Method and device for predicting aerodynamic characteristics of rough wall of hypersonic aircraft and medium

Abstract

The invention discloses a hypersonic aircraft rough wall aerodynamic characteristic prediction method and device and a medium, and relates to the field of aircraft aerodynamic characteristic prediction.The method comprises the steps that the roughness height used for describing the roughness shape and the corrected surface infiltration area ratio are obtained; based on the wall temperature ratio, the compressible correction factor and the zoom coefficient, establishing a hypersonic rough wall RANS model; based on the hypersonic flight vehicle model with the smooth surface, the rough height and the corrected surface infiltration area ratio, in combination with the hypersonic rough wall RANS model, by means of a computational fluid dynamics method, streaming flow field simulation of the hypersonic flight vehicle to be predicted with the rough surface is carried out, and simulation data is obtained; and performing data post-processing on the simulation data to obtain the resistance and the heat flow of the to-be-predicted hypersonic aircraft with the rough surface. According to the method, the rough wall resistance and the heat flow of the hypersonic aircraft can be accurately predicted.

Description

Technical Field

[0001] This application relates to the field of aircraft aerodynamic characteristic prediction, and in particular to a method, device and medium for predicting the aerodynamic characteristics of a rough wall of a hypersonic aircraft. Background Technology

[0002] Hypersonic vehicles typically experience aerodynamic heating during flight, necessitating the deployment of heat-resistant protection systems to effectively resist high-temperature damage caused by aerodynamic thermal loads. Currently, the most mature and widely used thermal protection technology is ablation thermal protection. However, ablation introduces surface roughness into the vehicle, significantly altering its aerodynamic characteristics and increasing drag and surface heat flux. Therefore, it is necessary to consider the impact of surface roughness when predicting the aerodynamic characteristics of hypersonic vehicles. Computational Fluid Dynamics (CFD) combined with classical turbulence models to solve the Reynolds-Averaged Navier-Stokes Equations (RANS equations) is the most commonly used method in practical engineering for simulating the aerodynamic environment of aircraft. However, the roughness generated by ablation is relatively small, approximately 0.1 mm to 2 mm. Directly simulating the flow around this roughness would require an enormous amount of computation, making this method unsuitable for engineering applications. An efficient and accurate method for simulating the aerodynamic characteristics of rough walls involves introducing the roughness effect by adding a roughness correction to the classical RANS equations (i.e., the rough-wall RANS equations). In the rough-wall RANS equations, only the wall boundary conditions of the turbulence model need to be modified to introduce the roughness effect, without requiring detailed simulation of small-scale flows around the rough wall. The computational cost is comparable to that of the classical RANS equations simulating smooth-wall flows. However, existing rough-wall RANS equations are proposed for low-speed incompressible flows and are not applicable to hypersonic flows. Furthermore, the classical rough-wall RANS equations significantly overestimate the predicted thermal flux of the rough wall (i.e., over-predicted thermal flux). This phenomenon is effectively addressed by the variable turbulence Prandtl number method proposed by Aupoix under low-speed conditions, but it still exists in hypersonic flows. Summary of the Invention

[0003] The purpose of this application is to provide a method, device, and medium for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles, so as to achieve accurate prediction of rough wall drag and heat flow of hypersonic vehicles.

[0004] To achieve the above objectives, this application provides the following solution:

[0005] In a first aspect, this application provides a method for predicting the aerodynamic characteristics of rough walls in hypersonic vehicles, including:

[0006] Obtain the roughness height and the corrected surface wetting area ratio used to describe the roughness shape; the roughness height is calculated based on the shape parameters obtained from scanning the rough surface and the Driling fitting formula; the corrected surface wetting area ratio is calculated based on the ratio of the rough surface area to the original smooth surface area.

[0007] A hypersonic rough wall RANS model is established based on wall temperature ratio, compressibility correction factor and scaling factor.

[0008] Based on a hypersonic vehicle model with a smooth surface, the roughness height, and the corrected surface wetting area ratio, combined with the hypersonic rough wall RANS model, computational fluid dynamics methods are used to simulate the flow field around the hypersonic vehicle to be predicted with a rough surface, and simulation data is obtained; the simulation data includes the velocity distribution and temperature distribution of the flow field.

[0009] The simulated data is post-processed to obtain the drag and heat flux of the hypersonic vehicle to be predicted with a rough surface.

[0010] Optionally, a hypersonic rough wall RANS model is established based on the wall temperature ratio, compressibility correction factor, and scaling factor, specifically including:

[0011] Based on the roughness height, determine the local equivalent roughness height Reynolds number of the wall surface;

[0012] The model parameter S is calculated based on the compressibility correction factor and the equivalent roughness height Reynolds number. R ;

[0013] According to the model parameter S R Determine the boundary conditions for the rough wall RANS model;

[0014] The velocity profile downward displacement is determined based on the equivalent roughness height Reynolds number and the wall temperature ratio.

[0015] Based on the corrected surface wetting area ratio, the scaling factor is calculated to complete the establishment of the hypersonic rough wall RANS model.

[0016] Optionally, based on the roughness height, the equivalent roughness height Reynolds number of the local surface is determined, specifically including:

[0017] Using formula Determine the local equivalent roughness height Reynolds number of the wall; where k s + The equivalent roughness height Reynolds number; k s The roughness height; u τ ν is the wall shear rate; wis the kinematic viscosity coefficient of the fluid at the wall surface.

[0018] Optionally, the model parameter S is calculated based on the compressibility correction factor and the equivalent roughness height Reynolds number. R Specifically, it includes:

[0019] Using formula Calculate model parameters S R Among them, S R For model parameters; k s + α is the equivalent roughness height Reynolds number; α is the compressibility correction factor.

[0020] Optionally, the formula for calculating the compressibility correction factor is:

[0021]

[0022] Where α is the compressibility correction factor; k s ρ is the roughness height; ρ is the local density of the fluid; ρ w μ is the density of the fluid at the wall; μ is the local viscosity coefficient of the fluid; μ w is the viscosity coefficient of the fluid at the wall.

[0023] Optionally, based on the model parameters S R Determine the boundary conditions for the rough-walled RANS model, specifically including:

[0024] Using formula Determine the boundary conditions for the rough-walled RANS model; where ω represents the boundary conditions of the rough-walled RANS model; u τ S is the wall shear velocity; v is the kinematic viscosity at the wall; S R These are the model parameters.

[0025] Optionally, the velocity profile downward shift is determined based on the equivalent roughness height Reynolds number and the wall temperature ratio, specifically including:

[0026] Using formula Determine the downward displacement of the velocity profile; where ΔU + κ is the downward displacement of the velocity profile; k is a constant; s + The equivalent roughness height Reynolds number is given by Q; Q is the ΔU under adiabatic conditions. + ΔU under cold wall conditions + The difference; Q=-ln(T w / T aw );T w / T aw The wall temperature ratio; T w T represents the wall temperature. awTo restore temperature.

[0027] Optionally, the scaling factor is calculated based on the modified surface wetting area ratio, specifically including:

[0028] Using formula β r =Pr r，smooth / (Pr t，smooth +ΔPr t Calculate the scaling factor; where β r Pr is the scaling factor; t,smooth For turbulent Prandtl number; ΔPr t This represents the change in Prandtl number caused by roughness. ΔU + The velocity profile is shifted downwards; A and B are model parameters; A = (0.0155 - 0.0035S) corr )(1-exp[-12(S corr -1)]), B=-0.08+0.25exp[-10(S corr -1)], where α is the compressibility correction factor; k s y is the roughness height; y is the vertical distance from the midpoint of the flow field to the wall.

[0029] In a second aspect, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for predicting the rough-wall aerodynamic characteristics of a hypersonic vehicle as described above.

[0030] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for predicting the rough-wall aerodynamic characteristics of a hypersonic vehicle as described above.

[0031] According to the specific embodiments provided in this application, this application has the following technical effects:

[0032] This application provides a method, device, and medium for predicting the aerodynamic characteristics of rough walls in hypersonic vehicles. It obtains a roughness height and a corrected surface wetting area ratio to describe the roughness shape. The roughness height is calculated based on the shape parameters obtained from scanning the rough surface and the Driling fitting formula. The corrected surface wetting area ratio is calculated based on the ratio of the rough surface area to the original smooth surface area. A hypersonic rough wall RANS model is established based on the wall temperature ratio, compressibility correction factor, and scaling factor. Based on a smooth hypersonic vehicle model, the roughness height, and the corrected surface wetting area ratio, combined with the hypersonic rough wall RANS model, computational fluid dynamics methods are used to simulate the flow field around the predicted hypersonic vehicle with a rough surface, obtaining simulation data. Post-processing of the simulation data yields the drag and heat flux of the predicted hypersonic vehicle with a rough surface. This application, by combining a newly proposed rough wall ω-boundary condition suitable for hypersonic flow and a corrected RANS energy equation, achieves accurate prediction of the rough wall drag and heat flux of hypersonic vehicles. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 A comparison chart of drag increments between the original rough wall RANS model simulation and the high-precision numerical simulation provided in an embodiment of this application;

[0035] Figure 2 A comparison diagram of heat flux increments between the original rough wall RANS model simulation and the high-precision numerical simulation provided in an embodiment of this application;

[0036] Figure 3 A flowchart illustrating a method for predicting the aerodynamic characteristics of a hypersonic vehicle with rough walls, provided in an embodiment of this application;

[0037] Figure 4 This is a graph showing the trend of Q as a function of wall temperature ratio;

[0038] Figure 5 ΔU for RANS simulation + Trend graph of Mach number and wall temperature ratio;

[0039] Figure 6 ΔU is obtained from RANS simulation. + +Q follows 100 / (αS) R Distribution map;

[0040] Figure 7 Validation diagram for drag increment prediction using RANS model of hypersonic rough wall;

[0041] Figure 8 This is a validation diagram of the heat flux increment prediction for the hypersonic rough wall RANS model.

[0042] Figure 9 This is a schematic diagram of a pointed cone model;

[0043] Figure 10 A diagram showing the distribution of St numbers on the surface of a pointed cone.

[0044] Figure 11 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0045] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0046] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] The classic RANS equations for rough walls are based on the k-ω turbulence model. In the original k-ω turbulence model simulating smooth surfaces, the turbulent kinetic energy k and specific dissipation rate ω at the wall are relatively large to ensure that the turbulent kinetic energy k is zero in regions very close to the wall. The ω at the wall is then modified as follows:

[0048]

[0049] Among them, u τ S is the wall shear velocity; v is the kinematic viscosity at the wall; S R These are the model parameters.

[0050] The original larger value was changed to one that is the same as the parameter S. R The relevant finite values. As the specific dissipation rate decreases at and near the wall, the turbulence simulated by the RANS equations intensifies, leading to increased surface friction and heat flux. This is used to simulate the effect of roughness on surface resistance and heat flux. Parameter S R The determination depends on the key roughness function. This is represented by the wall shear velocity u. τ Define dimensionless velocity U + =u / u τLet u be the tangential velocity of the wall. τ and the wall kinematic viscosity coefficient ν w Define dimensionless coordinates y + =u τ y / ν w U + Along y + The distribution curve is velocity-type, where y represents the perpendicular distance from that point in the flow field to the wall. After roughness causes an increase in wall stress, u... τ It increases with the increase of wall stress, therefore U under rough wall conditions + Compared to the case of a smooth wall under the same conditions, there will be a decrease in ΔU. + The rough function describes ΔU + Relationship with roughness height:

[0051]

[0052] Where κ is a constant; The equivalent roughness height Reynolds number; k s This represents the roughness height.

[0053] Meanwhile, in the RANS equation simulation, in low-speed flow, after changing the ω-wall boundary condition to formula (1), ΔU also appears in the RANS equation. + And ΔU + With S R They satisfy a logarithmic relationship:

[0054]

[0055] By combining formulas (2) and (3) and simultaneously performing progressive correction on small roughness, S can be established. R and The relationship between them:

[0056]

[0057] However, both formulas (2) and (3) are proposed for low-speed flow. In hypersonic flow, Mach number effect, wall heat transfer effect, etc. will affect ΔU + This has a significant impact. A rough-wall RANS model was used to simulate hypersonic rough-wall turbulent boundary layer flow under different incoming Mach numbers and different wall temperature-recovery temperature ratios (wall temperature ratios). The drag increment results were compared between RANS and high-precision numerical simulations, using the results as a reference. Figure 1As shown, (a) is the comparison result under different Mach number conditions, and (b) is the comparison result under different wall temperature ratio conditions. It can be seen that the failure of formula (2) and formula (3) under supersonic conditions leads to the inaccuracy of the Wilcox rough wall RANS model in simulating rough wall resistance, especially under high Mach number and low wall temperature ratio conditions, the prediction error of resistance increment reaches up to 29.3%. Figure 2 The heat flux increment results of RANS and high-precision numerical simulation were compared. (a) shows the comparison results under different Mach number conditions, and (b) shows the comparison results under different wall temperature ratio conditions. It can be seen that the heat flux predicted by RANS is significantly higher under all conditions, with a maximum error of 81.4%.

[0058] The results and analysis above show that the rough-wall RANS model has large prediction errors for drag and heat flux under hypersonic conditions, indicating that the rough-wall RANS model is not suitable for hypersonic flow. Therefore, it is necessary to establish a new rough-wall RANS model suitable for hypersonic flow to achieve accurate prediction of rough-wall drag and heat flux under hypersonic conditions.

[0059] This application proposes a method for predicting the drag and heat flux of rough walls under hypersonic conditions (i.e., a method for predicting the aerodynamic characteristics of rough walls in hypersonic vehicles). It mainly includes proposing rough wall ω-boundary conditions suitable for hypersonic flow to achieve accurate prediction of rough wall drag, and modifying the RANS energy equation to achieve accurate prediction of rough wall heat flux under hypersonic conditions.

[0060] The rough wall ω boundary condition still adopts the form of formula (1), but the parameter S R The value of S needs to be changed. Clearly define S. R The value of ΔU depends on two aspects: firstly, in the hypersonic rough-walled turbulent boundary layer, the influence of ΔU... + The key parameter for ΔU + With k s + The first step is to recalibrate the roughness function, i.e., to propose a new roughness function suitable for hypersonic flows; the second step is to analyze the influence of ΔU on hypersonic flows simulated by RANS. + The key parameter for ΔU + With S R The relationship is then redefined. Finally, the new ΔU is combined. + With k s + and ΔU + With S R The calibration relationship is used to establish S. R With k s + The relationship was then established, ultimately determining the rough wall ω boundary condition applicable to hypersonic flow.

[0061] In the correction of the RANS energy equation, the heat flux decomposition method is first used to analyze the main factors leading to over-prediction of heat flux in the rough wall RANS model. This identifies the dominant term in the RANS energy equation causing over-prediction of heat flux, and appropriate correction coefficients are used to correct this dominant term, thereby achieving accurate prediction of heat flux in rough walls under hypersonic conditions. Combining the newly proposed rough wall ω boundary condition applicable to hypersonic flow with the corrected RANS energy equation, accurate prediction of hypersonic rough wall drag and heat flux is achieved.

[0062] In one exemplary embodiment, such as Figure 3 As shown, a method for predicting the aerodynamic characteristics of a hypersonic vehicle with rough walls is provided, including the following steps:

[0063] S1: Obtain the roughness height and the corrected surface wetting area ratio used to describe the roughness shape; the roughness height is calculated based on the shape parameters obtained from scanning the rough surface and the Driling fitting formula; the corrected surface wetting area ratio is calculated based on the ratio of the rough surface area to the original smooth surface area.

[0064] S2: A hypersonic rough wall RANS model is established based on the wall temperature ratio, compressibility correction factor, and scaling factor.

[0065] S3: Based on the smooth surface hypersonic vehicle model, the roughness height, and the corrected surface wetting area ratio, combined with the hypersonic rough wall RANS model, computational fluid dynamics methods are used to simulate the flow field around the rough-surfaced hypersonic vehicle to be predicted, obtaining simulation data. The simulation data includes the velocity distribution and temperature distribution of the flow field.

[0066] S4: Perform post-processing on the simulation data to obtain the drag and heat flux of the hypersonic vehicle to be predicted with a rough surface.

[0067] In this embodiment, the simulated data is post-processed. Heat flux density is calculated from the temperature gradient and thermal conductivity at the wall surface, and frictional drag is calculated from the velocity gradient and viscosity coefficient at the wall surface. The total frictional drag and pressure drag of the entire vehicle are obtained by area integration of the frictional drag and wall pressure distribution. This allows for the determination of the drag and heat flux of the predicted hypersonic vehicle with a rough surface.

[0068] As an optional implementation, S2 specifically includes:

[0069] S21: Determine the local equivalent roughness height Reynolds number of the wall based on the roughness height.

[0070] As an optional implementation, S21 specifically includes:

[0071] Using formula Determine the local equivalent roughness height Reynolds number of the wall; where k s + The equivalent roughness height Reynolds number; k s The roughness height; u τ ν is the wall shear rate; w is the kinematic viscosity coefficient of the fluid at the wall surface.

[0072] S22: Calculate the model parameter S based on the compressibility correction factor and the equivalent roughness height Reynolds number. R .

[0073] As an optional implementation, S22 specifically includes:

[0074] Using formula Calculate model parameters S R ; where k s + α is the equivalent roughness height Reynolds number; α is the compressibility correction factor.

[0075] The formula for calculating the compressibility correction factor is as follows:

[0076] ρ is the local density of the fluid; ρ w μ is the density of the fluid at the wall; μ is the local viscosity coefficient of the fluid; μ w is the viscosity coefficient of the fluid at the wall.

[0077] S23: According to the model parameters S R Determine the boundary conditions for the rough wall RANS model.

[0078] As an optional implementation, S23 specifically includes:

[0079] Using formula Determine the boundary conditions for the rough-walled RANS model; where ω represents the boundary conditions of the rough-walled RANS model; u τ The wall shear rate is denoted as .

[0080] S24: Determine the velocity profile downward displacement based on the equivalent roughness height Reynolds number and the wall temperature ratio.

[0081] As an optional implementation, S24 specifically includes:

[0082] Using formula Determine the downward displacement of the velocity profile; where ΔU + κ is the downward displacement of the velocity profile; k is a constant;s + The equivalent roughness height Reynolds number is given by Q; Q is the ΔU under adiabatic conditions. + ΔU under cold wall conditions + The difference; Q=-ln(T w / T aw );T w / T aw The wall temperature ratio; T w T represents the wall temperature. aw To restore temperature.

[0083] S25: Calculate the scaling factor based on the modified surface wetting area ratio to complete the establishment of the hypersonic rough wall RANS model.

[0084] As an optional implementation, the scaling factor is calculated based on the modified surface wetting area ratio, specifically including:

[0085] Using formula β r =Pr r，smooth / (Pr t，smooth +ΔPr t Calculate the scaling factor; where β r Pr is the scaling factor; t,smooth For turbulent Prandtl number; ΔPr t This represents the change in Prandtl number caused by roughness. ΔU + The velocity profile is shifted downwards; A and B are model parameters; A = (0.0155 - 0.0035S) corr )(1-exp[-12(S corr -1)]), B=-0.08+0.25exp[-10(S corr -1)].

[0086] This application primarily focuses on the field of aerodynamic characteristic prediction methods for hypersonic vehicles, proposing a method for predicting drag and heat flux of rough walls under hypersonic conditions, thereby improving the accuracy of drag and heat flux prediction using roughness RANS models under hypersonic conditions. This application is mainly divided into two parts. The first part achieves accurate drag prediction of supersonic rough walls, including two steps: firstly, under hypersonic conditions, by recalibrating ΔU... + With k s + The relationship, and secondly, under hypersonic conditions, calibrating ΔU + With S R The relationship. By simultaneously solving ΔU + With k s + ΔU + With S RThe first part establishes the ω-boundary condition of the RANS model for hypersonic rough walls, enabling accurate prediction of drag on rough walls. The second part modifies the energy equation of the rough wall RANS model to achieve accurate prediction of heat flux on hypersonic rough walls. Ultimately, this application realizes a method for predicting drag and heat flux on rough walls under hypersonic conditions.

[0087] Step 1: Calibrate ΔU under hypersonic conditions + With k s + Relationship

[0088] This application collects high-precision numerical simulation data of supersonic rough-wall turbulent boundary layers from existing literature, and obtains drag and velocity profiles U of rough walls under different shapes, heights, and flow conditions. + Distribution. Using high-precision numerical simulation data as a reference, the distribution of ΔU... + With k s + The relationships were recalibrated. The first set of data consists of high-precision numerical simulation results from Wang and Gao (Wang, Y., and Gao, Z., "Roughness Effects on Compressible Turbulent Boundary Layers under Different Mach Numbers and Wall Temperature Conditions," Physics of Fluids, Vol. 36, No. 2, 2024, p. 025144.), with flow conditions and results shown in Table 1. The second set consists of high-precision numerical simulation results from Modesti et al. (Modesti, D., Sathyanarayana, S., Salvadore, F., and Bernardini, M., "Direct Numerical Simulation of Supersonic Turbulent Flows over RoughSurfaces," Journal of Fluid Mechanics, Vol. 942, 2022, p. A44.), with flow conditions and results shown in Table 2.

[0089] When the wall surface changes from smooth to rough, it usually causes a significant increase in wall drag, which in turn causes a downward shift in the velocity profile ΔU. + ΔU + It is directly related to the increase in drag caused by roughness. In incompressible flow, ΔU + With k s +A relation that satisfies the logarithmic form is usually called a rough function, and its form is shown in formula (5).

[0090]

[0091] Wherein, ΔU + Velocity profile U of a smooth wall s + Velocity profile U of rough wall r + The difference represents the velocity profile U caused by surface roughness. + The downward shift; k s + For the equivalent roughness high Reynolds number, k s The equivalent roughness height is the roughness, and the parameter describing the roughness height can be calculated from the shape parameters obtained by roughness topography scanning and the Driling fitting formula; u τ The wall shear rate is... Where, τ w For the wall shear stress, ρ w ν represents the fluid density at the wall. w Let be the kinematic viscosity of the fluid at the wall; κ is a constant of 0.41. In incompressible flow, ΔU + By k s + Directly determined. This is determined by observing ΔU under hypersonic conditions collected in Tables 1 and 2. + k s + Data revealed that, under hypersonic conditions, besides k... s + In addition, ΔU + It will also be affected by the wall temperature ratio T w / T aw The significant impact of T. w T represents the wall temperature. aw To restore temperature, γ is the specific heat ratio, Ma e and T e These are the Mach number and static temperature at the outer edge of the boundary layer, respectively.

[0092] Table 1. Working conditions and results of high-precision numerical simulations for Wang and Gao.

[0093]

[0094]

[0095] Table 2. Working conditions and results of the high-precision numerical simulation by Modesti et al.

[0096] Case R03_500 R2_500 R2_1000 R4_500 R4_1000 Ma 0.3 2.0 2.0 4.0 4.0 <![CDATA[T w / T aw ]]> 0.978 0.467 0.467 0.130 0.130 <![CDATA[k s + ]]> 78 78 160 78 160 <![CDATA[ΔU + ]]> 7.32 6.45 5.02 8.51 7.32

[0097] T w / T aw For ΔU + The effect is considered in ΔU through offset Q. + In the calibration formula, Q is ΔU under adiabatic conditions. + With low T w / T aw ΔU under the condition (i.e., cold wall) + The difference. Therefore, a new ΔU is proposed. + The calibration formula is shown in formula (6).

[0098]

[0099] Observe Q as T w / T aw The changing trends of Q and T were observed. w / T aw They exhibit a strong correlation and show a logarithmic pattern, such as Figure 4 As shown in the figure. Therefore, the form of Q is proposed as shown in formula (7).

[0100] Q = -ln(T) w / T aw (7)

[0101] This enables the realization of ΔU under hypersonic conditions. + With k + s Re-evaluation of relationships.

[0102] Step 2: Apply boundary conditions and ΔU to the rough wall RANS model + Recalibrate.

[0103] The boundary conditions of the rough wall RANS model are determined by formula (8).

[0104]

[0105] By applying the ω boundary condition shown in formula (8), the downward displacement ΔU of the velocity profile can be simulated. + The phenomenon observed. In low-speed flow, the input parameter S... R With ΔU + It satisfies the logarithmic relationship, as shown in formula (9).

[0106]

[0107] Among them, S R These are model parameters; indicating that in low-speed flow, ΔU + From input parameter S RThe only certainty. However, in hypersonic flow, Figure 5 Numerical experimental results show that, except for parameter S R In addition, ΔU + It is also affected by Mach number and wall temperature ratio. Under supersonic conditions, it is necessary to... R With ΔU + The relationship is recalibrated. This application introduces a compressibility correction factor α, defined as 2k... s The average variation of internal density and viscosity coefficient is shown in Equation (10).

[0108]

[0109] Where ρ and ρ w These represent the fluid density at the local location and at the wall, respectively; μ and μ w These are the viscosity coefficients of the fluid at the local location and at the wall, respectively.

[0110] Depend on Figure 6 The RANS numerical experiment results show that 100 / (αS) R ) and ΔU + It satisfies the logarithmic relationship shown in formula (11). The definition and value of Q are the same as in step 1.

[0111]

[0112] This completes the equations for the ω boundary conditions and ΔU in RANS under hypersonic conditions. + Recalibration. By simultaneously solving ΔU + With k s + The relation (formula (6)) and ΔU + With S R The relationship (Formula (11)) can be used to establish the relationship between the actual roughness height and the input parameter S in the roughness wall RANS model. R The relationship between them.

[0113]

[0114] At the same time, for k s + For smaller cases, corrections are made to establish the RANS model ω boundary condition suitable for simulating hypersonic rough-walled turbulent boundary layer flow, as shown in Equation (13). The model can achieve the simulation of hypersonic rough-walled turbulent boundary layer flow without capturing the fine flow structure around the roughness, simply by inputting the roughness height k. s This allows for the use of the RANS model for rough wall flow under hypersonic conditions to represent ΔU. + Accurate predictions by U. + Definition, It can be seen that the downward displacement of the velocity profile caused by roughness is ΔU + This is because increased roughness increases the wall's resistance τ. w This is the cause. Therefore, the model achieves the effect of ΔU + Accurate simulation is equivalent to achieving accurate prediction of the resistance of rough walls.

[0115]

[0116] Step 3: Correcting the energy equation of the rough-walled RANS model improves the accuracy of heat flow prediction.

[0117] When the wall surface changes from smooth to rough, the roughness not only causes a change in drag but also increases the heat flux. Furthermore, the increase in heat flux caused by roughness is significantly lower than the increase in drag. After correcting the wall boundary conditions in steps 1 and 2, the predicted change in heat flux becomes comparable to the change in drag. Therefore, other methods are still needed to improve the model's accuracy in predicting heat flux over rough walls.

[0118] The problem of overestimating heat flux prediction exists in both low-speed and hypersonic flows. A method to correct for the turbulent heat conduction term (Aupoix, B., and Spalart, PR, “Extensions of the Spalart-Allmaras Turbulence Model to Account for Wall Roughness,” International Journal of Heat and Fluid Flow, Vol. 24, No. 4, 2003, pp. 454-462.) has successfully achieved accurate prediction of rough wall heat flux under low-speed conditions. However, in hypersonic flows, in addition to the turbulent heat conduction term, the Reynolds stress work term also has a significant impact on wall heat flux (Li, J., Yu, M., Sun, D., Liu, P., Yuan, X., 2022. Wall heat transfer in high-enthalpy hypersonic turbulent boundary layers. Physics of Fluids 34, 085102.).

[0119] Therefore, under hypersonic conditions, the method for correcting the turbulent heat conduction term is applied to both the turbulent heat conduction term and the Reynolds stress work term. The scaling factor is defined as β. r ,β r The calculation is shown in formula (14).

[0120] β r =Pr r，smooh / (P r,mooth +ΔPrt (14)

[0121] Among them, Pr t,smooth ΔPr is the Prandtl number for turbulence, taken as a constant of 0.9. t The change in Prandtl number caused by roughness is calculated as follows:

[0122]

[0123] Wherein, ΔU + The roughness height and wall temperature conditions can be calculated using formula (6), where α is the compressibility correction factor calculated in step 2, and can be calculated using formula (10) from the simulated flow field. A and B are model parameters, and their calculation methods are as follows:

[0124] A = (0.0155 - 0.0035S) corr )(1-exp[-12(S corr -1)]) (16)

[0125] B = -0.08 + 0.25exp[-10(S)] corr -1)] (17)

[0126] Among them, S corr The corrected surface wetted area ratio characterizes the relative increase in surface wetted area above the average height due to roughness, and is a shape parameter describing the roughness profile. The corrected energy equation is given below; the main difference between it and the uncorrected energy equation lies in the turbulent heat conduction term. and the work done by Reynolds stress Use scaling factor β r It has been scaled down.

[0127]

[0128] Where, μ t C is the turbulent viscosity coefficient; p t is the specific heat at constant pressure; u is the velocity; h is the net enthalpy; k is the turbulent kinetic energy; t ij For viscous stress; τ ij σ represents the Reynolds stress; σ is a parameter of the original k-ω turbulence model.

[0129] Parameter β r The value of is less than 1, so the turbulent transport term and the Reynolds stress work term in the energy equation are suppressed, and the simulated wall heat flux will decrease accordingly. This can solve the problem of the heat flux prediction of the supersonic rough wall RANS model being too high and improve the accuracy of the model's prediction of wall heat flux.

[0130] In summary, this application achieves accurate prediction of drag in a hypersonic rough wall RANS model by proposing new wall boundary conditions in steps 1 and 2; and achieves accurate prediction of heat flux in a hypersonic rough wall RANS model by modifying the energy equation in step 3. These two parts are independent of each other, and their simultaneous application enables accurate prediction of drag and heat flux in hypersonic rough walls.

[0131] The method for predicting heat flux from hypersonic rough wall resistance can be divided into the following steps:

[0132] Step a: First, obtain the parameter k that describes the roughness shape. s S corr Among them, k s S can be calculated using the shape parameters obtained from scanning the rough surface and the Driling fitting formula. corr The ratio of the rough surface area obtained from the scan to the original smooth surface area can be calculated. Add formula (5) to the CFD code to calculate the local k of the wall surface. s + .

[0133] Step b: Add the following to the code: calculate the local compressibility correction factor α of the wall according to formula (10), and then calculate the roughness height Reynolds number k according to formula (13). s + Calculate parameter S R , by parameter S R The value of ω is calculated according to formula (8) and used as the local value of ω at the wall surface.

[0134] Step c: From the input k s + and T w / T aw Calculate ΔU according to formula (6) + , and by the input S corr Calculate the magnitudes of parameters A and B according to formulas (16) and (17), and then use A, B, and ΔU. + Calculate ΔPr according to the formula. t Then calculate the scaling factor β according to formula (14). r When calculating viscous flux, the corresponding turbulent heat conduction term and Reynolds stress work term are multiplied by a scaling factor β. r .

[0135] After completing the above steps, the hypersonic rough-wall RANS model is embedded in the CFD code. After embedding the hypersonic rough-wall RANS model, in the CFD simulation, a smooth-surfaced hypersonic vehicle model and the input roughness shape parameter k can be used. s S corrWe conducted flow field simulations around a hypersonic vehicle with a rough surface. The drag and heat flux of the vehicle with a rough surface can be obtained using conventional data post-processing.

[0136] The following uses the high-precision numerical simulation results of Wang and Gao as a benchmark to verify the accuracy of the hypersonic rough wall RANS model in predicting the drag and heat flux of a rough-walled flat plate under different Mach numbers and wall temperatures. The flow conditions are consistent with those in Table 1. The simulation results of the drag increment caused by roughness are compared between the modified model and the original model as follows: Figure 7 As shown in the figure, the modified rough-wall RANS model significantly improves the accuracy of drag prediction under hypersonic conditions, reducing the prediction error from a maximum of 29.3% in the original model to below 4%. A comparison of the predicted heat flux increments by the modified and original models is shown below. Figure 8 As shown, the revised model significantly improves the accuracy of predicting heat flux increments. The prediction error has decreased from 50.2%–81.4% to below 11%.

[0137] Subsequently, numerical simulations were conducted using Holden's hypersonic flow around a rough-walled cone to verify the accuracy of the rough-walled RANS model. Two flow conditions were selected, with an incoming Mach number of 7.9, an incoming temperature of 81.11 K, and an incoming pressure of 2544.17 Pa in both cases. The ratio of wall temperature to total temperature, T... w / T0 are 0.2 and 0.3 respectively. Model dimensions are as follows: Figure 9 As shown, the head blunt radius R n =0.00254mm, equivalent roughness height is 0.203mm, S corr It is 1.17. Figure 10 The St number distribution calculated using a modified rough-wall RANS model under wall temperature conditions is presented, and compared with the results calculated using the original model and wind tunnel experimental results. Figure 10 It can be seen that the corrected rough-wall RANS model has a significantly improved accuracy in predicting heat flux in hypersonic boundary layers compared to the original model.

[0138] The beneficial effects of this application compared to related technologies are as follows:

[0139] This improves the prediction accuracy of the rough-wall RANS model for surface drag under hypersonic conditions. By analyzing ΔU under hypersonic conditions... + With k describing the roughness height s + RANS boundary condition parameters S R The recalibration established the parameter S in the rough wall RANS model. R With input k s +The relationship between them was established, and the ω boundary condition of the rough wall RANS model applicable to hypersonic flow was established, thereby improving the accuracy of drag prediction under hypersonic conditions.

[0140] The accuracy of the RANS model for predicting surface heat flux under hypersonic conditions has been improved. By introducing correction coefficients into the turbulent heat conduction and Reynolds stress work terms in the RANS energy equation, the problem of over-predicting heat flux under hypersonic conditions is effectively solved, and the model's prediction accuracy for heat flux over rough walls is significantly improved.

[0141] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described method for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles.

[0142] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the above-described method for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles.

[0143] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the above-described method for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles.

[0144] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 11 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and databases. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network. When executed by the processor, the computer program implements a method for predicting the aerodynamic characteristics of rough walls in hypersonic vehicles.

[0145] Those skilled in the art will understand that Figure 11The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0146] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0147] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0148] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0149] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0150] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for predicting the aerodynamic characteristics of a rough-walled hypersonic vehicle, characterized in that, include: Obtain the roughness height and the corrected surface wetting area ratio used to describe the roughness shape; the roughness height is calculated based on the shape parameters obtained from scanning the rough surface and the Driling fitting formula; the corrected surface wetting area ratio is calculated based on the ratio of the rough surface area to the original smooth surface area. A hypersonic rough wall RANS model is established based on wall temperature ratio, compressibility correction factor and scaling factor. Based on a hypersonic vehicle model with a smooth surface, the roughness height, and the corrected surface wetting area ratio, combined with the hypersonic rough wall RANS model, computational fluid dynamics methods are used to simulate the flow field around the hypersonic vehicle to be predicted with a rough surface, and simulation data is obtained; the simulation data includes the velocity distribution and temperature distribution of the flow field. The simulated data is post-processed to obtain the drag and heat flux of the hypersonic vehicle to be predicted with a rough surface.

2. The method for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles according to claim 1, characterized in that, A hypersonic rough wall RANS model is established based on the wall-temperature ratio, compressibility correction factor, and scaling factor, specifically including: Based on the roughness height, determine the local equivalent roughness height Reynolds number of the wall surface; The model parameter S is calculated based on the compressibility correction factor and the equivalent roughness height Reynolds number. R ; According to the model parameter S R Determine the boundary conditions for the rough wall RANS model; The velocity profile downward displacement is determined based on the equivalent roughness height Reynolds number and the wall temperature ratio. Based on the corrected surface wetting area ratio, the scaling factor is calculated to complete the establishment of the hypersonic rough wall RANS model.

3. The method for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles according to claim 2, characterized in that, Based on the roughness height, the equivalent roughness height Reynolds number of the wall surface is determined, specifically including: Using formula Determine the local equivalent roughness height Reynolds number of the wall; where k s + The equivalent roughness height Reynolds number; k s The roughness height; u τ ν is the wall shear rate; w is the kinematic viscosity coefficient of the fluid at the wall surface.

4. The method for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles according to claim 2, characterized in that, The model parameter S is calculated based on the compressibility correction factor and the equivalent roughness height Reynolds number. R Specifically, it includes: Using formula Calculate model parameters S R Among them, S R For model parameters; k s + α is the equivalent roughness height Reynolds number; α is the compressibility correction factor.

5. The method for predicting the aerodynamic characteristics of a hypersonic vehicle with rough walls according to claim 1, characterized in that, The formula for calculating the compressibility correction factor is as follows: Where α is the compressibility correction factor; k s ρ is the roughness height; ρ is the local density of the fluid; ρ w μ is the density of the fluid at the wall; μ is the local viscosity coefficient of the fluid; μ w is the viscosity coefficient of the fluid at the wall.

6. The method for predicting the aerodynamic characteristics of a rough wall of a hypersonic vehicle according to claim 2, characterized in that, According to the model parameter S R Determine the boundary conditions for the rough-walled RANS model, specifically including: Using formula Determine the boundary conditions for the rough-walled RANS model; where ω represents the boundary conditions of the rough-walled RANS model; u τ S is the wall shear velocity; v is the kinematic viscosity at the wall; S R These are the model parameters.

7. The method for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles according to claim 2, characterized in that, The velocity profile downward displacement is determined based on the equivalent roughness height Reynolds number and the wall temperature ratio, specifically including: Using formula Determine the downward displacement of the velocity profile; where ΔU + κ is the downward displacement of the velocity profile; k is a constant; s + The equivalent roughness height Reynolds number is given by Q; Q is the ΔU under adiabatic conditions. + ΔU under cold wall conditions + The difference; Q=-ln(T w / T aw );T w / T aw The wall temperature ratio; T w T represents the wall temperature. aw To restore temperature.

8. The method for predicting the aerodynamic characteristics of rough walls of hypersonic vehicles according to claim 2, characterized in that, The scaling factor is calculated based on the corrected surface wetting area ratio, specifically including: Using formula β r =Pr r,smooth / (Pr t,smooth +ΔPr t Calculate the scaling factor; where β r Pr is the scaling factor; t,smooth For turbulent Prandtl number; ΔPr t This represents the change in Prandtl number caused by roughness. ΔU + Let A be the downward displacement of the velocity profile; A and B are model parameters; A = (0.015 - 0.0035S) corr )(1-exp[-12(S corr -1)]), B=-0.08+0.25exp[-10(S corr -1)], where α is the compressibility correction factor; k s y is the roughness height; y is the vertical distance from the midpoint of the flow field to the wall.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the method for predicting the rough-wall aerodynamic characteristics of a hypersonic vehicle according to any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the method for predicting the aerodynamic characteristics of a hypersonic vehicle with rough walls as described in any one of claims 1-8.

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