Method for predicting two-dimensional flow separation of a cylinder at high speed
By establishing a linear relationship between the flow separation angle and the separation Mach number, and using the Navier-Stokes equations to calculate the wake field, the problems of computational complexity and limited Mach number range in existing technologies are solved, enabling rapid prediction and optimized design of high-speed flow separation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA ACAD OF AEROSPACE AERODYNAMICS
- Filing Date
- 2026-03-31
- Publication Date
- 2026-07-21
AI Technical Summary
Existing methods for predicting high-speed flow separation are computationally complex and have a limited range of applicable Mach numbers, resulting in long computation times and wasted resources, making it difficult to meet the rapid design requirements of reentry vehicles.
The separation Mach number is defined using the incoming Mach number and the incoming Reynolds number. The separation angle of the two-dimensional cylindrical flow is predicted by a linear function. The wake field is calculated using the Navier-Stokes equations, and a linear relationship between the flow separation angle and the separation Mach number is established. The applicable Mach number range is 6-30.
It enables rapid prediction of flow separation angle, reduces computation time and resource waste, improves optimization design efficiency, and is applicable to most flight conditions of reentry vehicles.
Smart Images
Figure CN122433581A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of aerodynamic thermal environment simulation technology, and in particular to a method for predicting the separation of two-dimensional cylindrical flow under high-speed conditions. Background Technology
[0002] Separation phenomena in hypersonic flows have long been a core concern in the field of aerodynamics. When an aircraft traverses the atmosphere at hypersonic speeds, the resulting complex flow structure exhibits unique physical characteristics, including shock wave / boundary layer interference effects, large-scale separation regions, highly unsteady wake structures, and the resulting complex aerodynamic and thermal environment. These phenomena are particularly pronounced for blunt-nosed aircraft, directly affecting their aerodynamic characteristics and posing significant challenges to the design of thermal protection systems.
[0003] Flight tests, ground-based wind tunnel experiments, and numerical simulations are the main approaches to studying the aerodynamic problems of hypersonic vehicles. Flight tests provide reliable and accurate data, but they are resource-intensive and time-consuming, and are difficult to scale up. Wind tunnel experiments use scaled-down models for physical testing, which can accurately reproduce physical phenomena and directly measure aerodynamic and thermal quantities. However, they lack flexibility, it is difficult to modify the design parameters of the fabricated models, and they are subject to problems such as size effects, boundary effects, and interference from experimental supports. Numerical simulations offer high flexibility and low cost, can obtain all physical quantities within the flow field, and are easy to parametrically study and optimize. Therefore, many studies adopt this approach.
[0004] However, in numerical simulations of the reentry phase of a reentry vehicle, the separation vortex of its rear body is enveloped by the subsonic region. Downstream information within this computational region can propagate upstream, resulting in extremely slow convergence in this area. To accurately capture this vortex, a mesh matching the vortex's characteristic structure is required, making the simulation computationally challenging and resource-intensive. Furthermore, the simulation is prone to divergence, leading to wasted computational resources. This significantly increases the computation time for individual reentry vehicle examples and prolongs the optimization design cycle for reentry vehicles.
[0005] Engineering prediction methods can quickly predict the angle at which flow separation occurs, reducing computation time and wasting computational resources, and improving the efficiency of optimization design. Existing prediction methods use shock wave Reynolds number or wake Reynolds number as independent variables, which requires a series of very complex calculations. Moreover, the applicable Mach number range is only 6-10, which has significant limitations and is not applicable to typical reentry flight conditions. Therefore, in the rapid engineering design phase, quickly obtaining the angle of flow separation is particularly important for simulation calculations to reduce iteration cycles. Summary of the Invention
[0006] To address the issues of computational complexity and limited applicability of existing prediction methods in practical engineering applications, this invention provides a method for predicting the separation of two-dimensional cylindrical flows under high-speed conditions, offering a reference for rapid engineering design.
[0007] This invention provides a method for predicting the separation of two-dimensional cylindrical flows under high-speed conditions, comprising the following steps: S1. Select multiple different combinations of incoming flow characteristic parameters as input parameters for the two-dimensional cylindrical flow field calculation. The incoming flow characteristic parameters include at least the incoming flow Mach number and the incoming flow Reynolds number. S2. Construct a computational domain suitable for two-dimensional cylindrical flow calculations and generate a mesh. Perform wake field calculations on the same mesh to obtain the flow separation angle under different working conditions. S3. Calculate the separation Mach number under different operating conditions based on the incoming Mach number and incoming Reynolds number corresponding to different operating conditions. The calculation formula is as follows: Ma s = Ma 0.5 Re -0.3 ; in, Ma s To separate Mach numbers, Ma For the Mach number of the incoming flow, Re The incoming Reynolds number; S4. Express the separation angle of a two-dimensional cylindrical flow as a linear function of the separation Mach number: θ = k × Ma s + d, Where θ is the two-dimensional cylindrical flow separation angle; k and d are calculated by least squares based on the flow separation angle obtained in step S2 and the separation Mach number obtained in step S3.
[0008] Furthermore, in step S2, the Navier-Stokes equations are used to calculate the wake field data.
[0009] Furthermore, in step S1, multiple sets of different combinations of incoming flow characteristic parameters are selected based on the actual operating conditions of high flow. Each set of incoming flow characteristic parameters also includes incoming flow temperature, incoming flow composition, and the mass fraction of the incoming flow composition.
[0010] Furthermore, in step S1, the incoming Mach number is selected from 6 to 30, the incoming Reynolds number is selected from 40,000 to 80,000, the incoming temperature is selected from 120 to 200K, and the incoming component is selected from one or more of air, nitrogen, and oxygen.
[0011] Furthermore, in step S2, the node coordinates, topology, grid scale, and number of grids remain constant throughout all working condition calculations.
[0012] Furthermore, the separation Mach number reflects the relative strength of shear force and viscous force during gas flow separation.
[0013] In summary, compared with the prior art, the present invention has the following advantages: The technical solution of this invention defines a separation Mach number based on the incoming Mach number and the incoming Reynolds number. The flow separation angle is linearly related to the separation Mach number. The flow separation angle of a two-dimensional cylinder under corresponding operating conditions is predicted by a relevant linear function. The data processing is relatively simple, reducing the waste of calculation time and computing resources. It realizes the rapid prediction of the flow separation position of a two-dimensional cylinder and improves the efficiency of optimization design. The method provided by this invention is applicable to the Mach number range of 6-30, which can cover most flight conditions of reentry vehicles. Attached Figure Description
[0014] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0015] Figure 1 The flow field calculation grid generated in the embodiments of the present invention; Figure 2 This is a schematic diagram of the flow separation angle θ in an embodiment of the present invention; Figure 3 This is a graph showing the relationship between the flow separation angle and the classification Mach number for 18 calculation conditions in this embodiment of the invention. Figure 4 This is a graph showing the relationship between the flow separation angle and the separation Mach number for cylinders of different radii in this invention. Figure 5 This is a comparison diagram of the relationship between the flow separation angle and the separation Mach number for cylinders with different incoming Reynolds numbers and different radii in this invention. Detailed Implementation
[0016] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0017] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.
[0018] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly; for example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0019] Example A method for predicting separation in two-dimensional cylindrical flows under high-speed conditions. Figure 1 The flow field calculation mesh generated for this embodiment has a cylinder radius of 32mm. Based on the region of interest, the mesh near the forebody shock wave and the wake separation vortex is densified to capture a more refined flow field structure and numerical values. The specific steps are as follows: S1. Select multiple sets of different incoming flow characteristic parameter combinations as input parameters for the two-dimensional cylindrical flow field calculation; each set of incoming flow characteristic parameters includes incoming flow Mach number, incoming flow Reynolds number, incoming flow temperature, incoming flow composition, and the mass fraction of the incoming flow composition; the specific parameters are as follows: incoming flow Mach number is 6, 10, 15, 20, 25, 30, incoming flow Reynolds number is 40000, 60000, 80000, incoming flow gas composition is N2 (100%), incoming flow temperature is 168K, and there are a total of 18 calculation conditions (each calculation condition includes the above five incoming flow characteristic parameters).
[0020] S2. Construct a computational domain suitable for two-dimensional cylindrical flow calculations and generate a mesh (i.e., Figure 1The wake field is calculated on the same grid, and the governing equation for the flow field calculation is the Navier-Stokes equation to obtain the flow separation angle under different operating conditions. Numerical discretization of the Navier-Stokes equation is a conventional technique in this field. In this invention, the flow separation angle is obtained based on the gas vector parameters obtained after solving the Navier-Stokes equation.
[0021] S3. Calculate the separation Mach number under different operating conditions based on the corresponding incoming Mach number and incoming Reynolds number. The calculation formula is as follows: Ma s = Ma 0.5 Re -0.3 ; in, Ma s To separate Mach numbers, Ma For the Mach number of the incoming flow, Re The incoming Reynolds number; S4. Express the separation angle of a two-dimensional cylindrical flow as a linear function of the separation Mach number: θ = k × Ma s + d, Where θ is the two-dimensional cylindrical flow separation angle; k and d are calculated by least squares based on the flow separation angle obtained in step S2 and the separation Mach number obtained in step S3.
[0022] In this embodiment, θ is calculated to be 118.31 × Ma s +116.75, a schematic diagram of the flow separation angle θ is shown below. Figure 2 As shown ( Figure 2 The data also includes the cylinder diameter D, wake length L, and the location of the flow separation point on the cylinder surface. The flow separation angle θ is the circumferential angle from the front stagnation point along the cylinder surface to the boundary layer separation point.
[0023] Figure 3 The paper demonstrates the relationship between the flow separation angle and the separation Mach number for 18 calculation conditions. Under multiple sets of different incoming flow conditions, the flow separation angle exhibits a good linear distribution law with the change of the separation Mach number. In addition, the paper also provides the relationship between the flow separation angle and the separation Mach number for different incoming flow Reynolds numbers. The data points are all concentrated near the linear function, indicating that the linear function established in this invention has high accuracy and stability under multiple conditions.
[0024] Furthermore, this invention also calculated the wake field for different cylinder radii (r = 0.032 m, 0.1 m, and 0.2 m, respectively). Figure 4The relationship between the flow separation angle and the separation Mach number for cylinders with different radii is presented, with the data points concentrated near the linear function. For cylinder structures of different radii, the flow separation angle and the separation Mach number maintain a stable linear relationship, indicating that this method is not limited by a single cylinder radius and has geometric universality.
[0025] Figure 5 The curves obtained by fitting different radii are compared with the linear function, showing that under different geometric parameters and different incoming Reynolds number parameters, the flow separation angle and separation Mach number exhibit a stable and consistent linear relationship, thus verifying that the linear prediction method proposed in this invention has strong versatility and engineering applicability.
[0026] 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for predicting the separation of two-dimensional cylindrical flow under high-speed conditions, characterized in that, Includes the following steps: S1. Select multiple different combinations of incoming flow characteristic parameters as input parameters for the two-dimensional cylindrical flow field calculation. The incoming flow characteristic parameters include at least the incoming flow Mach number and the incoming flow Reynolds number. S2. Construct a computational domain suitable for two-dimensional cylindrical flow calculations and generate a mesh. Perform wake field calculations on the same mesh to obtain the flow separation angle under different working conditions. S3. Calculate the separation Mach number under different operating conditions based on the incoming Mach number and incoming Reynolds number corresponding to different operating conditions. The calculation formula is as follows: Ma s = Ma 0.5 Re -0.3 ； in, Ma s To separate Mach numbers, Ma For the Mach number of the incoming flow, Re The incoming Reynolds number; S4. Express the separation angle of a two-dimensional cylindrical flow as a linear function of the separation Mach number: θ= k × Ma s + d, Where θ is the two-dimensional cylindrical flow separation angle; k and d are calculated by least squares based on the flow separation angle obtained in step S2 and the separation Mach number obtained in step S3.
2. The method according to claim 1, characterized in that, In step S2, the Navier-Stokes equations are used to calculate the wake field data.
3. The method according to claim 1, characterized in that, Step S1 selects multiple sets of different combinations of incoming flow characteristic parameters based on the actual operating conditions of high-speed flow. Each set of incoming flow characteristic parameters also includes incoming flow temperature, incoming flow composition, and the mass fraction of the incoming flow composition.
4. The method according to claim 3, characterized in that, In step S1, the incoming Mach number is selected from 6 to 30, the incoming Reynolds number is selected from 40,000 to 80,000, the incoming temperature is selected from 120 to 200 K, and the incoming component is selected from one or more of air, nitrogen, and oxygen.
5. The method according to claim 1, characterized in that, In step S2, the node coordinates, topology, grid size, and number of grids remain constant throughout all working condition calculations.
6. The method according to claim 1, characterized in that, The separation Mach number reflects the relative strength of shear force and viscous force during gas flow separation.