Singularities on the flow between two rotating surfaces

Summary Two coaxial surfaces of revolution rotate about the common axis of symmetry with almost the same angular velocity. At large Reynolds numbers, three singular surfaces are found. One over each surface of revolution and a cylindrical shear layer touching the outer surface. Outside the cylinder the velocity is determined by the velocity distribution over the two boundary layers, while inside the cylinder the fluid is at rest.With 5 Figures     

Transient response behavior of an axisymmetric stagnation flow on a circular cylinder due to time dependent free stream velocity

An analysis is presented to investigate the unsteady response behavior of an axisymmetric stagnation flow on a circular cylinder due to transient free stream velocity. The governing boundary layer equations are integrated by the steepest descent method. Numerical results have been presented for the unsteady wall stress by assuming explicit time dependent forms for the free stream velocity.     

Oscillatory turbulent flow in a cylindrical channel

Results are presented from a study of an unsteady turbulent boundary layer in a cylinder with different flow conditions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 6, pp. 908–912, June, 1986.     

Parametric method of calculating an unsteady laminar boundary layer in an incompressible liquid with suction or injection

The equation for the unsteady boundary layer at a porous wall is reduced with the help of three series of parameters to a universal form not containing explicitly either the velocity at the outer edge of the boundary layer or the velocity of suction or injection.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 4, pp. 698–703, October, 1976.     

Stresses in cross-ply laminated circular cylinders of axially variable thickness

Summary This paper presents the results from an analytical investigation of the behavior of composite circular cylinders subjected to internal and external surface loading. The present cylinder consists of a number of homogeneous ply groups of axially variable thickness. Each ply group forming a layer is treated as an individual thin elastic cylinder of generally orthotropic material with interfacial stresses on the inner and outer surfaces of the layer as boundary loading. The deformation and stresses in each layer can be expressed in terms of interfacial stresses along the exterior surfaces of each layer. All displacement and stresses throughout the composite cylinder can be determined subsequently after satisfying boundary conditions at the inside and outside surfaces of the cylinder in conjunction with the recurrence relationship among interfacial stresses. Numerical results are presented for different values of the inner-to-outer ratio, number of layers, stacking sequence, axially-variable-thickness parameter, and load factor. Based on the presented results, conclusions can be drawn concerning the cylinder behavior and its sensitivity to different parameter variations.     

Shear flow past a square cylinder near a wall

A numerical study on the wake behind a square cylinder placed parallel to a wall has been made. The cylinder is considered to be within the boundary layer of the wall, so that the outside flow is taken to be due to uniform shear. Flow has been investigated in the laminar Reynolds number (based on the cylinder height) range. The interaction of wall boundary layer on the vortex shedding at Reynolds number up to 1400.0 has been investigated for cylinder to wall gap height 0.5 and 0.25 times the cylinder height. The gap flow between the cylinder and wall during a period of vortex shedding has been obtained. The governing unsteady Navier–Stokes equations are discretised through the finite volume method on staggered grid system. An algorithm SIMPLE has been used to compute the discretised equations iteratively. Our results show that at the gap height 0.5 times the cylinder height the vortex shedding occurs at a Strouhal number greater than for an isolated cylinder. Vortex shedding suppression occurs and wake becomes steady up to a certain value of Reynolds number at gap height 0.25 time the cylinder height. At higher Reynolds number the formation of a single row of negative vortices behind the cylinder when it is in close proximity to wall is noteworthy. Due to the shear, the drag experienced by the cylinder is found to decrease with the reduction of gap height.     

Interfacial Effects on Stress Transfer in Fiber-Reinforced Composites

A three-dimensional solution for a fiber-reinforced circular cylinder is presented for axisymmetric force and displacement boundary conditions. The solution, which can satisfy all the boundary conditions prescribed on the curved and end surfaces of the cylinder, can be used directly in the micromechanical analysis of fiber-reinforced composites to investigate the typical representative volume element (RVE). The element consists of a combined circular cylinder composed of a solid inner circular cylinder of transversely isotropic fiber, a concentric outer circular cylinder of isotropic matrix material, and an interface layer between the fiber and the matrix. The radial and tangential flexural compliances of the interfacial material are considered, and their effects on the stress transfer at the interface are studied parametrically. The numerical results presented show that the material properties of the interfacial layer have significant influences on the stress distribution within the RVE, particularly at the cross sections near the ends of the cylinder, where external loads are applied.     

Vortex shedding suppression for laminar flow past a square cylinder near a plane wall: a two-dimensional analysis

Summary A numerical study on the uniform shear flow past a long cylinder of square cross-section placed parallel to a plane wall has been made. The cylinder is considered to be within the boundary layer of the wall. The maximum gap between the plane wall to the cylinder is taken to be 0.25 times the cylinder height. We investigated the flow when the regular vortex shedding from the cylinder is suppressed. The governing unsteady Navier-Stokes equations are discretized through the finite volume method on staggered grid system. A pressure correction based iterative algorithm, SIMPLER, has been used to compute the discretised equations iteratively. We found that the critical value of the gap height for which vortex shedding is suppressed depends on the Reynolds number, which is based on the height of the cylinder and the incident stream at the surface of the cylinder. At high Reynolds number (Re ≥ 500) however, a single row of negative vortices occurs for wall to cylinder gap height L ≥ 0.2. The shear layer that emerges from the bottom face of the cylinder reattaches to the cylinder itself at this gap hight.     

Thermal Convection in an Annular Two-Layer System Under Combined Action of Buoyancy and Thermocapillary Forces

A set of two-dimensional numerical simulations of thermal convection of two immiscible liquid layers with a non-deformable interface was carried out in an annular cavity with the outer heated cylinder and the inner cooled cylinder using the finite-volume method. Bottom and top surfaces were bounded by two rigid and heat-insulated walls. The results show that the conversion of the thermal convection depends on the Marangoni number, the aspect ratio and the curvature of the annular cavity. For a sufficiently small Marangoni number, the flow is steady and there is one cell in each fluid layer. When the Marangoni number exceeds the critical value, the convective flow becomes instable and generates an unsteady multi-cell structure. In the case of the closed annular cavity, the value of the critical Marangoni number is higher than that in the infinite layer, and decreases with the increase of the aspect ratio.     

Calculation of heat flux from the region behind a reflected shock wave into the shock tube edge

We have numerically calculated the process of conjugated unsteady heat exchange during the formation of a boundary transient temperature layer as a result of the interaction of a shock wave with a flat edge surface of a shock tube. The results of calculations can be used in the analysis of the experimental data. The time variation of the heat flux and the temperature at the gas-solid interface is determined. The heat flux distribution profiles are obtained for two limiting variants of the boundary conditions on the outer surface of the shock tube.     

Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids

This paper examines the unsteady boundary layer magnetohydrodynamic flow and convective heat transfer of an exponentially stretching surface saturated by nanofluids in the presence of thermal radiation. The combined effect of stratifications (thermal and concentration) in the unsteady boundary layer flow past over a stretching surface embedded in a porous medium is analyzed. The system of coupled nonlinear differential equations are solved numerically by developing finite difference scheme together with the Newton’s linearization technique, which allows us to control nonlinear terms smoothly. The study shows that the thermal boundary layer thickness significantly increases with the increase of Brownian motion, thermophoresis number and magnetic field strength. The unsteadiness behavior of the flow of nanofluid has reducing effect on both momentum and thermal boundary layer thickness. The Brownian motion has controlling effect on nanoparticle migration. The entropy generation by means of Bejan number has strong impact on the applied magnetic field, dissipation of energy, thermal radiation and Biot number.     

Unsteady mixed convection flow of a thermomicropolar fluid on a long thin vertical cylinder

The unsteady laminar mixed convection boundary layer flow of a thermomicropolar fluid over a long thin vertical cylinder has been studied when the free stream velocity varies with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite difference scheme in combination with the quasilinearization technique. The results show that the buoyancy, curvature and suction parameters, in general, enhance the skin friction, heat transfer and gradient of microrotation, but the effect of injection is just opposite. The skin friction and heat transfer for the micropolar fluid are considerably less than those for the Newtonian fluids. The effect of microrotation parameter is appreciable only on the microrotation gradient. The effect of the Prandtl number is appreciable on the skin friction, heat transfer and gradient of microtation.     

Numerical simulation of the separated fluid flows at large Reynolds numbers

The variety of flow regimes (steady separated, periodically separated-‘Karman vortex street’, unsteady turbulent) and their characteristic peculiarities (separation and reattachment points, secondary separation, boundary layer, instability of the shear mixing layer, etc.) require the construction of effective numerical methods, which will be able to simulate adequately the considered flows. MERANGE ? SMIF–a splitting method for physical factors of incompressible fluids¹-is used for calculations of the steady and unsteady fluid flows past a circular cylinder in a wide range of Reynolds numbers (10° < Re < lo6). The finite-difference scheme for this method is of second order accuracy in the space variables, has minimal numerical viscosity and is also monotonic. Use of the Navier-Stokes equations with the corresponding transformation of Cartesian co-ordinates allows the calculations to be made by one algorithm both in a boundary layer and out of it. The method allows calculations at Re = ∞ cc and simulation of d‘Alembert’s paradox. Some results on the classical problem of the flow around a circular cylinder for a wide range of Reynolds numbers are discussed. The crisis of the total drag coefficient and the sharp rise of the Strouhal number are simulated numerically (without any turbulence models) for the critical Reynolds numbers (Re ≈ 4 × 10⁵), and are in a good agreement with experimental data.     

Efficient least squares finite elements for two-dimensional laminar boundary layer analysis

This paper presents the formulations of essentially one-dimensional least squares and Galerkin-least squares finite elements for the numerical solution of two-dimensional laminar boundary layer equations. An iterative technique to cope with the non-linearity of the boundary layer equations, in conjunction with the least squares finite element method, is proposed. Through exhaustive numerical investigations in the retarded flow over a plate, flow past a circular cylinder, the flow past an elliptic cylinder, the accuracy and applicability of the proposed method are demonstrated.     

Group method analysis of unsteady free-convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder

Summary The transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection from the outer surface of a vertical circular cylinder. The application of two-parameter group reduces the number of independent variables by two, and consequently the system of the governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions. The ordinary differential equations are solved numerically using a fourth-order Runge-Kutta scheme and the gradient method. Numerical results are obtained for the study of the boundary-layer characteristics. The general analysis developed in this study corresponds to the case of surface temperature that varies exponentially with time and uniform with respect to the axial coordinate, i.e., in the formT _w =ae ^bt , wherea andb are constants. The effect of Prandtl number,Pr, andb on the boundary layer characteristics and the maximum value of the vertical component of the velocity are studied.     

Unsteady two-dimensional and axisymmetric MHD boundary-layer flows

Summary Nonsimilar solution of the unsteady laminar incompressible magneto-hydrodynamic boundary layer flow and heat transfer for an electrically conducting fluid over two-dimensional and axisymmetric bodies in the presence of an applied magnetic field has been obtained. The effects of surface mass transfer, Joule heating and viscous dissipation are included in the analysis. Numerical computation have been carried out for the flow over a circular cylinder and a sphere using an implicit finite difference scheme in combination with a quasi-linearization technique. It is observed that magnetic field and suction cause the location of vanishing skin friction to move downstream while, the effect of injection is just the opposite. The effect of magnetic field on the skin friction is more pronounced as compared to its effect on the heat transfer. On the other hand, the heat transfer is strongly affected by the viscous dissipation and the effect is more for larte times. However, heat transfer responds comparatively less to the fluctuations of the free stream than the skin friction.     

Physicomathematical models for theories of nondestructive testing of thermophysical properties

The present work is devoted to the solution of some two-dimensional unsteady heat conduction problems for an infinite orthotropic cylinder with boundary conditions of the first- and second kind with a circular discontinuity line of temperature and specific heat flux. A solution of the two-dimensional unsteady heat conduction problem for an orthotropic cylinder is obtained with the aid of Laplace-Hankel transformations.Belarusian State University, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 6, pp. 1011–1022, 1995.     

Three-dimensional wall-bounded laminar boundary layer with span-wise cross free stream and moving boundary

In the current work, the 3D boundary layers of wall-bounded flow configurations were extended to the situations with span-wise cross moving boundary and free stream. The unsteady boundary layer is also addressed for the Falkner–Skan wedge flow with a span-wise oscillating wall or oscillating free stream. The span-wise secondary boundary layer equation is obtained using similarity transformation technique and solved analytically in terms of the primary stream-wise boundary layer flow solutions. Different fluid motion behaviors are found for these new solutions. It is found that for the span-wise secondary boundary layer flow there is no flow separation for any wall cross moving velocity, which is different from the primary stream-wise boundary layers with a reverse flow. For the unsteady boundary layer with an oscillating wall or free stream, it is seen that the solution is different from the Stokes oscillating plate or free stream problem. The unsteady wall drag increases with the increase in the oscillating frequency and decreases with increasing the primary span-wise free stream magnitude. The velocity overshooting near the wall is also seen for an oscillating free stream for a large oscillating frequency or a lower primary stream-wise free stream magnitude.     

非紧致边界气动噪声数值预测方法

通过寻找满足非紧致边界的精确格林函数,发展了一种基于声模拟理论的非紧致边界气动噪声数值预测方法。该方法首先采用边界积分方法计算满足相应边界条件的精确格林函数,然后采用精确格林函数求解FW-H方程,进行远场气动噪声预测。考虑了非紧致边界对声波传播的散射作用,适用于尺寸较大且几何外形复杂的边界与非定常流动相互作用诱发的气动噪声的数值预测。以雷诺数90 000、马赫数0.2的圆柱绕流诱发的气动噪声为例,数值预测了非紧致边界条件下的气动噪声,并与采用自由空间格林函数求解FW-H的计算结果进行了对比,对该方法进行了验证。     

A flat plate in a rotating,stratified flow

Summary The boundary layer over a flat plate of semi-infinite extent in a stratified and rotating flow grows forward from the trailing edge, and is characterized by an intrinsic length scaleL, which represents the distance from the trailing edge at which vortex stretching becomes just as important in the boundary layer as baroclinic vorticity production. Near the trailing edge, the layer is essentially the layer in a purely stratified flow; far upstream (manyL), it is an Ekman layer. The boundary layer entrains no fluid, but induces at its edge a transverse velocity component which drives an higher-order streamwise outer flow. If the flow is bounded above and below by horizontal planes, the Wiener-Hopf solution for this outer flow indicates that the disturbance decays rapidly downstream, but the transverse velocity component is non-zero far upstream.