Numerical simulations of complex aircraft configurations using structured overset grids with implicit hole-cutting

Aerospace Science and Technology 94 (2019) 105402

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Numerical simulations of complex aircraft configurations using structured overset grids with implicit hole-cutting Weiqing Jiang, Yong Zhang, Aiming Yang ∗ Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China

a r t i c l e

i n f o

Article history: Received 24 April 2019 Received in revised form 15 September 2019 Accepted 15 September 2019 Available online 18 September 2019 Keywords: Overset grids Implicit hole-cutting High-lift configurations

a b s t r a c t A structured overset-grids method with enhanced implicit hole-cutting has been developed to simulate the flow around aircraft configurations, especially high-lift configurations. The current research uses the implicit hole-cutting method to improve the automation of domain connectivity and optimize the overlapping areas. Some enhancements for the original implicit hole-cutting method are proposed to make it more effective. Furthermore, a simple method for calculating the force on the overlapping solid surfaces is also presented. Jameson’s second-order finite volume method is utilized to solve the NavierStokes equations. A wing-body configuration and two high-lift configurations are numerically tested and the numerical results are compared with the experimental data. © 2019 Elsevier Masson SAS. All rights reserved.

1. Introduction Grid generation is the most time-consuming part of the whole computational fluid dynamics (CFD) process, especially when dealing with complex aircraft configurations. The grids used in modern CFD can be grouped into two main categories: structured grids and unstructured grids. Under the framework of structured grids, the overset-grids method [1] is arguably the best choice to generate the grids around a complex aircraft configuration. In this method, the complex geometric configuration is firstly decomposed into several components with simple geometry, so that grids around these components can be easily created separately. The component grid blocks are allowed to overlap with each other arbitrarily without careful consideration. The inter-grid data communication among these overlapped blocks is achieved through interpolation. The overset-grids method greatly improves the efficiency and reduces the difficulty of grid generation for complex geometric configurations. Because of these advantages, this grid method has been widely used in the past decades [2–8]. Although this method has its own benefits in efficiency and simplicity, the traditional overset-grids method, or the oversetgrids method with explicit hole-cutting, involves an expensive preprocessing procedure before the flow computation, so that the flow solutions can be accurately transferred among the overlapped grid blocks. This pre-processing procedure consists of the follow-

*

Corresponding author. E-mail address: [email protected] (A. Yang).

https://doi.org/10.1016/j.ast.2019.105402 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.

ing three steps: (1) Hole cutting, i.e., identifying the hole cells which are inside the hole boundaries containing all solid bodies. The smallest hole boundary is obviously the body surface. The hole cells are the invalid grid cells and should be blanked out in the flow computation. (2) Identifying the interpolated boundary cells (IBCs) which are the immediate neighbors of the hole cells. Generally, two layers of fringe cells are used to maintain the secondorder accuracy. (3) Identifying the donor cells which provide the data to the IBCs. An important problem related to hole-cutting in the traditional method is how to optimize the hole boundaries to ensure the accuracy of data communication. At present, some effective optimization methods have been proposed [23,24], which makes the traditional overset-grids method widely used in computational fluid dynamics. Unlike the traditional method, the oversetgrids method based on implicit hole-cutting (IHC) presented by Lee and Baeder [9] is only a donor cell selection process based on the criterion of cell geometry such as the cell volume. The detection of the solid bodies is the byproduct of this process, so the hole-cutting is completed implicitly. In this method, the hole cells need not be identified and blanked out in the flow solver, since the pseudo information at those points can’t contaminate the flow solution. The IHC has the advantages in terms of the automation of pre-processing and the optimal hole boundaries. Because of these superiorities, the IHC method has been applied to some engineering applications and has attracted some research attentions in recent years [10–12]. However, this method is seldom used to engineering applications with extremely complex geometry, such as three-dimensional high-lift configurations.

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The focus of the present study is to introduce the enhanced IHC to the flow simulation of three-dimensional high-lift configurations. Because of the flow and geometric complexity, accurate and efficient simulation of high-lift configurations is still a challenging problem in the field of CFD. In the current work, the IHC is used not only to improve the automation of grid assembly, but also to optimize the hole boundaries, which can make the inter-grid data communication among the overlapping zones more precise. In order to facilitate flow visualization and improve computational efficiency, the original IHC method is improved in this paper. In addition, a convenient and effective method for calculating forces on overlapping surfaces is suggested.

The Navier-Stokes equations in integral form can be written as

‹ WdV +

V

(H − H v ) • ndS = 0

(1)

∂V

where V is a control volume with surface ∂ V and unit normal n, W are the conservative variables, H and H v are the convective and viscous flux tensors. They are given by

⎤

⎡

⎡

ρ ⎢ ρu ⎥ ⎥ ⎢ ⎥ ⎢ W = ⎢ ρv ⎥ ⎥ ⎢ ⎣ ρw ⎦ ρE ⎡

ρV

⎤

d dt

(Wi , j ,k ) = Ri , j ,k (W)

(6)

In these equations, V i , j ,k is the volume, Wi , j ,k is the volume average of the conservative variables stored at the cell center, R(W) is the residual given by

⎤

ρ HV

Qi , j ,k (W) =

(7)

6 

(H − H v ) f • S f

(8)

f =1

D(W) is the artificial dissipation consisting of the second-order and fourth-order dissipation terms. The purpose of adding artificial dissipation is to eliminate numerical instability. The semi-discrete equations (6) are integrated in time using the implicit LU-SGS scheme [16]. Since only the steady solution is of interest, the time derivative term is approximated by first-order discretization as

V i , j ,k

⎢ ρ uV + pi ⎥ ⎥ ⎢ ⎥ ⎢ Hc = ⎢ ρ vV + pj ⎥ ⎥ ⎢ ⎣ ρ wV + pk ⎦ 0

V i , j ,k

where Q(W) is the net flux

2.1. Governing equations

˚

The cell-centered finite volume method developed by Jameson et al. [15] is used to solve the Navier-Stokes equations. For an arbitrary control volume (i, j, k), the semi-discrete form of Eq. (1) is given as follows

Ri , j ,k (W) = Q(W)i , j ,k − D(W)i , j ,k

2. Numerical methods

∂ ∂t

2.2. Space discretization and time integration

Wn+1 − Wn

t

+ Rn+1 (W) = 0

(9)

Then the residual R is linearized as follows

Rn+1 = Rn + (2)



∂R ∂W

n

 2 Wn + oWn 

(10)

where Wn = Wn+1 − Wn . The second and higher order terms are dropped from the above formulation. Substituting Eq. (10) into Eq. (9) and splitting the Jacobian matrices, we obtain

⎢ τxx i + τxy j + τxz k ⎥ ⎥ ⎢ ⎥ ⎢ H v = ⎢ τxy i + τ y y j + τ yz k ⎥ ⎥ ⎢ ⎣ τxz i + τ yz j + τzz k ⎦ x i +  y j +  z k

(L + D + U)Wn = −Rn

where ρ is the density, u, v, and w are the three Cartesian components of velocity V, p is the pressure, E is the total energy, H is the total enthalpy, τ is the viscous stress. x ,  y and z are expressed as

(3)

z = u τxz + v τ yz + w τzz + k∂ T /∂ z



L = − A+ + B+ + C+ i −1, j ,k i , j −1,k i , j ,k−1   V i , j ,k D= + σ (ρA + ρB + ρC ) t



(4)

The turbulence transport equation for the turbulence variable, νˆ is given by

(12)

Here, A± , B± and C± are the split Jacobian matrices and given by

A± =

where k is the heat conductivity and T is the temperature. The turbulent eddy viscosity is predicted by the one-equation Spalart-Allmaras model [13] and is given by the expression

μt = ρ νˆ f ν 1

The three operators L, D and U are defined as follows

U = A− + B− + C− i +1, j ,k i , j +1,k i , j ,k+1

x = u τxx + v τxy + w τxz + k∂ T /∂ x  y = u τxy + v τ y y + w τ yz + k∂ T /∂ y

(11)

A ± σρ A I 2

,

B± =

B ± σρ B I 2

,

C± =

C ± σρ B I 2

(13)

where A, B and C are the flux Jacobian matrices in the three coordinate direction, ρA , ρB and ρC are their corresponding spectral radii, I is the identity matrix, σ is a constant greater than one. Eq. (11) can be approximately factored into

(L + D)D−1 (U + D)Wn = −Rn

(14)

The solution for the above equations is completed by an L sweep and a U sweep, in which the matrix inversion is not necessary.



Dν Dt







= P (ν ) − D diss (ν ) + D di f f (ν )

(5)

Here, the three right-hand terms are turbulence production, dissipation and diffusion source terms, respectively. The details of this equation can be found in [14].

2.3. Grid generation A typical overset grid system consists of two parts: the off-body Cartesian grid (background grid) covering the entire computational domain and the near-body curvilinear grids capturing the near-

W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

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Fig. 1. Illustration of the original IHC method.

field flow, especially the viscous boundary-layer flow. The generation of body-fitted grids with high quality is a time-consuming work. In this study, the hyperbolic grid generation method [17] is employed to generate component volume grids, since this method does not need to define the far-field boundary grid and can maintain the orthogonality near the body surface. The scale of the first layer grid can be adjusted arbitrarily to model the near-field viscous flow as well. 2.4. The IHC method The original IHC method [9] contains two steps: (1) Define the quality criterion for all grid cells in the overlapping regions. This parameter is used to identify the most suitable donor cell based on some physical or geometrical standard such as volume, wall distance or aspect ratio. (2) Search donor cells for every cell in the overlapping regions. For a cell P, if there exists a donor cell with higher quality than cell P, then cell P is marked as an interpolated cell. If there is no donor cell or none of the donor cells is of higher quality than cell P, then cell P is marked as a calculated cell. In this method, there is no hole cell, and thus the tedious process of identification and modification of hole boundaries is avoided. Take a two-dimensional case as an example. A body-fitted grid around a cylinder overlaps with a Cartesian background grid shown in Fig. 1(a). In the overlapping region, the grid quality of the cylinder grid cells is better than that of the background grid cells. As shown in Fig. 1(b), the background grid cells that can find donor cell from the cylinder grid are marked as interpolated cells, the others are marked as calculated cells. Although the background cells located inside the solid surface are labeled as calculated cells, their values do not affect the computational results since these cells are surrounded by interpolated cells. As mentioned above, the original IHC method can only distinguish between calculated cells and interpolated cells by comparing cell quality, no blanked cells (hole cells) are identified during this process, which is different from the traditional overset method. This in turn leads to two problems. The first is that the cells inside the solid surface make the flow visualization difficult. The second problem is that the number of interpolated cells is too large, which results in too much unnecessary calculation and the interpolated boundary is too close to the solid surface where the gradient of flow variables may be large. In order to improve the above prob-

lems, some enhancements are made to the original IHC method in this study. Firstly, the grid cells inside solid bodies are marked as blanked cells before implicit hole-cutting. This process is accomplished by flooding algorithm, which is widely used in the field of image processing. The first step of this process is to specify a calculated cell located in the solid surface, and the selection of this cell is arbitrary. Then a recursive algorithm is used to remove all the calculated cells associated with this specified cell. This process is somewhat similar to the spread of infectious diseases. The initially specified cell can be considered as the source of infection. The calculated cells adjacent to this source cell are infected and then become the other sources of infection. The interpolated cells around the solid surface can be considered as immune cells and will not be infected. The algorithm in FORTRAN can be given as follows recursive subroutine hole_blank (i, j, k) if (iblank(i, j, k)==1.and.(iblank(i-1, j, k).ne.0.or. iblank(i+1, j, k).ne.0 & .or. iblank(i, j-1, k).ne.0.or. iblank(i, j+1, k).ne.0 & .or. iblank(i, j, k-1).ne.0.or. iblank(i, j, k+1).ne.0)then iblank(i, j, k) = -1 call hole_blank (i-1, j, k) call hole_blank (i+1, j, k) call hole_blank (i, j-1, k) call hole_blank (i, j+1, k) call hole_blank (i, j, k-1) call hole_blank (i, j, k+1) endif return end

In this algorithm, the value of iblank represents the nature of the cell, 1 represents the calculated cell, 0 represents the interpolated cell, and - 1 represents the hole cell (blanked cell). Secondly, during the donor search process, grid cells that have donor cells with better quality than themselves are marked as noncalculated cells rather than interpolated cells. Only several layers of non-calculated cells adjacent to the calculated cells are defined as interpolated cells according to the accuracy of the flow solver. This process is still accomplished by applying the flooding algorithm. In addition, the product of cell volume and wall distance is chosen as the cell quality criterion in the current research. According

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W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

Fig. 2. Illustration of the enhanced IHC method.

to the experience of Xu et al. [10], the introduction of wall distance can significantly reduce the number of orphan cells, which are interpolated cells that could not find their donor cells. Take the previous case as an example again. After the enhanced IHC, the background grid is shown in Fig. 2. The background cells

that fall inside the solid surface, which are identified as calculated cells in the original IHC, are blanked out from the computational domain. Most of the background cells defined as interpolation elements in the original IHC have become non-computational elements in the improved method. In this case, only two layers of grid cells adjacent to the calculated cells are identified as interpolated cells. The above example is not enough to show that the enhanced IHC can effectively handle a complex aircraft configuration, so some two-dimensional problems arising from complex aircraft configurations, such as a thin airfoil, a multi-element airfoil and a wing-body cross-section, are investigated using the improved method. Fig. 3 shows the hole-cutting result for the thin-airfoil problem using the present method. As can be seen in Fig. 3(b) and (c), near the trailing edge of the airfoil, two edges of a background grid cell intersect with the airfoil boundary, but the corresponding grid points are outside the boundary, which is called the thinairfoil problem. Fig. 3(d) demonstrates that the thin-airfoil problem can be solved automatically using the enhanced IHC method. Because the quality of the airfoil mesh near the trailing edge is better than that of the background mesh intersecting with the solid boundary, these background grid cells are recognized as interpolated cells. The second case is a multi-element airfoil problem as showed in Fig. 4. The two airfoil meshes are overlapped each other and covered by the background grid. The final hole-cutting result, as demonstrated in Fig. 4(e), shows that the proposed method can

Fig. 3. A thin airfoil.

W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

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Fig. 4. A multi-element airfoil.

deal with the multi-body problem successfully. The third example is a wing-body cross-section, as shown in Fig. 5, around which there are a wing-grid, a body-grid, a collar-grid and a background grid. The only additional step is to add a layer of ghost grid to the normal end of the body grid in order to implement the flooding algorithm smoothly when dealing with the overlapping between the body grid and the wing grid. Fig. 5(d) gives the satisfactory hole-cutting results, which shows that the current method can deal with the wing-body problem. 2.5. Aerodynamic force computation on overset surface grids The total aerodynamic forces acting on the aircraft are obtained by integrating the aerodynamic forces on the surface grids. Unlike the multi-block patched grid technique, the overset-grids method faces the problem that there are overlapping areas between solid surfaces, which brings difficulties to the calculation of surface forces. In order to solve this problem, we present a method that is based on the results of implicit hole-cutting. Taking a wing-body combination as an example, the surface grid on the body consists of two overlapping parts: body surface grid and collar surface grid, as shown in Fig. 6. In this example, we firstly choose the collar surface grid as the main grid, that is, all the calculated cells on this surface grid are involved in the calculation of forces. It is worth pointing out that the outer boundary of the calculated cells on the collar surface grid is not necessarily a grid line, but is generated automatically after the IHC process. Then the next step is to find on the body surface grid the calculated cells that intersect with the outer boundary of the collar

surface. A parameter, area ratio parameter a, is introduced to the calculated cells on the body surface grid, as shown in Fig. 7. This parameter represents the ratio of the non-overlapping area to the total area, which is used to calculate the contribution of the cell to the force. The force acting on the cell can be expressed as follows

Fi = a i •  Fi

(15)

where ai denotes the area ratio of the i-th interpolated cell, Fˆ i refers to the force acting on the i-th interpolated cell, which has not been corrected by overlapping area, and Fi is the modified force which is actually applied to integrate the total force acting on the body. In this paper, a simple approximation method is used to calculate the area ratio parameter. As shown in Fig. 7, solid dots and squares represent the centers of calculated cells in zone 1 and zone 2, respectively. The grid centers are connected by dashed lines, while the grid vertices are connected by solid lines. At First, the calculated cells in zone 1, which are adjacent to the outer boundary of calculated cells in zone 2, are divided into N × N pieces of sub-cells. In current computations, N is set to be 10. If the grid quality is not too bad, the area of each sub-cell is approximately equal. Then we identify the number of sub-cells that are completely inside or intersect the calculated cells in zone 2. We define this number as M, and area ratio parameter can be approximately given by

a≈1−

M N×N

(16)

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W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

Fig. 5. A wing-body cross-section.

3. Results and discussions Since the focus of this investigation is to explore the application of overset-grids method with IHC in dealing with complex aircraft configurations, the grid convergence study was not carried out in the following computations. The choice of the number of grid points in the present study referred to the data of the first Drag Prediction Workshop (DPW-I) [20] and the first AIAA CFD High Lift Prediction Workshop (HiLiftPW-1) [21]. 3.1. DLR-F4 wing-body model

Fig. 6. Surface grids on the wing-body configuration.

Although this method has a certain degree of approximation, the accuracy is sufficient for the second-order flow solver, as used in the present study. It should be pointed out that the proposed method of force calculation is only of first-order accuracy and only considers two overlapping surfaces. Therefore, this method is not suitable for the problem of using high-order scheme or containing multiple overlapping surfaces.

The first test case is the DLR-F4 wing-body model [18] that is widely used for CFD verification. This model was used in this study as a simple example to verify the effectiveness of the present method. Overset grids around the semi-span model are shown in Fig. 8. The overset grid system includes not only wing grid, fuselage grid and background grid, but also cap grid and collar grid. The collar grid connects the fuselage and the wing, which provides the donor cells for the interpolated cells that could not find their donor cells in the wing grid or fuselage grid. The cap grid is generated around the wing tip to enclose the geometry. The total grid number is approximately 5.1 × 106. The free-stream flow conditions are as follows: the Mach number is 0.75 and the Reynolds number is 3.0 × 106.

W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

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Fig. 7. Illustration of force computation on overlapped surfaces.

Fig. 8. Overset grids for DLR-F4 model.

In order to compare the influence of implicit hole-cutting

that implicit hole-cutting makes the interpolation between over-

method and the explicit hole-cutting method without hole opti-

lapping grids more accurate and can be used as an optimization

mization on the computed results, the two overset methods were

method for hole boundaries.

applied simultaneously in this case. Fig. 9 presents the contour lines of pressure on the plane of 50% semi-span at angle of attack

α = 1.0◦ . It is obvious from this figure that the interpolated

boundary is far from the solid surface and the contours near the interpolated boundary are fairly smooth with the implicit hole-

The computed surface pressure coefficient distributions at different spanwise locations at angle of attack

α = 1.0◦ are compared

with the experimental data [18] in Fig. 10. The lift and drag curves are plotted in Fig. 11. The above numerical results shown in Fig. 10

cutting method. However, this is not the case with the explicit

and Fig. 11 are based on the implicit hole-cutting method, which

hole-cutting method without hole optimization. This also indicates

agree well with the experimental data.

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W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

Fig. 9. Comparison of pressure contour lines with different hole-cutting methods.

Fig. 10. Pressure coefficient distributions.

3.2. NASA trapezoidal (trap) wing with full-span flap The NASA trap wing model [19] is a three-element high-lift configuration that has been widely used to assess a CFD code’s ability to accurately predict the aerodynamic performance of high

lift configurations. Although this model cannot ideally represent a transport aircraft in a high-lift configuration, the flow field is characterized by the main flow physics of high-lift configuration flow. The trap wing model has a series of different configurations and the full-span flap configuration, which was the research model in

W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

Fig. 11. Lift and drag coefficients.

the first AIAA CFD High Lift Prediction Workshop, was chosen in this test case. The geometry conditions of Config.1 of this model used in this computation are as follows: the slat deflection is 30◦ and the flap deflection is 25◦ , the slat gap and flap gap are both 0.015c, where c is the mean aerodynamic chord. Since the geometry of this model is relatively simple, the overset grids for it were downloaded directly from the website of the

9

first AIAA CFD High Lift Prediction Workshop. Depending on our existing computing resources, the coarse grid with approximately 6.5 × 106 cells have been adopted in this computation. The overset grids system for the full-span flap model is shown in Fig. 12. The free-stream flow conditions are as follows: the Mach number is 0.2 and the Reynolds number is 4.63 × 106 . Stream lines and pressure contours on the surface of the fullspan flap model at angel of attack α = 13.0◦ are displayed in Fig. 13. It can be observed that flow separation occurs near the trailing edge of the flap. Figs. 14 and 15 depict the surface pressure coefficient distributions at different span-wise stations at α = 13.0◦ and the lift and drag coefficients versus angle of attack. It can be seen that the computed results agree well with the experimental data [19], although there are minor differences at high angles of attack for the lift and drag coefficients. This example is just used to check whether the overset-grids method with the enhanced IHC developed in this study can be used to calculate a high-lift configuration. The numerical results demonstrate that the answer is yes. 3.3. NASA trap wing with semi-span flap Compared with the full-span flap configuration, the geometry of the NASA trap wing with semi-span flap is more complex and closer to a real high-lift configuration. Because of the narrow gap between the main wing and the flap both in the chord-wise and

Fig. 12. Overset grids for the NASA Trap Wing with full-span flap.

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W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

Fig. 15. Lift and drag coefficients.

Fig. 13. Surface stream lines and pressure contours.

of the flap, the slat and the main wing. The total grid number is approximately 6.7 × 106 . The free-stream flow conditions are as follows: the Mach number is 0.2 and the Reynolds number is 4.21 × 106 . The flow in the narrow gap between the main wing and the flap/slat is very complex and is difficult to be simulated successfully with the explicit hole-cutting method without hole optimization. In this research, the overlapping grids after the enhanced IHC and the contour lines of pressure on the plane of 50% semi-span at α = 14.0◦ are demonstrated in Fig. 17 (only calculated cells are displayed). Due to the interpolated cells and the corresponding donors are highly matched, the computed contour lines cross the gaps smoothly and continuously. The surface pressure coefficient distributions at different spanwise stations at α = 14.0◦ are presented in Fig. 18. Fig. 19 plots the lift coefficient and drag coefficient curves. From the above figures, it can be seen that the calculated pressure distributions are in good agreement with the experimental values [22], which is due to the accuracy of data transfer in the IHC. Limited by the oneequation turbulence model and the coarse computational grids, there is minor difference between the calculated drag coefficients and the experimental data. The influence of these factors on lift coefficients does not seem to be as great as that of drag coefficients, and the calculated values agree well with the experimental data. The above results in this case preliminarily indicate that the overset grids generation scheme and the preprocessing method with the enhanced IHC developed in this study are qualified to deal with complex high-lift configurations. 4. Conclusions

Fig. 14. Pressure coefficient distributions.

span-wise direction, the mesh generation for this model is much more difficult than its full-span counterpart. The geometry and the experimental data for this high-lift model can be found in [22]. The overset grids for this configuration, shown in Fig. 16, were generated by ourselves, in which two collar grids were generated to connect the fuselage with the main wing and the slat, six cap grids were generated for all internal and external tip faces

In this paper, an overset-grids method with the enhanced implicit hole-cutting was developed and applied to simulate the flow around some complex aircraft configurations. Although the original IHC is a highly automatic method, there are some disadvantages that are unfavorable for its wide application. In this research, the hole cells were blanked out using the flooding algorithm that is widely used in the field of graph processing, which made the flow visualization no longer difficult. In order to avoid too many interpolated cells and too close the interpolated boundaries to the solid surfaces, the flooding method was also used to enlarge the interpolated boundaries as large as possible. In addition, the product of cell volume and wall distance was chosen as the quality criterion, which could reduce the number of ghost points. Furthermore, an approximate force computation method based on the IHC results was presented to calculate the surface force on the overlapping surfaces. The developed overset method was used to simulate three aircraft configurations that include two high-lift

W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

Fig. 16. Overset grids for the NASA Trap Wing with part span flap.

Fig. 17. Overset grids and pressure contours at y/b = 0.5 section.

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W. Jiang et al. / Aerospace Science and Technology 94 (2019) 105402

Fig. 19. Lift and drag coefficients.

References

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Fig. 18. Pressure coefficient distributions.

configurations, the computed results agreed well with the experimental data, especially the pressure contour lines are very smooth near the interpolated boundaries. The numerical results demonstrate that the present overset method with the enhanced IHC is qualified to compute the complex flow around the aircraft configurations including high-lift configurations.

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Declaration of competing interest

[19] P. Johnson, K. Jones, M. Madson, Experimental Investigation of a Simplified 3D High Lift Configuration in Support of CFD Validation, AIAA paper 2000-4217, 2000.

The authors declared that they have no conflict of interest to this work.

[20] J.C. Vassberg, P.G. Buning, C.L. Rumsey, Drag prediction for the DLR-F4 wing/body using OVERFLOW and CFL3D on an Overset Mesh, AIAA Paper 2002-0840, 2002.

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