Method and system for analyzing stability of boundary layer of high-enthalpy ablated wall surface

Abstract

The invention relates to a stability analysis method and system for a boundary layer of a high-enthalpy ablated wall surface, and is applied to the technical field of aerospace, and the method comprises the steps: taking a Landau-Teller equation and a chemical reaction rate equation as source items, constructing a control equation, and solving the control equation to obtain a steady laminar flow field; analyzing the steady laminar flow field by using LST to obtain a transmission coefficient eigenvalue; if the first modal time scale and the second modal time scale are greater than or equal to 1, correcting the first modal time scale and the second modal time scale based on the roughness of each position of the wall surface of the high-speed aircraft, and constructing a first modal linear operator and a second modal linear operator; further constructing NPSE, and solving to obtain an NPSE result; when an NPSE result is decomposed and linearized according to Fourier subharmonics, a coupling source item of a subharmonic equation is constructed according to a second modal linear operator, secondary instability analysis is carried out, and a transition initial position and the amplitude and frequency of disturbance development are obtained. And the accuracy of stability analysis can be improved.

Description

Technical Field

[0001] This application relates to the field of aerospace aerodynamic thermal environment prediction and boundary layer stability modeling technology, and in particular to a method and system for analyzing the stability of boundary layers on high-enthalpy ablation walls. Background Technology

[0002] Under hypersonic flight conditions, the aerodynamic heating of the aircraft's windward surface is intense, leading to ablation and material stripping of the wall material and creating a complex boundary layer flow environment with high enthalpy and high reactivity. In this environment, air components decompose and vibratory excitation occur, causing thermochemical non-equilibrium, which severely affects boundary layer stability and consequently alters flow transition behavior and heat flux distribution.

[0003] Solving thermochemical nonequilibrium flows is significantly more complex than solving equilibrium flows, both in terms of physical models and numerical methods. Physically, it requires modeling the relaxation of internal energy components and the calculation of chemical reaction rates, involving disciplines such as statistical thermophysics and physical chemistry. Furthermore, it necessitates considering the strong coupling between finite-rate thermochemical processes and the flow. Current mainstream approaches involve adding energy component conservation equations for vibrational and electronic energy, as well as component mass conservation equations, to the Navier-Stokes equations to describe the generation, convection, and diffusion processes of different energy components and component masses. In this case, molecular internal energy and component fractions cannot be uniquely determined by local variables but are dependent on the upstream and downstream flow fields.

[0004] Current research on high-enthalpy boundary layers mainly focuses on the dominant modes and their growth rates, with less attention paid to perturbation structures and energy transfer mechanisms. The analytical methods are primarily LST (Linear Stability Theory), linear PSE (Parabolized Stability Equations), and e N While methods exist for analyzing secondary instability and the weakly nonlinear evolution of disturbances and the flow field in the later stages of transition, research on these methods is limited. NPSE (Nonlinear Parabolized Stability Equations) and SIT (Secondary Instability Theory) are important tools for analyzing secondary instability and the weakly nonlinear evolution of disturbances in flows, but their application in thermochemical nonequilibrium flows is almost nonexistent. Current stability analyses are mostly based on the assumption of smooth walls, neglecting the disturbance effect of hypersonic ablation induced by ablation on the wall surface, and failing to reflect the excitation effect and stability influence of actual ablated walls on disturbance modes. Summary of the Invention

[0005] To address the aforementioned technical problems, this application provides a method and system for analyzing the boundary layer stability of high-enthalpy ablation walls.

[0006] According to a first aspect of this application, a method for analyzing the boundary layer stability of a high-enthalpy ablation wall is provided, comprising: By using the Landau-Teller equation and chemical reaction rate equation for multiple gas components as source terms, the governing equations for thermochemical nonequilibrium flow are constructed, and the governing equations are solved to obtain a steady laminar flow field. The steady laminar flow field was analyzed using the linear stability theory (LST) to obtain the eigenvalues ​​of the transmission coefficient. If the intrinsic value of the transmission coefficient is greater than or equal to 1, the first mode time scale and the second mode time scale are corrected based on the roughness of each position on the wall of the high-speed aircraft to obtain the corrected first mode time scale and the corrected second mode time scale. Based on the modified first modal time scale, construct the first modal linear operator; based on the modified second modal time scale, construct the second modal linear operator. Based on the first and second modal linear operators, the nonlinear parabolic stability equation NPSE is constructed and solved to obtain the NPSE result; When the NPSE results are decomposed and linearized according to Fourier subharmonics, the coupled source terms of the subharmonic equation are constructed based on the second-mode linear operator, and a second-order instability analysis is performed to obtain the transition start position and the amplitude and frequency of the disturbance development.

[0007] Optionally, the method for analyzing the boundary layer stability of high-enthalpy ablation walls further includes: Based on the steady laminar flow field, the instability disturbance equation is solved to obtain the local disturbance velocity; The disturbance displacement and disturbance excitation intensity of the boundary layer are determined based on the roughness of the surface at various locations of the high-speed aircraft and the local disturbance velocity. The first integration parameter is obtained by integrating the disturbance displacement at each location, and the second integration parameter is obtained by integrating the roughness at each location. Based on the disturbance excitation intensity, a differential equation for the envelope amplitude of the first mode is constructed, and the downstream envelope amplitude at infinity is determined based on the differential equation, the first integral parameter, and the second integral parameter. The step of constructing NPSE based on the first modal linear operator and the second modal linear operator includes: An NPSE is constructed based on the first modal envelope amplitude, the first modal linear operator, and the second modal linear operator, wherein the downstream envelope amplitude at infinity is the initial envelope amplitude of the NPSE.

[0008] Optionally, the step of correcting the first and second modal time scales based on the roughness of various locations on the surface of the high-speed vehicle to obtain corrected first and second modal time scales includes: For each position, according to the formula: Determine the dimensionless roughness parameter at the location. , in, This indicates the equivalent gravel height at the stated location. The dimensions of the adhesive inner layer of the wall at the stated location; According to the formula: Determine the corrected first modal timescale ; According to the formula: Determine the corrected second modal timescale , in, This indicates the time scale of the first mode. This indicates the time scale of the second mode. , , , , This represents a constant that has been calibrated beforehand.

[0009] Optionally, a first modal linear operator is constructed based on the modified first modal time scale, and a second modal linear operator is constructed based on the modified second modal time scale, including: According to the formula: Constructing the first-mode linear operator ; According to the formula: Constructing the second-mode linear operator ; in, and This indicates the term that plays a dominant role in the evolution of the perturbation. Represents the complex wave number. Indicates frequency, The velocity represents the velocity in a steady laminar flow field. Indicates the remaining items.

[0010] Optionally, the boundary layer disturbance displacement and disturbance excitation intensity are determined based on the roughness of the surface at various locations on the high-speed vehicle and the local disturbance velocity, including: According to the formula: Determine the disturbance displacement at each location. ; According to the formula: Determine the intensity of disturbance excitation at each location. , in, This represents the surface roughness distribution function of the aircraft. This indicates the velocity of the local disturbance.

[0011] Optionally, based on the perturbation excitation intensity, a differential equation for the envelope amplitude of the first mode is constructed, and the downstream envelope amplitude at infinity is determined based on the differential equation, the first integral parameter, and the second integral parameter, including: Based on the intensity of the disturbance Construct the differential equation of the envelope amplitude of the first mode. ; According to the formula: Determine the downstream envelope amplitude at infinity , in, Indicates the first integral parameter. Indicates the second integral parameter. , Represents the efficiency function; and The interval representing the distribution of rough elements. This indicates that the rough element is at a certain frequency. The distribution of the wall normal velocity perturbation introduced below, Represents the adjoint characteristic function. express The complex conjugate transpose of .

[0012] Optionally, the method for analyzing the boundary layer stability of high-enthalpy ablation walls further includes: When using LST to analyze the steady laminar flow field, according to the formula: and Determine the critical frequency of the rough disturbance response. ; Real-time monitoring of dominant frequency disturbances in the boundary layer ,like ≥ It is determined that the transition may be delayed; if < This indicates that the turning point may occur earlier than expected.

[0013] Optionally, the coupled source terms of the subharmonic equation are constructed based on the second-mode linear operator, including: Based on the second-modal linear operator Constructing the coupled source terms of the subharmonic equation .

[0014] Optionally, solving the governing equations to obtain a steady laminar flow field includes: The generalized minimum residual method (GMRES), the linear relaxation algorithm (LR), and the shock wave assembly method are used to solve the governing equations to obtain the steady laminar flow field.

[0015] According to a second aspect of this application, a high-enthalpy ablation wall boundary layer stability analysis system is provided, comprising: The steady laminar flow field determination module is used to construct the governing equations for thermochemical nonequilibrium flow by using the Landau-Teller equations and chemical reaction rate equations for multiple gas components as source terms, and to solve the governing equations to obtain the steady laminar flow field. The linear stability theory analysis module is used to analyze the steady laminar flow field using the linear stability theory (LST) to obtain the eigenvalues ​​of the transmission coefficient. The time scale correction module is used to correct the first mode time scale and the second mode time scale based on the roughness of each position on the wall of the high-speed aircraft if the eigenvalue of the transmission coefficient is greater than or equal to 1, so as to obtain the corrected first mode time scale and the corrected second mode time scale. The linear operator construction module is used to construct a first-mode linear operator based on the modified first-mode time scale and a second-mode linear operator based on the modified second-mode time scale. The NPSE result solving module is used to construct the NPSE based on the first modal linear operator and the second modal linear operator, and solve for the NPSE result. The second-order instability analysis module is used to construct coupled source terms of the subharmonic equation based on the second-mode linear operator when decomposing and linearizing the NPSE results according to Fourier subharmonics, and to perform second-order instability analysis to obtain the transition start position and the amplitude and frequency of the disturbance development.

[0016] Optionally, the high-enthalpy ablation wall boundary layer stability analysis system further includes: The local disturbance velocity determination module is used to solve the instability disturbance equation based on the steady laminar flow field to obtain the local disturbance velocity. The disturbance displacement and disturbance excitation intensity determination module is used to determine the disturbance displacement and disturbance excitation intensity of the boundary layer based on the roughness of the surface of the high-speed aircraft at various locations and the local disturbance velocity. The integration parameter determination module is used to integrate the disturbance displacement at each location to obtain the first integration parameter, and to integrate the roughness at each location to obtain the second integration parameter. The envelope amplitude construction module is used to construct a differential equation for the envelope amplitude of the first mode based on the disturbance excitation intensity, and to determine the downstream envelope amplitude at infinity based on the differential equation, the first integral parameter, and the second integral parameter. The NPSE result solving module is specifically used to construct the NPSE based on the first mode envelope amplitude, the first mode linear operator, and the second mode linear operator, and to solve for the NPSE result, wherein the downstream envelope amplitude at infinity is the initial envelope amplitude of the NPSE.

[0017] Optionally, the time-scale correction module is specifically used to, if the eigenvalue of the transmission coefficient is greater than or equal to 1, for each position, according to the formula: Determine the dimensionless roughness parameter at the location. ,in, This indicates the equivalent gravel height at the stated location. This indicates the dimensions of the viscous inner layer of the wall at the stated location; according to the formula: Determine the corrected first modal timescale According to the formula: Determine the corrected second modal timescale , in, This indicates the time scale of the first mode. This indicates the time scale of the second mode. , , , , This represents a constant that has been calibrated beforehand.

[0018] Optionally, the linear operator construction module is specifically used to construct the linear operator according to the formula: Constructing the first-mode linear operator According to the formula: Constructing the second-mode linear operator ; in, and This indicates the term that plays a dominant role in the evolution of the perturbation. Represents the complex wave number. Indicates frequency, The velocity represents the velocity in a steady laminar flow field. Indicates the remaining items.

[0019] Optionally, the disturbance displacement and disturbance excitation intensity determination module is specifically used to determine the disturbance displacement and disturbance excitation intensity according to the formula: Determine the disturbance displacement at each location. According to the formula: Determine the excitation intensity of the disturbance at each location. ; in, This represents the surface roughness distribution function of the aircraft. This indicates the velocity of the local disturbance.

[0020] Optionally, the envelope amplitude construction module is specifically used to determine the amplitude based on the perturbation excitation intensity. Construct the differential equation of the envelope amplitude of the first mode. And according to the formula: Determine the downstream envelope amplitude at infinity , in, Indicates the first integral parameter. Indicates the second integral parameter. , Represents the efficiency function; and The interval representing the distribution of rough elements. This indicates that the rough element is at a certain frequency. The distribution of the wall normal velocity perturbation introduced below, Represents the adjoint characteristic function. express The complex conjugate transpose of .

[0021] Optionally, the high-enthalpy ablation wall boundary layer stability analysis system further includes: The critical frequency determination module is used to determine the critical frequency based on the formula when analyzing the steady laminar flow field using LST: and Determine the critical frequency of the rough disturbance response. ; The transition time determination module is used to monitor the dominant frequency disturbance in the boundary layer in real time. ,like ≥ It is determined that the transition may be delayed; if < This indicates that the turning point may occur earlier than expected.

[0022] Optionally, the second-order instability analysis module is specifically used to decompose and linearize the NPSE results according to Fourier harmonics, based on the second-mode linear operator. Constructing the coupled source terms of the subharmonic equation A secondary instability analysis was performed to obtain the transition initiation position and the amplitude and frequency of the disturbance development.

[0023] Optionally, the steady laminar flow field determination module is specifically used to construct the control equations for thermochemical nonequilibrium flow by using the Landau-Teller equations and chemical reaction rate equations for multiple gas components as source terms, and to solve the control equations using the generalized minimum residual method (GMRES), the linear relaxation algorithm (LR), and the shock wave assembly method to obtain the steady laminar flow field.

[0024] According to a third aspect of this application, an electronic device is provided, comprising: a processor configured to execute a computer program stored in a memory, wherein the computer program, when executed by the processor, implements the method described in the first aspect.

[0025] According to a fourth aspect of this application, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0026] According to a fifth aspect of this application, a computer program product is provided that, when the computer program product is run on a computer, causes the computer to perform the method described in the first aspect.

[0027] The technical solution provided in this application has the following advantages compared with the prior art: By using the Landau-Teller equations and chemical reaction rate equations for multiple gas components as source terms, the governing equations for thermochemical nonequilibrium flow are constructed, thus introducing the thermochemical nonequilibrium reaction mechanism into the boundary layer stability analysis model. Simultaneously, the induced effect of ablation surface roughness perturbation on the unstable modes is considered. Specifically, based on the roughness at various locations on the high-speed vehicle wall, the time scales of the first and second modes are corrected, and linear operators for the first and second modes are constructed. This leads to the construction of the NPSE (NP-complete response equation), and the NPSE results are obtained. When the NPSE results are decomposed and linearized according to Fourier subharmonics, coupled source terms of the subharmonic equations are constructed based on the second-mode linear operator. This allows the phase-frequency characteristics of the source terms to reflect the modulation of the second-mode response by the rough wall surface in advance, thereby more realistically reflecting the coupling process. In this embodiment, the roughness-induced modal response is pre-fixed into the equation coefficients, ensuring that the subsequent nonlinear evolution (NPSE) and secondary stability analysis (SIT) are based on the pre-modulated "roughness time history", thus correctly reflecting the comprehensive influence of the rough wall on instability and transition, thereby improving the accuracy of boundary layer stability analysis. Attached Figure Description

[0028] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0029] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1This is a flowchart of a method for analyzing the boundary layer stability of high-enthalpy ablation walls in an embodiment of this application; Figure 2 This is a flowchart of the method for determining the envelope amplitude in the embodiments of this application; Figure 3 This is a schematic diagram comparing the growth rate of the two-dimensional perturbation mode with frequency in the embodiments of this application with literature data; Figure 4(a) is a schematic diagram comparing the analysis results of the growth rate curves of the embodiments of this application and Kline et al.; Figure 4(b) is a schematic diagram comparing the analysis results of the phase velocity curves of the embodiment of this application with those of Kline et al.; Figure 5(a) is a schematic diagram comparing the flow velocity in three cases; Figure 5(b) is a schematic diagram comparing the temperature and vibration temperature in four cases; Figure 5(c) is a schematic diagram comparing the oxygen mass fraction in three cases; Figure 6 This is a schematic diagram of a high-enthalpy ablation wall boundary layer stability analysis system in an embodiment of this application; Figure 7 This is a schematic diagram of the structure of an electronic device in an embodiment of this application. Detailed Implementation

[0031] To better understand the above-mentioned objectives, features, and advantages of this application, the solution of this application will be further described below. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0032] Many specific details are set forth in the following description in order to provide a full understanding of this application, but this application may also be implemented in other ways different from those described herein; obviously, the embodiments in the specification are only some embodiments of this application, and not all embodiments.

[0033] See Figure 1 , Figure 1 This is a flowchart of the high-enthalpy ablation wall boundary layer stability analysis method in the embodiments of this application, which may include the following steps: Step S102: Using the Landau-Teller equation and chemical reaction rate equation for multiple gas components as source terms, construct the governing equation for thermochemical nonequilibrium flow, and solve the governing equation to obtain the steady laminar flow field.

[0034] In hypersonic high-enthalpy flows, air components undergo various thermodynamic and chemical processes, such as molecular dissociation. Therefore, compared with the basic form of the Navier-Stokes equations, conservation equations for vibrational energy components and component mass can be added.

[0035] 1) Continuity equation for mixed gases: ; Let be the density of the gas mixture, and u be the velocity tensor of the gas mixture; 2) Component mass conservation equation: ; Let be the density of the s-th gas component. Let be the mass diffusion flux of the s-th gas component. This refers to the source term for the formation of chemical components, i.e., the reaction rate; Assuming the number of components in the gas mixture is M, based on the continuity equation for the gas mixture, the s-th gas component can be any M-1 components. This application uses a five-component system (N2, O2, NO, N, O) as an example for illustration. The s-th gas component in the component mass conservation equation can be any four of the five components.

[0036] Based on component concentration chemical reaction equilibrium constant The expression is: ; The expression for the chemical reaction rate is: ; in, and These are the stoichiometric coefficients of the reactants and products, where s represents different components, r represents different reactions, and c represents the chemical stoichiometric coefficients of the products. i This indicates the concentration of the i-th component, indicated by the superscript. This represents the concentration of the i-th substance in the r-th reaction among the products. This represents the concentration of the i-th substance in the r-th reaction among the reactants. The universal gas constant is 8.314 J / molK. Let i be the stoichiometric coefficient of reactant i. Let be the stoichiometric coefficient of product i.

[0037] forward reaction rate constant Fitting using the Arrhenius relation: ; Let T represent the forward chemical reaction rate of the r-th chemical reaction equation, and let T represent the temperature. , and There are three fitting parameters.

[0038] The reverse reaction rate constant of the r-th reaction for: ,in, Let be the chemical equilibrium constant for the r-th reaction.

[0039] 3) Momentum equation: ; 4) Energy equation: ; Where H is the specific total enthalpy of the mixture, and E is the specific total internal energy. For translational rotational energy, Vibrational energy, , ; and For the thermal conductivity component, Let enthalpy be the molecular component of the s-th component. For viscous stress tensor, ; The viscosity coefficient, The second viscosity coefficient, for a five-component mixture, is λ = -2 / 3. I is the unit tensor, and T is the rotational / translational temperature. The vibration temperature.

[0040] 5) Vibrational energy equation: Since the gases with vibrational energy in the five components are (N2, O2, NO), the subscript m takes values ​​from 1 to 3. As the source term for vibrational energy generation, the Landau-Teller equations are used to describe the non-equilibrium process of finite-rate energy exchange between vibrational energy and translational / rotational energy: ; It is the vibrational energy of the m-th component under thermal equilibrium conditions; It is the vibration temperature; This refers to the vibrational relaxation time, which takes into account the intermolecular collision characteristics and can be determined through semi-empirical fitting or the Park modified model. It is relative to vibrational energy.

[0041] 6) Gas law: ; Represents the component gas constant, = / , The universal gas constant is 8.314 J / molK. Let be the molecular molar mass of the s-th component; This refers to the mass fraction of the s-th component, primarily used for weighting component components, such as the specific total enthalpy H, specific total internal energy E, and specific vibrational energy of a mixture. .

[0042] ; ; ; Before performing stability analysis, it is necessary to obtain a high-precision steady laminar flow field. Laminar flow calculation methods are mainly divided into shock wave capture and shock wave assembly methods. Among them, the shock wave assembly method has the advantages of high calculation accuracy and efficiency; therefore, this method is adopted in the embodiments of this application. In thermochemical nonequilibrium flow, the time scale of chemical reactions is much smaller than that of the flow process, so time-progressive solutions to the Navier–Stokes equations exhibit strong numerical rigidity.

[0043] To improve computational convergence speed, the most popular time-progression method in CFD (Computational Fluid Dynamics) is the implicit scheme GMRES (Generalized Minimum Residual Method). However, current time-progression schemes for shock assembly methods are mainly explicit or semi-implicit, resulting in slower convergence speeds. Optionally, combining GMRES, LR (Linear Relaxation Algorithm), and the shock assembly method can be used to solve the governing equations, obtaining a steady laminar flow field, thereby improving the convergence speed and stability of the computation.

[0044] Step S104: Analyze the steady laminar flow field using LST to obtain the eigenvalues ​​of the transmission coefficient.

[0045] LST is used to analyze the stability behavior of boundary layer disturbances during their initial, small-scale development phase. This method is based on the assumption of "local parallel flow," which considers the baseflow to change slowly along its direction and can be approximated as a two-dimensional steady flow dependent only on the normal coordinate y. Based on this, the physical quantities such as velocity, density, and temperature in the Navier-Stokes equations are decomposed into stable basic flows. and small disturbance , means as follows: ; Disturbance The formal construction is as follows: ; Substituting the decomposed variables into the governing equations and linearizing them (ignoring nonlinear disturbance terms), we obtain a set of ordinary differential equations for the disturbance variables, constituting an eigenvalue problem. Solving this problem yields eigenvalues ​​(such as complex wave number α or frequency ω) and the corresponding eigenmodes (disturbance structure). If αi < 0 or ωi > 0, it indicates that the disturbance amplifies with space or time, and the flow is linearly unstable; if all modes decay, the flow is linearly stable.

[0046] Specifically, the problem of establishing eigenvalues ​​for rough perturbation scattering: , The disturbance variable is represented by its components: velocity tensor u, normal velocity v, temperature T, and density. The disturbance amplitude is expressed as: ; Continuity equation: ; Momentum equation in the x-direction: ; Energy equation: ; The above system of equations is rearranged to obtain discrete matrix A, where B is a weighted energy inner product operator used to construct the perturbation energy norm. ; in, for The complex conjugate transpose of ; W(y) is the weight matrix, which can be:

[0047] Where T is the eigenvalue of the transmission coefficient, |T| is greater than or equal to 1, indicating roughness enhancement instability, and |T| is less than 1, indicating suppression of instability.

[0048] Optionally, the imaginary part of the efficiency function The zero-crossing point with frequency ω is defined as the critical frequency of the rough disturbance response. This is used for online dynamic transition criteria. That is, when analyzing a steady laminar flow field using LST, the formula is used: and Determine the critical frequency of the rough disturbance response. Efficiency function The efficiency function is used to evaluate the impact of roughness on different frequency modes. The imaginary part of the efficiency function quantifies whether the growth rate is enhanced (positive) or suppressed (negative). The frequency at which the imaginary part is zero is defined as the critical frequency of the roughness disturbance response. This frequency defines the boundary between enhancement and suppression, serving as the core of the dynamic transition criterion. When the dominant frequency of the environmental disturbance... Approaching or exceeding When this is achieved, it can be determined that the "roughness-induced instability mechanism" will dominate the transition process. Therefore, real-time monitoring of the dominant frequency disturbance in the boundary layer is crucial. ,like ≥ This indicates that "roughness suppression" is dominant, and the transition may be delayed; if < This indicates that "roughness enhancement" is dominant, suggesting that the transition may occur earlier than expected.

[0049] Step S106: If the intrinsic value of the transmission coefficient is greater than or equal to 1, the first mode time scale and the second mode time scale are corrected based on the roughness of each position on the wall of the high-speed aircraft to obtain the corrected first mode time scale and the corrected second mode time scale.

[0050] If the eigenvalue of the transmission coefficient is greater than or equal to 1, it indicates roughness-enhanced instability. Therefore, the inducing effect of ablation surface roughness perturbation on the instability mode can be considered. Since the effects of nonparallelism and nonlinearity on perturbation are neglected in LST, the NPSE method can be used to parabolicize the perturbation equations and then efficiently solve them using the flow-propelling method. NPSE is essentially a set of perturbation evolution equations that propagate along the flow direction, and its general form is: ; ; Among them, the first modal linear operator The first modal time scale Second-mode linear operator The second modal time scale It is used to modulate the rate of local instability growth. This represents the perturbation field of the first mode. The nonlinear operator representing the first mode. This represents the perturbation field of the second mode. This represents the nonlinear operator for the second mode.

[0051] In related technologies, the first modal time scale Second mode time scale The same applies to all perturbation modes. However, under rough wall conditions, the response rates of different modes are reshaped by the roughness distribution: small-scale roughness has a stronger transient excitation for the TS mode and exhibits a dual response for the second mode.

[0052] In this embodiment, the roughness of the high-speed aircraft wall at various locations is used to determine the time scale of the first mode. Second mode time scale Make corrections to the corrected first modal timescale. and the corrected second modal timescale Replace the "frozen" or "normal base current" time scale in NPSE, making the operator and It can adaptively amplify or suppress the growth of corresponding modes under different roughness conditions. In other words, and By modifying the main diagonal terms of the linear operator (corresponding to the eigenfrequency and growth rate of the mode), a roughness-induced time response effect is "pre-injected" into the NPSE solution process, ensuring that subsequent nonlinear evolution (including second-order instability) is carried out on the basis of the modulation.

[0053] Optionally, for each position, according to the formula: Dimensionless roughness parameters for determining location , The equivalent gravel height indicating the location. The dimensions of the viscous inner layer of the wall indicate the location.

[0054] According to the formula: Determine the corrected first modal timescale According to the formula: Determine the corrected second modal timescale ,in, This indicates the time scale of the first mode. This indicates the time scale of the second mode. , , , , This represents a constant that has been calibrated beforehand.

[0055] Step S108: Construct a first modal linear operator based on the corrected first modal time scale, and construct a second modal linear operator based on the corrected second modal time scale.

[0056] The linear operator of NPSE can be expressed as: ; in, O(y) represents the part that plays a dominant role in the evolution of the perturbation, and O(y) represents the remaining terms. The "frequency-phase velocity" term controls the adjustment of the disturbance's phase and amplitude. Optionally, according to the formula: Constructing the first-mode linear operator According to the formula: Constructing the second-mode linear operator ,in, and This indicates the term that plays a dominant role in the evolution of the perturbation. Represents the complex wave number. Indicates frequency, The velocity represents the velocity in a steady laminar flow field. Indicates the remaining items.

[0057] Step S110: Construct NPSE based on the first modal linear operator and the second modal linear operator, and solve for the NPSE result.

[0058] During each flow step in the NPSE numerical solution, the first-mode linear operator and the second-mode linear operator are used according to the current mode to be tracked (primary, secondary, or mixed). If iteration is required (mixed primary and secondary modes), the mixed operator includes both τ1 and τ2 terms, and their respective frequency-phase velocity factors are adjusted accordingly.

[0059] To accurately capture the initial excitation mechanism of hypersonic boundary layer instability caused by wall micro-roughness, a three-layer theory with a large Reynolds number is employed. The equivalent wall roughness shape function f(x) is coupled with the boundary layer displacement function A(x) to construct a roughness-induced pressure-displacement mapping relationship in non-parallel flow. The perturbation pressure-displacement coupling relationship is extracted, providing input for subsequent modal amplitude equations. Figure 2 As shown, the method for determining the envelope amplitude includes the following steps: Step S202: Based on the steady laminar flow field, solve the instability disturbance equation to obtain the local disturbance velocity.

[0060] The physical wall roughness is represented as a series of tiny protrusions, and the equivalent roughness shape distribution f(x) is defined, which is generally a sinusoidal waveform unless otherwise specified. The instability perturbation equation is solved in the lower deck to obtain the local perturbation velocity. The lower deck is the thinnest layer closest to the wall, where viscous forces dominate and the velocity gradient is extremely large, typically satisfying the no-slip boundary condition (wall velocity is 0). Since the perturbation in the z-direction is much smaller than that in the flow direction, the perturbation equations for the lower compressible boundary layer simplify to two dimensions: ; ; ; ; in, The values ​​are taken from the middle layer of the steady flow field, with the initial pressure P set to 0. After iterative convergence, the local perturbation velocity is obtained. .

[0061] Step S204: Determine the disturbance displacement and disturbance excitation intensity of the boundary layer based on the roughness and local disturbance velocity at various locations on the surface of the high-speed aircraft.

[0062] The roughness distribution function f(x) characterizes the shape of the wall. The displacement function of the boundary layer is obtained by integrating the local disturbance velocity along the Y direction at the wall. Optionally, according to the formula: Determine the disturbance displacement at each location. According to the formula: Determine the excitation intensity of the disturbance at each location. ,in, This represents the surface roughness distribution function of the aircraft. This indicates the velocity of the local disturbance.

[0063] Step S206: Integrate the disturbance displacement at each location to obtain the first integration parameter, and integrate the roughness at each location to obtain the second integration parameter. This can be expressed as: , , Indicates the first integral parameter. This represents the second integral parameter.

[0064] Step S208: Based on the perturbation excitation intensity, construct the differential equation of the envelope amplitude of the first mode, and determine the downstream envelope amplitude at infinity based on the differential equation, the first integral parameter, and the second integral parameter.

[0065] Optionally, based on the intensity of the disturbance excitation Construct the differential equation of the envelope amplitude of the first mode. According to the formula: Determine the downstream envelope amplitude at infinity ,in, The first mode envelope amplitude is a complex number that includes both amplitude and phase. for The integral solution is also a complex number, whose modulus gives the total amplification / attenuation, and its argument gives the cumulative phase.

[0066] in, , The efficiency function is defined as a complex number resulting from the inner product of the original perturbation operator. It is a sensitivity measure of the mode to rough excitation and is used in the study of the sensitivity and stability of high-speed boundary layers based on global stability analysis. and The interval representing the distribution of rough elements. This indicates that the rough element is at a certain frequency. ω The distribution of the wall normal velocity perturbation introduced below, ; Represents the adjoint characteristic function. express The complex conjugate transpose of , where e represents the boundary layer, and : represents positive correlation. This represents the velocity of the boundary layer flow field.

[0067] Furthermore, an NPSE can be constructed based on the first-mode envelope amplitude, the first-mode linear operator, and the second-mode linear operator. Here, the downstream envelope amplitude at infinity... The initial envelope amplitude of the NPSE reflects the pre-modulation effect of roughness. The roughness-induced model provides the "NPSE initial envelope amplitude + phase", which provides the entry condition for NPSE marching and ensures that all subsequent nonlinear evolution and secondary instability analysis start in a state that has been "modulated by roughness".

[0068] The perturbation expression for NPSE is: ; in, This represents a function of the perturbation component of a flow field variable with respect to its three-dimensional spatial coordinates and its time coordinates. For amplitude, As the phase, at the inlet section x=x0 entering the NPSE propulsion, will The ingress amplitude and phase of the incorporated principal mode are represented as follows: , .

[0069] Used to correct the initial NPSE value, in order to analyze the local magnification / suppression features in the rough region, it can be calculated. The entire process. The real number represents the amplitude component. It is phase. It is a complex number, containing both magnitude and phase, therefore, and Implicitly includes the original And roughness phase correction. This indicates the phase used in NPSE propulsion in related technologies, q n It is the modal structure function of the nth mode in the transverse direction (normal y, span z). This represents the modal structure function of the first mode in the transverse direction (normal y, span z).

[0070] In step S112, when the NPSE result is decomposed and linearized according to Fourier subharmonics, the coupled source terms of the subharmonic equation are constructed according to the second mode linear operator, and a second instability analysis is performed to obtain the transition start position and the amplitude and frequency of the disturbance development.

[0071] During linearization, it can be based on the second-mode linear operator. Constructing the coupled source terms of the subharmonic equation That is, using the second modal time scale Construct a coupling source term to couple with the subharmonic / second-order instability mode equation of the main mode (first mode).

[0072] Specifically, in the second-order instability analysis, there exists a primary mode perturbation field (first mode, frequency f) and a subharmonic mode (frequency f / 2 or other combined frequencies). When the Navier–Stokes equations are expanded and linearized to handle these perturbations, a driving source generated by the quadratic term of the primary mode perturbation appears on the right-hand side of the subharmonic equations. This driving source term is the coupling source term, which reflects the driving effect of the primary mode's nonlinearity on the growth of the submode. Using the second-mode timescale... By replacing the original second-mode timescale to construct the coupled source term, the phase-frequency characteristics of the source term can reflect the modulation of the second-mode response by the rough wall in advance, thus more realistically reflecting the coupling process.

[0073] Thermochemical nonequilibrium calculations were performed using the above method, and the specific results are as follows: Example 1: Mach 10 Adiabatic Flat Plate Boundary Layer Case. This example uses the Mach 10 thermal equilibrium and chemical nonequilibrium adiabatic flat plate boundary layer case by Miró et al., with an inflow temperature of 600 K, a far-field N2 proportion of 0.78, and a unit Reynolds number of 6.6 × 10⁶ / m. The flow direction x is compared. * The growth rate of the two-dimensional perturbation mode at 0.6m varies with frequency as follows: Figure 3 As shown, the calculation results of the embodiments of this application are consistent with the data in the literature.

[0074] Example 2: Flow around a sharp wedge with a Mach number of 20 and a half-apex angle of 6°. The calculation parameters are shown in Table 1.

[0075] Table 1

[0076] Compared with the analysis results of Kline et al., for example Figure 4a and Figure 4b As shown, the results of this application's embodiments agree well with the literature data within the second modal range. However, downstream of the second mode, the disturbance develops into an unstable supersonic mode, with oscillations appearing in both its growth rate and phase velocity curves. The results of this application's embodiments show stronger oscillations in this region.

[0077] Example 3: Adiabatic flat plate boundary layer at Mach 10. The parameters for this example are shown in Table 2.

[0078] Table 2

[0079] In some regions of the flow field, especially upstream, chemical non-equilibrium is often present. This non-equilibrium state does not conflict with the steady flow field and does not change with the calculation time. Instead, it reaches downstream before reaching reaction equilibrium. This leads to two extreme cases: (1) Thermochemical freezing: all regions of the flow field are considered to be in the unreacted stage. The freezing state commonly occurs at the far end of the incoming flow in real calculations. (2) Chemical equilibrium flow: all regions are considered to have reached chemical reaction equilibrium. Obviously, the chemical non-equilibrium state lies between the two.

[0080] Figure 5(a) shows a comparison of flow velocities for the three cases; Figure 5(b) shows a comparison of temperature and vibration temperature for the three cases; and Figure 5(c) shows a comparison of oxygen mass fraction for the three cases. Here, TFCF represents chemical freezing, TNCN represents chemical non-equilibrium, and TECE represents chemical reaction equilibrium. The parameters obtained from chemical non-equilibrium fall between the two, consistent with the theory, thus verifying the accuracy of the calculation results in this application.

[0081] The high-enthalpy ablation wall boundary layer stability analysis method of this application considers the inductive effect of ablation wall roughness disturbance on the unstable mode, and couples the release of reaction heat with the disturbance evolution. That is, it introduces the high-enthalpy ablation wall disturbance and the thermochemical non-equilibrium reaction mechanism into the boundary layer stability analysis model, improving the physical consistency of the model and making up for the shortcomings of existing methods that ignore the excitation of disturbance sources and energy coupling. This helps to establish a more accurate transition prediction model and provides key support for the design of aerodynamic thermal protection systems for aircraft. Furthermore, by combining GMRES, LR, and shock wave assembly methods to solve the governing equations, it can accelerate the calculation of convergent, high-precision steady laminar flow fields.

[0082] This application also provides a high-enthalpy ablation wall boundary layer stability analysis system, see [link to relevant documentation]. Figure 6 The high-enthalpy ablation wall boundary layer stability analysis system 600 includes: The steady laminar flow field determination module 602 is used to construct the governing equations of thermochemical nonequilibrium flow by taking the Landau-Teller equations and chemical reaction rate equations of multiple gas components as source terms, and solve the governing equations to obtain the steady laminar flow field. The linear stability theory analysis module 604 is used to analyze the steady laminar flow field using the linear stability theory (LST) to obtain the eigenvalues ​​of the transmission coefficient. The time scale correction module 606 is used to correct the first mode time scale and the second mode time scale based on the roughness of each position on the wall of the high-speed aircraft if the eigenvalue of the transmission coefficient is greater than or equal to 1, so as to obtain the corrected first mode time scale and the corrected second mode time scale. The linear operator construction module 608 is used to construct a first-mode linear operator based on the modified first-mode time scale and a second-mode linear operator based on the modified second-mode time scale. The NPSE result solving module 610 is used to construct the NPSE based on the first mode linear operator and the second mode linear operator, and solve for the NPSE result. The second-order instability analysis module 612 is used to construct the coupled source terms of the subharmonic equation based on the second-mode linear operator when decomposing and linearizing the NPSE results according to the Fourier subharmonics, and to perform second-order instability analysis to obtain the transition start position and the amplitude and frequency of the disturbance development.

[0083] Optionally, the high-enthalpy ablation wall boundary layer stability analysis system 600 also includes: The local disturbance velocity determination module is used to solve the instability disturbance equation based on a steady laminar flow field to obtain the local disturbance velocity. The disturbance displacement and disturbance excitation intensity determination module is used to determine the disturbance displacement and disturbance excitation intensity of the boundary layer based on the roughness and local disturbance velocity at various locations on the surface of the high-speed aircraft. The integration parameter determination module is used to integrate the disturbance displacement at each location to obtain the first integration parameter, and to integrate the roughness at each location to obtain the second integration parameter. The envelope amplitude construction module is used to construct the differential equation of the envelope amplitude of the first mode based on the perturbation excitation intensity, and to determine the downstream envelope amplitude at infinity based on the differential equation, the first integral parameter, and the second integral parameter. The NPSE result solving module 610 is specifically used to construct the NPSE based on the first mode envelope amplitude, the first mode linear operator, and the second mode linear operator, and to solve for the NPSE result, wherein the downstream envelope amplitude at infinity is the initial envelope amplitude of the NPSE.

[0084] Optionally, the time-scale correction module 606 is specifically used to, for each location, adjust the time scale according to the formula if the eigenvalue of the transmission coefficient is greater than or equal to 1: Dimensionless roughness parameters for determining location ,in, The equivalent gravel height indicating the location. The dimensions of the viscous inner layer of the wall represent the location; according to the formula: Determine the corrected first modal timescale According to the formula: Determine the corrected second modal timescale , in, This indicates the time scale of the first mode. This indicates the time scale of the second mode. , , , , This represents a constant that has been calibrated beforehand.

[0085] Optionally, the linear operator building module 608 is specifically used to construct the linear operator based on the formula: Constructing the first-mode linear operator According to the formula: Constructing the second-mode linear operator , in, and This indicates the term that plays a dominant role in the evolution of the perturbation. Represents the complex wave number. Indicates frequency, The velocity represents the velocity in a steady laminar flow field. Indicates the remaining items.

[0086] Optionally, the disturbance displacement and disturbance excitation intensity determination module is specifically used to determine the disturbance displacement and disturbance excitation intensity according to the formula: Determine the disturbance displacement at each location. According to the formula: Determine the excitation intensity of the disturbance at each location. , in, This represents the surface roughness distribution function of the aircraft. This indicates the velocity of the local disturbance.

[0087] Optionally, the envelope amplitude construction module is specifically used to determine the excitation intensity of the disturbance. Construct the differential equation of the envelope amplitude of the first mode. And according to the formula: Determine the downstream envelope amplitude at infinity ; in, Indicates the first integral parameter. Indicates the second integral parameter. , Represents the efficiency function. and The interval representing the distribution of rough elements. This indicates that the rough element is at a certain frequency. The distribution of the wall normal velocity perturbation introduced below, Represents the adjoint characteristic function. express The complex conjugate transpose of .

[0088] Optionally, the high-enthalpy ablation wall boundary layer stability analysis system 600 also includes: The critical frequency determination module is used when analyzing steady laminar flow fields using LST, based on the formula: and Determine the critical frequency of the rough disturbance response. ; The transition time determination module is used to monitor the dominant frequency disturbance in the boundary layer in real time. ,like ≥ It is determined that the transition may be delayed; if < This indicates that the turning point may occur earlier than expected.

[0089] Optionally, the second-order instability analysis module 612 is specifically used to decompose and linearize the NPSE results according to Fourier harmonics, based on the second-mode linear operator. Constructing the coupled source terms of the subharmonic equation A secondary instability analysis was performed to obtain the transition initiation position and the amplitude and frequency of the disturbance development.

[0090] Optionally, the steady laminar flow field determination module 602 is specifically used to construct the governing equations of thermochemical nonequilibrium flow by taking the Landau-Teller equations and chemical reaction rate equations of multiple gas components as source terms, and solve the governing equations using the generalized minimum residual method GMRES, the linear relaxation algorithm LR combined with the shock wave assembly method to obtain the steady laminar flow field.

[0091] The specific details of each module or unit in the above-mentioned device have been described in detail in the corresponding methods, so they will not be repeated here.

[0092] This application also provides an electronic device, including: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to execute the above-described high-enthalpy ablation wall boundary layer stability analysis method.

[0093] Reference Figure 7 , Figure 7 This is a schematic diagram of the structure of an electronic device in an embodiment of this application. The specific embodiments of this application do not limit the specific implementation of the electronic device.

[0094] like Figure 7 As shown, the electronic device may include: a processor 402, a communication interface 404, a memory 406, and a communication bus 408.

[0095] The processor 402, communication interface 404, and memory 406 communicate with each other via communication bus 408.

[0096] Communication interface 404 is used to communicate with other electronic devices or servers.

[0097] The processor 402 is used to execute program 410, specifically the relevant steps in the above method embodiments.

[0098] Specifically, program 410 may include program code that includes computer operation instructions.

[0099] Processor 402 may be a central processing unit, a specific integrated circuit, or one or more integrated circuits configured to implement the embodiments of this application. The smart device includes one or more processors, which may be processors of the same type, such as one or more CPUs; or processors of different types, such as one or more CPUs and one or more ASICs.

[0100] Memory 406 is used to store program 410. Memory 406 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0101] Specifically, program 410 can be used to cause processor 402 to execute the steps in the above embodiments of the high enthalpy ablation wall boundary layer stability analysis method.

[0102] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the devices and modules described above can be referred to the corresponding process descriptions in the foregoing method embodiments, and will not be repeated here.

[0103] In this embodiment of the application, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the above-described method for analyzing the stability of the boundary layer of a high-enthalpy ablation wall.

[0104] It should be noted that the computer-readable storage medium shown in this application can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory, read-only memory, erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the computer-readable storage medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0105] In this embodiment of the application, a computer program product is also provided, which, when run on a computer, causes the computer to execute the above-described high-enthalpy ablation wall boundary layer stability analysis method.

[0106] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0107] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments described herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analyzing the boundary layer stability of a high-enthalpy ablation wall, characterized in that, include: By using the Landau-Teller equation and chemical reaction rate equation for multiple gas components as source terms, the governing equations for thermochemical nonequilibrium flow are constructed, and the governing equations are solved to obtain a steady laminar flow field. The steady laminar flow field was analyzed using the linear stability theory (LST) to obtain the eigenvalues ​​of the transmission coefficient. If the intrinsic value of the transmission coefficient is greater than or equal to 1, the first mode time scale and the second mode time scale are corrected based on the roughness of each position on the wall of the high-speed aircraft to obtain the corrected first mode time scale and the corrected second mode time scale. Based on the modified first modal time scale, construct the first modal linear operator; based on the modified second modal time scale, construct the second modal linear operator. Based on the first and second modal linear operators, the nonlinear parabolic stability equation NPSE is constructed and solved to obtain the NPSE result; When the NPSE results are decomposed and linearized according to Fourier subharmonics, the coupled source terms of the subharmonic equation are constructed based on the second-mode linear operator, and a second-order instability analysis is performed to obtain the transition start position and the amplitude and frequency of the disturbance development.

2. The method for analyzing the boundary layer stability of high-enthalpy ablation walls according to claim 1, characterized in that, Also includes: Based on the steady laminar flow field, the instability disturbance equation is solved to obtain the local disturbance velocity; The disturbance displacement and disturbance excitation intensity of the boundary layer are determined based on the roughness of the surface at various locations of the high-speed aircraft and the local disturbance velocity. The first integration parameter is obtained by integrating the disturbance displacement at each location, and the second integration parameter is obtained by integrating the roughness at each location. Based on the disturbance excitation intensity, a differential equation for the envelope amplitude of the first mode is constructed, and the downstream envelope amplitude at infinity is determined based on the differential equation, the first integral parameter, and the second integral parameter. The step of constructing NPSE based on the first modal linear operator and the second modal linear operator includes: An NPSE is constructed based on the first modal envelope amplitude, the first modal linear operator, and the second modal linear operator, wherein the downstream envelope amplitude at infinity is the initial envelope amplitude of the NPSE.

3. The method for analyzing the boundary layer stability of high-enthalpy ablation walls according to claim 1, characterized in that, The process of correcting the first and second modal time scales based on the roughness of various locations on the surface of the high-speed aircraft to obtain corrected first and second modal time scales includes: For each position, according to the formula: Determine the dimensionless roughness parameter at the location. , in, This indicates the equivalent gravel height at the stated location. The dimensions of the viscous inner layer of the wall at the stated location; According to the formula: Determine the corrected first modal timescale. ; According to the formula: Determine the corrected second modal timescale. , in, This indicates the time scale of the first mode. This indicates the time scale of the second mode. , , , , This represents a constant that has been calibrated beforehand.

4. The method for analyzing the boundary layer stability of high-enthalpy ablation walls according to claim 1, characterized in that, Based on the modified first modal time scale, a first modal linear operator is constructed, and based on the modified second modal time scale, a second modal linear operator is constructed, including: According to the formula: Constructing the first-mode linear operator ; According to the formula: Constructing the second-mode linear operator ; in, and This indicates the term that plays a dominant role in the evolution of the perturbation. Represents the complex wave number. Indicates frequency, The velocity represents the velocity in a steady laminar flow field. Indicates the remaining items.

5. The method for analyzing the boundary layer stability of high-enthalpy ablation walls according to claim 2, characterized in that, The boundary layer disturbance displacement and disturbance excitation intensity are determined based on the roughness of the surface at various locations on the high-speed vehicle and the local disturbance velocity, including: According to the formula: Determine the disturbance displacement at each location. ; According to the formula: Determine the intensity of disturbance excitation at each location. , in, This represents the surface roughness distribution function of the aircraft. This indicates the velocity of the local disturbance.

6. The method for analyzing the boundary layer stability of high-enthalpy ablation walls according to claim 2, characterized in that, Based on the disturbance excitation intensity, a differential equation for the envelope amplitude of the first mode is constructed, and the downstream envelope amplitude at infinity is determined based on the differential equation, the first integral parameter, and the second integral parameter, including: Based on the intensity of the disturbance Construct the differential equation of the envelope amplitude of the first mode. ; According to the formula: Determine the downstream envelope amplitude at infinity ; in, Indicates the first integral parameter. Indicates the second integral parameter. , Represents the efficiency function; and The interval representing the distribution of rough elements. This indicates that the rough element is at a certain frequency. The distribution of the wall normal velocity perturbation introduced below, Represents the adjoint characteristic function. express The complex conjugate transpose of .

7. The method for analyzing the boundary layer stability of high-enthalpy ablation walls according to claim 5, characterized in that, The method further includes: When using LST to analyze the steady laminar flow field, according to the formula: and Determine the critical frequency of the rough disturbance response. ; Real-time monitoring of dominant frequency disturbances in the boundary layer ,like ≥ It is determined that the transition may be delayed; if < It is determined that the turning point may occur earlier than expected. in, This indicates that the rough element is at a certain frequency. The distribution of the wall normal velocity perturbation introduced below, express The complex conjugate transpose This represents the adjoint characteristic function.

8. The method for analyzing the boundary layer stability of a high-enthalpy ablation wall according to claim 1, characterized in that, The coupled source terms of the subharmonic equation are constructed based on the second-mode linear operator, including: Based on the second-modal linear operator Constructing the coupled source terms of the subharmonic equation ; in, This indicates taking the partial derivative with respect to the X coordinate. This represents the perturbation field of the first mode. This represents the perturbation field of the second mode.

9. The method for analyzing the boundary layer stability of a high-enthalpy ablation wall according to claim 1, characterized in that, Solving the governing equations to obtain the steady laminar flow field includes: The generalized minimum residual method (GMRES), the linear relaxation algorithm (LR), and the shock wave assembly method are used to solve the governing equations to obtain the steady laminar flow field.

10. A system for analyzing the boundary layer stability of a high-enthalpy ablation wall, characterized in that, include: The steady laminar flow field determination module is used to construct the governing equations for thermochemical nonequilibrium flow by using the Landau-Teller equations and chemical reaction rate equations for multiple gas components as source terms, and to solve the governing equations to obtain the steady laminar flow field. The linear stability theory analysis module is used to analyze the steady laminar flow field using the linear stability theory (LST) to obtain the eigenvalues ​​of the transmission coefficient. The time scale correction module is used to correct the first mode time scale and the second mode time scale based on the roughness of each position on the wall of the high-speed aircraft if the eigenvalue of the transmission coefficient is greater than or equal to 1, so as to obtain the corrected first mode time scale and the corrected second mode time scale. The linear operator construction module is used to construct a first-mode linear operator based on the modified first-mode time scale and a second-mode linear operator based on the modified second-mode time scale. The NPSE result solving module is used to construct the nonlinear parabolic stability equation NPSE based on the first modal linear operator and the second modal linear operator, and solve for the NPSE result. The second-order instability analysis module is used to construct coupled source terms of the subharmonic equation based on the second-mode linear operator when decomposing and linearizing the NPSE results according to Fourier subharmonics, and to perform second-order instability analysis to obtain the transition start position and the amplitude and frequency of the disturbance development.

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