Method and system for predicting transition location coupled with transport equation and transition intermittency factor

Abstract

The application relates to the technical field of aerospace engineering, and provides a transition position prediction method and system coupling a roughness influence factor transport equation and a transition intermittency factor, which comprises the following steps: acquiring input parameters, performing Reynolds average basic flow field solving, and obtaining a dimensionless roughness parameter; the input parameters comprise the three-dimensional shape of an aircraft, inflow and wall surface conditions, and roughness distribution parameters; when the dimensionless roughness parameter is within a preset applicable range, and the current wall surface defect type is not mainly dominated by isolated cavities, sudden steps or large-scale separation defects, pre-calibrated model parameters matched with the input parameters are called; a roughness influence factor transport equation and a transition intermittency factor coupling model using the pre-calibrated model parameters are used to solve the flow field corresponding to the input parameters, and a transition position is predicted and output. The application realizes high fidelity and cross-condition portability of roughness-induced transition prediction under complex shapes and arbitrary roughness distribution.

Description

Technical Field

[0001] This invention relates to the field of aerospace engineering technology, and in particular to a method and system for predicting transition locations by coupling transport equations with transition intermittency factors. Background Technology

[0002] During hypersonic flight, boundary layer transition directly leads to a significant increase in wall friction drag and heat flux density, which has a decisive impact on the safety margin of the thermal protection system and the overall performance of the aircraft. With the continuous development of the field of hyperenthalpic and hypersonic aerodynamics and boundary layer transition prediction, significant progress has been made in numerical simulation techniques for boundary layer transition mechanisms and aerodynamic environment prediction. In particular, engineering transition models based on the Reynolds-averaged Navier-Stokes equations (RANS) framework, such as transition models based on the intermittent factor γ, have been widely used in the aircraft design stage. At the same time, for the problem of uneven distributed roughness caused by the ablation of thermal protection materials under extreme conditions of high enthalpy and long flight time, a large number of experimental studies have also clearly confirmed that this type of roughness can significantly promote boundary layer instability and increase the aerodynamic heating increment in the turbulent region by 2 to 3 times.

[0003] Currently, in engineering practice, the existing technical solutions for addressing the aerodynamic heating increment caused by ablation roughness mainly rely on empirical safety margin design. This involves artificially increasing the thermal protection margin in numerical prediction results or design specifications to avoid the precise impact of roughness. At the numerical simulation level, existing transition models, such as commonly used engineering models based on the intermittent factor γ, typically introduce the roughness effect directly into the transition model or turbulence model as a local empirical correction when dealing with distributed roughness-induced transition. This is then coupled with the RANS equations to obtain aerodynamic and thermodynamic parameters such as wall heat flux.

[0004] However, the aforementioned method of introducing roughness effects in the form of local empirical corrections is essentially a static adjustment of local parameters. It is difficult to achieve transferable and extrapolable predictions under the conditions of complex aircraft shapes and spatially distributed roughness. This leads to redundancy in the quality of thermal protection systems, increased costs, and imprecise risk assessments. Furthermore, existing roughness correction methods generally lack a unified convergence control strategy in the coupled solution process of RANS transition equations. This can easily cause numerical instability when dealing with strong roughness conditions, or make the calculation results highly sensitive to numerical parameters such as computational grid scale and relaxation coefficients, which seriously restricts their reliable application in complex engineering models. Summary of the Invention

[0005] This invention provides a method and system for predicting transition positions by coupling transport equations with transition intermittent factors. This method addresses the shortcomings of existing technologies where static local parameter adjustments are difficult to achieve transferable and extrapolable predictions under complex aircraft shapes and spatially distributed roughness conditions. It achieves high fidelity and cross-condition portability for roughness-induced transition prediction under complex shapes and arbitrary roughness distributions.

[0006] This invention provides a method for predicting transition locations by coupling transport equations with transition intermittent factors, comprising: acquiring input parameters, solving the Reynolds-averaged basic flow field to obtain dimensionless roughness parameters; the input parameters include the three-dimensional shape of the aircraft, incoming flow and wall conditions, and roughness distribution parameters; determining that the dimensionless roughness parameters are within a preset applicable range, and that the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects, and then calling pre-calibrated model parameters that match the input parameters; the pre-calibrated model parameters are obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients based on high-enthalpy wind tunnel transition experimental data or flight test data, with transition location error and peak heat flux error as objective functions; and using the roughness influence factor transport equation coupled with transition intermittent factor coupled model that calls the pre-calibrated model parameters to solve the flow field corresponding to the input parameters, predicting and outputting the transition location.

[0007] According to the present invention, a method for predicting transition locations by coupling transport equations and transition intermittent factors is provided. This method utilizes a roughness influence factor transport equation coupled with a transition intermittent factor coupled model that calls pre-calibrated model parameters to solve the flow field corresponding to the input parameters, predicting and outputting the transition location. The method includes: constructing a roughness excitation function based on dimensionless roughness parameters; solving the roughness influence factor transport equation by combining the called pre-calibrated model parameters to obtain the roughness influence factor distribution across the entire field; coupling the roughness influence factor distribution to the Fu-Wang transition equation set; modifying the generation term of the transition intermittent factor and / or the transition initiation criterion; and performing coupled iterative solution using a preset convergence control strategy until the convergence condition is met, outputting the predicted transition location and intermittent factor field.

[0008] According to the present invention, a method for predicting transition locations by coupling transport equations and transition intermittent factors is provided to obtain the distribution of roughness influence factors across the entire field. The method includes: determining the generation term based on the transport equation coefficients in the pre-calibrated model parameters, combined with the roughness excitation function, the local strain rate scalar measure, and the near-wall distribution function; determining the dissipation term based on the transport equation coefficients in the pre-calibrated model parameters, combined with the current roughness influence factor and the local characteristic frequency; and solving the roughness influence factor transport equation based on the generation and dissipation terms to obtain the distribution of roughness influence factors across the entire field.

[0009] According to the present invention, a method for predicting transition locations by coupling transport equations and transition intermittent factors is provided. Based on generation and dissipation terms, the roughness influence factor transport equation is solved, including: based on generation and dissipation terms, combined with physical limiting and boundary conditions, the roughness influence factor transport equation is solved; wherein, physical limiting is used to restrict the value of the solved roughness influence factor to be between a first preset value and a preset maximum roughness influence factor; boundary conditions are used to restrict the roughness influence factor to be equal to the roughness excitation function at the wall boundary, or to adopt a zero gradient condition, and to set the roughness influence factor to a second preset value at the inlet and far-field boundaries.

[0010] According to the present invention, a method for predicting transition locations by coupling transport equations with transition intermittent factors is provided. The roughness influence factor distribution is coupled to the Fu-Wang transition equation system to correct the generation terms of the transition intermittent factors. The method includes: obtaining the original intermittent factor generation terms in the Fu-Wang transition equation system; constructing a roughness correction function based on the roughness influence factor distribution and the intermittent factor correction coefficients in the pre-calibrated model parameters; and using the roughness correction function to amplify and correct the original intermittent factor generation terms.

[0011] According to the present invention, a method for predicting transition locations by coupling transport equations with transition intermittent factors is provided. The roughness influence factor distribution is coupled to the F.W. transition equation set, and the generation terms of the transition intermittent factors and the transition initiation criteria are modified. The method includes: obtaining the critical momentum-thickness Reynolds number used to determine the transition initiation in the F.W. transition equation set; and reducing the critical momentum-thickness Reynolds number based on the roughness influence factor distribution, so that the critical momentum-thickness Reynolds number decreases when the roughness increases.

[0012] According to the present invention, a method for predicting transition locations by coupling transport equations and transition intermittent factors is provided. The Reynolds-meaned basic flow field includes a set of flow field control equations. A preset convergence control strategy is used to perform coupled iterative solutions, including: in each external iteration, updating the Reynolds-meaned equations, the roughness influence factor transport equations, the transition intermittent factor equations, and the turbulence equations in a stepwise manner, and applying corresponding relaxation factors to the roughness influence factor and the transition intermittent factor respectively during the update process; using an asymptotic loading strategy for the roughness conditions or roughness excitation functions at the wall boundary, gradually increasing them from the initial preset value to the target true value; during the iteration process, reducing the residuals of the flow field control equations to a set threshold, and using the transition start position and the rate of change of peak heat flux both being less than a preset proportion as a dual convergence criterion.

[0013] According to the present invention, a method for predicting transition locations by coupling transport equations with transition intermittent factors includes the following steps before calling pre-calibrated model parameters that match the input parameters: acquiring high-enthalpy wind tunnel transition test data or flight test data to form multiple sample operating conditions covering different ranges of dimensionless roughness parameters and Mach and Reynolds numbers; for each sample operating condition, using transition location error and peak heat flux error as objective functions, performing hierarchical optimization calibration of the source term coefficients and intermittent factor correction coefficients in the roughness influence factor transport equation to obtain pre-calibrated model parameters; wherein, the hierarchical optimization strategy includes first calibrating the source term coefficients of the roughness influence factor transport equation, and then calibrating the intermittent factor correction coefficients based on the calibrated source term coefficients; based on the calibration results, associating and storing the calibration coefficient sets corresponding to different cases with the corresponding sample operating conditions.

[0014] According to the present invention, a method for predicting transition locations by coupling transport equations with intermittent transition factors, after obtaining dimensionless roughness parameters, further includes: when the dimensionless roughness parameters are determined to be less than the lower limit of a preset applicable range, performing flow field separation state detection; the flow field separation state detection includes checking the sign of wall shear stress, separation state, and friction velocity definition; when the dimensionless roughness parameters are determined to be greater than the upper limit of a preset applicable range, saturating and limiting the dimensionless roughness parameters, the roughness excitation function constructed based on the dimensionless roughness parameters, and the distribution of roughness influence factors, and outputting an out-of-range alarm; when the current wall defect type is determined to be an isolated cavity defect, combining it with a separation-induced transition model; wherein, the separation-induced transition model is obtained by introducing a cavity-induced generation term related to the instability intensity index into the intermittent factor transport equation, and the instability intensity index is generated by extracting wall quantity based on the Reynolds-averaged basic flow field and constructing a characteristic function characterizing the instability intensity of the cavity separation shear layer.

[0015] This invention also provides a transition location prediction system coupled with a transport equation and a transition intermittent factor, comprising: a parameter acquisition module, which acquires input parameters, solves the Reynolds-averaged basic flow field, and obtains dimensionless roughness parameters; the input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and roughness distribution parameters; a parameter calling module, which, when the dimensionless roughness parameters are within a preset applicable range and the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects, calls pre-calibrated model parameters that match the input parameters; the pre-calibrated model parameters are obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients based on high-enthalpy wind tunnel transition experimental data or flight test data, with transition location error and peak heat flux error as objective functions; and a location prediction module, which uses the roughness influence factor transport equation coupled with the transition intermittent factor coupled model that calls the pre-calibrated model parameters to solve the flow field corresponding to the input parameters, predict and output the transition location.

[0016] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements a method for predicting transition locations by coupling the transport equation with the transition intermittent factor as described above.

[0017] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a transition position prediction method coupled with a transition intermittency factor as described above.

[0018] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements a method for predicting transition locations by coupling transport equations with transition intermittent factors as described above.

[0019] The present invention provides a method and system for predicting transition locations by coupling transport equations and transition intermittency factors. This method obtains dimensionless roughness parameters by solving the Reynolds-averaged basic flow field based on the acquired input parameters. This accurately reflects the basic flow field data that reflects the complex three-dimensional geometric effects of hypersonic flight and the characteristics of the real gas thermal environment. It automatically extracts key dimensionless parameters characterizing roughness effects from complex flow field variables, achieving a parameterized mapping from macroscopic flight conditions to microscopic roughness disturbances. Based on the obtained dimensionless roughness parameters, it determines whether the model meets the applicable conditions, accurately identifying the model's applicable boundaries and avoiding the risk of model failure under extreme conditions or non-dominant defect types. If the conditions are met, it calls model parameters based on high-enthalpy wind tunnel and flight test data, calibrated through hierarchical optimization. This endows the algorithm with high fidelity and multi-objective collaborative optimization capabilities under high-enthalpy real gas effects. This method achieves adaptive optimal matching of model parameters with varying operating conditions. By using a pre-calibrated model parameter roughness influence factor transport equation coupled with a transition intermittent factor coupling model, it solves the nonlinear dynamic process of roughness disturbance energy evolution and boundary layer transition from laminar to turbulent flow within the flow field. This yields high-precision prediction results of transition locations, achieving high fidelity and cross-condition portability in roughness-induced transition prediction under complex shapes and arbitrary roughness distributions. This overcomes the limitations of traditional empirical formulas, which have large prediction deviations for complex operating conditions. It enables refined and quantitative prediction of surface roughness-induced transition phenomena in hypersonic vehicles at an engineering-acceptable computational cost. This facilitates precise location of transition locations and high heat flux abrupt change zones, allowing for targeted optimization of heat protection material grades and localized thickening of heat protection coatings upstream of the transition, effectively avoiding over-design weight increase and the risk of heat protection failure. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating the method for predicting transition locations by coupling transport equations with transition intermittent factors provided by the present invention. Figure 2 This is a schematic diagram of the structure of the transition location prediction system that couples the transport equation with the transition intermittency factor provided by the present invention; Figure 3 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0023] Figure 1 This is a flowchart illustrating the transition location prediction method coupled with the transport equation and transition intermittency factor provided by the present invention, as shown below. Figure 1 As shown, the method includes the following: S11, obtain the input parameters, perform the Reynolds-averaged Navier-Stokes equations (RANS) basic flow field solution, and obtain the dimensionless roughness parameters; the input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and the roughness distribution parameters; S12, when the dimensionless roughness parameters are within the preset applicable range and the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects, the pre-calibrated model parameters that match the input parameters are called; the pre-calibrated model parameters are obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients based on high enthalpy wind tunnel transition test data or flight test data, with transition position error and peak heat flux error as objective functions; S13 uses the roughness influence factor transport equation and the transition intermittent factor coupled model, which calls the pre-calibrated model parameters, to solve the flow field corresponding to the input parameters, predict and output the transition position.

[0024] It should be noted that the following describes in detail the method for predicting transition locations by coupling the transport equation with the transition intermittent factor of the present invention.

[0025] Step S11: Obtain the input parameters and solve the Reynolds-averaged basic flow field to obtain the dimensionless roughness parameters; the input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and the roughness distribution parameters.

[0026] In this embodiment, obtaining input parameters and solving the Reynolds-mean-base flow field to obtain dimensionless roughness parameters includes: obtaining input parameters and solving the Reynolds-mean-base flow field based on the input parameters to obtain wall shear stress, friction velocity, and wall heat flux; and obtaining dimensionless roughness parameters based on wall shear stress, friction velocity, and roughness distribution parameters.

[0027] It should be added that the dimensionless roughness parameter is expressed as:

[0028]

[0029] in, Represents a dimensionless roughness parameter; Indicates the density at the wall surface; Indicates the viscosity at the wall surface; Indicates friction speed; The equivalent gravel height can be given in advance based on prior knowledge and actual design requirements, and is not further limited here; This represents the wall shear stress.

[0030] In addition, the three-dimensional shape can also be input in the form of a mesh, depending on the actual design requirements, and no further restrictions are made here; the incoming flow and wall conditions are used to characterize the undisturbed air parameters at a distance and whether the object surface is thermally insulating, slipping, etc.; the roughness distribution parameters are used to characterize the roughness of each location on the wall. In the actual design process, the roughness distribution parameters can include equivalent gravel height or morphology parameters.

[0031] In an optional embodiment, after obtaining the dimensionless roughness parameter, the method further includes: when the dimensionless roughness parameter is determined to be less than the lower limit of a preset applicable range, performing flow field separation state detection; the flow field separation state detection includes checking the sign of the wall shear stress, the separation state, and the definition of friction velocity; when the dimensionless roughness parameter is determined to be greater than the upper limit of a preset applicable range, saturating and limiting the dimensionless roughness parameter, the roughness excitation function constructed based on the dimensionless roughness parameter, and the distribution of roughness influence factors and outputting an out-of-range alarm; when the current wall defect type is determined to be an isolated cavity defect, combining it with a separation-induced transition model; wherein, the separation-induced transition model is obtained by introducing a cavity-induced generation term related to the instability intensity index into the intermittent factor transport equation, and the instability intensity index is generated by extracting the wall quantity based on the Reynolds-averaged basic flow field and constructing a characteristic function characterizing the instability intensity of the cavity separation shear layer.

[0032] It should be noted that by classifying and implementing measures based on dimensionless roughness parameters and defect types, the optimal allocation of computational resources and the global maximization of prediction accuracy are achieved, overcoming the blind spots in the applicability of a single physical model to cross-scale and cross-morphological flow problems.

[0033] Specifically, when the dimensionless roughness parameter is less than the lower limit of the preset applicable range, the flow field separation state detection is performed to accurately switch the calculation logic from roughness-dominated to viscosity-dominated, and to overcome the over-prediction distortion problem under small roughness conditions, thereby improving the physical reality of the flow field under small disturbance conditions.

[0034] When the dimensionless roughness parameter exceeds the upper limit of the preset applicable range, the distribution of the dimensionless roughness parameter, roughness excitation function, and roughness influence factor is saturated and limited, and an out-of-range alarm is output. This overcomes the problem of RANS equation iteration collapse and calculation divergence caused by the exponential amplification of mathematical model variables under extreme roughness, and solves the rigid defect of the program crashing directly due to out-of-range. This achieves forced fallback and system-level safety protection for flow field calculation under harsh working conditions.

[0035] When the current wall defect type is an isolated cavity defect, the separation-induced transition model is used in conjunction to solve the shortcomings of the traditional equivalent sand roughness model, which only considers normal disturbance, cannot capture the shear layer uplift inside the cavity, and has complex non-equilibrium mechanisms. It also overcomes the pain point that the high cost of high-precision direct numerical simulation (DNS) is too high to be used in engineering design, and realizes the accurate prediction of the transition start position induced by complex cavities under the RANS framework at low cost.

[0036] Step S12: If the dimensionless roughness parameters are within the preset applicable range and the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects, call the pre-calibrated model parameters that match the input parameters. The pre-calibrated model parameters are obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients based on high enthalpy wind tunnel transition test data or flight test data, with transition position error and peak heat flux error as objective functions.

[0037] In an optional embodiment, before calling the pre-calibrated model parameters that match the input parameters, the process includes: acquiring high-enthalpy wind tunnel transition test data or flight test data to form multiple sample operating conditions covering different ranges of dimensionless roughness parameters and Mach number and Reynolds number ranges; for each sample operating condition, using transition position error and peak heat flux error as objective functions, performing hierarchical optimization calibration on the source term coefficients and intermittent factor correction coefficients in the roughness influence factor transport equation to obtain pre-calibrated model parameters; wherein, the hierarchical optimization strategy includes first calibrating the source term coefficients of the roughness influence factor transport equation, and then calibrating the intermittent factor correction coefficients based on the calibrated source term coefficients; based on the calibration results, associating and storing the calibration coefficient sets corresponding to different cases with the corresponding sample operating conditions.

[0038] It should be added that the source term coefficients include the coefficients of the model to be calibrated. , and diffusion coefficient The intermittent factor correction coefficient includes the coefficients of the model to be calibrated. Initial value or inlet boundary value of roughness influence factor For details, please refer to the following text, which will not be repeated here. In addition, if quantitative prediction is required, the wind tunnel or flight high-fidelity calibration data should be expanded and the model coefficients should be redefined, or the model should be switched to a fully rough wall model, an isolated rough element model, a cavity model, a mutation defect-induced transition model, or a weighted coupling with the above models.

[0039] It should be noted that by forming multiple sample operating conditions, the problem of model distortion caused by the inability of conventional low-speed wind tunnel data at room temperature to truly reflect the real gas effects of hypersonic high enthalpy is addressed. This enables the calibration data source to cross over to extreme high-speed flight environments, improving the physical fidelity and representativeness of the underlying training dataset. For each sample operating condition, the source term coefficients and intermittent factor correction coefficients in the roughness influence factor transport equation are optimized and calibrated hierarchically, using transition position error and peak heat flux error as objective functions. This overcomes the blindness of traditional empirical models that rely solely on manual parameter tuning of a single aerodynamic parameter, leading to compromises and omissions among multiple objectives. The two most critical safety indicators in the aerospace field are used as anchor points for joint optimization, improving the scientific nature of model parameter calibration and the accuracy of multi-objective coordination. Furthermore, based on the calibration results, the calibration coefficients are associated and stored with the corresponding sample operating conditions, realizing a dynamic adaptive scheduling mechanism for model parameters. This enhances the engineering universality and retrieval efficiency of the roughness transition model in complex wide-speed domains and the entire roughness spectrum. In addition, after calibration, this method can reduce the error in predicting the transition position from about 50% in the traditional model to ≤15% under the condition of ablation of rough surfaces.

[0040] Step S13: Using the roughness influence factor transport equation and the transition intermittent factor coupled model with the pre-calibrated model parameters, the flow field corresponding to the input parameters is solved, and the transition position is predicted and output.

[0041] In this embodiment, the roughness influence factor transport equation and the transition intermittent factor coupled model, which call pre-calibrated model parameters, are used to solve the flow field corresponding to the input parameters, predict and output the transition position, including: constructing a roughness excitation function based on dimensionless roughness parameters, and solving the roughness influence factor transport equation in combination with the called pre-calibrated model parameters to obtain the roughness influence factor distribution of the entire field; coupling the roughness influence factor distribution to the Fu-Wang transition equation system, modifying the generation term of the transition intermittent factor and / or the transition initiation criterion, and performing coupled iterative solution using a preset convergence control strategy until the convergence condition is met, and outputting the predicted transition position and intermittent factor field.

[0042] It should be noted that by constructing a roughness excitation function based on dimensionless roughness parameters, the discrete, static geometrical abrupt changes of the wall are transformed into a continuous, dynamic energy source of spatial disturbance within the flow field. This enhances the physical realism and spatial resolution of the flow field evolution process under roughness disturbance. Furthermore, by combining this with pre-calibrated model parameters to solve the transport equation for the roughness influence factor, the three-dimensional continuous distribution of roughness disturbance energy within the entire flow field is accurately obtained. This overcomes the shortcomings of uncalibrated theoretical equations, which are prone to serious calculation biases and energy distortions under complex conditions across velocity domains and scales. It improves the quantitative characterization accuracy and adaptability of the underlying mathematical model to actual physical disturbances, thereby reducing the roughness influence factor distribution. By coupling the transition equations to the FW-W transition equations and modifying the generation term of the transition intermittent factor and the transition initiation criterion, a deep mathematical nesting of external wall geometric disturbances and internal flow transition nonlinear dynamics mechanisms is achieved. This addresses the inherent functional deficiency of the classical FW transition model, which is only applicable to smooth walls and completely lacks a triggering mechanism when facing rough walls. It enhances the dynamic response capability and mechanism integration of the macroscopic transition prediction system to complex surface defects, and then iteratively solves the problem to achieve a stable numerical solution of complex nonlinear equations and outputs upgraded results from a single transition point to the entire space transition transition zone. This improves the numerical robustness and engineering practical value of CFD calculations under hypersonic extreme conditions.

[0043] It should be added that the original Fu-Wang model contains the following three transport equations concerning the pulsating kinetic energy k, the unit dissipation rate ω of k, and the intermittent factor γ:

[0044]

[0045]

[0046] in, Indicates the mass density of the fluid; Indicates pulsating kinetic energy; Indicates time; Represents velocity vector In the Components on each coordinate; Representing spatial coordinates In the Components on each coordinate; Indicates molecular viscosity; Indicates the effective viscosity coefficient; This indicates a generated term, and the subscript indicates the corresponding turbulence variable. , The generated items; Indicates the unit dissipation rate; This represents the rate of dissipation of turbulent kinetic energy; Indicates constant coefficients; express Dissipation terms; Indicates a destructive item; express Dissipation terms; This indicates the intermittent factor.

[0047] Specifically, based on dimensionless roughness parameters, a roughness excitation function is constructed, including: based on dimensionless roughness parameters, combined with Mach number, Reynolds number and wall temperature, a roughness excitation function that monotonically increases with dimensionless roughness height is constructed.

[0048] It should be added that the roughness excitation function is expressed as:

[0049] in, Represents the roughness excitation function; Represents a function used to describe the intensity of the surface roughness. This represents a function used to describe compressibility. This represents a function used to respond to the high enthalpy effect; Represents the Mach number; Indicates wall temperature; The recovery temperature can be approximated by the total temperature at the outer edge of the boundary layer.

[0050] In addition, the distribution of roughness influence factors across the entire field is obtained, including: determining the generation term based on the transport equation coefficients in the pre-calibrated model parameters, combined with the roughness excitation function, the local strain rate scalar measure, and the near-wall distribution function; determining the dissipation term based on the transport equation coefficients in the pre-calibrated model parameters, combined with the current roughness influence factor and the local characteristic frequency; and solving the roughness influence factor transport equation based on the generation and dissipation terms to obtain the distribution of roughness influence factors across the entire field.

[0051] It should be added that the near-wall distribution function is used to characterize the dimensionless wall distance. The function is described; the local strain rate scalar measure is used to characterize the velocity gradient generated by the relative motion between adjacent flow layers during fluid flow; the local characteristic frequency is used to characterize the characteristic frequency of turbulent fluctuations in the flow field. Additionally, a transportable roughness influence factor is proposed. This allows the roughness effect to evolve along the flow direction and maintain extrapolability under complex shapes and distributed roughness conditions.

[0052] Furthermore, the transport equation for the roughness influence factor is expressed in a conserved form as follows:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] in, Indicates the mass density of the fluid; This represents the distribution of roughness influencing factors; Represents the velocity vector; Indicates molecular viscosity; Indicates turbulent viscosity or equivalent viscosity; Indicates the diffusion coefficient; Indicates a generating term; Represents dissipation terms; These represent the transport equation coefficients in the pre-calibrated model parameters; This represents a scalar measure of local strain rate; This represents the near-wall distribution function, used to confine the roughness effect to the near-wall region and achieve a smooth transition; Indicates dimensionless wall distance; Represents the strain rate tensor. , Represents velocity vector In the , Components on each coordinate; , Representing spatial coordinates In the , Components on each coordinate; These represent the transport equation coefficients in the pre-calibrated model parameters; Representing local characteristic frequencies, such as This ensures that the dissipation scale is consistent with the flow characteristics.

[0059] Furthermore, based on the generation and dissipation terms, the roughness influence factor transport equation is solved, including: based on the generation and dissipation terms, combined with physical limiting and boundary conditions, the roughness influence factor transport equation is solved; wherein, physical limiting is used to restrict the value of the roughness influence factor obtained by the solution to be between a first preset value and a preset maximum roughness influence factor; boundary conditions are used to restrict the roughness influence factor to be equal to the roughness excitation function at the wall boundary, or to adopt a zero gradient condition, and to set the roughness influence factor to a second preset value at the inlet and far-field boundaries.

[0060] It should be added that the boundary conditions can be in the form of Dirichlet or Robin, for example, they can be expressed as:

[0061] Alternatively, the boundary conditions can also be homogeneous Neumann boundary conditions, expressed as:

[0062] in, Represents the distribution of roughness influencing factors The value at the wall surface; Indicates the wall surface value; express Gradient at the wall; This represents the unit vector normal to the wall.

[0063] It should be noted that the first and second preset values ​​can be set according to actual design requirements and prior experience; for example, they can be 0. The preset maximum roughness influence factor can be taken as the maximum value of the calibration range or set adaptively according to the working conditions; no further limitations are made here. Additionally, by providing... A unified method for constructing source terms, dissipation terms, and boundary conditions is provided, along with physical limiting and asymptotic loading strategies to improve numerical stability.

[0064] Furthermore, physical limiting is also used to restrict the gradient of the roughness influence factor.

[0065] In addition, the roughness influence factor distribution is coupled to the Fu-Wang transition equation system to correct the generation term of the transition intermittent factor, including: obtaining the original intermittent factor generation term in the Fu-Wang transition equation system; constructing a roughness correction function based on the roughness influence factor distribution and the intermittent factor correction coefficient in the pre-calibrated model parameters; and using the roughness correction function to amplify and correct the original intermittent factor generation term.

[0066] It should be noted that by coupling with the Fu-Wang transition equation system and modifying the γ generation term and initial criterion, the roughness-induced transition can be quantitatively predicted, and a stable solution usable in engineering can be achieved through a unified solution process and convergence control. Compared with the traditional model, the prediction error of the transition position can be reduced from about 50% to ≤15%.

[0067] It should be added that the roughness correction function increases with the increase of the roughness influence factor, and degenerates into the original model when the roughness influence factor or the dimensionless roughness parameter is 0.

[0068] Furthermore, the corrected intermittent factor is expressed as:

[0069] in, This represents the corrected intermittent factor; Indicates the original intermittent factor; Represents the Reynolds number. Follow To increase the value, one can choose linear, power-law, or saturation-type functions, such as: or , This represents the initial value or inlet boundary value of the roughness influence factor, and through this correction, a quantitative enhancement of roughness on transition-induced factors is achieved, while maintaining the current... or It degenerates into the original model.

[0070] Furthermore, the roughness influence factor distribution is coupled to the Fu-Wang transition equation system to modify the generation term of the transition intermittent factor and the transition initiation criterion, including: obtaining the critical momentum-thickness Reynolds number used to determine the transition initiation in the Fu-Wang transition equation system; and reducing the critical momentum-thickness Reynolds number based on the roughness influence factor distribution so that the critical momentum-thickness Reynolds number decreases as the roughness increases.

[0071] It should be added that the corrected critical momentum thickness Reynolds number is expressed as:

[0072] in, This indicates the corrected critical momentum thickness Reynolds number; Indicates the critical momentum thickness Reynolds number; This represents the roughness transition influence coefficient.

[0073] Furthermore, the coupled solution can employ either loose coupling (step-by-step iteration) or strong coupling (same linearized system) methods. Loose coupling is preferred to adapt to existing RANS solver architectures, facilitating direct embedding into existing RANS solvers and aerodynamic-thermal design processes, thus supporting weight reduction and risk assessment of thermal protection systems. Specifically, the Reynolds-averaged basic flow field includes the flow field governing equations. A preset convergence control strategy is used to execute the coupled iterative solution, including: in each external iteration, step-by-step updates are performed according to the order of the Reynolds-averaged equations, the roughness influence factor transport equation, the transition intermittent factor equation, and the turbulence equation, with corresponding relaxation factors applied to the roughness influence factor and transition intermittent factor during the update process; an asymptotic loading strategy is used for the roughness conditions or roughness excitation functions at the wall boundaries, gradually increasing from the initial preset value to the target true value; during the iteration process, the residuals of the flow field governing equations are reduced to a set threshold, and the transition initiation position and the rate of change of peak heat flux are both less than a preset proportion as dual convergence criteria.

[0074] It should be noted that in each external iteration, by performing step-by-step updates as described above and applying corresponding relaxation factors to the roughness influence factor and transition interval factor respectively, the problem of excessive rigidity of the solution matrix and severe numerical oscillations caused by the cross-dependence of variables in various equations in a strongly coupled multiphysics system is overcome. This achieves decoupling and smooth transition between macroscopic variables and microscopic transition parameters of the flow field, improving the numerical stability and computational robustness of the complex nonlinear iterative process. By adopting an asymptotic loading strategy for the roughness condition or roughness excitation function at the wall boundary, the direct application of strong roughness perturbation is avoided in the early stages of computation when the flow field is not yet stable, thus preventing the flow field parameters from being affected. This addresses the problem of drastic abrupt changes causing computational instability, thereby achieving the gentle injection of roughness disturbance energy and adaptive taming of the flow field. This improves the fault tolerance of iterative calculations to extreme initial conditions and the success rate of convergence to a steady-state solution. By reducing the residuals of the flow field control equations to a set threshold during the iteration process and combining them with dual convergence criteria, the pseudo-convergence phenomenon that may occur when relying solely on mathematical residuals to determine convergence is overcome. This solves the convergence discrimination problem caused by the extreme sensitivity of physical quantities to disturbances in hypersonic transition prediction, and thus achieves dual closed-loop verification of mathematical accuracy and engineering physical accuracy, improving the reliability of transition location prediction results and aerodynamic thermal environment calculation results.

[0075] In an alternative embodiment, the equivalent gravel height is input as a distributed rough slab or cone example. The distribution and incoming flow conditions were analyzed using the Fu-Wang transition model, and the solution was obtained according to the method described above. The transition location was determined and calibrated by analyzing the wind tunnel heat flux distribution. The results show that, compared to not considering the transition conditions... The coupled baseline model exhibits significantly reduced transition position errors and stable convergence.

[0076] In an optional embodiment, the arc wind tunnel ablation morphology data is converted into an equivalent model using a case study of ablation of a rough surface with a complex shape. Distribution, Construction And apply boundary conditions to the wall, using a progressive loading strategy to gradually increase the load. To reach the target level, ensure the convergence of the coupled solution, and output the transition surface and peak heat flux location to provide a basis for local reinforcement of thermal protection.

[0077] In an alternative embodiment, in conjunction with the high enthalpy real gas effect, in the RANS solution of high-temperature real gases (including dissociation / recombination), or Non-equilibrium correction terms (such as those characterized by enthalpy or Damköhler number) can be introduced to maintain model consistency under high enthalpy conditions. This embodiment does not change the core protection scope of the present invention.

[0078] In summary, this invention, through solving the Reynolds-averaged basic flow field based on the acquired input parameters, obtains dimensionless roughness parameters. This accurately reflects the basic flow field data that reflects the complex three-dimensional geometric effects of hypersonic flight and the characteristics of the real gas thermal environment. It automatically extracts key dimensionless parameters characterizing the roughness effect from complex flow field variables, achieving a parameterized mapping from macroscopic flight conditions to microscopic roughness disturbances. Based on the obtained dimensionless roughness parameters, it determines whether the model meets the calling criteria, accurately identifying the applicable boundaries of the model and avoiding the risk of model failure under extreme conditions or non-dominant defect types. When the criteria are met, it calls model parameters based on high-enthalpy wind tunnel and flight test data, calibrated through hierarchical optimization. This endows the algorithm with high fidelity and multi-objective collaborative optimization capabilities under high-enthalpy real gas effects, enabling model parameters to adapt to varying operating conditions. The adaptive optimal matching method utilizes a coupled model of roughness influence factor transport equation and transition intermittent factor, which calls pre-calibrated model parameters, to solve the nonlinear dynamic process of roughness disturbance energy evolution and boundary layer transition from laminar to turbulent flow within the flow field. This yields high-precision prediction results of transition locations, achieving high fidelity and cross-condition portability in roughness-induced transition prediction under complex shapes and arbitrary roughness distributions. This overcomes the limitation of traditional empirical formulas having large prediction deviations for complex conditions, enabling refined and quantitative prediction of surface roughness-induced transition phenomena in hypersonic vehicles at an engineering-acceptable computational cost. This facilitates precise location of transition locations and high heat flux abrupt change zones, allowing for targeted optimization of heat protection material grades and localized thickening of heat protection coating layouts upstream of the transition, effectively avoiding over-design weight increase and the risk of heat protection failure.

[0079] The following describes the transition location prediction system coupled with the transport equation and the transition intermittency factor provided by the present invention. The transition location prediction system coupled with the transport equation and the transition intermittency factor described below can be referred to in correspondence with the transition location prediction method coupled with the transport equation and the transition intermittency factor described above.

[0080] Figure 2 A schematic diagram of a transition location prediction system coupled with a transport equation and a transition intermittency factor is shown. The system includes: The parameter acquisition module 21 acquires the input parameters, performs Reynolds-averaged basic flow field solution, and obtains dimensionless roughness parameters. The input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and the roughness distribution parameters. The parameter calling module 22 determines that the dimensionless roughness parameters are within the preset applicable range, and that the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects. Then, it calls the pre-calibrated model parameters that match the input parameters. The pre-calibrated model parameters are obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients based on high enthalpy wind tunnel transition test data or flight test data, with transition position error and peak heat flux error as objective functions. The position prediction module 23 uses the roughness influence factor transport equation and the transition intermittent factor coupled model, which calls the pre-calibrated model parameters, to solve the flow field corresponding to the input parameters, predict and output the transition position.

[0081] It should be noted that the specific principles of the embodiments of the present invention are the same as those of the above method embodiments. For details, please refer to the method embodiments above. More detailed explanations will not be repeated here.

[0082] Figure 3 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 3 As shown, the electronic device may include: a processor 310, a communications interface 320, a memory 330, and a communications bus 340, wherein the processor 310, the communications interface 320, and the memory 330 communicate with each other through the communications bus 340. The processor 310 can call logic instructions in the memory 330 to execute a transition location prediction method coupled with the transport equation and the transition intermittent factor. This method includes: acquiring input parameters, solving the Reynolds-averaged basic flow field to obtain dimensionless roughness parameters; the input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and roughness distribution parameters; determining that the dimensionless roughness parameters are within a preset applicable range, and that the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects, and then calling pre-calibrated model parameters that match the input parameters; the pre-calibrated model parameters are obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients based on high-enthalpy wind tunnel transition test data or flight test data, with transition location error and peak heat flux error as objective functions; and using the roughness influence factor transport equation coupled with the transition intermittent factor model that calls the pre-calibrated model parameters to solve the flow field corresponding to the input parameters, predicting and outputting the transition location.

[0083] Furthermore, the logical instructions in the aforementioned memory 330 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0084] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the transition position prediction method coupled with the transport equation and transition intermittent factor provided by the above methods. The method includes: acquiring input parameters, solving the Reynolds-averaged basic flow field, and obtaining dimensionless roughness parameters; the input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and the roughness distribution parameters; and determining that the dimensionless roughness parameters are within a preset applicable range. When the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects, the pre-calibrated model parameters that match the input parameters are invoked. The pre-calibrated model parameters are obtained by hierarchical optimization and calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients based on high-enthalpy wind tunnel transition test data or flight test data, with transition position error and peak heat flux error as objective functions. The roughness influence factor transport equation and transition intermittent factor coupled model that invokes the pre-calibrated model parameters are used to solve the flow field corresponding to the input parameters, predict and output the transition position.

[0085] Furthermore, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, this computer program implements a method for predicting the transition location by coupling the transport equations and transition intermittent factors provided by the methods described above. This method includes: acquiring input parameters; solving the Reynolds-averaged basic flow field to obtain dimensionless roughness parameters; the input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and roughness distribution parameters; determining that the dimensionless roughness parameters are within a preset applicable range, and that the current wall defect type is not isolated. When concave cavities, abrupt steps, or large-scale separation defects are dominant, pre-calibrated model parameters that match the input parameters are invoked. The pre-calibrated model parameters are obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients based on high-enthalpy wind tunnel transition experimental data or flight test data, with transition position error and peak heat flux error as objective functions. The roughness influence factor transport equation and transition intermittent factor coupled model, which invokes the pre-calibrated model parameters, is used to solve the flow field corresponding to the input parameters, predict and output the transition position.

[0086] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0087] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting transition locations by coupling transport equations with transition intermittency factors, characterized in that, include: Obtain the input parameters, perform Reynolds-averaged basic flow field solution, and obtain the dimensionless roughness parameters; The input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and the roughness distribution parameters; the Reynolds-averaged basic flow field includes the flow field governing equations. When the dimensionless roughness parameter is determined to be within a preset applicable range, and the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects, a pre-calibrated model parameter matching the input parameter is invoked. The pre-calibrated model parameter is obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficient and the intermittent factor correction coefficient based on high enthalpy wind tunnel transition test data or flight test data, with transition position error and peak heat flux error as objective functions. By using the roughness influence factor transport equation coupled with the transition intermittent factor model with the pre-calibrated model parameters, the flow field corresponding to the input parameters is solved, and the transition position is predicted and output, including: Based on the dimensionless roughness parameters, a roughness excitation function is constructed, and combined with the pre-calibrated model parameters, the roughness influence factor transport equation is solved to obtain the roughness influence factor distribution across the entire field. The roughness influence factor distribution is coupled to the Fu-Wang transition equation system, the generation term of the transition intermittent factor and / or the transition initiation criterion are modified, and a preset convergence control strategy is used to perform coupled iterative solution, including: In each external iteration, the equations are updated step by step in the order of Reynolds-averaged equation, roughness influence factor transport equation, transition intermittent factor equation and turbulence equation, and corresponding relaxation factors are applied to the roughness influence factor and transition intermittent factor respectively during the update process. A progressive loading strategy is adopted for the roughness conditions or roughness excitation functions at the wall boundary, gradually increasing them from the initial preset value to the target true value; During the iteration process, the residuals of the flow field control equations are reduced to a set threshold, and the transition start position and the rate of change of peak heat flux are both less than a preset ratio as dual convergence criteria; Until the convergence condition is met, output the predicted transition position and intermittent factor field; Before invoking the pre-calibrated model parameters that match the input parameters, the process includes: Acquire high-enthalpy wind tunnel transition test data or flight test data to form multiple sample operating conditions covering different ranges of dimensionless roughness parameters as well as Mach number and Reynolds number ranges; For each of the aforementioned sample operating conditions, with the transition position error and peak heat flux error as objective functions, the source term coefficients and intermittent factor correction coefficients in the roughness influence factor transport equation are subjected to hierarchical optimization calibration to obtain the pre-calibrated model parameters; wherein, the hierarchical optimization strategy includes first calibrating the source term coefficients of the roughness influence factor transport equation, and then calibrating the intermittent factor correction coefficients based on the calibrated source term coefficients; Based on the calibration results, the calibration coefficient sets corresponding to different situations are associated and stored with the corresponding sample working conditions.

2. The method for predicting transition locations by coupling transport equations with transition intermittency factors according to claim 1, characterized in that, The distribution of roughness influence factors across the entire field is obtained, including: Based on the transport equation coefficients in the pre-calibrated model parameters, and in combination with the roughness excitation function, the local strain rate scalar measure, and the near-wall distribution function, the generating term is determined; Based on the transport equation coefficients in the pre-calibrated model parameters, and combined with the current roughness influence factor and local feature frequency, the dissipation term is determined; Based on the generation term and the dissipation term, the roughness influence factor transport equation is solved to obtain the roughness influence factor distribution across the entire field.

3. The method for predicting transition locations by coupling transport equations with transition intermittency factors according to claim 2, characterized in that, Based on the generation term and the dissipation term, the roughness influence factor transport equation is solved, including: Based on the generation term and the dissipation term, and in combination with physical limiting and boundary conditions, the roughness influence factor transport equation is solved. The physical limiting is used to restrict the value of the roughness influence factor obtained by the solution to be between a first preset value and a preset maximum roughness influence factor. The boundary conditions are used to restrict the roughness influence factor to be equal to the roughness excitation function at the wall boundary, or to adopt a zero gradient condition, and to set the roughness influence factor to a second preset value at the inlet and far-field boundaries.

4. The method for predicting transition locations by coupling transport equations with transition intermittency factors according to claim 1, characterized in that, The roughness influence factor distribution is coupled to the Fu-Wang transition equation system, and the generation term of the transition intermittent factor is modified, including: Obtain the original intermittent factor generating terms in the symbol-Wang transition equation system; Based on the roughness influence factor distribution and the intermittent factor correction coefficient in the pre-calibrated model parameters, a roughness correction function is constructed; The roughness correction function is used to amplify and correct the original intermittent factor generation term.

5. The method for predicting transition locations by coupling transport equations with transition intermittency factors according to claim 1, characterized in that, The roughness influence factor distribution is coupled to the Fu-Wang transition equation system, and the generation term of the transition intermittent factor and the transition initiation criterion are modified, including: Obtain the critical momentum-thickness Reynolds number used to determine the onset of transition in the aforementioned symbol-Wang transition equation set; Based on the roughness influence factor distribution, the critical momentum thickness Reynolds number is reduced and corrected so that the critical momentum thickness Reynolds number decreases as the roughness increases.

6. The method for predicting transition locations by coupling transport equations with transition intermittency factors according to claim 1, characterized in that, After obtaining the dimensionless roughness parameters, the following steps are also included: When the dimensionless roughness parameter is determined to be less than the lower limit of the preset applicable range, flow field separation state detection is performed; the flow field separation state detection includes checking the sign of wall shear stress, separation state, and friction velocity definition; When the dimensionless roughness parameter is determined to be greater than the upper limit of the preset applicable range, the dimensionless roughness parameter, the roughness excitation function constructed based on the dimensionless roughness parameter, and the roughness influence factor distribution are saturated and limited, and an out-of-range alarm is output. When the current wall defect type is determined to be an isolated cavity defect, it is used in conjunction with the separation-induced transition model. The separation-induced transition model is obtained by introducing a cavity-induced generation term related to the instability intensity index into the intermittent factor transport equation. The instability intensity index is generated by extracting the wall quantity based on the Reynolds-averaged basic flow field and constructing a characteristic function that characterizes the instability intensity of the cavity separation shear layer.

7. A transition location prediction system coupling transport equations with transition intermittency factors, characterized in that, include: The parameter acquisition module acquires input parameters, performs Reynolds-averaged basic flow field calculation, and obtains dimensionless roughness parameters; the input parameters include the three-dimensional shape of the aircraft, the incoming flow and wall conditions, and the roughness distribution parameters. The parameter calling module determines that the dimensionless roughness parameter is within a preset applicable range, and that the current wall defect type is not dominated by isolated cavities, abrupt steps, or large-scale separation defects. Then, it calls the pre-calibrated model parameters that match the input parameters. These pre-calibrated model parameters are obtained by hierarchical optimization calibration of the roughness influence factor transport equation coefficients and intermittent factor correction coefficients, using high-enthalpy wind tunnel transition test data or flight test data, with transition position error and peak heat flux error as objective functions. The location prediction module uses the roughness influence factor transport equation coupled with the transition intermittent factor coupled model, which calls the pre-calibrated model parameters, to solve the flow field corresponding to the input parameters, predict and output the transition location; The Reynolds-averaged basic flow field includes the flow field governing equations; the location prediction module is used for: Based on the dimensionless roughness parameters, a roughness excitation function is constructed, and combined with the pre-calibrated model parameters, the roughness influence factor transport equation is solved to obtain the roughness influence factor distribution across the entire field. The roughness influence factor distribution is coupled to the Fu-Wang transition equation system, the generation term of the transition intermittent factor and / or the transition initiation criterion are modified, and a preset convergence control strategy is used to perform coupled iterative solution, including: In each external iteration, the equations are updated step by step in the order of Reynolds-averaged equation, roughness influence factor transport equation, transition intermittent factor equation and turbulence equation, and corresponding relaxation factors are applied to the roughness influence factor and transition intermittent factor respectively during the update process. A progressive loading strategy is adopted for the roughness conditions or roughness excitation functions at the wall boundary, gradually increasing them from the initial preset value to the target true value; During the iteration process, the residuals of the flow field control equations are reduced to a set threshold, and the transition start position and the rate of change of peak heat flux are both less than a preset ratio as dual convergence criteria; Until the convergence condition is met, output the predicted transition position and intermittent factor field; The system is also used for: Before calling the pre-calibrated model parameters that match the input parameters, high enthalpy wind tunnel transition test data or flight test data are obtained to form multiple sample working conditions covering different ranges of dimensionless roughness parameters as well as Mach number and Reynolds number ranges. For each of the aforementioned sample operating conditions, with the transition position error and peak heat flux error as objective functions, the source term coefficients and intermittent factor correction coefficients in the roughness influence factor transport equation are subjected to hierarchical optimization calibration to obtain the pre-calibrated model parameters; wherein, the hierarchical optimization strategy includes first calibrating the source term coefficients of the roughness influence factor transport equation, and then calibrating the intermittent factor correction coefficients based on the calibrated source term coefficients; Based on the calibration results, the calibration coefficient sets corresponding to different situations are associated and stored with the corresponding sample working conditions.

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