A hypersonic transition and forced motion coupled dynamic derivative prediction method

Abstract

The application provides a hypersonic transition and forced motion coupled dynamic derivative prediction method, and belongs to the technical field of aerospace data processing. The method comprises the following steps: based on a standard Reynolds shear stress transport turbulence model framework, an intermittent factor transport equation and a transition starting momentum thickness Reynolds number transport equation are used to construct an initial transition model; the transport equation of the initial transition model is firstly corrected, and according to the compressible boundary layer theory and the cross-flow correlation, the initial transition model is corrected in terms of compressibility and cross-flow effect, so that a corrected transition model is obtained; rigid dynamic mesh technology is used to perform coupled calculation on the corrected transition model and forced vibration, so that unsteady aerodynamic force and moment are obtained; and integral method is used to identify the unsteady aerodynamic force and moment, so that a prediction combined dynamic derivative is obtained. The application has full-dimensional dynamic derivative analysis capability, breaks through the speed domain limit, and realizes full coverage of subsonic or transonic or supersonic to hypersonic working conditions.

Description

Technical Field

[0001] This invention belongs to the field of aerospace data processing technology, and particularly relates to a method for predicting the dynamic derivative of hypersonic transition and forced motion coupling. Background Technology

[0002] Boundary layer transition refers to the process by which fluid within the boundary layer changes from laminar to turbulent flow. This phenomenon involves complex fluid dynamics mechanisms; the process is influenced by multiple factors, significantly affecting flow characteristics, aerodynamic forces, torque distribution, and heat transfer characteristics. Aircraft dynamic characteristics refer to the way an aircraft's motion state changes over time when subjected to external disturbances or control inputs. The dynamic derivative is an aerodynamic parameter describing the dynamic characteristics of an aircraft, representing the rate of change of aerodynamic forces and torques with respect to motion parameters (such as angular velocity and angular acceleration) during unsteady motion. It is a crucial parameter for evaluating the dynamic stability of an aircraft. As a core parameter in the design of aircraft aerodynamic dynamic characteristics, the dynamic derivative plays a key role in trajectory planning and motion stability assessment. This parameter is not only a fundamental aerodynamic indicator for evaluating aircraft dynamic performance but also the original basis for constructing control systems; its accurate prediction directly affects the reliability of aircraft design and performance evaluation. Prior to the 1990s, the prediction of dynamic derivatives mainly relied on empirical and semi-empirical methods, such as modified Newtonian theory, Nevorticon flow theory, Newton-Boltzmann theory, and modified shock-expansion wave theory. After the 1990s, with the rapid development of computational fluid dynamics (CFD) technology and computer hardware, methods based on numerically solving the Euler or Navier-Stokes equations to obtain dynamic derivatives gradually became mainstream. Scholars both domestically and internationally have conducted in-depth research on methods for obtaining dynamic derivatives through numerical simulation of forced or free oscillation processes.

[0003] Previous flight tests and wind tunnel experiments have shown that boundary layer transition significantly affects the dynamic characteristics of aircraft, causing phenomena such as pitch instability. In the 1960s, researchers observed that when an aircraft has an angle of attack, the transition positions on the leeward and windward sides exhibit an asymmetrical distribution, and this asymmetry is closely related to the angle of attack; this phenomenon is called asymmetric transition. In the 1970s, with in-depth research on slender reentry vehicles, it was discovered that during reentry, boundary layer transition flow leads to significant anomalies in the cone's motion. This discovery prompted the academic community to focus on the asymmetric transition phenomenon and its impact on the aerodynamic characteristics of aircraft.

[0004] Research on the impact of transition on aircraft dynamic characteristics started relatively early in China, and current researchers mainly focus on... Using a blunt cone model as the research object, a single-degree-of-freedom aerodynamic free-axis vibration experiment was conducted in a wind tunnel at Ma=6. The study focused on the coupling effect between the unsteady aerodynamic forces of the boundary layer transition region shifting back and forth during model rotation around the pitch axis and the aircraft motion. The results show that the coupling effect between dynamic transition and pitch motion may lead to a decrease in the pitch stability of the blunt cone aircraft. Existing researchers have used the cone angle... Taking Mach 6 flow at a pointed cone as the research object, the influence of transition on the static / dynamic stability of the pointed cone under different Reynolds numbers and angles of attack was studied through forced vibration dynamic derivative measurement experiments. The results show that asymmetric transition is the fundamental cause of changes in the static or dynamic stability of the pointed cone, and is closely related to the position of the transition region relative to the center of mass. Currently, there is a lack of numerical simulation methods for calculating the dynamic derivative of an aircraft by coupling a transition model with forced vibration. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a method for predicting the dynamic derivative of hypersonic transition and forced motion coupling. This method solves the problems of low accuracy in calculating unsteady aerodynamic loads, poor dynamic derivative analysis capabilities, speed domain limitations, and difficulty in achieving full coverage of subsonic, transonic, supersonic, and hypersonic operating conditions in existing numerical simulation methods for aircraft dynamic derivatives.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: a method for predicting the dynamic derivative of hypersonic transition and forced motion coupling, comprising the following steps:

[0007] S1. Based on the standard Reynolds shear stress transport turbulence model framework, an initial transition model is constructed using the intermittent factor transport equation and the transition initial momentum thickness Reynolds number transport equation.

[0008] S2. The transport equations of the initial transition model are initially modified, and the compressibility and crossflow effects of the initial transition model are modified according to the compressible boundary layer theory and crossflow correlation to obtain the modified transition model.

[0009] S3. Using rigid dynamic mesh technology, coupled calculations are performed on the modified transition model and forced vibration to obtain unsteady aerodynamic forces and moments;

[0010] S4. Based on pitch forced motion, the unsteady aerodynamic forces and torques are identified using the integral method to obtain the predicted combined dynamic derivatives.

[0011] The beneficial effects of this invention are as follows: By establishing an initial transition model, this invention makes the improved transition model applicable to hypersonic boundary layer transition models. It applies dynamic mesh technology to achieve coupled calculation of the transition model and forced vibration, enabling the model to generate multi- or single-degree-of-freedom steady-state vibrations while maintaining preset frequency and amplitude parameters. Combined with parameter identification algorithms, it obtains predicted combined dynamic derivatives. This enables the dynamic derivative prediction method to have full-dimensional dynamic derivative analysis capabilities, breaking through velocity domain limitations and achieving full coverage of subsonic, transonic, supersonic, and hypersonic operating conditions.

[0012] By describing small-amplitude pitch vibrations using rigid dynamic mesh technology, the modified transition model and forced vibration are coupled for calculation. The rigid dynamic mesh technology achieves separation of mesh and motion. Throughout the motion, the relative positions between mesh nodes remain unchanged, thus eliminating the need to regenerate new meshes and effectively ensuring mesh quality. Furthermore, it eliminates the need to calculate additional physical quantities such as mesh deformation, significantly reducing the computational load.

[0013] Further, S1 includes the following steps:

[0014] S101. Based on the standard Reynolds shear stress transport turbulence model framework, and by fitting experimental data, the intermittent factor transport equation and the momentum-thickness Reynolds number transport equation at the transition initiation position are obtained.

[0015] S102. Using the transport equation of transition initial momentum thickness Reynolds number, obtain the separation intermittent factor, and use the intermittent factor transport equation to obtain the effective intermittent factor;

[0016] S103. Using the effective intermittent factor, the turbulent kinetic energy transport equation in the standard Reynolds shear stress transport turbulence model is modified to obtain the initial transition model.

[0017] Furthermore, the expression for the initial transition model is as follows:

[0018] ;

[0019] ;

[0020] ;

[0021] in, Indicates density, This represents the kinetic energy of turbulent fluctuations. Represents a time variable. Represents the velocity component. Represents spatial variables, Indicates the molecular viscosity coefficient. Represents model constants. Represents the turbulent eddy viscosity coefficient. This represents the generating term of the modified turbulent kinetic energy transport equation. This represents the dissipation term in the modified turbulent kinetic energy transport equation. Indicates the effective intermittent factor. This represents the generating term of the turbulent kinetic energy transport equation in the original Standard Reynolds shear stress transport turbulence model. This represents the dissipation term in the turbulent kinetic energy transport equation of the original Standard Reynolds shear stress transport turbulence model. Indicates the intermittent factor. This indicates the separation of intermittent factors.

[0022] The beneficial effects of the above-mentioned further solutions are as follows: By adding the intermittent factor transport equation and the momentum-thickness-Reynolds number transport equation at the beginning of the transition to the standard Reynolds shear stress transport turbulence model framework, the present invention obtains an initial transition model, making the numerical simulation data of the transition more accurate and having a higher degree of fit with the actual model.

[0023] Furthermore, S2 includes the following steps:

[0024] S201. By controlling the length of the transition zone, the transport equation of the initial transition model is initially modified, and the local variables are calculated using engineering methods.

[0025] S202. Based on the compressible boundary layer theory and local variables, a compressible boundary layer correlation function is constructed to analyze the relationship between the pressure gradient parameter and the Mach number, obtain the pressure gradient parameter correction, and introduce the compressible correction into the transition initial momentum thickness Reynolds number transport equation to obtain the compressible correction transition model.

[0026] S203. Based on the crossflow correlation and local variables, construct the crossflow correlation function, and by modifying the model constants and local variables in the crossflow correlation function, perform crossflow effect correction on the compressible correction transition model to obtain the corrected transition model.

[0027] Furthermore, in step S201, the length of the transition region is controlled by a transition region length function, the expression of which is shown below:

[0028] ;

[0029] ;

[0030] in, The function representing the length of the transition region. This represents the viscous sublayer damping function. Represents the wall vortex Reynolds number. Indicates density, Indicates the distance along the normal direction of the wall. Indicates the turbulent specific dissipation rate. This represents the molecular viscosity coefficient.

[0031] Furthermore, the expression for the compressible boundary layer correlation function is as follows:

[0032] ;

[0033] ;

[0034] in, This represents the compressible boundary layer correlation function. Represents the vortex Reynolds number. This represents the critical momentum thickness Reynolds number. Represents a local function. and Both represent local variables. Indicates the wall temperature. , , All of these represent fixed parameters.

[0035] Furthermore, the expression for the cross-flow correlation function is as follows:

[0036] ;

[0037] in, Represents the cross-flow correlation function. Represents the crossflow intensity term. Represents model constants.

[0038] The beneficial effects of the above-mentioned further solutions are as follows: By modifying the control transition region length function of the initial transition model and using the local variables calculated by engineering methods, the present invention transforms the initial transition model into a transition model with new criteria applicable to hypersonic transition prediction, thereby improving the accuracy of dynamic derivative prediction.

[0039] Based on the compressible boundary layer theory, the original pressure gradient parameters were corrected by analyzing the relationship between the pressure gradient parameters and the Mach number. The compressibility correction was added to the calculation of the original transition initiation momentum thickness Reynolds number, thus realizing the compressibility correction of the transition model. By constructing a crossflow correlation function and correcting the model constants and local variables, the crossflow effect correction of the transition model was realized, thereby improving the prediction accuracy of the hypersonic transition of the transition model.

[0040] Furthermore, step S4 includes the following steps:

[0041] S401. Based on pitch forced motion and body coordinate system, set the form of forced motion around the center of mass, and obtain the first and second derivatives of pitch angle;

[0042] S402. Based on the preset classical dynamic aerodynamic model, and the angle of attack of the forced motion form, Taylor expansion is performed to obtain the aerodynamic model after Taylor expansion.

[0043] S403. Substitute the first and second derivatives of the pitch angle into the aerodynamic model expanded by Taylor, retain the linear terms, obtain the predicted aerodynamic model, and record the coefficient expressions.

[0044] S404. Based on the coefficient expression, using the integral method, by integrating the predicted aerodynamic model over one period, the unsteady aerodynamic forces and torques are identified, and the predicted combined dynamic derivatives are obtained.

[0045] Furthermore, the expression for the predicted aerodynamic model is as follows:

[0046] ;

[0047] in, This indicates a predictive aerodynamic model. This indicates a pre-defined classical dynamic aerodynamic model. This represents the aerodynamic model expanded by Taylor. Indicates pitch angle, This represents the first derivative of the pitch angle. This represents the second derivative of the pitch angle. Indicates the reduction frequency. Indicates the pitch oscillation amplitude. Represents a time variable.

[0048] Furthermore, the expression for the predicted combined dynamic derivative is as follows:

[0049] ;

[0050] ;

[0051] in, Represents the dynamic derivative of the combined static moment. The sinusoidal weighted periodic integral representing the pitch moment. Represents the dynamic derivative of combined damping. The cosine-weighted periodic integral representing the pitch moment. Indicates the initial time of integration. Indicates the periodic time.

[0052] The beneficial effects of the above-mentioned further solutions are as follows: This invention uses the integral method as the parameter identification algorithm to dynamically identify and predict the combined dynamic derivative, thereby reducing the probability of prediction error. It adopts periodic integration, in which the integral term is linearly related to the oscillation amplitude. The integration is constructed using the orthogonality of trigonometric functions to separate the aerodynamic signal from high-frequency noise in the frequency domain. Furthermore, it eliminates the dependence on the initial state through periodic integration, thereby improving computational efficiency and prediction accuracy. Attached Figure Description

[0053] Figure 1 This is a flowchart of the method of the present invention.

[0054] Figure 2 This is a simulation diagram of the blunt cone standard model in this embodiment.

[0055] Figure 3 This is a schematic diagram of the geometry and computational mesh of the blunt cone model in this embodiment.

[0056] Figure 4 The diagram shows the flow field structure at different moments during the blunt cone transition in this embodiment.

[0057] Figure 5 This is a comparison chart of the calculation results and experimental results in this embodiment.

[0058] Figure 6 This is a graph showing the changes in angle of attack and torque in this embodiment.

[0059] Figure 7 This is a hysteresis loop diagram showing the laminar flow and transition pitch moment coefficients versus angle of attack in this embodiment. Detailed Implementation

[0060] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0061] Before describing this embodiment, the following terms will be explained:

[0062] SST turbulence model framework: Standard Reynolds shear stress transport turbulence model framework;

[0063] Etkin aerodynamic model: a model used to describe the aerodynamic hysteresis effect in the dynamic motion of aircraft;

[0064] Blasius boundary layer: an incompressible boundary layer on a flat plate when there is no pressure gradient;

[0065] CFD: Computational Fluid Dynamics.

[0066] Example 1

[0067] like Figure 1 As shown, this invention provides a method for predicting the dynamic derivative of hypersonic transition and forced motion coupling, the implementation method of which is as follows:

[0068] S1. Based on the standard Reynolds shear stress transport turbulence model framework, an initial transition model is constructed using the intermittent factor transport equation and the transition initial momentum thickness Reynolds number transport equation. The specific steps are as follows:

[0069] S101. Based on the standard Reynolds shear stress transport turbulence model framework, and by fitting experimental data, the intermittent factor transport equation and the momentum-thickness Reynolds number transport equation at the transition initiation position are obtained.

[0070] S102. Using the transport equation of transition initial momentum thickness Reynolds number, obtain the separation intermittent factor, and use the intermittent factor transport equation to obtain the effective intermittent factor;

[0071] S103. Using the effective intermittent factor, the turbulent kinetic energy transport equation in the standard Reynolds shear stress transport turbulence model is modified to obtain the initial transition model.

[0072] In this embodiment, the initial transition model is γ. The Reθ transition model, based on the SST turbulence model framework, adds two additional transport equations: the intermittent factor transport equation and the momentum-thickness-Reynolds number transport equation at the transition initiation point. These two transport equations are obtained by fitting experimental data, and their specific expressions are shown below:

[0073] ;

[0074] ;

[0075] in, Indicates density, Indicates the intermittent factor. Represents a time variable. Represents the velocity component. Represents spatial variables, Indicates the molecular viscosity coefficient. Represents the turbulent eddy viscosity coefficient. and All represent model constants. This represents the generating term of the intermittent factor transport equation. This represents the dissipation term in the intermittent factor transport equation. This indicates the momentum-thickness Reynolds number at the initial position of the transition. The generating term of the transport equation represents the momentum-thickness Reynolds number at the initial position of the transition;

[0076] The generating term of the intermittent factor transport equation and dissipation terms The expression is as follows:

[0077] ;

[0078] ;

[0079] in, This function represents the length of the transition region and is used to control the length of the transition region. The magnitude of the strain rate tensor. This represents the switch function that triggers the transition. Represents the vorticity tensor. Indicates the control intermittent factor The dissipation function, , , , All represent model constants;

[0080] The generating term of the momentum-thickness Reynolds number transport equation at the transition initiation position. The expression is as follows:

[0081] ;

[0082] in, This indicates a fixed parameter of 0.03. The Reynolds number represents the new transitional momentum thickness in a free flow. This represents the boundary layer indicator factor. Its value is 1 when inside the boundary layer and 0 when outside the boundary layer. This parameter is used to turn off... The source terms of the transport equation are only allowed to diffuse within the boundary layer.

[0083] In this embodiment, the separation intermittent factor γ is obtained using the transition initial momentum thickness Reynolds number transport equation. The Reθ transition model predicts the flow-induced separation by using a separation intermittent factor, and the effective intermittent factor is obtained using the intermittent factor transport equation; the expression for the separation intermittent factor is shown below:

[0084] ;

[0085] in, This represents a constant, which can be adjusted. The size of the value is used to adjust the model's sensitivity to separation-induced transition. Represents the vortex Reynolds number. This represents the critical momentum thickness Reynolds number. This indicates the function to be separated and then reattached.

[0086] The expression for the effective interval factor is as follows:

[0087] ;

[0088] Using the effective intermittency factor to modify the generating terms of the turbulent kinetic energy transport equation in the original SST turbulence model and dissipation terms The model is then modified to couple with the SST turbulence mode, resulting in an initial transition model. The expression for the initial transition model is shown below:

[0089] ;

[0090] ;

[0091] in, This represents the kinetic energy of turbulent fluctuations. This represents the generating term of the modified turbulent kinetic energy transport equation. This represents the dissipation term in the modified turbulent kinetic energy transport equation. Represents model constants;

[0092] Specific dissipation rate in the original SST turbulence model The transport equation is expressed as follows:

[0093] ;

[0094] in, Indicates the turbulent specific dissipation rate. This represents the generating term in the specific dissipation rate transport equation. This represents the dissipation term in the specific dissipation rate transport equation. This represents the mixing function, which is 1 within the boundary layer and 0 for free flow. and All of these represent model constants.

[0095] S2. The transport equations of the initial transition model are initially modified, and based on the compressible boundary layer theory and crossflow correlation, the initial transition model is modified for compressibility and crossflow effects to obtain the modified transition model. The specific steps are as follows:

[0096] S201. By controlling the length of the transition zone, the transport equation of the initial transition model is initially modified, and the local variables are calculated using engineering methods.

[0097] S202. Based on the compressible boundary layer theory and local variables, a compressible boundary layer correlation function is constructed to analyze the relationship between the pressure gradient parameter and the Mach number, obtain the pressure gradient parameter correction, and introduce the compressible correction into the transition initial momentum thickness Reynolds number transport equation to obtain the compressible correction transition model.

[0098] In this embodiment, for γ The transport equations of the Reθ transition model were modified to provide new criteria applicable to hypersonic transition prediction. By controlling the length of the transition region, the initially modified γ was obtained. Reθ transition model; through The transition region length function controls the length of the transition region, and its expression is shown below:

[0099] ;

[0100] ;

[0101] in, This represents the viscous sublayer damping function. Represents the wall vortex Reynolds number. Indicates the distance along the normal direction of the wall;

[0102] Local variables were calculated using engineering methods. and local variables The nonlocal Mach number at the outer edge of the boundary layer is determined. .

[0103] In this embodiment, the initially corrected γ The Reθ transition model undergoes compressibility correction. Based on compressible boundary layer theory and local variables, a high-speed boundary layer local correlation function based on the self-similar solution of the compressible boundary layer is constructed, and the specific expression is shown below:

[0104] ;

[0105] ;

[0106] in, This represents the compressible boundary layer correlation function. Represents the vortex Reynolds number. This represents the critical momentum thickness Reynolds number. Represents a local function. and Both represent local variables. Indicates the wall temperature. , , Both represent parameters calculated from local variables, and their calculation expressions are shown below:

[0107]

[0108] Based on the compressible boundary layer theory, by analyzing the relationship between the pressure gradient parameter and the Mach number, the following expression for the correction of the pressure gradient parameter is obtained:

[0109] ;

[0110] in, This represents the corrected pressure gradient parameters. Original pressure gradient parameters, This indicates the specific heat ratio; in this embodiment, it is taken as 1.4.

[0111] At the original transition initial momentum thickness Reynolds number The calculation incorporates a compressibility correction, resulting in the corrected original transition initial momentum thickness Reynolds number. Thus, a compressible and corrected transition model is obtained;

[0112] The expression for the compressibility correction is as follows:

[0113] ;

[0114] ;

[0115] in, This represents the corrected original transition initial momentum thickness Reynolds number. This represents the initial momentum thickness Reynolds number of the original transition.

[0116] S203. Based on the crossflow correlation and local variables, construct the crossflow correlation function, and by modifying the model constants and local variables in the crossflow correlation function, perform crossflow effect correction on the compressible correction transition model to obtain the corrected transition model.

[0117] In this embodiment, crossflow correlation is based on the concept of local helicity, which is widely used as a crossflow indicator in models based on local correlation. The crossflow correlation function is constructed, and its expression is as follows:

[0118] ;

[0119] in, Represents the cross-flow correlation function. Represents the crossflow intensity term. The model constant is calibrated to 28.0 in noisy environments and 28.0 in quiet environments (free-flow turbulence intensity). (much less than 0.1%) was calibrated to 45.0; the expression for the crossflow intensity term is constructed as follows:

[0120] ;

[0121] ;

[0122] ;

[0123] in, The dimensionless crossflow intensity can be defined by local helicity. Indicates the magnitude of the local velocity. Indicates the distance along the normal direction of the wall. Indicates local helicity;

[0124] By modifying the model constants and local variables in the crossflow correlation function, the crossflow effect is corrected on the compressible transition model, resulting in the corrected transition model.

[0125] The initial function of the modified transition model is defined as follows:

[0126] ;

[0127] in, This indicates the primary transition trigger function. This represents the fourth-power enhancement term of the primary trigger function. This indicates a strengthening of the transition criterion. Represents the turbulence shielding function. This represents the switch function that triggers the transition, and is the final transition start function.

[0128] S3. Using rigid dynamic mesh technology, the modified transition model and forced vibration are coupled and calculated to obtain unsteady aerodynamic forces and moments.

[0129] In this embodiment, rigid dynamic mesh technology is used to describe small-amplitude pitch vibration, thereby realizing the coupled calculation of the modified transition model and forced vibration to obtain unsteady aerodynamic forces and moments;

[0130] The idea behind rigid dynamic meshing is to rigidly connect the computational mesh to the physical object's shape, allowing them to move together. Using solvers from computational fluid dynamics, unsteady aerodynamic forces and moments are calculated. Compared to unstructured mesh reconstruction techniques, which require significant computational resources and are time-consuming and labor-intensive (e.g., sliding meshing requires constructing different sliding surfaces and generating different meshes when simulating different types of motion), this approach offers a more efficient solution.

[0131] For large-scale calculations under various working conditions, the rigid dynamic mesh technique offers significant advantages: Throughout the unsteady calculation process, the mesh does not need to be regenerated, it is simple and applicable to motion of any magnitude, and the mesh topology remains unchanged during unsteady motion. Therefore, it eliminates the need to generate different meshes for different motion types, achieving separation of mesh and motion. In other words, the relative positions between mesh nodes remain constant throughout the entire motion process, thus eliminating the need to regenerate a new mesh and effectively ensuring mesh quality. Furthermore, since it eliminates the need to calculate additional physical quantities such as mesh deformation, the computational load is significantly reduced. This is particularly advantageous for numerical simulations of boundary layer transition coupled with forced motion.

[0132] S4. Based on pitch forced motion, the unsteady aerodynamic forces and torques are identified using the integral method to obtain the predicted combined dynamic derivatives. The specific steps are as follows:

[0133] S401. Based on pitch forced motion and body coordinate system, set the form of forced motion around the center of mass, and obtain the first and second derivatives of pitch angle;

[0134] S402. Based on the preset classical dynamic aerodynamic model, and the angle of attack of the forced motion form, Taylor expansion is performed to obtain the aerodynamic model after Taylor expansion.

[0135] S403. Substitute the first and second derivatives of the pitch angle into the aerodynamic model expanded by Taylor, retain the linear terms, obtain the predicted aerodynamic model, and record the coefficient expressions.

[0136] S404. Based on the coefficient expression, using the integral method, by integrating the predicted aerodynamic model over one period, the unsteady aerodynamic forces and torques are identified, and the predicted combined dynamic derivatives are obtained.

[0137] In this embodiment, based on pitch forced motion, the integral method is used to identify unsteady aerodynamic torques and obtain the predicted combined dynamic derivatives; the preset classical dynamic aerodynamic model is the Etkin classical dynamic aerodynamic model.

[0138] The pitch damping derivative is the total damping derivative of the pitch channel, and is a combined derivative that includes the direct damping derivative. and the derivative of the time difference of the washing flow It directly reflects the dynamic stability of the pitch channel, and is referred to in engineering as... For static derivative, The pitch damping derivative;

[0139] The identification using the integral method can employ the single-point method, the integral method, and the least squares method.

[0140] In the body-axis coordinate system, the forced motion form (dimensionless form) around the center of mass is set as follows:

[0141] ;

[0142] ;

[0143] in, Indicates the angle of action. Indicates pitch angle, Indicates the reduction frequency. Indicates the angular frequency of oscillation. Indicates the reference length. Indicates the incoming flow velocity;

[0144] Then, by differentiating the pitch angle, we obtain the first and second derivatives of the pitch angle, whose expressions are shown below:

[0145] ;

[0146] in, This represents the first derivative of the pitch angle. This represents the second derivative of the pitch angle. This represents the pitch oscillation amplitude. Considering the longitudinal motion of the aircraft, if the magnitude of the center of mass velocity is kept constant, according to the Etkin classic dynamic aerodynamic model, its expression is as follows:

[0147] ;

[0148] in, express The pitch moment coefficient at any given moment. This represents the derivative of the pitch moment coefficient with respect to the angle of attack. Represents a time variable. express The change in angle of attack relative to the equilibrium position at any given moment. express The change in the rate of change of angle of attack relative to the equilibrium position at any given time. express The change in pitch angular velocity relative to the equilibrium position at any given time. express The change in the rate of change of pitch angular velocity relative to the equilibrium position at any given moment;

[0149] Furthermore, a Taylor expansion is performed on the angle of attack based on the forced motion form, resulting in the Taylor-expanded aerodynamic model, expressed as follows:

[0150] ;

[0151] in, , The subscript 0 indicates the angle of attack. The value at that location.

[0152] In this embodiment, the aerodynamic model expanded by Taylor can also be written as:

[0153] ;

[0154] in, Defined as angle of attack The pitch static derivative at that point, Defined as the pitch derivative. Defined as the second-order term of the pitch motion derivative, and substituting the expressions for the first and second derivatives of the pitch angle into the aerodynamic model after Taylor expansion, while retaining the linear terms, the predicted aerodynamic model is obtained, and the coefficient expressions are recorded; the expression of the predicted aerodynamic model is as follows:

[0155] ;

[0156] in, This indicates a predictive aerodynamic model. This indicates a pre-defined classical dynamic aerodynamic model. This represents the aerodynamic model expanded by Taylor;

[0157] The expression for the recording coefficient is:

[0158] ;

[0159] Furthermore, by using the integral method, the unsteady aerodynamic forces and torques are identified by integrating the predicted aerodynamic model over one period, and the predicted combined dynamic derivatives are obtained.

[0160] The expression for the predicted combination dynamic derivative is as follows:

[0161] ;

[0162] ;

[0163] in, Represents the dynamic derivative of the combined static moment. The sinusoidal weighted periodic integral representing the pitch moment. Represents the dynamic derivative of combined damping. The cosine-weighted periodic integral representing the pitch moment. Indicates the initial time of integration. Indicates the periodic time;

[0164] This indicates a preset classical dynamic aerodynamic model, used as a torque coefficient in the prediction. After simulation, the solver can directly output specific values. Due to forced motion, the angle of attack varies between -2 and +2, and a torque coefficient can be output for each angle of attack, thus obtaining... With angle of attack The changing curve function is integrated to obtain the longitudinal combined dynamic derivative from the unsteady aerodynamic forces and torques; the aerodynamic forces and torques are dimensionless, and the torque coefficient and aerodynamic force coefficient are used in the prediction.

[0165] This embodiment provides a method for predicting the dynamic derivative of hypersonic transition and forced motion coupling. The transition model used is based on the correlation between low-speed wind tunnel experiments and the Blasius boundary layer, establishing a γ-ray... An improved Reθ transition model is applied to hypersonic boundary layer transition. Dynamic mesh technology is then used to couple the transition model with forced vibration calculations, enabling the model to generate multi / single-degree-of-freedom steady-state vibrations while maintaining preset frequency and amplitude parameters. Numerical simulations yield response data for each degree of freedom, which, combined with a parameter identification algorithm, allows for the acquisition of dynamic stability derivatives. Comparison between numerical calculations and experiments demonstrates the method's high accuracy. Corresponding to forced vibration methods in wind tunnel testing, the CFD method with dynamic parameter identification represents a feasible technical path for calculating dynamic derivatives. This method achieves accurate calculation of unsteady aerodynamic loads by setting forced vibration conditions with parameters such as amplitude and frequency.

[0166] Example 2

[0167] In this embodiment, as Figure 2 and Figure 3 As shown, the calculation model uses the HSCM-3 blunt cone standard model specified in GJB-4399-2002, and its geometric characteristic parameters are: half cone angle. Cone length L =421 mm, base diameter =148.3 mm, head radius =8.75 mm. This configuration has typical blunt tip characteristics, with a bluntness ratio of... =0.118, the model's centroid is located at the cone length =64%. The reference cone length is L =0.421 m. The reference area is the bottom cross-sectional area S=0.0173. Calculation conditions: at Mach number =6, forced vibration amplitude A=2°, dimensionless reduced frequency is taken as =0.1, where Calculation yields =37.2Hz, calculation time step=0.0001, internal iteration 50 steps; under the above conditions, dynamic transition and laminar dynamic comparison calculations were carried out, and the calculation conditions are shown in Table 1.

[0168] Table 1

[0169]

[0170] In Table 1, Case represents a calculation example. Re ∞ / m represents the unit Reynolds number. AOA Indicates angle of attack. T ∞ K represents the incoming flow temperature. Tu ∞ ,% indicates turbulent flow intensity.

[0171] In this embodiment, as Figure 4 As shown, the Mach number and intermittent factor calculation results of the flow field at different times in the transition model are displayed. The Mach number contour map of the symmetry plane at t=0s shows the intermittent factor distribution on the wall. Under the action of high Mach number and strong compression effect airflow, a significant detached bow-shaped shock wave structure will form at the blunt leading edge. The times t=0.079s and t=0.124s correspond to the pitch forced motion at the angle of attack, respectively. and By comparing the flow fields at different angles of attack, it was found that the wall streamlines were curved under non-zero angle of attack conditions, resulting in a significant crossflow effect. Furthermore, the crossflow-induced transition could also be observed from the distribution of the wall intermittent factor.

[0172] In this embodiment, lateral flow is the key controlling factor inducing boundary layer transition in the blunt-nosed cone, such as... Figure 5 As shown, the comparison results of wall heat flux distribution at t=0.229 s under laminar and transition states are presented. The numerical calculation results and experimental observation data show a high degree of agreement at the transition front location (deviation <2%), effectively verifying the reliability of the dynamic transition model and the coupled solution method of forced motion. Figure 6 As shown, the curves of angle of attack and pitching moment versus time reveal significant unsteady dynamic characteristics: within the same period, there is a significant phase lag between the trough of the angle of attack and the peak moment calculated by the transition model, while the phase lag between the peak moment calculated by the laminar flow is relatively small. This difference mechanism essentially reflects the transient effects in the process of flow separation and vortex structure evolution. Figure 7As shown, the combined dynamic derivative analysis based on the integral resolution method indicates that the hysteresis loops of the pitch moment coefficient in both laminar and transition conditions exhibit a counterclockwise rotation characteristic. According to aeroelasticity theory, the rotation direction of the loop determines the sign of the dynamic derivative, while the enclosing area characterizes its numerical magnitude. Quantitative comparison shows that the hysteresis loop area in the transition condition is reduced by approximately 35.55% compared to the laminar state, and its ellipticity parameter decreases from 1.25 to 0.92. This change in geometric characteristics reveals that the boundary layer transition process induced by lateral flow significantly weakens the pitch damping characteristics of the aircraft.

[0173] The static stability derivative and dynamic stability derivative obtained by the integral method are shown in Table 2.

[0174] Table 2

[0175]

[0176] It can be seen that the coupling effect of crossflow-induced transition and pitch channel forced motion leads to a decrease in the static / dynamic stability of the blunt cone. This is consistent with the conclusions obtained in the experiment, and further proves the correctness of the calculation method for the coupling of dynamic transition and forced motion in this paper.

Claims

1. A method for predicting the dynamic derivative of hypersonic transition and forced motion coupling, characterized in that, Includes the following steps: S1. Based on the standard Reynolds shear stress transport turbulence model framework, an initial transition model is constructed using the intermittent factor transport equation and the transition initial momentum thickness Reynolds number transport equation. S2. The transport equations of the initial transition model are initially modified, and based on the compressible boundary layer theory and crossflow correlation, the initial transition model is modified for compressibility and crossflow effects, resulting in the modified transition model, specifically: S201. By controlling the length of the transition zone, the transport equation of the initial transition model is initially modified, and the local variables are calculated using engineering methods. S202. Based on the compressible boundary layer theory and local variables, a compressible boundary layer correlation function is constructed to analyze the relationship between the pressure gradient parameter and the Mach number, obtain the pressure gradient parameter correction, and introduce the compressible correction into the transition initial momentum thickness Reynolds number transport equation to obtain the compressible correction transition model. By the original transition initial momentum thickness Reynolds number The calculation incorporates a compressibility correction, resulting in the corrected original transition initial momentum thickness Reynolds number. Thus, a compressible and corrected transition model is obtained; The expression for the compressibility correction is as follows: in, This represents the corrected original transition initial momentum thickness Reynolds number. Indicates the initial momentum thickness Reynolds number at the original transition; S203. Based on the crossflow correlation and local variables, construct the crossflow correlation function, and by modifying the model constants and local variables in the crossflow correlation function, perform crossflow effect correction on the compressible correction transition model to obtain the corrected transition model. The initial function of the modified transition model is defined as follows: in, This represents the compressible boundary layer correlation function. Represents the vortex Reynolds number. This represents the critical momentum thickness Reynolds number. Represents a local function. and Both represent local variables. Indicates the wall temperature. Represents the cross-flow correlation function. Represents the crossflow intensity term. Represents model constants. This indicates the primary transition trigger function. This represents the fourth-power enhancement term of the primary trigger function. This indicates a strengthening of the transition criterion. Represents the turbulence shielding function. Represents the turbulent Reynolds number. This represents the switch function that triggers the transition. , , All represent fixed parameters; S3. Using rigid dynamic mesh technology, coupled calculations are performed on the modified transition model and forced vibration to obtain unsteady aerodynamic forces and moments; S4. Based on pitch forced motion, the unsteady aerodynamic forces and torques are identified using the integral method to obtain the predicted combined dynamic derivatives.

2. The method for predicting the dynamic derivative of hypersonic transition and forced motion coupling according to claim 1, characterized in that, S1 includes the following steps: S101. Based on the standard Reynolds shear stress transport turbulence model framework, and by fitting experimental data, the intermittent factor transport equation and the momentum-thickness Reynolds number transport equation at the transition initiation position are obtained. S102. Using the transport equation of transition initial momentum thickness Reynolds number, obtain the separation intermittent factor, and use the intermittent factor transport equation to obtain the effective intermittent factor; S103. Using the effective intermittent factor, the turbulent kinetic energy transport equation in the standard Reynolds shear stress transport turbulence model is modified to obtain the initial transition model.

3. The method for predicting the dynamic derivative of hypersonic transition and forced motion coupling according to claim 2, characterized in that, The expression for the initial transition model is as follows: in, Indicates density, This represents the kinetic energy of turbulent fluctuations. Represents a time variable. Represents the velocity component. Represents spatial variables, Indicates the molecular viscosity coefficient. Represents model constants. Represents the turbulent eddy viscosity coefficient. This represents the generating term of the modified turbulent kinetic energy transport equation. This represents the dissipation term in the modified turbulent kinetic energy transport equation. Indicates the effective intermittent factor. This represents the generating term of the turbulent kinetic energy transport equation in the original Standard Reynolds shear stress transport turbulence model. This represents the dissipation term in the turbulent kinetic energy transport equation of the original Standard Reynolds shear stress transport turbulence model. Indicates the intermittent factor. This indicates the separation of intermittent factors.

4. The method for predicting the dynamic derivative of hypersonic transition and forced motion coupling according to claim 1, characterized in that, In step S201, the length of the transition region is controlled by a transition region length function, the expression of which is as follows: in, The function representing the length of the transition region. This represents the viscous sublayer damping function. Represents the wall vortex Reynolds number. Indicates density, Indicates the distance along the normal direction of the wall. Indicates the turbulent specific dissipation rate. This represents the molecular viscosity coefficient.

5. The method for predicting the dynamic derivative of hypersonic transition and forced motion coupling according to claim 1, characterized in that, S4 includes the following steps: S401. Based on pitch forced motion and body coordinate system, set the form of forced motion around the center of mass, and obtain the first and second derivatives of pitch angle; S402. Based on the preset classical dynamic aerodynamic model, and the angle of attack of the forced motion form, Taylor expansion is performed to obtain the aerodynamic model after Taylor expansion. S403. Substitute the first and second derivatives of the pitch angle into the aerodynamic model expanded by Taylor, retain the linear terms, obtain the predicted aerodynamic model, and record the coefficient expressions. S404. Based on the coefficient expression, using the integral method, by integrating the predicted aerodynamic model over one period, the unsteady aerodynamic forces and torques are identified, and the predicted combined dynamic derivatives are obtained.

6. The method for predicting the dynamic derivative of hypersonic transition and forced motion coupling according to claim 5, characterized in that, The expression for the predictive aerodynamic model is as follows: in, This indicates a predictive aerodynamic model. This indicates a pre-defined classical dynamic aerodynamic model. This represents the aerodynamic model expanded by Taylor. Indicates pitch angle, This represents the first derivative of the pitch angle. This represents the second derivative of the pitch angle. Indicates the reduction frequency. Indicates the pitch oscillation amplitude. Represents a time variable.

7. The method for predicting the dynamic derivative of hypersonic transition and forced motion coupling according to claim 6, characterized in that, The expression for the predicted combination dynamic derivative is as follows: in, Represents the dynamic derivative of the combined static moment. The sinusoidal weighted periodic integral representing the pitch moment. Represents the dynamic derivative of combined damping. The cosine-weighted periodic integral representing the pitch moment. Indicates the initial time of integration. Indicates the periodic time.

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