Oblique-Shock-Wave/Boundary-Layer Interaction Using Near-Wall Reynolds-Stress Models

A synthesis is presented of the predictive capability of a family of near-wall wall-normal free Reynolds stress models (which are completely independent of wall topology, i.e., of the distance fromthe wall and the normal-to-thewall orientation) for oblique-shock-wave/turbulent-boundary-layer interactions. For the purpose of comparison, results are also presented using a standard low turbulence Reynolds number k–ε closure and a Reynolds stress model that uses geometric wall normals and wall distances. Studied shock-wave Mach numbers are in the range MSW = 2.85–2.9 and incoming boundary-layer-thickness Reynolds numbers are in the range Reδ0 = 1–2×106. Computations were carefully checked for grid convergence. Comparison with measurements shows satisfactory agreement, improving on results obtained using a k–ε model, and highlights the relative importance of redistribution and diffusion closures, indicating directions for future modeling work.

Influence of inflow turbulence in shock-wave/turbulent-boundary-layer interaction computations

The influence of inflow turbulence on the results of Favre–Reynolds-averaged Navier–Stokes computations of supersonic oblique-shock-wave/turbulent-boundary-layer interactions (shock-wave Mach-number MSW ∼2.9), using seven-equation Reynolds-stress model turbulence closures, is studied. The generation of inflow conditions (and the initialization of the flowfield) for mean flow, Reynolds stresses, and turbulence length scale, based on semi-analytic grid-independent boundary-layer profiles, is described in detail. Particular emphasis is given to freestream turbulence intensity and length scale. The influence of external-flow turbulence intensity is studied in detail both for flat-plate boundary-layer flow and for a compression-ramp interaction with large separation. It is concluded that the Reynolds-stress model correctly reproduces the effects of external flow turbulence.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.

Compressible boundary-layer flow at a three-dimensional stagnation point with massive blowing

The effect of massive blowing rates on the steady laminar compressible boundary-layer flow with variable gas properties at a 3-dim. stagnation point (which includes both nodal and saddle points of attachment) has been studied. The equations governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique for nodal points of attachment but employing a parametric differentiation technique instead of quasilinearization for saddle points of attachment. It is found that the effect of massive blowing rates is to move the viscous layer away from the surface. The effect of the variation of the density- viscosity product across the boundary layer is found to be negligible for massive blowing rates but significant for moderate blowing rates. The velocity profiles in the transverse direction for saddle points of attachment in the presence of massive blowing show both the reverse flow as well as velocity overshoot.

Boundary-layer convective heat transfer in a convergent channel

In this paper the numerical solution of the heat transfer problem in a convergent channel with uniform and non-uniform wall temperatures under boundary-layer approximations has been presented. Also, a semi-analytical solution for uniform wall temperature has been obtained.

Semi-similar solution of an unsteady compressible three-dimensional stagnation point boundary layer flow with massive blowing

A semi-similar solution of an unsteady laminar compressible three-dimensional stagnation point boundary layer flow with massive blowing has been obtained when the free stream velocity varies arbitrarily with time. The resulting partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme with a quasi-linearization technique in the nodal point region and an implicit finite-difference scheme with a parametric differentiation technique in the saddle point region. The results have been obtained for two particular unsteady free stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. Results show that the skin-friction and heat-transfer parameters respond significantly to the time dependent arbitrary free stream velocity. Velocity and enthalpy profiles approach their free stream values faster as time increases. There is a reverse flow in the y-wise velocity profile, and overshoot in the x-wise velocity and enthalpy profiles in the saddle point region, which increase as injection and wall temperature increase. Location of the dividing streamline increases as injection increases, but as the wall temperature and time increase, it decreases.

Unsteady Incompressible Two-Dimensional and Axisymmetric Turbulent Boundary Layer Flows

The unsteady turbulent incompressible boundary-layer flow over two-dimensional and axisymmetric bodies with pressure gradient has been studied. An eddy-viscosity model has been used to model the Reynolds shear stress. The unsteadiness is due to variations in the free stream velocity with time. The nonlinear partial differential equation with three independent variables governing the flow has been solved using Keller's Box method. The results indicate that the free stram velocity distribution exerts strong influence on the boundary-layer characteristics. The point of zero skin friction is found to move upstream as time increases.

Unsteady free Convection MHD Boundary Layer Flow Near a Three-Dimensional Stagnation Point

The unsteady free convection boundary layer hydromagnectic flow near a stagnation point of a three-dimensional body with applied magnetic field and time-dependent wall temperature has been studied. Both semi-semilar and self-similar cases have been considered. The equations governing the above flow have been solved numerically using an implicit finite-difference scheme due to Keller. The magnetic field is found to reduce both the heat transfer and skin friction. The effect of the variation of the wall temperature with time and of mass transfer is found to be more pronounced on the heat transfer than on the skin friction. In self-similar case, for decelerating flow, there is temperature overshoot in the presence of fmagnetic field, but in semi-similar case overshoot occurs even without magnetic field due to the unsteadiness

Unsteady laminar incompressible second-order boundary-layer flow at a three-dimensional stagnation point

The unsteadely laminar incompressible second-order boundary-layer flow at the stagnation point of a three-dimensional body has been studied for both nodal and saddle point regions. The effects of mass transfer and Prandtl number have been taken into account. The equations governing the flow have been solved numerically using an implicit finite-difference scheme. It has been found that the parameter characterizing the unsteadiness in the velocity of the free stream, the nature of the stagnation point, the mass transfer and Prandtl number strongly affect the second-order skin friction and heat transfer. The overall skin friction becomes less due to second-order effects but the heat transfer has the opposite behaviour. For large injection, the second-order skin-friction and heat-transfer results prevail over the first-order boundary layer results whereas for the case of large suction the behaviour is just the opposite.

Unsteady compressible 3-dimensional boundary-layer flow near an asymmetric stagnation point with mass transfer

The heat and mass transfer for unsteady laminar compressible boundary-layer flow, which is asymmetric with respect to a 3-dimensional stagnation point (i.e. for a jet incident at an angle on the body), have been studied. It is assumed that the free-stream velocity, wall temperature, and surface mass transfer vary arbitrarily with time and also that the gas has variable properties. The solution in the neighbourhood of the stagnation point has been obtained by series expansion in the longitudinal distance. The resulting partial differential equations have been solved numerically using an implicit finite-difference scheme. The results show that, in contrast with the symmetric flow, the maximum heat transfer does not occur at the stagnation point. The skin-friction and heat-transfer components due to asymmetric flow are only weakly affected by the mass transfer as compared to those components associated with symmetric flow. The variation of the wall temperature with time has a strong effect on the heat transfer component associated with the symmetric part of the flow. The skin friction and heat transfer are strongly affected by the variation of the density-viscosity product across the boundary layer. The skin friction responds more to the fluctuations of the free stream oscillating velocities than the heat transfer. The results have been compared with the available results and they are found to be in excellent agreement.

Incompressible boundary layer for longitudinal flow over a cylinder with an applied magnetic field

The flow, heat and mass transfer problem for a steady laminar incompressible boundary layer flow in an electrically conducting fluid over a longitudinal cylinder with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the magnetic field and dissipation parameter. The effect of the mass transfer is more pronounced on the skin friction than on the heat transfer. The results have been compared with those of the series solution, the asymptotic solution, the Glauert and Lighthill's solution, local similarity, local nonsimilarity and difference-differential methods. Good agreement is found with all of them, except with the results of the local similarity and series solution methods.

An Analysis of a Boundary Layer Diffusion Flame Over a Porous Flat Plate in a Confined Flow

A numerical analysis of the gas dynamic structure of a two-dimensional laminar boundary layer diffusion flame over a porous flat plate in a confined flow is made on the basis of the familiar boundary layer and flame sheet approximations neglecting buoyancy effects. The governing equations of aerothermochemistry with the appropriate boundary conditions are solved using the Patankar-Spalding method. The analysis predicts the flame shape, profiles of temperature, concentrations of variousspecies, and the density of the mixture across the boundary layer. In addition, it also predicts the pressure gradient in the flow direction arising from the confinement ofthe flow and the consequent velocity overshoot near the flame surface. The results of thecomputation performed for an n-pentane-air system are compared with experimental data andthe agreement is found to be satisfactory.

Unsteady, three-dimensional, boundary-layer flow due to a stretching surface

Abstract is not available.