Turbulent Boundary Layer Flows Above a Porous Surface Subject to Flow Injection

• Published in: Journal of engineering mechanics Vol. 132; no. 10; pp. 1133 - 1140
• Main Authors: Lin, Pengzhi, Karunarathna, S. A
• Format: Journal Article
• Language: English
• Published: Reston, VA American Society of Civil Engineers 01.10.2006
• Subjects: Boundary layer and shear turbulence; Classical statistical mechanics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Kinetic theory; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; TECHNICAL NOTES; Turbulent flows, convection, and heat transfer; Flow rate; Logarithmic function; Porous materials; Roughness; Turbulent boundary layer; Rough surfaces; Velocity; Porous media; Advection; Shear stress; Modelling; Kinetics; Porosity; Kinetic energy; Fluid injection; Reynolds equation; Boundary layers; Surface flow; Strain rate; Boundary layer flow
• ISSN: 0733-9399; 1943-7889
• DOI: 10.1061/(ASCE)0733-9399(2006)132:10(1133)

A new analytical expression for velocity profile in a fully developed turbulent boundary layer above a porous surface subject to flow injection is derived by solving the coupled Reynolds equations and turbulent kinetic energy equation. The advection of turbulent kinetic energy is considered during the derivation, whereas the earlier studies have neglected it. The new solution reduces to the universal logarithmic law in the case of no flow injection. For the small injection, the solution can be expanded into a series form in terms of the normalized injection velocity. The leading order terms are found to be equivalent to those in the earlier works in which the advection of turbulent kinetic energy has been neglected in the derivation. The new solution can provide more accurate prediction of bed shear stress for a wide range of flow injection rate, fluid type (e.g., from air to water), and surface roughness. On the other hand, the earlier theories may significantly underestimate bed shear stress under high injection rates.