone-impeller coupling parameterization expression, extracting geometric sensitive parameters of the expander impeller with the rectifying cone, extracting vortex cavitation characteristic quantity, establishing an impeller-rectifying cone geometric collaborative optimization problem aiming at vortex cavitation inhibition and self-adapting solving of the problem.
Referring to fig. 1a and 1b, the numerical prediction of the two-phase vortex cavitation of the cryogenic liquid expander specifically includes the following steps:
establishing a complete machine model comprising a volute, a nozzle, an impeller with a rectifying cone and a diffuser pipe runner to reflect the real flow in the expander, carrying out grid division on each component river basin by using ICEM and CFX-TURBORID, and then connecting through an interface to form a complete machine grid.
A Rayleigh-Plesset (PR) cavitation model is selected to describe the internal cavitation flow of the cryogenic liquid expander. The cavitation model regards cavitation as a volume fraction control equation for a two-phase three-component system, with each component having an assumed mixed phase mass, momentum, and energy equation of the same velocity, and employs the PR equation for predicting vaporization rate and cavitation generation and destruction.
And describing the braided vortex flow of the whole machine of the liquid expansion machine and the downstream of the impeller by combining a k-epsilon model and a variable wall function method. The dynamic and static Rotor interfaces between the nozzle and the impeller and between the impeller and the diffuser pipe are processed by a Frozen Rotor model, and the calculation consumption is reduced on the basis of keeping the circumferential distribution characteristics of flow field parameters.
Expressing physical parameters including density, enthalpy, entropy, viscosity coefficient and saturated vapor pressure as a binary function of temperature and pressure, and solving by combining a total energy equation to consider the thermodynamic effect of the cryogenic fluid;
and compiling a physical property interface file by using CEL (CFX Expression language), and introducing CFX and combining a total energy equation to solve so as to realize real-time update of physical property parameters along with the change of local pressure and temperature in the calculation process, and simultaneously, monitoring the convergence of the solution of the temperature field in real time in the iterative solution process of numerical simulation so as to ensure the solution precision of the temperature field.
Referring to fig. 2a to 2d, the specific operation process of analyzing the interference mechanism of the impeller-fairing cone and the vortex cavitation and judging the optimal coupling mode is as follows:
1) aiming at three forms of an impeller outlet equal-diameter spherical rectifying cone, an ellipsoidal rectifying cone and a spherical head tapered rectifying cone, a group of initialization designs are respectively completed;
2) aiming at the initial design of different forms of rectifier cones, performing geometric modeling and grid division, performing research on the downstream vortex cavitation flow characteristics of the impeller under the coupling of the non-rectifier cone and the different forms of rectifier cones by using a low-temperature liquid expander two-phase vortex cavitation numerical prediction method, capturing the circumferential unbalanced velocity gradient characteristics of the outlet of the impeller and the coupling characteristics of the outlet of the impeller and a downstream sudden expansion region, and diagnosing key geometric factors causing the remarkable deterioration of the downstream flow of the impeller;
3) and continuously changing the geometric form and parameters of the blade, developing geometric sensitivity research, obtaining the correlation between the geometric shapes of the rectifying cones and the vortex cavitation in different forms and different parameters, and determining the optimal rectifying cone form matched with the working condition and the coupling parameterization design scheme of the rectifying cone and the three-dimensional impeller on the basis.
Referring to fig. 3a and 3b, the specific process of geometric parameterization expression and sensitive parameter extraction of the expander impeller with the fairing cone is as follows:
the three-dimensional impeller geometry is defined by a meridian contour line two-dimensional line and a three-dimensional twisted blade together, the meridian contour line two-dimensional line respectively defines a wheel disc line and a wheel cover line through two parabola curves 1-4 and 2-3, and a rectifying cone outer contour line which is smoothly connected with the meridian contour line, takes a spherical head part with a taper as an example, and adopts an arc head part and a tangent line part to define an axisymmetric contour line with the taper; the pressure surface and the suction surface of the three-dimensional twisted blade are straight-line surfaces, and can be defined by two-dimensional blade profiles at the blade root (wheel disc) and the blade top (wheel cover), referring to fig. 3c, the camber lines of the blade profiles at the blade root and the blade top are parameterized by using bezier curves shown in fig. 3d, and the coordinates of control points of the bezier curves are adjusted in the design process, so that the fine optimization of the three-dimensional blade is realized. According to the definition, the impeller-rectifying cone geometry can realize the cooperative deformation control of the three-dimensional impeller and the rectifying cone geometry by adjusting the geometric parameters of the sub-meridian contour line and the coordinates of the control points of the camber line of the blade profile. And an own program is compiled based on the geometric parameterization method, and the geometric parameterization method is used for quickly generating an impeller three-dimensional geometric file including a meridian contour line and three-dimensional blades according to different geometric parameter control variables in the optimization process and is used for numerical simulation.
The specific steps of sensitive parameter extraction are as follows: the geometric parameters of the meridian contour line and the coordinate parameters of the control points of the camber line of the blade profile are changed to obtain the geometric parameters of impellers and rectifying cones with different shapes, and geometric modeling, grid division and flow field numerical simulation and analysis are carried out on the geometric parameters and the rectifying cones. Analyzing the flow field data obtained after simulation, and obtaining the geometric parameters sensitive to vortex-cavitation flow by variable sensitivity analysis, wherein the geometric parameters specifically comprise meridian plane geometric parameters, rectifying cone geometric parameters and three-dimensional geometric parametersCoordinate parameters of a plurality of control points of camber lines of blade tops and blade root blade profiles, wherein the meridian plane geometric parameters comprise the inner diameter R of an impeller outlet1Impeller outlet outer diameter R2And an included angle alpha between the outer end surface of the inducer and the radial surface1The geometrical parameters of the fairing cone comprise the angle beta of the fairing cone and the diameter D of the head of the fairing cone without dimension0/D1And the sensitive geometric parameters and the coordinates are used as optimization variables, and the three-dimensional impeller and the rectifying cone are subjected to cooperative fine adjustment in the optimization design, so that the effective control of vortex cavitation flow is realized.
And compiling a self-contained program based on the geometric parameterization method, and quickly generating a three-dimensional geometric file including the meridian plane molded line, the rectifying cone molded line and the three-dimensional blade according to different geometric parameter control variables in the optimization process for numerical simulation.
The specific mode of extracting the vortex cavitation characteristic quantity and constructing the vortex cavitation inhibition objective function is as follows:
vortex-cavitation flow at the downstream of the impeller of the low-temperature liquid expander is highly coupled, the mechanism analysis is carried out on the vortex-cavitation flow in different forms through a large number of numerical simulations, and the average gas volume fraction vfrac of the suction surface of the impeller blade is extractedaveAs the characteristic quantity of cavitation degree at the outlet of the impeller, the average vortex strength lambda in the diffuser pipe at the downstream of the impelleraveAs the characteristic quantity of vortex flow, the specific connotation and the calculation mode are as follows:
and (3) cavitation flow characterization quantity at an impeller outlet and calculation thereof: dividing the average gas volume fraction of the suction surface of the impeller blade by vfracaveAs a cavitation degree characterization quantity at the impeller outlet, the cavitation degree characterization quantity not only reflects the intensity of cavitation at the impeller outlet, but also is positively correlated with the cavitation intensity in a downstream diffuser, namely vfracaveThe integral average of the gas volume fraction on the suction surface of the blade is calculated by the following formula:
Figure BDA0002925035670000101
vfrac is the local gas volume fraction, dA is the infinitesimal Area, AreabladeIs the surface area of the suction surface of the blade.
And (3) vortex flow characterization quantity and calculation: average vortex strength lambda in a diffuser pipe at the downstream of an impelleraveAs a characteristic quantity of swirl flow, it is defined as an area-weighted average of swirl intensity λ on a symmetrical middle section of the diffuser pipe axis, i.e.
Figure BDA0002925035670000111
Wherein dA is infinitesimal Area, AreatubeMiddle cross-sectional area, λ, of diffuser pipeciThe local vortex intensity can be obtained by performing eigenvalue analysis on the following velocity gradient tensor D obtained by numerical simulation, specifically:
Figure BDA0002925035670000112
the characteristic value lambda satisfies:
λ3+Pλ2+Qλ+R＝0
wherein the content of the first and second substances,
Figure BDA0002925035670000113
Q＝(d22d33-d23d32)+(d11d22-d12d21)+(d33d11-d13d31)
R＝d11(d23d32-d22d33)+d12(d21d33-d31d23)+d13(d31d22-d21d32)
setting:
Figure BDA0002925035670000114
Figure BDA0002925035670000115
when the following conditions are satisfied:
Figure BDA0002925035670000116
the tensor D has a real eigenvalue λrAnd a pair of conjugated complex eigenvalues λcr±iλciWherein:
setting:
Figure BDA0002925035670000117
Figure BDA0002925035670000121
then:
Figure BDA0002925035670000122
Figure BDA0002925035670000123
Figure BDA0002925035670000124
wherein λ isciThe local vortex intensity is calculated as required.
In order to inhibit the generation of vortex-cavitation at the same time, the cavitation degree characterization quantity vfrac at the outlet of the impeller is synthesizedaveAnd average swirl strength lambda in diffuser downstream of impelleraveConstructing the following vortex-cavitation inhibition optimization multi-objective function:
Figure RE-GDA0003104837840000128
Figure RE-GDA0003104837840000129
wherein the content of the first and second substances,
Figure DEST_PATH_GDA00031048378400001210
representing geometric sensitivity parameters of impellers and cones sensitive to vortex-cavitation flow, RefrioriginalAnd Refri respectively represents the refrigeration capacity produced by the expansion machines before and after optimization, the objective function is used for simultaneously minimizing the gas volume fraction of the suction surface of the blade and the internal vortex strength of the diffuser pipe at the downstream of the impeller, and the constraint condition is used for ensuring that the refrigeration capacity of the expansion machines before and after optimization does not remarkably decrease so as to meet the requirements of air separation and low-temperature processes.
The process of efficiently solving the multi-target complex non-linear optimization problem aiming at the vortex-cavitation inhibition comprises the following steps:
the method combines a multi-objective self-adaptive sampling proxy model method, a collaborative optimization algorithm, an expander impeller geometric parameterization method with a rectifying cone and a low-temperature two-phase vortex cavitation flow numerical prediction method to establish a collaborative optimization design platform of the anti-cavitation rectifying cone and the impeller of the low-temperature liquid expander as shown in figure 4, and the method mainly comprises the following functional modules:
a geometric parameterization module: an automatic program is compiled based on an expander impeller geometric parametric expression method with a rectifying cone, and geometric files including impeller meridian plane molded lines, rectifying cone molded lines and three-dimensional blades are quickly generated according to different geometric parameter variables and are used for numerical analysis.
An automatic numerical prediction module for vortex cavitation flow: based on the liquid expander low-temperature two-phase vortex cavitation flow numerical prediction method, the whole process of numerical simulation is fully automatically completed by calling a CFD module through a self-owned program, and in the optimization process, the vortex cavitation flow automatic numerical prediction module is called in batch, and the specific process is as follows: firstly, starting a geometric parameterization module to obtain a three-dimensional geometric file of a candidate design; secondly, importing the geometric model into grid software, and performing automatic grid division through a topology template technology; thirdly, setting two-phase numerical simulationThe method comprises the steps of importing a grid, a physical model, setting boundary conditions, a cavitation model and a turbulence model; fourthly, starting a CFD solver to solve in parallel through a self-owned program; fifthly, after calculation convergence, calling a post-processing module to obtain flow field data needed everywhere; sixth, respectively calculating
Figure RE-GDA0003104837840000131
And
Figure RE-GDA0003104837840000132
and the objective function calculation is completed.
The agent model initialization module: aiming at geometric sensitive parameters of an impeller and a rectifying cone of the expander, determining geometric parameters of NUM groups of impellers and rectifying cones in a variation range by using DOE (Design of Experiment), and aiming at geometric parameters of each group
Figure RE-GDA0003104837840000141
Corresponding three-dimensional impeller and rectifying cone geometry, obtaining flow field data thereof through a vortex cavitation flow automatic numerical prediction module, and calculating characteristic quantity
Figure RE-GDA0003104837840000142
And
Figure RE-GDA0003104837840000143
the numerical value of (c). On the basis, multiple corresponding objective function values of M groups of variable combinations are calculated, geometric parameters and corresponding objective function values are stored in a database module, and variables are controlled in the NUM groups
Figure RE-GDA0003104837840000144
And corresponding objective function value
Figure RE-GDA0003104837840000145
Is used for predicting an objective function value corresponding to an unknown variable combination and guiding the optimization aiming at inhibiting the vortex cavitation in the optimization processAnd (6) carrying out the process.
The self-adaptive sampling-collaborative optimization module: an optimization method module with the characteristics of multi-target adaptive sampling-collaborative optimization is established based on a Kriging Surrogate Model, a multi-target improved expectation Matrix (EIM) method and a collaborative Co-evolution Algorithm (CCEA), and is suitable for solving a nonlinear optimization problem requiring time-consuming numerical simulation.
The kriging agent model is responsible for establishing a correlation between geometric variables in the sample database and corresponding objective function values, and is used for predicting the objective function values of unknown variable combinations and guiding the optimization process aiming at vortex-cavitation inhibition. For the following multi-objective optimization function with m optimization objectives, the fitted kriging proxy model can provide the optimization variables at the same time
Figure RE-GDA0003104837840000146
A predicted value of
Figure RE-GDA0003104837840000147
And predicted standard deviation
Figure RE-GDA0003104837840000148
Figure RE-GDA0003104837840000151
For known minimum values y in the sample libraryi，minI is more than or equal to 1 and less than or equal to m, in optimizing variables
Figure RE-GDA0003104837840000152
To improve the value
Figure RE-GDA0003104837840000153
In that
Figure RE-GDA0003104837840000154
An expectation function, i.e. a multi-objective improved expectation matrix (Expected improvement)ment Matrix, EIM) is defined as:
Figure RE-GDA0003104837840000155
construction while taking model predictions into account
Figure RE-GDA0003104837840000156
And predicted standard deviation
Figure RE-GDA0003104837840000157
By maximizing the normalized number of the multi-objective Improvement expectation Matrix (EIM)
Figure RE-GDA0003104837840000158
Namely, it is
Figure RE-GDA0003104837840000159
And searching the most potential candidate design to consider the predicted optimal value and the predicted uncertainty of the proxy model and indicate the potential areas where the optimal design is most likely to exist and the areas where the model is poor in prediction accuracy.
Figure RE-GDA00031048378400001510
And using the candidate design obtained by searching for improving the model precision and global searching, wherein k is the number of multi-target pareto frontier non-dominant points obtained by non-dominant sorting from NUM evaluated sample points.
The auxiliary optimization problem is a high-dimensional nonlinear optimization problem, and is difficult to solve. The method solves the problem by using a coevolution algorithm CCEA. According to the method, through variable correlation analysis, a multi-dimensional optimization problem is decomposed into a plurality of sub-problems which are easy to solve for collaborative solving, and a new design sample with potential is obtained quickly
Figure RE-GDA00031048378400001511
And modified proxy model parameters
Figure RE-GDA00031048378400001512
I.e. to perform global searches simultaneously to
For newly obtained samples
Figure RE-GDA0003104837840000161
And calling a vortex cavitation flow automatic numerical prediction module to obtain flow field data and calculate a corresponding objective function value according to the corresponding three-dimensional impeller and the corresponding geometry of the rectifying cone, adding a new sample and the objective function of the new sample into a database at the same time, and performing next optimization.
And carrying out iterative loop according to the steps, continuously interacting through a self-adaptive sampling-collaborative optimization module to continuously improve the precision of the proxy model and provide a more optimal design until a preset optimization search termination criterion is met, and outputting the optimized impeller and the optimized fairing cone geometry.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (8)

1. The method for designing the collaborative optimization of the anti-cavitation rectification cone of the low-temperature liquid expander is characterized in that the rectification cone is additionally arranged on an impeller of the low-temperature liquid expander, and the three-dimensional geometric shapes of the impeller and the rectification cone of the low-temperature liquid expander are collaboratively optimized to control the vortex cavitation flow at the downstream of the impeller, and specifically comprises the following steps: the method comprises the steps of sequentially carrying out two-phase vortex cavitation numerical prediction of the low-temperature liquid expander, analysis of an impeller-rectifying cone and vortex cavitation interference mechanism and judgment of an optimal coupling mode, establishing rectifying cone-impeller coupling parameterization expression, extracting geometric sensitive parameters of the expander impeller with the rectifying cone, extracting vortex cavitation characteristic quantity, establishing a vortex cavitation inhibition objective function, establishing an impeller-rectifying cone geometric collaborative optimization problem aiming at inhibiting vortex cavitation and solving the problem in a self-adaptive mode.
2. The collaborative optimization design method for the anti-cavitation rectification cone of the cryogenic liquid expander as recited in claim 1, wherein the numerical prediction of the two-phase vortex cavitation of the cryogenic liquid expander specifically comprises the following steps:
establishing a complete machine model comprising a volute, a nozzle, an impeller with a rectifying cone and a diffuser pipe runner, describing two-phase flow in the liquid expander by adopting a Rayleigh-Plesset cavitation model according to the complete machine model, and describing the braid-shaped vortex flow at the downstream of the impeller of the liquid expander by utilizing a turbulence model and a variable wall function method; meanwhile, the thermophysical property is expressed as a function of temperature and pressure and is solved by combining a total energy equation so as to consider the thermodynamic effect of the low-temperature fluid and update the change of the physical property along with the pressure and the temperature in the calculation process in real time.
3. The method for collaborative optimization design of the anti-cavitation rectification cone of the cryogenic liquid expander according to claim 1, wherein the specific operation processes of the analysis of the interference mechanism of the impeller-rectification cone and the vortex cavitation and the judgment of the optimal coupling mode are as follows:
and (3) analyzing an impeller-rectifying cone and vortex cavitation interference mechanism according to the working condition parameters of the low-temperature liquid expander, establishing a correlation relation between the geometric shape of the rectifying cone and the vortex cavitation, determining an optimal rectifying cone form matched with the working condition and an optimal impeller-rectifying cone coupling mode according to the correlation relation, and constructing a coupling parameterization design scheme of the rectifying cone and the three-dimensional impeller.
4. The method for the collaborative optimization design of the anti-cavitation rectification cone of the cryogenic liquid expander as claimed in claim 1, wherein a parameterized expression of rectification cone-impeller coupling is constructed based on an impeller-rectification cone optimal coupling mode, that is, the geometry of an impeller with the rectification cone is jointly expressed by a meridian plane two-dimensional contour line and a three-dimensional twisted blade, the meridian plane two-dimensional contour line is described by using a parameterized impeller crown line, a wheel disc line and a rectification cone outer contour line which is in sliding connection with the meridian plane two-dimensional contour line, and the three-dimensional twisted blade performs deformation control on a three-dimensional blade tip and a blade root middle arc line by using a spline curve control point.
5. The method for the collaborative optimization design of the anti-cavitation rectification cone of the cryogenic liquid expander according to claim 1, wherein the specific process of extracting the geometric sensitive parameters of the impeller of the expander with the rectification cone is as follows:
the method comprises the steps of obtaining the geometric parameters of impellers and rectifying cones with different shapes by changing the geometric parameters of meridian contour lines and the coordinate parameters of control points of camber lines of blade profiles, then carrying out grid division and numerical solution of two-phase flow fields, then carrying out variable sensitivity analysis on simulation results, obtaining a plurality of geometric parameters of meridian contour lines and control points of camber lines of blade profiles which are sensitive to vortex-cavitation flow, taking the sensitive geometric parameters and the coordinates as optimization variables, and carrying out cooperative fine adjustment on the geometric parameters of three-dimensional impellers and rectifying cones in the optimization design.
6. The collaborative optimization design method for the anti-cavitation rectification cone of the cryogenic liquid expander as recited in claim 1, wherein the characterization of the vortical cavitation flow in the cryogenic liquid expander comprises the following steps:
by analyzing the mechanism of vortex-cavitation flow in different forms, the average gas volume fraction vfrac of the suction surface of the impeller blade is extractedaveAnd taking the value as the characteristic quantity of cavitation degree at the outlet of the impeller, and taking the average vortex intensity lambda in a diffuser pipe at the downstream of the impelleraveThe distribution of the gas volume fraction vfrac of the blade suction surface is predicted by two-phase numerical simulation, and the local vortex intensity lambda is obtained by performing eigenvalue analysis on a local velocity gradient tensor obtained by numerical simulation.
7. The collaborative optimization design method for the anti-cavitation rectification cone of the cryogenic liquid expander as recited in claim 1, wherein the constructed vortex-cavitation inhibition multi-objective optimization function is:
Figure RE-FDA0003104837830000031
Figure RE-FDA0003104837830000032
wherein the content of the first and second substances,
Figure RE-FDA0003104837830000033
refri, a geometric parameter of impeller and fairing cone sensitivity to vortex-cavitation floworiginalAnd Refri is the refrigeration capacity produced by the front and rear expanders respectively.
8. The method for designing the cavitation-resistant rectification cone collaborative optimization of the cryogenic liquid expander as claimed in claim 1, wherein the efficient adaptive solving process of the impeller-rectification cone geometric collaborative optimization problem aiming at the suppression of the vortex cavitation is as follows:
1) aiming at the geometric sensitive parameters of the impeller and the rectifier cone of the expander, NUM variable combinations are determined in the variation range of the geometric sensitive parameters of the impeller and the rectifier cone of the expander by utilizing DOE experimental design, and aiming at the parameters in each variable combination
Figure RE-FDA0003104837830000039
Corresponding three-dimensional impeller and rectifying cone geometry, obtaining flow field information through numerical simulation of the whole machine, and calculating a vortex-cavitation inhibition multi-objective optimization function to obtain an objective function value
Figure RE-FDA0003104837830000034
2) According to the parameters
Figure RE-FDA0003104837830000035
And its corresponding objective function value
Figure RE-FDA0003104837830000036
Fitting an initial proxy model of each optimization target;
3) construction while taking model predictions into account
Figure RE-FDA0003104837830000037
And predicted standard deviation
Figure RE-FDA0003104837830000038
Wherein m is the number of optimization objectives, and the number of criteria for improving the expectation matrix by maximizing the multi-objectives
Figure RE-FDA0003104837830000041
Namely, it is
Figure RE-FDA0003104837830000042
Searching the most potential candidate design, wherein the searched most potential candidate design is as follows:
Figure RE-FDA0003104837830000043
Figure RE-FDA0003104837830000044
optimizing the agent model and the global search through the searched most potential candidate design, wherein k is the number of multi-target pareto frontier non-dominant points obtained through non-dominant sorting from NUM evaluated sample points;
4) solving using a coevolution optimization algorithm
Figure RE-FDA0003104837830000045
And constructing an optimization mode characterized by self-adaptive sampling-collaborative optimization to obtain a potential candidate design, dynamically updating the proxy model by using a two-phase numerical simulation result and a multi-target function value corresponding to the candidate design, and carrying out next iteration global search until a preset termination condition is met, and outputting the optimized impeller and the optimized fairing cone geometry.
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