ALBERT

Description: The profiles and thicknesses of normal shock waves in argon at Mach numbers of 1.335, 1.454, 1.576, and 1-713 were determined experimentally by means of a free-molecule probe whose equilibrium temperature is related by kinetic theory to the local flow properties and their gradients. Comparisons were made between the experimental shock profiles and the theoretical profiles calculated from the Navier-Stokes equations, the Grad 13-moment equations, and the Burnett equations. New, very accurate numerical integrations of the Burnett equations were obtained for this purpose with results quite different from those found by Zoller, to whom the solution of this problem is frequently attributed. The experimental shock profiles were predicted with approximately equal success by the Navier-Stokes and Burnett theories, while the 13-moment method was definitely less satisfactory. A surprising feature of the theoretical results is the relatively small difference in predictions between the Navier-Stokes and Burnett theories in the present range of shock strengths and the contrastingly large difference between predictions of Burnett and the 13-moment theories. It is concluded that the Navier-Stokes equations are correct for weak shocks and that within the present shock strength range the Burnett equations make no improvement which merits the trouble of solving them. For shocks of noticeably greater strength, say with a shock Mach number of more than 2.5, it remains fundamentally doubtful that any of these theories can be correct.

Description: Measurements of the statistical properties of the fluctuating wall pressure produced by a subsonic turbulent boundary layer are described. The measurements provide additional information about the structure of the turbulent boundary layer; they are applicable to the problems of boundary-layer induced noise inside an airplane fuselage and to the generation of waves-on water. The spectrum of the wall pressure is presented in dimensionless form. The ratio of the root-mean-square wall pressure to the free-stream dynamic pressure is found to be a constant square root of bar P(sup 2)/q(sub infinity) = 0.006 independent of Mach number and Reynolds number. In addition, space- time correlation measurements in the stream direction show that pressure fluctuations whose scale is greater than or equal to 0.3 times the boundary-layer thickness are convected with the convection speed U(sub c) = 0.82U(sub infinity) where U(infinity) is the free-stream velocity and have lost their identity in a distance approximately equal to 10 boundary-layer thicknesses.

Description: Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

Description: An experimental investigation of the mixing of two coaxial gas streams was conducted over a range of subsonic jet Mach numbers and temperatures. Three configurations were investigated. One had no innerbody in the primary or inner pipe and was designed to give flat velocity profiles at the exit of the primary pipe. The other two configurations had innerbodies in the primary pipe. These were designed to give velocity profiles similar to those existing at the inlet of propulsive systems such as afterburners. Curves of axial velocity and temperature profiles across the radius are presented at various axial stations. For the two configurations with the innerbody, data are shown at stations out to approximately 8 primary-pipe diameters from the exit of the primary pipe. For the flat-velocity-profile configuration, data are shown at distances extending downstream at 22 primary-pipe diameters from the exit of the primary pipe.

Description: Techniques which have been used for finishing and quantitatively specifying surface roughness on boundary-layer-transition models are reviewed. The appearance of a surface as far as roughness is concerned can be misleading when viewed either by the eye or with the aid of a microscope. The multiple-beam interferometer and the wire shadow method provide the best simple means of obtaining quantitative measurements.

Description: Wind-tunnel tests have been made to determine the location of the boundary-layer transition on three hemispheres having surface roughness (absolute) values of 50, 580, and 2760 microinches. After the initial test run of the smoothest (50 microinch) hemisphere, holes ranging in depth from 1500 to 2500 microinches were noticed in the meridian where transition was observed. The holes were believed to be caused by particles in the air stream. Shadowgraph pictures were obtained of all hemispheres and surface temperature measurements were made on one hemisphere (580 microinches). Tests at high Reynolds numbers (6.4 to 7.5 x 10(exp 6) and a Mach number of 2.48 did not indicate any transition on the 50-microinch surface hemisphere before the holes appeared. However, after the holes were noticed, transition locations as low as 50 deg(measured from the stagnation point) were observed at similar Reynolds numbers and Mach numbers. It is felt the transition resulted from the holes. Similar transition locations of approximately 500 were also observed in the tests of hemispheres with surface roughness values of 580 and 2760 microinches at high Reynolds numbers (6.4 x 10(exp 6) to 7.5 x 10(exp 6)) and at a Mach number of 2.48. The results at a Mach number of 2.48 indicate that an absolute surface roughness value of 50 microinches was not critical in causing boundary-layer tran sition at Reynolds numbers of 6.4 to 7.5 x 10(exp 6) whereas roughness values of 580 and 2760 microinches were greater than critical. Transition Reynolds numbers based on momentum thickness, R(sub phi T) varied over a range of approximately 480 to 300 for transition locations, alpha, on the hemisphere from 880 to 410 (measured from the stagnation point). A maximum value of R(phi) of 660 (based on alpha = 90 deg) was obtained with the 50-microinch surface hemisphere at a Mach number of 2.48.

Description: Tests were made on a 10-foot-diameter hemispherical nose at Reynolds numbers up to 10 x 10(exp 6) and at a maximum Mach number of about 0.1 to determine the effects of a highly favorable pressure gradient on boundary-layer transition caused by roughness. Both two-dimensional and three-dimensional roughness particles were used, and the transition of the boundary layer was determined by hot-wire anemometers. The roughness Reynolds number for transition R(sub k,t) caused by three-dimensional particles such as Carborundum grains, spherical particles, and rimmed craters was found. The results show that for particles immersed in the boundary layer, R(sub k,t) is independent of the particle size or position on the hemispherical nose and depends mainly on the height-to-width ratio of the particle. The values of R(sub k,t) found on the hemispherical nose compare closely with those previously found on a flat plate and on airfoils with roughness. For two-dimensional roughness, the ratio of roughness height to boundary-layer displacement thickness necessary to cause transition was found to increase appreciably as the roughness was moved forward on the nose. Also included in the investigation were studies of the spread of turbulence behind a single particle of roughness and the effect of holes such as pressure orifices.

Description: A theory is derived for determining the loads and motions of a deeply immersed prismatic body. The method makes use of a two-dimensional water-mass variation and an aspect-ratio correction for three-dimensional flow. The equations of motion are generalized by using a mean value of the aspect-ratio correction and by assuming a variation of the two-dimensional water mass for the deeply immersed body. These equations lead to impact coefficients that depend on an approach parameter which, in turn, depends upon the initial trim and flight-path angles. Comparison of experiment with theory is shown at maximum load and maximum penetration for the flat-bottom (0 deg dead-rise angle) model with bean-loading coefficients from 36.5 to 133.7 over a wide range of initial conditions. A dead-rise angle correction is applied and maximum-load data are compared with theory for the case of a model with 300 dead-rise angle and beam-loading coefficients from 208 to 530.

Description: An analytical heat transfer solution is derived and evaluated for the general case of a turbulently flowing liquid metal which suddenly encounters a step-function boundary temperature in a channel system. Local Nusselt moduli, dimensionless mixed-mean fluid temperatures, and arithmetic-mean Nusselt moduli are given as functions of Reynolds and Prandtl moduli and a dimensionless axial-distance modulus. These solutions are compared with known solutions of more specific systems as well as with a set of experimental liquid-metal heat transfer data for a thermal entrance region.

Description: Heat-transfer and pressure-drop data were obtained experimentally for the gas side of a liquid-metal to air, compact finned-tube heat exchanger. The heat exchanger was fabricated from 0.185-inch Inconel tubing in an inline array. The fins were made of 310 stainless-steel- clad copper with a total thickness of 0.010 inch, and the fin pitch was 15.3 fins per inch. The liquid used as the heating medium was sodium. The heat-exchanger inlet gas temperature was varied from 5100 to 1260 R by burning JP fuel for airflow rates of 0.4 to 10.5 pounds per second corresponding to an approximate Reynolds number range of 300 to 9000. The sodium inlet temperature was held at 1400 R with the exception of a few runs taken at 1700 and 1960 R. The maximum ratio of surface temperature to air bulk temperature was 1.45. Friction-factor data with heat transfer were best represented by a single line when the density and viscosity of Reynolds number were evaluated at the average film temperature. At the lower Reynolds numbers reported, the friction data with heat transfer plotted slightly above the friction data without heat transfer. The density of the friction factor was calculated at the average bulk temperature. Heat-transfer results of this investigation were correlated by evaluating the physical properties of air (specific heat, viscosity, and thermal conductivity) at the film temperature.