CN113158356B - Collaborative optimization design method for anti-cavitation rectification cone of low-temperature liquid expander - Google Patents
Collaborative optimization design method for anti-cavitation rectification cone of low-temperature liquid expander Download PDFInfo
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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 a rectifying cone-impeller coupling parameterization expression, extraction of geometric sensitive parameters of an expander impeller with a rectifying cone, extraction of vortex cavitation characteristic quantity, establishment of a vortex cavitation inhibition target function, establishment of an impeller-rectifying cone geometric collaborative optimization problem aiming at inhibiting vortex cavitation and self-adaptive solution of the problem.
Description
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 air separation device and a liquefied natural gas device, and is used for replacing a throttling 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 at the downstream of the impeller of the low-temperature liquid expansion machine causes impact and corrosion damage to the surface material of the blade, can induce the vibration of the machine set, and seriously threatens the stable operation of the liquid expansion machine and the main process low-temperature device. Therefore, the method has great significance for realizing effective control on the cavitation flow of the low-temperature liquid expander.
For normal temperature hydraulic machinery, some anti-cavitation design methods have been disclosed. For example, patent 201110202524.5 "an anti-cavitation centrifugal pump impeller optimal design method", patent 201510679202.8 "a high anti-cavitation centrifugal impeller hydraulic design method" all improve the anti-cavitation performance of the centrifugal pump impeller by optimally designing the geometric shape of the centrifugal pump impeller; patent 201110183162.X 'method for inhibiting back cavitation of blades of a francis turbine', the lowest point of pressure of the back of the blades is drilled, so that the formation of cavitation is destroyed, and the anti-cavitation performance of the turbine is improved.
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 discloses a turbine pump inducer cavitation flow numerical prediction method based on a cavitation model. In the disclosure, only patents 201810008748.4 of "an effective control method for vortex cavitation flow in a cryogenic liquid expander" and 201810009053 of "an optimal design method for anti-cavitation of a two-phase cryogenic liquid expander" are provided for the cryogenic liquid expander, and the anti-cavitation performance of the cryogenic liquid expander is improved by respectively 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 of:
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 the total energy equation is combined to solve 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 analysis of the interference mechanism of the impeller-rectifying cone and the vortex cavitation and the judgment of the optimal coupling mode is 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.
The method comprises the following specific process of extracting geometric sensitive parameters of the expansion machine impeller with the rectifying cone:
the method comprises the steps of simulating and obtaining the geometric parameters of impellers and rectifying cones in 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, carrying out variable sensitivity analysis on simulation results, and obtaining a plurality of geometric parameters of meridian contour lines and control point parameters of camber lines of blade profiles which are sensitive to vortex-cavitation flow, wherein the geometric parameters of the meridian contour lines comprise the inner diameter R of an impeller outlet 1 Impeller outlet outer diameter R 2 The included angle alpha between the outer end surface of the inducer and the radial surface 1 Cone angle beta and dimensionless cone head diameter D 0 /D 1 The blade profile camber line control point parameters comprise control point coordinate parameters of the blade top of the three-dimensional blade and the blade root camber line.
Internal vortex cavitation flow of low-temperature liquid expanderThe dynamic characterization expression 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 extracted ave As 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 impeller ave The 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:
wherein,
refri, a geometric parameter of impeller and fairing cone sensitivity to vortex-cavitation flow original And Refri is used for optimizing the refrigerating capacity produced by the front and rear expanders respectively.
The efficient self-adaptive solving process of the geometric collaborative optimization problem of the impeller-rectifier cone with the aim of inhibiting the vortex cavitation comprises the following steps:
1) Aiming at the geometric sensitive parameters of the impeller and the fairing cone of the expander, NUM variable combinations are determined in the variation range of the geometric sensitive parameters of the impeller and the fairing cone of the expander by utilizing DOE experimental design, and aiming at the parameters in each variable combination, NUM variable combinations are determined
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
2) According to the parameters
And its corresponding objective function value
Fitting an initial proxy model of each optimization target;
3) Construction while taking model predictions into account
And predicted standard deviation
Wherein m is the number of optimization objectives, and the number of criteria for improving the expectation matrix by maximizing the multi-objectives
Namely, it is
Searching the most potential candidate design, wherein the searched most potential candidate design is as follows:
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
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 expander, when in specific operation, the rectification cone is additionally arranged on the impeller of the low-temperature liquid expander, and the three-dimensional geometric shapes of the impeller of the low-temperature liquid expander and the rectification cone 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 expander is improved, the unit vibration, the machine halt and the shutdown of an air separation liquefaction device are avoided, and the performance and the operation reliability of the low-temperature liquid expander 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 representation 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 low-temperature 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 binary functions of temperature and pressure, and solving by combining a total energy equation so as to consider the thermodynamic effect of the cryogenic fluid;
and compiling a physical property interface file by using a CEL (CFX Expression Language), introducing the CFX into the 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 fig. 2d, the specific operation processes of the analysis of the interference mechanism of the impeller-rectifying cone and the vortex cavitation and the discrimination of the optimal coupling mode are 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 downstream vortex cavitation flow characteristic research of an impeller under the coupling of a non-rectifier cone and different forms of rectifier cones by using a low-temperature liquid expander two-phase vortex cavitation numerical prediction method, capturing the peripheral unbalanced velocity gradient characteristic of an impeller outlet and the coupling characteristic of the peripheral unbalanced velocity gradient characteristic and a downstream sudden expansion region, and diagnosing key geometric factors causing the obvious 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 geometric shape of the impeller-rectifying cone can realize the cooperative deformation control of the geometric shapes of the three-dimensional impeller and the rectifying cone by adjusting the geometric parameters of the sub-meridian contour line and the coordinates of the control point 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 flow field data obtained after simulation, and obtaining geometric parameters sensitive to vortex-cavitation flow through variable sensitivity analysis, wherein the geometric parameters specifically comprise meridian plane geometric parameters, rectification cone geometric parameters and coordinate parameters of a plurality of control points of three-dimensional blade top and blade root profile camber lines, and the meridian plane geometric parameters comprise impeller outlet inner diameter R 1 Impeller outlet outer diameter R 2 And an included angle alpha between the outer end surface of the inducer and the radial surface 1 The geometrical parameters of the rectifier cone comprise the cone angle beta of the rectifier cone and the head diameter D of the non-dimensional rectifier cone 0 /D 1 And 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 a self-contained program is compiled based on the geometric parameterization method, and the geometric parameterization method is used for quickly generating a three-dimensional geometric file including an impeller meridian plane molded line, a rectifying cone molded line and a three-dimensional blade according to different geometric parameter control variables in an optimization process and is used 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 extracted ave As 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 impeller ave As 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 vfrac ave As 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 vfrac ave The integral average of the gas volume fraction on the suction surface of the blade is calculated by the following formula:
vfrac is the local gas volume fraction, dA is the infinitesimal Area, area blade Is the surface area of the suction surface of the blade.
And (3) vortex flow characterization quantity and calculation: the average vortex strength lambda in the diffuser pipe at the downstream of the impeller ave As a swirl flow characteristic quantity, it is defined as an area-weighted average of swirl intensity λ in a diffuser axisymmetric middle section, i.e.
Wherein dA is infinitesimal Area, area tube Middle cross-sectional area, λ, of diffuser pipe ci The local vortex intensity can be obtained by performing eigenvalue analysis on the following velocity gradient tensor D obtained by numerical simulationThe body is as follows:
the characteristic value lambda satisfies:
λ 3 +Pλ 2 +Qλ+R＝0
wherein,
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 )
setting:
when the following conditions are satisfied:
the tensor D has a real eigenvalue λ r And a pair of conjugated complex eigenvalues λ cr ±iλ ci Wherein:
setting:
then:
wherein λ is ci The local vortex strength 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 synthesized ave And average swirl strength lambda in diffuser downstream of impeller ave Constructing the following vortex-cavitation inhibition optimization multi-objective function:
wherein,
representing geometric sensitivity parameters of impellers and cones sensitive to vortex-cavitation flow, refri original And Refri represents the refrigeration capacity produced by the expander before and after optimization respectively, and the objective function is used for simultaneously minimizing the gas volume fraction of the suction surface of the blade and the internal rotation of the diffuser pipe at the downstream of the impellerThe vortex strength and the constraint condition are used for ensuring that the cold quantity of the expansion mechanism does not decrease remarkably before and after optimization 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:
a multi-objective self-adaptive sampling proxy model method, a collaborative optimization algorithm, an expander impeller geometric parameterization method with a rectifier cone and a low-temperature two-phase vortex cavitation flow numerical prediction method are combined to establish a collaborative optimization design platform of the anti-cavitation rectifier cone and the impeller of the low-temperature liquid expander shown in the figure 4, and the main functional modules and the concrete implementation of the platform are as follows:
a geometric parameterization module: an automatic program is compiled based on an expander impeller geometric parameterization 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 numerical simulation process is fully automatically completed by calling a CFD (computational fluid dynamics) module through a self-contained program, and in the optimization process, the vortex cavitation flow automatic numerical prediction module is called in batches, and the specific process is as follows: firstly, starting a geometric parameterization module to obtain a three-dimensional geometric file of a candidate design; step two, importing the geometric model into grid software, and performing automatic grid division through a topological template technology; thirdly, setting two-phase numerical simulation, including importing a grid, a physical property 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
And
and accomplish the purposeAnd (4) calculating a standard function.
The agent model initialization module: aiming at geometric sensitive parameters of an expander impeller and a rectifying cone, geometric parameters of NUM groups of impellers and rectifying cones are determined in the variation range of the geometric sensitive parameters by using DOE (Design of Experiment), and aiming at geometric parameters of each group
Corresponding three-dimensional impeller and rectifying cone geometry, obtaining flow field data thereof through an eddy cavitation flow automatic numerical prediction module, and calculating characteristic quantity
And
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
And corresponding objective function value
Fitting a relatively rough initial proxy model, wherein the proxy model is used for predicting an objective function value corresponding to an unknown variable combination and guiding an optimization process aiming at inhibiting the vortex cavitation in the optimization 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.
Wherein, the kriging agent model is responsible for establishing the phase of the geometric variable and the corresponding objective function value in the sample databaseAnd the correlation is used for predicting an objective function value of the unknown variable combination and guiding an 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
A predicted value of
And predicted standard deviation
For known minimum values y in the sample library i，min I is more than or equal to 1 and less than or equal to m, in optimizing variables
Improved value of
In that
The expectation function at (i.e., the multi-objective Improvement expectation Matrix (EIM)) is defined as:
construction while taking into account model predictors
And predicted standard deviation
By maximizing the number of specifications of a desired Matrix (EIM)
Namely, it is
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.
And using the candidate design obtained by searching for improving model accuracy and global searching, wherein k is the number of multi-target pareto leading edge 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
And modified proxy model parameters
I.e. to perform global searches simultaneously to
For newly obtained samples
Corresponding three-dimensional impeller and rectifying cone geometry, calling an eddy cavitation flow automatic numerical prediction module to obtain flow field data and calculating a corresponding objective function valueAnd storing the newly added sample and the target function thereof into a database at the same time, and performing the 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 (5)
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: sequentially carrying out two-phase vortex cavitation numerical prediction, analysis of an impeller-rectifying cone and vortex cavitation interference mechanism and judgment of an optimal coupling mode, establishment of a rectifying cone-impeller coupling parameterization expression, extraction of geometric sensitive parameters of an expander impeller with a rectifying cone, extraction of vortex cavitation characteristic quantity, establishment of a vortex cavitation inhibition target function, establishment of an impeller-rectifying cone geometric collaborative optimization problem aiming at inhibiting vortex cavitation and self-adaptive solution of the problem;
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 of the suction surface of the blade of the impeller is extractedGas volume fraction vfrac ave And taking the value as the characteristic quantity of the cavitation degree at the outlet of the impeller, and taking the average vortex strength lambda in the diffuser pipe at the downstream of the impeller ave The method is used as a vortex flow characterization quantity, wherein the distribution of the gas volume fraction vfrac of the suction surface of the blade 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 method is characterized in that the constructed vortex-cavitation inhibition multi-objective optimization function is as follows:
wherein,
refri, a geometric parameter of impeller and fairing cone sensitivity to vortex-cavitation flow original And Refri respectively optimizes the refrigeration capacity produced by the front and rear expansion machines;
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 fairing cone of the expander, NUM variable combinations are determined in the variation range of the geometric sensitive parameters of the impeller and the fairing cone of the expander by utilizing DOE experimental design, and aiming at the parameters in each variable combination, NUM variable combinations are determined
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
2) According to the parameters
And its corresponding objective function value
Fitting an initial proxy model of each optimization target;
3) Construction while taking model predictions into account
And predicted standard deviation
Wherein m is the number of optimization objectives, and the normalized number of expectation matrices is improved by maximizing the multi-objectives
Namely, it is
Searching the most potential candidate design, wherein the searched most potential candidate design is as follows:
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
And constructing an optimization mode characterized by self-adaptive sampling-cooperative 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 cone geometry.
2. The cooperative optimization design method for the anti-cavitation rectification cone of the cryogenic liquid expander according to 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 the total energy equation is combined to solve 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 according to claim 1, wherein a parameterized expression of the rectification cone-impeller coupling is established based on an impeller-rectification cone optimal coupling mode, that is, the impeller geometry 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 cover 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 top and a blade root mean camber 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 geometric sensitive 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.
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