Approximate solutions to MHD Falkner-Skan flow over permeable wall

The magnetohydrodynamic (MHD) Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method (DTM) with the Padé approximation called DTM-Padé. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.     

Experimental investigation of turbulence in a supersonic flow

The structure of disturbances carried by the flow into the working section of a supersonic wind tunnel has been investigated by means of a constant-current hot-wire anemometer. In order to generate the disturbances grids consisting of round rods were introduced upstream from the nozzle throat. It was found that in the working section the disturbances consist of non-correlating vortex, entropy and acoustic modes. The latter is generated by the boundary layer on the nozzle walls and the first two by the grids. The spectral compositions of the various modes are compared. Because of the presence of grid turbulence the point of laminar-turbulent transition in the boundary layer on a flat plate varied widely.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–124, May–June, 1990.     

Selection of convective rolls in a thin evaporating-fluid layer in an air flow

The process of selection of longitudinal convective rolls in a thin layer of evaporating fluid immersed in an air turbulent boundary layer flow is studied numerically. The dependence of the two-dimensional flow patterns on the Rayleigh number and boundary conditions is analyzed. Calculations with account for the thermocapillary effect are carried out. The numerical results are compared with experimental data.     

The influence of boundary layers on supersonic inlet flow unstart induced by mass injection

A transverse jet is injected into a supersonic model inlet flow to induce unstart. Planar laser Rayleigh scattering from condensed CO₂ particles is used to visualize flow dynamics during the unstart process, while in some cases, wall pressure traces are simultaneously recorded. Studies conducted over a range of inlet configurations reveal that the presence of turbulent wall boundary layers strongly affect the unstart dynamics. It is found that relatively thick turbulent boundary layers in asymmetric wall boundary layer conditions prompt the formation of unstart shocks; in symmetric boundary conditions lead to the propagation of pseudo-shocks; and in both cases facilitate fast inlet unstart, when compared with thin, laminar boundary layers. Incident shockwaves and associated reflections are found to affect the speed of pressure disturbances. These disturbances, which induce boundary layer separation, are found to precede the formation of unstart shocks. The results confirm the importance of and need to better understand shock-boundary layer interactions in inlet unstart dynamics.     

Response of skin panels to combined self- and boundary layer-induced fluctuating pressure

Fluctuating pressures are a critical consideration in the life-prediction of thin-gauge hot-structures operating in high-speed flow. Sources include both boundary layer turbulence and self-induced components, where the latter arises from panel vibrations. While a considerable body of research is available for the structural response of thin-gauge panels to self-induced pressure fluctuations, the response to boundary layer turbulence is not well-understood due to the complexity in modeling the loads. Important open issues are the degree of coupling between the boundary layer induced fluctuating loads and the thermo-structural response, and also the potential for interactions between a turbulent boundary layer and structural response to result in structural instabilities. This study seeks to address these issues by incorporating a phenomenological model for turbulent boundary layer loads into an aerothermoelastic framework. The enhanced aerothermoelastic model is then used to study the combined effect of self- and boundary layer-induced fluctuating pressures on responses of simple panels, and to characterize features in the turbulent boundary layer loads that can lead to large amplitude structural vibrations. The developed phenomenological model predicts that the magnitude of the boundary layer induced fluctuating pressure increases with increasing panel inclination, and decreases with increasing temperature. Furthermore, it is found that both RMS magnitude and phase angle of the boundary layer induced pressure loads play key roles in panel response. Certain combinations of these features, coupled with the self-induced pressure fluctuations, are found to cause onset of fluid–structural instabilities earlier than observed when pressure fluctuations from the turbulent boundary layer are either neglected or decoupled from the panel response.     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.     

Boundary layer development in a gas flow with stagnation enthalpy varying across the streamlines

We consider a laminar boundary layer for which the stagnation enthalpy specified in the initial section is variable with height. Such problems arise, for example, for bodies located in the wake behind another body, for hypersonic flow past slender blunted bodies (as a result of the large transverse entropy gradients in the highentropy layer), for stepwise variation of the temperature of a surface on which there is an already developed boundary layer, for sudden expansion of the boundary layer as a result of its flow past a corner of the surface, etc.Strictly, we should in such cases solve the boundary layer equations (if the longitudinal gradients are much smaller than the transverse) with the specified initial distribution of the quantities. However, from the physical point of view, the distributed region may be broken down into two regions, the near-wall boundary layer and an outer region which is a gas flow with constant velocity and the specified initial temperature profile, whose calculation yields the edge conditions for the boundary layer. The boundary between the regions is determined from the condition of adequately smooth matching of the solutions. This approach is much preferable to the first, since it permits avoiding (within the framework of boundary layer theory) the difficulties associated with the presence of a possible singularity at the initial point of the surface due to the discontinuity of the boundary conditions at this point, and also permits using conventional boundary layer theory if the effect of the viscosity in the outer region is not significant. However, this partition requires additional justifications of the possibility of independent determination of the solution in the outer region and the determination of the edge of the boundary layer, considered as the region of influence of the wetted surface. The boundary layer in a nonuniform flow has been considered in several works for a linear initial velocity or temperature profile [1–3].It should be noted that the linear initial enthalpy or velocity profiles for constant gas properties do not undergo changes under the influence of viscosity or thermal conductivity. Thus the fundamental characteristic features noted above which are associated with the presence of the two regions and their interaction in essence cannot be investigated using these examples.In this study we obtain and analyze the exact solutions of the equations of the compressible boundary layer for a power-law variation of the initial stagnation enthalpy profile as a function of the stream function for a constant initial velocity. Here it is shown that the influence of the boundary conditions at the wall are actually localized in the near-wall boundary layer, which is similar in dimensions to the conventional velocity or thermal boundary layers. In the region which is external with relation to this layer, in accordance with the physical picture described above, the solution coincides with the solution of the Cauchy problem for the heat conduction equation, which describes the development of the initial temperature profile in an infinite steady-state flow with constant velocity.It is shown that for the sufficiently smooth initial profiles which are of interest in practice the outer flow undergoes practically no changes until we reach the inner boundary layer, and it may be calculated using the perfect gas laws.     

Influence of spatial modulation of the temperature field on the stability of two-dimensional steady flow in a horizontal layer of fluid

A study is made of the stability of the steady periodic regime that arises in a horizontal layer of fluid in the presence of spatial modulation of of the temperature on the solid bottom boundary. The upper free boundary of the layer is in contact with the atmosphere. The fundamental resonance values of the wave number of the modulation are found; there are five of them. If the temperature of the lower boundary of the layer is constant, and the temperature gradient is not too large, the fluid is in equilibrium. When the temperature gradient passes through the critical value, the equilibrium ceases to be stable, and steady convection develops in the fluid [1]. In the presence of spatial modulation of the temperature on the lower boundary of the layer the fluid cannot be in equilibrium, and a spatially periodic steady regime is established in it. The aim of the present paper is to find the critical values of the temperature gradient at which this fundamental steady regime becomes unstable and a secondary steady regime develops in the fluid. An analogous problem for the case when both boundaries of the layer are free surfaces and without allowance for the influence of the atmosphere has been solved by Vozovoi and Nepomnyashchii [2].     

MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface

Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable sur- face in the presence of magnetic field. To achieve this, one parameter linear group trans- formation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method （HAM） to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non- Newtonian fluid （Powell-Eyring model） parameters ε and δon the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ε whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.     

Turbulent structure of air flow over wind-induced gravity waves

This is the second paper in a group of three that reports the systematic measurements of wind-generated water waves in a wind tunnel experiment. Here, the structure of the boundary layer on the air side of the water?Cair interface was analysed and compared with the boundary layer over a smooth plane rigid wall. The contribution of the wave-induced Reynolds stress was detected through filtering the spectrum of velocity fluctuations. Wave-induced Reynolds stresses became negligible for z?>?5 H _rms. The intermittency factor in the boundary layer over water waves was similar to that in a boundary layer over a rigid plane wall, with several differences near the interface. Here, the presence/absence of water damps out the turbulence. The quadrant analyses revealed that ejection and sweep events were dominant and more concentrated. At small fetches, the large-amplitude negative streamwise perturbations were preferentially lifted. Turbulence energy production peaked at z/???=?0.2 and had a distribution similar to that observed for a self-preserving boundary layer with a strong adverse gradient pressure. The quadrant analysis contribution to the energy production revealed that ejections still dominated the balance and that the production was spatially modulated in the wind direction with a couple of cells and with a minimum in the area of the free surface wave height reduction.     

Flutter of infinite elastic plates in the boundary-layer flow at finite Reynolds numbers

The stability of an infinite elastic plate in supersonic gas flow is investigated taking into account the presence of the boundary layer formed on the plate surface. The effect of viscous and temperature disturbances of the boundary layer on the behavior of traveling waves is studied at large but finite Reynolds numbers. It is shown that in the case of the small boundary layer thickness viscosity can have both stabilizing and destabilizing effect depending on the phase velocity of disturbance propagation.     

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

Effects of riblets upon flow stability

The onset of transition in the boundary layer over a grooved surface is studied by introducing the presence of grooves into the standarde ⁹ model with the aid of a previously obtained equivalent boundary condition. Under conditions of self-similarity and smallness of the grooves, Tollmien-Schlichting waves are found to be excited at a slightly smaller Reynolds number and Görtler vortices at a slightly larger one than on a smooth surface.     

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.     

Influence of polymer additives in a flow on the hydrodynamic characteristics of two-dimensional profiles

The problem of separationless flow of homogeneous dilute polymer solutions over two-dimensional profiles is considered. The complete flow is divided by the outer edge of the boundary layer and the wake into two regions: a region of irrotational flow and a region of viscous flow — the boundary layer and wake. The characteristics of the two regions are matched at their boundary. The problem is solved by successive approximation with allowance for the mutual influence of the two regions on each other. The influence of the irrotational region on the viscous region is taken into account through the distribution of the pressure on the boundary of the wake and the boundary layer. The influence of the viscous part of the flow is taken into account by the introduction of an associated vortex whose intensity is equal to the integral of the vorticity in the complete viscous region, and also by the introduction of additional velocities on the boundary of the wake and the boundary layer. These deform the streamlines in the irrotational part of the flow and ensure that they match the flow pattern in the real fluid. The results of the calculations of the hydrodynamic characteristics of a Zhukovskii profile are compared with experimental data. The influence of the introduction into the flow of polymer additives on the distributed and total characteristics of the flow at a number of Reynolds numbers is analyzed for the example of the modified profile NACA66.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–41, October–December, 1981.     

Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF).The parabolic equations obtained from FVF are numer...     

Experimental study on flow control of the turbulent boundary layer with micro-bubbles

The effect of micro-bubbles on the turbulent boundary layer in the channel flow with Reynolds numbers (Re) ranging from \(0.87\times 10 ^{5}\) to \(1.23\times 10^{5}\) is experimentally studied by using particle image velocimetry (PIV) measurements. The micro-bubbles are produced by water electrolysis. The velocity profiles, Reynolds stress and instantaneous structures of the boundary layer, with and without micro-bubbles, are measured and analyzed. The presence of micro-bubbles changes the streamwise mean velocity of the fluid and increases the wall shear stress. The results show that micro-bubbles have two effects, buoyancy and extrusion, which dominate the flow behavior of the mixed fluid in the turbulent boundary layer. The buoyancy effect leads to upward motion that drives the fluid motion in the same direction and, therefore, enhances the turbulence intense of the boundary layer. While for the extrusion effect, the presence of accumulated micro-bubbles pushes the flow structures in the turbulent boundary layer away from the near-wall region. The interaction between these two effects causes the vorticity structures and turbulence activity to be in the region far away from the wall. The buoyancy effect is dominant when the Re is relatively small, while the extrusion effect plays a more important role when Re rises.     

Bifurcation of the stationary Ekman flow into a stable periodic flow

The two cases of stationary Ekman boundary layer flow of an incompressible fluid near i) a plane boundary and ii) a free surface with constant shear are considered. It is proven that a stable secondary flow in the form of traveling waves bifurcates from the stationary flow at a certain Reynolds number, and that the stationary flow is unstable above this number. The values of the critical Reynolds number and of the numbers that characterize the traveling wave are computed and compared with experimental values.     

Numerical modeling of the disturbances of the separated flow in a rounded compression corner

Numerical modeling of the time-dependent supersonic flow over a compression corner with different roundness radii is performed on the basis of the solution of the two-dimensional Navier-Stokes equations in the regimes corresponding to local boundary layer separation. The development of unstable disturbances generated by local periodic injection/suction in the preseparated boundary layer is calculated. The results are compared with those of similar calculations for a flat plate. It is shown that the natural oscillations of the boundary-layer second mode stabilize in the separation zone and grow intensely downstream of the reattachment point. The acoustic modes excited within a separation bubble are studied using numerical calculations and an asymptotic analysis.     

Heat transfer and supersonic flow structure in surface cavities

The characteristics of the flow and heat transfer in two- and three-dimensional open cavities on plane and cylindrical surfaces in a supersonic stream in the presence of a turbulent boundary layer have been investigated experimentally. The effects of the Mach number, boundary layer thickness, the shape of the cavity, and its angle of inclination to the free-stream direction on the flow parameters in the mixing layer above the cavity and the heat flux and pressure distribution on the surface of the cavity and its bottom are descirbed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 74–80, July–August, 1998.