Large-eddy simulation of nonlinear evolution and breakdown to turbulence in high-speed boundary layers

The nonlinear evolution and laminar-turbulent breakdown of a boundary-layer flow along a cylinder at Mach 4.5 is investigated with large-eddy temporal simulation. The results are validated using the direct numerical simulation data of Pruett and Zang. The structure of the flow during the transition process is studied in terms of the vorticity field. The subgrid scales are modeled dynamically, where the model coefficients are determined as part of the solution from the local resolved field. In the numerical simulation the dynamic-model coefficients are obtained by using both the strain-rate contraction of Germano et al. and the least-squares contraction of Lilly; they produced some differences in the details of the vorticity structure inside the transition region. A new dynamic model that utilizes the second-order velocity structure function is used to parametrize the small-scale field. The evolution to turbulence is successfully simulated with dynamic subgrid-scale modeling at least in terms of average quantities as well as vorticity fields. This is achieved with one-sixth of the grid resolution used in direct numerical simulation.This work was sponsored by the Theoretical Flow Physics Branch of the Fluid Mechanics Division of NASA Langley Research Center under Contract NAS1-19320.     

Direct numerical simulation of stable and unstable turbulent thermal boundary layers

This paper presents direct numerical simulations (DNS) of stable and unstable turbulent thermal boundary layers. Since a buoyancy-affected boundary layer is often encountered in an urban environmental space where stable and unstable stratifications exist, exploring a buoyancy-affected boundary layer is very important to know the transport phenomena of the flow in an urban space. Although actual observation may qualitatively provide the characteristics of these flows, the relevant quantitative turbulent quantities are very difficult to measure. Thus, in order to quantitatively investigate a buoyancy-affected boundary layer in detail, we have here carried out for the first time time- and space-developing DNS of slightly stable and unstable turbulent thermal boundary layers. The DNS results show the quantitative turbulent statistics and structures of stable and unstable thermal boundary layers, in which the characteristic transport phenomena of thermally stratified boundary layers are demonstrated by indicating the budgets of turbulent shear stress and turbulent heat flux. Even though the input of buoyant force is not large, the influence of buoyancy is clearly revealed in both stable and unstable turbulent boundary layers. In particular, it is found that both stable and unstable thermal stratifications caused by the weak buoyant force remarkably alter the structure of near-wall turbulence.     

Similarity solution of thermal boundary layers for laminar narrow axisymmetric jets

In this work, the similarity equation describing the thermal boundary layers of laminar narrow axisymmetric jets is derived based on boundary layer assumptions. The equation is solved exactly. Some properties of the thermal jet are discussed. By introducing new-defined non-dimensional coordinates, the similarity solution results in a “universal” format. The results can also be applied in the boundary layer problem of species diffusion.     

Direct numerical simulation of particle transport by hairpin vortices in a laminar boundary layer

The transport of solid particles by coherent wall structures is studied here. This phenomenon is present in numerous environmental and engineering flows. The flow above a wall-mounted hemisphere is used for generating hairpin vortices in a laminar boundary layer in a controlled way. By means of direct numerical simulation (DNS) of the fluid flow and simultaneous Lagrangian tracking of particles, the influence of hairpin vortices on solid particles released in the wake of the obstacle is analyzed.     

A numerical method for calculating unsteady two-dimensional laminar boundary layers

Summary A method for calculating unsteady two dimensional boundary layers in laminar incompressible flow has been developed and tested. No restrictive assumptions are made regarding the time-dependent terms in the boundary-layer equation. The differential equations are solved with an implicit difference scheme similar to that employed for steady two-dimensional boundary layers. At each step, here, known conditions at three stations are used to calculate the conditions at a new (fourth) station. The entire field is covered by a succession of these steps.

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Übersicht Es wird ein Verfahren zur Berechnung von zeitabhängigen zweidimensionalen Grenzschichten in laminarer inkompressibler Strömung entwickelt und auf seine Genauigkeit geprüft. Dabei werden keine einschränkenden Annahmen über die zeitabhängigen Glieder in der Grenzschichtgleichung gemacht. Die Differentialgleichungen werden durch ein implizites Differenzen-Verfahren gelöst, das dem gewöhnlich für stetige zweidimensionale Grenzschichten verwendeten ähnlich ist. Hier werden für jeden Schritt schon bekannte Werte an drei Stellen benutzt, um die Werte an einer neuen (vierten) Stelle zu berechnen. Das ganze Feld wird auf diese Weise schrittweise überdeckt.

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This work was done while the author was at The John Hopkins University, on leave from the Royal Aircraft Establishment, Farnborough. It was supported in part by a grant from the National Science Foundation (Geophysical Fluid Mechanics, GA-641X). British Crown Copyright, reproduced with the permission of the Controller, Her Britannic Majesty's Stationery Office.     

On the numerical computation of laminar boundary layers at a phase-changing,gas-liquid interface

The two-dimensional, laminar boundary-layer equations of heat, mass and momentum at a smooth, phase-changing, gas-liquid interface are solved numerically by the Keller Box method. The gas and liquid regimes are embedded in a single marching scheme which computes interfacial parameters implicitly. Results of both self-similar and non-similar boundary-layer computations are presented and effects of mild pressure gradient, a mean current in the liquid, and free-stream vapour concentration on the interfacial parameters are analysed. In order to assess the accuracy of the method, several self-similar problems are solved by Runge-Kutta integration and results are compared to those obtained by the finite-difference scheme. Agreement is excellent in all cases.     

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.     

Near critical phenomena in laminar boundary layers

Asymptotic analysis of boundary layer separation in the limit of large Reynolds number Re→∞ has shown that in a number of cases which are of importance from a practical point of view solutions of the resulting interaction equations describing two-dimensional (2-D) steady flows exist up to a limiting value Γ_c of the relevant controlling parameter Γ only while two branches of solutions exist in a regime Γ<Γ_c. The present study aims at a better understanding of near critical flows |Γ-Γ_c|→0 and in particular the changes of the flow behaviour associated with the passage of Γ through Γ_c.     

Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration

Direct numerical simulations of an axisymmetric jet with off-source volumetric heat addition are presented in this paper. The system solved here involves a three-way coupling between velocity, concentration and temperature. The computations are performed on a spherical coordinate system, and application of a traction free boundary condition at the lateral edges allows physical entrainment into the computational domain. The Reynolds and Richardson numbers based on local scales employed in the simulations are 1000 and 12 respectively. A strong effect of heat addition on the jet is apparent. Heating causes acceleration of the jet, and an increased dilution due to an increase in entrainment. Further, the streamwise velocity profile is distorted, and the cross-stream velocity is inward for all radial locations for the heated jet. Interestingly, the maximum temperature is realized off-axis and a short distance upstream of the exit of the heat injection zone (HIZ). The temperature width is intermediate between the scalar and velocity widths in the HIZ. Normalized rms of the concentration and temperature increases in the HIZ, whereas that of streamwise, cross-stream and tangential velocities increases rapidly after decreasing. Both mass flux and entrainment are larger for the heated jet as compared to their unheated counterparts. The buoyancy flux increases monotonically in the HIZ, and subsequently remains constant.     

Similar laminar boundary layers in incompressible micropolar fluids

Summary A search for similar solutions reveals as only possible similar boundary layer flow in micropolar fluids the flow near a stagnation point. The corresponding equations have been solved numerically by means of a shooting method. Consideration is given not only to the coupling parameterC ₁ and the microdiffusivity parameterC ₂ but also to the microinertia parameterC ₃. It is shown that macroscopic properties of steady boundary layer flows are not very much affected by these parameters, while the microrotation and therefore the inner structure of the layer is very sensitive to all three parameters. These properties of the microstructure can become important in certain unsteady flow problems; then also the macroscopic behaviour may be different to the behaviour of Newtonian fluids.

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Zusammenfassung In der vorliegenden Untersuchung wird gezeigt, daß ähnliche Grenzschichten in mikropolaren Flüssigkeiten nur in der Nähe eines Staupunkts existieren. Die zugehörigen gewöhnlichen Differentialgleichungen werden mit einem Einschießverfahren numerisch gelöst. Neben dem KopplungsparameterC ₁ und dem MikrorotationsparameterC ₂ wird dabei auch der Einfluß der Mikroträgheit im ParameterC ₃ berücksichtigt. Es zeigt sich, daß diese Parameter die makroskopischen Eigenschaften stationärer Grenzschichtströmungen relativ wenig beeinflussen, während sich die Mikrorotation und damit die innere Struktur der Grenzschicht mit diesen Parametern sehr stark ändern kann. Man kann vermuten, daß diese Eigenschaften mikropolarer Flüssigkeiten bei instationären Vorgängen durchaus auch im makroskopischen Verhalten zu größeren Abweichungen gegenüber newtonschen Flüssigkeiten führen können.

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With 6 figures and 1 table     

Two phase boundary layers in laminar film boiling

The laminar film boiling is analyzed by means of an integral procedure. The method treats the film boiling as a two phase boundary layer problem; thereby the effect of the interfacial shear on the heat transfer rate can be investigated. The problem is attacked by simultaneously solving the vapor and liquid boundary layer equations. An extensive comparison of the predicted results with the exact solutions substantiates the validity of the present integral procedure. Even the details of the velocity and temperature profiles turn out to be in close agreement with the exact solutions.     

Flow instability in the zone of laminar axisymmetric boundary layer separation

The stability of flow with laminar boundary layer separation from a body of revolution aligned with an incompressible gas stream is investigated in a wind tunnel. In several experimental regimes with respect to the Reynolds number hot-wire anemometry is used to determine the main parameters of disturbances which grow behind the separation line, thus initiating transition to the turbulent flow state. The relations between the frequencies, the spatial growth rates of the most “hazardous” disturbances, and the integral characteristics of velocity profiles obtained in the study are in good agreement with the analogous data for plane separation flows.     

Nonequilibrium laminar boundary layer of dissociating air on axisymmetric bodies

Results are presented of numerical calculations of a nonequilibrium laminar boundary layer on axisymmetric bodies whose surface has arbitrary catalytic activity using a proposed technique. In the published studies devoted to the exact numerical methods for calculating the boundary layer with chemical reactions, it is assumed that the surface of the body is either noncatalytic or has infinite catalytic activity [1], that thermochemical equilibrium exists at the surface [2], or that the temperature and composition of the gas at the surface are given [3, 4]. This problem has been examined in the approximate formulation in several papers, specifically [5].The authors wish to thank V. V. Lunev and I. N. Murzinov for their counsel and comments.     

Direct numerical simulation of a particle-laden flow in a flat plate boundary layer

In this paper, a direct numerical simulation of particle-laden flow in a flat plate boundary layer is performed, using the Eulerian–Lagrangian point-particle approach. This is, as far as we know, the first simulation of a particle-laden spatially-developing turbulent boundary layer with two-way coupling. A local minimum of the particle number density is observed in the close vicinity of the wall. The present simulation results indicate that the inertial particles displace the quasi-streamwise vortices towards the wall, which, in turn, enhance the mean streamwise fluid velocity. As a result, the skin-friction coefficient is increased whereas the boundary layer integral thicknesses are reduced. The presence of particles augments the streamwise fluctuating velocity in the near-wall region but attenuates it in the outer layer. Nevertheless, the wall-normal and spanwise velocity fluctuations are significantly damped, and so is the Reynolds stress. In addition, the combined effect of a reduced energy production and an increased viscous dissipation leads to the attenuation of the turbulent kinetic energy.     

Stability characteristics of laminar boundary layers over compliant walls

The stability characteristics of laminar boundary layers over compliant walls was studied by the linear theory. Unlike the previous authors, the coupled motion of the fluid and solid was required to satisfy the continuity conditions of both the velocity and stress at the interface. Results of calculations show that as the speed ratio or density ratio exceeds a certain threshold value, the two types of unstable waves will no longer be distinguishable, and the tangential component of the disturbance stress is no longer negligible. So the neglect of it, as the previous authors did, is unjustified. The project is supported by the National Natural Science Fundation of China.     

Self-similar thermal boundary layers on plane and axisymmetric bodies

This paper proposes an approximate solution procedure for the prediction of the forced convection heat transfer through self-similar laminar boundary layers. The differential equations governing the viscous and thermal boundary layers have been reduced to a pair of algebraic equations for the boundary layer shape factor and the boundary layer thickness ratio. The local Nusselt number predicted under various pressure gradients turns out to be in excellent agreement with that of the exact solution over a wide range of the Prandtl number.     

Direct simulation of breakdown to turbulence following oblique instability waves in a supersonic boundary layer

The late stages of transition to turbulence in a Mach two boundary layer are investigated by direct numerical simulation of the compressible Navier-Stokes equations. The primary instability at this Mach number consists of oblique waves, which are known to form a pattern of quasi-streamwise vortices. It is found that breakdown does not follow immediately from these vortices, which decay in intensity. The generation of new vortices is observed by following the evolution of the pressure and vorticity in the simulation, and analysed by consideration of vorticity stretching. It is found that the slight inclined and skewed nature of the quasi-streamwise vortices leads to a production of oppositely signed streamwise vorticity, which serves as a strong localised forcing of the shear layer alongside the original vortices, formed by convection and stretching of spanwise vorticity. The shear layer rolls up into many new vortices, and is followed by a sharp increase in the energy of higher frequencies and in the skin friction.