Three-Dimensional Laminar Boundary Layer with Small Cross-Flow

Abstract

Important problems involving three-dimensional boundary layer occur in almost all internal and external aerodynamic configurations. For many of these, the flow outside the boundary layer may be resolved into a large principal component and a small crosswise velocity. In this paper, three-dimensional laminar boundary-layer flows over flat and curved surfaces are treated under such a simplification. For flat surfaces, the solutions demonstrate the effect of the free stream turning on the velocity profiles in the crosswise and primary flow directions. When the surface curvature is large and varies so as to resemble a corner, the computed examples show the manner in which the asymmetric behavior of the boundary layer results from the cross-flow. The detailed examples are ehosen to illustrate flows occurring on the casing and in the blade fillets of turbomachinery.

3D Boundary Layer Theory

“…For these equations boundary conditions have the form (1). A solution of these equations will be matched with the boundary layer solution at s !…”

“…The small perturbation theory for inviscid flows is well developed and widely applied to estimate aerodynamic characteristics of real flight apparatus. Also it has been attempted to develop such theory for the boundary layer [1]. However, the zero approximation ("flat plate" approximation, zero cross-flow approximation) only given a rational contribution and were used in calculations.…”

Eulerian derivation of non-inertial Navier–Stokes and boundary layer equations for incompressible flow in constant pure rotation

“…The studies that make use of the non-inertial boundary layer equations ( [6], [7], [8], [9], [10]) are applied to blade configurations that is approximated as flat In most studies, the non-inertial conservation of mass and momentum equations are not explicitly derived ( [6], [7], [9]). The equations are merely stated and used in subsequent analysis.…”

“…No mention is made of the conservation of energy equation. [10] and [8] cited the Lagrangian method of derivation used in [2].…”

“…The resulting boundary layer equations were solved using a combination of parametric methods [6], perturbation methods [8] and numerical solution of similarity equations [9], [10]. In this study the boundary layer are resolved directly using the finite volume method.…”