ALBERT

Description: Some ablating bodies entering the atmosphere will melt or soften. Under deceleration, the soft or melted surface will tend to develop instabilities of the Lamb-Taylor type. Two situations involving viscous incompressible fluids are investigated here: one where the liquid layer has constant viscosity and finite thickness, and the other, where the viscosity increases exponentially with distance away from the interface, and the layer is semi-infinite in extent.It can be demonstrated, that if one neglects gradients in the flow direction, the rate of growth of interface disturbances in a plane normal to the axis of an axially symmetric blunt body is independent of the flow velocity. The fact that the deceleration and liquid thickness vary with time along a trajectory is also included in the analysis. Results of calculations for the amplification factor and the most amplified wavelength are given.A mechanism due to the deceleration is postulated, which would cause the formation of longitudinal grooves on the surface of an axially symmetric blunt body while entering the atmosphere.

Description: A new problem in hydrodynamic stability is investigated. Given two contiguous viscous incompressible fluids, the fluid on one side of the plane interface being bounded by a solid wall and that on the other side being unbounded, the problem is to determine the hydrodynamic stability when the fluids are in steady unidirectional motion, parallel to the interface, with uniform rate of shear in each fluid. The mathematical analysis, based on small disturbance theory, leads to a characteristic value problem in a system of two linear ordinary differential equations. The essential dimensionless parameters that appear in the present problem are the viscosity ratiom, the density ratior, the Froude numberF, and the Weber numberW, as well as the parameters α,R(which is proportional here to the flow rate of the inner fluid) andc, that occur in the study of hydrodynamic stability of a single fluid. The results obtained are presented graphically for most fluid combinations of possible interest. The neutral stability curve in the (α,R)-plane is single-looped, as in the boundary layer case. The calculated critical Reynolds numbers are higher than the values observed in liquid film cooling experiments. (In these experiments, the outer fluid is usually a turbulent gas, in which the thickness of the laminar sublayer is of the same order of magnitude as the liquid film thickness.) General agreement between the theoretical and experimental values exists for all critical quantities except the Reynolds number. Gravity and surface tension are found here to have a destabilizing effect on the flow, in agreement with experimental evidence. Semi-infinite plane Couette flow is a special case of the present problem and the known stability of this flow is recovered. The linear velocity profile of two adjacent fluids with the same viscosity, but different densities, is shown to be unstable for high enough Reynolds numbers. The Reynolds stress distribution for a neutral oscillation in the general case is discussed qualitatively.

Description: This paper is concerned with the rates at which atoms and molecules react in the air that flows over a body flying through the atmosphere at hypersonic speeds. Using air as a working fluid, a series of shock tube experiments were carried out to provide information about these rates. Mach angle measurements were made to determine the state of the gas in three situations of interest. Flow over flat plates was used to determine the state of the gas behind the incident normal shock; temperatures in the gas that passed through the shock varied between 2000 and 6000°:K and densities between standard and 1/80 of standard density. Flow over wedges was employed to decelerate the flow behind the incident shock to a small supersonic Mach number; here temperatures downstream of the oblique shock increased, at most, 2000°:K above the free stream value. A Prandtl-Meyer expansion was used to cool rapidly the dissociated gas, so that the recombination process could be investigated; temperatures dropped at most 2500°:K and the densities varied between standard and 1/200 of the standard value. In some cases, the initial degree of dissociation of air was over 45%. The results (figure 11) indicate that the dissociation and recombination relaxation times of the chemical species found in air are very fast, when compared to the time it takes a particle of gas to flow either around a blunt body in hypersonic flight or past smtill models in shock tubes. Thus the shock tube is shown to be an instrument capable of supplying air at high temperatures in thermodynamic equilibrium (figure 5). In the case of a non-melting blunt body of about 1 ft. diameter flying through the atmosphere at hypersonic speeds, the present results imply that, when the gas behind the detached shock is in thermodynamic equilibrium, the flow will also be in equilibrium as it expands around the body, provided its speed is greater than 10 000 ft./sec at altitudes below 180 000 ft. (figure 12). © 1957, Cambridge University Press. All rights reserved.