No abstract

This paper reports the bistability of curved compression ramp (CCR) flows, revealing that both separation and attachment states can be stably established in CCR flows. A thought experiment is firstly proposed, in which it is possible to construct two different stable CCR flows with the same boundary condition through two different processes. Both processes consist of the same three steps but in different orders, so as to investigate the effects of initial condition and evolutionary history on CCR flows. To answer whether CCR flows' bistability is possible, direct numerical simulations are performed to replicate the thought experiment, confirming its existence conjecture. To answer how CCR flows' bistability is possible, a virtual separation disturbance is imposed into the flows to investigate three characteristic adverse pressure gradients, clarifying the necessary and sufficient conditions for the emergence of bistable states. As a classic type of shock wave boundary layer interaction (SBLI) and usual local geometric configurations of aircraft, CCR flows' bistability implies global flows of real supersonic/hypersonic flight dominated by SBLI could also have multistable states.

In the present study, we perform direct numerical simulations to investigate the spatial development and basic flow statistics in the supersonic turbulent boundary layers at the free-stream Mach number of 2.0 over smooth and disturbed walls, the latter of which enforces extra Reynolds shear stress in the streamwise direction to emulate the drag increment and mean streamline curvature effects of rough walls. Such disturbances escalate the growth rate of turbulent boundary layer thickness and the shape factor. It is found that under the rescaled global coordinate, the mean velocity, Reynolds stresses and pressure fluctuation variances manifest outer-layer similarity, whereas the average and fluctuation variances of temperature and density do not share such a property. Compressibility effects are enhanced by the wall disturbances, yet not sufficiently strong to directly impact the turbulent kinetic energy transport under the presently considered flow parameters. The generalized Reynolds analogy that relates the mean velocity and temperature can be satisfied by incorporating the refinement in modifying the generalized recovery coefficient, and that associates the fluctuating velocity and temperature works reasonably well, indicating the passive transport of temperature fluctuations. The dispersive motions are dominant and decay exponentially below the equivalent sand grain roughness height $k_s$, above which the wall disturbances are distorted to form unsteady motions responsible for the intensified density and pressure fluctuations in the free-stream travelling isentropically as the acoustic radiations.

Based on the Helmholtz–Rayleigh minimal dissipation theorem, a theoretical model is proposed to predict both the plateau and peak of pressure in a compression ramp flow with large separation (CRFLS). Since the total dissipation of CRFLS is mainly contributed by the shock waves, the steady flow pattern can be determined by minimizing the shock dissipation among all the possible configurations. The predictions agree well with both experimental data and numerical simulations, covering a wide range of free-stream Mach number and ramp angle. This method could be applied to other flow systems where the dissipation is dominated by shock waves.

Cathode erosion hinders the development of high-power arc heaters, and the inhomogeneous erosion of the copper cathode results in catastrophic failures. In this work, the arc erosion behavior of a chromium cathode was investigated compared with copper. The former was relatively homogeneous with shallow erosion pits. The eroded microstructure suggests that the surface chromic oxide layer could suppress the formation of deep craters. The maximum erosion depth and the erosion rate of chromium were lower than those of copper. The single erosion pits on chromium gradually extended and disappeared, suggesting a reduction in the input energy flux density. The underlying mechanism for the homogeneous erosion behavior of the chromium cathode was proposed. The homogeneous erosion behavior of the chromium cathode makes it a promising candidate for high-power arc heaters.