AN ESTIMATE OF THE MINIMUM REYNOLDS NUMBER FOR TRANSITION FROM LAMINAR TO TURBULENT BOUNDARY-LAYER FLOW BY MEANS OF ENERGY CONSIDERATIONS

摘要

In a turbulent flow both the viscous and the Reynolds shearing stresses dissipate, me an-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 mini-mum 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 Uach 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. For example, in incompressible flow the minimum Reynolds number is about 54 at the stagnation point of a body of revolution and about 57 at the stagnation point of a two-dimensional body. The estimated minimum Reynolds numbers for transition are compared with the smallest Reynolds numbers for which turbulent flow has been reported.