Effective inflow conditions for turbulence models in aerodynamic calculations

The selection of inflow values for one- and two-equation turbulence models at boundaries far upstream of an aircraft is considered. Inflow values are distinguished from the ambient values near the body, which may be much smaller because the long approach can allow a deep decay. Ambient values should be selected first, and inflow values that will lead to them after the decay should be second; this is not always possible, especially for the time scale. The decay of turbulence in two-equation models during the approach to the aircraft is shown; in computational fluid dynamics practice, the time scale has often been set too short for this decay to be calculated accurately on typical grids. A simple remedy for both issues is to arrest decay below the chosen ambient values, either by imposing floor values, or preferably by adding weak source terms. A physical justification for overriding the equations in this manner is proposed. Selecting laminar ambient values is easy if the boundary layers are to be tripped, but it is common to seek ambient values that will cause immediate transition in shear layers. This opens up a wide range of values, and selection criteria are discussed. The turbulent Reynolds number, or ratio of eddy viscosity to laminar viscosity has a huge dynamic range that makes it unwieldy; it has been widely misused, particularly by setting upper limits on it. The value of the complete turbulent kinetic energy in a wind tunnel or the atmosphere is also dubious as an input to the model, because its spectrum contains length scales irrelevant to the turbulence in the boundary and shear layers. Concretely, the ambient eddy viscosity must be small enough to preserve potential cores in small geometry features such as flap gaps. The ambient-frequency scale should also be small enough, compared with shear rates in the boundary layer. Specific ranges of values are recommended and demonstrated for airfoil flows.