The present paper deals with the stability properties of a planar channel flow driven by air injection through porous walls. Experimental investigations have been carried out in the so-called VECLA facility and a theoretical linear stability analysis has been performed. The nonparallel effects are studied by using three different stability approaches. They appear to be very significant for this particular flow. This study provides indeed an interesting example of an instability mechanism strongly related to the vertical component (usually negligible) of the mean flow. The obtained results finally agree very well with the measurements with respect to the amplified frequency range and to the streamwise amplification of the instability waves.

No abstract

Under some conditions, the flow in solid propellant motors may exhibit large fluctuations at a frequency tuned to that of a longitudinal acoustic mode. This problem is investigated in the present study with the so-called VECLA experimental facility and the linear stability theory. Many hot wire measurements have been compared to the theoretical results, demonstrating thereby the presence of intrinsic instabilities for this type of flow. The instability amplifies a selected frequency range, which mainly depends on the height of the channel and on the injection velocity. The obtained results seem to indicate that if this range does not contain the longitudinal acoustic mode, the flow becomes turbulent downstream, and if it contains this mode, an acoustic resonance is observed.

The numerical solution of laminar, two-dimensional, compressible, and unsteady Navier-Stokes equations is aimed at a complete description of acoustic boundary layers that develop above a burning pro pell ant. Such acoustic boundary layers can be responsible for the so-called flow turning losses. They can govern the local unsteady flow conditions that are seen by the burning propellant to which it finally responds. In those respects, a complete understanding of such acoustic boundary layers is essential to improve existing solid rocket stability prediction codes. The full numerical solution of the Navier-Stokes equations incorporates into the analysis all the features of two-dimensional rocket chamber mean flowfield in a natural manner. After a standing wave pattern is established through forcing at a given frequency, a special Fourier treatment is used to transform the numerical results in a form directly comparable to available linear acoustic data. The presented results indicate that the acoustic boundary layer is substantially thinner than predicted by simplified models. Moreover, its acoustic admittance is found to vary significantly along the chamber, a result that is of major importance to stability predictions. Finally, the acoustic field is found to be rotational over a significant volume of the chamber. Nomenclature a -speed of sound A = excitation amplitude A () = amplitude, or modulus of a complex quantity (2 = grid cell area C p9 C v = constant pressure, volume specific heats E = total specific internal energy, E = C V T + (u 2 + v 2 )/2 FT = complex Fourier component at excitation frequency of a time varying quantity / = frequency h = chamber half-height / = complex number, / = V -1 k -thermal conductivity L = chamber length M = Mach number n -unit normal vector Pr = Prandtl number, Pr = \iC p /k p = pressure r = perfect gas constant (Re)o = reference Reynolds number, (Re) 0 = p 0 a^L/^Q T = temperature or time period of an oscillation t = time U = column vector of conservative flow variables u = axial flow velocity v = transverse or normal flow velocity x = axial coordinate Y = dimensionless acoustic admittance, Y = p 0 a 0 v'/yp' y = transverse coordinate 7 = ratio of specific heats X = coefficient of bulk viscosity fi = dynamic viscosity v = kinematic viscosity p = density Received June 2, 1988; presented as Paper 88-2940 at the AIAA/ ASME/SAE/ASEE 24th Joint Propulsion Conference, a x ,a y = normal stresses T xy> T yx -shear stresses $() = argument of a complex quantity or phase angle (expressed in degrees) co = angular frequency 0 = vorticity Subscripts, Superscripts ()o = reference state Q = steady-state value ()' = unsteady component ()/", = injection ()/ = stagnation value

No abstract