Method and system for multi-field coupling prediction of hypersonic flow instability

Abstract

The application discloses a hypersonic flow instability multi-field coupling prediction method and system, relates to the technical field of modern high-speed aircraft design, and comprises the following steps: acquiring the multi-physical field parameter distribution of a hypersonic flow field; based on a shock wave-boundary layer interaction mechanism, constructing an instability sensitive graph data structure by taking the multi-physical field parameters as input, setting graph nodes in the shock wave influence area, the boundary layer area and the intersection area thereof, and calculating the connection weight between the nodes; performing multi-scale decomposition on the instability sensitive graph data structure, and extracting instability modes of the shock wave scale, the vortex scale and the molecular scale; screening the instability modes by adopting a hypersonic stability criterion, and determining a dominant instability mode; and constructing an instability evolution prediction model based on the dominant instability mode, and outputting the spatiotemporal evolution law of the hypersonic flow instability. The application can solve the problem that the flow instability phenomenon under the complex multi-physical field environment of hypersonic speed is difficult to accurately predict.

Description

Technical Field

[0001] This invention relates to the field of modern high-speed aircraft design technology, and in particular to a method and system for predicting multi-field coupling instability in hypersonic flow. Background Technology

[0002] Modern high-speed aircraft design technology is a comprehensive field involving the intersection and integration of multiple disciplines and technologies. Its aim is to design aircraft that can operate effectively under hypersonic conditions. Therefore, how to use advanced technologies to improve the intelligence level and safety of modern high-speed aircraft design has become one of the urgent problems to be solved.

[0003] In the field of modern high-speed aircraft design, traditional single-temperature models cannot accurately describe the non-equilibrium energy exchange between electrons and heavy particles in plasma under hypersonic conditions, resulting in inaccurate simulation results. Furthermore, existing fluid dynamics and electromagnetic field analysis methods are usually performed independently, lacking effective multi-physics coupling analysis methods, making it difficult to fully understand the physical processes under high-speed flow environments. At the same time, traditional numerical simulation methods are difficult to handle the integration and analysis of data at different scales from micro to macro. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a multi-field coupling prediction method for hypersonic flow instability to solve the problem of accurate prediction of flow instability phenomena in complex multi-physics environments at hypersonic speeds.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] In a first aspect, the present invention provides a multi-field coupling prediction method for hypersonic flow instability, comprising:

[0008] S1. Obtain the multiphysics parameter distribution of the hypersonic flow field;

[0009] S2. Based on the shock wave-boundary layer interaction mechanism, an instability sensitivity graph data structure is constructed with multi-physics parameters as input. Graph nodes are set in the shock wave influence area, the boundary layer area and their intersection area, and the connection weights between nodes are calculated.

[0010] S3. Perform multi-scale decomposition on the instability sensitivity map data structure to extract instability modes at the shock wave scale, vortex scale, and molecular scale.

[0011] S4. Use hypersonic stability criteria to screen instability modes and determine the dominant instability mode;

[0012] S5. Construct an instability evolution prediction model based on the dominant instability mode and output the spatiotemporal evolution law of hypersonic flow instability.

[0013] Preferably, the method for setting the graph nodes in step S2 includes:

[0014] Set up shock wave instability nodes in regions where the pressure gradient exceeds a first preset threshold;

[0015] Set shear instability nodes in regions where the velocity gradient exceeds a second preset threshold;

[0016] A coupled instability node is set in the region where the shock wave and boundary layer meet;

[0017] The instability strength index of each node is calculated according to the following formula:

[0018]

[0019] in, Where p is the pressure gradient modulus, δ is the boundary layer thickness, and p is the pressure gradient modulus. avg For local average pressure, U is the normal velocity gradient. ∞ For the incoming flow velocity, T e For electron temperature, T h This is the temperature of heavy particles.

[0020] Preferably, the connection weights between nodes in step S2 are determined based on the physical transmission mechanism, and the weight calculation formula is as follows:

[0021] w ij =W conv ·f conv (Pe ij ,|r i -r j |)+W diff ·f diff (Pe ij ,|r i -r j |)+W em

[0022] ·f em (Re m,ij ,|r i -r j |)

[0023] in, The Peckley number characterizes the intensity of competition between convection and diffusion. i ,u j Let r be the velocity of nodes i and j. i ,r j Where v is the node location and v is the kinematic viscosity; The magnetic Reynolds number, σ is the magnetic diffusivity. e W is the electrical conductivity, μ0 is the free magnetic permeability; conv W diff W em These are the weighting coefficients for convective transport, diffusion transport, and electromagnetic transport, respectively; f conv f diff f em These are the corresponding convective transport function, diffusion transport function, and electromagnetic transport function, respectively.

[0024] Preferably, the specific form of each transfer function is as follows:

[0025]

[0026]

[0027] Δt is the convection characteristic length, Δt is the time step, and CFL is the dimensionless CFL number; The length of the diffusion characteristic; ω is the characteristic length of the plasma, c is the speed of light, and ω is the velocity of light. p The plasma frequency.

[0028] Preferably, the multi-scale decomposition in step S3 includes:

[0029] We construct Laplace operators at three scale levels: a shock-scale operator to capture pressure wave propagation characteristics, a vortex-scale operator to capture rotational structure evolution characteristics, and a molecular-scale operator to capture viscous diffusion characteristics.

[0030] Eigenvalue decomposition is performed on the Laplacian operator at each scale to obtain the instability modes at the corresponding scale;

[0031] The modes at the three scales are merged to form a complete multi-scale instability mode set.

[0032] Preferably, the hypersonic stability criterion in step S4 includes a critical growth rate determination, and the critical growth rate is calculated as follows:

[0033]

[0034] Where Ma is the Mach number, Re is the Reynolds number, and Ha is the Hartmann number.

[0035] Preferably, the determination of the dominant instability mode in step S4 is based on a comprehensive assessment of the mode growth rate, spatial influence range, and energy contribution.

[0036] Preferably, the instability evolution prediction model in step S5 includes:

[0037] An instability evolution equation based on the linear superposition of dominant modes is established, in the following form:

[0038]

[0039] Among them, Ψ k Let λ be the time-dependent amplitude of the k-th dominant instability mode. k For a linear growth rate, N kmn These are nonlinear coupling coefficients;

[0040] The spatiotemporal distribution prediction results of the unstable field variables are obtained by solving the evolution equation.

[0041] Preferably, the multiphysics parameters in step S1 include density field, velocity field, pressure field, temperature field, electron temperature field, and magnetic field strength.

[0042] Secondly, the present invention provides a multi-field coupled prediction system for hypersonic flow instability, comprising:

[0043] The data acquisition module is used to acquire and preprocess the multiphysics parameters of the hypersonic flow field;

[0044] The graph construction module is used to set graph nodes in the shock wave influence area, boundary layer area and their intersection area according to preset thresholds, calculate the node instability strength index, and calculate the connection weight between nodes based on convective transmission, diffusion transmission and electromagnetic transmission mechanisms to construct an instability sensitive graph data structure.

[0045] The multi-scale decomposition module is used to construct feature extraction operators at the shock wave scale, vortex scale, and molecular scale, perform eigenvalue decomposition on each scale operator, extract the corresponding unstable modes, and merge them to form a complete unstable mode set.

[0046] The mode screening module is used to determine the dominant instability mode based on critical growth rate determination and comprehensive importance assessment;

[0047] The prediction module is used to construct an instability evolution prediction model based on the dominant instability mode, which includes nonlinear interactions, and solve the evolution equation to output the spatiotemporal distribution law of instability.

[0048] The beneficial effects of this invention are as follows:

[0049] (1) This invention achieves systematic prediction of instability phenomena in hypersonic multiphysics coupled flow by organically combining instability sensitivity map data structure and multi-scale decomposition technology. By setting targeted nodes in the shock wave influence region, boundary layer region and their intersection region and calculating connection weights based on physical mechanisms, the computational efficiency is improved compared with the traditional global grid method, while ensuring accurate capture of key instability regions, providing a computationally feasible and physically reasonable prediction method for complex hypersonic flow instability problems;

[0050] (2) By introducing a nodal instability strength index that integrates pressure gradient, velocity gradient, and the temperature difference between electrons and heavy particles, a quantitative characterization of the multiphysics coupling effect is achieved. Combined with the connection weight calculation based on Peckley number and magnetic Reynolds number, the competitive relationship between convective transport, diffusion transport, and electromagnetic transport mechanisms is effectively captured, so that the constructed instability sensitivity map can accurately reflect the physical transport characteristics and instability sensitivity distribution in the hypersonic flow field;

[0051] (3) Three-scale Laplace operators are used to capture the characteristics of pressure wave propagation, rotational structure evolution, and viscous diffusion, respectively. The corresponding instability modes at each scale are extracted through eigenvalue decomposition, effectively separating the instability phenomena dominated by different physical mechanisms. This multi-scale processing method avoids the limitations of single-scale analysis and can comprehensively identify instability mechanisms at all levels from macroscopic shock wave structure to microscopic diffusion process, improving the completeness and accuracy of mode identification;

[0052] (4) By introducing a critical growth rate determination formula that considers Mach number, Reynolds number and Hartmann number, and combining it with a comprehensive evaluation of modal growth rate, spatial influence range and energy contribution, the goal of accurately screening the dominant instability mode from a large number of candidate modes was achieved.

[0053] (5) Establish an instability evolution equation that includes linear growth terms and nonlinear coupling terms. The interaction between different modes is described by the nonlinear coupling coefficient, which can accurately predict the complete evolution process of instability from linear development to nonlinear saturation. Attached Figure Description

[0054] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a flowchart of the method of the present invention;

[0056] Figure 2 This is a diagram illustrating the technical implementation of the present invention;

[0057] Figure 3 This is a system structure diagram of the present invention. Detailed Implementation

[0058] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0059] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0060] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0061] like Figure 1 As shown, this invention provides a multi-field coupling prediction method for hypersonic flow instability, comprising the following steps:

[0062] S1. Obtain the multiphysics parameter distribution of the hypersonic flow field;

[0063] S2. Based on the shock wave-boundary layer interaction mechanism, an instability sensitivity graph data structure is constructed with multi-physics parameters as input. Graph nodes are set in the shock wave influence area, the boundary layer area and their intersection area, and the connection weights between nodes are calculated.

[0064] S3. Perform multi-scale decomposition on the instability sensitivity map data structure to extract instability modes at the shock wave scale, vortex scale, and molecular scale.

[0065] S4. Use hypersonic stability criteria to screen instability modes and determine the dominant instability mode;

[0066] S5. Construct an instability evolution prediction model based on the dominant instability mode and output the spatiotemporal evolution law of hypersonic flow instability.

[0067] like Figure 2 As shown, the technical implementation process of this invention is as follows: First, by acquiring multiple physical field parameters such as density field, velocity field, pressure field, temperature field, electron temperature field, and magnetic field strength, an instability sensitivity map is constructed in the shock wave-affected region, boundary layer region, and their intersection region. This map includes an instability intensity index and connection weights based on convection transport, diffusion transport, and electromagnetic transport mechanisms. Then, the map is decomposed into multiple scales at the shock wave scale, vortex scale, and molecular scale to extract instability modes dominated by different physical mechanisms. The dominant instability modes are selected using hypersonic stability criteria that consider Mach number, Reynolds number, and Hartmann number. Finally, an instability evolution prediction model containing linear growth terms and nonlinear coupling terms is established to accurately predict the spatiotemporal evolution of hypersonic flow instability.

[0068] Specifically, in one embodiment of the present invention, step S1 includes:

[0069] First, obtain the density field ρ(x,y,z,t), which reflects the spatial variation of the material distribution in the flow field. Second, obtain the velocity field. The flow includes three components: flow direction, normal direction, and spanwise direction, used to characterize the flow's motion state and shear properties. Third, the pressure field p(x,y,z,t) is obtained, which is fundamental for shock wave identification and pressure gradient calculation. Fourth, the temperature field T(x,y,z,t) is obtained, reflecting the thermodynamic state of the flow field.

[0070] To address the multiphysics coupling characteristics of hypersonic velocities, it is also necessary to obtain the electron temperature field T. e (x,y,z,t) and magnetic field strength The electron temperature field reflects the plasma effect generated by gas ionization under high-temperature conditions, while the magnetic field strength describes the interaction between the electromagnetic field and the flow field. All parameters are discretized using a uniform spatial grid and time step to form a standardized multiphysics parameter dataset.

[0071] Specifically, in one embodiment of the present invention, step S2 includes:

[0072] S2.1 Basic Structure of Instability Sensitivity Diagram

[0073] Definition of a graph: Instability sensitivity graph G = (V, E, W), where: V = v1, v2, ..., v n : A set of nodes, where each node represents a spatial location in the flow field that is susceptible to instability; E = e ij : Edge set, connecting pairs of nodes with physical coupling; W = w ij Weight set: quantifies the coupling strength between nodes.

[0074] Data structure representation: Stored in adjacency matrix form, matrix A n×n Medium element A ij =w ij A represents the connection weight between node i and node j. If the two nodes are not connected, then A is the connection weight. ij =0.

[0075] S2.2 Node Setup and Attribute Definition

[0076] By scanning the entire computation domain, nodes are placed at locations that meet the following conditions:

[0077] Shock wave instability node: when At this point, shock wave instability nodes are set at the grid point (x, y, z). These nodes are mainly distributed in the pressure jump regions before and after the shock wave. First preset threshold. Where ρ ∞ For the incoming flow density, U ∞ L represents the incoming flow velocity. refThis is the reference length (taken as the characteristic length of the object). This threshold is determined based on the magnitude of the shock wave intensity to ensure that significant pressure jump regions can be captured.

[0078] Shear instability node: when At this time, shear instability nodes are set. These nodes are mainly distributed inside the boundary layer and in the shear layer region. The second preset threshold ε2 = 0.01 × U ∞ / δ, where δ is the boundary layer thickness. This threshold is determined based on the typical shear rate within the boundary layer, and is typically taken as 1% of the shear rate at the outer edge of the boundary layer as the identification standard.

[0079] Coupled instability node: Set in the region that simultaneously meets the above two conditions (each with a 50% threshold), representing the key location of shock wave-boundary layer interaction.

[0080] Each node v i It has an instability strength index, the calculation formula of which is:

[0081]

[0082] in, Where p is the pressure gradient modulus, δ is the boundary layer thickness, and p is the pressure gradient modulus. avg For local average pressure, U is the normal velocity gradient. ∞ For the incoming flow velocity, T e For electron temperature, T h This is the temperature of heavy particles.

[0083] The purpose of this indicator: to quantify the importance of nodes: I node The larger the value, the stronger the instability sensitivity at that location, and the higher the weight in subsequent modal analysis; Modal extraction weight: In eigenvalue decomposition, the node instability intensity is used as the diagonal element of the weight matrix, affecting the calculation of the eigenvector; Dominant mode screening: Combining the node instability intensity distribution, the mode that contributes the most to the overall instability is identified.

[0084] Two nodes v i and v j Conditions for establishing a connection between them:

[0085] Spatial distance criterion: |r i -r j | <R max , where R max =3δ is the maximum connection distance; Physical correlation criterion: at least one of the following conditions must be met: Convective connection: there is significant convective transmission between the two nodes (Pe ij >1); Diffusion connection: Diffusion transmission between two nodes cannot be ignored (|r i -r j |<2L diffElectromagnetic connection: Electromagnetic coupling effect exists (Re). m,ij >0.1 and |r i -r j | <L em ).

[0086] Connection weight w ij Characterizing the physical coupling strength between two nodes:

[0087] w ij =W conv ·f conv (Pe ij ,|r i -r j |)+W diff ·f diff (Pe ij ,|r i -r j |)+W em

[0088] ·f em (Re m,ij ,|r i -r j |)

[0089] in, The Peckley number characterizes the intensity of competition between convection and diffusion. i ,u j Let r be the velocity of nodes i and j. i ,r j Where v is the node location and v is the kinematic viscosity; The magnetic Reynolds number, σ is the magnetic diffusivity. e W is the electrical conductivity, μ0 is the free magnetic permeability; conv W diff W em These are the weighting coefficients for convective transport, diffusion transport, and electromagnetic transport, respectively; f conv f diff f em These are the corresponding convection transport function, diffusion transport function, and electromagnetic transport function, respectively. Where W... conv W diff W em The sum is 1.

[0090] The specific forms of each transfer function are as follows:

[0091]

[0092] Δt is the convection characteristic length, Δt is the time step, and CFL is the dimensionless CFL number; The length of the diffusion characteristic; ω is the characteristic length of the plasma, c is the speed of light, and ω is the velocity of light. p The plasma frequency.

[0093] The algorithm flow for constructing graph data structures is as follows:

[0094] Initialization: Create an empty node set V and adjacency matrix A; Node scan: Traverse all grid points and determine node positions and types based on threshold conditions; Strength calculation: Calculate the instability strength index I for each node. node Connection establishment: For all node pairs (i,j), check the connection criterion; if the condition is met, calculate the weight w. ij Matrix filling: The weight values ​​are filled into the adjacency matrix A to form the final graph data structure.

[0095] The completed instability sensitivity map includes:

[0096] Node information table: Node coordinates (x) i ,y i ,z i Type (shock wave / shear / coupling), instability intensity; Adjacency matrix: an n×n matrix storing the connection weights between all nodes; Degree matrix: a diagonal matrix D, where D... ii =∑ j w ij Let be the degree of node i.

[0097] Specifically, in one embodiment of the present invention, step S3 includes:

[0098] Hypersonic flow instability involves physical processes across multiple spatiotemporal scales. The shock wave scale primarily captures pressure wave propagation and shock wave structure changes, with its characteristic timescale being the acoustic timescale. The vortex scale primarily captures the evolution of rotating structures and shear layer instability, with its characteristic timescale being the convection timescale. The molecular scale primarily captures viscous diffusion and thermal conduction effects, with its characteristic timescale being the diffusion timescale. These three physical mechanisms are coupled under hypersonic conditions, jointly determining the complex behavior of flow instability.

[0099] To capture these physical processes at different scales, three targeted Laplacian operators need to be constructed. Each operator highlights the transport characteristics at the corresponding scale by applying specific physical weights to the underlying connectivity weights of the instability sensitivity graph.

[0100] Shock scaling operators are primarily used to capture the propagation characteristics of pressure waves. Based on the fundamental connection weight matrix obtained in step S2, the weights are weighted according to the physical characteristics of the shock wave. Shock scaling Laplace operator:

[0101]

[0102] Shock weight calculation:

[0103]

[0104] Where w ij The basic connection weights for step S2, Let be the magnitude of the pressure gradient at node i. For reference pressure, L ref Let |r| represent the length of the object's features. i -r j | represents the distance between nodes, L shock =L ref The characteristic length of the shock wave is given. The pressure gradient intensity factor reflects the driving force intensity of shock wave propagation, while the distance attenuation factor reflects the spatial extent of the shock wave's influence. Reference pressure gradient p. ref / L ref Based on the flow pressure, the characteristic length of the shock wave is taken as the characteristic dimension of the object, usually the chord length or diameter.

[0105] The vortex-scale operator is used to capture the evolutionary characteristics of rotating structures, highlighting shear-driven instability mechanisms. Vortex-scale Laplace operator:

[0106]

[0107] vortex weight calculation:

[0108]

[0109] Where ω i Let U be the vortex modulus at node i. ∞ Let L be the inflow velocity, δ be the boundary layer thickness, and L be the flow velocity. vortex =δ is the characteristic length of the vortex. The vorticity intensity factor is based on the vorticity at the node and the reference vorticity U. ∞ The ratio / δ is determined, and the reference vorticity represents the typical shear rate at the outer edge of the boundary layer. The characteristic length of the vortex is taken as the boundary layer thickness, usually defined as the 99% velocity boundary layer thickness, reflecting the main influence range of the vortex structure.

[0110] Molecular-scale operators are used to capture viscous diffusion characteristics, reflecting the effects of viscosity and thermal conductivity. Molecular-scale Laplacian operator:

[0111]

[0112] Molecular weight calculation:

[0113]

[0114] Where Re δ,i =U i δ / v i Let U be the local Reynolds number at node i.i v is the velocity at the node. i For local kinematic viscosity, The molecular characteristic length is given. The reciprocal of the Reynolds number reflects the relative importance of the viscous effect, with viscous diffusion being more significant in low Reynolds number regions. The molecular characteristic length is determined based on viscous diffusion theory and reflects the characteristic influence range of viscous diffusion. Under hypersonic conditions, viscosity changes significantly due to temperature effects, requiring consideration of the spatial distribution of local viscosity.

[0115] Eigenvalue decomposition is performed on the Laplacian operator at each of the three scales:

[0116]

[0117] Where scale∈{shock,vortex,molecular} For the k-th eigenvalue, This is the corresponding feature vector.

[0118] The physical meaning of eigenvalues ​​corresponds to the linear growth rate or decay rate of each mode. Positive eigenvalues ​​indicate unstable growth modes, while negative eigenvalues ​​indicate stable decay modes. The physical meaning of eigenvectors corresponds to the spatial distribution pattern of unstable disturbances, with each component of the vector representing the disturbance amplitude at the corresponding node.

[0119] In the numerical solution process, the Lanczos algorithm, specifically designed for large sparse symmetric matrices, is employed. This algorithm exhibits good convergence and computational efficiency. The convergence criterion is set as the relative error of the eigenvalues ​​being less than 10. -6 The eigenvector residual is less than 10. -8 Mode selection: The shock scale is retained up to min(50, 0.1N). total ) modes; vortex scale retention min(100, 0.2N) total ) modalities; molecular scale retention min(30, 0.05N) total There are ) modes. Where N total This represents the total number of nodes in the graph.

[0120] The modes at the three scales are merged to form a complete multi-scale instability mode set. Specifically, a complete mode matrix is ​​constructed, whose column vectors successively contain the modes at the shock scale, the modes at the vortex scale, and the modes at the molecular scale. At the same time, corresponding eigenvalue vectors and scale identifier vectors are constructed. The former records the growth rate of each mode, and the latter identifies the physical scale to which each mode belongs (1-shock wave, 2-vortex, 3-molecule).

[0121] Specifically, in one embodiment of the present invention, step S4 includes:

[0122] A stability criterion specifically designed for hypersonic conditions was used for modal screening. This criterion considers the combined effects of high Mach number, Reynolds number, and magnetic field effects on flow stability, and can accurately identify modes with the potential for instability growth.

[0123] Critical growth rate calculation:

[0124]

[0125] Where Ma is the Mach number, representing the intensity of the compressibility effect; Re is the Reynolds number, representing the ratio of inertial force to viscous force; and Ha is the Hartmann number, representing the intensity of the influence of the magnetic field on the flow.

[0126] Parameter calculation method: Mach number Ma = U ∞ / a ∞ U ∞ Let a be the incoming flow velocity. ∞ The velocity of the incoming flow; Reynolds number Re = ρ ∞ U ∞ L ref / μ ∞ , where ρ ∞ For the incoming flow density, L ref For reference length, μ ∞ For the inflow dynamic viscosity; Hartmann number Where B is the magnetic flux density, σ e is the electrical conductivity.

[0127] The critical growth rate is the threshold at which a mode begins to exhibit unstable growth under given hypersonic flow conditions. Only when the eigenvalues ​​of the mode exceed this critical value does the mode possess the potential for unstable growth.

[0128] Critical growth rate determination is performed on all modes (including modes at three scales), and stable modes that do not meet the instability condition are eliminated. Screening condition: λ k >λ crit ;where λ k This represents the eigenvalue of the k-th mode, i.e., the linear growth rate of that mode. Under hypersonic conditions, many modes remain stable due to strong viscous dissipation or magnetic field stabilization, and this criterion is needed to identify and eliminate them.

[0129] After determining the critical growth rate, the candidate unstable mode set φ is obtained. k , in A set of modal indices that satisfy the instability condition.

[0130] For candidate instability modes determined by the critical growth rate, a comprehensive importance assessment is conducted based on three dimensions: modal growth rate, spatial influence range, and energy contribution.

[0131] The modal growth rate directly reflects the growth rate of the unstable mode and is the primary indicator for judging the importance of the mode. Normalized growth rate score:

[0132]

[0133] Where S growth,k The growth rate of the k-th mode is scored, with a value ranging from (0,1). The higher the growth rate of a mode, the closer its score is to 1, indicating that the mode has a stronger ability to experience unstable growth during the linear phase.

[0134] Spatial influence range measures the extent to which the unstable modes are distributed in physical space; modes with a larger influence range have a more significant disturbance effect on the overall flow field. Calculation of spatial influence range:

[0135]

[0136] in Let r be the amplitude of the k-th mode at node i. i N is the distance from node i to the geometric center. total Total number of nodes. Normalized score for scope of influence:

[0137]

[0138] This index reflects the spatial distribution characteristics of modes, with modes exhibiting high localization. k Mode R with smaller values ​​and higher globalization k The value is relatively large.

[0139] The energy contribution assessment mode represents the proportion of energy during the entire instability process, calculated using a weighted average based on the nodal instability strength. Modal energy contribution calculation:

[0140]

[0141] in Let I be the node instability strength weight matrix. i Let E be the instability strength index of node i. k It directly reflects the relative importance of the mode in the instability process, and its value ranges from (0,1). The sum of the energy contributions of all modes is 1.

[0142] The three evaluation dimensions are weighted and combined to construct a comprehensive importance index. Comprehensive importance calculation:

[0143] S k =α·S growth,k +β·S range,k +γ·E k

[0144] Where α, β, and γ are weighting coefficients, satisfying α + β + γ = 1.

[0145] Candidate instability modes are ranked based on a comprehensive importance index, and the top few modes are selected as dominant instability modes. Mode ranking: All candidate modes are ranked according to their comprehensive importance S. k Sort the modes from largest to smallest to obtain an ordered mode sequence. Determine the number of dominant modes: Threshold method: Select S. k >S threshold All modes, where S threshold =0.1, suitable for situations where the distribution of modal importance is relatively uniform; cumulative contribution method: select modes whose cumulative comprehensive importance reaches 80% of the total, to ensure that the dominant mode set covers the main instability features.

[0146] The output of step S4 includes the set of dominant instability modes and their related information. Dominant mode matrix: Each column represents the spatial distribution of a dominant instability mode. Dominant mode eigenvalues: The linear growth rate corresponding to each dominant mode. Overall importance vector: Record the overall importance score of each dominant modality. Scale identifier vector: Identify the physical scale to which each dominant mode belongs (1-shock wave, 2-vortex, 3-molecule).

[0147] Specifically, in one embodiment of the present invention, step S5 includes:

[0148] The evolution of instability in hypersonic flow can be described using mode decomposition. In the linear phase, each instability mode evolves independently, its growth rate determined by its corresponding eigenvalue. As instability develops, nonlinear interactions begin to occur between modes, which determine the later-stage behavior and final saturation state of the instability evolution. Based on mode decomposition theory, any instability field variable can be represented as a linear superposition of the dominant instability modes. The time evolution of each mode is governed by an ordinary differential equation containing linear growth terms and nonlinear coupling terms. By solving this set of coupled evolution equations, the evolution law of the instability field variable over time can be obtained. The instability evolution prediction model adopts the evolution equation form based on the linear superposition of dominant modes:

[0149]

[0150] Among them, Ψ k Let λ be the time-dependent amplitude of the k-th dominant instability mode, representing the intensity change of this mode during its evolution; k The linear growth rate is represented by the dominant modal characteristic value selected in step S4; N kmn is the nonlinear coupling coefficient, which describes the nonlinear influence of the m-th and n-th modes on the evolution of the k-th mode.

[0151] In this equation, the evolution of each mode includes two contributions, the first part being λ. k Ψ k The first term is a linear term, describing the self-growth or decay of the mode; the second part is ∑. m,n N kmn Ψ m Ψ n The term is nonlinear, describing the influence of interactions between different modes on the evolution of that mode.

[0152] Nonlinear coupling coefficient N kmn The calculations are based on the physical mechanisms of hypersonic flow and the spatial distribution characteristics of its modes:

[0153]

[0154] Where φ k (r) is the spatial distribution function of the k-th dominant mode. Ω is a nonlinear operator, r is the computational domain, and r is the spatial position vector.

[0155] Nonlinear operators Construction based on nonlinear terms of the Navier-Stokes equations:

[0156]

[0157] Where u m ,u n The velocity perturbations p for the m-th and n-th modes are respectively. m ,p n ρ0 represents the corresponding pressure disturbance and ρ0 represents the reference density.

[0158] To solve the instability evolution equation, appropriate initial and boundary conditions need to be set.

[0159] Initial conditions set: in This represents the initial amplitude of the k-th mode. The initial amplitude is determined based on the initial disturbance distribution in the flow field: in This represents the initial perturbation velocity field distribution.

[0160] Methods for setting initial disturbances: Random disturbance method: Add small-amplitude random disturbances to the flow field, with the amplitude usually taken as 0.1%-1% of the incoming flow velocity; Specific disturbance method: Set specific forms of initial disturbances according to actual physical problems, such as disturbances caused by wall roughness; Experimental data method: Set initial conditions based on experimentally measured disturbance data.

[0161] The evolution equations were solved using the fourth-order Runge-Kutta method.

[0162] Time step determined:

[0163]

[0164] Where C CFL =0.1-0.5 are the CFL coefficients, λ max For the maximum linear growth rate, N max For the maximum nonlinear coupling coefficient, |Ψ max | represents the maximum modal amplitude at the current moment.

[0165] Convergence criterion: The calculation is considered converged when the relative rate of change of the amplitude of all modes is less than a set threshold.

[0166]

[0167] Where ∈ conv =10 -6 The convergence threshold is defined by the superscript n, which represents the number of time steps.

[0168] After obtaining the time-dependent amplitudes of each dominant mode by solving the evolution equations, the complete spatiotemporal distribution of the unstable field variables can be reconstructed.

[0169] Field variable reconstruction:

[0170]

[0171] Where u disturb (r,t) represents the spatiotemporal distribution of the perturbation velocity field, p disturb (r,t) represents the spatiotemporal distribution of the perturbation pressure field, p k (r) represents the pressure distribution corresponding to the k-th mode, N dominant The total number of dominant modes.

[0172] Calculation of complete field variables:

[0173] u(r,t)=u base (r)+u disturb (r,t)

[0174] p(r,t)=p base (r)+p disturb (r,t)

[0175] Where u base (r) and p base (r) represents the velocity and pressure distributions of the basic flow field, respectively.

[0176] Step S5 outputs include the spatiotemporal distribution prediction results of instability evolution and related analytical indicators. Time series output: Outputs the evolution curves Ψ of the amplitude of each dominant mode over time.k (t), used to analyze the growth and decay trends of each mode. Spatial distribution output: Outputs the spatial distribution u of the perturbation field at different times. disturb (r,t i ) and p disturb (r,t i ), where t i For the selected time series. Instability development stage identification: Linear stage: when |∑ m,n N kmn Ψ m Ψ n |<0.1|λ k Ψ k At the first moment, the mode is in the linear development stage; in the nonlinear stage: when the nonlinear term begins to dominate, instability enters the nonlinear development stage; in the saturation stage: when... At that time, the mode reaches saturation.

[0177] like Figure 3 As shown, the present invention also provides a hypersonic flow instability multi-field coupling prediction system, the system being used to implement the method described in any of the above claims, the system comprising:

[0178] The data acquisition module is used to acquire and preprocess the multiphysics parameters of the hypersonic flow field;

[0179] The graph construction module is used to set graph nodes in the shock wave influence area, boundary layer area and their intersection area according to preset thresholds, calculate the node instability strength index, and calculate the connection weight between nodes based on convective transmission, diffusion transmission and electromagnetic transmission mechanisms to construct an instability sensitive graph data structure.

[0180] The multi-scale decomposition module is used to construct feature extraction operators at the shock wave scale, vortex scale, and molecular scale, perform eigenvalue decomposition on each scale operator, extract the corresponding unstable modes, and merge them to form a complete unstable mode set.

[0181] The mode screening module is used to determine the dominant instability mode based on critical growth rate determination and comprehensive importance assessment;

[0182] The prediction module is used to construct an instability evolution prediction model based on the dominant instability mode, which includes nonlinear interactions, and solve the evolution equation to output the spatiotemporal distribution law of instability.

[0183] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-field coupled prediction method for hypersonic flow instability, characterized in that, include: S1. Obtain the multiphysics parameter distribution of the hypersonic flow field; S2. Based on the shock wave-boundary layer interaction mechanism, an instability sensitivity graph data structure is constructed with multi-physics parameters as input. Graph nodes are set in the shock wave influence area, the boundary layer area and their intersection area, and the connection weights between nodes are calculated. S3. Perform multi-scale decomposition on the instability sensitivity map data structure to extract instability modes at the shock wave scale, vortex scale, and molecular scale. S4. Use hypersonic stability criteria to screen instability modes and determine the dominant instability mode; S5. Construct an instability evolution prediction model based on the dominant instability mode and output the spatiotemporal evolution law of hypersonic flow instability; The methods for setting the graph nodes in step S2 include: Set up shock wave instability nodes in regions where the pressure gradient exceeds a first preset threshold; Set shear instability nodes in regions where the velocity gradient exceeds a second preset threshold; A coupled instability node is set in the region where the shock wave and boundary layer meet; The instability strength index of each node is calculated according to the following formula: ； in, For the pressure gradient magnitude, For boundary layer thickness, For local average pressure, The normal velocity gradient, For the incoming flow velocity, For electron temperature, The heavy particle temperature; In step S2, the connection weights between nodes are determined based on the physical transmission mechanism, and the weight calculation formula is as follows: ； in, The Peckley number characterizes the intensity of competition between convection and diffusion. Let i be the velocity of nodes i and j. For node position, Kinematic viscosity; The magnetic Reynolds number, Magnetic diffusivity, For electrical conductivity, The vacuum permeability; , , These are the weighting coefficients for convective transport, diffusion transport, and electromagnetic transport, respectively. , , These are the corresponding convective transport function, diffusion transport function, and electromagnetic transport function, respectively. The instability evolution prediction model in step S5 includes: An instability evolution equation based on the linear superposition of dominant modes is established, in the following form: ； in, The time-dependent amplitude of the k-th dominant instability mode. For linear growth rate, Let be the nonlinear coupling coefficient, describing the th The and the first The dominant instability mode affects the first The nonlinear effects of the evolution of the dominant instability mode; The spatiotemporal distribution prediction results of the unstable field variables are obtained by solving the evolution equation.

2. The multi-field coupling prediction method for hypersonic flow instability as described in claim 1, characterized in that, The specific forms of each transfer function are as follows: ； ； ； For convection characteristic length, For time step, The number is a dimensionless CFL. The length of the diffusion characteristic; The characteristic length of the plasma, At the speed of light, The plasma frequency.

3. The multi-field coupling prediction method for hypersonic flow instability as described in claim 1, characterized in that, The multi-scale decomposition in step S3 includes: We construct Laplace operators at three scale levels: a shock-scale operator to capture pressure wave propagation characteristics, a vortex-scale operator to capture rotational structure evolution characteristics, and a molecular-scale operator to capture viscous diffusion characteristics. Eigenvalue decomposition is performed on the Laplacian operator at each scale to obtain the instability modes at the corresponding scale; The modes at the three scales are merged to form a complete multi-scale instability mode set.

4. The multi-field coupling prediction method for hypersonic flow instability as described in claim 1, characterized in that, The hypersonic stability criterion in step S4 includes the determination of the critical growth rate, which is calculated as follows: ； in, Mach number, Let Reynolds number be 1. It is a Hartmann number.

5. The multi-field coupling prediction method for hypersonic flow instability as described in claim 1, characterized in that, The determination of the dominant instability mode in step S4 is based on a comprehensive assessment of the mode growth rate, spatial influence range, and energy contribution.

6. The multi-field coupling prediction method for hypersonic flow instability as described in claim 1, characterized in that, The multiphysics parameters in step S1 include density field, velocity field, pressure field, temperature field, electron temperature field, and magnetic field strength.

7. A multi-field coupled prediction system for hypersonic flow instability, characterized in that, The system is used to implement the method as described in any one of claims 1-6, the system comprising: The data acquisition module is used to acquire and preprocess the multiphysics parameters of the hypersonic flow field; The graph construction module is used to set graph nodes in the shock wave influence area, boundary layer area and their intersection area according to preset thresholds, calculate the node instability strength index, and calculate the connection weight between nodes based on convective transmission, diffusion transmission and electromagnetic transmission mechanisms to construct an instability sensitive graph data structure. The multi-scale decomposition module is used to construct feature extraction operators at the shock wave scale, vortex scale, and molecular scale, perform eigenvalue decomposition on each scale operator, extract the corresponding unstable modes, and merge them to form a complete unstable mode set. The mode screening module is used to determine the dominant instability mode based on critical growth rate determination and comprehensive importance assessment; The prediction module is used to construct an instability evolution prediction model based on the dominant instability mode, which includes nonlinear interactions, and solve the evolution equation to output the spatiotemporal distribution law of instability.

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