Slip flow due to a stretching cylinder

The slip flow due to a stretching cylinder is studied. A similarity transform reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations. Asymptotic solutions for large Reynolds number and small slip show the problem can be related to the existing two-dimensional stretching cases. Due to algebraic decay, the equations are further transformed through a compressed variable, and then integrated numerically. It is found that slip greatly reduces the magnitudes of the velocities and the shear stress.     

Elliptic cylinder in inviscid shear flow

We examine the flow of a plane parallel inviscid stream about an elliptic contour. There is vorticity far ahead of the body because of nonuniformity of the velocity profile. In the case of a small vorticity parameter the velocity profile will be parabolic. In contrast with [1] and [2], we assume the existence of additional circulational flow around the contour. The magnitude of this flow circulation is determined from the condition under which the flow leaves the trailing edge of the body (the analog of the Chaplygin-Zhukovskii postulate in potential flow).The results obtained in this study can be used, in particular, to evaluate the flow past a two-dimensional body in the wake behind another body.The author wishes to thank G. A. Dombrovskii for his interest in this study.     

Large eddy simulation of flow around a rectangular cylinder

A large eddy simulation (LES) of turbulent flow around a stationary rectangular cylinder at high Reynolds number of 2.2×10⁴ is conducted as the first step to prove the applicability of LES to practical engineering problems. Time-averaged and phase-averaged velocities and turbulent stresses are obtained and they are compared with the experimental data. To investigate mesh dependence on computational results of the LES, two kinds of grid resolution are used. In addition, the effect of a second-order upwind scheme QUICK for convection terms is also investigated due to its dependence on grid resolution. The drag coefficients, the base pressure coefficients and Strouhal numbers are in fairly good agreement with the experimental results, while the computational results show that the artificial dissipative and dispersive effect of QUICK is large in the vicinity of the cylinder in our computation. Thus, it is necessary to use higher-order upwind schemes to reduce the numerical errors, since it is effective in applying LES to practical engineering problems with complicated geometry.     

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.     

Underlay mechanism in lift-drag phase diagrams for shear flow over cylinder

The characteristics of a uniform-shear flow over a circular cylinder are in- vestigated numerically by using the alternative-direction implicit （ADI） algorithm and a fast Fourier transform （FFT） one in the exponential-polar coordinates for Re = 150 and 0 ≤ K ≤ 0.46. The diagram of lift-drag phase, implying the detail information about the fluctuations of drag and lift as well as the flow patterns in the wake and fluctuating pres- sure on the cylinder surface, is used to describe the effects of the shear rate on the flow. Results show that the upper （or lower） closed curve of a phase diagram corresponds to the first （or second） half shedding cycle. The lift-drag phase diagram will move down-left with the increase of shear rate K such that the lift is exerted from the upper side to the lower side, and the drag on the first half shedding cycle is smaller than that on the second half.     

Effects of an asymmetrical confined flow on a rectangular cylinder

The effects of an asymmetric confined flow on a cylinder of rectangular cross-section are investigated and discussed. Experiments are performed in a wind tunnel by placing cylinders of different cross-sections at various elevations from the floor of the test-section. The Reynolds number is varied within the range 6×10³–4×10⁴. Forces exciting the cylinder are measured by built-in dynamometers placed inside the cylinder structure. The flow is characterized by mean and fluctuating local velocity components to define the inflow distribution and the ensuing wake region. The mean dimensionless force coefficients are then calculated and analyzed. The frequency analysis of the force components acting on the cylinder provides the dynamic characterization of the loading and of the wake shedding. The experimental results highlight that the presence of the wall strongly influences the system dynamics also when the cylinder is placed at a relatively large elevation from the wall itself. The cylinder aspect ratio governs effects of the wall condition on the force coefficients and the Strouhal number.     

PIV investigation of flow behind surface mounted permeable ribs

The flow behind surface mounted permeable rib geometries, i.e. solid, slit, split-slit and inclined split-slit ribs have been studied using flow visualization and PIV (2-C and 3-C) technique in streamwise and cross-stream measurement planes. The objective behind this study is to understand the flow structures responsible for heat transfer/mixing enhancement with simultaneous pressure penalty reduction by permeable rib geometries. The Reynolds number based on the rib height has been set equal to 5,538 and the open area ratio of permeable ribs is equal to 20%. The permeable rib geometries have shorter reattachment length in comparison to the solid rib. The maximum 41% reduction in reattachment length is observed for the inclined split-slit rib. The splitter mounted inside the slit leads to two corner vortices behind it. The corner vortices drag the flow from the primary recirculation bubble region towards the rib resulting in drop of the reattachment length. Two horseshoe vortices are present in the flow through the slit at both sides of the splitter due to the upstream flow separation. The slit inclination moves these horseshoe vortices closer to the bottom wall. A film like flow through the slit is present near the downstream corner of the inclined split-slit rib. The spanwise velocity gradient due to the splitter leads to vorticity and turbulence enhancement by vortex stretching. The inclination of the slit and the use of a splitter inside the slit are two important design parameters responsible in generation of near-wall longitudinal vortices. The flow field behind permeable ribs is dominated by vortical structures with definable critical flow patterns, i.e. node, saddle and foci. These predominant swirling flow motions contribute to the mixing enhancement behind permeable rib geometries. On leave from Mechanical Engineering Department, IIT Kanpur, U.P. 208016, India     

Slow visco-elastic flow past a cylinder in a rectangular channel

This paper is concerned with the flow of a visco-elastic liquid through a rectangular channel containing a cylindrical obstruction placed either in a symmetric or asymmetric position with respect to the centre of the channel. Numerical predictions of the flow are obtained using a well established finite element Galerkin mixed formulation. The influence of elasticity on the streamline pattern is found to be negligible, and one only observes changes due to different geometries, i.e. relative positions of cylinder and channel. However, both elasticity and a variable viscosity are found to have significant effects on the forces exerted on the cylinder.     

Measurements of the flow over a low-aspect-ratio cylinder mounted on a ground plane

The flow over a finite-height cylinder of aspect ratio 1, with one end mounted on a ground plane and the other end free, has been studied by means of surface flow visualisation, particle image velocimetry (PIV) and surface pressure measurements. The diameter-based Reynolds number was 200,000. The mean flow topology has been identified in three areas: the horseshoe vortex system, the separated flow over the free-end and the wake region. Evidence is shown for the existence of a three-horseshoe vortex system, while the mean flow over the free-end consists of an arch vortex with its bases on the forward half of the free-end. There are two tip vortices coming off the free-end. The wake region is found to be highly unsteady, with considerable variation from the mean flow.     

不同剪切率来流作用下柔性圆柱涡激振动数值模拟

采用浸入边界法对细长柔性圆柱在线性剪切流条件下的涡激振动进行三维数值模拟。细长柔性圆柱振动采用三维索模型模拟,其两端铰接,质量比为6,长细比为50,无量纲顶张力为496。来流为线性剪切流,剪切率从0到0.024变化,最大雷诺数为250。研究发现:剪切流作用下柔性立管横流向振动表现为驻波模式,而顺流向振动表现为行波-驻波混合模式。随着剪切率增大,振动频谱呈现多频响应,振动能量逐渐向低频转移。阻力系数平均值随着展向变化,脉动阻力系数和升力系数的均方根值均表现为“双峰”模式。流固能量传递系数沿立管轴向的分布表明,振动激励区集中于高流速区,而振动阻尼区多位于低流速区。剪切率较小时,圆柱的泻涡为平行交叉模式;剪切率较大时,圆柱的泻涡为倾斜泻涡模式,且由于泻涡频率沿立管轴向变化,尾流发生涡裂现象,形成泻涡频率不同的胞格结构。      

Magnetohydrodynamic flow through a rectangular duct due to a periodic pressure gradient-II

An analysis is made of the flow of an incompressible, viscous, electrically conducting fluid in a long channel of rectangular cross section due to a periodic pressure gradient, in the presence of a uniform transverse magnetic field. Exact solutions are obtained and asymptotic forms valid for large Hartmann numbers in the boundary layers parallel to the field are discussed.     

Magnetohydrodynamic flow through a rectangular duct due to a periodic pressure gradient

Summary The flow of an incompressible, viscous, electrically conducting fluid in a long channel of rectangular cross section due to a periodic pressure gradient, in the presence of a uniform transverse magnetic field is investigated. Exact solutions are obtained and asymptotic forms valid for large Hartmann numbers are discussed.     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

Experimental investigation of flow and heat transfer in rectangular cross-sectioned duct with baffles mounted on the bottom surface with different inclination angles

In this study, steady-state forced convection heat transfer and pressure drop characteristics in a horizontal rectangular cross-sectioned duct, baffles mounted on the bottom surface with different inclination angles were investigated experimentally in the Reynolds number range from 1 × 10³ to 1 × 10⁴. The study was performed under turbulent flow conditions. Effects of different baffle inclination angles on flow and heat transfer were studied. Results are also presented in terms of thermal enhancement factor. It is observed that increasing in baffle inclination angle enhances the heat transfer and causes an increase in pressure drop in the duct.     

Influence of single rectangular groove on the flow past a circular cylinder

In the present study, flow control mechanism of single groove on a circular cylinder surface is presented experimentally using Particle image velocimetry (PIV). A square shaped groove is patterned longitudinally on the surface of the cylinder with a diameter of 50 mm. The flow characteristics are studied as a function of angular position of the groove from the forward stagnation point of the cylinder within 0° ≤ θ ≤ 150°. In the current work, instantaneous and time-averaged flow data such as vorticity, ω streamline, Ψ streamwise, u/U_o and transverse, v/U_o velocity components, turbulent kinetic energy, TKE and RMS of streamwise, u_rms and transverse, v_rms velocity components are utilized in order to present the results of quantitative analyses. Furthermore, Strouhal numbers are calculated using Karman vortex shedding frequency, f_k obtained from single point spectral analysis. It is concluded that a critical angular position of the groove, θ = 80° is observed. The flow separation is controlled within 0° ≤ θ < 80°. At θ = 80°, the flow separation starts to occur in the upstream direction. The instability within the shear layer is also induced on grooved side of the cylinder with frequencies different than Karman vortex shedding frequency, f_k.