Hypersonic aircraft boundary layer transition prediction method considering wall surface ablation

Abstract

The invention discloses a hypersonic flight vehicle boundary layer transition prediction method considering wall surface ablation. The method comprises the following steps: determining a free incoming flow condition of a flight vehicle, a geometric shape of the flight vehicle and a wall surface ablation model; according to the given flight working condition, considering the wall surface ablation boundary condition, and calculating a basic flow field of the corresponding working condition by solving a Navier-Stokes equation; secondly, establishing a linear stability analysis equation by adopting LST, and performing flow stability analysis on the basic flow field by considering a linearization wall surface ablation condition to obtain disturbance growth rate distribution of small disturbances with different frequencies; according to the obtained disturbance growth rate distribution, an e-N method is adopted, envelope lines of amplification factor N values of disturbance of different frequencies in the flow direction are calculated, experience transition N values are compared, and the transition position is predicted. According to the method, basic flow field calculation and stability analysis of the wall surface ablation effect are considered, the flow state of the hypersonic aircraft in the flight process is met, and the boundary layer transition prediction position can be predicted more accurately.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to a method for predicting boundary layer transition of a hypersonic aircraft taking into account wall ablation effects. Background Art

[0002] During the flight of a hypersonic vehicle, the surface temperature will rise sharply due to the compressibility of the air around the vehicle and the combined effects of shock waves and viscosity. This will cause the vehicle structure to face severe thermal load challenges, requiring corresponding thermal protection measures to reduce wall friction and heat flux. Ablation thermal protection, as a typical thermal protection method, injects ablation products into the boundary layer through wall reactions, increasing the boundary layer thickness and changing the boundary layer shape, which will have a significant impact on the boundary layer transition position. After the boundary layer transition, the wall heat flux will increase significantly, usually by 3-5 times, and the impact on aerodynamic heat is very significant. Therefore, accurately predicting the transition position can provide important theoretical support for the optimization of aircraft aerodynamic layout and the design of thermal protection systems.

[0003] Currently, academic research focuses on the effects of wall ablation on vehicle wall friction and thermal flow. However, research on the effect of ablation on the transition location of a vehicle is insufficient and requires further investigation. Given the high requirements and high cost of transition experiments, it is necessary to develop a transition prediction method for the boundary layer of a hypersonic vehicle that considers the effects of wall ablation. Summary of the Invention

[0004] In view of the above-mentioned prior art, the present invention considers the influence of wall ablation on the transition position and provides an accurate boundary layer transition prediction method.

[0005] In order to solve the above technical problems, the present invention proposes a hypersonic vehicle boundary layer transition prediction method considering wall ablation, comprising the following steps:

[0006] S1. Obtaining flight conditions of the aircraft, including aircraft free flow conditions, aircraft geometry, and a wall ablation model; the aircraft free flow conditions include flow Mach number, flow temperature, and flow pressure;

[0007] S2. According to the flight condition of step S1, establishing an aircraft wall ablation boundary condition based on a wall ablation model, and calculating the basic flow field under the flight condition by solving the Navier-Stokes equations based on the wall ablation boundary condition;

[0008] S3. Using linear stability theory to establish a linear stability analysis equation, taking into account the linearized wall ablation condition of the disturbance amount, perform flow stability analysis on the basic flow field calculated in step S2, and obtain the disturbance growth rate distribution of small disturbances of different frequencies;

[0009] S4. Based on the disturbance growth rate distribution obtained in step S3, the eN method is used to calculate the envelope of the amplification factor N value along the flow direction of disturbances of different frequencies, and the transition position is predicted by comparing the empirical transition N value.

[0010] Furthermore, the hypersonic vehicle boundary layer transition prediction method of the present invention comprises:

[0011] In step S2, the aircraft wall ablation boundary conditions are established based on the wall ablation model, including:

[0012] (a) For wall pressure, the normal momentum flux gradient is zero,

[0013]

[0014] Where ρ represents density, p represents pressure, and u n represents the normal velocity, and n represents the wall normal;

[0015] (b) For the mass fractions of the wall components, establish the vehicle wall mass balance equation:

[0016]

[0017] Among them, ρ s represents the density of component s, D s represents the diffusion coefficient of component s, Y s represents the mass fraction of component s, m w,s represents the wall mass flow rate of component s produced by wall ablation;

[0018] (c) For the wall temperature, establish the vehicle wall energy balance equation:

[0019]

[0020] Among them, κ, κ v Represents the thermal conductivity coefficients of translation temperature and rotation temperature, T v represents the vibration temperature, T represents the translation temperature; ε is the radiation emissivity, which is usually taken as 0.9 for carbon surface, and σ is the Stefan-Boltzmann constant; H s represents the total enthalpy of component s; considering the wall temperature thermal equilibrium, T v =T;

[0021] (d) For the wall velocity, solve the wall normal velocity using the overall mass balance equation:

[0022]

[0023] In step S3, a linear stability analysis equation is established using linear stability theory, including:

[0024] Based on the non-equilibrium compressible Navier-Stokes equation, the non-equilibrium compressible Navier-Stokes equation is expanded into a small perturbation form and linearized to obtain the linearized perturbation equation. The basic form is as follows:

[0025]

[0026] Among them, φ′=[ρ′,u′,v′,w′,T′,Y s ′,T v ′] is the perturbation of the physical quantity, s, n, z are the body-fitting coordinates, h i is the Lame coefficient; Γ,A,B,C,D,H ij is a coefficient matrix and is only related to the background flow field;

[0027] According to the linear stability theory, the perturbation quantity is written in the form of normal mode as follows:

[0028]

[0029] Where ω represents the frequency of the disturbance, α represents the streamwise wave number of the disturbance, and β represents the spanwise wave number;

[0030] Substituting Equation (6) into the linearized perturbation equation, we obtain the linear stability analysis equation as follows:

[0031]

[0032] The linear stability analysis equation is an eigenvalue problem, which can be expressed as Where L is a linear operator;

[0033] In order to solve the linear stability analysis equation, the linearized wall ablation condition of the disturbance is established, including:

[0034] (a) Mass balance of wall components:

[0035]

[0036] (b) Total wall mass balance relationship:

[0037]

[0038] (c) Wall energy balance relationship:

[0039]

[0040] (d) The wall velocity disturbance is zero:

[0041] u′=v′=0 (11)

[0042] (e) Wall temperature perturbation thermal equilibrium:

[0043] T v ′=T′ (12)

[0044] In step S4, the disturbance growth rates of small disturbances of different frequencies are integrated along the flow direction to obtain the distribution of the amplification factors N of small disturbances of different frequencies along the flow direction; the integral formula is as follows:

[0045]

[0046] Among them, A0 represents the initial amplitude of the disturbance, A is the growth of the disturbance wave amplitude, -α i is the growth rate of the disturbance wave.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] (1) The present invention establishes the ablation boundary conditions required for basic flow calculation and stability analysis, and based on this ablation boundary, proposes a basic flow field calculation and stability analysis method considering the wall ablation effect.

[0049] (2) The analysis method proposed in the present invention is consistent with the flow state during the flight of a hypersonic aircraft, and can more accurately predict the boundary layer transition position, thereby providing theoretical support for optimizing the aerodynamic layout and thermal protection design of hypersonic aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A flowchart of the prediction method of the present invention;

[0051] Figure 2 Comparison of wall heat flux with and without wall ablation conditions in a blunt cone boundary layer at Mach number Ma=20 and flight altitude 26km

[0052] Figure 3 This is a comparison chart of wall temperature with and without wall ablation conditions in the blunt cone boundary layer at Mach number Ma=20, flight altitude 26km.

[0053] Figure 4 Comparison of the second mode growth rate distribution cloud map with and without wall ablation conditions at Mach number Ma=20 and flight altitude 26km in the blunt cone boundary layer, where (a) is the second mode growth rate distribution cloud map with wall ablation, and (b) is the second mode growth rate distribution cloud map without wall ablation.

[0054] Figure 5 This is a comparison chart of the N-factor envelope with and without wall ablation conditions at Mach number Ma=20, flight altitude 26km, and in the blunt cone boundary layer. DETAILED DESCRIPTION

[0055] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention in any way.

[0056] This embodiment provides a hypersonic vehicle boundary layer transition prediction method considering wall ablation, such as Figure 1 The specific steps are as follows:

[0057] S1. Determining the flight conditions of the aircraft, including the aircraft free flow conditions, the aircraft geometry, and the wall ablation model; the aircraft free flow conditions include the flow Mach number, flow temperature, and flow pressure;

[0058] In this step, a blunt cone boundary layer is considered for a free flow at zero angle of attack of Ma = 20 at an altitude of 30 km. The blunt cone has a spherical radius of 6.35 mm, a semi-cone angle of 7°, and a total length of 800 mm. The basic flow field is calculated with and without consideration of wall ablation, and the stability analysis is performed.

[0059] The wall ablation model considers the carbon ablation model. The specific wall reaction model is shown in Table 1.

[0060] Table 1 Wall ablation model

[0061] S2. According to the flight conditions given in step S1, establish the aircraft wall ablation boundary conditions based on the wall ablation model, and calculate the basic flow field corresponding to the flight conditions by solving the Navier-Stokes (NS) equations based on the wall ablation boundary conditions.

[0062] In this step, the non-equilibrium compressible NS equations are solved:

[0063]

[0064] Where t is the time variable, x and r are the axial and radial spatial coordinates respectively, Q represents the conserved variable, E and F are the inviscid fluxes in the x and r directions respectively, and E v 、F v are the viscous fluxes in the x and r directions respectively, S represents the source term generated by gas phase reaction and vibration relaxation, and M represents the source term generated by the conversion of the equation from rectangular coordinates to cylindrical coordinates.

[0065] Considering the wall ablation boundary condition:

[0066] (a) For the wall pressure, consider the normal momentum flux gradient to be zero

[0067]

[0068] Where ρ represents density, p represents pressure, and u n represents the normal velocity, and n represents the wall normal.

[0069] (b) For the mass fractions of the wall components, establish the vehicle wall mass balance equation:

[0070]

[0071] Among them, ρ s represents the density of component s, D s represents the diffusion coefficient of component s, Y s represents the mass fraction of component s, m w,s represents the wall mass flow rate of component s produced by wall ablation.

[0072] (c) For the wall temperature, establish the vehicle wall energy balance equation:

[0073]

[0074] Among them, κ, κ v Represents the thermal conductivity coefficients of translation temperature and rotation temperature, T v represents the vibration temperature, T represents the translation temperature. ε is the radiation emissivity, which is usually taken as 0.9 for carbon surface, σ=5.67×10 -8 (W / (m 2 ·K 4 )) is the Stefan-Boltzmann constant. H s represents the total enthalpy of component s.

[0075] Considering the thermal balance of the wall temperature, T v =T.

[0076] (d) For the wall velocity, solve the wall normal velocity using the overall mass balance equation:

[0077]

[0078] The NS equations are solved using the finite difference method, the time advancement adopts the second-order Runge-Kutta method, the original variables are reconstructed using the third-order MUSCL format, the convection term uses the AUSMPW+ flux splitting format, and the viscosity term uses the fourth-order central difference format. The basic flow field considering the wall ablation effect can be obtained. Figure 2 A comparison of wall heat flux with and without considering wall ablation is given. Figure 3 A comparison of wall temperature with and without consideration of wall ablation is given. It can be seen that wall ablation increases the wall heat flux.

[0079] S3. Linear stability theory (LST) is used to establish a linear stability analysis equation. Considering the linearized wall ablation condition of the disturbance amount, the flow stability analysis of the basic flow field obtained above is performed to obtain the disturbance growth rate distribution of small disturbances of different frequencies.

[0080] In this step, based on the non-equilibrium compressible NS equations, it is expanded into a small perturbation form and linearized to obtain the linearized perturbation equation. Its basic form can be written as:

[0081]

[0082] Among them, φ′=[ρ′,u′,v′,w′,T′,Y s ′,T v ′] is the perturbation of the physical quantity, s, n, z are the body-fitting coordinates, h i is the Lame coefficient. Γ,A,B,C,D,H ij is a coefficient matrix, which is only related to the background flow field.

[0083] According to the linear stability theory (LST), the disturbance is written in the form of normal mode:

[0084]

[0085] Where ω represents the frequency of the disturbance, α represents the streamwise wave number of the disturbance, and β represents the spanwise wave number.

[0086] Substituting the above perturbation form into the linearized perturbation equation, we can obtain the control equation of LST, that is, the linear stability analysis equation:

[0087]

[0088] in:

[0089]

[0090] This governing equation is an eigenvalue problem and can be expressed as where L is a linear operator.

[0091] In order to solve the governing equations of LST, the wall ablation boundary conditions of the disturbance are established, including:

[0092] (a) Mass balance of wall components:

[0093] (b) Total wall mass balance relationship:

[0094] (c) Wall energy balance relationship:

[0095]

[0096] (d) The wall velocity disturbance is zero: u′ = v′ = 0

[0097] (e) Thermal equilibrium of wall temperature disturbance: T v ′=T′

[0098] The far-field boundary conditions are met

[0099] The growth rate cloud obtained in this step is as follows Figure 4 As shown, after Figure 4 Comparing (a) and (b), we can see that the wall ablation effect increases the overall growth rate.

[0100] S4. Based on the disturbance growth rate distribution obtained in step S3, the eN method is used to calculate the envelope of the amplification factor N value along the flow direction of disturbances of different frequencies, and the transition position is predicted by comparing the empirical transition N value.

[0101] In this step, the growth rates of small disturbances of different frequencies are integrated along the flow direction to obtain the distribution of the amplification factors N of small disturbances of different frequencies along the flow direction. The integral formula is given as follows:

[0102]

[0103] Among them, A0 represents the initial amplitude of the disturbance, A is the growth of the disturbance wave amplitude, -α i is the growth rate of the disturbance wave.

[0104] Figure 5 The envelope of the N value obtained in this step is given. It is believed that a transition occurs when the N value reaches 4. Figure 5 It can be obtained that the transition position of the ablated wall is x = 0.66m, and the transition position of the non-ablated wall is x = 0.69m.

[0105] Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments. The above-mentioned specific embodiments are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can make many improvements and changes without departing from the purpose of the present invention, which are all protected by the present invention.

Claims

1. A method for predicting boundary layer transition of a hypersonic vehicle considering wall ablation, comprising the following steps: S1. Determining the flight conditions of the aircraft, including the aircraft free flow conditions, the aircraft geometry, and the wall ablation model; the aircraft free flow conditions include the flow Mach number, flow temperature, and flow pressure; S2. According to the flight condition of step S1, establishing an aircraft wall ablation boundary condition based on a wall ablation model, and calculating the basic flow field under the flight condition by solving the Navier-Stokes equations based on the wall ablation boundary condition; S3. Using linear stability theory to establish a linear stability analysis equation, taking into account the linearized wall ablation condition of the disturbance amount, perform flow stability analysis on the basic flow field calculated in step S2, and obtain the disturbance growth rate distribution of small disturbances of different frequencies; S4. Based on the disturbance growth rate distribution obtained in step S3, the eN method is used to calculate the envelope of the amplification factor N value along the flow direction of disturbances of different frequencies, and the transition position is predicted by comparing the empirical transition N value.

2. The hypersonic vehicle boundary layer transition prediction method according to claim 1, wherein: In step S2, the aircraft wall ablation boundary conditions are established based on the wall ablation model, including: (a) For wall pressure, the normal momentum flux gradient is zero, Where ρ represents density, p represents pressure, and u n represents the normal velocity, and n represents the wall normal; (b) For the mass fractions of the wall components, establish the vehicle wall mass balance equation: Among them, ρ s represents the density of component s, D s represents the diffusion coefficient of component s, Y s represents the mass fraction of component s, m w,s represents the wall mass flow rate of component s produced by wall ablation; (c) For the wall temperature, establish the vehicle wall energy balance equation: Among them, κ, κ v Represents the thermal conductivity coefficients of translation temperature and rotation temperature, T v represents the vibration temperature, T represents the translation temperature; ε is the radiation emissivity, which is usually taken as 0.9 for carbon surface, and σ is the Stefan-Boltzmann constant; H s represents the total enthalpy of component s; considering the wall temperature thermal equilibrium, T v =T; (d) For the wall velocity, solve the wall normal velocity using the overall mass balance equation:

3. The hypersonic vehicle boundary layer transition prediction method according to claim 1, wherein: In step S3, a linear stability analysis equation is established using linear stability theory, including: Based on the non-equilibrium compressible Navier-Stokes equation, the non-equilibrium compressible Navier-Stokes equation is expanded into a small perturbation form and linearized to obtain the linearized perturbation equation. The basic form is as follows: Among them, φ′=[ρ′,u′,v′,w′,T′,Y s ′,T v ′] is the perturbation of the physical quantity, s, n, z are the body-fitting coordinates, h i is the Lame coefficient; Γ,A,B,C,D,H ij is a coefficient matrix and is only related to the background flow field; According to the linear stability theory, the perturbation quantity is written in the form of normal mode as follows: Where ω represents the frequency of the disturbance, α represents the streamwise wave number of the disturbance, and β represents the spanwise wave number; Substituting Equation (6) into the linearized perturbation equation, we obtain the linear stability analysis equation as follows: The linear stability analysis equation is an eigenvalue problem, which can be expressed as Where L is a linear operator; In order to solve the linear stability analysis equation, the linearized wall ablation condition of the disturbance is established, including: (a) Mass balance relationship of wall components: (b) Total wall mass balance relationship: (c) Wall energy balance relationship: (d) The wall velocity disturbance is zero: u′=v′=0 (11) (e) Wall temperature perturbation thermal equilibrium: T v ′=T′ (12)。 4. The hypersonic vehicle boundary layer transition prediction method according to claim 1, wherein: In step S4, the disturbance growth rates of small disturbances of different frequencies are integrated along the flow direction to obtain the distribution of the amplification factors N of small disturbances of different frequencies along the flow direction; the integral formula is as follows: Among them, A0 represents the initial amplitude of the disturbance, A is the growth of the disturbance wave amplitude, -α i is the growth rate of the disturbance wave.

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