Study of CFD variation on transport configurations from the second drag-prediction workshop
Introduction
Drag prediction to the level of accuracy desired by airframe manufacturers is currently not possible with CFD. Grid resolution and numerical accuracy, as well as transition and turbulence modeling issues cause uncertainty and prevent confident assessments. It is therefore important to routinely examine CFD capabilities in this area by methodically assessing the influence of various numerical parameters and physical models.
A Drag Prediction Workshop (DPW-I) was held in June 2001 to determine the numerical variation on a simple wing-body configuration (DLR-F4) [1]. Several papers were written assessing the overall results of that workshop [2], [3], including statistical analysis. DPW-I results involving the current authors were also summarized [4], [5]. A second Drag Prediction Workshop (DPW-II) was held in June 2003 for the generic DLR-F6 configuration [6], [7], [8], both as a wing-body alone (WB) as well as wing-body with nacelle-pylon (WBNP). The current paper summarizes a contribution to this effort with two CFD codes widely used in the U.S. aerospace industry: OVERFLOW and CFL3D.
OVERFLOW [9], [10] is an overset (Chimera), structured grid Navier–Stokes flow solver based on the finite difference method. It can be run using second-order central differencing or third-order upwind differencing with flux difference-splitting (FDS). For all results in this study, FDS was used. OVERFLOW is advanced in time with first-order implicit time advancement. It was developed at NASA for multiple/moving body transonic aerodynamics problems, and has been used for a wide variety of geometries and flow regimes, from low subsonic through hypersonic speeds [11], [12].
CFL3D [13] is a finite volume method that has also been used extensively for complex aerospace applications. It uses third-order upwind-biased spatial differencing on the convective and pressure terms, and second-order differencing on the viscous terms; it is globally second-order spatially accurate. FDS is employed to obtain fluxes at the cell faces. It is advanced in time with an implicit three-factor approximate factorization method.
For this DPW-II study, required single point (fixed CL) and drag polar cases were run using two different supplied grid systems for both the WB and WBNP configurations. The effect of grid was investigated, and flow solver options evaluated included turbulence model choice, free transition (“fully turbulent”) vs. specified transition, code, and viscous model (thin-layer in one direction vs. thin-layer in three directions vs. full Navier–Stokes).
The choice of turbulence model typically has less effect on aerodynamic forces in the attached flow regimes that characterize cruise than at off-design conditions in the presence of flow separation. Although the lift coefficient values for the DPW-II workshop cases were below buffet, there was evidence of separated regions in the experiment. Therefore, the behavior of three different turbulence models was examined and documented. These models included the one-equation Spalart-Allmaras (SA) [14], two-equation Menter shear-stress transport (SST) [15], and two-equation explicit algebraic stress in k-omega form (EASM-ko) [16], [17].
This paper is organized as follows. Section 2 briefly outlines key points from the numerical methods and turbulence models of the two codes, then Section 3 summarizes the computations performed for this study. Results are given in Section 4, and summary and conclusions are made in Section 5.
Section snippets
Numerical methods
Details concerning the equations and numerical methods in OVERFLOW [9], [10], [11], [12] and CFL3D [13] are given in their respective references. Here, we briefly point out some of the key issues relevant to the current study.
The Navier–Stokes equations can be written in vector form for an arbitrary coordinate system (ξ, η, ζ) as:where is the vector of conserved variables , and J is the metric Jacobian, ρ is density, u, v, w are
Computations performed
Table 1, Table 2, Table 3 detail the nearly 90 computations performed for the current effort, whose combined purpose was to study: (1) grid effects using the same code and turbulence model, (2) turbulence model effects using the same grid and code, (3) transition location effects using the same grid, code and turbulence model, (4) the effect of code (OVERFLOW compared to CFL3D) using the same grid and turbulence model, and (5) viscous modeling effects using the same grid, code, and turbulence
Results
All cases were computed at M = 0.75, at a Reynolds number of Re = 21246.5 per mm, which corresponds to Re = 3 × 106 based on MAC. The grids each represented half of the full configuration, and symmetry boundary conditions were applied along the center plane.
Summary and conclusions
In summary, the two CFD codes OVERFLOW and CFL3D were used to quantify CFD variations for a wing-body (WB) and wing-body-nacelle-pylon (WBNP) DLR-F6 configuration used in the second drag prediction workshop (DPW-II). Comparisons were also made with experiment. In general, lift was overpredicted for both WB and WBNP, and drag was underpredicted for WB and overpredicted (at low angles) for WBNP. The reason for lift overprediction, which almost all CFD methods presented at the DPW-II workshop had
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