Chapter 3: Laminar Boundary Layer: Differential Analysis

Jiun-Jih Miau Department of Aeronautics and

Astronautics National Cheng Kung University (NCKU)

Real Fluid Dynamics for IPSA students at NCKU, 2015

Introduction

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Reading assignments: 1. Lighthill, M. L., Introduction, boundary layer theory, in Laminar

Boundary Layers, edited by L. Rosenhead, Chapter II, Oxford University Press, 1963.

2. Prandtl, L., Motion of fluids with very little viscosity. NACA TM452, 1928, translated from a paper of Prantl of 1927 (1904).

3. Tani. I., History of boundary layer theory. Ann. Rev. Fluid Mech., Vol. 9, pp. 87-111, 1977.

4. White, F. M., Viscous fluid flow, Chapters 1 and 2. McGraw-Hill, 1974.

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• The boundary-layer assumption is applicable when the Reynolds number is large. Cases of boundary layer phenomena:

1. wall-bounded shear layer 2. free shear layer: jet, wake and mixing layer

Similarity solutions

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Reading assignments: 1. White, F. M., Viscous fluid flow. McGraw-Hill, 1974, Chapter 4.

2. Schlichting, H., Boundary-layer theory. McGraw-Hill, 1968, Chapter 7.

By introducing the similarity parameter, one can reduce the PDE momentum equations to an ODE equation. Thus, the solution can be obtained in a much easier manner. Physically speaking, the existence of a similarity solution implies that the corresponding flow behaves in a similar manner along the streamwise direction. Namely, the flow properties after non-dimensionalization hold the same regardless of the streamwise locations.