

One of the major handicaps of present scientific and commercial CFD codes is caused by the available set of wall boundary conditions. Usually users can choose between two standard approaches: the first is a so called "high Re" boundary condition that assumes a logarithmic lowofthewall for the walladjacent cells and the second is a "low Re" boundary condition which resolves the entire boundarylayer including the sublayer with a very fine mesh. Unfortunately both require specific mesh properties, that strongly depend on the flow field. Consequently the user needs to know details of the flow in advance when he creates his mesh. To overcome this problem a basic formulation for a universal wall boundary condition is described here. The new method is based on the "high Re" boundary condition. This standard approach is extended by blending to a "low Re" boundarycondition in regions were the local gridresolution provides small distances to the wall. The presented blending procedure allows the method to adapt itself to the local flow regime without any extra user input. The new universal boundary condition therefor has no specific requirements to the nearwall grid resolution and is applicable to 2D as well as 3D flows. As the new method promises to be meshindependent it simplifies the meshgeneration process and might be an important improvement for CFD applications in industrial flows. Grotjans and Menter [4] presented a similar approach based on the wall function formulation that also provides universal meshes but always causes the same disadvantage as the highRe formulation. The new method is implemented and tested at two simple 2D flows: a turbulent channel flow of Kim et al. [6] and the ONERAA airfoil flow at maximum lift condition. Additionally the method was already applied to other airfoil flows, e.g. wallmounted wing by Devenport and Simpson [3], the threedimensional wing in a wind tunnel from the GARTEUR AG29 investigation [8], the transonic RAE2822 airfoil [7] and the A310 threeelement high lift configuration. The new approach will provide conditions for mean momentum and turbulence properties for the walladjacent cells. A blending function between the highReboundarycondition is introduced that is based on the nondimensional distance to the wall: and In order to form a hybrid version Y^{+} is replaced by a Taylor series expansion for :The expansion is converging very fast for small arguments. Whereas for large arguments convergence is much smaller than for the term. A proper approach is to cut off behind the 9^{th} order term. The wall shear stress is required to solve the momentum equation. To determine this property an iterative algorithm is introduced that need to be solved pointwise at each single iteration. The wall shear stress or the shear stress velocity must be stored for the next iteration. In addition to the blending of U^{+} all turbulent quantities have to be handled in a similar way. As for both the lowRe and the highRe formulation the same Neumanntype boundary condition for the turbulent kinetic energy can be used, it is not modified Additionally the production of turbulent kinetic energy is manipulated in the walladjacent control volume (marked by the index P) The boundary condition for the second turbulent quantity is reduced to a boundary condition for the turbulent lengthscale which can be applied to an equation for the dissipation rate or the turbulent frequency . Wolfshtein [14] formulated an approximation for the near wall length scale: based on the turbulent Reynolds number Re_{k}. The parameter =0.2 differs from the quantity given by Wolfshtein (=0.263) to ensure the correct blending from the wall function into the lowRe formulation. An investigation of the asymptotic evolution of turbulent lengthscales to the wall yields an expression for the turbulent length scale. By expressing the exponential function by the linear truncation of a Taylor series expansion can be analysed in the walladjacent control volume. A boundary condition for the turbulent frequency can be derived by a similar approach. A universal boundary condition for SpalartAllmaras [10] type oneequation model is given by the same method. In combination with this new b.c. it is recommended to use the Edwards modification [2] of the SpalartAllmaras model due to its improved stability in the near wall region. Problems can occur in the case of very large quantities of Y^{+} > 400 and the eddyviscosity has to be limited. For basic validation the new boundary condition is applied to a simple turbulent channel flow. In this case changing the inflow Reynoldsnumber at a given mesh can easily modify the nearwall mesh resolution. High Reynoldsnumbers will raise the nondimensional distance. By applying the new hybrid boundary condition the velocity profile in the channel flow can be predicted with high quality for a wide range of Reynoldsnumbers. Figure 1 shows the results obtained by a Wilcox model [12]. The walladjacent cell moves from about Y^{+} = 1 for Re = 3640 up to Y^{+} > 10 for Re = 56000 while remaining the same velocities. Figure 1: Nondimensional velocity in a turbulent channel flow for different Reynoldsnumbers, obtained by hybrid wall boundary condition and Wilcox model. Figure 2: Turbulent kinetic energy and shear stresses in a turbulent channel flow for different Reynoldsnumbers, obtained by hybrid wall boundary condition and Wilcox model. In Figure 2 velocity, turbulent kinetic energy and shear stresses are plotted for different Reynolds numbers and different mesh resolutions respectively. The results prove that at least for this simple flow the mesh influence completely vanishes by applying the new universal boundary condition. Nevertheless the insufficient representation of k compared to DNS by Kim, Moin and Moser [6] can not be improved. Similar plots can be provided for models and a SpalartAllmaras one equation model. As these plots are almost identical to Figure 2 we skipped plotting them here. In the following validation test case the combined influence of the new boundary condition and the numerical mesh in a crucial flow situation will be studied. The flow around an ONERA Aairfoil at Re = 2x10^{6}, Ma = 0.15 and 13.3° angle of attack features a laminar separation bubble with turbulent reattachment combined with turbulent separation in the region close to the trailing edge. As simulations of this test case are very sensitive to details of the turbulence mesh it is a proper test for the new boundary condition [5]. Investigations are focussed on the SpalartAllmaras model that is known to produce satisfying result for this flow. Transition is fixed at x/c = 0.12 on the upper and x/c = 0.30 at the lower surface. According to older investigations an adapted 22000 cell mesh (LG) is used that provides a maximum distance to the wall in the first control volume of Y^{+} < 1.3. Results of this mesh are compared to those obtained from a modified mesh (HG) with a nondimensional distance plotted in Figure 3. It varies from Y^{+} = 2 to Y^{+} = 20 with the same number of cells.
Figure 3: Near wall Y+ distribution of the highRe mesh (HG) for the ONERA Aairfoil
Table 1: Measured and calculated lift and drag coefficient of the ONERA Aairfoil, Re = 2.10^{6}, = 13,3°. Results obtained on the two meshes with different boundary conditions are plotted in Table 1. On the LG mesh results of the universal and the lowRe b.c. are identical therefore only the latter is plotted. Figure 4 and 5 show pressure distributions and skinfriction for the different boundary conditions on the HG mesh compared to results on the fine LG mesh. The latter results are in good agreement with the experiments capturing both separations with correct size. As expected the capability of predicting pressure induced separation dramatically drops with the coarser mesh HG. The universal boundary (HYB) shows superior results compared to the standard wall function formulation but suffers from an overpredicted shear stress in the leading edge regions. According to be specific Y^{+} distribution a difference between the universal and the high Re boundary condition only occurs downstream of x/c=0.4. The results obtained by the lowRe boundary condition on the HG mesh have to be handled with care. Velocity profiles and boundarylayer thickness seems to be superior to other results but the skin friction at the transition location is underpredicted and is very close to flow separation in the leading edge region with catastrophic result for the entire flow field. The new hybrid boundary condition is able to lead to more reliable results and improves the stability of the method at least for this particular flow. 