AN ESTIMATE OF THE MINIMUM REYNOLDS NUMBER FOR TRANSITION FROM LAMINAR TO TURBULENT BOUNDARYLAYER FLOW BY MEANS OF ENERGY CONSIDERATIONS,
Abstract
In a turbulent flow both the viscous and the Reynolds shearing stresses dissipate mean-flow mechanical energy whereas, in a laminar flow, the Reynolds shearing stresses are absent; the rate of dissipation of both types of flow varies with the Reynolds number. Because the total dissipation of mechanical energy in a turbulent flow is large enough to supply both the viscous and the Reynolds stress dissipation, it is inferred that transition cannot begin unless the Reynolds number is large enough for the rate of dissipation of the turbulent flow to exceed that of the laminar flow. This concept leads to the criterion for the calculation of the minimum Reynolds number for transition in a boundary layer, namely, that the laminar- and turbulent-friction coefficients be equal. The minimum Reynolds number based on the boundary-layer momentum thickness is estimated to be about 44 for incompressible flow over a flat plate. For an insulated plate, this number rises to 214 at a Mach number of 10. Computations of the effect of pressure gradient indicate that a favorable pressure gradient causes a small increase in the minimum Reynolds number for transition. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 03, 1960
- Accession Number
- AD0437345
Entities
People
- Neal Tetervin
Organizations
- Naval Ordnance Laboratory