A numerical simulation method for the multi-axis angular motion of a rotating projectile

Abstract

This invention belongs to the field of aerodynamics technology for rotating projectiles, specifically relating to a numerical simulation method for the multi-axis angular motion of a rotating projectile. Based on the projectile's external shape model, a spherical flow field mesh is generated, dividing the mesh into an inner and outer domain. Data is transferred via interpolation at the interface. The global computational domain is used to calculate the steady-state flow field. After flow field convergence, the steady-state flow field parameters are used as the initial flow field for multi-axis angular motion simulation. Multi-axis angular motion modeling is performed on the inner domain mesh, obtaining the coordinates of the inner domain mesh nodes at different times. Multi-axis angular motion simulation is then achieved, including unsteady flow field calculations. The flow field simulation is realized through sliding mesh technology and mesh dynamic motion technology. This invention solves the difficult problems of multi-axis angular motion modeling, complex motion mesh implementation, and complex flow simulation, and streamlines the multi-axis angular motion simulation process, providing a reference for engineering applications.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamics technology of rotating projectiles, and specifically relates to a numerical simulation method for the multi-axis angular motion of a rotating projectile. Background Technology

[0002] Low-cost guided missiles simplify their control systems by rotating around their longitudinal axis, achieving pitch and yaw control through a single channel while reducing trajectory dispersion caused by eccentric effects from mass, thrust, and aerodynamics. However, when an axisymmetric missile rotates at a certain angle of attack, the combined effects of the missile's rotational speed and crossflow cause the flow structure to become symmetrical about the plane of attack, inducing additional lateral forces and yaw moments, known as the Magnus effect. Although the lateral force is only 1 / 100 to 1 / 10 of the normal force, the yaw moment always causes the missile to swing out of the plane of attack, disrupting flight stability. Furthermore, disturbances during flight cause the missile to undergo circular motion around its velocity vector, manifesting as precession, nutation, and conical motion. These series of rotations around the missile's axis are collectively referred to as multi-axis angular motion. Multi-axis angular motion leads to increased drag, reduced range, increased dispersion, and even instability.

[0003] Current aerodynamic research primarily focuses on single-degree-of-freedom rotational motion, obtaining flow mechanisms for the Magnus effect induced by the shape of the projectile-body, wing-body, and canard-body-tail combination. These mechanisms mainly include boundary layer displacement and thickness asymmetric distortion, asymmetric flow separation, asymmetric transition, the impact of asymmetric vortex shedding on the tail fin from the forebody's leeward side, the hindering effect of the projectile body on the wing root flow, and canard washout interference. Numerical simulations of multi-axis angular motion of projectiles and rockets are not addressed. Furthermore, current flight stability studies typically use linear or cubic nonlinear aerodynamic models to represent external loads, meaning the aerodynamic characteristics are usually based on steady-state conditions or only rotational motion, without considering the effects of multi-axis angular motion, resulting in discrepancies with actual flight processes.

[0004] Since lateral force and yaw moment are small quantities, obtaining accurate lateral force and yaw moment is a difficult problem that needs to be overcome in related research and development. At present, engineering studies generally use flight tests or wind tunnel tests, which are difficult to guarantee accuracy; and in existing numerical studies, projectiles and rockets usually only perform rotational motion, and numerical simulation of multi-axis angular motion processes is still very difficult. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] The technical problem to be solved by this invention is: how to provide a numerical simulation method suitable for multi-axis angular motion of a rotating projectile, which solves the difficult problems of multi-axis angular motion modeling, complex motion mesh implementation, and complex motion flow simulation, and streamlines the multi-axis angular motion simulation process to facilitate engineering applications.

[0007] (II) Technical Solution

[0008] To address the aforementioned technical problems, this invention provides a numerical simulation method for the multi-axis angular motion of a rotating projectile, comprising the following steps:

[0009] Step 1: Based on the rotating projectile shape model, generate a spherical flow field mesh, divide the mesh into an inner domain and an outer domain, and use the sliding mesh technique to interpolate and transfer data at the interface between the inner and outer domains.

[0010] Step 2: Based on the flight conditions, use the global computational domain to calculate the steady state flow field. After the flow field converges, use the steady flow field parameters as the initial flow field for multi-axis angular motion simulation.

[0011] Step 3: Perform multi-axis angular motion modeling for the inner domain mesh, and obtain the coordinates of the inner domain mesh nodes at different times through coordinate transformation based on the initial flight attitude;

[0012] Step 4: Based on grid dynamic motion technology, realize the unsteady simulation calculation of multi-axis angular motion; realize the simulation of flow field by solving fluid control equations; realize the simulation of motion through internal grid motion;

[0013] Step 5: Once the simulation termination condition is met, the calculation is terminated.

[0014] In step one, the mesh size at the interface between the inner and outer domain meshes is the same.

[0015] In step one, the height of the first layer of mesh must be maintained near the rotating bullet wall.

[0016] In step one, the mesh generation tools used include Gambit, ICEM, Pointwise, and HyperMesh.

[0017] In step one, the mesh is a hexahedral structure mesh.

[0018] In step two, the fluid control equation is the Reynolds-averaged Navier-Stokes equation, and a steady-state algorithm is used to obtain the steady flow field under different flight conditions.

[0019] In step two, the solvers used include Fluent, CFD++, and CFX.

[0020] In step three, based on the initial flight attitude, mathematical modeling of multi-axis angular motion is carried out on the inner domain grid, involving composite transformations of motion between the inertial coordinate system, the quasi-projectile coordinate system, the projectile coordinate system, the nutation coordinate system, and the precession coordinate system, in order to obtain the coordinates of the inner domain grid nodes at different times.

[0021] In step four, when using the grid dynamic motion technology, a custom program is written based on the mathematical model of multi-axis angular motion. At the same time, the initial values ​​of the coordinates of the inner domain grid nodes are stored separately and repeatedly called in each calculation time step to realize the simulation of motion. Furthermore, the unsteady Reynolds-averaged Navier-Stokes equations are combined to simulate the complex motion flow field around the flow field.

[0022] The method addresses the challenges of multi-axis angular motion modeling, complex motion mesh implementation, and complex motion flow simulation, and streamlines the multi-axis angular motion simulation process for easier engineering applications.

[0023] (III) Beneficial Effects

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] (1) Compared with the traditional method of using steady calculation or single-degree-of-freedom rotation calculation to obtain the aerodynamic characteristics of the projectile, the present invention innovatively adopts the method of multi-axis angular motion modeling. That is, for the inner domain grid (including the coordinates of the projectile surface nodes), the coordinate transformation is performed according to the initial flight attitude to obtain the coordinates of the inner domain grid nodes at different times, thereby obtaining a mathematical model that represents the multi-axis angular motion, which is closer to the motion characteristics in the actual flight process.

[0026] (2) In the simulation calculation of multi-axis angular motion, the mesh dynamic motion technology is used. On the one hand, a custom program is written for the mathematical model of multi-axis angular motion, and on the other hand, the initial values ​​of the coordinates of the inner domain mesh nodes are stored separately and repeatedly called in each calculation time step, thereby realizing the simulation of motion. It solves the difficult problems of multi-axis angular motion modeling, complex motion mesh implementation, and complex motion flow simulation, and sorts out the multi-axis angular motion simulation process, providing a reference for engineering applications. Attached Figure Description

[0027] Figure 1 Flowchart for simulating the multi-axis angular motion of a rotating projectile;

[0028] Figure 2 This is a diagram showing the spatial grid and computational domain partitioning of the flow field.

[0029] Figure 3 A mathematical model diagram of multi-axis angular motion;

[0030] Figure 4 A flowchart for the programming of a mathematical model of multi-axis angular motion;

[0031] Figure 5-1 and Figure 5-2 This is a schematic diagram of the trajectory of the projectile axis within the cross-section of the projectile body.

[0032] Figure 5-1 A schematic diagram of the trajectory of the spring shaft at different precession angles; Figure 5-2 This is a schematic diagram of the trajectory of the spring shaft at different precession speeds.

[0033] Figure 6-1 and Figure 6-2 This is a graph showing the transient aerodynamic coefficients of a projectile / launch.

[0034] Figure 6-1 This is a schematic diagram of the transient normal force coefficient. Figure 6-2 This is a schematic diagram of the transient lateral force coefficient. Detailed Implementation

[0035] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0036] To address the aforementioned technical problems, this invention provides a numerical simulation method for the multi-axis angular motion of a rotating projectile, comprising the following steps:

[0037] Step 1: Based on the rotating projectile shape model, generate a spherical flow field mesh, divide the mesh into an inner domain and an outer domain, and use the sliding mesh technique to interpolate and transfer data at the interface between the inner and outer domains.

[0038] Step 2: Based on the flight conditions, use the global computational domain to calculate the steady state flow field. After the flow field converges, use the steady flow field parameters as the initial flow field for multi-axis angular motion simulation.

[0039] Step 3: Perform multi-axis angular motion modeling for the inner domain mesh, and obtain the coordinates of the inner domain mesh nodes at different times through coordinate transformation based on the initial flight attitude;

[0040] Step 4: Based on grid dynamic motion technology, realize the unsteady simulation calculation of multi-axis angular motion; realize the simulation of flow field by solving fluid control equations; realize the simulation of motion through internal grid motion;

[0041] Step 5: Once the simulation termination condition is met, the calculation is terminated.

[0042] In step one, the mesh size at the interface between the inner and outer domain meshes is the same.

[0043] In step one, the height of the first layer of mesh must be maintained near the rotating bullet wall.

[0044] In step one, the mesh generation tools used include Gambit, ICEM, Pointwise, and HyperMesh.

[0045] In step one, the mesh is a hexahedral structure mesh.

[0046] In step two, the fluid control equation is the Reynolds-averaged Navier-Stokes equation, and a steady-state algorithm is used to obtain the steady flow field under different flight conditions.

[0047] In step two, the solvers used include Fluent, CFD++, and CFX.

[0048] In step three, based on the initial flight attitude, mathematical modeling of multi-axis angular motion is carried out on the inner domain grid, involving composite transformations of motion between the inertial coordinate system, the quasi-projectile coordinate system, the projectile coordinate system, the nutation coordinate system, and the precession coordinate system, in order to obtain the coordinates of the inner domain grid nodes at different times.

[0049] In step four, when using the grid dynamic motion technology, a custom program is written based on the mathematical model of multi-axis angular motion. At the same time, the initial values ​​of the coordinates of the inner domain grid nodes are stored separately and repeatedly called in each calculation time step to realize the simulation of motion. Furthermore, the unsteady Reynolds-averaged Navier-Stokes equations are combined to simulate the complex motion flow field around the flow field.

[0050] The method addresses the challenges of multi-axis angular motion modeling, complex motion mesh implementation, and complex motion flow simulation, and streamlines the multi-axis angular motion simulation process for easier engineering applications.

[0051] Example 1

[0052] like Figure 1 As shown, the numerical simulation method for the multi-axis angular motion of a rotating projectile includes the following steps:

[0053] Based on the rotating projectile's shape model, the flow field space mesh is divided, defining inner and outer domains. The mesh size at the interface between the inner and outer domains remains consistent. Figure 2 As shown. When the inner domain moves, data transfer between the inner and outer domain meshes is achieved through interpolation using the sliding mesh technique at the interface. The height of the first mesh layer near the rotating projectile wall needs to satisfy the dimensionless wall distance y. + ~1. The meshing tool used can be Gambit, ICEM, Pointwise, or HyperMesh, and the mesh generated should be a hexahedral structure mesh.

[0054] Based on the flight conditions, the flow field was calculated using the global computational domain and a steady-state algorithm. After the flow field converged, these flow field parameters were used as the initial flow field for the multi-axis angular motion simulation. The fluid control equations were Reynolds-averaged Navier-Stokes equations.

[0055]

[0056] In the formula, W is the conserved variable, F is the inviscid flux, G is the viscous flux, and H is the source term. The solver used can be Fluent, CFD++, or CFX.

[0057] Multi-axis angular motion modeling is carried out, and the mathematical model is as follows: Figure 3 As shown. During numerical simulation, it is necessary to obtain the grid node coordinates in the inertial coordinate system at different times. Coordinate transformation involves the inertial coordinate system (i.e., the geodetic coordinate system OXYZ), the quasi-projectile coordinate system (i.e., the projectile axis is the X-axis, the Y-axis is always perpendicular to the X-axis and pointing upwards in the plane of attack, and the Z-axis is determined by the right-hand rule; this coordinate system does not rotate with the projectile's spin), and the projectile coordinate system (the difference from the quasi-projectile coordinate system is that this system rotates with the projectile's spin, with a relative rotation angle of θ). s Nutting coordinate system (with OQ as the X-axis, the coordinate system rotates with the nutation motion, with a relative rotation angle of θ). n ), Precession coordinate system (with OP as the X-axis, the coordinate system rotates with the precession motion, the rotation angle being θ). p The relative relationships between them. The grid node coordinates at different times can be obtained from the initial node coordinate values:

[0058]

[0059] Wherein, coordinate transformation matrix The transformation relationship between the initial coordinate values ​​and the quasi-projectile coordinate system, T s To define the transformation relationship between the quasi-projectile coordinate system and the projectile coordinate system. This represents the transformation relationship between the projectile coordinate system and the nutation coordinate system. The transformation relationship between the nutation coordinate system and the precession coordinate system is established. From this, the mathematical expression for the multi-axis angular motion of the rotating projectile is obtained. Further motion is applied to the inner domain mesh to simulate the multi-axis angular motion.

[0060] In the previous step, applying motion to the inner domain mesh requires the use of mesh dynamic motion technology. This involves writing a custom program for the mathematical model of multi-axis angular motion, and storing the initial coordinates of the inner domain mesh nodes separately and repeatedly calling them at each computation time step. The flowchart of the multi-axis angular motion mathematical model is shown below. Figure 4 As shown. Further simulations of complex motion around the flow field are performed using Reynolds-averaged Navier-Stokes equations. The simulation terminates when the termination condition is met.

[0061] The multi-axis angular motion simulation process proposed in this patent was used to simulate the multi-axis angular motion of a projectile-rocket model. The effects of precession angle and precession speed on motion and force characteristics were studied. The calculation conditions are shown in Table 1, with a total of 8 conditions. The time step was set to Δt = 0.00002s, and the calculation stopped after one complete precession cycle.

[0062] Table 1 Calculation Operating Condition Statistics

[0063]

[0064] Figure 5 shows a schematic diagram of the trajectory of the projectile shaft within the cross-section of the projectile under different operating conditions, where A = α. p / α n B = ω n / ω p .

[0065] At different precession angles, ω s :ω n :ω p When = 513.6:171.2:-42.8, the transient aerodynamic coefficient curves over one precession cycle are shown in Figure 6. From the above results, it can be seen that:

[0066] When the precession angle is zero, the specific form of multi-axis angular motion is the superposition of the spin motion around the projectile axis and the conical motion of the projectile axis around the velocity axis, and the trajectory of the projectile axis in the cross section is circular; when the precession angle is not zero, the specific form of multi-axis angular motion is the superposition of spin, precession, and nutation; when the precession angle is equal to the nutation angle, the trajectory of the projectile axis is a multi-lobed incycloid; when the precession angle increases, the trajectory of the projectile axis no longer cross-links; when the precession angular velocity gradually increases, the number of "petals" of the trajectory of the projectile axis increases, and the area of ​​the "petals" gradually increases, and the "petals" overlap and cross-link with each other.

[0067] The four large-cycle fluctuations of the transient force curve are caused by the nutation speed being four times the precession speed, while the 64 small-cycle fluctuations are generated by spin motion. As the precession angle increases, the amplitudes of the four large-cycle fluctuations of the transient normal force and lateral force increase, and the magnitude of the transient normal force also increases; while the amplitude of the 64 small-cycle fluctuations of the transient lateral force first increases and then decreases, α... p It is at its maximum at 12.6°.

[0068] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A numerical simulation method for the multi-axis angular motion of a rotating projectile, characterized in that, It includes the following steps: Step 1: Based on the rotating projectile shape model, generate a spherical flow field mesh, divide the mesh into an inner domain and an outer domain, and use the sliding mesh technique to interpolate and transfer data at the interface between the inner and outer domains. Step 2: Based on the flight conditions, use the global computational domain to calculate the steady-state flow field. After the flow field converges, use the steady-state flow field parameters as the initial flow field for multi-axis angular motion simulation. Step 3: Perform multi-axis angular motion modeling for the inner domain mesh, and obtain the coordinates of the inner domain mesh nodes at different times through coordinate transformation based on the initial flight attitude; Step 4: Based on grid dynamic motion technology, realize the unsteady simulation calculation of multi-axis angular motion; realize the simulation of flow field by solving fluid control equations; realize the simulation of motion through internal grid motion; Step 5: Once the simulation termination condition is met, the calculation is terminated.

2. The numerical simulation method for the multi-axis angular motion of a rotating projectile as described in claim 1, characterized in that, In step one, the mesh size at the interface between the inner and outer domain meshes is the same.

3. The numerical simulation method for the multi-axis angular motion of a rotating projectile as described in claim 2, characterized in that, In step one, the height of the first layer of mesh must be maintained near the rotating bullet wall.

4. The numerical simulation method for the multi-axis angular motion of a rotating projectile as described in claim 3, characterized in that, In step one, the mesh generation tools used include Gambit, ICEM, Pointwise, and HyperMesh.

5. The numerical simulation method for the multi-axis angular motion of a rotating projectile as described in claim 4, characterized in that, In step one, the mesh is a hexahedral structure mesh.

6. The numerical simulation method for the multi-axis angular motion of a rotating projectile as described in claim 5, characterized in that, In step two, the fluid control equation is the Reynolds-averaged Navier-Stokes equation, and a steady-state algorithm is used to obtain the steady flow field under different flight conditions.

7. The numerical simulation method for the multi-axis angular motion of a rotating projectile as described in claim 6, characterized in that, In step two, the solvers used include Fluent, CFD++, and CFX.

8. The numerical simulation method for the multi-axis angular motion of a rotating projectile as described in claim 7, characterized in that, In step three, based on the initial flight attitude, mathematical modeling of multi-axis angular motion is carried out for the inner domain grid, involving composite transformations of motion between the inertial coordinate system, the quasi-projectile coordinate system, the projectile coordinate system, the nutation coordinate system, and the precession coordinate system, in order to obtain the coordinates of the inner domain grid nodes at different times.

9. The numerical simulation method for the multi-axis angular motion of a rotating projectile as described in claim 8, characterized in that, In step four, when using the grid dynamic motion technology, a custom program is written based on the mathematical model of multi-axis angular motion. At the same time, the initial values ​​of the coordinates of the inner domain grid nodes are stored separately and repeatedly called in each calculation time step to realize the simulation of motion. Furthermore, the unsteady Reynolds-averaged Navier-Stokes equations are combined to simulate the complex motion flow field around the flow field.

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