November 2022
Intermediate to advanced
576 pages
10h 56m
English
Content preview from Introduction to Theoretical and Mathematical Fluid Dynamics
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21 Flows at High Reynolds Numbers
Large Reynolds number flows correspond to fluids having small viscosity like those discussed in Chapters 5–10. The effects of fluid viscosity are crucial to the calculation of quantities like skin friction. For flows past streamlined bodies at large Reynolds numbers, Prandtl (1904) proposed that it suffices to recognize the effects of viscosity only in a thin boundary layer adjacent to the body and that the rest of the flow may be considered inviscid. As a first approximation, the inviscid-flow equations are solved with appropriate boundary conditions, ignoring the presence of the boundary layer. However, in general, the inviscid flow will not satisfy the condition of no-slip of the fluid at the body. Therefore, it is necessary to introduce a boundary layer between the inviscid flow and the body to adjust the inviscid solution so that the no-slip condition at the body is satisfied. The vorticity that is generated along the surface of the body is diffused across and convected along the boundary layer. Consequently, the flow is not irrotational within the boundary layer. Besides, the presence of the boundary layer helps explain the common phenomenon of separation of flow behind many bodies placed in the flow.
21.1 Prandtl’s Boundary-Layer Concept
Consider the vorticity generated at the surface of a body placed in a flow with velocity U. Certain qualitative features of boundary layers may be explained by considering the relative importance of ...
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