Shock-less Hypersonic Intakes

The accuracy of CFD for simulating hypersonic air intake flow is verified by calculating the flow inside a Busemann type intake. The CFD results are then compared against the “exact” solution for the Busemann intake as calculated from the Taylor-McColl equations for conical flow. The method proposed by G. Emanuel (the Lens Analogy) for generating an intake shape that transforms parallel and uniform hypersonic (freestream) flow isentropically to another parallel and uniform, less hypersonic, flow has been verified by CFD (SOLVER II) simulation, based on Finite Volume Method (FVM). The shock-less (isentropic) nature of the Lens Analogy (LA) flow shapes has been explored at both on and off-design Mach numbers. The Lens Analogy (LA) method exhibits a limit line (singularity) for low Mach number flows, where the streamlines perform an unrealistic reversal in direction. CFD calculations show no corresponding anomalies.

Shock-less Hypersonic Intakes

The accuracy of CFD for simulating hypersonic air intake flow is verified by calculating the flow inside a Busemann type intake. The CFD results are then compared against the “exact” solution for the Busemann intake as calculated from the Taylor-McColl equations for conical flow. The method proposed by G. Emanuel (the Lens Analogy) for generating an intake shape that transforms parallel and uniform hypersonic (freestream) flow isentropically to another parallel and uniform, less hypersonic, flow has been verified by CFD (SOLVER II) simulation, based on Finite Volume Method (FVM). The shock-less (isentropic) nature of the Lens Analogy (LA) flow shapes has been explored at both on and off-design Mach numbers. The Lens Analogy (LA) method exhibits a limit line (singularity) for low Mach number flows, where the streamlines perform an unrealistic reversal in direction. CFD calculations show no corresponding anomalies.

On the moving contact line singularity

Given that contact line between liquid and solid phases can move regardless how negligibly small are the surface roughness, Navier slip, liquid volatility, impurities, deviations from the Newtonian behavior, and other system- dependent parameters, the problem is treated here from the pure hydrodynamical point of view only. In this note, based on straightforward logical considerations, we would like to offer a new idea of how the moving contact line singularity can be resolved and provide support with estimates of the involved physical parameters as well as with an analytical local solution.

Contact lines with a contact angle

This work builds on the foundation laid by Benney & Timson (Stud. Appl. Maths, vol. 63, 1980, pp. 93–98), who examined the flow near a contact line and showed that, if the contact angle is $18{0}^{\circ } $, the usual contact-line singularity does not arise. Their local analysis, however, does not allow one to determine the velocity of the contact line and their expression for the shape of the free boundary involves undetermined constants. The present paper considers two-dimensional Couette flows with a free boundary, for which the local analysis of Benney & Timson can be complemented by an analysis of the global flow (provided that the slope of the free boundary is small, so the lubrication approximation can be used). We show that the undetermined constants in the solution of Benney & Timson can all be fixed by matching the local and global solutions. The latter also determines the contact line’s velocity, which we compute among other characteristics of the global flow. The asymptotic model derived is used to examine steady and evolving Couette flows with a free boundary. It is shown that the latter involve brief intermittent periods of rapid acceleration of contact lines.