An enhanced prediction method for adverse pressure multi-walled surface large separation flow field

Abstract

The present application relates to a kind of enhanced prediction methods for inverse pressure multi-wall surface large separation flow field, belong to computational fluid dynamics technical field;Method steps include: the equivalent wall distance expression reflecting the coupling dissipation effect of multi-wall surface is constructed;Strain rate is revised turbulent generation term;The revision of equivalent wall distance and generation term strain rate of all grid points of Spalart-Allmaras turbulence model is completed;Global optimization is carried out to model parameter set and boundary parameter set using average ensemble Kalman filter;The generation term and dissipation term related to wall in standard Spalart-Allmaras turbulence model are revised by equivalent wall distance, and then the generation term related to strain rate is revised, to obtain revised Spalart-Allmaras turbulence model;Optimized parameters are substituted into the control equation of revised Spalart-Allmaras turbulence model to carry out three-dimensional flow field numerical prediction.The present application effectively reduces the prediction deviation of corner separation flow field, significantly improves the precision and robustness of inverse pressure multi-wall surface large separation flow field prediction, and shows good engineering application prospect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of computational fluid dynamics, and particularly relates to an enhanced prediction method for reverse pressure multi-wall surface large separation flow field. BACKGROUND

[0002] With the development of aero-engines towards high efficiency, high load and compact structure, the modeling and prediction of complex internal flow in the compressor face higher precision requirements. As the core component of energy conversion, the internal flow state of the compressor is directly related to the performance of the whole machine. In order to ensure its stable operation under extreme conditions, it is urgent to develop a numerical prediction method with high precision and strong robustness.

[0003] Affected by the dual trends of high load and compact structure, the internal flow field of the compressor presents significant three-dimensionality and unsteadiness, significantly increasing the complexity of flow simulation. Especially in the multi-wall structure area composed of the blade root and the end wall, the flow is affected by the combined action of strong geometric constraints and reverse pressure gradient, which easily induces three-dimensional corner separation. This kind of separation process is accompanied by nonlinear characteristics such as shear layer deflection, vortex structure evolution and flow reattachment, which has strong three-dimensional turbulent characteristics, and further causes the decline of aerodynamic performance, and even induces unstable flow, affecting the safety margin and working range of the engine.

[0004] The above-mentioned complex separation flow formed under the combined action of multi-wall structure constraints and reverse pressure gradient is usually referred to as "reverse pressure multi-wall surface large separation flow field". Its flow mechanism is highly complex and has large scale span, which is a key difficult problem in current turbulence modeling and high-performance computing. Although high-fidelity methods such as direct numerical simulation or large eddy simulation can reveal the fine structure of such flow, they are limited by the extremely high demand for computing resources, and it is difficult to meet the requirements of rapid iteration and parameter sweeping in the engineering design process. Therefore, the current engineering practice still widely uses the turbulence model based on the Reynolds-averaged Navier-Stokes equation for prediction. Such model has both computational efficiency and numerical stability, and is the mainstream choice for complex engineering flow modeling.

[0005] The traditional Spalart-Allmaras turbulence model has fundamental limitations in predicting such flow:

[0006] Wall effect simplification distortion: a single minimum wall distance is used, which cannot represent the coupling dissipation effect of adjacent walls on turbulent viscosity;

[0007] Lack of physical mechanism: the standard strain rate term ignores the influence of reverse pressure gradient and helicity on turbulent generation, resulting in lag in predicting the starting position of corner separation;

[0008] Parameter empirical dependence: model constants depend on calibration conditions, and the error is significantly amplified when extrapolated to non-design conditions (such as negative attack angle).

[0009] Current improvements based on traditional turbulence models still have obvious deficiencies:

[0010] Data-driven methods correct the Spalart-Allmaras turbulence model through machine learning, but do not embed multi-wall physical mechanisms, and the accuracy drops sharply when generalized to three-dimensional blades;

[0011] Local correction strategies add a pressure gradient term to the Spalart-Allmaras turbulence model, but do not solve the coupling problem of multi-wall interference and helicity effect.

[0012] Therefore, a method that combines multi-physical mechanism modeling and uncertainty optimization is urgently needed to fundamentally break through the prediction bottleneck of inverse pressure multi-wall surface separated flow field. SUMMARY

[0013] The technical problem to be solved is:

[0014] In order to avoid the shortcomings of the prior art, the present application provides an enhanced prediction method for inverse pressure multi-wall surface large separated flow field, which corrects the generation term and dissipation term related to the wall in the Spalart-Allmaras turbulence model by introducing an equivalent wall distance expression that can reflect the multi-wall surface effect, to improve the accuracy of turbulence viscosity calculation under multi-wall constraints. Without iteration, the prediction deviation of the corner separation flow field is effectively reduced, the accuracy and robustness of the inverse pressure multi-wall surface large separated flow field prediction are significantly improved, and good engineering application prospects are shown.

[0015] The technical solution of the present application is: an enhanced prediction method for inverse pressure multi-wall surface large separated flow field, the specific steps are as follows:

[0016] Construct an equivalent wall distance expression that reflects the coupling dissipation effect of multi-wall surface Expression:

[0017]

[0018] In the formula, represents a to-be-determined parameter for adjusting the weight of the influence of multi-wall surface; represents the serial number of the effective solid wall, , represents the total number of effective solid walls; represents the minimum vertical distance from any grid point to the th effective solid wall;

[0019] Correct the turbulence generation term strain rate , introduce a correction function related to the inverse pressure gradient and helicity:

[0020]

[0021] wherein, denotes the local strain rate scalar; denotes the eddy viscosity; denotes the von Karman constant; denotes the buffer function in the standard Spalart-Allmaras model; denotes the correction function related to the inverse pressure gradient and the vorticity, and the expression is as follows:

[0022]

[0023] wherein, denotes the undetermined parameter; denotes the dimensionless inverse pressure gradient influence factor; denotes the cosine value of the angle between the dimensionless local pressure gradient direction and the velocity direction; denotes the dimensionless vorticity influence factor; is the hyperbolic tangent function;

[0024] The above steps are repeated to complete the correction of the equivalent wall distance and the strain rate of the generation term of the Spalart-Allmaras turbulence model for all grid points;

[0025] The model parameter set and the boundary parameter set are globally optimized by using the average ensemble Kalman filter, wherein, denotes the empirical parameter; denotes the incoming flow velocity, denotes the attack angle;

[0026] The modified Spalart-Allmaras turbulence model is obtained by correcting the wall-related generation term and dissipation term in the standard Spalart-Allmaras turbulence model through the equivalent wall distance and then correcting the strain rate-related generation term;

[0027] The optimized parameters are substituted into the control equation of the modified Spalart-Allmaras turbulence model to carry out numerical prediction of a three-dimensional flow field.

[0028] A further technical solution of the present application is that the effective solid wall needs to meet the following conditions: the line connecting the wall and the current grid point has no other solid obstacles in the calculation domain and can establish a direct connection; when the equivalent wall distance degenerates into the minimum distance of a single wall .

[0029] A further technical solution of the present application is that the dimensionless factors are respectively defined as:

[0030]

[0031]

[0032]

[0033]

[0034] wherein, represents static pressure; represents the first directional component of spatial coordinates, ; represents the pressure gradient component along the first directional component; represents the first directional component of velocity vector; represents the first directional component of vorticity vector, represents vorticity magnitude; represents velocity vector module; represents local pressure gradient module; represents fluid density; represents fluid kinematic viscosity; represents reference Reynolds number.

[0035] A further technical solution of the present application is that the physical response mechanism of the correction function is:

[0036] When the adverse pressure gradient is enhanced, increases, improving the turbulent energy generation rate predicted by the generation term strain rate;

[0037] When the local vortex intensity is large, increases, and the generation term strain rate matches the local flow structure.

[0038] A further technical solution of the present application is that the optimization method of the model parameter set and the boundary parameter set comprises:

[0039] In combination with the controllable range of incoming flow parameters in numerical simulation and experiments, the value range of each parameter is set, a complete parameter space is constructed, Latin hypercube sampling method is used for random sampling in the parameter space, and groups of parameter samples are generated, wherein, ; represents sample serial number, represents total number of samples;

[0040] Three-dimensional numerical simulation is performed on each group of parameter samples, and physical quantities at measurement points are extracted, ; construct state vector :

[0041]

[0042] Calculate the mean of state vector and covariance matrix ;

[0043]

[0044]

[0045] According to the uncertainty of experimental measuring instrument randomly generate Gaussian distribution of measurement point error vector , wherein , indicates the error vector sequence number, L indicates the total number of error vectors; construct measurement error matrix , calculate the uncertainty covariance matrix :

[0046]

[0047] Calculate the Kalman gain matrix :

[0048]

[0049] In the formula, the observation matrix ; wherein, is a zero matrix with dimension corresponding to the part of the state vector related to the model parameters and boundary parameters; is a order unit matrix corresponding to the part of the state vector related to the measurement point physical quantity;

[0050] Combine the experimental measurement physical quantity data and its corresponding measurement point error vector , Kalman filter correction is carried out on each state vector to obtain the correction vector corresponding to the th sub-sample , ;

[0051]

[0052] In the formula, the error vector sequence number and the sub-sample sequence number exist a bijective relationship, indicating that each sub-sample corresponds to a unique set of error vectors, so the corresponding index set satisfies .

[0053] Average the correction vectors corresponding to all parameter samples and sub-samples to obtain an average state vector :

[0054]

[0055] wherein, The first seven components correspond to the optimized model parameter set .

[0056] A further technical solution of the application is that the generation term in the modified Spalart-Allmaras turbulence model is The expression is: .

[0057] A further technical solution of the application is that the dissipation term in the modified Spalart-Allmaras turbulence model is The expression is as follows:

[0058]

[0059] wherein, ; ; is a standard Spalart-Allmaras model buffer correction function;

[0060] .

[0061] A further technical solution of the application is that the method is used in the separation prediction of the blade angle area

[0062] The modified Spalart-Allmaras turbulence model is applied to the numerical simulation of a three-dimensional flow field, and key flow field characteristics are output, including the velocity field distribution and the surface static pressure coefficient distribution;

[0063] The model accuracy is verified by comparing experimental data, and the verification indicators include at least one macroscopic aerodynamic performance parameter, including the blade surface isentropic Mach number and the static pressure coefficient; wherein the absolute deviation of the macroscopic aerodynamic performance parameter prediction is reduced by not less than in the area less affected by the multi-wall effect, and by not less than .

[0064] An electronic device comprises at least one processor, and a memory in communication connection with the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the enhanced prediction method for a multi-wall surface large separation flow field facing adverse pressure.

[0065] A computer readable storage medium stores computer instructions for enabling a processor to implement the enhanced prediction method for a multi-wall surface large separation flow field facing adverse pressure when the processor executes the computer instructions.

[0066] Advantages

[0067] The present application has the advantages that: the present application provides an enhanced prediction method for a multi-wall surface large separation flow field facing adverse pressure, by introducing the physical correction of equivalent wall distance and strain rate, combining the parameter optimization strategy based on the average ensemble Kalman filter, the system improvement of the Spalart-Allmaras turbulence model is realized. Compared with the traditional model improvement method which only relies on empirical adjustment, the present application considers the physical pertinence (considering the multi-wall interference, strong adverse pressure gradient and helicity characteristics) and the non-empirical parameters (realizing the identification and optimization of model parameters based on data assimilation of the average ensemble Kalman filter) in the correction process, without iteration, the prediction accuracy of the standard Spalart-Allmaras turbulence model in the complex flow region such as corner separation is effectively improved. The specific effect analysis is as follows:

[0068] 1. By introducing the equivalent wall distance expression, the coupling dissipation effect of adjacent walls on the turbulent viscosity is effectively quantified, and the wall effect distortion problem caused by the single wall distance in the traditional model is solved. Correction function Embedding the dimensionless adverse pressure gradient influence factor And the dimensionless helicity influence factor Significantly enhance the model's ability to capture strong adverse pressure gradient induced separation and three-dimensional vortex evolution, accurately predict the corner separation starting position and reattachment behavior.

[0069] 2. The average ensemble Kalman filter is used to optimize the uncertainty of the parameter set, combined with experimental data and numerical simulation, to break through the limitations of traditional empirical calibration and avoid error amplification when extrapolated to non-design conditions.

[0070] In the verification level, the modified Spalart-Allmaras turbulence model constructed by the present application significantly improves the accuracy of the prediction of flow characteristics under the correction condition (angle of attack is 0° and 6°), and still maintains a low prediction deviation under the extrapolation condition (angle of attack is -2°), overcoming the general problem of accuracy decline of traditional improvement methods under non-training conditions. From Figure 3As shown, when the relative static pressure coefficient is used as the verification index, the effect of the multi-wall effect is relatively small. In the high-angle region, the absolute deviation of the prediction is in the angle of attack. α= 0° and α= At 6° operating conditions, the absolute prediction deviation was reduced by 66.2% and 65% respectively; in the 5.4% blade height region, which is significantly affected by the multi-wall effect, the absolute prediction deviation was reduced at the angle of attack. α= 0° and α= Under 6° operating conditions, the losses were reduced by 86.5% and 80.7% respectively. (From...) Figure 4 As shown, when using the relative static pressure coefficient as the verification index, the angle of attack will be... α= The modified Spalart–Allmaras turbulence model under 0° operating conditions is directly applied to the angle of attack. α = At -2°, the absolute prediction bias in the 50% leaf height region and the 5.4% leaf height region decreased by 57.3% and 86.3%, respectively; at the angle of attack... α= The modified Spalart–Allmaras turbulence model under 6° operating conditions is directly applied to the angle of attack. α= At -2°, the absolute prediction bias in the 50% leaf height region and the 5.4% leaf height region decreased by 54.1% and 82.7%, respectively. These results demonstrate that the method of this invention possesses good generalization ability while improving model accuracy, significantly enhancing its practicality and application value in predicting complex three-dimensional engineering flow fields. Attached Figure Description

[0071] Figure 1 This is a flowchart of an enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, according to an embodiment of the present invention.

[0072] Figure 2 This is a schematic diagram of the NACA65-009 blade cascade structure in an embodiment of the present invention, which is formed by stacking in the spanwise direction to create the three-dimensional blade of this embodiment.

[0073] Figure 3 This is a distribution diagram of surface static pressure coefficient before and after data assimilation under different blade height sections and different working conditions in an embodiment of the present invention;

[0074] Figure 4 This is a distribution diagram of the surface static pressure coefficient under extrapolation conditions for two modified Spalart-Allmaras turbulence models in the embodiments of the present invention. Detailed Implementation

[0075] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0076] In the existing Reynolds-averaged Navier-Stokes (RANS) turbulence model, the Spalart-Allmaras (SA) turbulence model has strong advantages in engineering applications due to its simple structure, high computational efficiency and wide application range. However, the SA turbulence model is based on a single-equation closure and isotropic eddy viscosity assumption, and its response capability is limited when facing adverse pressure-induced separation and complex three-dimensional shear flow. It is difficult to accurately capture the starting position of the corner separation, the reattachment path and its evolution behavior, often showing problems such as excessive diffusion of turbulent viscosity, delayed separation prediction, etc., thus limiting its applicability in complex separated flow fields. Existing improvements mainly focus on adjusting model coefficients or introducing additional empirical source terms, but there are generally problems such as insufficient physical mechanism coverage, strong dependence on empirical parameters, poor model universality, etc. Therefore, it is urgent to propose a method to improve the prediction accuracy of the Spalart-Allmaras turbulence model for adverse pressure multi-wall large separation flow fields under the premise of controlling the computational cost.

[0077] In recent years, the data assimilation method based on the ensemble Kalman filter has shown good prospects in turbulence model parameter optimization. This method can combine experimental data and its uncertainty to dynamically update the model empirical parameters, thereby effectively reducing the prediction error. However, there are still two challenges in its application to adverse pressure multi-wall large separation flow fields: first, current methods are mostly limited to adjusting global empirical parameters, and fail to fully reflect key flow mechanisms such as multi-wall structure, strong adverse pressure gradient and helicity effect, resulting in insufficient physical correction; second, parameter optimization usually relies on specific working conditions, making it difficult to ensure the generalization accuracy of the model under non-standard working conditions, limiting its reliability and scalability in engineering design optimization.

[0078] Therefore, the present application provides an enhanced prediction method for adverse pressure multi-wall large separation flow fields, as shown in Figure 1 , which comprises the following steps:

[0079] Step 1: Correction of the equivalent wall distance of the generation term and dissipation term of the standard Spalart-Allmaras turbulence model for multi-wall effect:

[0080] (1)

[0081] In formula (1), represents the minimum vertical distance from any grid point to the th effective solid wall, t represents the serial number of the effective solid wall, , represents the total number of effective solid walls; represents a to-be-determined parameter for adjusting the weight of the multi-wall effect (optimized by the ensemble Kalman filter algorithm in step 3).

[0082] Specifically, the minimum vertical distance from the th grid point to the th effective solid wall surface is denoted as , and the equivalent wall distance of the th grid point is denoted as , i.e., the equivalent wall distance of all grid points is modified. Wherein, the grid point represents a calculation point used to discretize the calculation domain in numerical simulation, usually located at the control volume center or grid intersection position.

[0083] The effective solid wall surface represents the solid wall surface that is not blocked in the geometric sense and can establish a direct line between the current grid point, i.e., the line from the grid point to the solid wall surface does not pass through any other solid obstacle within the calculation domain.

[0084] The wall distance adopted by the standard Spalart-Allmaras turbulence model generation term and dissipation term represents the minimum vertical distance from each grid point to the th effective solid wall surface, specifically . The wall distance is only applicable to single-wall flow and outflow problems represented by a single flat plate, and fails to reflect the combined influence of multiple wall surfaces on local flow structure and turbulent viscosity dissipation, resulting in a significant reduction in calculation accuracy in corner separation flow and various internal flow problems with multiple wall surfaces.

[0085] When , the equivalent wall distance degenerates to the wall distance . Therefore, the wall distance can be regarded as a special form of the equivalent wall distance , indicating that the equivalent wall distance maintains consistency with the traditional wall distance while having more extensive adjustability and adaptability, thus being mathematically reasonable.

[0086] Step 2: The correction process of the strain rate of the modified Spalart-Allmaras turbulence model generation term for the inverse pressure gradient and helicity effect is as follows:

[0087] The strain rate term adopted by the standard Spalart-Allmaras turbulence model in predicting complex inverse pressure gradient and multi-wall large separation flow. In the formula, is the local strain rate scalar; is the eddy viscosity; is the von Karman constant; is the buffer correction function in the standard Spalart-Allmaras turbulence model. By introducing the modified equivalent wall distance , the modified strain rate term is obtained is:

[0088]

[0089] Since only a single strain rate term is adopted The model fails to describe the flow characteristics of this kind of flow, and the prediction accuracy is reduced. Therefore, on the basis of the Spalart-Allmaras turbulence model modified in step 1, a correction function related to the adverse pressure gradient and the helicity is further introduced to enhance the sensitivity of the generation term to the local flow characteristics, so that the model can adaptively adjust the turbulence energy generation process according to the pressure gradient and the vortex intensity in the actual flow field, and improve the prediction accuracy and robustness of the model for large separation flow fields. Specifically, the modified strain rate is:

[0090] (2)

[0091] In formula (2), the local strain rate scalar is denoted by is denoted by is denoted by is denoted by is denoted by a correction function related to the adverse pressure gradient and the helicity, and the expression is as follows:

[0092]

[0093] In the formula, the hyperbolic tangent function is denoted by is denoted by a cosine function, both of which are standard mathematical operators acting on the variables in the parentheses; is denoted by a pending parameter; is denoted by a dimensionless adverse pressure gradient influence factor; is denoted by the cosine value of the angle between the dimensionless local pressure gradient direction and the velocity direction; is denoted by a dimensionless helicity influence factor. The dimensionless factors are defined as follows:

[0094]

[0095]

[0096]

[0097]

[0098] In the formula, Indicates static pressure; The first representing the spatial coordinates directional components ; Indicates the direction along the spatial coordinates. Pressure gradient in each direction component; The first velocity vector represents the velocity vector. One directional component; The first vortex vector represents the first vortex vector. One directional component, Indicates the vortex modulus; Indicates the magnitude of the velocity vector; Indicates the magnitude of the local pressure gradient; Indicates fluid density; Indicates the kinematic viscosity of a fluid; Indicates the reference Reynolds number.

[0099] The strain rate of the generated terms at all grid points is corrected by introducing a correction function. The resulting modified Spalart–Allmaras turbulence model can dynamically adjust the turbulence energy generation process according to the relative strength of the adverse pressure gradient and helicity in the local flow field: when the adverse pressure gradient increases, Increasing the strain rate improves the turbulent energy generation rate predicted by the generated term; when the local vortex intensity is large, The corresponding term will also be improved, and the strain rate of the generated term will match the local flow structure. This correction physically reflects the key mechanisms affecting turbulence generation in complex flow fields, helps reduce prediction bias caused by model simplification, and significantly improves the accuracy and robustness of the model in predicting large separation flow fields with multiple walls under adverse pressure.

[0100] Step 3: Identification and optimization of empirical and undetermined parameters of the modified Spalart–Allmaras turbulence model based on average ensemble Kalman filtering:

[0101] Step 3-1: Set the model parameters for the standard Spalart–Allmaras turbulence model. (Including empirical parameters) and parameters to be determined The set of boundary parameters introduced by considering the uncertainty of incoming flow conditions caused by wind tunnel boundary disturbances. (Including incoming flow velocity) and attack angle Parameter floating is performed. The floating range is set based on the adjustment precision of the incoming flow parameters and the numerical experiments. A typical floating range can be set as follows: incoming flow velocity... The floating range is Angle of attack The floating range is , the experience parameters and the undetermined parameters float in the range of their nominal values. Latin hypercube sampling method is used to randomly sample in the space, generating groups of parameter samples .

[0102] Step 3-2: three-dimensional flow field numerical simulation is carried out for groups of parameter samples respectively, and the physical quantities of measurement points in the corresponding flow field are extracted, wherein . , represents the number of measurement points in the chord length region of the blade in the experiment; the measured physical quantities can generally be surface isentropic Mach number, static pressure coefficient, static pressure, etc. In actual optimization, the measured physical quantity data in the region consistent with the numerical model should be selected. The model parameter set, boundary parameter set and corresponding physical quantity are combined into a state vector :

[0103] (3)

[0104] By constructing the state vector corresponding to each sample, the corresponding relationship between the model parameters and the flow field physical quantities is established, providing input data for subsequent parameter identification and optimization.

[0105] Step 3-3: calculate the sample mean vector and the covariance matrix based on all state vectors

[0106]

[0107] (4)

[0108] Step 3-4: considering the uncertainty of experimental measurement data, assuming that it obeys Gaussian distribution with zero mean and standard deviation , randomly generate groups of Gaussian distribution measurement point error vectors , wherein , and construct an error matrix composed of each error vector . According to this, the corresponding uncertainty covariance matrix is calculated:

[0109] (5)

[0110] Step 3-5: based on the covariance matrix , the uncertainty covariance matrix and the observation matrix , the Kalman filter gain matrix of the i-th sub-sample is calculated :

[0111] (6)

[0112] In formula (6), the observation matrix is used to extract the corresponding measurement physical quantity in the state vector as the filter observation. Among them, is a zero matrix with a dimension of , corresponding to the part of the state vector related to the model parameters and boundary parameters; is a order unit matrix, corresponding to the part of the state vector related to the measurement physical quantity.

[0113] Step 3-6: Combine the experimental measurement physical quantity data and the corresponding measurement error vector , Kalman filter correction is performed on each state vector to obtain the corrected vector corresponding to the i-th sub-sample , :

[0114] (7)

[0115] In formula (7), the error vector index and the sub-sample index have a bijective relationship, indicating that each sub-sample corresponds to a unique set of error vectors, so the corresponding index set satisfies .

[0116] Step 3-7: Take the average of the corrected results corresponding to all parameter samples and sub-samples to obtain the average state vector :

[0117] (8)

[0118] Among them, the first seven components are the optimized model parameter set .

[0119] Step 4: Three-dimensional numerical simulation and verification based on the modified Spalart-Allmaras turbulence model:

[0120] The modified wall distance in step 1, the modified strain rate in step 2, and the optimized model parameter set in step 3 are combined.Substitute the generation term of the standard Spalart-Allmaras turbulence model control equation And the dissipation term Among them, the modified Spalart-Allmaras turbulence model is constructed, which is specifically expressed as:

[0121]

[0122]

[0123] Wherein, the strain rate In step 2 is defined as ; Wall distance In step 1 is defined as ; ; ; ; The standard Spalart-Allmaras turbulence model buffer correction function.

[0124] The modified Spalart-Allmaras turbulence model equation is applied to the numerical simulation of three-dimensional flow field, and the key flow characteristics including the velocity field and the surface static pressure coefficient distribution are obtained. By comparing and analyzing with the experimental measurement data, it is proved that the model has good working condition generalization ability while significantly improving the prediction accuracy of the reverse pressure multi-wall large separation flow field.

[0125] The application also provides an electronic device, comprising at least one processor, and a memory in communication connection with the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the enhanced prediction method for the reverse pressure multi-wall large separation flow field.

[0126] The application also provides a computer readable storage medium, which stores computer instructions for enabling a processor to execute the enhanced prediction method for the reverse pressure multi-wall large separation flow field when the processor executes the computer instructions.

[0127] The above technical solutions are further described below in combination with examples:

[0128] In this embodiment, a low-speed compressor blade designed by using a NACA65-009 airfoil is taken as the research object, which is formed by stacking the two-dimensional cascade shown in Figure 2 in the span direction. The nominal inlet main flow velocity of the blade is m / s, and the design attack angle is . In the experiment, the blade and The pressure surface and suction surface at the top of the blade are arranged together. The static pressure coefficient distribution on the blade surface was obtained from several measuring points.

[0129] To conduct parameter identification and model optimization, the incoming flow velocity is... m / s, angle of attack is and The typical operating conditions were modified and simulated. Figure 3 A comparison is presented between the static pressure coefficient distribution on the blade surface calculated based on the standard Spalart–Allmaras turbulence model and experimental measurements. As can be seen from the figure, there is a significant discrepancy between the numerical simulation and experimental data, indicating that the standard Spalart–Allmaras turbulence model is insufficient to accurately describe complex flow structures such as corner separation under current operating conditions, thus verifying the necessity of model modification.

[0130] The specific implementation steps for this example are as follows:

[0131] Step 1: Correction of equivalent wall distances for the generator and dissipative terms of the standard Spalart–Allmaras turbulence model for multi-wall effects:

[0132] (1)

[0133] In equation (1), Indicates grid point up to the 1st The minimum vertical distance between effective solid walls; This represents the undetermined parameters used to adjust the weights of multi-wall influence, which are identified and optimized using the average ensemble Kalman filter algorithm in step 3. Specifically, the equivalent wall distances of all grid points are corrected. From the first grid point to the... The minimum vertical distance between each effective solid wall surface is expressed as: , No. The equivalent wall distance of each grid point is expressed as: The grid points refer to the computational points used to discretize the computational domain in the numerical simulation, and are usually located at the center of the control volume or the intersection of the grids; the effective solid wall refers to the solid wall that is geometrically unobstructed and can be directly connected to the current grid point, that is, the line connecting the grid point to the solid wall does not cross any other solid obstacles in the computational domain.

[0134] Step 2: Correction for adverse pressure gradient and helicity effects: Correction of strain rate in the Spalart–Allmaras turbulence model generator term:

[0135] (2)

[0136] In equation (2), Represents a local strain rate scalar; Indicates eddy viscosity; Represents the von Kármán constant; This represents the buffer correction function in the standard Spalart–Allmaras turbulence model; The correction function related to the inverse pressure gradient and helicity is expressed as follows:

[0137]

[0138] In the formula, Represents the hyperbolic tangent function. The cosine function is represented by standard mathematical operators that act on the variables within the parentheses. Indicates parameters to be determined; This represents the dimensionless inverse pressure gradient influence factor. This represents the cosine of the angle between the dimensionless local pressure gradient direction and the velocity direction. This represents the dimensionless helicity influence factor. The dimensionless factor is defined as follows:

[0139]

[0140]

[0141]

[0142]

[0143] In the formula, Indicates static pressure; The first representing the spatial coordinates directional components ; Indicates the direction along the spatial coordinates. Pressure gradient in each direction component; The first velocity vector represents the velocity vector. One directional component; The first vortex vector represents the first vortex vector. One directional component, Indicates the vortex modulus; Indicates the magnitude of the velocity vector; Indicates the magnitude of the local pressure gradient; Indicates fluid density; Indicates the kinematic viscosity of a fluid; Indicates the reference Reynolds number.

[0144] Step 3: Identification and optimization of empirical and undetermined parameters of the modified Spalart–Allmaras turbulence model based on average ensemble Kalman filtering:

[0145] Step 3-1: Set the model parameters for the standard Spalart–Allmaras turbulence model. (Including empirical parameters) and parameters to be determined The set of boundary parameters introduced by considering the uncertainty of incoming flow conditions caused by wind tunnel boundary disturbances. (Including incoming flow velocity) and attack angle Parameter floating is performed. The floating range is set based on the adjustment precision of the incoming flow parameters and the numerical experiments. A typical floating range can be set as follows: incoming flow velocity... The floating range is Angle of attack The floating range is The fluctuation range of empirical parameters and undetermined parameters is their nominal value. Based on this, the Latin hypercube method is used for random sampling to generate... Group parameter samples ,in .

[0146] The above parameter samples will be used in the subsequent three-dimensional numerical simulation and the model parameter identification process of the average ensemble Kalman filter algorithm.

[0147] Step 3-2: Conduct three-dimensional flow field numerical simulations for each of the 60 sets of parameter samples, and extract the physical quantities at each measuring point in the corresponding flow field. ,in , This indicates the number of measurement points in the blade chord region during the experiment; in this example, the measured physical quantity is the surface static pressure coefficient. In actual optimization, the measured physical quantity data should be selected from the region where the experimental setup and numerical model are consistent. Because the experiment forces the flow on the blade surface to transition to turbulence, the pressure surface and suction front edge of the blade are... Sandpaper was applied to the area. Therefore, only one location is selected in this example. The surface static pressure coefficient at each measuring point, i.e. The model parameters, boundary parameters, and corresponding physical quantities are combined into a state vector. :

[0148] (3)

[0149] Step 3-3: Based on all state vectors Calculate the sample mean vector Covariance Matrix

[0150]

[0151] (4)

[0152] Steps 3-4: Consider the uncertainty of the experimental measurement data, assuming it follows a zero mean and a standard deviation of . Gaussian distribution, randomly generated Group measurement point error vector ,in And construct the error matrix by combining the error vectors. Based on this, the corresponding uncertainty covariance matrix is ​​calculated. :

[0153] (5)

[0154] Steps 3-5: Based on the covariance matrix Uncertainty covariance matrix and observation matrix Calculate the first Kalman filter gain matrix for each subsample :

[0155] (6)

[0156] In the formula, the observation matrix This is used to extract the physical quantities of the corresponding measurement points in the state vector as filtered observations. For dimension The zero matrix corresponds to the part of the state vector that is related to the model parameters and boundary parameters; for The identity matrix of order 1 corresponds to the part of the state vector that is related to the physical quantity at the measurement point.

[0157] Steps 3-6: Combine experimental measurements of physical quantities data Error vector of corresponding measuring point For each state vector Perform Kalman filtering correction to obtain the first... The correction vector corresponding to each subsample , :

[0158] (7)

[0159] In the formula, the error vector index With subsample number The existence of a bijective relation means that each subsample corresponds to a unique set of error vectors, and therefore the corresponding set of indices satisfies... .

[0160] Steps 3-7: Average the correction results of all parameter samples and subsamples to obtain the averaged state vector. :

[0161] (8)

[0162] in, The first seven components are the optimized set of model parameters. In this example, the parameter results identified and optimized based on the average ensemble Kalman filter algorithm are shown in the table below. For both operating conditions, the correction results for the inlet velocity are close to... , The intake angle correction is close to the nominal value, while The nominal value of the intake angle under operating conditions is significantly reduced. Among the various parameters, except for... , Apart from the significant differences, the other parameters are quite similar, indicating that the two correction terms, pressure gradient and helicity effect, have different weights in the two operating conditions.

[0163]

[0164] Step 4: Three-dimensional numerical simulation and verification based on the enhanced Spalart–Allmaras turbulence model:

[0165] The corrected wall distance from step 1 The strain rate corrected in step 2 and the optimized model parameters identified in step 3 Substituting the generating terms into the governing equations of the standard Spalart–Allmaras turbulence model and dissipation terms In this paper, a modified Spalart–Allmaras turbulence model is constructed, specifically expressed as follows:

[0166]

[0167]

[0168] Among them, strain rate The definition in step 2 is Wall distance The definition in step 1 is ; ; ; ; This is the buffer correction function for the standard Spalart–Allmaras model.

[0169] The modified Spalart–Allmaras turbulence model governing equations were applied to three-dimensional flow field numerical simulations under two typical operating conditions to obtain the relative hydrostatic pressure coefficient distribution on the blade surface. Comparing the numerical simulation results with experimental measurements under the corresponding operating conditions, the absolute deviation of the modified Spalart–Allmaras turbulence model predictions can be determined as follows:

[0170]

[0171] Combination Figure 3 The figures shown are in two typical blade height sections ( and At the location, the predicted distribution of the surface hydrostatic coefficient of the aggregated sample and the corrected result shows that, in At the leaf height section, the prediction results for each parameter sample show a relatively consistent overall trend, with a relatively concentrated numerical distribution; while at... The leaf height section, i.e. the multi-walled corner region near the leaf root, shows more obvious dispersion in the prediction results between different samples, reflecting the stronger flow sensitivity characteristics of this region.

[0172] The results above show that the modified model significantly reduces the deviation from experimental measurements at both cross-sectional locations compared to the standard Spalart–Allmaras turbulence model, especially in the region near the wall. Higher elevations exhibit better predictive consistency, meeting the proposed qualification verification criteria (a reduction of at least [percentage missing] in areas less affected by the multi-wall effect). In areas significantly affected by the multi-wall effect, the reduction is no less than This result verifies the effectiveness of the enhanced prediction method for large separation flow fields with multiple walls under adverse pressure proposed in this invention in improving the modeling accuracy of complex separation flows in the corner region. It proves that the enhanced prediction method for large separation flow fields with multiple walls under adverse pressure proposed in this invention effectively improves the prediction accuracy of the standard Spalart–Allmaras turbulence model in the corner separation region.

[0173] To verify the generalization ability of the proposed turbulence model correction parameters under non-training conditions, an inlet angle of 10° was selected. The extrapolated operating conditions were used for simulation analysis. During the simulation, the standard Spalart–Allmaras turbulence model and a model based on… and Two sets of corrected parameter models were identified and optimized for each operating condition, denoted as SA-0 and SA-6 respectively. In all operating conditions, the incoming flow velocity was uniformly set to... m / s, intake angle is .

[0174] Figure 4Three models were shown. and The distribution of relative static pressure coefficient on the blade surface at two typical cross-sectional positions at the blade height is shown in the figure, and compared with experimental measurement results. It can be observed from the figure that: For the blade height section, the prediction results among different models showed little difference, and all three models were able to capture the overall pressure distribution characteristics well; while... In the blade height section, i.e. the multi-wall interference region near the endwall, the prediction results of the standard Spalart–Allmaras turbulence model deviate significantly from the experimental data, showing a problem of insufficient response to the characteristics of three-dimensional separated flow.

[0175] In contrast, both modified Spalart–Allmaras turbulence models (SA-0 and SA-6) showed significant improvements at this cross section, exhibiting high consistency with experimental results and exhibiting small differences between them. The specific absolute biases of the predictions from the two modified Spalart–Allmaras turbulence models are as follows:

[0176]

[0177] The above results show that the modified model obtained based on different operating conditions still has good predictive ability under non-training conditions, meets the proposed qualification verification index, and verifies the enhanced prediction method for large separation flow fields with multiple walls under adverse pressure proposed in this invention. It not only significantly improves the prediction accuracy of the standard Spalart–Allmaras turbulence model under training conditions, but also maintains stable and reliable performance under extrapolation conditions, and has good engineering applicability and promotion potential.

[0178] In summary, this invention addresses the typical adversarial multi-wall large-separation flow problem in the corner region of a three-dimensional compressor blade. It systematically enhances the predictive power of the standard Spalart–Allmaras turbulence model from two levels: physical modeling and parameter optimization. By introducing an equivalent wall distance correction, the wall effects under multi-wall constraints are accurately characterized. By combining local adversarial gradient and helicity characteristics, the strain rate is corrected, improving the model's response to strong separation and vortex evolution mechanisms. Furthermore, the average ensemble Kalman filter method is employed to identify and optimize the empirical parameters in the model, significantly reducing the model's dependence on experimental conditions and empirical settings.

[0179] The corrected model performs well under calibration conditions (e.g., intake angle is...). and Significant improvements in prediction accuracy were achieved under extrapolation conditions (such as an inlet angle of 100°). The method also exhibits good generalization performance. Validation results show that this method effectively overcomes the bias problem of traditional models in corner separation prediction, and has good generalization value and broad application prospects.

[0180] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. An enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, characterized in that... The specific steps are as follows: Construct the equivalent wall distance that reflects the dissipation effect of multi-wall coupling. expression: In the formula, This represents the undetermined parameter used to adjust the weights of multi-wall influences; t The serial number indicating the effective solid wall surface. , This represents the total number of effective solid walls. Represents any grid point up to the 1st The minimum vertical distance between effective solid walls; Corrected turbulence generation term strain rate Introduce correction functions related to the inverse pressure gradient and helicity: In the formula, Represents a local strain rate scalar; Indicates eddy viscosity; Represents the von Kármán constant; This represents the buffer correction function in the standard Spalart–Allmaras turbulence model; The correction function related to the inverse pressure gradient and helicity is expressed as follows: In the formula, Indicates parameters to be determined; This represents the dimensionless inverse pressure gradient influence factor. This represents the cosine of the angle between the dimensionless local pressure gradient direction and the velocity direction. This represents the dimensionless helicity influence factor. It is the hyperbolic tangent function; Repeat the above steps to correct the equivalent wall distance and generated strain rate for all grid points in the Spalart–Allmaras turbulence model; The average ensemble Kalman filter is used to analyze the model parameter set. and boundary parameter set Perform global optimization, including Indicates empirical parameters; Indicates the incoming flow velocity. Indicates the angle of attack; By correcting the wall-related generation and dissipation terms in the standard Spalart–Allmaras turbulence model using equivalent wall distance, and then correcting the strain rate-related generation terms, a modified Spalart–Allmaras turbulence model is obtained. The optimized parameters were substituted into the control equations of the modified Spalart–Allmaras turbulence model to conduct three-dimensional flow field numerical prediction.

2. The enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, as described in claim 1, is characterized in that: The effective solid wall must satisfy the following conditions: the line connecting the wall to the current grid point must be free of other solid obstacles in the computational domain and a direct connection can be established; when At that time, the equivalent wall distance Degenerates into minimum distance on a single wall surface .

3. The enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, as described in claim 1, is characterized in that: The dimensionless factors are defined as follows: In the formula, Indicates static pressure; The first representing the spatial coordinates One directional component, ; Indicates along the first Pressure gradient components in each direction; The velocity vector is represented in the th... Directional components; The vorticity vector is represented in the th... Directional components, Indicates the magnitude of vorticity; Indicates the magnitude of the velocity vector; Indicates the magnitude of the local pressure gradient; Indicates fluid density; Indicates the kinematic viscosity of a fluid; Indicates the reference Reynolds number.

4. The enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, as described in claim 3, is characterized in that: The correction function The physical response mechanism is as follows: When the adverse pressure gradient increases Increase the strain rate of the generated term to improve the turbulent energy generation rate; When the local vortex intensity is large Increase the strain rate of the generated term to match the local flow structure.

5. The enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, as described in claim 3, is characterized in that: The optimization methods for the model parameter set and boundary parameter set include: Combining the controllable range of incoming flow parameters in numerical simulations and experiments, we set the value intervals for each parameter, constructing a complete parameter space. Then, we use the Latin hypercube sampling method to randomly sample from the parameter space to generate... Group parameter samples ,in, ; j Indicates the sample number. Indicates the total number of samples; Perform a three-dimensional numerical simulation on each set of parameter samples to extract... Physical quantities at each measuring point , Constructing state vectors : Calculate the mean of the state vector and covariance matrix ; Randomly generated based on the uncertainty of the experimental measuring instrument. Group Gaussian distribution measurement point error vector ,in , l Indicates the error vector index. L Represent the total number of error vectors; construct the measurement error matrix. Calculate the uncertainty covariance matrix : Calculate the Kalman gain matrix : In the formula, the observation matrix ;in, For dimension The zero matrix corresponds to the part of the state vector that is related to the model parameters and boundary parameters; for The identity matrix of order 1 corresponds to the part of the state vector that is related to the physical quantity at the measurement point; Combined with experimental measurement of physical quantity data Its corresponding measurement point error vector For each state vector Perform Kalman filtering correction to obtain the first... The correction vector corresponding to each subsample , : In the formula, the error vector index With subsample number The existence of a bijective relation means that each subsample corresponds to a unique set of error vectors, and therefore the corresponding set of indices satisfies... ; The average state vector is obtained by averaging the correction vectors corresponding to all parameter samples and subsamples. : in, The first seven components correspond to the optimized model parameter set. .

6. The enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, as described in claim 5, is characterized in that: Generative terms in the modified Spalart–Allmaras turbulence model The expression is as follows: 。 7. The enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, as described in claim 6, is characterized in that: The dissipation term in the modified Spalart–Allmaras turbulence model The expression is as follows: In the formula, , ; ; This is the buffer correction function for the standard Spalart–Allmaras turbulence model.

8. The enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, as described in claim 1, is characterized in that: The method is used in blade corner region separation prediction: The modified Spalart–Allmaras turbulence model was applied to the three-dimensional flow field numerical simulation, and key flow field characteristics were output, including velocity field distribution and surface static pressure coefficient distribution. The model accuracy was verified by comparing experimental data. The verification indicators included at least one macroscopic aerodynamic performance parameter, which included the blade surface isentropic Mach number and hydrostatic coefficient. Specifically, the absolute deviation of the macroscopic aerodynamic performance parameter prediction should decrease by at least [amount missing] in regions less affected by multi-wall effects. In areas significantly affected by the multi-wall effect, the reduction is no less than .

9. An electronic device, characterized in that: The method includes at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the enhanced prediction method for large separation flow fields with multiple walls under adverse pressure as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions that enable a processor to implement the enhanced prediction method for large separation flow fields with multiple walls under adverse pressure, as described in any one of claims 1-8.

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