Method for predicting transition position of high-Mach-number boundary layer
By combining the correction of the γ-Reθ transition model with the correction of the high Mach number boundary layer, the problem of low transition prediction accuracy is solved, and more accurate transition position prediction and model localization are achieved.
Patent Information
- Application Number
- CN202411827322.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-12
- Publication Date
- 2025-05-02
AI Technical Summary
The existing γ-Reθ transition model cannot accurately predict the transition position in the high Mach number boundary layer, resulting in a significant forward transition of the boundary layer, affecting the calculation of the aerodynamic thermal performance of the aircraft.
The basic flow field of high Mach number laminar flow was calculated by using computational fluid mechanics, and the linear stability analysis method was used to predict the transition start position of the boundary layer, and the transition momentum thickness Reynolds number in the γ-Reθ transition model was corrected based on the incoming flow Mach number, and a γ-Reθ transition model with high Mach number was constructed.
The calculation accuracy of transition prediction of high Mach number boundary layer is improved, and the problem of predicting the transition starting position is significantly higher under high Mach number conditions is solved, and the transition model is fully localized and suitable for large-scale parallel computing.
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Figure CN119918443A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of aerospace technology, and in particular relates to a method for predicting the transition position of a high Mach number boundary layer. Background Art
[0002] With the continuous development of high-speed aircraft, the requirements for the accuracy of aircraft aerodynamic data in engineering design are becoming increasingly higher. Since the friction and heat flow of the turbulent boundary layer can reach 3 to 5 times that of the laminar boundary layer, how to accurately predict the boundary layer transition has become an important and inevitable issue in the design of high-speed aircraft.
[0003] The commonly used transition prediction method in engineering is γ-Re θ Transition model, γ-Re θ The transition model is constructed by adding the transition momentum thickness Reynolds number The transport equation is used to transport the non-local quantities outside the boundary layer into the boundary layer, thereby controlling the generation of the intermittent factors inside the boundary layer, thereby achieving complete localization of the transition model.
[0004] But γ-Re θ There are a large number of empirical relationships in the transition model, which are obtained by calibration using low-speed flat plate test data. In the high Mach number boundary layer, the critical transition momentum thickness Reynolds number will increase rapidly with the increase of Mach number, such as Figure 2 As shown, the original γ-Re θ When calculating the high Mach number boundary layer transition, the transition model will significantly move the boundary layer transition forward, thereby affecting the calculation of the aerodynamic thermal performance of the aircraft.
[0005] In summary, the existing γ-Re θ The transition model cannot meet the needs of high Mach number boundary layer transition prediction. In order to achieve accurate prediction of the transition position of the high Mach number boundary layer, it is urgent to construct a transition model of the high Mach number boundary layer. Summary of the invention
[0006] The present invention aims to solve at least one of the technical problems existing in the prior art.
[0007] The present invention provides a method for predicting a transition position of a high Mach number boundary layer. The method for predicting a transition position of a high Mach number boundary layer comprises:
[0008] S1: For high Mach number inflow, the basic laminar flow field is calculated using computational fluid dynamics methods;
[0009] S2: Based on the high Mach number laminar basic flow field calculated in step S1, a linear stability analysis method is used to predict the transition development process of the high Mach number boundary layer, and the starting position of the boundary layer transition under different incoming flow Mach numbers is obtained;
[0010] S3: Based on the transition start position obtained in step S2, the γ-Re θ The transition momentum thickness Reynolds number in the transition model is corrected; based on the corrected transition momentum thickness Reynolds number, the high Mach number corrected γ-Re θ Transition model;
[0011] S4: γ-Re corrected for high Mach numbers θ The transition model predicts the boundary layer transition location under high Mach number conditions.
[0012] Furthermore, in S1, the calculation object is a two-dimensional flat plate shape, and the control equation used in the calculation is the single-component calorimetric complete gas NS equation.
[0013] Further, in S2, according to the two-dimensional flat plate laminar boundary layer flow field calculated in step S1, the linear stability analysis method is used to calculate the development law of the small disturbance unstable wave in the boundary layer, and the N value is obtained by integrating along the flow direction. T =7 is used as the transition criterion N value to determine the starting position of boundary layer transition.
[0014] Further, in S3, according to the boundary layer transition starting positions corresponding to the different incoming flow Mach numbers obtained in step S2, the specific value of the transition momentum thickness Reynolds number is adjusted until γ-Re θ The transition starting position predicted by the transition model is consistent with the transition starting position calculated in step S2 based on the linear stability analysis method, and the transition momentum thickness Reynolds number at this time is taken as the corrected value.
[0015] Furthermore, the transition momentum thickness Reynolds number under a series of incoming flow Mach numbers is calibrated: Re' θt =Re θt H(Ma ∞ ), Re' θt is the corrected transition momentum thickness Reynolds number, Re θt is the transition momentum thickness Reynolds number before correction, Ma ∞ is the incoming Mach number, ranging from 2 to 8 Ma; and the coefficient H (Ma ∞ )for
[0016] Furthermore, the high Mach number corrected γ-Re θ Transition Model:
[0017]
[0018] Among them, γ represents the intermittent factor, ρ represents the density, t represents the time, and x jrepresents the coordinate component, u j represents the velocity component, μ represents the laminar viscosity coefficient, μ t represents the turbulent viscosity coefficient, σ f is a model parameter, with a value of 1.0, P γ represents the intermittent factor generation term, E γ represents the dissipation term of the intermittent factor, represents the momentum thickness Reynolds number, σ θt is a model parameter with a value of 2.0, P θt A generated term representing the momentum thickness Reynolds number, which is related to the corrected transition momentum thickness Reynolds number.
[0019] The technical solution of the present invention provides a method for predicting the transition position of a high Mach number boundary layer. The influence of the incoming flow Mach number on the transition starting position of the high Mach number boundary layer is studied by a linear stability analysis method, and the results of the linear stability analysis are used to predict the transition position of the γ-Re θ Transition momentum thickness Reynolds number Re in the transition model θt The empirical relationship is modified to construct the incoming flow Mach number Ma ∞ and transition momentum thickness Reynolds number Re θt A correction relationship is constructed to construct a prediction method suitable for the transition position of the high Mach number boundary layer, which improves the calculation accuracy of the high Mach number boundary layer transition prediction. Compared with the prior art, the technical solution of the present invention can solve the original γ-Re θ The empirical relationship in the transition model is calibrated for a low-speed flat plate and cannot be applied to the technical problem of predicting boundary layer transition at high Mach numbers. BRIEF DESCRIPTION OF THE DRAWINGS
[0020] The included drawings are used to provide a further understanding of the embodiments of the present invention, which constitute a part of the specification, are used to illustrate the embodiments of the present invention, and together with the text description, explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.
[0021] Figure 1 A schematic flow chart of a method for predicting a transition position of a high Mach number boundary layer provided according to a specific embodiment of the present invention is shown;
[0022] Figure 2 A comparison of the transition starting positions obtained by different transition models is shown. DETAILED DESCRIPTION
[0023] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0024] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.
[0025] Unless otherwise specifically stated, the relative arrangement, numerical expressions and numerical values of the parts and steps set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to actual proportional relationships. The technology, methods and equipment known to those of ordinary skill in the relevant art may not be discussed in detail, but in appropriate cases, the technology, methods and equipment should be considered as a part of the specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values.
[0026] like Figure 1 As shown, according to a specific embodiment of the present invention, a method for predicting the transition position of a high Mach number boundary layer is provided, the method comprising:
[0027] S1: For high Mach number inflow, the basic laminar flow field is calculated using computational fluid dynamics methods;
[0028] S2: Based on the high Mach number laminar basic flow field calculated in step S1, a linear stability analysis method is used to predict the transition development process of the high Mach number boundary layer, and the starting position of the boundary layer transition under different incoming flow Mach numbers is obtained;
[0029] S3: Based on the transition start position obtained in step S2, the γ-Re θ The transition momentum thickness Reynolds number in the transition model is corrected; based on the corrected transition momentum thickness Reynolds number, a high Mach number corrected γ-Reθ Transition model;
[0030] S4: γ-Re corrected for high Mach numbers θ The transition model predicts the boundary layer transition location under high Mach number conditions.
[0031] Using this configuration, a method for predicting the transition position of the high Mach number boundary layer is provided. The influence of the incoming flow Mach number on the transition starting position of the high Mach number boundary layer is studied by linear stability analysis method, and the results of linear stability analysis are used to predict the transition starting position of the γ-Re θ Transition momentum thickness Reynolds number Re in the transition model θt The empirical relationship is modified to construct the incoming flow Mach number Ma ∞ and transition momentum thickness Reynolds number Re θt A prediction method suitable for the transition position of the high Mach number boundary layer is constructed based on the modified relationship of , which improves the calculation accuracy of the high Mach number boundary layer transition prediction.
[0032] First, in the present invention, S1 is executed: for high Mach number incoming flow, a computational fluid dynamics method is used to calculate the laminar basic flow field.
[0033] As a specific embodiment of the present invention, the calculation object is a two-dimensional flat plate shape, and the control equation used in the calculation is the single-component calorimetric complete gas NS equation.
[0034] Furthermore, after obtaining the laminar basic flow field, S2 is executed: based on the high Mach number laminar basic flow field calculated in the previous step, the linear stability analysis method (Linear Stability Theory, LST) is used to predict the transition development process of the high Mach number boundary layer, and the starting position of the boundary layer transition under different incoming flow Mach numbers is obtained.
[0035] As a specific embodiment of the present invention, according to the two-dimensional flat plate laminar boundary layer flow field calculated in step S1, the linear stability analysis method is used to calculate the development law of small disturbance unstable waves in the boundary layer, and the N value is obtained by integrating along the flow direction. T =7 is used as the transition criterion N value to determine the starting position of boundary layer transition.
[0036] Further, after the linear stability analysis method is used to obtain the boundary layer transition starting position under different incoming flow Mach numbers, S3 is executed: based on the transition starting position obtained in step S2, the γ-Re θ The transition momentum thickness Reynolds number in the transition model is corrected; based on the corrected transition momentum thickness Reynolds number, the high Mach number corrected γ-Re θ Transition model.
[0037] As a specific embodiment of the present invention, according to the corresponding boundary layer transition starting position under different incoming flow Mach numbers obtained in step S2, the specific value of the transition momentum thickness Reynolds number is adjusted until γ-Re θ The transition starting position predicted by the transition model is consistent with the transition starting position calculated based on the LST method in step S2. The transition momentum thickness Reynolds number at this time is taken as the corrected value, and the transition momentum thickness Reynolds number under a series of incoming flow Mach numbers is calibrated: Re' θt =Re θt H(Ma ∞ ), Re' θt is the corrected transition momentum thickness Reynolds number, Re θt is the transition momentum thickness Reynolds number before correction, Ma ∞ is the incoming Mach number, ranging from 2 to 8 Ma; and the coefficient H (Ma ∞ )for
[0038] Furthermore, the high Mach number corrected γ-Re θ Transition Model:
[0039]
[0040] Among them, γ represents the intermittent factor, ρ represents the density, t represents the time, and x j represents the coordinate component, u j represents the velocity component, μ represents the laminar viscosity coefficient, μ t represents the turbulent viscosity coefficient, σ f is a model parameter, with a value of 1.0, P γ represents the intermittent factor generation term, E γ represents the dissipation term of the intermittent factor, represents the momentum thickness Reynolds number, σ θt is a model parameter with a value of 2.0, P θt A generated term representing the momentum thickness Reynolds number, which is related to the corrected transition momentum thickness Reynolds number.
[0041] Furthermore, in constructing the high Mach number corrected γ-Re θ After the transition model, execute S4, according to the high Mach number corrected γ-Re θ The transition model predicts the boundary layer transition location under high Mach number conditions.
[0042] The present invention predicts the transition development process of high Mach number boundary layer under different incoming flow Mach numbers according to the flow stability method, and calculates the γ-Re θ The empirical relationship in the transition model is modified to improve γ-Reθ The accuracy of the transition model in predicting high Mach number boundary layer transition. θ When the transition model predicts the high Mach number boundary layer transition, the predicted transition starting position is significantly forward, and there is no need to introduce non-local quantities. The transition model calculation can be fully localized and is suitable for large-scale parallel computing.
[0043] In order to have a further understanding of the present invention, the method for predicting the transition position of the high Mach number boundary layer of the present invention is described in detail below in conjunction with specific embodiments.
[0044] In this embodiment, the performance of the high Mach number boundary layer transition prediction method provided by the present invention is verified by taking the pointed cone shape as the test model. The flow field input conditions include: Mach number 9.6, static temperature 53.4K, and Reynolds number per unit length 6.38×106m -1 , angle of attack 0°, turbulence intensity of incoming flow 1%, wall boundary condition is no-slip isothermal wall, wall temperature is set to 0.3 times the total temperature of the incoming flow, the radius of the cone head is 0.152mm, Figure 2 The experimental measurement results, the original γ-Re θ Comparison of the transition starting position predicted by the transition model and the transition prediction method provided by the present invention, the original γ-Re θ The transition starting position predicted by the transition model is significantly earlier than the experimental results, while the transition starting position predicted by the revised transition model is consistent with the experimental results, which proves the rationality and feasibility of the present invention.
[0045] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Claims
1. A method for predicting the transition position of a high Mach number boundary layer, characterized in that: The method for predicting the transition position of the high Mach number boundary layer comprises: S1: For high Mach number inflow, the basic laminar flow field is calculated using computational fluid dynamics methods; S2: Based on the high Mach number laminar basic flow field calculated in step S1, a linear stability analysis method is used to predict the transition development process of the high Mach number boundary layer, and the starting position of the boundary layer transition under different incoming flow Mach numbers is obtained; S3: Based on the transition start position obtained in step S2, the γ-Re θ The transition momentum thickness Reynolds number in the transition model is corrected; based on the corrected transition momentum thickness Reynolds number, a high Mach number corrected γ-Re θ Transition model; S4: γ-Re corrected for high Mach numbers θ The transition model predicts the boundary layer transition location under high Mach number conditions.
2. The method for predicting the transition position of a high Mach number boundary layer according to claim 1, characterized in that: In S1, the calculation object is a two-dimensional flat plate shape, and the control equation used in the calculation is the single-component calorimetric complete gas NS equation.
3. The method for predicting the transition position of a high Mach number boundary layer according to claim 2, characterized in that: In S2, according to the two-dimensional flat plate laminar boundary layer flow field calculated in step S1, the linear stability analysis method is used to calculate the development law of small perturbation unstable waves in the boundary layer, and the N value is obtained by integrating along the flow direction. T =7 is used as the transition criterion N value to determine the starting position of boundary layer transition.
4. The method for predicting the transition position of a high Mach number boundary layer according to claim 3, characterized in that: In S3, according to the boundary layer transition starting position corresponding to the different incoming flow Mach numbers obtained in step S2, the specific value of the transition momentum thickness Reynolds number is adjusted until γ-Re θ The transition starting position predicted by the transition model is consistent with the transition starting position calculated in step S2 based on the linear stability analysis method, and the transition momentum thickness Reynolds number at this time is taken as the corrected value.
5. The method for predicting the transition position of a high Mach number boundary layer according to claim 4, characterized in that: The transition momentum thickness Reynolds number is calibrated for a series of incoming flow Mach numbers: Re' θt =Re θt H(Ma ∞ ), Re' θt is the corrected transition momentum thickness Reynolds number, Re θt is the transition momentum thickness Reynolds number before correction, Ma ∞ is the incoming Mach number, ranging from 2 to 8 Ma; and the coefficient H (Ma ∞ )for 6. The method for predicting the transition position of a high Mach number boundary layer according to claim 1, characterized in that: Constructing the high Mach number corrected γ-Re based on the corrected transition momentum thickness Reynolds number θ Transition Model: Among them, γ represents the intermittent factor, ρ represents the density, t represents the time, and x j represents the coordinate component, u j represents the velocity component, μ represents the laminar viscosity coefficient, μ t represents the turbulent viscosity coefficient, σ f is a model parameter, with a value of 1.0, P γ represents the intermittent factor generation term, E γ represents the dissipation term of the intermittent factor, represents the momentum thickness Reynolds number, σ θt is a model parameter with a value of 2.0, P θt A generated term representing the momentum thickness Reynolds number, which is related to the corrected transition momentum thickness Reynolds number.