Friction and heat transfer in laminar and turbulent boundary layers on axisymmetric bodies in nonuniform supersonic flows

Generalized expressions are obtained for calculating the heat fluxes and frictional stresses of the laminar and turbulent flow regimes in a boundary layer in the case of uniform and nonuniform flow past bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 65–72, March–April, 1984.     

Thermal boundary condition effects on heat transfer in turbulent rough-wall boundary layers

Measurements and predictions are presented which investigate the effects of thermal boundary condition on heat transfer in the turbulent rough-wall boundary layer. Stanton number measurements are reported for the turbulent flow of air over rough plates with a variety of thermal boundary conditions on two separate rough surfaces. The cases considered are constant wall temperature, constant wall heat flux, step wall temperature, and piecewise linear wall temperature distributions. These measurements and data from other sources are compared with predictions using finite difference solutions of the discrete element roughness model and with superposition solutions. The predictions and the measurements are in good to excellent agreement.In dieser Arbeit werden Messungen und Berechnungen gezeigt, die den Einfluß der thermischen Randbedingungen auf die Wärmeübertragung in turbulenten Grenzschichten an rauhen Wänden untersuchen. Es werden Messungen der Stanton Zahl für turbulente Luftströmung über rauhe Platten an zwei separaten Oberflächen unter einer Reihe von thermischen Randbedingungen dargestellt. Die betrachteten Fälle sind konstante Wandtemperatur, konstanter Wärmestrom durch die Wand, abgestufte Wandtemperatur und stückweise konstante Wandtemperatur. Diese Messungen, sowie Daten anderer Untersuchungen, werden mit Berechnungen durch Finite-Differenzen Lösungen des Diskrete-Elemente-Rauhheits-Modells und Superpositionslösungen verglichen. Berechnungen und Messungen liegen in guter bis ausgezeichneter Übereinstimmung.     

Visualization of the structure of supersonic turbulent boundary layers

A series of flow visualizations has been performed on two flat-plate zero-pressure-gradient supersonic boundary layers. The two different boundary layers had moderate Mach numbers of 2.8 and 2.5 and Re 's of 82, 000 and 25, 000 respectively. A number of new visualization techniques were applied. One was a variation of conventional schlieren employing selective cut-off at the knife edge plane. Motion pictures of the flow were generated with this technique. Droplet seeding was also used to mark the flow, and high speed movies were made to show structure evolution. Still pictures were also taken to show details within the large-scale motions. Finally, Rayleigh scattering was used to construct planar images of the flow. Together, these techniques provide detailed information regarding the character and kinematics of the large-scale motions appearing in boundary layers in supersonic flow. Using these data, in concert with existing hot-wire data, some suggestions are made regarding the characteristics of the average large-scale motion.This work was supported by the Air Force Office of Scientific Research under Grant 89-0120, monitored by Dr. James M. McMichael. Also, the authors wish to thank Prof. R. B. Miles for his contributions to the Rayleigh scattering portion of this project.     

A model for adiabatic supersonic turbulent boundary layers

An asymptotic analysis of the equations describing supersonic turbulent flow over an adiabatic wall is carried out for high Reynolds numbers, Re, and mainstream Mach numbers, M _e=O(1). A general expression for the adiabatic-wall temperature is derived. The asymptotic theory constrains the types of turbulence models that are suitable to represent the effects of viscous dissipation. A simple algebraic turbulence model is proposed and comparisons with measured total enthalpy profile data show good agreement, capturing the overshoot observed in total enthalpy near the boundarylayer edge.This work was supported by NASA Langley Research Center under Grant NAG-1-832 and the Air Force Office of Scientific Research under Grants AFOSR-91-0069 and F49620-93-0130; Dr. Ruban was supported by a grant from United Technologies Corporation.     

Prediction of resolvent mode shapes in supersonic turbulent boundary layers

This work applies resolvent analysis to compressible zero-pressure-gradient turbulent boundary layers with freestream Mach numbers between 2 and 4, focusing exclusively on large scale motions in the outer region of the boundary layer. We investigate the effects of Mach number on predicted flow structures, and in particular, look at how such effects may be attributed to changes in mean properties. By leveraging the similarity between the compressible and incompressible resolvent operators, we show that the shape of the streamwise velocity and temperature components of resolvent response modes in the compressible regime can be approximated by applying ideas from wavepacket pseudospectral theory to a simple scalar operator. This gives a means of predicting the shape of resolvent mode components for compressible flows without requiring the singular value decompositions of discretized operators. At a Mach number of 2, we find that accurate results are obtained from this approximation when using the compressible mean velocity profile. At Mach numbers of 3 and 4, the quantitative accuracy of these predictions is improved by also considering a local effective Reynolds number based on the local mean density and viscosity.     

Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones

For direct numerical simulation (DNS) of turbulent boundary layers, gen- eration of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.     

Shock-induced turbulent boundary layers

Experimental data for an incompressible turbulent moving surface boundary layer are reviewed and a theoretical extension of their predictions is suggested for the case of finite free stream velocities. It is argued that such a boundary layer provides an incompressible analogue for shock-induced turbulent boundary layers. Coles's transformation is used to predict the behaviour of the shock-induced case from the incompressible analogue. These predictions are used to attempt to correlate the available experimental shock-induced turbulent boundary layer data. It is felt that the correlations are reasonably successful for some of the data. It is suggested that the remaining data have been affected by the premature arrival of the contact region and reflected rarefaction wave.     

Investigation of turbulent boundary layers on perforated surfaces in the presence of blowing

The results are given of an investigation of the averaged and fluctuation velocity and concentration fields of the turbulent boundary layers on perforated surfaces in the presence of blowing. The influence of the boundary conditions on the permeable wall on the parameters of the boundary layer is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 32–38, September–October, 1981.     

Bursting frequency in turbulent boundary layers

Employing laser Doppler anemometry and VITA techniques, the bursting frequency in turbulent boundary layers has been measured over the Reynolds-number range 320 to 1470. The result indicates that the mean and non-dimensional bursting frequency scaled with the variables appropriate for the wall region was constant and independent of Reynoids number. When the same data are plotted using the outer variables of boundary layer to normalize the bursting frequency, the non-dimensional frequency increases as the Reynolds number increases. This is in agreement with the results of Blackwelder et al. (1983) who used hot wire anemometry and VITA technique. The project is supported by the National Natural Science Foundation of China     

Interactive boundary layers in turbulent flow

An asymptotic analysis of the structure of the flow at high Reynolds number around a streamlined body is presented. The boundary layer is turbulent. This question is studied with the successive complementary expansion method, SCEM. The starting point is to look for a uniformly valid approximation (UVA) of the velocity field, including the boundary layer and the external flow. Thanks to the use of generalized expansions, SCEM leads to the theory of interactive boundary layer, IBL. For many years, IBL model has been used successfully to calculate aerodynamic flows. Here, the IBL model is fully justified with rational mathematical arguments. The construction of a UVA of the velocity profile in the boundary layer is also studied. To cite this article: J. Cousteix, J. Mauss, C. R. Mecanique 335 (2007).     

Some equilibrium turbulent boundary layers

Using the Coles additive law of the wall and law of the wake for the mean velocity profile of a two-dimensional turbulent boundary layer, a differential equation for the friction and wake parameters is derived from the momentum integral equation with a view to finding out the conditions under which the boundary layer can exhibit equilibrium. It is predicted that equilibrium is possible for boundary layers in favorable pressure gradient over smooth as well as k-type rough walls. When the roughness height is allowed to increase linearly with the streamwise distance, equilibrium exists also in zero pressure gradient. For a d-type rough wall, equilibrium is possible for a certain range of pressure gradients, from favorable to adverse. Most of the predictions are verified by evaluating the friction and wake parameters from the available experimental data on mean velocity measurements.     

Skin friction and heat transfer in rapidly oscillating boundary layers

The influence of rapid oscillations in the outer part of a boundary layer upon the time-averaged skin friction and heat transfer is investigated analytically. The oscillations are taken to be harmonic. The only restriction on the oscillation amplitude is that it should be sufficiently small to permit the use of the boundary layer equations. The derived asymptotic formulae show the explicit dependence of momentum transfer on the frequency and the time-averaged boundary layer flow. For the heat transfer similar formulae can be derived in a number of limiting cases, viz. when the Prandtl number is either large or small.     

Propagation of disturbances in three-dimensional supersonic boundary layers

The propagation of disturbances in three-dimensional boundary layers under the conditions of a global and a local strong inviscid-viscous interaction is analyzed. A system of subcharacteristics is found based on the condition for the pressure-related subcharacteristic, and an algebraic relation that gives the propagation velocity of disturbances is obtained. The velocity of propagation of disturbances is calculated for two- and three-dimensional flows. The studied problem is of great importance for accurately formulating problems for three-dimensional unsteady boundary-layer equations and for constructing adequate computational models. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 116–127, May–June, 1999.     

Self-preservation of rough-wall turbulent boundary layers

It is proposed that all fully rough-wall boundary layers should satisfy self-preservation more closely than a smooth-wall boundary layer. Previous work has shown that the self-preserving forms of the momentum and turbulent kinetic energy equations for a zero pressure gradient turbulent boundary layer, at sufficiently high Reynolds number, require that the wall shear stress is constant with x, and the layer thickness increases linearly with x. Measurements in two rough wall boundary layers suggest these conditions are met without assuming a form for the mean velocity distribution, and are more likely to exist in a fully rough wall layer than a smooth wall layer.     

Multiple distortion of a supersonic turbulent boundary layer

Two experiments were performed to study the response of a supersonic turbulent boundary layer to successive distortions. In the first experiment (Case 1), the flow passed over a forward-facing ramp formed by 20° compression corner followed by a 20° expansion corner located about 4_o downstream, where _o is the incoming boundary layer thickness. In the second experiment (Case 2), the forward-facing ramp was constructed of curved compression and expansion surfaces with the same turning angles and total step height as in Case 1. The radii of curvature for the compression and expansion surfaces were equal to 12_o. In both experiments, the flow relaxation was observed over a distance equal to 12_o. In this relaxation region, the mean and turbulent flow behavior of the boundary layer was measured. The mean velocity profile was found to be altered by the distortion. Recovery of the profile began near the wall and occurred rapidly, but in the outer part of the boundary layer, recovery proceeded slowly. Turbulence measurements revealed a dramatic reduction in the turbulence shear stress and a progressively decaying streamwise Reynolds stress profile.     

Infrared thermography investigations in transitional supersonic boundary layers

The study of boundary-layer transition in supersonic flows is conducted employing infrared thermography (IRT). Several models of swept wings are tested in a blow-down facility at Mach number 2.4. The effects of wing sweep and other parameters (angle of attack, leading-edge contour, presence/absence of surface roughness) are successfully observed. The transition front is clearly identified, demonstrating the utility of IRT for this type of study. The technique is particularly indicated for flows that are sensitive to surface alterations (roughness), such as transitional boundary layers, because it does not require interaction with the model or the flow under investigation. The additional advantage of no need for special apparatus, except for the infrared camera, makes IRT well suited for both wind-tunnel and in-flight testing. Practical problems and limitations encountered when dealing with IRT in high-speed flows are also discussed.