A method for designing a profile of a moving-axis spun supersonic direct connection simulator

Abstract

A method for designing the profile of a supersonic direct-drive simulator with a shift-axis rotation mechanism is disclosed, belonging to the field of aerodynamic testing. This invention includes the following steps: Step 1. Based on the geometric constraints of the shift-axis distance, an improved method for solving transonic flow and axial characteristic points is used to obtain the initial throat profile and supersonic development profile of the direct-drive simulator; Step 2. The contraction profile is selected and determined based on inlet conditions, throat area, and contraction curve parameters; Step 3. Based on the simulator's outlet cross-sectional shape requirements, and combining the contraction profile obtained in Step 2 and the supersonic development profile obtained in Step 1, the inlet shape is obtained through rotation. The supersonic direct-drive simulator of this invention does not have a complex actuation control mechanism, relying on aerodynamic principles, and is simple and reliable in structure.

Description

Technical Field

[0001] This invention relates to a linear design method for a supersonic direct-drive simulator, belonging to the field of aerodynamic testing. Background Technology

[0002] Supersonic simulators are widely used in aerospace aerodynamics testing to construct flow field structures that meet certain outflow conditions. Typical supersonic simulators, such as wind tunnels or ejector nozzles, are designed to obtain curves with contraction and expansion characteristics. Under certain pressure ratio conditions, the desired supersonic flow structure can be formed at the nozzle exit. The distribution of flow field parameters at the exit can be uniform or non-uniform.

[0003] These simulators typically exhibit two-dimensional or axisymmetric flow characteristics: for two-dimensional structures, the axis of symmetry lies on the plane of symmetry, and the simulator outlet is generally square or rectangular; for axisymmetric structures, the axis of rotation lies on the central axis, and the simulator outlet is generally circular. Their wall curves consist of a subsonic contraction section, a throat section, and a supersonic expansion section. The contraction section usually uses a cubic or quintic smooth curve; the throat section uses the transonic flow field solution as its initial value; the supersonic expansion section is based on characteristic line theory (combined with boundary layer correction techniques), and its design methods can be categorized into two types:

[0004] One type is the partial characteristic line design method based on the flow spring assumption, such as the Foelsch method and the Crown method. The general idea is to use multiple curves in the initial section to transform the sonic flow at the throat into a supersonic flow spring at the inflection point. The drawback of this method is that the wall profile at the inflection point is non-differentiable, resulting in internal flow field disturbances that significantly impact the overall simulator performance. To improve the smoothness of the simulator wall, improved design methods with continuous curvature have emerged based on the above methods. For example, Kenney uses a pre-defined wall profile after the inflection point to smooth the transition profile. Although these improved methods improve the outlet flow field quality to some extent, they all rely on the flow spring assumption, leaving the profile design before the inflection point lacking a theoretical basis.

[0005] Another type is the complete method of characteristics, which can be further divided into the direct method of characteristics and the reverse method of characteristics. The direct method of characteristics determines the boundary characteristic line parameters and location by specifying the curve form (such as a circular arc) of the expansion section immediately adjacent to the throat, based on the simulator's outlet design Mach number. The reverse method of characteristics obtains the inviscid boundary by combining the distribution of given axial flow parameters (such as axial Mach number or velocity distribution) with streamline tracing techniques. Comparatively, the complete method of characteristics eliminates the fountain region assumption, strengthens the theoretical basis of the design, and therefore may yield better flow field quality.

[0006] In recent years, the demand for simulators with spin-type structures has been increasing, especially the desire to design direct-connect simulators that can directly meet the needs of supersonic flow research near the wall of curved structures. From a geometric and flow characteristic perspective, this type of simulator differs from traditional two-dimensional or axisymmetric simulators, resulting in expansion characteristics that differ from two-dimensional or axisymmetric nozzles. To achieve higher flow field quality at the exit, further development in design methodologies is needed. Summary of the Invention

[0007] This invention aims to provide a direct-drive supersonic simulator with a shift-axis spin-forming structure, which can significantly improve the simulation capability of supersonic flow fields with spin-forming structures and enhance outlet quality. A brief overview of the invention is provided below to offer a basic understanding of certain aspects of it. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention.

[0008] The technical solution of this invention:

[0009] A method for designing the profile of a supersonic direct-drive simulator with a shift-axis spin-forming profile is disclosed. The simulator's cross-section includes an inlet section, a contraction-expansion surface, an outlet section, and a central spin-forming wall arranged sequentially. The contraction-expansion surface is a surface formed by a contraction and a supersonic development profile. The specific implementation process of this invention includes the following steps:

[0010] Step 1. Based on the geometric constraints of the axis shift distance, the initial value line of the throat and the supersonic development profile are obtained by using the improved transonic flow and axial characteristic point solution method.

[0011] The axis shift distance is the radial distance from the center rotating wall to the virtual rotation axis;

[0012] Step 2. Select and determine the contraction section profile based on inlet conditions, throat area, and contraction section curve parameters;

[0013] Step 3. Based on the requirements of the simulator's exit cross-sectional shape, and combining the contraction section obtained in Step 2 and the supersonic development profile obtained in Step 1, the inlet shape is obtained by a rotation method, that is, by rotating around the virtual rotation axis by a given design angle to obtain the overall profile shape of the direct-connect simulator.

[0014] The simulator's exit cross-section is a sector or ring with a certain circumferential angle.

[0015] Preferably, the specific implementation steps of step 1 are as follows:

[0016] Step 11. Determine the exit area relationship based on the exit conditions of the direct-connected simulator;

[0017] The subsonic airflow enters the channel 2, bounded by the contraction and expansion surfaces, at the inlet of the direct-connected simulator and accelerates continuously. It first reaches sonic speed at the minimum cross-section of the channel, i.e., the throat position. The airflow further accelerates to supersonic speed in the expansion section until it reaches the design Mach number required for the simulator outlet. The relationship between the design Mach number and the outlet area is derived from the flow rate formula within the simulator as follows:

[0018]

[0019] in, For simulator export area, The minimum cross-sectional area of ​​the simulator. For the simulator's output Mach number, is the specific heat ratio of the gaseous medium;

[0020] Step 12. Design the supersonic development profile of the nozzle based on the characteristic line theory. The relationship is as follows:

[0021]

[0022] in, For x-axis or y-axis coordinates, For vertical or radial coordinates, The local airflow direction angle, For the local Mach number angle, The velocity is the flow velocity along the lateral or axial direction. The velocity is the longitudinal or radial flow velocity. For the local speed of sound, Represents two-dimensional flow. Indicates axisymmetric flow. The sign for the difference in parameter values; the subscript ± indicates the direction of movement to the right or left along the feature line; The slope of the characteristic line;

[0023] Step 13. When using the method of characteristics to calculate the supersonic flow field, an initial value line needs to be given and used as the boundary condition of the method of characteristics. Combined with the Mach number distribution on the central axis, the wall profile is solved by determining the initial characteristic line from the transonic analytical solution of the throat. Combined with the axial Mach number distribution, the internal characteristic line network of the nozzle is obtained. The supersonic section profile is obtained on the characteristic line network using the streamline tracing method.

[0024] The line tracing method involves solving for the shape profile by spatially advancing along the streamline direction. The specific streamline equations are as follows:

[0025]

[0026] Step 14. Expand the perturbation function into a power series of y, where the coefficients are functions of x. Then, use the boundary conditions to determine these coefficient functions (specifically, use a first-order approximation of the Sauer method, expand the perturbation function into a power series of y, where the coefficients are functions of x, and perform axis shifting on the derivation results of the original Sauer method), and perform axis shifting on the boundary conditions:

[0027] Using the curve corresponding to the y-direction perturbation velocity of 0 as the starting line, the equation of the axis-shifting starting line can be obtained as follows:

[0028]

[0029] in, The required axis shift distance is the radial distance from the center rotating wall 4 to the virtual rotation axis 5. The curvature of the throat surface is determined by the following relationship:

[0030]

[0031] in, The dimensionless radial height of the throat. The dimensionless curvature of the throat;

[0032] The supersonic development profile is obtained using the inverse characteristic line design method (i.e., based on the above characteristic line method, using the Mach number distribution of the flow field as a known condition, and inversely calculating the parameters and coordinates of the spatial characteristic line grid points). This involves first setting a Mach number distribution along the axis that meets the requirements for both continuity and smoothness, ensuring continuous wall curvature, and ensuring the Mach number along the axis satisfies the requirement of continuous second derivative. Then, a suitable interpolation method is used to give the Mach number distribution, satisfying the following at the axis boundary:

[0033]

[0034] Point B is the intersection of the transonic initial line and the axis, and point C is the intersection of the downstream leftward characteristic line of the supersonic development line and the axis.

[0035] Preferred method: In step 2, the shrinkage section profile adopts a conventional design method of bicubic or quintic curve, such as the Vitósinski formula or the Vitósinski formula with axis shift correction.

[0036] The present invention has the following beneficial effects:

[0037] This invention provides a design method for a shift-axis rotary supersonic direct-drive simulator, capable of designing a direct-drive simulator that directly meets the needs of supersonic flow research near the wall of curved structural components. The design method of this invention is a fixed-profile design scheme; different requirements can be met by changing the design Mach number and area ratio of the simulator outlet. The supersonic direct-drive simulator designed using this invention has no complex actuation control mechanism, relying on aerodynamic principles, resulting in a simple and reliable structure. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the structural form of the supersonic direct-drive simulator with a shift-axis rotation according to the present invention;

[0039] Figure 2 This is a cross-sectional view of the direct-connect simulator. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the present invention.

[0041] Specific implementation method one, such as Figure 1 and Figure 2 As shown in the schematic diagram, the supersonic direct-drive simulator with a shifting axis provided in this embodiment consists of an inlet section 1, a curved wall 2 formed by contraction and supersonic development profiles, an outlet section 3, and a central rotating wall 4. In this embodiment, "rotating" refers to a form that rotates around a virtual rotation axis, and the circumferential angle can be arbitrarily changed.

[0042] The process of implementing the profile design method for a direct-drive supersonic simulator with a shift-axis rotation type is as follows:

[0043] First, the area relationship is determined based on the exit conditions of the direct-connect simulator.

[0044] Subsonic airflow enters the channel formed by the contraction and supersonic development profiles at the inlet of the direct-connected simulator and accelerates continuously. It first reaches sonic speed at the minimum cross-section of the channel, i.e., the throat position. The airflow further accelerates to supersonic speed in the expansion section until it reaches the design Mach number required for the simulator outlet. From the flow rate formula within the simulator, the relationship between the design Mach number and the outlet area can be derived as follows:

[0045]

[0046] in, For simulator export area, The minimum cross-sectional area of ​​the simulator. For the simulator's output Mach number, is the specific heat ratio of the gaseous medium.

[0047] Furthermore, based on the characteristic line theory, the supersonic development profile of the nozzle is designed, with the following relationship:

[0048]

[0049] in, For x-axis or y-axis coordinates, For vertical or radial coordinates, The local airflow direction angle, For the local Mach number angle, The velocity is the flow velocity along the lateral or axial direction. The velocity is the longitudinal or radial flow velocity. For the local speed of sound, Represents two-dimensional flow. This indicates axisymmetric flow.

[0050] When using the method of characteristics to calculate supersonic flow fields, initial characteristic lines need to be given and used as boundary conditions for the method of characteristics. Combined with the Mach number distribution along the central axis, the development profile is solved. The initial characteristic lines are determined from the throat transonic analytical solution. Combined with the axial Mach number distribution (usually in the form of a Bezier curve or B-spline curve), a characteristic line network inside the nozzle is obtained. The supersonic profile can then be obtained on this characteristic line network using streamline tracing techniques.

[0051] To address transonic flow problems, researchers have proposed various approximate solutions based on the full velocity potential equation. Sauer provides an effective first-order approximate solution. The basic idea is to expand the perturbation function into a power series of y, where the coefficients are functions of x, and then use boundary conditions to determine these coefficient functions. In this implementation, the original conditions need to be shifted.

[0052] Using the curve corresponding to the y-direction perturbation velocity of 0 as the starting line, the equation of the axis-shifting starting line can be obtained as follows:

[0053]

[0054] in, The required axis shift distance, i.e. Figure 1 The radial distance from the center wall of rotation (④) to the virtual axis of rotation (⑤). The curvature of the throat surface is determined by the following relationship:

[0055]

[0056] in, The dimensionless radial height of the throat. The curvature of the throat is dimensionless.

[0057] Furthermore, the supersonic development profile is obtained using the inverse characteristic line design method. This involves first establishing a Mach number distribution along the axis that meets both continuity and smoothness requirements; the final supersonic development profile is then entirely determined by the distribution function. To ensure continuous wall curvature, the Mach number along the axis should satisfy second derivative continuity; therefore, a suitable interpolation method should be used to define the Mach number distribution. At the axis boundary, the following conditions are met:

[0058]

[0059] Point B is the intersection of the transonic initial line and the axis, and point C is the intersection of the downstream leftward characteristic line of the supersonic development line and the axis.

[0060] Furthermore, the displacement thickness of the boundary layer can be determined by directly solving the boundary layer equation, and the contraction section profile is usually in the form of a cubic or quintic curve.

[0061] This embodiment provides a direct-connect simulator design method that meets the needs of supersonic flow research near the wall of arc-shaped structural components. This embodiment is only an exemplary description of this patent and does not limit its scope of protection. Those skilled in the art can also make local modifications, as long as they do not exceed the spirit and essence of this patent, they are all within the scope of protection of this patent.

Claims

1. A method for designing the profile of a supersonic direct-drive simulator with a shift-axis spin-forming mechanism, wherein the cross-section of the simulator comprises an inlet section (1), a contraction-expansion surface (2), an outlet section (3), and a central spin-forming wall (4) arranged sequentially, characterized in that, Includes the following steps: Step 1. Based on the geometric constraints of the axis-shifting distance, and using an improved method for solving transonic flow and axial characteristic points, the initial value line of the throat and the supersonic development profile of the direct-connect simulator are obtained. The specific implementation steps are as follows: Step 11. Determine the exit area relationship based on the exit conditions of the direct-connected simulator; The subsonic airflow enters the channel 2, bounded by the contraction and supersonic development profiles, at the inlet of the direct-connected simulator and accelerates continuously. It first reaches sonic speed at the minimum cross-section of the channel, i.e., the throat position. The airflow further accelerates to supersonic speed in the expansion section until it reaches the design Mach number required for the simulator outlet. The relationship between the design Mach number and the outlet area is derived from the flow rate formula within the simulator as follows: ； in, For simulator export area, The minimum cross-sectional area of ​​the simulator. For the simulator's output Mach number, is the specific heat ratio of the gaseous medium; Step 12. Design the supersonic development profile of the nozzle based on the characteristic line theory. The relationship is as follows: ； in, For x-axis or y-axis coordinates, For vertical or radial coordinates, The local airflow direction angle, For the local Mach number angle, The velocity is the flow velocity along the lateral or axial direction. The velocity is the longitudinal or radial flow velocity. For the local speed of sound, Represents two-dimensional flow. Indicates axisymmetric flow. The sign for the difference in parameter values; the subscript ± indicates the direction of movement to the right or left along the feature line; The slope of the characteristic line; Step 13. When using the method of characteristics to calculate the supersonic flow field, an initial value line needs to be given and used as the boundary condition of the method of characteristics. Combined with the Mach number distribution on the central axis, the wall profile is solved. The initial characteristic line is determined by the transonic analytical solution of the throat. Combined with the axial Mach number distribution, the internal characteristic line network of the nozzle is obtained. The supersonic section profile is obtained on the characteristic line network using the streamline tracing method. Step 14. Expand the perturbation function into a power series of y, where the coefficients are functions of x. Then, use the boundary conditions to determine these coefficient functions and perform an axis shifting operation on the original conditions: Using the curve corresponding to the y-direction perturbation velocity of 0 as the starting line, the equation of the axis-shifting starting line can be obtained as follows: ； in, The required axis shift distance is the radial distance from the center rotating wall (4) to the virtual rotation axis 5. The curvature of the throat surface is determined by the following relationship: ； in, The dimensionless radial height of the throat. The dimensionless curvature of the throat; The supersonic development profile is obtained using the inverse characteristic line design method. First, a Mach number distribution with both continuity and smoothness is established along the axis, ensuring continuous wall curvature. The Mach number along the axis must satisfy the continuity of its second derivative. Then, a suitable interpolation method is used to define the Mach number distribution, satisfying the following at the axis boundary: ； Point B is the intersection of the transonic initial line and the axis, and point C is the intersection of the downstream leftward characteristic line of the supersonic development line and the axis. Step 2. Select and determine the contraction section profile based on inlet conditions, throat area, and contraction section curve parameters; Step 3. Based on the requirements of the simulator's exit cross-sectional shape, and combining the contraction section obtained in Step 2 and the supersonic development profile obtained in Step 1, obtain the inlet shape through a spinning method.

2. The method for designing the profile of a supersonic direct-drive simulator with a shift-axis rotation as described in claim 1, characterized in that: In step 2, the contraction section profile adopts the conventional design method of bicubic or quintic curves.

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