An Inflow Method for Axisymmetric Turbulent Boundary Layers Along Very Long Slender Cylinders

Abstract

Generating acceptable inflow conditions for the turbulent boundary layer (TBL) growth along long thin cylinders is a challenging task. Previous production methods such as rescale/recycling, artificial turbulence, and antecedent databases are difficult to implement because the downstream physics do not conform to consistent scaling laws. An alternate inflow approach that involves only recycling the fluctuating elements coupled with a dynamic form of Spalding’s relationship for assigning the mean quantities shows promise for spatially resolving the axisymmetric turbulence along the thin cylinder. Applying this inflow technique for resolving the turbulent scales along a flat plate at a tested momentum-based Reynolds number of Reθ = 670 showed excellent agreement with the experimental data as well as the analytical results from the momentum-integral method. A minor adjustment length of approximately two inflow TBL thicknesses was necessary to attain consistent streamwise growth of the boundary layer as well as a simultaneous reduction of the skin friction. Unlike the flat plate, implementing the inflow technique for the thin cylinder required a feedback mechanism during the early transition phase to capture the downstream realistic turbulence. This initial process invoked downstream evaluation of the three parameters that comprise Spalding’s relationship that were periodically fed upstream to the inflow boundary. The validation test case (Reθ = 620) showed excellent agreement with the experimental measurements in terms of the radial profiles (in cylinder wall units) of the streamwise mean and the normal Reynolds stress. Both the adjustment and turbulence de-correlation axial lengths were under two boundary layer thicknesses from the inlet boundary. Given a useful inflow technique for the thin cylinder permits much needed numerical investigations to complement the present scarcity in the experimental evidence and address numerous unknown characteristics of the TBL spatial growth.