Shock position

Abstract: A study of shock-buffet onset and instability mechanism via Reynolds-averaged Navier―Stokes simulations on several airfoils is presented. The numerical setup and the Spalart―AUmaras turbulence closure are validated based on wind-tunnel data from NACA 0012 and RA16SC1 airfoils. The paper presents simulations of the flow past three • airfoils: the subsonic NACA 0012, the supercritical RA16SC1, and the thin, transonic/supersonic NACA 64A204, at pre- and postbuffet conditions, and within a cycle of developed shock buffet. The shock-buffet cycle is found to be »■• similar in nature for all airfoils, originating in unstable interaction of the shock and the separation bubble. Simulation results support the notion that buffet onset is not related to the bursting of the separation bubble behind the shock. Shock-buffet categorizing is posited as a transonic prestall instability phenomenon that depends on the shock strength and location. Shock-buffet onset conditions occur when the shock position is behind and sufficiently close to the upper-surface maximum curvature location. Additionally, it is suggested that offset conditions are when the shock is at an upstream location and the flow aft of it is fully separated.

Abstract: Preliminary results from electric field measurements in the environment of Mars using the plasma-wave system on board Phobos 2 are reported. Electron-plasma oscillations observed upstream of the bow shock correspond to a solar-wind density of 2/cu cm. The shock-foot boundary was crossed up to three times on each orbit. The shock ramp was detected at altitudes between 0.45 and 0.75 Mars radii R(M) above the planetary surface. The density increased by about a factor of two at the ramp. The shock position, although variable, seems to be consistent with previous measurements. The downstream magnetosheath contained broadband electric-field noise below the plasma frequency. The boundary of th obstacle, or plasmapause, was crossed at altitudes of the order of 0.28 R(M); the cold plasma density was highly variable within the planetopause and reached the unexpected value of 700/cu cm on the third orbit, at 0.25 R(M) altitude. Bursts of waves with frequencies below the electron cyclotron frequency occur within the planetopause.

Abstract: We prove the existence of a solution to the weak regular reflection problem for the unsteady transonic small disturbance (UTSD) model for shock reflection by a wedge. In weak regular reflection, the state immediately behind the reflected shock is supersonic and constant. The flow becomes subsonic further downstream; the equation in self-similar coordinates is degenerate at the sonic line. The reflected shock becomes transonic and begins to curve there; its position is the solution to a free boundary problem for the degenerate equation. Using the Rankine-Hugoniot conditions along the reflected shock, we derive an evolution equation for the transonic shock, and an oblique derivative boundary condition at the unknown shock position. By regularizing the degenerate problem, we construct uniform bounds; we apply local compactness arguments to extract a limit that solves the problem. The solution is smooth in the interior and continuous up to the degenerate boundary. This work completes a stage in our program to construct self-similar solutions of two-dimensional Riemann problems. In a series of papers, we developed techniques for solving the degenerate elliptic equations that arise in self-similar reductions of hyperbolic conservation laws. In other papers, especially in joint work with Gary Lieberman, we developed techniques for solving free boundary problems of the type that arise from Rankine-Hugoniot relations. For the first time, in this paper, we combine these approaches and show that they are compatible. Although our construction is limited to a finite part of the unbounded subsonic region, it suggests that this approach has the potential to solve a variety of problems in weak shock reflection, including Mach and von Neumann reflection in the UTSD equation, and the analogous problems for the unsteady full potential equation. © 2002 John Wiley & Sons, Inc.