GROUND EFFECT OF FLOW AROUND AN ELLIPTIC CYLINDER IN A TURBULENT BOUNDARY LAYER

The flow characteristics around an elliptic cylinder with an axis ratio of AR=2 located near a flat plate were investigated experimentally. The elliptic cylinder was embedded in a turbulent boundary layer whose thickness is larger than the cylinder height. For comparison, the same experiment was carried out for a circular cylinder having the same vertical height. The Reynolds number based on the height of the cylinder cross-section was 14000. The pressure distributions on the cylinder surface and on the flat plate were measured for various gap distances between the cylinder and the plate. The wake velocity profiles behind the cylinder were measured using hot-wire anemometry. In the near-wake region, the vortices are shed regularly only when the gap ratio is greater than the critical value of G/B=0·4. The critical gap ratio is larger than that of a circular cylinder. The variation of surface pressure distributions on the elliptic cylinder with respect to the gap ratio is much smaller than that on the circular cylinder. This trend is more evident on the upper surface than the lower one. The surface pressures on the flat plate recover faster than those for the case of the circular cylinder at downstream locations. As the gap ratio increases, the drag coefficient of the cylinder itself increases, but the lift coefficient decreases. For all gap ratios tested in this study, the drag coefficient of the elliptic cylinder is about half that of the circular cylinder. The ground effect of the cylinder at small gap ratio constrains the flow passing through the gap, and restricts the vortex shedding from the cylinder, especially in the lower side of the cylinder wake. This constraint effect is more severe for the elliptic cylinder, compared to the circular cylinder. The wake region behind the elliptic cylinder is relatively small and the velocity profiles tend to approach rapidly to those of a flat plate boundary layer     

Squeezing of a viscous fluid between elliptic plates

A viscous fluid is squeezed between two parallel elliptic plates. If the gap width varies as the inverse square root of time, exact similarity equations may be obtained. The nonlinear two-point boundary value problem is then solved by perturbation theory and also integrated numerically by a new homotopy method. Nonunique solutions exist for the separation of the plates. This paper shows two-dimensional or axisymmetric boundary conditions may yield non-two-dimensional and nonaxisymmetric solutions.     

Effect of thermal gradient on vibration of non-homogeneous visco-elastic elliptic plate of variable thickness

An analysis and numerical results are presented for free transverse vibrations of non-homogeneous visco-elastic elliptic plate whose temperature and thickness spatial variations both are parabolic along a line through plate centre. The variation in density is assumed as parabolic along a line through plate centre, which raise non-homogeneity of the plate materials and make problem interesting as introducing variation in non-homogeneity of the material mass density reduce the problem practical importance in comparison to homogenous plate. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement corresponding to the first two modes of vibrations of a clamped non-homogeneous visco-elastic elliptic plate for various values of taper constant, thermal constants, non-homogeneity constant and aspect ratio are obtained and shown graphically.     

Stress analysis in two dimensional electrostrictive material with an elliptic rigid conductor

This paper presents the governing equations of electrostrictive materials. The stress and electric field solutions for an infinite plate with a rigid elliptic conductor under applied load at infinity are given. The asymptotic expansions of the solution for a narrow elliptic conductor show that the stresses and the electric fields near the end of a narrow elliptic conductor possess r⁻¹ and r^−1/2 forms respectively in a local coordinate system with the origin at its focus.     

Deformation of a tensile membrane adjacent to a moving wall caused by viscous flow

Theoretical analysis is done for deformation of a tensile membrane caused by viscous flow between the membrane and a solid boundary (wafer) placed adjacent to the membrane. The membrane and its support are assumed to have circular shapes. The boundary is assumed to move perpendicularly to the membrane by a small fraction of the gap width. The Hele–Shaw flow theory is applied to the flow. Variation of the central gap width is obtained, and it is shown that the maximum membrane deformation depends on the membrane tension and the final gap width. The dependence agrees with experimental results.     

Numerical simulation of the effects of plate separation and inclination on heat transfer in buoyancy driven open channels

 Effects of plate separation and inclination on free convection between asymmetrically heated vertical and inclined parallel plates have been simulated. The upper isothermally heated plate is facing downwards, the lower plate is passively heated by the upper one. The plate inclinations are chosen to be 0^∘, 30^∘, 45^∘ with respect to vertical position. Three-dimensional laminar numerical simulations are obtained by solving the full elliptic governing equations using a commercial finite volume based computational fluid dynamics (CFD) code. Comparisons of computational results with experiments and data from the literature are made in terms of relevant dimensionless numbers. It was observed that plate spacing and inclination influence the overall heat transfer rate. Received on 3 November 1998     

Ground effects on separated laminar flows past an inclined flat plate

The appearance of a ground surface can play an important role in the flow structures for the flows past a flat plate. We conduct two-dimensional numerical simulations on viscous flows past a flat plate inclined at an angle of attack of \(20^\circ \) with ground effects using a finite-volume method. Results show that the effects on the separated flow from the ground are highly dependent on the gap (G) between the plate and the ground. As the gap decreases, the strength of vortices generated from the trailing edge is restrained, which is consistent with experimental observations. Further decrease in the gap even eliminates the vortex shedding and yields a steady flow. It is also found that the flow between the gap can either be accelerated at large gap ratios (\({G/L >1}\), G is the gap, L is the plate length), or be decelerated at small gap ratios (\({G/L <1}\)). Furthermore, the numerical results show that the wake flow behind the plate can significantly change the distribution of surface shear stress on the ground. Specifically, the mean shear stress on the ground in the downstream region at a gap ratio \(G/L = 2.0\) is one order of magnitude larger than that at a small gap ratio \(G/L = 0.3\), and the length of the downstream region where the shear stress can be effectively changed is much larger than the plate length, which provides a guideline to manipulate the ground wall surface shear stress using an inclined plate in the vicinity of the wall.     

Hall effects on the magnetohydrodynamic shear flow past an infinite porous flat plate subjected to uniform suction or blowing

An analysis is made of Hall effects on the steady shear flow of a viscous incompressible electrically conducting fluid past an infinite porous plate in the presence of a uniform transverse magnetic field. It is shown that for suction at the plate, steady shear flow solution exists only when S²<Q, where S and Q are the suction and magnetic parameters, respectively. The primary flow velocity decreases with increase in Hall parameter m. But the cross-flow velocity first increases and then decreases with increase in m. Similar results are obtained for variation of the induced magnetic field with m. It is further found that for blowing at the plate, steady shear flow solution exists only when , where S₁ is the blowing parameter.     

Experimental research on heat transfer of natural convection in vertical rectangular channels with large aspect ratio

This work presents the experimental research on the steady laminar natural convection heat transfer of air in three vertical thin rectangular channels with different gap clearance. The much higher ratio of width to gap clearance (60–24) and the ratio of length to gap clearance (800–320) make the rectangular channels similar with the coolant flow passage in plate type fuel reactors. The vertical rectangular channels were composed of two stainless steal plates and were heated by electrical heating rods. The wall temperatures were detected with the K-type thermocouples which were inserted into the blind holes drilled in the steal plates. Also the air temperatures at the inlet and outlet of the channel were detected. The wall heat fluxes added to the air flow were calculated by the Fourier heat conduction law. The heat transfer characteristics were analyzed, and the average Nusselt numbers in all the three channels could be well correlated with the Rayleigh number or the modified Rayleigh number in a uniform correlation. Furthermore, the maximum wall temperatures were investigated, which is a key parameter for the fuel’s integrity during some accidents. It was found that even the wall heat flux was up to 1500 W/m², the maximum wall temperature was lower than 350 °C. All this work is valuable for the plate type reactor’s design and safety analysis.     

Corner Singularities and Regularity Results for the Reissner/Mindlin Plate Model

The theory for elliptic boundary value problems for general elliptic systems is used in order to investigate systematically corner singularities and regularity for weak solutions to a broad class of boundary value problems for the Reissner/Mindlin plate model in polygonal domains. The regularity results for the deflection of the midplane and for the rotation of fibers normal to the midplane are formulated in Sobolev spaces H ^s , where s>1 is a real number. The number s depends on the geometry, the material parameters and the boundary conditions in general and is related to a decomposition of the fields in a singular and a regular part. The leading singular terms are calculated for a wide class of boundary conditions (36 combinations). The results are critically compared with those known from a stress potential approach.     

Numerical study of the wall effect on particle sedimentation

ABSTRACT

In this article, we investigate the abnormal settling of two-disk systems and elliptical shaped particles in infinite two-dimensional channels filled with an incompressible viscous fluid. We apply a distributed Lagrange multiplier/fictitious domain method (DLM/FDM) for the direct numerical simulation of these particulate flows. Due to the wall effect, the two-disk systems can form chains which settle stably instead of having the particles moving apart. Also, sedimentation with the long axis moving to vertical positions in the middle of the infinite channel has been observed for the elliptic shaped particles. The critical Reynolds number for having such an abnormal settling behaviour decreases as the width of the channel increases.     

ANISOTROPIC EFFECTS OF QUASI-ISOTROPIC COMPOSITES (II)——APPLICATIONS AND MICRO-MECHANICAL ANALYSIS

Up to now, the analysis on anisotropic effects of quasi-isotropic composites to material structures has not been found in literatures. In the present paper the strength model for triaxial woven materials proposed in Part (I) ^[1] is applied to study the problems of an infinitely large plate of triaxial woven material containing either an elliptic hole or a crack. To the elliptic hole problem the remote critical loading as a function of the geometric parameters of woven materials is analysed, and to the crack problem, the cracking orientation is examined. Finally, the elasticity and strength models for a triaxial woven material proposed in Part(I) are verified in terms of micro-mechanical analysis.Project supported by the National Natural Science Foundation of China and the State Education Commission Foundation of China     

Dynamics of interaction between a squeezed layer of a viscous incompressible fluid and an elastic three-layer plate

We study the hydrodynamic response of a thin layer of a viscous incompressible fluid squeezed between impermeable walls. We consider the distribution of pressure and force dynamic characteristics of the fluid layer in the case of forced flows along the gap between a vibration generator (which is a rigid plane) exhibiting harmonic vibrations and a stator (which is an elastic freely supported three-layer plate). The inertial forces of the viscous fluid motion and the stator elastic properties are taken into account. The amplitude and phase frequency characteristics of the elastic three-layer plate are found from the solution of the plane problem.     

Formation of a 2D vortex pair and its 3D breakup: an experimental study

 Vortex pairs are studied using a dye tracing visualisation technique and a particle tracking velocimetry system. The vortex pairs are produced by gravity induced inlets of water issued through a uniform gap. The inlet Reynolds number is Re=Ud/ν≈875 in all tests (d being the gap width and U the cross sectional mean velocity), i.e. the flow is in the laminar regime. Initially, the dipolar vortex structure is two-dimensional, but after travelling a distance of a few times its own width, the flow structure becomes unstable, breaks up and changes into a three-dimensional flow structure. The breakup appears to be caused by an axial flow in the core centres of each vortex of the dipolar structure. These axial flows are induced by boundary effects related to the von Karman viscous pump. After the breakup, it is believed that a vortex ring is formed through reconnection of rudiments from the dipolar structure mediated by the wall induced vorticity. Received: 20 November 1995/Accepted: 14 November 1996     

The effect of a splitter plate on the flow around a finite prism

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height square prism was investigated experimentally in a low-speed wind tunnel. Measurements of the mean drag force and vortex shedding frequency were made at Re=7.4×10⁴ for square prisms of aspect ratios AR=9, 7, 5 and 3. Measurements of the mean wake velocity field were made with a seven-hole pressure probe at Re=3.7×10⁴ for square prisms of AR=9 and 5. The relative thickness of the boundary layer on the ground plane was δ/D=1.5–1.6 (where D is the side length of the prism). The splitter plates were mounted vertically from the ground plane on the wake centreline, with a negligible gap between the leading edge of the plate and rear of the prism. The splitter plate heights were always the same as the heights of prisms, while the splitter plate lengths ranged from L/D=1 to 7. Compared to previously published results for an “infinite” square prism, a splitter plate is less effective at drag reduction, but more effective at vortex shedding suppression, when used with a finite-height square prism. Significant reduction in drag was realized only for short prisms (of AR≤5) when long splitter plates (of L/D≥5) were used. In contrast, a splitter plate of length L/D=3 was sufficient to suppress vortex shedding for all aspect ratios tested. Compared to previous results for finite-height circular cylinders, finite-height square prisms typically need longer splitter plates for vortex shedding suppression. The effect of the splitter plate on the mean wake was to narrow the wake width close to the ground plane, stretch and weaken the streamwise vortex structures, and increase the lateral entrainment of ambient fluid towards the wake centreline. The splitter plate has little effect on the mean downwash. Long splitter plates resulted in the formation of additional streamwise vortex structures in the upper part of the wake.     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

Effects of strong anchoring on the dynamic moduli of heterogeneous nematic polymers

We focus on the linear viscoelastic response of heterogeneous nematic polymers to small amplitude oscillatory shear, paying special attention to the macroscopic influence of strong plate anchoring conditions. The model consists of the Stokes hydrodynamic equations with viscous and nematic stresses, coupled to orientational dynamics and structure driven by the flow gradient, an excluded-volume potential, and a two-constant distortional elasticity potential. We show that the dynamical response simplifies when plate anchoring is either tangential or homeotropic, recovering explicitly solvable Leslie–Ericksen–Frank behavior together with weakly varying order parameters across the plate gap. With these plate conditions, we establish “model consistency” so that all experimental driving conditions (plate-controlled velocity [strain] or shear stress, imposed oscillatory pressure) yield identical dynamic moduli for the same material parameters and anchoring conditions, eliminating the culpability of device influence in scaling behavior. Two physical predictions emerge that imply significant macroscopic elastic and viscous effects controlled by plate anchoring relative to flow geometry: (1) The storage modulus is enhanced by two to three orders of magnitude for homeotropic relative to parallel anchoring, across all frequencies. (2) The loss modulus exhibits enhancement of a factor of two to three for homeotropic over tangential anchoring, restricted to low frequencies. We further deduce a scaling law for the dynamic moduli versus anisotropy of the distortional elasticity potential.

Streamwise vibrations of a plate in a viscous fluid flow in a channel,induced by forced transverse vibrations of the plate

Aeroelastic vibrations of a plate aligned at a zero angle of attack in a viscous incompressible fluid flow in a channel with parallel walls are considered within the framework of a plane model. Forced vibrations of the plate in the transverse direction give rise an unsteady component of the flow friction force, induced by the perturbation of the fluid flow velocity by the vibrating plate. Under the assumption of the laminar character of the fluid flow, it is demonstrated that this force can excite streamwise vibrations of the plate if the channel width is small as compared with the plate length; these streamwise vibrations have the same order as the transverse vibrations of the plate excited by external forces.     

Suppression of Low-frequency Variations in Vortex Shedding by a Splitter Plate Behind a Bluff Body

Measurements of instantaneous pressure fluctuations on a trapezoidal cross-section cylinder indicate that the low-frequency variations embedded in the vortex-shedding process can be successfully suppressed by insertion of a splitter plate whose length is twice the maximum width of the trapezoidal cylinder. The experiments were performed at Reynolds numbers in a range of 5 × 10³ to 4·5 × 10⁴. Spanwise correlation of the pressure fluctuations measured on the cylinder further indicates that the suppression of low-frequency variations improves the degree of two-dimensionality of vortex shedding. These findings are attributed to the presence of the splitter plate having an effect on stabilizing the vortex formation length which is comparable to the length of the splitter plate, thus eliminating the low-frequency variations embedded in the base pressure.