EXPERIMENTAL INVESTIGATION OF THE EFFECTS OF COOLING ON FRICTION AND ON BOUNDARY-LAYER TRANSITION FOR LOW-SPEED GAS FLOW AT THE ENTRY OF A TUBE

摘要

The effect of cooling on boundary-layer transition in the steady flow of air in the entrance of a smooth round tube has been investigated experimentally. Runs were made at diameter Reynolds numbers varying from 50,000 to 106,000. The levels of disturbance were such as to yield adiabatic length Reynolds numbers (based on the length to the start of transition) ranging from 500,000 to 1,800,000. Transition was determined from logarithmic plots of local apparent friction factor against length Reynolds number. Temperature differences between the wall and the free stream up to 270° F were applied, but no significant effect of cooling on the point of transition was found.nFor a gas the theory of stability based on vanishingly small disturbances predicts a large increase in the minimam value of Reynolds number at which the laminar velocity profile first becomes unstable on a flat plate when the plate is cooled. In addition, the theory predicts that the initial rate of amplification of the disturbance is reduced by cooling. Because of pressure gradients, the flow in the entrance of a tube is not exactly the same as that on a flat plate, but the behavior of the flow is thought to be very similar to that on a flat plate when the boundary-layer thickness is small compared with the tube radius, as it was throughout these tests. It appears, therefore, that, in the tests reported here, transition may not have been brought about by amplification of the so-called Toll mien-Schlichting waves of the current laminar instability theory. This suggests that study of the nonlinear terms of the differential equations of motion will be necessary before the mechanism of transition can be fully understood.nThe present results indicate that the effect of cooling on transition is not likely to be significant in any normal internal flow. The measured effect on transition, even when only very slight disturbances, are present, is always at least one order of magnitude less than the effect theoretically predicted for the point at which the laminar velocity profile first becomes unstable.