A wind tunnel test method for flow field aerodynamic characteristics of aircraft head-of-wing seam

Abstract

The present disclosure provides a wind tunnel test method for flow field aerodynamic characteristics of an aircraft head annular gap. The method comprises: constructing an equivalent scaled test model; determining the flow field aerodynamic characteristics of the equivalent scaled test model; constructing a simplified test model; determining the flow field aerodynamic characteristics of the simplified test model; determining whether the surface pressure distribution difference of the same position in the two models is within a preset range, and in the case that the surface pressure distribution difference is within the preset range, using the simplified test model as the test model of the aircraft head to carry out the wind tunnel test. The present disclosure constructs the equivalent scaled test model of the aircraft head, simplifies the annular gap by using a circular nozzle, analyzes the flow field aerodynamic characteristics of the two test models, uses the simplified test model with the same flow field aerodynamic characteristics as the equivalent scaled test model to carry out the wind tunnel test, and uses the wind tunnel test result as the wind tunnel test result of the aircraft head, which is convenient for subsequent optimization process.

Description

Technical Field

[0001] This disclosure relates to the field of aircraft testing technology, and in particular to a wind tunnel testing method and apparatus for the aerodynamic characteristics of the flow field of annular seam in the nose of an aircraft. Background Technology

[0002] The reverse jet at the aircraft nose, as an active flow control method, interacts with the incoming flow to alter the flow field structure at the aircraft nose and is widely used in the drag reduction and heat dissipation design of high-speed aircraft. Domestic and international scholars have conducted extensive research on the layout and parameters of the reverse jet at the aircraft nose. The interaction between the reverse jet and the external flow significantly alters the surface and spatial flow of the aircraft nose, necessitating accurate prediction of the drag reduction and heat dissipation effectiveness of the reverse jet. Wind tunnel testing and numerical prediction are crucial means to provide these results, and wind tunnel testing is also an important way to verify the accuracy of numerical simulation methods and guide their improvement.

[0003] The reverse jet configuration of the aircraft nose circumferential slot is a typical reverse jet layout. The slot width is generally within 1mm. Under the existing wind tunnel size conditions, the circumferential slot size of the scaled-down model is too small, which poses a problem that cannot be directly processed, resulting in the inability to conduct corresponding wind tunnel tests and affecting the optimization process of the aircraft nose. Summary of the Invention

[0004] The purpose of this disclosure is to provide a wind tunnel testing method and apparatus for the aerodynamic characteristics of the flow field of annular gaps in aircraft nose cones, in order to solve the problem that there is no existing wind tunnel testing design method for the aerodynamic characteristics of jets in aircraft nose cone gaps.

[0005] The embodiments of this disclosure adopt the following technical solution: a wind tunnel test method for the aerodynamic characteristics of the flow field of an annular slot in the nose of an aircraft, comprising: scaling down the nose of the aircraft according to a preset scaling ratio to form an equivalent scaled-down test model; determining the flow field aerodynamic characteristics of the equivalent scaled-down test model under wind tunnel test conditions; simplifying the annular slot in the equivalent scaled-down test model into N circumferentially uniformly distributed circular nozzles to form a simplified test model, where N is a positive integer; determining the flow field aerodynamic characteristics of the simplified test model under the wind tunnel test conditions; determining whether the difference in surface pressure distribution at the same location in the two models is within a preset range based on the flow field aerodynamic characteristics of the equivalent scaled-down test model and the flow field aerodynamic characteristics of the simplified test model; if the difference in surface pressure distribution is within the preset range, using the simplified test model as the test model for the nose of the aircraft to conduct wind tunnel tests; if the difference in surface pressure distribution is not within the preset range, adjusting the number and cross-sectional area of ​​the circular nozzles until the difference in surface pressure distribution is within the preset range.

[0006] In some embodiments, the method further includes: calculating the cross-sectional area of ​​the annular seam in the equivalent scaled-down test model, so that the sum of the cross-sectional areas of all the circular nozzles is the same as the cross-sectional area of ​​the annular seam.

[0007] In some embodiments, N is an even number greater than or equal to 8.

[0008] In some embodiments, the flow field aerodynamic characteristics of both the equivalent scaled-down test model and the simplified test model are determined based on numerical simulation.

[0009] In some embodiments, the turbulence model used in the numerical simulation method is the SA model, and the governing equations are the three-dimensional compressible Reynolds-averaged Navier-Stokes equations. Based on the turbulence model and boundary conditions, the governing equations are discretized to obtain discrete terms and the discretized governing equations. The discretized governing equations are solved based on the discrete terms to obtain discrete values ​​of the aerodynamic characteristics of the flow field.

[0010] In some embodiments, the discrete terms include at least: convection term discrete, viscous term discrete, and time term discrete; wherein the convection term discrete is represented using a second-order precision Roe scheme, the viscous term discrete is represented using a central difference scheme, and the time term discrete uses the LU-SGS implicit method.

[0011] In some embodiments, the centers of the N circular nozzles are located on the center line of the simplified annular seam, and the N circular nozzles are centrally symmetrically distributed.

[0012] This disclosure also provides a wind tunnel testing apparatus for the aerodynamic characteristics of the flow field of an annular slot in the nose of an aircraft, comprising: an equivalent model construction module for scaling down the nose of the aircraft according to a preset scaling ratio to form an equivalent scaled-down test model; a first determination module for determining the aerodynamic characteristics of the flow field of the equivalent scaled-down test model under wind tunnel test conditions; a simplified model construction module for simplifying the annular slot in the equivalent scaled-down test model into N circumferentially uniformly distributed circular nozzles to form a simplified test model, where N is a positive integer; and a second determination module for determining the simplified model under the wind tunnel test conditions. The test model's flow field aerodynamic characteristics; the test model optimization module, used to determine whether the difference in surface pressure distribution at the same location in the two models is within a preset range based on the flow field aerodynamic characteristics of the equivalent scaled-down test model and the simplified test model; if the difference in surface pressure distribution is within the preset range, the simplified test model is used as the test model for the aircraft's nose to conduct wind tunnel tests; if the difference in surface pressure distribution is not within the preset range, the number and cross-sectional area of ​​the circular nozzles are adjusted until the difference in surface pressure distribution is within the preset range.

[0013] The beneficial effects of this disclosure are as follows: an equivalent scaled-down test model of the aircraft nose is constructed, and the annular gap is simplified by using a circular nozzle. By analyzing the flow field aerodynamic characteristics of the two test models, a simplified test model with the same flow field aerodynamic characteristics as the equivalent scaled-down test model is used for wind tunnel testing, which serves as the wind tunnel test result of the aircraft nose, facilitating the implementation of subsequent optimization processes. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in 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 some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart of a wind tunnel test method for the flow field aerodynamic characteristics of an annular gap in the nose of an aircraft, as described in the first embodiment of this disclosure.

[0016] Figure 2 This is a schematic diagram of the equivalent scaled-down test model in the first embodiment of this disclosure;

[0017] Figure 3 This is a simplified experimental model diagram in the first embodiment of this disclosure;

[0018] Figure 4 This is a schematic diagram of the wind tunnel test structure for the flow field aerodynamic characteristics of the aircraft nose circumferential gap in the second embodiment of this disclosure. Detailed Implementation

[0019] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0020] The reverse jet at the aircraft nose, as an active flow control method, interacts with the incoming flow to alter the flow field structure at the aircraft nose and is widely used in the drag reduction and heat dissipation design of high-speed aircraft. Domestic and international scholars have conducted extensive research on the layout and parameters of the reverse jet at the aircraft nose. The interaction between the reverse jet and the external flow significantly alters the surface and spatial flow of the aircraft nose, necessitating accurate prediction of the drag reduction and heat dissipation effectiveness of the reverse jet. Wind tunnel testing and numerical prediction are crucial means to provide these results, and wind tunnel testing is also an important way to verify the accuracy of numerical simulation methods and guide their improvement.

[0021] The reverse jet configuration of the aircraft nose circumferential slot is a typical reverse jet layout. The slot width is generally within 1mm. Under the existing wind tunnel size conditions, the circumferential slot size of the scaled-down model is too small, which poses a problem that cannot be directly processed, resulting in the inability to conduct corresponding wind tunnel tests and affecting the optimization process of the aircraft nose.

[0022] To address the aforementioned problems, the first embodiment of this disclosure provides a wind tunnel testing method for the aerodynamic characteristics of the flow field in the nose circumferential gap of an aircraft, the flowchart of which is shown below. Figure 1 As shown, it mainly includes steps S10 to S50:

[0023] S10, according to the preset scaling ratio, the nose of the aircraft is reduced to form an equivalent scaled-down test model;

[0024] S20, Under wind tunnel test conditions, determine the flow field aerodynamic characteristics of the equivalent scaled-down test model;

[0025] S30 simplifies the circumferential gap in the equivalent scaled-down test model into N circumferentially uniformly distributed circular nozzles to form a simplified test model, where N is a positive integer;

[0026] S40, Under wind tunnel test conditions, determine the flow field aerodynamic characteristics of the simplified test model;

[0027] S50, based on the aerodynamic characteristics of the flow field of the equivalent scaled-down test model and the aerodynamic characteristics of the flow field of the simplified test model, determine whether the difference in surface pressure distribution at the same location in the two models is within a preset range. If the difference in surface pressure distribution is within the preset range, use the simplified test model as the test model for the aircraft nose to conduct wind tunnel tests. If the difference in surface pressure distribution is not within the preset range, adjust the number and / or cross-sectional area of ​​the circular nozzles until the difference in surface pressure distribution is within the preset range.

[0028] In this embodiment, the preset scaling ratio can be set according to the actual size of the aircraft's nose and the wind tunnel size; this embodiment does not limit the specific value of the ratio. For example... Figure 2As shown, after the aircraft nose is scaled down, the size of the circumferential seam in the equivalent scaled-down test model is usually less than 1 mm. The actual manufacturing process cannot meet the requirements for the preparation of circumferential seams of the corresponding size. Therefore, by simplifying the equivalent scaled-down test model, a simplified test model that is easy to manufacture and has the same flow field aerodynamic characteristics as the equivalent scaled-down test model is obtained as the test subject for the wind tunnel test of the aircraft nose.

[0029] After determining the equivalent scaled-down test model, the process aerodynamic characteristics of the model were determined under wind tunnel test conditions to serve as the basis for selecting a simplified test model. Subsequently, the annular gap in the equivalent scaled-down test model was simplified into N circumferentially uniformly distributed circular nozzles. Taking advantage of the ease of fabrication of circular nozzles, a simplified test model was constructed, such as... Figure 3 As shown, where N is a positive integer, the flow field aerodynamic characteristics can be made the same as those of the equivalent scaled-down experimental model by designing a specific number of circular nozzles.

[0030] Specifically, when simplifying the equivalent scaled-down test model, the cross-sectional area S of the circumferential seam in the equivalent scaled-down test model can be determined first. Then, based on the cross-sectional area of ​​the circular nozzles achievable with current technology, the value of N can be determined so that the sum of the cross-sectional areas of all circular nozzles is the same as the cross-sectional area S of the circumferential seam in the equivalent scaled-down test model. It should be noted that the value of N is preferably set to an even number greater than or equal to 8 to ensure that multiple circular nozzles are evenly distributed circumferentially at the head of the model, thus better replicating the aircraft characteristics.

[0031] Furthermore, considering the ease of fabrication, this embodiment uses circular nozzles to represent the annular seam, and sets the centers of N circular nozzles on the model to be located on the center line of the original annular seam. All circular nozzles are centrally symmetrically distributed to reproduce the aerodynamic characteristics of the flow field at the nose of an aircraft with an annular seam. In some embodiments, the simplified nozzles can also be implemented using elliptical nozzles, but polygonal nozzles cannot be used. The angle between adjacent straight sides will cause changes in the aerodynamic characteristics at that location, making it impossible to completely reproduce the flow field aerodynamic characteristics of the equivalent scaled-down experimental model. At the same time, it is also impossible to perfectly reproduce specific angles when fabricating the solid model.

[0032] In the actual design process, a set of circular nozzle cross-sectional areas and their quantity N can be selected first, and the aerodynamic characteristics of the flow field of the simplified test model under the same wind tunnel test conditions can be determined accordingly. It should be understood that the aerodynamic characteristics of the flow field of both the equivalent scaled-down test model and the simplified test model can be determined using numerical simulation. Furthermore, to eliminate the influence of other variables on the analysis results, the simulation process of the numerical simulation method used for the flow field aerodynamic characteristics of both models should be completely consistent.

[0033] In some embodiments, the turbulence model in the numerical simulation method can be the SA model, and the governing equations are the three-dimensional compressible Reynolds-averaged Navier-Stokes equations. Based on the turbulence model and boundary conditions, the governing equations are discretized to obtain discrete terms and the discretized governing equations. The discretized governing equations are then solved based on the discrete terms to obtain discrete values ​​of the aerodynamic characteristics of the flow field. Finally, the aerodynamic characteristics of the flow field of the corresponding model can be determined through numerical analysis, feature extraction, and other operations. The discrete terms include at least: convection term discretization, viscous term discretization, and time term discretization. The convection term discretization uses the second-order accurate Roe scheme, the viscous term discretization uses the central difference scheme, and the time term discretization uses the LU-SGS implicit method.

[0034] Typically, the aerodynamic characteristics of a flow field include, but are not limited to, forces and moments, surface pressure distribution, flow structure, turbulence characteristics, and heat transfer characteristics. This embodiment focuses primarily on the surface pressure distribution. In this embodiment, based on the aerodynamic characteristics of the flow field of the equivalent scaled-down test model and the simplified test model, it can be determined whether the difference in surface pressure distribution at the same location in the two models is within a preset range, which can be limited to ±1%. If the difference in surface pressure distribution is within the preset range, the simplified test model can be directly used as the test model for the aircraft nose to conduct wind tunnel tests. If the difference in surface pressure distribution is not within the preset range, the number and cross-sectional area of ​​the circular nozzles are adjusted until the difference in surface pressure distribution is within the preset range, and the simplified test model that finally meets the conditions is used as the test model for the aircraft nose to conduct wind tunnel tests.

[0035] It is important to note that when adjusting the number and cross-sectional area of ​​the circular nozzles, the dimensions of the nozzles must meet the limitations of the manufacturing process and the constraints on the value of N. Furthermore, if multiple simplified experimental models corresponding to different cross-sectional areas and N values ​​exist, and the differences in surface pressure distribution at the same location between these models and the equivalent scaled-down experimental model are all within a preset range, then the simplified experimental model corresponding to the set with the largest N value and the smallest circular nozzle cross-sectional area should be selected. This will allow the design of the circular nozzles to closely approximate the design of the circumferential seam, resulting in more accurate aerodynamic characteristics of the flow field.

[0036] This embodiment constructs an equivalent scaled-down test model of the aircraft nose and simplifies the circumferential gap using a circular nozzle. By analyzing the flow field aerodynamic characteristics of the two test models, a simplified test model with the same flow field aerodynamic characteristics as the equivalent scaled-down test model is used for wind tunnel testing to serve as the wind tunnel test result of the aircraft nose, which facilitates the subsequent optimization process of the aircraft nose.

[0037] Based on the same inventive concept, the second embodiment of this disclosure provides a wind tunnel testing device for the aerodynamic characteristics of the flow field of an annular gap in the nose of an aircraft, as shown in the schematic diagram below. Figure 4 As shown, the system mainly includes: an equivalent model construction module 10 for scaling down the aircraft head according to a preset scaling ratio to form an equivalent scaled-down test model; a first determination module 20 for determining the flow field aerodynamic characteristics of the equivalent scaled-down test model under wind tunnel test conditions; a simplified model construction module 30 for simplifying the annular gap in the equivalent scaled-down test model into N circumferentially uniformly distributed circular nozzles to form a simplified test model, where N is a positive integer; a second determination module 40 for determining the flow field aerodynamic characteristics of the simplified test model under wind tunnel test conditions; and a test model optimization module 50 for determining whether the surface pressure distribution difference at the same location in the two models is within a preset range based on the flow field aerodynamic characteristics of the equivalent scaled-down test model and the simplified test model. If the surface pressure distribution difference is within the preset range, the simplified test model is used as the test model for the aircraft head to conduct wind tunnel tests; if the surface pressure distribution difference is not within the preset range, the number and cross-sectional area of ​​the circular nozzles are adjusted until the surface pressure distribution difference is within the preset range.

[0038] In some embodiments, the first determining module 20 is further configured to calculate the cross-sectional area of ​​the circumferential seam in the equivalent scaled-down test model, so that the sum of the cross-sectional areas of all the circular nozzles is the same as the cross-sectional area of ​​the circumferential seam.

[0039] In some embodiments, N is an even number greater than or equal to 8.

[0040] In some embodiments, both the first determining module 20 and the second determining module 40 determine the flow field aerodynamic characteristics of the equivalent scaled-down experimental model and the simplified experimental model based on numerical simulation. Specifically, in the numerical simulation, the turbulence model is the SA model, and the governing equations are the three-dimensional compressible Reynolds-averaged Navier-Stokes equations. Based on the turbulence model and boundary conditions, the governing equations are discretized to obtain discrete terms and the discretized governing equations. The discretized governing equations are solved based on the discrete terms to obtain discrete values ​​of the flow field aerodynamic characteristics. The discrete terms include at least: convection term discretization, viscous term discretization, and time term discretization; wherein, the convection term discretization is represented by the second-order accurate Roe scheme, the viscous term discretization is represented by the central difference scheme, and the time term discretization uses the LU-SGS implicit method.

[0041] In some embodiments, the simplified model building module 30 places the centers of the N circular nozzles on the center line of the simplified annular seam, and the N circular nozzles are centrally symmetrically distributed.

[0042] In this embodiment, the test model optimization module 50 determines whether the difference in surface pressure distribution at the same location in the two models is within a preset range based on the flow field aerodynamic characteristics of the equivalent scaled-down test model and the simplified test model. The preset range can be limited to ±1%. If the difference in surface pressure distribution is within the preset range, the simplified test model can be directly used as the test model for the aircraft nose to conduct wind tunnel tests. If the difference in surface pressure distribution is not within the preset range, the test model optimization module 50 instructs the simplified model construction module 30 to adjust the number and cross-sectional area of ​​the circular nozzles, and the second determination module 40 redetermines the flow field aerodynamic characteristics of the adjusted simplified model until the difference in surface pressure distribution is within the preset range. Finally, the simplified test model that meets the conditions is used as the test model for the aircraft nose to conduct wind tunnel tests.

[0043] It is important to note that when the simplified model building module 30 adjusts the number and cross-sectional area of ​​the circular nozzles, it should ensure that the size of the circular nozzles meets the limitations of the manufacturing process and the value of N. Furthermore, if multiple simplified experimental models with the same cross-sectional area and N value exist, and the differences in surface pressure distribution at the same location between these models and the equivalent scaled-down experimental model are all within a preset range, then the experimental model optimization module 50 selects the simplified experimental model corresponding to the set of data with the largest N value and the smallest circular nozzle cross-sectional area. This is to make the design of the circular nozzle as close as possible to the design of the annular seam, thereby obtaining more accurate aerodynamic characteristics of the flow field.

[0044] This embodiment constructs an equivalent scaled-down test model of the aircraft nose and simplifies the circumferential gap using a circular nozzle. By analyzing the flow field aerodynamic characteristics of the two test models, a simplified test model with the same flow field aerodynamic characteristics as the equivalent scaled-down test model is used for wind tunnel testing to serve as the wind tunnel test result of the aircraft nose, which facilitates the subsequent optimization process of the aircraft nose.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this disclosure, and are not intended to limit them. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this disclosure.

Claims

1. A wind tunnel testing method for the aerodynamic characteristics of the flow field in the nose circumferential gap of an aircraft, characterized in that, include: The nose of the aircraft was scaled down according to a preset scaling ratio to form an equivalent scaled-down test model; Under wind tunnel test conditions, the flow field aerodynamic characteristics of the equivalent scaled-down test model were determined; The circumferential gap in the equivalent scaled-down test model is simplified into N circumferentially uniformly distributed circular nozzles to form a simplified test model, where N is a positive integer; Under the wind tunnel test conditions, the flow field aerodynamic characteristics of the simplified test model were determined; Based on the flow field aerodynamic characteristics of the equivalent scaled-down test model and the flow field aerodynamic characteristics of the simplified test model, determine whether the difference in surface pressure distribution at the same location in the two models is within a preset range. If the difference in surface pressure distribution is within the preset range, use the simplified test model as the test model for the nose of the aircraft to conduct wind tunnel tests. If the difference in surface pressure distribution is not within the preset range, adjust the number and cross-sectional area of ​​the circular nozzles until the difference in surface pressure distribution is within the preset range; The flow field aerodynamic characteristics of both the equivalent scaled-down test model and the simplified test model are determined based on numerical simulation. In the numerical simulation, the SA model is selected as the turbulence model, and the three-dimensional compressible Reynolds-averaged Navier-Stokes equations are used as the governing equations. Based on the turbulence model and boundary conditions, the governing equations are discretized to obtain discrete terms and the discretized governing equations. Based on the discrete terms, the discretized governing equations are solved to obtain the discrete values ​​of the flow field aerodynamic characteristics.

2. The wind tunnel testing method for the aerodynamic characteristics of the flow field according to claim 1, characterized in that, Also includes: Calculate the cross-sectional area of ​​the circumferential seam in the equivalent scaled-down test model so that the sum of the cross-sectional areas of all the circular nozzles is the same as the cross-sectional area of ​​the circumferential seam.

3. The wind tunnel testing method for the aerodynamic characteristics of the flow field according to claim 1, characterized in that, N is an even number greater than or equal to 8.

4. The wind tunnel testing method for the aerodynamic characteristics of the flow field according to claim 1, characterized in that, The discrete terms include at least: convection term discrete, viscous term discrete, and time term discrete; wherein the convection term discrete is represented using the second-order precision Roe scheme, the viscous term discrete is represented using the central difference scheme, and the time term discrete uses the LU-SGS implicit method.

5. The wind tunnel testing method for the aerodynamic characteristics of the flow field according to any one of claims 1 to 4, characterized in that, The centers of the N circular nozzles are located on the center line of the simplified annular seam, and the N circular nozzles are centrally symmetrically distributed.

6. A wind tunnel testing apparatus for the aerodynamic characteristics of the flow field in the nose circumferential gap of an aircraft, characterized in that, include: The equivalent model construction module is used to scale down the nose of the aircraft according to a preset scaling ratio to form an equivalent scaled-down test model. The first determining module is used to determine the flow field aerodynamic characteristics of the equivalent scaled-down test model under wind tunnel test conditions. A simplified model construction module is used to simplify the circumferential gap in the equivalent scaled-down test model into N circumferentially uniformly distributed circular nozzles to form a simplified test model, where N is a positive integer; The second determining module is used to determine the flow field aerodynamic characteristics of the simplified test model under the wind tunnel test conditions; The test model optimization module is used to determine whether the difference in surface pressure distribution at the same location in the two models is within a preset range based on the flow field aerodynamic characteristics of the equivalent scaled-down test model and the flow field aerodynamic characteristics of the simplified test model. If the difference in surface pressure distribution is within the preset range, the simplified test model is used as the test model for the nose of the aircraft to conduct wind tunnel tests. If the difference in surface pressure distribution is not within the preset range, adjust the number and cross-sectional area of ​​the circular nozzles until the difference in surface pressure distribution is within the preset range; The flow field aerodynamic characteristics of both the equivalent scaled-down test model and the simplified test model are determined based on numerical simulation. In the numerical simulation, the SA model is selected as the turbulence model, and the three-dimensional compressible Reynolds-averaged Navier-Stokes equations are used as the governing equations. Based on the turbulence model and boundary conditions, the governing equations are discretized to obtain discrete terms and the discretized governing equations. Based on the discrete terms, the discretized governing equations are solved to obtain the discrete values ​​of the flow field aerodynamic characteristics.

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