Method and device for predicting three-dimensional shock wave reflection type transformation position on concave wall surface

Abstract

The invention provides a method and a device for predicting a three-dimensional shock wave reflection type transformation position on a concave wall surface, and relates to the field of hypersonic aerodynamics. Under the wide incoming flow Mach number, the shock wave angle is divided into different areas through determination of the key shock wave angle and combination of the Mach angle, and therefore effective analysis and prediction of shock wave reflection behaviors are achieved. In the first area, position prediction is carried out in combination with a hypersonic equivalence principle and a two-dimensional motion shock wave reflection model; and in the second region and the third region, establishing a linear equation for position prediction. According to the method, the calculation process is simple, complex mathematical derivation is reduced, high prediction precision can be kept in a large range, and the reliability of the result is ensured. Besides, the method can quickly respond to the change of given parameters, meets the requirements of different working conditions, provides important theoretical support and practical guidance for hypersonic flow research and related engineering design, and has wide application prospects and practical value.

Description

Technical Field

[0001] This invention relates to the field of hypersonic aerodynamics, and more particularly to a method and apparatus for predicting the position of three-dimensional shock wave reflection type transition on a concave wall surface. Background Technology

[0002] The internal and external flows of hypersonic vehicles are extremely complex, especially in the three-dimensional inlet and isolation section of air-breathing vehicles. The reflection of three-dimensional shock waves on concave walls significantly affects the aerodynamic performance and flow stability of the vehicle. To highlight the main characteristics of shock wave reflection on concave walls, studying the reflection of three-dimensional shock waves on concave walls in inviscid flow is of guiding significance. Under high Mach conditions, the shock wave reflection type is constrained by geometry. Changes in the position of the intersection point between the shock wave and the wall can cause the reflection type to change from Mach reflection to regular reflection, leading to abrupt changes in flow parameters and affecting flow stability. Therefore, accurately predicting the location of the reflection type transition has become a research focus.

[0003] Existing research mainly simplifies three-dimensional problems into two-dimensional shock wave reflection analyses, such as the hypersonic equivalence principle, which provides a basis for predicting the location of three-dimensional shock wave reflection type transitions. However, as the shock wave intensifies, the accuracy of this principle decreases, and the error becomes significant in the case of strong shock waves.

[0004] Therefore, existing methods still have limitations in predicting the location of the three-dimensional shock wave reflection type transition at high Mach number concave walls. New models need to be developed to comprehensively consider shock wave intensity, geometry, and flow characteristics, providing more reliable theoretical support for the design of hypersonic vehicles. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a method and apparatus for predicting the position of the three-dimensional shock wave reflection type transition on a concave wall surface, so as to solve the problem of inaccurate prediction of the position of the three-dimensional shock wave reflection type transition on a concave wall surface under high Mach number conditions.

[0006] To achieve the above objectives, the embodiments of the present invention provide the following technical solutions:

[0007] The first aspect of this invention discloses a method for predicting the location of a three-dimensional shock wave reflection type transition on a concave wall surface, the method comprising:

[0008] Based on the incoming Mach number and wall geometry, the first critical shock angle, the second critical shock angle, and the third critical shock angle are determined.

[0009] Based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into a first region, a second region, and a third region from smallest to largest.

[0010] In the first region, combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model, the position of the three-dimensional oblique shock wave reflection type change corresponding to the first region is predicted.

[0011] In the second region, based on the first key shock angle and the second key shock angle, the three-dimensional oblique shock wave reflection type transition position corresponding to the second region is predicted;

[0012] In the third region, based on the second key shock angle and the third key shock angle, the three-dimensional oblique shock wave reflection type transition position corresponding to the third region is predicted.

[0013] Preferably, determining the first critical shock angle, the second critical shock angle, and the third critical shock angle based on the incoming Mach number and the wall geometry includes:

[0014] Obtain the incoming Mach number and wall geometry;

[0015] The target shock angle corresponding to the incoming Mach number and the wall geometry is determined according to the von Neumann criterion.

[0016] Based on the target shock angle, the first fitting formula, the second fitting formula, and the third fitting formula, the first key shock angle, the second key shock angle, and the third key shock angle are calculated; wherein, the first fitting formula is: ; The target shock angle; It is the first constant; The first key shock angle is; the second fitting formula is... ; It is the second constant; The second key shock angle is; the third fitting formula is ; It is the third constant; This refers to the third key shock angle.

[0017] Preferably, based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into a first region, a second region, and a third region from smallest to largest, including:

[0018] Based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into a first region, a second region, and a third region from smallest to largest; wherein, the first region is I = […]. < ≤ The second region is Ⅱ=( < ≤ The third region is Ⅲ=( < ≤ ); The Mach number of the incoming flow; The three-dimensional oblique shock wave angle; This is the first critical shock angle; This is the second key shock angle; This refers to the third key shock angle.

[0019] Preferably, in the first region, predicting the three-dimensional oblique shock wave reflection type transition location corresponding to the first region by combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model includes:

[0020] In the first region, a correction formula is constructed by combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model; wherein, the hypersonic equivalence principle is: The two-dimensional motion shock wave reflection model is as follows: The corrected formula is: ; The location of the three-dimensional oblique shock wave reflection type change corresponding to the first region; The Mach number of the incoming flow; The preset shock angle; The Mach number for a two-dimensional motion shock wave; The position represents the change in the reflection type of the two-dimensional moving shock wave; k is a correction coefficient.

[0021] Based on the corrected formula, the location of the three-dimensional oblique shock wave reflection type transition corresponding to the first region is predicted.

[0022] Preferably, predicting the three-dimensional oblique shock wave reflection type transition position in the second region based on the first key shock wave angle and the second key shock wave angle includes:

[0023] In the second region, the three-dimensional oblique shock wave reflection type transition position corresponding to the first critical shock wave angle is determined, and the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle is determined;

[0024] Based on the three-dimensional oblique shock wave reflection type transition position corresponding to the first critical shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle, a first linear equation is constructed; wherein, the first linear equation is... ; This represents the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region; The position corresponding to the three-dimensional oblique shock wave reflection type change at the second key shock wave angle; The position of the three-dimensional oblique shock wave reflection type change corresponding to the first key shock wave angle; The Mach number of the incoming flow; The preset shock angle; This is the second key shock angle; This is the first critical shock angle;

[0025] Based on the first linear equation, the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region is predicted.

[0026] Preferably, in the third region, predicting the three-dimensional oblique shock wave reflection type transition position corresponding to the third region based on the second key shock wave angle and the third key shock wave angle includes:

[0027] In the third region, the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle is determined, and the three-dimensional oblique shock wave reflection type transition position corresponding to the third key shock wave angle is determined;

[0028] Based on the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the third critical shock wave angle, a second linear equation is constructed; wherein, the second linear equation is... ; This refers to the three-dimensional oblique shock wave reflection type transition position corresponding to the third region; The position corresponding to the three-dimensional oblique shock wave reflection type change at the second key shock wave angle; The position corresponding to the three-dimensional oblique shock wave reflection type change at the third key shock wave angle; The Mach number of the incoming flow; The preset shock angle; This refers to the third key shock angle; This is the second key shock angle;

[0029] Based on the second linear equation, the location of the three-dimensional oblique shock wave reflection type transition corresponding to the third region is predicted.

[0030] A second aspect of the present invention discloses a device for predicting the position of a three-dimensional shock wave reflection type transition on a concave wall surface, the device comprising:

[0031] A determining element is used to determine the first critical shock angle, the second critical shock angle, and the third critical shock angle based on the incoming Mach number and the wall geometry;

[0032] The division unit is used to divide the three-dimensional oblique shock angle into a first region, a second region, and a third region from small to large according to the incoming Mach number, the first key shock angle, the second key shock angle, and the third key shock angle.

[0033] The first prediction unit is used to predict the position of the three-dimensional oblique shock wave reflection type change in the first region by combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model.

[0034] The second prediction unit is used to predict the three-dimensional oblique shock wave reflection type transition position in the second region based on the first key shock wave angle and the second key shock wave angle.

[0035] The third prediction unit is used to predict the three-dimensional oblique shock wave reflection type transition position in the third region based on the second key shock wave angle and the third key shock wave angle.

[0036] Preferably, the determining unit includes:

[0037] The acquisition module is used to acquire the incoming Mach number and the wall geometry;

[0038] The first determining module is used to determine the target shock angle corresponding to the incoming Mach number and the wall geometry according to the von Neumann criterion.

[0039] The calculation module is used to calculate the first key shock angle, the second key shock angle, and the third key shock angle based on the target shock angle, the first fitting formula, the second fitting formula, and the third fitting formula; wherein, the first fitting formula is... ; The target shock angle; It is the first constant; The first key shock angle is; the second fitting formula is... ; It is the second constant; The second key shock angle is; the third fitting formula is ; It is the third constant; This refers to the third key shock angle.

[0040] Preferably, the partitioning unit is specifically used for:

[0041] Based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into a first region, a second region, and a third region from smallest to largest; wherein, the first region is I = […]. < ≤ The second region is Ⅱ=( < ≤ The third region is Ⅲ=( < ≤ ); The Mach number of the incoming flow; The three-dimensional oblique shock wave angle; This is the first critical shock angle; This is the second key shock angle; This refers to the third key shock angle.

[0042] Preferably, the first prediction unit includes:

[0043] The first construction module, in the first region, constructs a correction formula by combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model; wherein, the hypersonic equivalence principle is... The two-dimensional motion shock wave reflection model is as follows: The corrected formula is: ; The location of the three-dimensional oblique shock wave reflection type change corresponding to the first region; The Mach number of the incoming flow; The preset shock angle; The Mach number for a two-dimensional motion shock wave; The position represents the change in the reflection type of the two-dimensional moving shock wave; k is a correction coefficient.

[0044] The first prediction module, based on the correction formula, predicts the location of the three-dimensional oblique shock wave reflection type change corresponding to the first region.

[0045] Preferably, the second prediction unit includes:

[0046] The second determining module is used to determine, in the second region, the three-dimensional oblique shock wave reflection type transition position corresponding to the first critical shock wave angle, and the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle;

[0047] The second construction module is used to construct a first linear equation based on the three-dimensional oblique shock wave reflection type transition position corresponding to the first key shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle; wherein, the first linear equation is: ; This represents the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region; The position corresponding to the three-dimensional oblique shock wave reflection type change at the second key shock wave angle; The position of the three-dimensional oblique shock wave reflection type change corresponding to the first key shock wave angle; The Mach number of the incoming flow; The preset shock angle; This is the second key shock angle; This is the first critical shock angle;

[0048] The second prediction module is used to predict the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region based on the first linear equation.

[0049] Preferably, the third prediction unit includes:

[0050] The third determining module is used to determine, in the third region, the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle, and the three-dimensional oblique shock wave reflection type transition position corresponding to the third key shock wave angle;

[0051] The third construction module is used to construct a second linear equation based on the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the third key shock wave angle; wherein, the second linear equation is: ; This refers to the three-dimensional oblique shock wave reflection type transition position corresponding to the third region; The position corresponding to the three-dimensional oblique shock wave reflection type change at the second key shock wave angle; The position corresponding to the three-dimensional oblique shock wave reflection type change at the third key shock wave angle; The Mach number of the incoming flow; The preset shock angle; This refers to the third key shock angle; This is the second key shock angle;

[0052] The third prediction module is used to predict the three-dimensional oblique shock wave reflection type transition position corresponding to the third region based on the second linear equation.

[0053] Based on the above embodiments of the present invention, a method and apparatus for predicting the position of three-dimensional shock wave reflection type transition on a concave wall surface are provided, relating to the field of hypersonic aerodynamics. Under a wide incoming Mach number, by determining the key shock wave angle and combining it with the Mach angle, the shock wave angle is divided into different regions, thereby achieving effective analysis and prediction of shock wave reflection behavior. In the first region, position prediction is performed by combining the hypersonic equivalence principle and a two-dimensional moving shock wave reflection model; in the second and third regions, linear equations are established for position prediction. This method has a simple calculation process, reduces complex mathematical derivations, and can maintain high prediction accuracy over a wide range, ensuring the reliability of the results. Furthermore, this method can quickly respond to changes in given parameters, adapting to the needs of different operating conditions, providing important theoretical support and practical guidance for hypersonic flow research and related engineering design, and has broad application prospects and practical value. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0055] Figure 1 This is a schematic diagram of a three-dimensional oblique shock wave reflection system on a concave semi-cylindrical surface provided in an embodiment of the present invention;

[0056] Figure 2 A flowchart illustrating a method for predicting the position of a three-dimensional shock wave reflection type transition on a concave wall surface, as provided in an embodiment of the present invention;

[0057] Figure 3 This is a schematic diagram of a two-dimensional motion shock wave reflection system on a concave semi-circular surface provided in an embodiment of the present invention;

[0058] Figure 4 The goodness of fit provided for the embodiments of the present invention varies with A diagram illustrating the changes;

[0059] Figure 5 Shock angle provided for embodiments of the present invention , and Example graph comparing fitting results;

[0060] Figure 6 Example diagram of prediction results provided in embodiments of the present invention;

[0061] Figure 7This is a structural block diagram of a device for predicting the position of three-dimensional shock wave reflection type change on a concave wall surface, provided in an embodiment of the present invention. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.

[0063] In this application, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0064] As the background technology shows, three-dimensional shock wave reflections induce high pressure loads and flow instabilities in the internal and external flows of high Mach number aircraft. Existing studies usually simplify three-dimensional shock wave reflections into two-dimensional analysis to lay the foundation for position prediction, but the accuracy decreases under strong shock wave conditions.

[0065] Therefore, this invention provides a method and apparatus for predicting the position of three-dimensional shock wave reflection type transition on a concave wall surface, relating to the field of hypersonic aerodynamics. Under a wide incoming Mach number, by determining the key shock wave angle and combining it with the Mach angle, the shock wave angle is divided into different regions, thereby achieving effective analysis and prediction of shock wave reflection behavior. In the first region, position prediction is performed by combining the hypersonic equivalence principle and a two-dimensional moving shock wave reflection model; in the second and third regions, linear equations are established for position prediction. This method has a simple calculation process, reduces complex mathematical derivations, and can maintain high prediction accuracy over a wide range, ensuring the reliability of the results. Furthermore, this method can quickly respond to changes in given parameters, adapting to the needs of different operating conditions, providing important theoretical support and practical guidance for hypersonic flow research and related engineering design, and has broad application prospects and practical value.

[0066] See Figure 1 This diagram illustrates a three-dimensional oblique shock wave reflection system on a concave semi-cylindrical surface provided in an embodiment of the present invention. Figure 1 As shown, given the incoming Mach number In the case of a three-dimensional oblique shock wave 1, after being connected to the wall of the concave semi-cylindrical surface 2 with radius R via the Mach rod 3, Mach reflection will occur; while near the plane of symmetry, when the shock wave directly incident on the wall, regular reflection will occur. In this embodiment of the invention, the three-dimensional oblique shock wave reflection type transition position 4 is a point on the concave wall surface, and this point is also on the shock wave surface. For the prediction method of the three-dimensional oblique shock wave reflection type transition position 4, that is, the transition position from Mach reflection to regular reflection, please refer to this embodiment of the invention. Figure 2 The content shown is as shown.

[0067] See Figure 2 The diagram illustrates a flowchart of a method for predicting the location of a three-dimensional shock wave reflection type transition on a concave wall surface, provided by an embodiment of the present invention. This method is applicable to a given incoming Mach number. Under operating conditions ranging from 5 to 20, the method includes:

[0068] Step S201: Based on the incoming Mach number and the wall geometry, determine the first critical shock angle, the second critical shock angle, and the third critical shock angle.

[0069] It should be noted that within the cross-section of the concave semi-cylindrical surface, Figure 1 The three-dimensional oblique shock wave reflection type transformation position shown is determined by the angle between the wall tangent and the longitudinal coordinate axis. express.

[0070] For a given incoming Mach number and shock angle , It is uniquely determined, therefore it can be expressed by formula (1). .

[0071] (1)

[0072] In formula (1), The angle between the tangent to the wall and the longitudinal coordinate axis is... Figure 1 The three-dimensional oblique shock wave reflection type transition position is shown at point 4.

[0073] Understandably, in combination Figure 3 According to the hypersonic equivalence principle, the three-dimensional oblique shock wave reflection on the concave semi-cylindrical surface can be equivalent to the two-dimensional motion shock wave reflection on the concave semi-circular surface 5.

[0074] Specifically, on the concave semicircular surface 5, which has the same cross-sectional shape as the concave semi-cylindrical surface, when the shock wave Mach number is... At the same time, the two-dimensional moving shock wave 6, near the top of the concave semicircular surface 5, connects with the wall through the Mach rod 7 in the two-dimensional moving shock wave reflection, thus undergoing Mach reflection; while near the bottom of the concave semicircular surface 5, the two-dimensional moving shock wave directly incidents on the wall, resulting in regular reflection. The transition point 8 between Mach reflection and regular reflection (that is, the transition point between the two-dimensional moving shock wave reflection type) is the angle between the tangent of the concave semicircular surface 5 and the direction of shock wave motion. express.

[0075] exist Figure 3 Under the shown conditions, based on the Ben-Dor model and the principle of length scale, a prediction model for the change in the reflection type of the moving shock wave is established. With shock wave Mach number The relationship is expressed by formula (2).

[0076] (2)

[0077] In formula (2), This represents the ratio of the air velocity behind the moving shock wave to the sound velocity in front of the moving shock wave. It represents the ratio of the speed of sound behind the moving shock wave to the speed of sound before the moving shock wave.

[0078] It should be noted that, and With shock wave Mach number The relevant information is shown in formulas (3) and (4) below.

[0079] (3)

[0080] (4)

[0081] In formulas (3) and (4), Specific heat ratio.

[0082] In the specific implementation step S201, the given incoming Mach number and wall geometry are first obtained. Then, the target shock angle corresponding to the incoming Mach number and wall geometry is determined according to the von Neumann criterion. Next, at different incoming Mach numbers, based on the target shock angle... The first fitting formula, the second fitting formula, and the third fitting formula are used to calculate the first critical shock angle. Second critical shock angle and the third key shock angle .

[0083] It should be noted that the first fitting formula is: (5)

[0084] In formula (5), The target shock angle; It is the first constant; This is the first critical shock angle.

[0085] Understandably, the second fitting formula is: (6)

[0086] In formula (6), The target shock angle; It is the second constant; This is the second critical shock angle.

[0087] It should be noted that the third fitting formula is: (7)

[0088] In formula (7), The target shock angle; It is the third constant; This is the third critical shock angle.

[0089] It should be added that, , and These are different constants, obtained through prior simulation training.

[0090] Specifically, in the Mach number of the incoming stream Multiple numerical simulations were conducted within the range of 5 to 20. During the simulation process, data were extracted from the results of each numerical simulation. , and By changing , and Solve the calculation results of the above formulas (5) to (7), and the goodness of fit (R-squared) of the numerical simulation results to determine when = 14.4°, = 5.6°, The best fit is achieved when the angle is 4.1°, as shown below. Figure 4 As shown. Correspondingly, the key shock angle , and The relative error between the numerical simulation results and the calculation results above is less than 5%, such as Figure 5 As shown.

[0091] Step S202: Based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into the first region, the second region, and the third region from smallest to largest.

[0092] In the specific implementation step S202, the Mach angle is calculated based on the incoming Mach number (i.e., ), and the first critical shock angle, the second critical shock angle, and the third critical shock angle, to form a three-dimensional oblique shock angle It is divided into three regions from smallest to largest: Region 1, Region 2, and Region 3.

[0093] Among them, the first region I is [ < ≤ ]; The second region II is ( < ≤ ); the third region III is ( < ≤ ).

[0094] It is understandable that when the shock wave Mach number... Given the incoming Mach number and shock angle satisfy At the time, in comparison and The first critical shock angle correspond and The relative error reached 6%. Correspondingly, within the first region I, and The relative error is less than 6%, therefore the location of the three-dimensional oblique shock wave reflection type change in the first region is... Based on Make predictions.

[0095] Within Zone II and Zone III, and If the relative error is greater than 6%, a new method needs to be established to predict the three-dimensional oblique shock wave reflection type transition position corresponding to the second region, and to predict the three-dimensional oblique shock wave reflection type transition position corresponding to the third region. For specific prediction methods, please refer to the steps shown below.

[0096] It should be noted that, in combination Figure 1 and Figure 3 As shown, when a subsonic region exists downstream of Mach bar 3, the subsonic region affects the position 4 of the three-dimensional oblique shock wave reflection type transition. Therefore, the second critical shock angle... This corresponds to the subsonic region that appears after Mach 3, which is the second region. Accordingly, within the second region II, the flow after Mach 3 is entirely supersonic.

[0097] Within the third region (III), a subsonic region exists after Mach rod 3. When the three-dimensional oblique shock wave reflection type transition position 4 reaches the symmetry plane, the shock wave will no longer undergo a change in reflection type, a situation beyond the scope of this embodiment. Therefore, the third critical shock wave angle... The corresponding three-dimensional oblique shock wave reflection type change position 4 reaches the symmetry plane.

[0098] Furthermore, it can be understood that in three-dimensional shock wave reflection, if the flow behind the Mach bar is supersonic, then downstream disturbances will not affect the upstream shock wave structure. In this embodiment of the invention, this means that downstream disturbances will not change the location of the reflection type transition.

[0099] However, once a subsonic region appears after the Mach rod, downstream high-pressure disturbances will propagate forward through this region, thus affecting the location of the reflection type transition. Therefore, by determining whether a subsonic region exists downstream, a second region II and a third region III are defined: in the second region II, the flow downstream of the Mach rod is entirely supersonic; while in the third region III, a subsonic region exists downstream of the Mach rod.

[0100] It is important to note that the third critical shock angle The definition is as follows: a three-dimensional oblique shock wave will inevitably undergo Mach reflection on the sidewall of a concave curved surface, and will undergo a transformation from Mach reflection to regular reflection as it extends towards the plane of symmetry. However, when the transformation position reaches the plane of symmetry, the three-dimensional oblique shock wave will still undergo Mach reflection on the plane of symmetry, so the reflection type transformation phenomenon described in the embodiments of the present invention will no longer exist.

[0101] Step S203: In the first region, combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model, predict the location of the three-dimensional oblique shock wave reflection type transition corresponding to the first region.

[0102] In the specific implementation step S203, in the first region I [ < ≤ In the study, combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model, a modified formula is constructed to predict the location of the three-dimensional oblique shock wave reflection type change corresponding to the first region.

[0103] It is understandable that the hypersonic equivalence principle is as shown in formula (8).

[0104] (8)

[0105] The two-dimensional motion shock wave reflection model is shown in formula (9).

[0106] (9)

[0107] It should be noted that the correction formula is shown in formula (10).

[0108] (10)

[0109] In formulas (8) to (10), The location of the three-dimensional oblique shock wave reflection type change corresponding to the first region; The Mach number of the incoming flow; The preset shock angle; The Mach number of the two-dimensional motion shock wave satisfies the hypersonic equivalence principle. ; This is a two-dimensional motion shock wave reflection model; k is a correction coefficient, taken as... = 1.06.

[0110] Step S204: In the second region, based on the first critical shock angle and the second critical shock angle, predict the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region.

[0111] In the specific implementation of step S204, in the second region II ( < ≤ In this process, the first critical shock angle is determined. The corresponding three-dimensional oblique shock wave reflection type transition location, and the determination of the second critical shock wave angle. The corresponding three-dimensional oblique shock wave reflection type change location; secondly, based on the first key shock wave angle. The corresponding three-dimensional oblique shock wave reflection type change position, and the second key shock wave angle The corresponding three-dimensional oblique shock wave reflection type transition position is used to construct the first linear equation, as shown in formula (11). Finally, based on the first linear equation, the three-dimensional oblique shock wave reflection type transition position corresponding to the second region is predicted.

[0112] (11)

[0113] In formula (11), This represents the location where the three-dimensional oblique shock wave reflection type changes in the second region. The location of the three-dimensional oblique shock wave reflection type transition corresponding to the second critical shock wave angle, that is... = The position of the three-dimensional oblique shock wave reflection type change at that time is taken as follows: = 85°.

[0114] In formula (11), The position of the three-dimensional oblique shock wave reflection type change corresponding to the first critical shock wave angle; The Mach number of the incoming flow; The preset shock angle; This is the second critical shock angle; This is the first critical shock angle.

[0115] Step S205: In the third region, based on the second and third key shock angles, predict the location of the three-dimensional oblique shock wave reflection type transition corresponding to the third region.

[0116] In the specific implementation of step S205, in the third region III ( < ≤ In the process, the three-dimensional oblique shock wave reflection type change position corresponding to the second critical shock wave angle and the three-dimensional oblique shock wave reflection type change position corresponding to the third critical shock wave angle are determined. Then, based on the three-dimensional oblique shock wave reflection type change position corresponding to the second critical shock wave angle and the three-dimensional oblique shock wave reflection type change position corresponding to the third critical shock wave angle, a second linear equation is constructed, as shown in formula (12). Finally, based on the second linear equation, the three-dimensional oblique shock wave reflection type change position corresponding to the third region is predicted.

[0117] (12)

[0118] In formula (12), This represents the location of the three-dimensional oblique shock wave reflection type transition corresponding to the third region; The position of the three-dimensional oblique shock wave reflection type change corresponding to the second critical shock wave angle; The position of the three-dimensional oblique shock wave reflection type change corresponding to the third critical shock wave angle; The Mach number of the incoming flow; The preset shock angle; The third critical shock angle; This is the second critical shock angle.

[0119] In some specific embodiments, at the incoming Mach number Within the range of 5-20, multiple incoming Mach numbers are selected, and typical three-dimensional oblique shock wave angles are selected within regions I-III. Numerical simulations were performed on the reflection of three-dimensional oblique shock waves on a concave semi-cylindrical surface.

[0120] In the numerical simulation, the radius R of the concave semi-cylindrical surface was set to 17.5 mm, the incoming static pressure was 1200 Pa, and the incoming static temperature was 121 K. The simulation yielded the location of the three-dimensional oblique shock wave reflection type transition. The predicted three-dimensional oblique shock wave reflection type transition positions were compared with those of the first region, the second region, and the third region. Figure 6 As shown.

[0121] Combination Figure 6 The content shown, under different incoming Mach numbers, Initially, it showed good consistency and matched the prediction results of step S203. With... The increase of Mach number under different incoming flows While exhibiting significant dispersion, the predicted three-dimensional oblique shock wave reflection type transition positions for the second and third regions still maintain good agreement. Therefore, the prediction method for the three-dimensional shock wave reflection type transition positions on concave wall surfaces established in this embodiment of the invention can be well consistent with the patterns reflected by numerical calculation results.

[0122] This invention proposes a method for predicting the location of three-dimensional shock wave reflection type transitions on concave walls under a wide incoming Mach number. Based on the von Neumann criterion, this method divides the shock wave angle into different regions by determining the key shock angle and combining it with the Mach angle, thereby achieving effective analysis and prediction of shock wave reflection behavior. In region I, the location is predicted using the hypersonic equivalence principle and a two-dimensional moving shock wave reflection model; in regions II and III, linear equations are established for location prediction. This method features a simple calculation process, reduces complex mathematical derivations, and maintains high prediction accuracy over a wide range, ensuring the reliability of the results. Furthermore, this method can quickly respond to changes in given parameters, adapting to the needs of different operating conditions, providing important theoretical support and practical guidance for hypersonic flow research and related engineering design, and has broad application prospects and practical value.

[0123] Corresponding to the method for predicting the location of three-dimensional shock wave reflection type transition on a concave wall surface provided in the above embodiments of the present invention, see also... Figure 7 The diagram shows a structural block diagram of a device for predicting the position of three-dimensional shock wave reflection type change on a concave wall surface, provided by an embodiment of the present invention.

[0124] The device includes: a determination unit 701, a division unit 702, a first prediction unit 703, a second prediction unit 704, and a third prediction unit 705.

[0125] The determining unit 701 is used to determine the first critical shock angle, the second critical shock angle, and the third critical shock angle based on the incoming Mach number and the wall geometry.

[0126] The dividing unit 702 is used to divide the three-dimensional oblique shock angle into a first region, a second region, and a third region in ascending order based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle.

[0127] The first prediction unit 703 is used to predict the location of the three-dimensional oblique shock wave reflection type change in the first region by combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model.

[0128] The second prediction unit 704 is used to predict the three-dimensional oblique shock wave reflection type transition position in the second region based on the first key shock wave angle and the second key shock wave angle.

[0129] The third prediction unit 705 is used to predict the three-dimensional oblique shock wave reflection type transition position in the third region based on the second key shock wave angle and the third key shock wave angle.

[0130] This invention proposes a device for predicting the location of three-dimensional shock wave reflection type transitions on concave walls under a wide incoming Mach number. Based on the von Neumann criterion, the shock wave angle is divided into different regions by determining the key shock wave angle and combining it with the Mach angle, thereby achieving effective analysis and prediction of shock wave reflection behavior. In region I, the location is predicted by combining the hypersonic equivalence principle and a two-dimensional moving shock wave reflection model; in regions II and III, linear equations are established for location prediction. The device has a simple calculation process, reducing complex mathematical derivations, and can maintain high prediction accuracy over a wide range, ensuring the reliability of the results. In addition, the device can quickly respond to changes in given parameters, adapting to the needs of different operating conditions, providing important theoretical support and practical guidance for hypersonic flow research and related engineering design, and has broad application prospects and practical value.

[0131] Combination Figure 7 The content shown, the determination unit 701, includes: an acquisition module, a first determination module and a calculation module.

[0132] The acquisition module is used to acquire the incoming Mach number and the wall geometry.

[0133] The first determining module is used to determine the target shock angle corresponding to the incoming Mach number and the wall geometry according to the von Neumann criterion.

[0134] The calculation module is used to calculate the first key shock angle, the second key shock angle, and the third key shock angle based on the target shock angle, the first fitting formula, the second fitting formula, and the third fitting formula; wherein, the first fitting formula is... ; The target shock angle; It is the first constant; The first critical shock angle is; the second fitting formula is... ; It is the second constant; The second critical shock angle; the third fitting formula is ; It is the third constant; This is the third critical shock angle.

[0135] Combination Figure 7 The content shown, dividing unit 702, is specifically used to: divide the three-dimensional oblique shock angle into a first region, a second region, and a third region from smallest to largest according to the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle; wherein, the first region is I = [ < ≤ The second region is Ⅱ=( < ≤ The third region is Ⅲ = ( < ≤ ); The Mach number of the incoming flow; The angle of the three-dimensional oblique shock wave; The first critical shock angle; This is the second critical shock angle; This is the third critical shock angle.

[0136] Combination Figure 7 The content shown, the first prediction unit 703, includes: a first construction module and a first prediction module.

[0137] The first building module is used to construct a correction formula in the first region, combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model; wherein, the hypersonic equivalence principle is... The two-dimensional motion shock wave reflection model is as follows: The corrected formula is as follows: ; The location of the three-dimensional oblique shock wave reflection type change corresponding to the first region; The Mach number of the incoming flow; The preset shock angle; The Mach number for a two-dimensional motion shock wave; The position represents the change in the reflection type of the two-dimensional motion shock wave; k is a correction coefficient.

[0138] The first prediction module is used to predict the location of the three-dimensional oblique shock wave reflection type change in the first region based on the modified formula.

[0139] Combination Figure 7 The content shown, the second prediction unit 704, includes: a second determination module, a second construction module and a second prediction module.

[0140] The second determining module is used to determine, in the second region, the three-dimensional oblique shock wave reflection type transition position corresponding to the first critical shock wave angle, and the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle.

[0141] The second construction module is used to construct a first linear equation based on the three-dimensional oblique shock wave reflection type transition position corresponding to the first key shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle; wherein, the first linear equation is: ; This represents the location where the three-dimensional oblique shock wave reflection type changes in the second region. The position of the three-dimensional oblique shock wave reflection type change corresponding to the second critical shock wave angle; The position of the three-dimensional oblique shock wave reflection type change corresponding to the first critical shock wave angle; The Mach number of the incoming flow; The preset shock angle; This is the second critical shock angle; This is the first critical shock angle.

[0142] The second prediction module is used to predict the location of the three-dimensional oblique shock wave reflection type transition in the second region based on the first linear equation.

[0143] Combination Figure 7 The content shown, the third prediction unit 705, includes: a third determination module, a third construction module and a third prediction module.

[0144] The third determining module is used to determine, in the third region, the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle, and the three-dimensional oblique shock wave reflection type transition position corresponding to the third critical shock wave angle.

[0145] The third construction module is used to construct a second linear equation based on the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the third key shock wave angle; wherein, the second linear equation is: ; This represents the location of the three-dimensional oblique shock wave reflection type transition corresponding to the third region; The position of the three-dimensional oblique shock wave reflection type change corresponding to the second critical shock wave angle; The position of the three-dimensional oblique shock wave reflection type change corresponding to the third critical shock wave angle; The Mach number of the incoming flow; The preset shock angle; The third critical shock angle; This is the second critical shock angle.

[0146] The third prediction module is used to predict the location of the three-dimensional oblique shock wave reflection type transition in the third region based on the second linear equation.

[0147] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to method embodiments, the description is relatively simple, and relevant parts can be referred to the descriptions in the method embodiments. The systems and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0148] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0149] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the location of a three-dimensional shock wave reflection type transition on a concave wall surface, characterized in that, The method includes: Based on the incoming Mach number and wall geometry, the first critical shock angle, the second critical shock angle, and the third critical shock angle are determined. Based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into a first region, a second region, and a third region from smallest to largest. In the first region, combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model, the position of the three-dimensional oblique shock wave reflection type change corresponding to the first region is predicted. In the second region, based on the first key shock angle and the second key shock angle, the three-dimensional oblique shock wave reflection type transition position corresponding to the second region is predicted; In the third region, based on the second key shock angle and the third key shock angle, the three-dimensional oblique shock wave reflection type transition position corresponding to the third region is predicted.

2. The method according to claim 1, characterized in that, The determination of the first critical shock angle, the second critical shock angle, and the third critical shock angle based on the incoming Mach number and the wall geometry includes: Obtain the incoming Mach number and wall geometry; The target shock angle corresponding to the incoming Mach number and the wall geometry is determined according to the von Neumann criterion. Based on the target shock angle, the first fitting formula, the second fitting formula, and the third fitting formula, the first key shock angle, the second key shock angle, and the third key shock angle are calculated; wherein, the first fitting formula is: ; The target shock angle; It is the first constant; The first key shock angle is; the second fitting formula is... ; It is the second constant; The second key shock angle is; the third fitting formula is ; It is the third constant; This refers to the third key shock angle.

3. The method according to claim 1, characterized in that, Based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into a first region, a second region, and a third region from smallest to largest, including: Based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into a first region, a second region, and a third region from smallest to largest; wherein, the first region is I = […]. < ≤ The second region is Ⅱ=( < ≤ The third region is Ⅲ=( < ≤ ); The Mach number of the incoming flow; The three-dimensional oblique shock wave angle; This is the first critical shock angle; This is the second key shock angle; This refers to the third key shock angle.

4. The method according to claim 1, characterized in that, In the first region, combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model, the prediction of the three-dimensional oblique shock wave reflection type transition position corresponding to the first region includes: In the first region, a correction formula is constructed by combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model; wherein, the hypersonic equivalence principle is: The two-dimensional motion shock wave reflection model is as follows: The corrected formula is: ; The location of the three-dimensional oblique shock wave reflection type change corresponding to the first region; The Mach number of the incoming flow; The preset shock angle; The Mach number for a two-dimensional motion shock wave; The position represents the change in the reflection type of the two-dimensional moving shock wave; k is a correction coefficient. Based on the corrected formula, the location of the three-dimensional oblique shock wave reflection type transition corresponding to the first region is predicted.

5. The method according to claim 1, characterized in that, In the second region, based on the first key shock angle and the second key shock angle, predicting the three-dimensional oblique shock wave reflection type transition position corresponding to the second region includes: In the second region, the three-dimensional oblique shock wave reflection type transition position corresponding to the first critical shock wave angle is determined, and the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle is determined; Based on the three-dimensional oblique shock wave reflection type transition position corresponding to the first critical shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle, a first linear equation is constructed; wherein, the first linear equation is... ; This represents the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region; The position corresponding to the three-dimensional oblique shock wave reflection type change at the second key shock wave angle; The position of the three-dimensional oblique shock wave reflection type change corresponding to the first key shock wave angle; The Mach number of the incoming flow; The preset shock angle; This is the second key shock angle; This is the first critical shock angle; Based on the first linear equation, the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region is predicted.

6. The method according to claim 1, characterized in that, In the third region, based on the second key shock angle and the third key shock angle, the prediction of the three-dimensional oblique shock wave reflection type transition position corresponding to the third region includes: In the third region, the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle is determined, and the three-dimensional oblique shock wave reflection type transition position corresponding to the third key shock wave angle is determined; Based on the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the third critical shock wave angle, a second linear equation is constructed; wherein, the second linear equation is... ; This refers to the three-dimensional oblique shock wave reflection type transition position corresponding to the third region; The position corresponding to the three-dimensional oblique shock wave reflection type change at the second key shock wave angle; The position corresponding to the three-dimensional oblique shock wave reflection type change at the third key shock wave angle; The Mach number of the incoming flow; The preset shock angle; This refers to the third key shock angle; This is the second key shock angle; Based on the second linear equation, the location of the three-dimensional oblique shock wave reflection type transition corresponding to the third region is predicted.

7. A device for predicting the position of three-dimensional shock wave reflection type transition on a concave wall surface, characterized in that, The device includes: A determining element is used to determine the first critical shock angle, the second critical shock angle, and the third critical shock angle based on the incoming Mach number and the wall geometry; The division unit is used to divide the three-dimensional oblique shock angle into a first region, a second region, and a third region from small to large according to the incoming Mach number, the first key shock angle, the second key shock angle, and the third key shock angle. The first prediction unit is used to predict the three-dimensional oblique shock wave reflection type transition position in the first region by combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model. The second prediction unit is used to predict the three-dimensional oblique shock wave reflection type transition position in the second region based on the first key shock wave angle and the second key shock wave angle. The third prediction unit is used to predict the three-dimensional oblique shock wave reflection type transition position in the third region based on the second key shock wave angle and the third key shock wave angle.

8. The apparatus according to claim 7, characterized in that, The determining unit includes: The acquisition module is used to acquire the incoming Mach number and the wall geometry; The first determining module is used to determine the target shock angle corresponding to the incoming Mach number and the wall geometry according to the von Neumann criterion. The calculation module is used to calculate the first key shock angle, the second key shock angle, and the third key shock angle based on the target shock angle, the first fitting formula, the second fitting formula, and the third fitting formula; wherein, the first fitting formula is... ; The target shock angle; It is the first constant; The first key shock angle is; the second fitting formula is... ; It is the second constant; The second key shock angle is; the third fitting formula is ; It is the third constant; This refers to the third key shock angle.

9. The apparatus according to claim 7, characterized in that, The partitioning unit is specifically used for: Based on the incoming Mach number, the first critical shock angle, the second critical shock angle, and the third critical shock angle, the three-dimensional oblique shock angle is divided into a first region, a second region, and a third region from smallest to largest; wherein, the first region is I = […]. < ≤ The second region is Ⅱ=( < ≤ The third region is Ⅲ=( < ≤ ); The Mach number of the incoming flow; The three-dimensional oblique shock wave angle; This is the first critical shock angle; This is the second key shock angle; This refers to the third key shock angle.

10. The apparatus according to claim 7, characterized in that, The first prediction unit includes: The first construction module is used to construct a correction formula in the first region by combining the hypersonic equivalence principle and the two-dimensional motion shock wave reflection model; wherein, the hypersonic equivalence principle is... The two-dimensional motion shock wave reflection model is as follows: The corrected formula is: ; The location of the three-dimensional oblique shock wave reflection type change corresponding to the first region; The Mach number of the incoming flow; The preset shock angle; The Mach number for a two-dimensional motion shock wave; The position represents the change in the reflection type of the two-dimensional moving shock wave; k is a correction coefficient. The first prediction module is used to predict the location of the three-dimensional oblique shock wave reflection type change corresponding to the first region based on the correction formula.

11. The apparatus according to claim 7, characterized in that, The second prediction unit includes: The second determining module is used to determine, in the second region, the three-dimensional oblique shock wave reflection type transition position corresponding to the first critical shock wave angle, and the three-dimensional oblique shock wave reflection type transition position corresponding to the second critical shock wave angle; The second construction module is used to construct a first linear equation based on the three-dimensional oblique shock wave reflection type transition position corresponding to the first key shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle; wherein, the first linear equation is: ; This represents the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region; The position corresponding to the three-dimensional oblique shock wave reflection type change at the second key shock wave angle; The position of the three-dimensional oblique shock wave reflection type change corresponding to the first key shock wave angle; The Mach number of the incoming flow; The preset shock angle; This is the second key shock angle; This is the first critical shock angle; The second prediction module is used to predict the location of the three-dimensional oblique shock wave reflection type transition corresponding to the second region based on the first linear equation.

12. The apparatus according to claim 7, characterized in that, The third prediction unit includes: The third determining module is used to determine, in the third region, the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle, and the three-dimensional oblique shock wave reflection type transition position corresponding to the third key shock wave angle; The third construction module is used to construct a second linear equation based on the three-dimensional oblique shock wave reflection type transition position corresponding to the second key shock wave angle and the three-dimensional oblique shock wave reflection type transition position corresponding to the third key shock wave angle; wherein, the second linear equation is: ; This refers to the three-dimensional oblique shock wave reflection type transition position corresponding to the third region; The position corresponding to the three-dimensional oblique shock wave reflection type change at the second key shock wave angle; The position corresponding to the three-dimensional oblique shock wave reflection type change at the third key shock wave angle; The Mach number of the incoming flow; The preset shock angle; This refers to the third key shock angle; This is the second key shock angle; The third prediction module is used to predict the three-dimensional oblique shock wave reflection type transition position corresponding to the third region based on the second linear equation.

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