Xin He, Zhong Zhao， Rong Ma, Nianhua Wang, Laiping Zhang

(1. China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China 2. State Key Laboratory of Aerodynamics, Mianyang Sichuan 621000, China)

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Validation of HyperFLOW inSubsonic and Transonic Flow

Xin He1,2, Zhong Zhao1,*， Rong Ma1, Nianhua Wang1, Laiping Zhang1,2

(1. China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China 2. State Key Laboratory of Aerodynamics, Mianyang Sichuan 621000, China)

HyperFLOW，a structured/unstructured hybrid CFD software, is introduced in this paper. For HyperFLOW, the structured solver runs on structured grids, while the unstructured solver runs on unstructured grids, in order to fully take advantages of both grids and solvers. The architecture of HyperFLOW is briefly introduced firstly. Then, some typical cases are tested to validate both the structured and unstructured solver, including the Trap-Wing configuration from HiLiftPW-I and the DLR-F6 wing-body configuration from DPW-II. The performance of grid convergence is studied for both solvers. The numerical results demonstrate that HyperFLOW has good grid convergence property on both structured and unstructured grids. The computational results match well with the reference and experimental data, indicating acceptable credibility.

HyperFLOW, CFD Software, NASA Trap-Wing high-lift model, DLR-F6 wing-body

0 Introduction

Computational Fluid Dynamics (CFD) has been playing more and more important role in aeronautical/astronautical vehicle design and flow mechanism study. Many CFD codes, as well as some commercial CFD software, have been developed during the past two decades. Generally speaking, these flow solvers can be classified into two types: structured solver and unstructured solver respectively, according to the type of grid and data structure. A structured solver is defined by the directional nature of the computational methods and the Cartesian data structure. The geometry topology is defined directionally and the neighboring connectivity is defined by their indices (i,j,k). An unstructured solver is characterized by unordered data structure and the non-directional nature of the numerical method. It is necessary to store connectivity of cell-face-node.

Due to the high quality of structured grids, structured solver has the properties of high-efficiency and high-accuracy. Lower memory is required because no connectivity information needs to be stored except for the indices (i,j,k). However, when dealing with complex configurations, it would cost a lot of time to generate structured grids. The unstructured solver usually runs on unstructured grids, with the advantages of easier grid generation and reduction on overall turnaround time. Although the unstructured solvers are adopted more and more, the structured solvers are still playing an important role in some scopes, especially for hypersonic flows

and flow mechanism study.

As is known to all, the structured/unstructured hybrid grid is a better choice for complex geometries, because it combines the advantages of both structured and unstructured grids. Although hybrid grids are used in realistic applications, applications, almost all the flow solvers for hybrid grids should transfer the data structure of the structured grids into that of the unstructured grid. Consequently, the properties of high-efficiency and high-accuracy of structured grids are not inherited. Therefore, some in-house codes are trying to combine structured and unstructured solvers into a unified platform in recent years. Soetrisno [1] described an explicit parallel coupling between matching structured and unstructured grids. DLR has developed a hybrid solver named “TAU-ijk”[2], by integrating famous structured solver FLOWer with unstructured solver TAU. Two excellent flow solvers, OVERFLOW and USM3D, have been loosely coupled in form of libraries to build a hybrid solver named “DRAGONFLOW” [3,4]. Recently, a new fully integrated solver calledelsA-Hby ONERA for compressible flow simulation on structured and unstructured grids was presented [5,6].

Since 2005, we started to develop a hybrid CFD platform-HyperFLOW [7-9]. The goal is to integrate structured and unstructured solvers, as well as other multi-discipline solvers, into an unified platform with the same code language. After several years’ programming and testing, the first version of HyperFLOW has been accomplished and applied successfully for realistic applications. In recent years, we are engaged in updating the version of HyperFLOW and enhancing its capability.

In this paper, the architecture of HyperFLOW is briefly introduced firstly. Then, two typical cases are tested to validate both the structured and unstructured solver, including the Trap-Wing configuration from HiLiftPW-I and the DLR-F6 wing-body configuration from DPW-II. The performance of grid convergence is studied for both solvers. The numerical results demonstrate that HyperFLOW has good grid convergence property on both structured and unstructured grids.

1 Architecture of the Solvers

In order to integrate naturally the structured solver and the unstructured solver into an unified platform, we have to redesign the frame architecture and the data structure, since the data structures in two solvers are greatly different. Our final goal is to set up a platform for numerical virtual flight or digital flight, which will include the static and dynamic hybrid grid generator, the flight dynamics solver for rigid and morphing body, the solver for elastic structures, the flight controlling system, and so on. In order to meet all the requirements of structured and unstructured flow solver, and other multi-discipline solvers, and to enhance the universality and expansibility of HyperFLOW, the idea of modularization and the Object-Oriented technique was adopted to construct the new architecture, and C++ language was adopted for coding.

The sketch of the architecture of HyperFLOW is illustrated in Fig.1. Some basic Classes are extracted from our previous solver, and defined to satisfy the requirement of large-scale parallel CFD simulation and other purposes. The core of the software is ‘Zone’ Class. All the operations are based on ‘Zone’, which represents a sub-domain of the whole computational domain (discretized as grids). The left hand of ‘Zone’ Class is the ‘Geometry’ Class, and the corresponding ‘Grid’ Class. This ‘father’ class can derive two ‘son’ classes, ‘Structured Grid’ Class, and ‘Unstructured Grid’ Class, meanwhile, an ‘Interface’ Class can be defined also to communicate the information between the two ‘son’ classes. On the right hand, the ‘Solver’ Class is defined, including a series of flow solvers, such as solver for Navier-Stokes equations, solvers for different turbulence models. Other multi-discipline solvers can be derived from the ‘Solver’ Class. Furthermore, each solver can be divided into structured solver running on structured grids, and unstructured solver on unstructured grids. The structured solver and the unstructured solver, as well as other special solvers (such as solvers for turbulence models, MHD equations, high-order discontinuous Galerkin NS solver), exist in the code as a sub-class or a derived class (Fig.2). All the data transferring among these classes are stored in a data-base, whose format is very similar to the CGNS library. We named this database a ‘Running Data-base’, because it is online created during the software running, and released after the job termination.

Fig.2 Architecture of solvers.

In HyperFLOW, most of the underlying codes are reused for both structured solver and unstructured solver, because that the numerical methods adopted are almost the same for both solvers. In the actual implementation of numerical algorithms such as the time integration or the spatial discretization, the hybrid solver only calls polymorphic function in order to avoid taking care explicitly of structured and unstructured computational method treatments. Due to inheritance, when a pure virtual function is called by a polymorphic object, the concrete function is used in the corresponding derived class. This demonstrates the advantage of a fully-integrated approach versus coupling of separate codes or libraries by a master module, where code duplication would be unavoidable.

HyperFLOW was developed for sub-, transonic and hypersonic flow simulations. The basic numerical method in HyperFLOW is the well-known cell-centered, second-order accuracy, finite volume method for Reynolds-Averaged Navier-Stokes equations on structured/unstructured grids. The computational domain is decomposed into a set of partitions using METIS. Both structured solver and unstructured solver is parallelized using MPI message passing library for variable communication. In particular, each processor may run more than one grid zones when parallelization is utilized. Input interfaces to several popular grid data structures are provided, including CGNS, Plot3D, FieldView, and Fluent. The inviscid flux is calculated across the cell interfaces using Roe’s flux-difference splitting scheme, or other schemes, such as van-Leer, Steger-Warming, AUSM. Flow variables are advanced into steady state with LU-SGS implicit methods. Some turbulent models are integrated into the solver, such as S-A model [10], SST model [11]. The essential ingredients in this software are listed in Table 1.

Table 1 Numerical methods in HyperFLOW

2 Validation of HyperFLOW

Validation of CFD software is an important part of its development. The current work verifies the computation of flows over two wing-body cases using both structured and unstructured solvers.

The Richardson extrapolation is applied to estimate aerodynamic force convergence in the grid convergence study [12]. The extrapolated solution value is obtained using gridiand a fine gridjby:

(1)

(2)

where fkisadiscretesolutionvalueongridlevelk,andfexactistheexactsolution. eijisdifferencebetweenasolutionvariableongridiandgridj. rijisgridrefinefactor,i.e.,thecellnumberratiobetweengridiandj. pisspatialorderofaccuracy,ifthreediscretesolutionswhicharemonotonicasthegridisrefined, pisobtainedby:

(3)

NotethatEq. (3)istranscendentalinp,andthusmustbesolvediteratively.

2.1 NASA High-Lift Trap Wing Model

2.1.1 Trap Wing Configuration

The NASA Trap Wing model came from the first AIAA CFD High-Lift Prediction Workshop (HiLiftPW-Ⅰ) [13]. The prediction of high lift flows is a challenge for CFD codes. The difficulties come from the complexity of the geometry and the flow physics [14]. For configurations that include multiple elements, the flow physics are very complex and difficult to predict. The objective of this test is to assess the capability of numerical prediction for high lift flow fields. The focus of this case is on the assessment of grid convergence.

This configuration is a large chord, semi-span, three elements high lift wing-body configuration. The body is mounted on a standoff, which is fixed on the wall. The geometric details are listed in [14]. The Mach number isM∞=0.2, and Reynolds number based on mean aerodynamic chord isRe=4.0×106.

2.1.2 Computational Grids

Grid convergence behavior is analyzed using three successively refined grids, both for structured solver and unstructured solver. In this paper, three suits of grids are adopted.

1)Committee supplied grids (Grid1). This grid system is designated as UH8 (Unst-Mixed-Node centered-B) in the families of grids supplied by HiLiftPW-Ⅰ committee [13], generated by Solar of DLR. The surface is discretized with a quad-dominant, which allows for triangles to improve the overall mesh quality. Due to the mixed-element sur-face grid, the computational field is hexahedra- dominant, with some prismatic layer stacks.

2) Mixed unstructured grids (Grid2). This grid system is mixed unstructured grids, which are generated by the authors. Prisms are used to discretize the near wall field, and isotropic tetrahedral cells are used to discretize the off-wall field. Anisotropic tetrahedral cells are used to fill the gap between prisms and isotropic cells.

3) Multi-block structured grids (Grid3). In order to test the structured solver of HyperFLOW, a suit of multi-block structured grid is generated, with 355, 369, and 369 blocks, for the coarse, medium and fine grids, respectively.

The cell number of the three grid systems is listed in Table 2.

Table 2 Grid scale of Trap-Wing

2.1.3 Results

According to the suggestion of HiLiftPW-Ⅰ, the Spalart-Allmaras model is adopted to simulate the fully developed turbulent flow [14].

1) Case 1: Grid Convergence Behavior and Surface Pressure Coefficient.

The focus of this case is on the assessment of grid convergence for coarse, medium and fine grids, when angle of attack (AOA)=13°, 28°.

The integral force and pitching moment coefficients are plotted in Fig.3. The grid index factor is the inverse of the number of cells to the power of 2/3(N-2/3). It is convenient to identify the grid convergence trends of these three grid families: a straight line indicates second-order convergence rate [15]. For all the three grid systems, monotone data is acquired. The convergence trends of all force and moment coefficients are similar for all three grid systems, almost a straight line, except for Grid3 at 13°. The streamline near surface is shown in Fig.4. A macroscopic view on the near wall flow field shows no distinct differences between different grids and solvers. All computational results at 13° show larger flow separation on the flap than those at 28°.

2) Case 2: Force and Moment Coefficients. The focus of this case is on the ability of the structured/unstructured solver to predict the aerodynamic force and moment. For this study, computations are carried on all the three grid systems, and the angles of attack (AOA) include 6°, 13°, 21°, 28°, 32°, 34° and 37°, respectively.

The lift, drag, and pitching moment coefficients for whole grid families of the three grid systems are shown in Fig.5. Results from some famous CFD codes (elsA, USM3D, OverFlow) are listed in the figure as well [16-19]. Lower and upper experiment bounds are indicated by dash lines. It indicates that the numerical results approach closer to the experimental data with the grid refinement. The computations of both the structured and unstructured solvers of HyperFLOW match well with the reference data, for the lift and drag coefficients. However, the pitching moment coefficients scatter relatively larger, this phenomenon is similar to that of HiLiftPW-Ⅰ.

(a) α=13°

(b) α=28°Fig.3 Grid convergence for three grid systems: lift(CL), drag(CD), pitching moment(Cm) coefficient.

(a) α=13°

(b) α=28°Fig.4 Comparison of surface streamlines on medium grids: Grid1(left), Grid2(middle), Grid3(right).

(a) Grid1

(b) Grid2

(c) Grid3Fig.5 Lift, drag, pitching moment coefficient curves.

Predicting the flow at higher angles of attack nearing stall is difficult, due to the complex flow structure near the wing tip. Accurate simulation of the flow field near the wing tip turned out to be a challenge in HiLiftPW-Ⅰ also. As shown in Fig.6, a wing tip vortex forms and rolls up over the flap wing. Simulation by solving the RANS equations is not accurate enough to capture this vortex.

(a) Stream lines

(b) Pressure contour

2.2 DLR-F6 Wing Body Configuration

2.2.1 Geometry and Computational Conditions

The DLR-F6 wing-body configuration came from the second AIAA Drag Prediction Workshop (DPW-II) [20-21]. The focus of this workshop is to assess the state-of-the-art of the CFD drag prediction in the aircraft industry. In this paper, the configuration without nacelle-pylon is chosen to assess the drag prediction ability of the HyperFLOW solvers.

Two cases are tested:

Case 1: FixedCLsingle point grid refinement study, atM∞=0.75,CL=0.5, with fully turbulent boundary layer, based on coarse, medium and fine grids.

Case 2: Drag polar, atM∞=0.75,α= -3, -2, -1.5, -1, 0, 1, 1.5 deg.

The Reynolds number of both cases is 3.0×106, based on the wing mean aerodynamic chord of 0.1412 m.

2.2.2 Computational Grids

Similar to the Trap-Wing model, three suits of grids are adopted also. The first grid system, named as Grid1 in this paper, is supplied by DPW-III committee, in which the same configuration of DLR-F6 is adopted [20]. The second grid system, named as Grid2, generated by the authors, is similar to that in the Trap-Wing test case, in which prisms are used to discretize the near wall field, and tetrahedral cells are used to discretize the off-wall field. The third grid system, named as Grid3, is a multi-block structured grid, to test the structured solver. The cell numbers of these grids are listed in Table 3.

Table 3 Grid scale of DLR-F6 configuration

2.2.3 Results

To examine the convergence behavior, the predictedCD(drag coefficients) distribution and the extrapolation by Richardson method are shown respectively in Fig.7 for the three grid systems. The drag coefficients approach closer to the experimental data monotonously with the grid refinement. Especially, the Richardson extrapolated values match very well with the experimental data.

Fig.7 Drag convergence and extrapolation for Case 1.

Fig.8 shows CFD predicted separation bubble streamlines in the area of the trailing edge wing-body juncture. An overview on the near wall flow field shows no obvious difference between different grids and solvers. The separation bubble on the wing obtained by Grid2 is smaller than others, and the bubble on fuselage based on Grid3 is smaller than others.

Fig.8 Comparison of surface streamlines on medium grid: Grid1(left), Grid2(middle), Grid3(right).

(a) Grid1

(b) Grid2

(c) Grid3Fig.9 Lift, drag, pitching moment coefficients.

The lift, drag, and pitching moment curves for all the grid systems are plotted in Fig.9. The results show a consistently over-prediction of the lift. This behavior is also similar to that of DPW-II. However, both the unstructured solver based on Grid1 and Grid2, and the structured solver based on Grid3, exhibit excellent grid convergence behavior for lift and drag curves. For the drag polar curve, unstructured solver based on Grid1 exhibits the best behavior, which shows the closest approach to the experimental data as the grid refinement. From Fig.9, we can see that the force curves by the unstructured solver distribute more widely than those by the structured solver. The lift vs. pitching moment curves show relatively large difference, especially at higher angles of attack.

3 Conclusion and Future Work

In order to validate the in-house hybrid CFD platform, HyperFLOW, numerical simulations are carried out for the trap wing model and the DLR-F6 wing body. Both the unstructured and structured solvers in HyperFLOW are tested on a set of unstructured grids and structured grids. The behavior of grid convergence is studied emphatically. The numerical results are compared with the experimental data and other reference numerical results, which demonstrate the capability of HyperFLOW for the simulations of subsonic and transonic flows over complex geometries.

In order to combine the most valuable advantages of structured solver and unstructured solver, both solvers are integrated into HyperFLOW to form a hybrid solver. Although several three dimensional cases have been tested [7] for hybrid solver, more work are need to be done in the future, such as the study of robustness, computational efficiency, accuracy, etc.

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0258-1825(2016)02-0267-09

HyperFLOW亞跨聲速流動驗證

赫 新1,2, 趙 鐘1,*, 馬 戎1, 王年華1, 張來平1,2

(1. 中國空氣動力研究與發(fā)展中心, 四川 綿陽 621000; 2. 空氣動力學(xué)國家重點實驗室, 四川 綿陽 621000)

主要介紹了結(jié)構(gòu)/非結(jié)構(gòu)混合CFD軟件HyperFLOW的設(shè)計開發(fā)與驗證。HyperFLOW軟件在結(jié)構(gòu)網(wǎng)格上采用結(jié)構(gòu)算法，在非結(jié)構(gòu)網(wǎng)格上采用非結(jié)構(gòu)算法，以充分利用兩種網(wǎng)格及解算器的優(yōu)點。首先介紹了軟件的體系結(jié)構(gòu)和基本算法，然后采用NASA Trap-Wing高升力外形和DLR-F6翼身組合體，對軟件的結(jié)構(gòu)解算器和非結(jié)構(gòu)解算器進行了驗證。結(jié)果表明，該軟件的結(jié)構(gòu)解算器和非結(jié)構(gòu)解算器均有較好的網(wǎng)格收斂性，計算結(jié)果與其他參考結(jié)果和試驗數(shù)據(jù)均符合較好，具有可接受的可信度。

HyperFLOW；CFD軟件；NASA Trap-Wing高升力外形；DLR-F6翼身組合體

V211.3

A doi: 10.7638/kqdlxxb-2016.0002

*Research associate; bell_cardc@163.com.

format: He X, Zhao Z, Ma R, et al. Validation of HyperFLOW in subsonic and transonic flow[J]. Acta Aerodynamica Sinica, 2016, 34(2): 267-275.

10.7638/kqdlxxb-2016.0002. 赫新，趙鐘，馬戎，等. HyperFLOW亞跨聲速流動驗證(英文)[J]. 空氣動力學(xué)學(xué)報, 2016, 34(2): 267-275.

Received： 2015-12-15; Revised：2016-01-10

Supported by National Science Foundation of China (No. 11272339)