Vortex stretching in a laminar boundary layer flow

 A new technique to produce controlled stretched vortices is presented. The initial vorticity comes from a laminar boundary layer flow and the stretching is parallel to the initial vorticity. This low velocity flow enables direct observations of the formation and destabilization of vortices. Visualizations are combined with quasi-instantaneous measurements of a full velocity profile obtained with an ultra-sonic pulsed Doppler velocimeter. Several modes of destabilization are observed and include pairing of two vortices, hairpin deformation, and vortex breakdown into a coil shape. Received: 3 April 1996/ Accepted: 4 October 1996     

Particles migration in laminar boundary layer flow

The behavior of a suspension of neutrally buoyant solid particles in the moderate relative velocity region (close to the leading edge) in a laminar boundary layer along a flat plate, is investigated. The velocity fields of both the fluid and the solid particles and the density distribution of the solid particles are simultaneously obtained by the use of the Laser-Doppler technique.It is shown that in this longitudinal region of the two-phase suspension boundary layer, the solid particles which initially lead the fluid decelerate as they move downstream, until at a certain vertical distance they lag the fluid. Clearly defined one-way transverse migration of particles directed away from the plate is characteristic of this region.     

Analysis of a laminar boundary layer flow over a flat plate with injection or suction

An analysis is performed to study a laminar boundary layer flow over a porous flat plate with injection or suction imposed at the wall. The basic equations of this problem are reduced to a system of nonlinear ordinary differential equations by means of appropriate transformations. These equations are solved analytically by the optimal homotopy asymptotic method (OHAM), and the solutions are compared with the numerical solution (NS). The effect of uniform suction/injection on the heat transfer and velocity profile is discussed. A constant surface temperature in thermal boundary conditions is used for the horizontal flat plate.     

Transient compressible boundary layer on a wedge impulsively set into motion

Summary The development of a compressible boundary layer over a wedge impulsively set into motion is studied in this paper. The initial motion is independent of the leading edge effect and the solutions are those of a Rayleigh-type problem. The motion tends to an ultimate steady state of Falkner-Skan type. The equations governing the transient boundary layer from the initial steady state to the terminal steady-state change their character after certain time due to the leading edge effect and thereafter solution depends on both the end conditions. Numerical solutions are obtained through the second-order accuracy upwind scheme. The effects of the Falkner-Skan parameter and the surface temperature on the transient flow and heat transfer are also studied. It has been found that the flow separation does not occur form–0.0707 when _w = 1.5 (hot wall), andm–0.118 when _0.5 (cold wall).     

Effects of blowing or suction on the laminar boundary layer flow over a rotating cone

The effects of suction or blowing at the surface of a rotating cone in a quiet fluid on the skin friction and heat transfer are described. The equations which govern the fluid motion and thermal energy transfer are transformed by the boundary layer approximations and the resulting equations are solved under the condition that the suction or blowing velocity varies as x ⁿ (x: distance measured from the apex of the cone, n: arbitrary constant). The solutions are obtained as a perturbation from the basic laminar flow of an incompressible viscous fluid over the impermeable rotating cone. Detailed numerical calculations are performed for the case of an isothermal rotating cone with uniform blowing or suction, i.e. n=0, the Prandtl number being 0.72. Results are given for the shear stress, heat transfer and velocity and temperature fields. It is shown from the analysis that suction sharply increases the circumferential shear stress and the heat transfer at the surface.Nomenclature c proportional constant - C _fx dimensionless skin friction factor, _x /(V ²) - C _fx0 dimensionless skin friction factor for an impermeable cone - C _fy dimensionless circumferential skin friction factor, _y /(V ²) - C _fy0 dimensionless circumferential skin friction factor for an impermeable cone - c _p specific heat at constant pressure - f _k function of - g _k function of - h heat transfer coefficient, q/(T _w–T ) - k thermal conductivity of fluid - n arbitrary constant - Nu _x local Nusselt number, hx/k - Nu _x0 local Nusselt number for an impermeable cone - Pr Prandtl number - q heat transfer rate - r radius of a circular cross section of the cone, x sin - R _x Reynolds number, Vx/ - T temperature - T _w surface temperature of the cone - T temperature of the surrounding fluid - u fluid velocity in x-direction - v fluid velocity in y-direction - V circumferential velocity at the cone surface, r - w fluid velocity in z-direction - x coordinate along meridional section - y coordinate along a circular cross section - z coordinate perpendicular to both x and y - perturbation parameter, cx ⁿ /(x sin )^1/2 - dimensionless z-coordinate, z( sin /)^1/2 - _k function of - kinematic viscosity - density of fluid - _x skin friction in x-direction - _y circumferential skin friction - stream function - angular speed of the cone     

Theory of laminar boundary layer separation in supersonic flow

A method of calculation is constructed for the Navier-Stokes equations using asymptotic expansions for high Reynolds numbers and matching techniques to join solutions (for example, [1]). The equations and boundary conditions for the first approximation, the method, and the results of numerical integration for the region lying above the separation point, including the separation point as well, are presented. A comparison is made with experimental data, and corrections corresponding to the second approximation are estimated. On the basis of these results, the limits of applicability of the approximate theories that utilize the boundary layer equations are discussed.     

Effect of boundary layer on Mach reflection over a wedge surface

Abstract. In this paper, we consider the phenomenon of unsteady Mach reflection generated by a plane shock wave advancing over a straight wedge surface, with particular attention to the deviation of the flow field from the self-similar nature. We examine the observed change in angle between incident and reflected shocks, which is in contrast to the fact that the angle should remain constant with time in a self-similar flow. The effect of the boundary layer behind the advancing shock wave over the surface of the wedge is considered to cause this, and boundary layer theory is utilized to estimate the thickness of the layer. It is found that the thickness increases as to the time t compared with t by the overall expansion in the self-similar flow. Assuming that the thicker boundary layer is effectively equivalent to a change in wedge angle, the effect of the boundary layer on the flow field should be less in later stages with larger t values in accordance with the observation above. Received 6 March 2000 / Accepted 23 April 2001     

Mixed convection boundary layer flow past a wedge with permeable walls

The effects of suction/injection on steady laminar mixed convection boundary layer flow over a permeable horizontal surface of a wedge in a viscous and incompressible fluid is considered in this paper. The similarity solutions of the governing boundary layer equations are obtained for some values of the suction/injection parameter f ₀, the constant exponent m of the wall temperature as well as the mixed convection parameter λ. The resulting system of nonlinear ordinary differential equations is solved numerically for both assisting and opposing flow regimes using an implicit finite-difference scheme known as the Keller-box method. Numerical results for the reduced skin friction coefficient, the local Nusselt number, and the velocity and temperature profiles are obtained for various values of parameters considered. Dual solutions are found to exist for the case of opposing flow.     

Particle motion in a laminar boundary layer on the transverse velocity relaxation length

The properties of the equation of quasi-equiiibrium particle motion in the boundary layer on a flat plate are investigated. In particular, it is shown that in general it has a nonunique solution and that, depending on its initial velocity, the particle may approach the surface of the plate or move in the opposite direction.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 86–93, January–February, 1993.     

Numerical investigation of three-dimensional laminar boundary layer flow over spheroids at angles of attack

The flow in the laminar boundary layers on spheroids with axial ratios of 611 (prolate ellipsoid of revolution) and 616 (circular wing) at angles of attack of 5 and 10° is investigated numerically. The implicit finite-difference method described in [1] is employed. The results obtained are compared with the measurements reported in [2–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 59–68, November–December, 1990.     

Experimental study of a laminar air boundary layer over a water surface

The formation of a laminar boundary layer over a water surface has been experimentally studied for the case of a low wind speed of 3.77 m/s without pressure gradient. Velocity profiles were measured using a small total head tube with an external diameter D=0.7 mm in order to detect the velocity as close to the air/water interface as possible. Precision data were obtained by close attention being paid to near boundary correction procedures arising from the effects of viscous, velocity gradient and wall proximity on the pressure tube. Measurements for the first time support Lock's theory.     

The delay of transition of a laminar boundary layer over compliant wall

In a previous paper^[1], a method has been developed to study the stability characteristics of laminar boundary layers over compliant walls. In this paper, the effect of double layered compliant wall and Kramer type compliant wall on delaying the transition is investigated, and it is shown that there does exist the possibility to delay the transition by applying such compliant walls. The project supported by the National Natural Science Foundation of China.     

Dispersed multiphase flow with air-driven runback of a liquid layer at a moving boundary

Multiphase flow with impinging droplets on an icing surface with a flowing supercooled surface layer is investigated. The air-assisted flowing layer is modelled with the cross-phase shear stresses imparted at the moving liquid/air interface. Runback and runoff of the surface layer are predicted by mass flow across the boundaries between adjacent elements in the numerical formulation. This liquid runoff is determined by coupled heat and momentum balances for the unfrozen water layer. The numerical analysis is developed with a control-volume-based finite element method (CVFEM). An Eulerian formulation with volume averaging is developed to accommodate the near-wall elements containing both dispersed and continuous phases. The predicted results are successfully validated through comparisons with analytical solutions and measured data.     

The effect of variable properties on laminar boundary layer flow

The influence of temperature dependent fluid properties on laminar boundary layer flows is examined for wedge flows (Falkner-Skan). An asymptotic expansion for small heat transfer rates is applied under the boundary conditionsT _w= const andq _w=const. Linear deviations from the zero order solution (constant properties) can be given in a form known as the property ratio method. As a consequence this method is no longer an empirical one.     

A Dorodnitsyn finite element formulation for laminar boundary layer flow

The Dorodnitsyn boundary later formulation is given a finite element interpretation and found to generate very accurate and economical solutions when combined with an implicit, non-iterative marching scheme in the downstream direction. The algorithm is of order (Δ²u, Δx) whether linear or quadratic elements are used across the boundary layer. Solutions are compared with a Dorodnitsyn spectral formulation and a conventional finite difference formulation for three Falkner-Skan pressure gradient cases and the flow over a circular cylinder. With quadratic elements the Dorodnitsyn finite element formulation is approximately five times more efficient than the conventional finite difference formulation.     

Reynolds analogy in a dusty laminar boundary layer

The nonisothermal Blasius problem for a gas suspension is considered on the basis of the equations of a quasiequilibrium two-phase laminar boundary layer [1–3]. Approximate analytical expressions are obtained for the friction and heat transfer coefficients and their region of applicability is estimated; the Reynolds analogy between friction and convective heat transfer processes [4] is extended to the case of a dusty quasiequilibrium laminar boundary layer. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 160–162, November–December, 1986.