Differential and integral predictions of three-dimensional boundary layers: A critical comparison. (English) Zbl 0671.76081
BAIL III, Proc. 3rd Int. Conf. Boundary and interior layers, Dublin/Ireland 1984, Conf. Ser. 6, 131-144 (1984).
[For the entire collection see Zbl 0671.00015.]
Prediction of fully three-dimensional turbulent boundary layer flow necessitates empirical modelling. Quite different models are required for the alternative differential field and integral equations. Valuable evidence of validation therefore stems from a critical comparison of predictions from the two types of equation. A specific focus on high Reynolds number flow in ducts is assumed here although inference will be generally valid for most boundary layer flows subject to inviscid outer boundary conditions. The integral method has been developed for rotational outer flows. Although the boundary layer momentum integral, entrainment and displacement surface equations are derived in streamline coordinates, they are ultimately transformed to a general non-orthogonal axis system. Streamwise and crossflow profiles of the bi-directional type are adopted and an entrainment equation is used to predict the development of the shape factor. The differential method is based on the streamwise and crosswise velocity momentum equations and continuity equation. The turbulent stress terms are replaced by either analytical eddy viscosity expressions using the mean flow distributions or eddy viscosity expressions obtained from the solution of the turbulent energy equation. The resulting equations are hyperbolic and are solved numerically by an implicit forward integration finite-difference scheme.
Prediction of fully three-dimensional turbulent boundary layer flow necessitates empirical modelling. Quite different models are required for the alternative differential field and integral equations. Valuable evidence of validation therefore stems from a critical comparison of predictions from the two types of equation. A specific focus on high Reynolds number flow in ducts is assumed here although inference will be generally valid for most boundary layer flows subject to inviscid outer boundary conditions. The integral method has been developed for rotational outer flows. Although the boundary layer momentum integral, entrainment and displacement surface equations are derived in streamline coordinates, they are ultimately transformed to a general non-orthogonal axis system. Streamwise and crossflow profiles of the bi-directional type are adopted and an entrainment equation is used to predict the development of the shape factor. The differential method is based on the streamwise and crosswise velocity momentum equations and continuity equation. The turbulent stress terms are replaced by either analytical eddy viscosity expressions using the mean flow distributions or eddy viscosity expressions obtained from the solution of the turbulent energy equation. The resulting equations are hyperbolic and are solved numerically by an implicit forward integration finite-difference scheme.
