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Compressible flows over cavities with a series value of length-to-depth ratio (L/D) were investigated experimentally, with the objective being to elucidate the mechanism of the transition of types of cavity flows as their L/D increases or decreases. For open-type cavity flows, the freedom of backflow inside the cavity is found to be crucial in smoothing out adverse pressure gradient. The spreading of the shear layer and its gradual approach toward the cavity floor as L/D increases tend to suppress the freedom of backflow, causing the cavity flow to change from the open-type to the transitional-type. For closed-type cavity flows, the finite thickness of the upstream boundary layer leads to the presence of three kinds of characteristic lengths that correspond to the recirculation region, the deflection of the main flow and the recovery or the abrupt rise of the pressure, respectively. The compression fans at the foot of the impingement and the exit shock waves will approach each other well in advance of the possible merge of the vertices of the conventionally defined separation and recompression wakes. As the L/D of a closed cavity decreases, the reattached boundary layer on the mid-portion of the cavity floor will have less developing distance, thus it will be more susceptible to adverse pressure gradient and prone to separation. For the present two-dimensional cavity models, the critical values of L/D were found to be about 10 and 14 for the transition of cavity flows from the open-to the transitional-type and from the transitionalto the closed-type, respectively. The sum of the pressure lengths at the front and rear wakes agrees remarkably well with the second critical L/D.

A viscous one-dimensional compressible pipe flow under gravity effect is studied analytically. The compressible one-dimensional pipe flow with friction is called Fanno flow and the solution is given by analytical formula. In gas dynamics, the gravity effect is minimal and it is not included in the equations. However, it was shown by the present author that the elevation of a pipe could change the flow conditions in a one-dimensional compressible potential flow under gravity. The sonic condition is reached at the maximum height for an inviscid pipe flow. In this paper, the gravity effect is extended to the viscous one- dimensional pipe flow. Subsonic–supersonic transition is also possible by up and down of the pipe as in the inviscid flow, and it is found that the sonic condition deviates from the peak position of the pipe.

An efficient way to systematically reproduce inflow profiles across a compressible, turbulent boundary layer for the mean flow variables, as well as the turbulent quantities in one-equation and two-equation turbulence-models, from given external flow conditions and one boundary layer parameter, is described. The reproduced profiles are checked against both experimental results and numerical solution of boundary layer equations. Theoretical analysis shows that a new form of density-weighted velocity, rather the Van Driest density-weighted velocity, obeys the linear-law at the viscous sublayer in a compressible turbulent boundary layer. Especially for non-adiabatic wall at hypersonic Mach numbers, where there are large density gradients, these two kinds of density-weighted velocity could differ considerably. Therefore, the new form of density-weighted velocity proposed in this paper should be employed for the viscous sublayer. It is also shown that power-law fitting for the streamwise velocity gives an unacceptable profile in the viscous sublayer. An efficient way to specify the normal velocity profile is also proposed and tested. The reproduced normal velocity at the boundary layer edge is found to agree remarkably well with the numerical solution of boundary layer equations.

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plate are con ned to a very narrow zone near the wing root. This is probably due to the presence of a strong cross ow in the inboard direction, typical of forward-swept wings, that limits the spanwise propagationof the interferenceeffects.Therefore,one may conclude that, for these types of wings, the experimental data are affected by the interference with the splitter plate only in a limited zone close to the wing root. NomenclatureGr = Grashof number Nu = Nusselt number P = excess pressure Pr = Prandtl number p = static pressure Ra = Rayleigh number (DPr Gr ) Re = Reynolds number T = temperature t = time u, v = velocity components x, y = coordinates = vorticity à = stream function

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