Zero-pressure Gradient Research Articles

Heat transfer for highly cooled supersonic turbulent boundary layers

Introduction N efforts have been made to develop simple prediction schemes for skin friction and to evaluate Reynolds analogy factors 2Ch/Cf for turbulent supersonic and hypersonic boundary-layer flows on flat plates or equivalent zero pressure gradient surfaces. Such correlation schemes, which are useful for predicting turbulent heat transfer, are available for somewhat limited combinations of Mach number and wall cooling. l In this Note, a correlation of heat-transfer data is established for zero-pressure-gradient turbulent boundary layers with high wall cooling (Tw/Taw (hw/haw) >0.01. Although Me and hw/haw cannot be varied independently using room temperature models, hw/haw can be varied over a wide range, whereas the corresponding range of Me is relatively narrow.

Direct Measurement of Wall Shear Stress With Mass Transfer in a Low Speed Boundary Layer

A porous plate floating element is used to obtain direct measurements of shear stress in a transpired zero pressure gradient boundary layer from laminar asymptotic suction to blow-off. The thrust balance incorporates a feedback system which provides self centering of the porous element from zero shear stress up to the maximum encountered. Shear stress data obtained for suction and blowing conditions agree well with previously determined indirect data. The floating element data are well correlated by two equations, one for the suction mode, and one for the blowing mode, via simple modifications of an existing correlation.

A Study on the Flow around Bluff Bodies Immersed in Turbulent Boundary Layers : Part 2, The Pressure Forces Acting on Inclined Plates

This paper describes the results of an experimental study on the flow around two-dimensional sharp-edged plates attached to a plane wall at different inclinations to the flow. Experimental data were collected to investigate the effects of (1) inclination of the plate to the flow, (2) the charactristics of the smooth wall boundary layer in which they are immersed, on the pressure forces of the inclined plates. Further, the flow patterns around the inclined plate are examined in some detail. For flows with zero-pressure gradient, correlations are obtained between the variation of pressure forces and inclined plate height h, which is analogous in form to the law of the wall of a boundary layer velocity profile. This law of the wall is applicable up to h/δ = 1.21.5 in the range of inclination angles between 30°and 150° tested in this investigation. A method of calculating the pressure distributions on the front surface of the inclined plate is proposed based upon a flow model that can be analysed by a hodograph technique. The method, however, involves four parameters which must be determined on the basis of experimental informations.

Channel Flow Over a Smooth-to-Rough Surface Discontinuity With Zero Pressure Gradient

Measurements are given for the combined effects of a change of surface roughness and a simultaneous change of pressure gradient. The latter is negative in a fully developed turbulent, two-dimensional smooth channel flow upstream of the discontinuity, but is artificially held to a value of zero in the rough channel following the surface discontinuity. Measurements of mean velocity, turbulent intensity, and wall shear stress in the current zero pressure gradient apparatus are compared with similar measurements made in the same apparatus with a negative pressure gradient in the rough channel. Results indicate that removal of the pressure gradient in the rough channel does not affect the growth rate of the internal boundary layer nor that of the sublayer; nor does the modified pressure gradient greatly reduce the transitional overshoot of wall shear stress and turbulence intensity previously observed.

Roughness induced transition criteria for space shuttle-type vehicles

Tripping effectiveness of surface roughness on a delta wing shuttle orbiter model at 20 deg angle of attack is compared to that on plane and axisymmetrical bodies with and without longitudinal pressure gradients. The experimental data presented are compared on the basis of effective roughness Reynolds number since this parameter is not sensitive to flow conditions downstream of the roughness. The discussion covers the effective roughness Reynolds number as a function of roughness position Reynolds number, effective size ratio as a function of pressure gradient and distance from vehicle nose, and effect of spanwise roughness position on roughness effectiveness. It is shown that conventional criteria for sizing roughness elements which promote transition in two-dimensional zero-pressure gradient flows are insufficient for high-pressure gradient flows and three-dimensional flows. Roughness much smaller than that given by conventional criteria can cause transition and significantly increase the heating load.

Experimental results for the transpired turbulent boundary layer in an adverse pressure gradient

An experimental investigation of the fluid mechanics of the transpired turbulent boundary layer in zero and adverse pressure gradients was carried out on the Stanford Heat and Mass Transfer Apparatus. Profiles of (a) the mean velocity, (b) the intensities of the three components of the turbulent velocity fluctuations and (c) the Reynolds stress were obtained by hot-wire anemometry. The wall shear stress was measured by using an integrated form of the boundary-layer equation to ‘extrapolate’ the measured shear-stress profiles to the wall.The two experimental adverse pressure gradients corresponded to free-stream velocity distributions of the type u∞ ∞ xm, where m = −0·15 and −0·20, x being the streamwise co-ordinate. Equilibrium boundary layers (i.e. flows with velocity defect profile similarity) were obtained when the transpiration velocity v0 was varied such that the blowing parameter B = pv0u∞/τ0 and the Clauser pressure-gradient parameter $\beta\equiv\delta_1\tau_0^{-1}\,dp/dx $ were held constant. (τ0 is the shear stress at the wall and δ1 is the displacement thickness.)Tabular and graphical results are presented.

Investigation of Supersonic Turbulent Mixing Layer with Zero Pressure Gradient

The effect of compressibility on the mixing layer was investigated at Mach number 2.47. Pitot pressure, static pressure, and hot-wire surveys were conducted to investigate the mean flow and the fluctuation quantities. Similarities between supersonic and incompressible mixing layers were observed in normalized velocity profile, normalized power spectral density distribution, and convection velocity distribution. Spreading rate, normalized shear stress, and velocity fluctuation were found to be appreciably smaller than the respective incompressible results; e.g., the momentum thickness growth rates are 0.0073 and 0.035 for supersonic and incompressible flows, respectively. The difference between free and wall-bounded mixing layers is discussed. Development of turbulence structure of mixing layer with increasing Reynolds number was also investigated.

Aeroelastic Panel Optimization with Aerodynamic Damping

AFOSR TN-58-469, June 1958, Dept. of Aeronautics, Johns Hopkins University, Baltimore, Md. 5 Morkovin, M. V., Effects of Compressibility on Turbulent Flows, in The Mechanics of Turbulence, Gordon and Breach, New York, 1964, pp. 367-380. 6 Klebanoff, P. S., Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient, Kept. 1247, 1955, NACA. 7 Zoric,D.L., Approach of Turbulent Boundary Layer to Similarity, Ph.D. dissertation, 1968, Dept. of Civil Engineering, Colorado State University, Fort Collins, Colo. 8 Tieleman, H. W., Viscous Region of Turbulent Boundary Layer, Ph.D. thesis, 1967, Dept. of Civil Engineering, Colorado State University, Fort Collins, Colo. 9 Kistler, A. L., Fluctuation Measurements in a Supersonic Turbulent Boundary Layer, Physics of Fluids, Vol. 2, May-June 1959, pp. 290-296. 10 Sandborn, V. A., A Review of Turbulence Measurements in Compressible Flow, TM X-62, 337, March 1974, NASA.

Heat transfer and skin friction of a phase-changing interface of gas-liquid laminar flows

Gas and liquid laminar flows having a phase-changing (evaporation or condensation) interface at their common boundary are investigated numerically under the conditions of constant properties and of flat-surface boundary layers of zero-pressure gradient. The increase of the normal velocity at the interface associated with phase-changing modifies the velocity and temperature profiles so as to reduce the coefficients of skin-friction and heat-transfer at the interface. With an approximation for the velocity profile, these coefficients are analytically presented as functions of the parameter of the phase-change, that is, the normal and parallel velocities and the temperature or the vapor concentration at the interface.

The influence of pitch and twist on blade vibrations.

Boundary Layers, Journal of Aircraft, Vol. 7, No. 2, March-April 1970, pp. 137-140. Schlichting, H., Boundary Layer Theory, 6th ed., McGrawHill, New York, 1968, p. 555. Van Driest, E. R., Boundary Layer in Compressible Fluids, Journal of the Aeronautical Sciences, Vol. 18, 1951, pp. 145-160, 216. Maise, G. and McDonald, H., Mixing Length and Kinematic Eddy Viscosity in a Compressible Boundary Layer, AIAA Journal, Vol. 6, No. 1, Jan. 1968, pp. 73-80. Klebanoff, P., Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient, TN 3178,1954, NACA. Horstman, C. and Owen, F., Properties of a Compressible Boundary Layer, AIAA Journal, Vol. 10, No. 11, Nov. 1972, pp. 1418-1424. Seebaugh, W., An Investigation of the Interaction of a Shock Wave and a Turbulent Boundary Layer in Axially-Symmetric Internal Flow Including the Effect of Mass Bleed, Ph.D. thesis, 1968, Univ. of Washington, Seattle, Wash. Teeter, G., An Experimental Investigation of the Interaction of a Shock Wave with a Decelerated Turbulent Boundary Layer, M.S. thesis, 1971, Univ. of Washington, Seattle, Wash. Rose, W., The Behavior of a Compressible Turbulent Boundary Layer in a Shock-Wave-Induced Adverse Pressure Gradient, Ph.D. thesis, 1972, Univ. of Washington, Seattle, Wash.

Time Scales and Correlations in a Turbulent Boundary Layer

Space-time correlations with large streamwise separation were obtained in a turbulent boundary layer with a zero-pressure gradient. The auto and cross correlations of the velocities u and υ with streamwise spatial separation distances up to 20 boundary layer thicknesses revealed a difference in their structure and decay rate. Using conditional averaging techniques, the velocity product, uυ, was sampled in both the turbulent and nonturbulent zones. Further conditional sampling led to an average picture of the velocities in the interfacial bulges. Near the wall the space-time correlation results are consistent with the idea of retarded fluid being ejected outward from the wall region and influencing the intermittent region.

Application Of Zagarola/Smits Scaling InTurbulent Boundary Layers With PressureGradient

The empirical velocity scale determined for zero pressure gradient turbulent boundary layers of Zagarola and Smits [1], t/oo(<J*/£), is derived for boundary layers with and without pressure gradient using similarity principles. This scaling is successful in removing the Reynolds number dependence of the outer mean velocity profiles. Even more interesting, it produces three profiles in turbulent boundary layers regardless of the strength of the pressure gradient: one for Adverse Pressure Gradient, APG, one for Favorable Pressure Gradient, FPG, and one for Zero Pressure Gradient, ZPG. These results have been shown to be consistent with Castillo and George [2] obtained by means of similarity analysis of the RANS equations.

Rough wall turbulent boundary layers

This paper describes a detailed experimental study of turbulent boundary-layer development over rough walls in both zero and adverse pressure gradients. In contrast to previous work on this problem the skin friction was determined by pressure tapping the roughness elements and measuring their form drag.Two wall roughness geometries were chosen each giving a different law of behaviour; they were selected on the basis of their reported behaviour in pipe flow experiments. One type gives a Clauser type roughness function which depends on a Reynolds number based on the shear velocity and on a length associated with the size of the roughness. The other type of roughness (typified by a smooth wall containing a pattern of narrow cavities) has been tested in pipes and it is shown here that these pipe results indicate that the corresponding roughness function does not depend on roughness scale but depends instead on the pipe diameter. In boundary-layer flow the first type of roughness gives a roughness function identical to pipe flow as given by Clauser and verified by Hama and Perry &amp; Joubert. The emphasis of this work is on the second type of roughness in boundary-layer flow. No external length scale associated with the boundary layer that is analogous to pipe diameter has been found, except perhaps for the zero pressure gradient case. However, it has been found that results for both types of roughness correlate with a Reynolds number based on the wall shear velocity and on the distance below the crests of the elements from where the logarithmic distribution of velocity is measured. One important implication of this is that a zero pressure gradient boundary layer with a cavity type rough wall conforms to Rotta's condition of precise self preserving flow. Some other implications of this are also discussed.

Effect of longitudinal surface curvature on boundary layers

We consider here the higher order effect of moderate longitudinal surface curvature on steady, two-dimensional, incompressible laminar boundary layers. The basic partial differential equations for the problem, derived by the method of matched asymptotic expansions, are found to possess similarity solutions for a family of surface curvatures and pressure gradients. The similarity equations obtained by this anaylsis have been solved numerically on a computer, and show a definite decrease in skin friction when the surface has convex curvature in all cases including zero pressure gradient. Typical velocity profiles and some relevant boundary-layer characteristics are tabulated, and a critical comparison with previous work is given.

Profils de concentrations dans une couche limite laminaire figée avec une repartition continue et discontinue de catalyseur sur la paroi

A Method of integration of the laminar boundary-layer equations is presented for a fluid with constant properties, with emphasis on the resolution of the diffusion equation. This method is based on an iterative process. The first approximation is solved exactly, and dimensionless concentration profiles corresponding to various boundary conditions are presented. Comparison with the known exact solution, in the case of a flat plate, shows that the error is negligible, and depends upon the Schmidt number. For a non zero pressure gradient boundary layer, the results are greatly improved by solving the equations for the second approximation. The correction term is a function of the Schmidt number. For a flat plate (similar profiles) the accuracy, on velocity and concentration profiles, obtained with the second approximation is better than 1 per cent. The mass transfer at the wall is calculated, in the case of first order catalysis, and using the second approximation, as a function of the Schmidt number and the catalytic Damköhler number (ratio of the reaction constant to the flow velocity). The interest of the method lies in the fact that it can be used in cases where similarity does not apply; the corresponding numerical calculations are much simpler than the calculation by finite difference methods.

Film Cooling of an Adiabatic Flat Plate in Zero Pressure Gradient in the Presence of a Hot Mainstream and Cold Tangential Secondary Injection

Experimental investigations were conducted in order to clarify some of the problems of film cooling of an adiabatic flat plate in zero pressure gradient downstream of a tangential injection slot. The experimental conditions were a hot mainstream and cold secondary injection. Results are presented for wall temperature distributions at varying injected-to-mainstream mass flow ratios. Results are also presented of boundary layer temperature and velocity profiles in film cooling, for an injected-to-mainstream mass flow ratio of 0.88. The existing literature available in film cooling is reviewed.

Laminar Heat Transfer Over Blunt-Nosed Bodies at Hypersonic Flight Speeds

This paper deals wi th two l imit ing cases of laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds, or high s tagnat ion temperatures: (a) thermodynamic equil ibrium, in which the chemical reaction rates are regarded as fas compared to the rates of diffusion across streamlines; (b) diffusion as rate-governing, in which the volume recombination rates within the boundary layer are s low compared to diffusion across streamlines. In either case the gas density near the surface of a blunt-nosed body is m u c h higher than the density jus t outside the boundary layer, and the velocity and stagnation enthalpy profiles are m u c h less sensitive to pressure gradient than in the more familiar case of moderate temperature differences. In fact, in case (a), the nondimensionalized enthalpy gradient at the surface is represented very accurately by the classical zero pressure gradient value, and the surface heat-transfer rate distribution is obtained directly in terms of the surface pressure distribution. In order to i l lustrate the method , this solution is applied to the special cases of an unyawed hemisphere and an unyawed, b lunt cone capped by a spherical segment . In the opposite l imit ing case where diffusion is ratecontrolling the diffusion equation for each species is reduced to the same form as the low-speed energy equation, except that the Prandtl number is replaced by the Schmidt number . The simplifications introduced in case (a) are also applicable here, and the expression for surface heat transfer rate is similar; the maximum value of the ratio between the rate of heat transfer by diffusion alone and by heat conduction alone in the case of thermodynamic equil ibrium is given by: (Prandtl n o . / S c h m i d t no.)'. When the diffusion coefficient is es t imated by taking a reasonable value of a tom-molecule collision cross section this ratio is 1.30. Additional theoretical and (especially) experimental studies are clearly required before these s imple results are accepted.