A transition prediction method considering wall heating and cooling effects

Abstract

The application discloses a transition prediction method considering wall heating and cooling effects, and simplifies and modifies a stability basic transport transition model, so that the application range of the stability basic transport transition model is extended to the influence of the non-adiabatic wall effect considering the generalized wall heating and cooling, the localized momentum thickness Reynolds number expression and the transition starting momentum thickness Reynolds number expression considering the wall heating and cooling effects are constructed, and the two expressions are coupled into gamma the transport model, the transition transport model considering the wall heating and cooling effects is obtained after wind tunnel example verification, and then the transition prediction of the stratosphere high-altitude airship under the wall heating and cooling effects is realized. The experiment proves that the application can accurately reproduce the significant upstream movement of the transition front caused by the wall heating, and therefore the application provides a robust engineering basis for the aerodynamic design and optimization of the future laminar platform considering the non-adiabatic wall effect.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic boundary layer transition prediction technology, specifically relating to the design of a transition prediction method that considers the wall heating and cooling effect. Background Technology

[0002] Stratospheric and high-altitude airships hold significant promise in multiple fields due to their superior endurance and loiter capabilities. Compared to traditional fixed-wing aircraft, these platforms offer higher energy efficiency and lower operating costs. Achieving superior aerodynamic efficiency is crucial for maximizing loiter capability. Given their streamlined structure, laminar drag reduction techniques have become the primary strategy for achieving this performance goal. However, the operating environment presents complex adverse factors. Specifically, during the day, solar radiation and direct sunlight can significantly raise surface temperatures above ambient levels. Wall heating fundamentally alters boundary layer stability, leading to an earlier laminar-turbulent transition, thus severely diminishing the drag reduction effect. Therefore, accurately predicting the laminar-turbulent transition location under actual thermal conditions is a prerequisite for reliable airship design.

[0003] However, commonly used stability-based transition predictions are computationally very complex and difficult to apply directly to industrial 3D configurations with complex geometries. Furthermore, the optimization design of such configurations typically requires multiple iterations, making stability-based methods impractical for everyday use. In contrast, transport models such as the Langtry–Menter model rely solely on local flow variables and are well-suited for parallel computational fluid dynamics (CFD) and unstructured meshes, thus finding widespread application in industry. Therefore, increasing research aims to bridge this gap by deriving physical information corrections from high-fidelity datasets (generated through linear stability theory) and integrating them into transport models.

[0004] The effect of wall temperature on the transition process is highly dependent on the flow state and the dominant instability mechanism. In hydrodynamic flows (such as water flow), wall heating typically stabilizes Tollmien-Schlichting (TS) waves and delays transition. In high-speed aerodynamics, the effect depends on the instability mode: for hypersonic flows, wall heating promotes first-mode instability while stabilizing second-mode disturbances; in supersonic flows, heating usually leads to earlier transition; in subsonic (low subsonic and transonic) conditions associated with airships, wall heating has a significant instability effect, amplifying disturbances and accelerating transition, while wall cooling plays a stabilizing role.

[0005] The effects of wall heating or cooling have been studied in hypersonic and underwater flows. In the hypersonic domain, Kovalev incorporated the wall temperature ratio as a correction factor into the Langtry-Menter transition criterion and investigated the influence of the wall-to-free-flow temperature difference on the transition position of hypersonic vehicles. For underwater vehicles, Shen et al. combined the FSC equations with linear stability theory to calibrate key temperature-dependent transition parameters in the single-equation model derived from the original two-equation Langtry-Menter formula. The modified model can accurately predict the transition position of underwater vehicles in the presence of boundary layer temperature gradients.

[0006] However, no studies have yet incorporated the effects of wall heating / cooling into transport-based transition models for subsonic airflow. Therefore, when designing laminar airships using such models, the effects of wall heating cannot be considered in robust laminar design. This, in turn, leads to overly optimistic estimates of laminar drag reduction because the adverse effects of wall heating are not considered early in the design process, thus failing to yield truly robust solutions. Therefore, a transport-based transition model that considers the effects of wall heating and cooling is needed. Summary of the Invention

[0007] The purpose of this invention is to solve the problem that the commonly used stability-based transition prediction is computationally very complex and does not take into account the influence of wall heating. Therefore, a transition prediction method that takes into account the wall heating and cooling effect is proposed.

[0008] The technical solution of this invention is: a transition prediction method considering the wall heating and cooling effect, comprising the following steps:

[0009] S1. Construct a localized momentum-thickness Reynolds number expression that takes into account the wall heating and cooling effects.

[0010] S2. Construct an expression for the transition initial momentum thickness Reynolds number that takes into account the wall heating and cooling effects.

[0011] S3. Couple the localized momentum-thickness Reynolds number expression considering the wall heating and cooling effect and the transition initial momentum-thickness Reynolds number expression considering the wall heating and cooling effect into... γ The transport model was developed and verified by wind tunnel simulations, resulting in a transition transport model that considers the wall heating and cooling effects.

[0012] S4. A transition transport model considering the wall heating and cooling effect is used to predict the transition of stratospheric high-altitude airships under the wall heating and cooling effect.

[0013] Furthermore, the localized momentum-thickness Reynolds number expression considering the wall heating and cooling effects constructed in step S1 is as follows:

[0014]

[0015] in, Represents the maximum vorticity Reynolds number. This indicates the local momentum thickness Reynolds number. Represents the Reynolds number ratio. Indicates wall temperature With free flow temperature The ratio, Indicates local Pressure gradient parameters at the location, , and Three functions representing the pressure gradient parameters.

[0016] Furthermore, the three functions of the pressure gradient parameters , and The calculation formula is:

[0017]

[0018]

[0019]

[0020] in This represents the pressure gradient parameter.

[0021] Furthermore, pressure gradient parameters The calculation formula is:

[0022]

[0023] in This indicates the local momentum thickness. This represents the Hartree parameter. Indicates the flow velocity at the boundary layer boundary. This represents the kinematic viscosity coefficient at the boundary of the boundary layer.

[0024] Furthermore, the expression for the transition initial momentum thickness Reynolds number constructed in step S2, considering the wall heating / cooling effect, is as follows:

[0025]

[0026] in The thickness Reynolds number represents the transition momentum. Represents pressure gradient parameters Sum and ratio polynomial functions, Indicates the free-flow turbulence intensity. Indicates free-flow turbulence A polynomial function.

[0027] Furthermore, polynomial functions The expression is:

[0028]

[0029] in , , and Represents pressure gradient parameters The four functions.

[0030] Furthermore, pressure gradient parameters The four functions , , and The calculation formula is:

[0031]

[0032]

[0033]

[0034] Furthermore, polynomial functions The expression is:

[0035]

[0036]

[0037] in The natural logarithm of the free-flow turbulence intensity.

[0038] The beneficial effects of this invention are:

[0039] (1) This invention effectively corrects the Reynolds number ratio by considering the influence of wall heating / wall cooling effects on the laminar-turbulent transition. The mathematical expression enables the transport equation to be solved with higher accuracy for the local momentum-thickness Reynolds number under non-adiabatic wall boundary conditions. .

[0040] (2) This invention effectively corrects the transition initiation momentum thickness Reynolds number by considering the influence of wall heating / cooling effects on laminar-turbulent transition and integrating a transition prediction method based on linear stability theory. The mathematical expression of this allows the transport equation to be combined with stability-based transition prediction methods to solve the transition initiation momentum thickness Reynolds number under non-adiabatic wall boundary conditions more physically and with higher accuracy. .

[0041] (3) This invention forms an improved stability-based transition transport model for airships that considers the wall heating and cooling effect by using a localized momentum thickness Reynolds number expression that considers the wall heating and cooling effect and a transition initial momentum thickness Reynolds number expression that considers the wall heating and cooling effect. Through CFD simulation, it can effectively predict the transition position of heated airships, and the relative error between the model and the wind tunnel test results does not exceed 6%. Attached Figure Description

[0042] Figure 1 The diagram shown is a flowchart of a transition prediction method considering wall heating and cooling effects provided by an embodiment of the present invention.

[0043] Figure 2 The figure shows the localized momentum-to-thickness Reynolds number ratio considering the wall heating and cooling effect provided in Experimental Example 1 of the present invention. A schematic diagram comparing the results of the expression-fitted surface with the FSC equation.

[0044] Figure 3 The figure shown is the localized momentum-to-thickness Reynolds number ratio considering the wall heating / cooling effect provided in Experimental Example 1 of the present invention. A schematic diagram comparing the fitting curves of each temperature ratio expression with the results of the FSC equation.

[0045] Figure 4 The figure shown is the expression for the transition initial momentum thickness Reynolds number considering the wall heating and cooling effect, and the free-flow turbulence intensity provided in Experimental Example 2 of the present invention. Tu =0.05% Fitted Surface and Based on Linear Stability Theory A diagram showing the comparison of prediction results from different methods.

[0046] Figure 5 The figure shown is the expression for the transition initial momentum thickness Reynolds number considering the wall heating and cooling effect, and the free-flow turbulence intensity provided in Experimental Example 2 of the present invention. Tu =0.05% Fitting curves for each temperature ratio and based on linear stability theory A diagram showing the comparison of prediction results from different methods.

[0047] Figure 6 The figure shown is the expression for the transition initial momentum thickness Reynolds number considering the wall heating and cooling effect, and the free-flow turbulence intensity provided in Experimental Example 2 of the present invention. Tu =0.1% Fitted surface and linear stability theory A diagram showing the comparison of prediction results from different methods.

[0048] Figure 7 The figure shown is the expression for the transition initial momentum thickness Reynolds number considering the wall heating and cooling effect, and the free-flow turbulence intensity provided in Experimental Example 2 of the present invention. Tu =0.1% Fitting curves for each temperature ratio and based on linear stability theory A diagram showing the comparison of prediction results from different methods.

[0049] Figure 8 The diagram shown is a schematic of the flat plate mesh used for the calculation and verification of the transition transport model provided in Experiment Example 3 of this invention.

[0050] Figure 9 The diagram shown is a comparison of the present invention's transition transport model, linear stability theory, and experimental results for the flat plate calculation example with adiabatic wall boundary conditions provided in Experimental Example 3 of the present invention.

[0051] Figure 10 The diagram shown is a comparison of the present invention's transition transport model, linear stability theory, and experimental results for the non-adiabatic wall boundary condition plate wall cooling calculation example provided in Experimental Example 3 of the present invention.

[0052] Figure 11 The diagram shown is a comparison of the present invention's transition transport model, linear stability theory, and experimental results for the non-insulated wall boundary condition flat plate wall heating example provided in Experimental Example 3 of the present invention.

[0053] Figure 12 The diagram shown is a schematic diagram of the wind tunnel and airship model for the wall-heated airship test provided in Experimental Example 4 of the present invention.

[0054] Figure 13 The diagram shown is a schematic diagram of the heating film and transition detection principle on the airship model provided in Experimental Example 4 of the present invention.

[0055] Figure 14 The image shows the airship wind tunnel provided in Experimental Example 4 of this invention. V =75m / s, T w / T e A schematic diagram of the experimental thermal imaging results at a value of 1.29.

[0056] Figure 15 The diagram shown is a schematic diagram of the airship model mesh used in the verification of the transfer transport model of the present invention provided in Experiment Example 4 of the present invention.

[0057] Figure 16 The figure shown is the transfer transport model of the present invention and the experimental results provided in Experimental Example 4 of the present invention. V =50m / s, T w / T eA diagram comparing the transition positions at 1.00.

[0058] Figure 17 The figure shown is the transfer transport model of the present invention and the experimental results provided in Experimental Example 4 of the present invention. V =50m / s, T w / T e A comparative diagram of the transition positions at =1.19.

[0059] Figure 18 The figure shown is the transfer transport model of the present invention and the experimental results provided in Experimental Example 4 of the present invention. V =50m / s, T w / T e A comparative diagram of the transition positions at 1.29.

[0060] Figure 19 The figure shown is the transfer transport model of the present invention and the experimental results provided in Experimental Example 4 of the present invention. V =75m / s, T w / T e A diagram comparing the transition positions at 1.00.

[0061] Figure 20 The figure shown is the transfer transport model of the present invention and the experimental results provided in Experimental Example 4 of the present invention. V =75m / s, T w / T e A comparative diagram of the transition positions at =1.19.

[0062] Figure 21 The figure shown is the transfer transport model of the present invention and the experimental results provided in Experimental Example 4 of the present invention. V =75m / s, T w / T e A comparative diagram of the transition positions at 1.29.

[0063] Figure 22 The figure shown is the basic model and experimental results provided in Experimental Example 4 of this invention. V =75m / s, T w / T e A diagram comparing the transition positions at 1.00.

[0064] Figure 23The figure shown is the basic model and experimental results provided in Experimental Example 4 of this invention. V =75m / s, T w / T e A comparative diagram of the transition positions at =1.19.

[0065] Figure 24 The figure shown is the basic model and experimental results provided in Experimental Example 4 of this invention. V =75m / s, T w / T e A comparative diagram of the transition positions at 1.29. Detailed Implementation

[0066] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.

[0067] This invention provides a transition prediction method that considers the wall heating and cooling effects, such as... Figure 1 As shown, it includes the following steps S1~S4:

[0068] S1. Construct a localized momentum-thickness Reynolds number expression that takes into account the wall heating and cooling effects.

[0069] The basic model principle in this embodiment of the invention is the transition transport model proposed by François et al. The equation determines the local momentum-thickness Reynolds number. Has the critical threshold for triggering transition been reached—the transition momentum thickness Reynolds number? The ratio of the two in the form of as a sub-switch function Determine the master switch function Whether to set the value to 0. When the transition threshold is reached, Intermittent factor It begins to participate in transport, further activating the turbulent kinetic energy of the turbulence model in the SST model. The transport of these components allows for the solution of Reynolds stresses, introducing turbulence into laminar flow calculations and simulating transition processes. François et al., considering the localization of the transport equations, incorporated non-local quantities... Localization: ,in This represents the ratio of the maximum vorticity Reynolds number to the momentum-thickness Reynolds number. Represents the vorticity Reynolds number. For shape factor, This represents the distance from the local location within the boundary layer to the wall. This indicates the magnitude of the strain rate at a local location within the boundary layer. This indicates the local kinematic viscosity.

[0070] Considering that the above steps did not incorporate the effect of wall heating and cooling on the momentum-thickness Reynolds number, the calculated momentum-thickness Reynolds number under wall heating and cooling effects predicted using the traditional transition transport model is distorted. Therefore, it is necessary to introduce the wall heating effect and further localize this ratio. Thus, based on the laminar boundary layer data obtained from solving the FSC equations under non-adiabatic wall boundary conditions, the following localized ratio expression is obtained:

[0071]

[0072]

[0073]

[0074]

[0075] in Represents the maximum vorticity Reynolds number. This indicates the local momentum thickness Reynolds number. Represents the Reynolds number ratio. , and Three functions representing the pressure gradient parameters. ( ) indicates wall temperature With free flow temperature The ratio of (temperature at the boundary layer boundary) Indicates local Pressure gradient parameters at the location, Represents Hartree parameters, and has ,in Represents the inverse pressure gradient. Indicates zero pressure gradient. Indicates the compressive gradient. This indicates the local momentum thickness. Indicates the flow velocity at the boundary layer boundary. This represents the kinematic viscosity coefficient at the boundary layer. Specifically, the Reynolds number ratio is calculated solely using the local pressure gradient parameters and the wall free flow temperature ratio, thus yielding the desired momentum-thickness Reynolds number expression:

[0076]

[0077] S2. Construct an expression for the transition initial momentum thickness Reynolds number that takes into account the wall heating and cooling effects.

[0078] After completing the After localizing the solution, the next step is to use a switching function. Determine the intermittent factor Whether to begin transportation. Wall heating and cooling, besides... Besides affecting the calculation, it also affects the transition initial Reynolds number. The impact is also significant. Because the basic transport model does not consider the effect of wall heating and cooling on TS instability, its prediction of the transition initiation Reynolds number under wall heating is overly optimistic. Therefore, the laminar boundary layer data obtained from solving the FSC equations under non-adiabatic wall boundary conditions and the data based on linear stability theory... The method obtains multiple perturbation frequencies Value envelope, and use Mack relation The turning point is determined threshold Based on the data, the following expression for the initial Reynolds number of the transition is obtained:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] in The thickness Reynolds number represents the transition momentum. Represents pressure gradient parameters Sum and ratio polynomial functions, This represents the free-flow turbulence intensity, expressed as a percentage. Indicates free-flow turbulence polynomial functions, , , and Represents pressure gradient parameters The four functions, The natural logarithm of the free-flow turbulence intensity.

[0087] S3. Couple the localized momentum-thickness Reynolds number expression considering the wall heating and cooling effect and the transition initial momentum-thickness Reynolds number expression considering the wall heating and cooling effect into... γ The transport model was developed and verified by wind tunnel simulations, resulting in a transition transport model that considers the wall heating and cooling effects.

[0088] In this embodiment of the invention, γ The transport model refers to the transition transport model proposed by François et al. equation:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] in Indicates local density, Indicates the intermittent factor. Tensor representation of fluid velocity Tensor representation of the local spatial location of the fluid. Indicates time, for Generating terms of the equation for The breaking term of the equation, for The diffusion term of the equation, Indicates the local dynamic viscosity coefficient. Indicates the local turbulent viscosity coefficient. It is a constant and usually , The ratio representing the viscosity coefficient. This represents a switching function that determines whether and when a transition occurs. A switching function representing the effect of the transition momentum thickness Reynolds number on the initiation of transition. A switching function representing the effect of viscosity ratio on transition initiation. for The switching function, The thickness Reynolds number represents the transition momentum. This represents the localized result of the transition momentum thickness Reynolds number. This represents the ratio of vorticity Reynolds number to momentum-thickness Reynolds number. This represents the Mach number at the boundary layer boundary. Represents the Mach number of the free stream. Indicates the local static pressure. Indicates free flow pressure. Indicates the free-flow turbulence intensity. This indicates the specific heat ratio, typically with a value of 1.4. For shape factor, and For constant terms, Indicates the magnitude of vorticity. It represents the viscosity ratio function, used to suppress turbulence-damping and relativizing terms outside the laminar boundary layer or inside the viscous sublayer.

[0104] In this embodiment of the invention, the existing momentum-thickness Reynolds number expression considering the wall heating and cooling effect is replaced by the localized momentum-thickness Reynolds number expression constructed in step S1. γ Reynolds number ratio in transport models The expression is replaced by the existing expression for the transition initial momentum thickness Reynolds number, which considers the wall heating and cooling effects, constructed in step S2. γ Transitional momentum thickness Reynolds number in transport models The expression completes the task. γ Improvements to the transport model.

[0105] S4. A transition transport model considering the wall heating and cooling effect is used to predict the transition of stratospheric high-altitude airships under the wall heating and cooling effect.

[0106] The following four specific experimental examples further describe the effectiveness of the transition prediction method considering wall heating and cooling effects provided by this invention.

[0107] Experimental Example 1:

[0108] This experimental example combines the FSC equation considering the boundary layer temperature gradient with linear stability theory, and calculates the results for a plate model at a series of temperature ratios (…). ) and pressure gradient parameters ( The boundary layer distribution under ( ). Among them , , Highest score This extensive database makes it possible to derive the correlation between key transition instability parameters (critical thresholds) and their controlling factors. A key component of transition transport models is the momentum thickness Reynolds number. The local approximation. In the original Langtry–Menter formula, the maximum vorticity Reynolds number... With momentum, thickness, and Reynolds number The ratio between them is a key parameter However, the effect of the pressure gradient was ignored. To improve accuracy under a wider range of aerodynamic configurations, François et al. improved the correlation by explicitly considering the pressure gradient effect. Building upon this, this experimental example further explores and introduces the influence of the temperature difference between the wall and the free flow on this relationship— The expression in step S1 is obtained. Then, to verify the effect of this expression, a fitted surface is constructed using the expression, and the result is compared with the calculation result of the FSC equation. The result is as follows. Figure 2 As shown, the fitting effect of this ratio parameter is compared under different temperature ratios. The surface in the figure represents the fitting result of the improved expression of the present invention, and the scatter points represent the calculation result of the FSC equation. Figure 3 To create a more intuitive graph, the data for each temperature ratio are projected and plotted on a plane. The solid lines represent the fitting results of the improved expression of this invention for different temperature ratios, and the corresponding scatter points represent the calculation results of the FSC equation at the corresponding temperature ratio. Figure 2 and Figure 3 It can be seen that the localized momentum-thickness Reynolds number expression considering the wall heating and cooling effect constructed in step S1 achieves a very good fit with the calculation results of the FSC equation.

[0109] Experimental Example 2:

[0110] This experimental example uses the FSC equation, which considers the boundary layer temperature gradient, to calculate the temperature ratios at a range of temperatures ( ). ) and pressure gradient parameters ( After the boundary layer distribution is determined, it is then combined with the linear stability theory. The method yields the spatial amplification factor at each perturbation frequency. and received various Placeholder Value envelope Furthermore, based on the Mack relation, the free-flow turbulence intensity is obtained. Transition threshold below .exist At this point, a turning point was achieved. The momentum-thickness Reynolds number at that location is taken as the initial momentum-thickness Reynolds number of the transition. Using the acquired data, to The expression is improved to obtain the expression shown in step S2. For example... Figures 4-7 What is shown is A schematic diagram illustrating the fitting effect of the improved expression. Among them, Figure 4 and Figure 5 All Tu =0.05% result, Figure 6 and Figure 7 All Tu =0.1% result. Similarly, solid lines and surfaces represent the fitting effect of the improved expression, and scatter plots represent calculated values ​​based on the FSC equations and linear stability theory. According to Figures 4-7 The results show that the transition initial momentum thickness Reynolds number expression constructed in step S2, which considers the wall heating and cooling effect, achieves a very good fit with the calculation results based on the FSC equation and linear stability theory.

[0111] Experiment Example 3:

[0112] After improving the expression, we obtain the localized momentum-thickness Reynolds number expression considering the wall heating and cooling effect, and the transition-initial momentum-thickness Reynolds number expression considering the wall heating and cooling effect. We then compare these two expressions with… Equation coupling yields the stability-based transition transport model in step S3, which considers the wall heating and cooling effects. This model is then validated using a classic flat plate example. Figure 8 The grid shown has 361 flow points and 161 normal points. The first layer grid height is... The normal grid growth rate is 1.12. CFD simulation is performed using the transition transport model provided by this invention. The incoming flow condition is... , , The temperature ratios were compared separately. (Insulated wall surface) , (Wall heating) , (Wall cooling) is verified through calculation examples, such as... Figure 9 for The following verification results are presented. Since a significant difference between laminar and turbulent flow lies in the substantial difference in frictional resistance between the two boundary layers, with the frictional resistance of the turbulent boundary layer being much greater than that of the laminar boundary layer, the frictional resistance coefficient of the flat plate surface will be used as an indicator to judge the transition effect. Figure 9 The solid line represents the frictional resistance coefficient obtained from the simulation of the transfer transport model in this embodiment of the invention. Curves and solid square dots represent the experiment. As a result, the circular hollow points represent the results calculated by the linear stability theory (LST). Figure 9 It can be seen that the transition transport model provided by this invention matches the experimental results in terms of transition prediction for adiabatic wall boundary conditions, and simultaneously verifies that LST possesses experimental accuracy. Furthermore, through... Figure 10 and Figure 11 It can be seen that, under wall heating and cooling conditions, the transition prediction results of the transition transport model provided by this invention are in good agreement with the LST results. This completes the flat plate case verification of the transition transport model of this invention, proving that the transition model provided by this invention performs excellently on the flat plate case.

[0113] Experiment Example 4:

[0114] After completing the numerical verification of the flat plate, the next step is to conduct numerical verification of the complex 3D configuration—the airship. Figure 12 The diagram shows the wind tunnel and airship test model used in this example verification. Figure 13 This diagram illustrates the airship test model used in this experiment and the testing techniques employed on the airship model. It focuses on the incoming flow velocity at a 0° angle of attack. and The airship's surface temperature is higher than the surface temperature of the incoming airflow. , , Wind tunnel tests were conducted using infrared imaging technology; only a few examples are shown here. , Under operating conditions, such as Figure 14 The diagram shows the thermal imaging results of the wind tunnel test. Colors represent temperature distribution, with solid black circles indicating the airship's turning point and dashed black lines representing the percentage of the airship's flow direction. Then, using... Figure 15 The grid shown is simulated using the transition transport model provided by this invention through CFD simulation, yielding the following results: Figures 16-21 The results are shown below. The cloud map represents the transition transport model results provided by this invention; the red straight line is the predicted transition position line; and the solid black circles represent previous wind tunnel test results. It can be seen that the transition prediction results of the transition transport model provided by this invention are consistent with the wind tunnel test results for complex 3D airship configurations. Simultaneously, CFD simulations were performed using the same mesh on the basic model, yielding the following results: Figures 22-24The results show that the prediction results of the basic model differ significantly from the experimental results because the influence of wall heating / cooling effects is not considered. This completes the calculation example verification of the 3D airship using the transition transport model provided by this invention.

[0115] In summary, this invention demonstrates that the transition transport model provided by this invention significantly improves the accuracy of transition prediction under wall heating and cooling effects compared to the original basic model.

[0116] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A transition prediction method considering wall heating and cooling effects, characterized in that, Includes the following steps: S1. Construct a localized momentum-thickness Reynolds number expression that takes into account the wall heating and cooling effects; S2. Construct an expression for the transition initial momentum thickness Reynolds number that considers the wall heating and cooling effects; S3. Couple the localized momentum-thickness Reynolds number expression considering the wall heating and cooling effect and the transition initial momentum-thickness Reynolds number expression considering the wall heating and cooling effect into... γ The transport model was developed and verified by wind tunnel simulation, resulting in a transition transport model that considers the wall heating and cooling effect. S4. A transition transport model considering the wall heating and cooling effect is used to predict the transition of stratospheric high-altitude airships under the wall heating and cooling effect. The localized momentum-thickness Reynolds number expression considering the wall heating and cooling effect constructed in step S1 is as follows: in, Represents the maximum vorticity Reynolds number. This indicates the local momentum thickness Reynolds number. Represents the Reynolds number ratio. Indicates wall temperature With free flow temperature The ratio, Indicates local Pressure gradient parameters at the location, , and Three functions representing the pressure gradient parameters; The expression for the transition initial momentum thickness Reynolds number, which considers the wall heating / cooling effect, constructed in step S2 is as follows: in The thickness Reynolds number represents the transition momentum. Represents pressure gradient parameters Sum and ratio polynomial functions, Indicates the free-flow turbulence intensity. Indicates free-flow turbulence A polynomial function.

2. The transition prediction method considering wall heating and cooling effects according to claim 1, characterized in that, The three functions of the pressure gradient parameters , and The calculation formula is: in This represents the pressure gradient parameter.

3. The transition prediction method considering wall heating and cooling effects according to claim 2, characterized in that, The pressure gradient parameter The calculation formula is: in This indicates the local momentum thickness. This represents the Hartree parameter. Indicates the flow velocity at the boundary layer boundary. This represents the kinematic viscosity coefficient at the boundary of the boundary layer.

4. The transition prediction method considering wall heating and cooling effects according to claim 1, characterized in that, The polynomial function The expression is: in , , and Represents pressure gradient parameters The four functions.

5. The transition prediction method considering wall heating and cooling effects according to claim 4, characterized in that, The pressure gradient parameter The four functions , , and The calculation formula is: 。 6. The transition prediction method considering wall heating and cooling effects according to claim 1, characterized in that, The polynomial function The expression is: in The natural logarithm of the free-flow turbulence intensity.

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