Effect of a space-time source structure simulating a dielectric barrier discharge on the laminar boundary layer

The time-dependent pulse-periodic action of a surface electric discharge on a flat-plate laminar boundary layer is simulated theoretically. The effect of the discharge is estimated within the framework of the numerical solution of the boundary value problem for the time-dependent two-dimensional compressible boundary layer with additional terms in the momentum and energy conservation equations simulating the force and thermal action of the discharge on the gas flow with allowance for the pressure gradient across the boundary layer induced by the corresponding body force component. The effect of certain parameters of the problem formulated above on the gas velocity induced by the discharge in the boundary layer is also estimated.     

Shockwave�Cturbulent boundary layer interaction control using magnetically driven surface discharges

This study demonstrates the potential for shockwave?Cturbulent boundary layer interaction control in air using low current DC constricted surface discharges forced by moderate strength magnetic fields. An analytical model describing the physics of magnetic field forced discharge interaction with boundary layer flow is developed and compared to experiments. Experiments are conducted in a Mach 2.6 indraft air tunnel with discharge currents up to 300?mA and magnetic field strengths up to 5?Tesla. Separation- and non-separation-inducing shocks are generated with diamond-shaped shockwave generators located on the wall opposite to the surface electrodes, and flow properties are measured with schlieren imaging, static wall pressure probes and acetone flow visualization. The effect of plasma control on boundary layer separation depends on the direction of the Lorentz force (j × B). It is observed that by using a Lorentz force that pushes the discharge upstream, separation can be induced or further strengthened even with discharge currents as low as 30?mA in a 3-Tesla magnetic field. If shock-induced separation is present, it is observed that by using Lorentz force that pushes the discharge downstream, separation can be suppressed, but this required higher currents, greater than 80?mA. Acetone planar laser scattering is used to image the flow structure in the test section and the reduction in the size of recirculation bubble and its elimination are observed experimentally as a function of actuation current and magnetic field strength.     

Emergence of Fluid Rotation in the Marangoni Boundary Layer in the Region of Local Cooling of the Free Boundary

Rotation bifurcation in a steady axisymmetric thermocapillary flow of an incompressible fluid filling a semi-infinite space bounded by the free surface with a nonuniform distribution of temperature is studied. The fluid flow is calculated on the basis of Navier–Stokes equations under the assumption of small diffusion coefficients. It is shown that the bifurcation triggers rotational motion in a thin Marangoni boundary layer in the case of local cooling of the free boundary near the axis of symmetry and in the presence of an external flow; there is no rotation outside this layer. In the case of local heating of the free boundary, rotation is not observed.     

Singularities of the boundary layer equations and the structure of the flow in the vicinity of the convergence plane on conical bodies

The singularities of the boundary layer equations and the laminar viscous gas flow structure in the vicinity of the convergence plane on sharp conical bodies at incidence are analyzed. In the outer part of the boundary layer the singularities are obtained in explicit form. It is shown that in the vicinity of a singularity a boundary domain, in which the flow is governed by the shortened Navier-Stokes equations, is formed; their regular solutions are obtained. The viscous-inviscid interaction effect predominates in a region whose extent is of the order of the square root of the boundary layer thickness, in which the flow is described by a two-layer model, namely, the Euler equations in the slender-body approximation for the outer region and the three-dimensional boundary layer equations; the pressure is determined from the interaction conditions. On the basis of an analysis of the solutions for the outer part of the boundary layer it is shown that interaction leads to attenuation of the singularities and the dependence of the nature of the flow on the longitudinal coordinate, but does not make it possible to eliminate the singularities completely.     

Effect of thermal radiation on heat transfer in an unsteady copper–water nanofluid flow over an exponentially shrinking porous sheet

The effect of thermal radiation on an unsteady boundary layer flow and heat transfer in a copper–water nanofluid over an exponentially shrinking porous sheet is investigated. With the use of suitable transformations, the governing equations are transformed into ordinary differential equations. Dual non-similarity solutions are obtained for certain values of some parameters. Owing to the presence of thermal radiation, the heat transfer rate is greatly enhanced, and the thermal boundary layer thickness decreases.     

Passive control of the flow around a square cylinder using porous media

The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two‐dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier–Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control. The numerical results reveal the ability of porous media to both regularize the flow and to reduce the drag forces up to 30%. Copyright © 2004 John Wiley & Sons, Ltd.     

Three-dimensional instability analysis of boundary layers perturbed by streamwise vortices

A parametric study is presented for the incompressible, zero-pressure-gradient flat-plate boundary layer perturbed by streamwise vortices. The vortices are placed near the leading edge and model the vortices induced by miniature vortex generators (MVGs), which consist in a spanwise-periodic array of small winglet pairs. The introduction of MVGs has been experimentally proved to be a successful passive flow control strategy for delaying laminar-turbulent transition caused by Tollmien–Schlichting (TS) waves. The counter-rotating vortex pairs induce non-modal, transient growth that leads to a streaky boundary layer flow. The initial intensity of the vortices and their wall-normal distances to the plate wall are varied with the aim of finding the most effective location for streak generation and the effect on the instability characteristics of the perturbed flow. The study includes the solution of the three-dimensional, stationary, streaky boundary layer flows by using the boundary region equations, and the three-dimensional instability analysis of the resulting basic flows by using the plane-marching parabolized stability equations. Depending on the initial circulation and positioning of the vortices, planar TS waves are stabilized by the presence of the streaks, resulting in a reduction in the region of instability and shrink of the neutral stability curve. For a fixed maximum streak amplitude below the threshold for secondary instability (SI), the most effective wall-normal distance for the formation of the streaks is found to also offer the most stabilization of TS waves. By setting a maximum streak amplitude above the threshold for SI, sinuous shear layer modes become unstable, as well as another instability mode that is amplified in a narrow region near the vortex inlet position.     

Global stability analysis of axisymmetric boundary layer over a circular cylinder

This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier–Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi’s iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.     

Study of effect of a smooth hump on hypersonic boundary layer instability

Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied by using parabolized stability equations. Linear evolution of mode S over a hump is analyzed for Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier–Stokes equations. Hump with height smaller than local boundary layer thickness is considered. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect is confirmed for hump located at upstream and downstream of synchronization point, respectively. Results of parametric studies to examine the effect of hump height, location, etc., are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers.     

Axisymmetric flow and heat transfer of the Carreau fluid due to a radially stretching sheet: Numerical study

The prime objective of this article is to study the axisymmetric flow and heat transfer of the Carreau fluid over a radially stretching sheet. The Carreau constitutive model is used to discuss the characteristics of both shear-thinning and shear-thickening fluids. The momentum equations for the two-dimensional flow field are first modeled for the Carreau fluid with the aid of the boundary layer approximations. The essential equations of the problem are reduced to a set of nonlinear ordinary differential equations by using local similarity transformations. Numerical solutions of the governing differential equations are obtained for the velocity and temperature fields by using the fifth-order Runge–Kutta method along with the shooting technique. These solutions are obtained for various values of physical parameters. The results indicate substantial reduction of the flow velocity as well as the thermal boundary layer thickness for the shear-thinning fluid with an increase in the Weissenberg number, and the opposite behavior is noted for the shear-thickening fluid. Numerical results are validated by comparisons with already published results.     

Asymptotic Analysis of Viscous Fluctuations in Turbulent Boundary Layers

A two-dimensional boundary layer of an incompressible viscous fluid is investigated in the presence of velocity and pressure fluctuations. The characteristic Reynolds number is high and, as a consequence, the unsteady (turbulent) boundary layer is thin. An asymptotic approach is used to analyze the complete unsteady Navier–Stokes equations, which makes it possible to separate out the characteristic viscous and inviscid flow zones in the boundary layer and to solve the corresponding problems. The analytical expressions for the viscous fluctuations governed by the Hamel equation with a large value of the parameter are derived.     

碟式离心机层流边界层方程的对称性和不变解

为运用边界层理论进行碟式离心机的碟片型线设计,首先对于碟式离心机内部多个碟片浅层固液两相界面流动模型,从流体力学基本的N-S方程组出发,得出碟片间隙斜窄流二维层流边界层方程;其次,采用李群演绎算法,推导出系统偏微分方程组允许的无穷小对称和不变解,更重要的是给出了其详细的解析表达式和有关性质。结果发现,碟式离心机层流边界层厚度与碟片结构(如碟片尺寸和间距、转速)以及流体物性(如液相粘性系数)密切相关。本文研究为考虑边界和初始条件的流场边界层精确解析解提供了有效途径,也为边界层分离控制模型的各种数值算法提供了验证。     

Symmetry groups and similarity analysis for boundary layer control over a wedge using electric forces

In this paper, we consider the control of laminar, incompressible boundary layer for the ionized air flow over a flat plate and wedges through the application of an electric field. Group theory is used to find equivalence transformations of the resulting boundary layer equations. These transformations in turn reveal forms of the electric field function which lead to reductions of the equations via similarity variables. Differences in boundary layer thickness growth and velocity profiles as well as wall shear stresses are shown for the specific choices of the electric field function. The effects of suction and blowing type of boundary conditions are also demonstrated. The applied electric fields lead to a thinning of boundary layer thickness and an increase in wall shear stress. They are also shown to stabilize the velocity component profiles and suppress flow separation in reentrant corners.     

Approximate solution of the problem of the three-dimensional boundary layer in an incompressible fluid

A method of successive approximations is proposed for the solution of the equations of the three-dimensional incompressible boundary layer on bodies of arbitrary shape. A coordinate system connected with the streamlines of the external nonviscous flow is used. It is assumed that the velocity across the external streamlines is small. When the intensity of secondary flow is low the equations describing the boundary layer in an incompressible fluid are reduced to a form analogous to the equations for the boundary layer on axially symmetrical bodies. An approximate analytical solution is obtained for the velocity and for the friction in the form of equations which can be used for any problems of a three-dimensional incompressible boundary layer. The method developed was applied to the problem of the three-dimensional boundary layer at a plate with a cylindrical obstacle in the presence of a slip angle.     

Comment on the paper “Magnetohydrodynamic effects on natural convection flow of a nanofluid in the presence of heat source due to solar energy,N. Anbuchezhian,K. Srinivasan,K. Chandrasekaran,R. Kandasamy,Meccanica (2013) 48:307–321”

In the above paper a theoretical investigation of MHD convective flow and heat transfer of an incompressible viscous nanofluid past a porous vertical stretching sheet in the presence of variable stream condition is presented. The governing boundary layer equations are transformed by a Lie symmetry group transformation and the ordinary differential equations are solved numerically using Runge–Kutta Gill method.     

Euler flow solutions for transonic shock wave–boundary layer interaction

Steady 2D Euler flow computations have been performed for a wind tunnel section, designed for research on transonic shock wave–boundary layer interaction. For the discretization of the steady Euler equations, an upwind finite volume technique has been applied. The solution method used is collective, symmetric point Gauss–Seidel relaxation, accelerated by non-linear multigrid. Initial finest grid solutions have been obtained by nested iteration. Automatic grid adaptation has been applied for obtaining sharp shocks. An indication is given of the mathematical quality of four different boundary conditions for the outlet flow. Two transonic flow solutions with shock are presented: a choked and a non-choked flow. Both flow solutions show good shock capturing. A comparison is made with experimental results.     

Boundary layer flow of Reiner-Philippoff fluids

An analysis is made of the boundary layer flow of Reiner-Philippoff fluids. This work is an extension of a previous analysis by Hansen and Na [A.G. Hansen and T.Y. Na, Similarity solutions of laminar, incompressible boundary layer equations of non-Newtonian fluids. ASME 67-WA/FE-2, presented at the ASME Winter Annual Meeting, November (1967)], where the existence of similar solutions of the boundary layer equations of a class of general non-Newtonian fluids were investigated. It was found that similarity solutions exist only for the case of flow over a 90° wedge and, being similar, the solution of the non-linear boundary layer equations can be reduced to the solution of non-linear ordinary differential equations. In this paper, the more general case of the boundary layer flow of Reiner-Philippoff fluids over other body shapes will be considered. A general formulation is given which makes it possible to solve the boundary layer equations for any body shape by a finite-difference technique. As an example, the classical solution of the boundary layer flow over a flat plate, known as the Blasius solution, will be considered. Numerical results are generated for a series of values of the parameters in the Reiner-Philippoff model.     

Asymptotic theory of the Boltzmann system,for a steady flow of a slightly rarefied gas with a finite Mach number: General theory

A steady rarefied gas flow with Mach number of the order of unity around a body or bodies is considered. The general behaviour of the gas for small Knudsen numbers is studied by asymptotic analysis of the boundary-value problem of the Boltzmann equation for a general domain. The effect of gas rarefaction (or Knudsen number) is expressed as a power series of the square root of the Knudsen number of the system. A series of fluid-dynamic type equations and their associated boundary conditions that determine the component functions of the expansion of the density, flow velocity, and temperature of the gas is obtained by the analysis. The equations up to the order of the square root of the Knudsen number do not contain non-Navier–Stokes stress and heat flow, which differs from the claim by Darrozes (in Rarefied Gas Dynamics, Academic Press, New York, 1969). The contributions up to this order, except in the Knudsen layer, are included in the system of the Navier–Stokes equations and the slip boundary conditions consisting of tangential velocity slip due to the shear of flow and temperature jump due to the temperature gradient normal to the boundary.     

Effect of surface permeability on the structure of a separated turbulent flow and heat transfer behind a backward-facing step

The structure and heat transfer in a turbulent separated flow in a suddenly expanding channel with injection (suction) through a porous wall are numerically simulated with the use of two-dimensional averaged Navier–Stokes equations, energy equations, and v ²–f turbulence model. It is shown that enhancement of the intensity of the transverse mass flux on the wall reduces the separation region length in the case of suction and increases the separation region length in the case of injection up to complete boundary layer displacement. The maximum heat transfer coefficient as a function of permeability is accurately described by the asymptotic theory of a turbulent boundary layer.     

Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk

In this paper we have studied the effects of temperature dependent fluid properties such as density, viscosity and thermal conductivity and variable Prandtl number on unsteady convective heat transfer flow over a porous rotating disk. Using similarity transformations we reduce the governing nonlinear partial differential equations for flow and heat transfer into a system of ordinary differential equations which are then solved numerically by applying Nachtsheim–Swigert shooting iteration technique along with sixth-order Runge–Kutta integration scheme. Comparison with previously published work for steady case of the problem were performed and found to be in very good agreement. The obtained numerical results show that the rate of heat transfer in a fluid of constant properties is higher than in a fluid of variable properties. The results further show that consideration of Prandtl number as constant within the boundary layer for variable fluid properties lead unrealistic results. Therefore, modeling thermal boundary layers with temperature dependent fluid properties Prandtl number must treated as variable inside the boundary layer.