An improved transition prediction method based on transport equations

Abstract

The application discloses an improved transition prediction method based on a transport equation, and relates to the field of aerodynamics, and comprises the following steps: S1, coupling multiple types of parameters extracted from existing data of high Reynolds number to a streamwise transition criterion and a cross-flow transition criterion respectively, so as to improve the transition criterion through multi-parameter coupling; S2, coupling the improved transition criterion to a transport type transition model, and adopting a benchmark example set to determine a transition key trigger parameter and a transition length parameter F length ; S3, constructing a double-layer transition model parameter system in the calibrated transport type transition model; and S4, introducing multi-physical factor correction in the transport type model processed in S3. The application realizes high-precision transition prediction in the range of ten-million-level Reynolds number by optimizing the transition criterion, constructing a double-layer model parameter system and introducing multi-physical factor correction.

Description

Technical Field

[0001] This invention relates to the field of aerodynamics. More specifically, this invention relates to an improved transition prediction method based on transport equations. Background Technology

[0002] Boundary layer transition refers to the continuous process by which flow evolves from a stable laminar state to a chaotic turbulent state. This process significantly alters the frictional drag, heat flux distribution, pressure core location, and shock wave and separation flow characteristics of an aircraft surface, directly affecting the overall aerodynamic performance, thermal protection design, and flight stability of the aircraft. It is one of the core research issues in the field of aerodynamics.

[0003] With the development of aerospace technology, the flight speed and size of aircraft are constantly increasing, and the flow conditions are gradually covering the high Reynolds number range, with incoming Reynolds numbers expanding from the millions to the tens of millions. Among existing transition prediction methods, those based on the RANS framework... Transport-type transition models, with their advantages of simple construction and good scalability, have become the mainstream method for predicting engineering transitions. It should be noted that... It is a four-equation transition model widely used in computational fluid dynamics (CFD), developed by Menter. SST k-ω Turbulence models and those proposed by Langtry and Menter γ-Re θt The transition model is coupled together. k This represents the turbulent kinetic energy at the wall surface. ω Indicates specific dissipation rate. γ This represents the probability that the flow is in a turbulent state. However, this model has the following inherent limitations: 1. Most existing models only consider two basic parameters for transition criteria: free flow turbulence intensity and pressure gradient. They do not fully consider factors such as the length scale of the incoming turbulence and the local pressure gradient characteristics under strong pressure gradients. This leads to a large deviation between the predicted transition location and the experimental standard model results under high Reynolds number, high lift shape, and non-airfoil configuration. This manifests as a problem of a smaller predicted range in the laminar flow region under high Reynolds number.

[0004] 2. The model parameters of the existing model are calibrated only based on standard model data of low speed and low Reynolds number. Under high Reynolds number conditions, the contribution ratios of the generation, convection and diffusion terms in the transport equation change significantly, resulting in the model predicting too short transition positions under high Reynolds number conditions, which cannot cover high Reynolds number conditions of tens of millions.

[0005] 3. Existing models do not consider the influence of complex factors such as surface roughness and TS / CF instability mode coupling: The surface of actual aircraft inevitably has processing roughness, which will induce the transition position to be earlier; at the same time, under high Reynolds number conditions, the coupling instability of the flow TS wave and the crossflow CF wave will significantly change the transition mechanism, and the response of existing models to these factors is significantly different from the experimental results, and cannot achieve high-precision transition prediction under complex conditions.

[0006] Furthermore, most existing transition models are developed based on the small perturbation assumption and rely excessively on experimental data from low Reynolds number models for coefficient calibration. They struggle to characterize transition processes under complex environments such as strong pressure gradients, wall roughness, and crossflow mode coupling, thus failing to meet the aerodynamic design requirements of current high Reynolds number aircraft. Therefore, developing a high Reynolds number transition prediction method that is universal, robust, and efficient has become an urgent technical problem to be solved in this field. Summary of the Invention

[0007] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0008] To achieve these objectives and other advantages of the present invention, an improved transition prediction method based on transport equations is provided, comprising: S1. Multiple parameters extracted from existing high Reynolds number data are coupled to the flow direction transition criterion and the crossflow transition criterion respectively, so as to improve the transition criterion through multi-parameter coupling; S2 couples the improved transition criterion to In the transport-type transition model, and using a benchmark set of examples, the key transition trigger parameters and transition length parameters are analyzed. F length Perform calibration; S3, after calibration The following two-level transition model control mode parameter set is constructed in the transport-type transition model. Φ : In the above formula, Φ 1 represents the original model parameter set under low Reynolds number conditions. Φ 2 represents the optimized model parameter set after recalibration of the model parameters under high Reynolds number conditions. F tr (∙) is a transition function constructed based on the Reynolds number of the wall height. Re d The Reynolds number is the wall height. S4, after processing in S3 In the transport-type transition model, multiple physical factors are introduced for correction; The multiple physical factors include: surface roughness effect and TS / CF coupling effect.

[0009] Preferably, in S1, the multiple parameters include: free-flow turbulence intensity, inflow turbulence length scale, and dimensionless pressure gradient calibrated by local metric. and dimensionless pressure gradient ; Among them, the free-flow turbulence intensity, the length scale of the incoming turbulence, and the dimensionless pressure gradient are mentioned. As a flow parameter, it is coupled into the flow direction transition criterion; Free-flow turbulence intensity and dimensionless pressure gradient As an influencing parameter, it is coupled into the crossflow transition criterion.

[0010] Preferably, in S2, the key transition triggering parameter includes: the flow transition triggering Reynolds number. Re vc Crossflow transition triggers Reynolds number Re hec ; The benchmark set of calculation examples includes: traditional flat plate calculation examples, typical airfoil calculation examples, ellipsoidal calculation examples, and high-lift shape calculation examples.

[0011] Preferably, in S3, the mode parameters include: transport type Diffusion term, transition control function, and transition length parameter in a transport-type transition model F length .

[0012] Preferably, in S3, the Reynolds number of the wall height is... Re d It is characterized by the following formula: In the above formula, ρ For fluid density, U e The velocity at the edge of the boundary layer, d The normal distance to the wall. μ The dynamic viscosity of the fluid.

[0013] Preferably, in S4, the surface roughness effect correction refers to: using rough wall boundary conditions, introducing additional turbulent kinetic energy at the wall position to reduce the Reynolds number of the transition momentum thickness in the boundary layer, and then using the inductive effect of roughness on transition to complete the early prediction of the transition position under the rough wall. Based on existing experimental data for typical airfoils and flat plates, the mode parameters of the transition trigger function are recalibrated.

[0014] Preferably, in S4, the TS / CF coupling effect correction includes: Introducing coupling factors into traditional trigger functions O TSCF ,and O TSCF = Re He / Re v ,in, Re He For the Reynolds number associated with crossflow, Re v The Reynolds number is related to the flow direction; Based on coupling factor O TSCF Construct transition trigger function H ( O TSCF ), to obtain the improved trigger function. F onset : F onset =max( F onset，tw ，F onset，cf , H ( O TSCF )) In the above formula, F onset,tw This is the function that triggers the flow transition. F onset,cf This is the function that triggers the flow transition.

[0015] The present invention has at least the following beneficial effects: Firstly, this invention couples multiple parameters, such as the incoming flow turbulence length scale and the local pressure gradient, into the transition criterion, while simultaneously calibrating the pressure gradient parameter locally. This enables the model to adapt to complex conditions such as strong pressure gradients and large sweep angles, solving the problem of large prediction deviations in traditional models under high-lift shapes and non-wing-like configurations, and improving the adaptability of the transition criterion. Secondly, the dual-layer transition mode parameter system constructed in this invention achieves adaptive switching between low Reynolds number and high Reynolds number mode parameters through a transition function, expanding the applicable Reynolds number range of the model from the millions to the tens of millions, solving the defect of traditional models that predict transition positions too short at high Reynolds numbers, and achieving coverage of high Reynolds numbers. Third, this invention introduces surface roughness correction and TS / CF mode coupling correction, which can accurately predict the roughness-induced transition advance effect and the transition process under TS / CF coupling instability, significantly improving the transition prediction accuracy under complex real working conditions and realizing the coupling correction of multiple physical factors.

[0016] Fourth, this invention is based on the mature RANS framework and improves upon it. It retains the advantages of the original transport transition model, such as high computational efficiency and ease of engineering implementation, while significantly improving the prediction accuracy. It can be directly applied to the aerodynamic design and performance evaluation of high-speed aircraft and large transport aircraft, and has extremely high engineering application value and good engineering practicality.

[0017] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0018] Figure 1 To use the original Transition diagram of transport-type transition model after validation of DLR-F5 standard model; Figure 2 To adopt the improved version of this invention Transition diagram of transport-type transition model after validation of DLR-F5 standard model; Figure 3 To use the original A transport-type transition model, with a contour plot showing the transition prediction of the DLR-F5 standard model; Figure 4 To adopt the improved version of this invention A transport-type transition model, with a contour plot showing the transition prediction of the DLR-F5 standard model. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0020] In response to the existing Transport-type transition models suffer from shortcomings in high Reynolds number conditions, including insufficient consideration of transition criteria, limited model parameter calibration range, and poor adaptability to roughness and modal coupling effects. This invention provides an improved transition prediction method based on transport equations. By optimizing transition criteria, constructing a two-layer model parameter system, and introducing multi-physical factor corrections, it achieves high-precision transition prediction in the tens of millions of Reynolds number range.

[0021] Specifically, an improved transition prediction method based on transport equations mainly includes the following: 1. Multi-parameter coupling transition criterion calibration Stability analysis and high-precision experimental data at high Reynolds numbers were compiled, and the free-flow turbulence intensity ( FSTI ), the turbulent length scale of the incoming flow ( l ), based on local pressure gradient ( Flow parameters such as flow direction transition parameters are coupled into the flow direction transition criterion; for crossflow standing wave transition and crossflow wave transition problems, the free flow turbulence intensity is coupled with the pressure gradient based on local quantity calibration. This parameter is coupled into the crossflow transition criterion as an influencing parameter. Based on the results of the FSC boundary layer equation, the dimensionless pressure gradient ( and The parameter is calibrated more accurately using local quantities so that it can accurately reflect the local pressure gradient in strong compressive gradients, strong adverse compressive gradients, and large sweep angle lower boundary layers.

[0022] 2. Transition Model Coupling and Parameter Calibration Couple the new transition criteria into In the transport-type transition model, and focusing on the key transition triggering parameters (flow direction transition triggering Reynolds number)... Re vc Crossflow transition triggers Reynolds number Re hec ) and transition length parameters F length Calibration was performed; a set of benchmark examples, including traditional flat plates, airfoils, DLR 6:1 ellipsoids, and high-lift shapes, was used to verify and confirm the model's basic predictive capabilities. It should be noted that the DLR 6:1 ellipsoid is a classic aerodynamic verification example with experimental measurements and data provided by the German Aerospace Center (DLR). Its major axis to minor axis ratio is 6:1. This example is often used for CFD method verification, especially in the study of boundary layer transition, separated flow, and turbulence models, and is one of the internationally widely used standard test cases.

[0023] 3. Construction of the parameter system for the two-layer transition mode For high Reynolds numbers (Re>1×10⁻⁶) at subsonic and high subsonic speeds 6 Two-dimensional and three-dimensional examples were used to recalibrate the diffusion term, transition control function, and F length Equal mode parameter group Φ 2; Using Reynolds number based on wall height Re d Constructing a transition function F tr ( Re dThe parameter set of the two-layer transition model control mode is obtained. Φ : in, Φ 1 represents the original model parameter set under low Reynolds number conditions. Φ 2 represents the optimized model parameter set after recalibration of the model parameters under high Reynolds number conditions. F tr (∙) is a transition function constructed based on the Reynolds number of the wall height. Re d The wall height Reynolds number is used to achieve a lower incoming flow Reynolds number. Φ 1. When the Reynolds number is high, use Φ Adaptive switching of 2, constructing a high-performance transition model with coverage.

[0024] 4. Surface roughness effect correction Using Knop ( Knopp Roughness-based wall boundary conditions are used to reduce the Reynolds number of the transition momentum thickness in the boundary layer by introducing wall turbulent kinetic energy. This introduces the influence of roughness, enabling the prediction of earlier transition locations caused by roughness. For typical airfoils and flat plates with transition roughness, which are common problems both domestically and internationally, the mode parameters of the transition trigger function are calibrated. It should be noted that... Knopp Roughness wall boundary conditions were proposed by Knopp et al. in 2009 and are designed for... k–ω This is a rough wall extension method for turbulence models (especially the Menter SST model). Its core idea is to modify the turbulent kinetic energy at the wall. k Sum of dissipation ω By applying boundary conditions, rough walls are treated as smooth walls, thus simulating the effect of roughness on flow within the RANS framework.

[0025] 5. Correction of TS / CF coupling effect For the common TS / CF strongly coupled swept wing example in stability analysis, the original transition trigger function is a competing value between the flow transition trigger function and the crossflow transition trigger function. F onset =max( F onset，sw ，F onset，cf ), introducing coupling factors O TSCF =Re He / Re v Based on stability analysis data, the relationship between coupling factor and physical strong coupling is studied, and a triggering function considering coupling is designed. H ( OTSCF And calibrate the mode parameters, and redesign the model's trigger function as follows: F onset =max( F onset，sw ，F onset，cf , H ( O TSCF )) Example: Step 1: Multi-parameter coupling transition criterion calibration First, we collected high Reynolds number case data from the past two decades, obtained through stability analysis and high-precision experiments, and extracted the flow parameters, including: free inflow turbulence intensity (FSTI) and inflow turbulence length scale. l Parameters such as the local pressure gradient of the boundary layer.

[0026] Regarding the flow transition criterion, the aforementioned free-flow turbulence intensity, inflow turbulence length scale, and dimensionless pressure gradient corrected / calibrated based on local boundary layer flow rate are used. Coupled to the criterion, the criterion can simultaneously consider the effects of incoming flow turbulence characteristics and local pressure gradient.

[0027] For the crossflow transition problem, we will address both crossflow standing wave transition and crossflow wave transition by relating the free-flow turbulence intensity to the local dimensionless pressure gradient. As an influencing parameter, it is coupled into the transverse transition criterion (i.e., first, the critical triggering amount of the multi-parameter correction is applied, and then coupled into the transport model through the triggering function), thus making up for the deficiency of insufficient consideration of factors in the traditional transverse transition criterion. The specific coupling method is as follows: The Reynolds number triggered by the flow transition can be written as: Re vc =f v ( FSTI,l,λ θ1 ), f v (∙) represents the multi-parameter empirical correlation function / calibration function for the flow transition triggering Reynolds number, used to characterize the combined effects of free-flow turbulence intensity, inflow turbulence length scale, and local dimensionless pressure gradient on the critical triggering Reynolds number for flow transition. FSTI Indicates the free-flow turbulence intensity; The transverse transition triggering Reynolds number can be written as: Re hec =f h ( FSTI,λ θ2 ), f h(∙) represents the multi-parameter empirical correlation function / calibration function for triggering the crossflow transition Reynolds number, which is used to characterize the combined influence of free-flow turbulence intensity and local dimensionless pressure gradient on the critical triggering Reynolds number for crossflow transition; The flow trigger function can be written as ：F onset,tw =G v ( Re v / Re vc ), G v (∙) represents the flow transition triggering function, used to determine or quantify the degree of triggering of flow-direction TS wave-induced transition based on the ratio of the flow-direction-related Reynolds number to the flow transition triggering Reynolds number. Re v Represents the Reynolds number related to the direction of flow; The crossflow trigger function can be written as: F onset,cf =G h ( Re He / Re hec ), G h (∙) represents the crossflow transition trigger function, used to determine or quantify the degree of triggering of crossflow CF instability-induced transition based on the ratio of the crossflow-related Reynolds number to the crossflow transition trigger Reynolds number. Re he Represented as the Reynolds number associated with crossflow; The final race trigger function is: F onset =max(F onset,tw ,F onset,cf ) ; After introducing TS / CF coupling, it is further extended to: F onset =max( F onset,tw , F onset,cf , H(O TSCF ) ).

[0028] Subsequently, based on the calculation results of the FSC boundary layer equation, the dimensionless pressure gradient was analyzed. and Recalibration is performed: For boundary layer flows under strong compressive gradients, strong adverse pressure gradients, and large sweep angles, an accurate dimensionless pressure gradient is calculated using local flow parameters to replace the traditional global parameters. This allows the parameters to accurately reflect the local pressure gradient characteristics and avoids the prediction bias caused by global parameters.

[0029] Step two, with the objective of minimizing the error between the experimental transition position and the model-predicted transition position, [the following steps are taken]. Re vc , Re hec , F length The coefficients in the trigger function are iteratively optimized until the average transition position error meets the preset threshold.

[0030] The novel transition criterion obtained in step 1 is coupled to the existing... In the transport-type transition model, the original transition criterion is replaced.

[0031] Subsequently, the key parameters of the transition process were recalibrated, including the Reynolds number that triggers the flow transition. Re vc Crossflow transition triggers Reynolds number Re hec and transition length parameters F length .

[0032] The calibration process used a set of benchmark examples, including traditional flat plate examples, typical airfoil examples, DLR6:1 ellipsoid examples, and high-lift shape examples, covering different configurations and flow conditions to ensure the calibrated parameters have good universality. After calibration, the above examples were used to verify the model's basic predictive ability, confirming that the model's prediction accuracy under normal operating conditions meets the requirements.

[0033] Step 3: Construction of the two-layer transition mode parameter system For high Reynolds number operating conditions at subsonic and high subsonic speeds (incoming Reynolds number) Re >1×10 6 Selecting typical two-dimensional flat plate and three-dimensional swept wing examples, the diffusion term, transition control function, and transition length parameter in the transport-type transition model are analyzed. F length The model parameters were recalibrated to obtain the model parameter set under high Reynolds number conditions. Φ 2.

[0034] To achieve adaptive switching of parameters at different Reynolds numbers, a transition function based on the wall height Reynolds number is constructed, where the wall height Reynolds number is defined as: In the formula, ρ For fluid density, U e The velocity at the edge of the boundary layer, d The normal distance to the wall. μ The dynamic viscosity of the fluid.

[0035] Based on the Reynolds number of the wall height, a transition function is constructed. F tr ( Re d This transition function approaches 1 at low Reynolds numbers and approaches 0 at high Reynolds numbers, thus achieving a smooth transition of mode parameters. Based on this transition function, a two-layer transition mode parameter system is constructed: in, Φ 1 represents the mode parameter set under traditional low-Norms operating conditions. Φ 2 represents the recalibrated high Reynolds number model parameter set.

[0036] By using a two-layer transition mode parameter system, when the incoming Reynolds number is low, the model automatically adopts the original low Reynolds number parameters; when the Reynolds number rises to the high Reynolds number range, the model automatically switches to the newly calibrated high Reynolds number parameters, thus achieving parameter adaptation within the range.

[0037] Step 4, Surface roughness effect correction To address the surface roughness effect of actual aircraft, Knopp rough wall boundary conditions are introduced. By introducing additional turbulent kinetic energy at the wall location, the turbulent characteristics within the boundary layer are altered, thereby reducing the Reynolds number of the transition momentum thickness in the boundary layer. This simulates the induced effect of roughness on transition and enables the earlier prediction of the transition location under rough walls.

[0038] Subsequently, experimental data of typical airfoils and flat plates in the transition roughness region were collected. For these operating conditions, the mode parameters of the transition trigger function were recalibrated. It should be noted that "recalibration" refers to the calibration of the mode parameters in the transition trigger function, so that the trigger function under roughness conditions can reflect the effect of roughness-induced early transition. In other words, "recalibration" is used to determine the trigger function coefficients, threshold parameters or correction factors after roughness correction, so that the model can accurately reflect the change of transition position under different roughness conditions.

[0039] Step 5, TS / CF Coupling Effect Correction To address the strong coupling instability problem of TS / CF (flow TS wave, i.e., Tormin-Schlichting wave; crossflow CF vortex, i.e., crossflow vortex) commonly found in swept wings at high Reynolds numbers, the traditional transition triggering function is improved. The traditional triggering function only considers the competition between flow transition and crossflow transition, i.e.: F onset =max( F onset，tw ，F onset，cf ) in, F onset，tw This is the function that triggers the flow transition. F onset，cf This is the function that triggers the flow transition.

[0040] This invention introduces a coupling factor O TSCF = Re He / Re H ,in, Re He For the Reynolds number related to crossflow, Re H The flow-related Reynolds number is used to quantify the coupling strength between the TS wave and the CF wave.

[0041] Based on the coupled operating condition data obtained from stability analysis, the correspondence between the coupling factor and the physical strong coupling effect is studied, and a transition triggering function for the coupled operating condition is designed. H ( O TSCF ), and calibrate the mode parameters of the function.

[0042] Finally, by adding the coupled trigger function to the contention-based trigger function, we obtain the improved trigger function: F onset =max( F onset，tw ，F onset，cf , H ( O TSCF )) In this way, the model can simultaneously consider flow direction transition, crossflow transition, and the transition effect caused by the instability of their coupling, and accurately predict the transition process under coupled conditions.

[0043] Verification example: The DLR-F5 wing was selected as the verification object. The wing has a leading-edge sweep angle of 20°, uses a supercritical symmetric airfoil, a Mach number of 0.82, a model angle of attack of 2°, a reference chord length of 0.15 m, and a reference area of ​​0.16 m². 2 The Reynolds number is 1.5 × 10⁻⁶. 6 .

[0044] During verification, the original data were used respectively. Transport-type transition model and improvements of the present invention The transport-type transition model was validated against the DLR-F5 standard model. The sublimation method was used to visualize the transition effect on the upper surface. The visualization results are as follows: Figures 1-2 As shown, it should be noted that Figure 1 This is the original experimental result of visualizing the upper surface of the wing of the DLR-F5 using the sublimation method. It can be seen that the transition line appears as irregular stripes. Therefore, from... Figure 1 It can be seen from the original The transport-type transition model shows that the transition region is locally patchy or discontinuous, and fails to form a clear and continuous transition initiation line and termination line, which is insufficient for capturing the crossflow-induced transition near the wing root. Figure 2 It is Figure 1 A schematic diagram of the compiled test results, in which, Figure 2 The dashed line in the middle represents the pressure measurement section. The two gray lines along the flow direction are the transition start line and the transition end line, respectively. The gray area is a mixed region of transition and separation. The thick black line is the shock wave compression region. It can be seen that the improved model can more clearly capture the transition region that develops along the span and the shock wave-induced transition characteristics.

[0045] Furthermore, from Figure 3 The numerical simulation cloud map shows that the original Transport-type transition models can only capture turbulent reattachment ( Figure 3 (as shown at point A) and the laminar transition caused by the shock wave ( Figure 3 As shown at point B in the middle section), it cannot capture the crossflow transition phenomenon at the wing root of the DLR-F5; while from Figure 4 As can be seen from the numerical simulation cloud map, the model of this invention can not only capture Figure 4 The turbulent reattachment shown at point C and the laminar transition caused by the shock wave shown at point D can also capture the crossflow transition phenomenon at the root of the DLR-F5 (i.e., Figure 4 (The laminar transition caused by the crossflow at point E) should be noted that... Figures 3-4 The color of the cloud map changes from red to blue, mainly to illustrate the change of Mach number Ma from high speed to low speed.

[0046] Therefore, from Figures 3-4The prediction results show that the method proposed in this invention can accurately capture the transition process under coupled instability. The method of this invention can effectively solve the prediction defects of existing transition models under high Reynolds number conditions and has good accuracy.

[0047] The above solution is merely an illustration of a preferred example and is not limited thereto. When implementing this invention, appropriate substitutions and / or modifications can be made according to the user's needs.

[0048] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. An improved transition prediction method based on transport equations, characterized in that, include: S1. Multiple parameters extracted from existing high Reynolds number data are coupled to the flow direction transition criterion and the crossflow transition criterion respectively, so as to improve the transition criterion through multi-parameter coupling; S2 couples the improved transition criterion to In the transport-type transition model, and using a benchmark set of examples, the key transition trigger parameters and transition length parameters are analyzed. F length Perform calibration; S3, after calibration The following two-level transition model control mode parameter set is constructed in the transport-type transition model. Φ : In the above formula, Φ 1 represents the original model parameter set under low Reynolds number conditions. Φ 2 represents the optimized model parameter set after recalibration of the model parameters under high Reynolds number conditions. F tr (∙) is a transition function constructed based on the Reynolds number of the wall height. Re d The Reynolds number is the wall height. S4, after processing in S3 In the transport-type transition model, multiple physical factors are introduced for correction; The multiple physical factors include: surface roughness effect and TS / CF coupling effect.

2. The improved transition prediction method based on transport equations as described in claim 1, characterized in that, In S1, the various parameters include: free-flow turbulence intensity, inflow turbulence length scale, and dimensionless pressure gradient calibrated by local metric. and dimensionless pressure gradient ; Among them, the free-flow turbulence intensity, the length scale of the incoming turbulence, and the dimensionless pressure gradient are mentioned. As a flow parameter, it is coupled into the flow direction transition criterion; Free-flow turbulence intensity and dimensionless pressure gradient As an influencing parameter, it is coupled into the crossflow transition criterion.

3. The improved transition prediction method based on transport equations as described in claim 1, characterized in that, In S2, the key transition triggering parameters include: the flow transition triggering Reynolds number. Re vc Crossflow transition triggers Reynolds number Re hec ; The benchmark set of calculation examples includes: traditional flat plate calculation examples, typical airfoil calculation examples, ellipsoidal calculation examples, and high-lift shape calculation examples.

4. The improved transition prediction method based on transport equations as described in claim 1, characterized in that, In S3, the mode parameters include: transport type Diffusion term, transition control function, and transition length parameter in a transport-type transition model F length .

5. The improved transition prediction method based on transport equations as described in claim 1, characterized in that, In S3, the Reynolds number of the wall height. Re d It is characterized by the following formula: In the above formula, ρ For fluid density, U e The velocity at the edge of the boundary layer, d The normal distance to the wall. μ The dynamic viscosity of the fluid.

6. The improved transition prediction method based on transport equations as described in claim 1, characterized in that, In S4, the surface roughness effect correction refers to: using rough wall boundary conditions, introducing additional turbulent kinetic energy at the wall position to reduce the value of the transition momentum thickness Reynolds number in the boundary layer, and then using the inductive effect of roughness on transition to complete the early prediction of the transition position under the rough wall. Based on existing experimental data for typical airfoils and flat plates, the mode parameters of the transition trigger function are recalibrated.

7. The improved transition prediction method based on transport equations as described in claim 1, characterized in that, In S4, the TS / CF coupling effect correction includes: Introducing coupling factors into traditional trigger functions O TSCF ,and O TSCF = Re He / Re v ,in, Re He For the Reynolds number associated with crossflow, Re v The Reynolds number is related to the flow direction; Based on coupling factor O TSCF Construct transition trigger function H ( O TSCF ), to obtain the improved trigger function. F onset : F onset =max( F onset，tw ，F onset，cf , H ( O TSCF )) In the above formula, F onset,tw This is the function that triggers the flow transition. F onset,cf This is the function that triggers the flow transition.

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