Effect of the blockage ratio on the flow in a channel with a built-in square cylinder

The structures wakes behind a square cylinder in a laminar channel flow is conducted numerically. The Strouhal number, drag and lift coefficients were studied in a periodic flow for different blockage ratios =1/4, 1/6 and 1/8 at Reynolds number ranging from 62 to 300. The governing equations are solved by using control volume finite element method (CVFEM) adapted to the staggered grid. The SIMPLER algorithm is used for the velocity-pressure coupling. The critical Reynolds numbers corresponding to the onset of vortex shedding and its change from simple periodic to complex periodic motion are established. A discussion about the effect of the blockage ratio on the Strouhal number, the time-averaged drag coefficient and the amplitude of the lift coefficient is also presented.     

Steady non–Newtonian flow past a circular cylinder: a numerical study

Summary. The steady and incompressible flow of non–Newtonian fluids past a circular cylinder is investigated for power law indices n between 0.2 and 1.4, blockage ratios of 0.037, 0.082 and 0.164, and the Reynolds numbers Re of 1, 20 and 40, using a stream function/vorticity formulation. The governing field equations have been solved by using a second-order accurate finite difference method to determine the drag coefficient, wake length, separation angle and flow patterns, and to investigate their dependence on power law index, blockage ratio and Reynolds number. The results reported here provide fundamental knowledge on the dependence of engineering flow parameters on blockage ratio and power law index, and further show that the effects on stream line and iso-vorticity patterns which result from an increase in the blockage ratio are similar to those which result from a decrease in the power law index.     

Dependence of flow characteristics of rectangular cylinders near a wall on the incident velocity

Numerically simulated results are presented for a family of rectangular cylinders with aspect ratios r ₁ (=b/a with height a and width b) ranging from 0.1 to 1.0 (square cylinder) to gain a better insight into the dependency of the aerodynamic characteristics on the operational dimensionless parameters, namely Reynolds number Re and aspect ratio r ₁. This work describes the flow from a long cylinder of rectangular cross-section placed parallel to a wall and subjected to a uniform shear flow. The flow is investigated in the laminar Reynolds number range (based on the incident stream at the cylinder upstream face and the height of the cylinder) at cylinder to wall gap height 0.5 times the cylinder height. The governing unsteady Navier?CStokes equations are solved numerically through a finite volume method on a staggered grid system using QUICK scheme for convective terms. The resulting equations are then solved by an implicit, time-marching, pressure correction-based SIMPLE algorithm for Reynolds number up to 1,000. The critical Reynolds numbers at which vortex shedding from the cylinder is started are specified for both the cases: far from the wall and near to the wall. It is reported that the vortex shedding from the rectangular cylinder of lower aspect ratio r ₁ (???0.25) becomes regular and insensitive to the Reynolds number, while the aerodynamic characteristics of the rectangular cylinders with higher aspect ratio r ₁ (???0.5) are strongly dependent on the Reynolds number.     

Buoyancy-driven convective heat transfer from a semi-circular cylinder for various confinements

Buoyancy-driven convective heat transfer from a semi-circular cylinder for various confinements has been studied using numerical simulations for wide ranges of parameters, Reynolds numbers (1?≤?Re?≤?50), Richardson numbers (0?≤?Ri?≤?2), Prandtl numbers (0.7?≤?Pr?≤?50) and confinement ratios (0.2?≤?β?≤?0.8). A hot semi-circular cylinder is symmetrically kept in a 2D rectangular confinement. The circular side of the cylinder faces the upstream flow and the fluid flows against gravity in the channel. The governing equations are numerically solved using FLUENT and the results obtained are presented in the form of isotherms, streamlines, pressure coefficients, drag coefficients, Nusselt numbers, etc. The highest value of pressure coefficient increases with blockage ratio for all cases. The drag coefficient decreases with Re and shows complex phenomena with change in Ri and blockage ratio of the channel. Pressure drag has contributed more as compared with viscous drag in all cases. The curved surface showed more heat transfer than the flat surface of the semi-circular cylinder. The value of β also has great influence at large value of Peclect numbers (=?2500). Overall average heat transfer in terms of average Nusselt number is a function of Ri, Re, Pr and β.     

Separation characteristics of fluid flow inside two parallel plates with wavy surface

Separation characteristics of fluid flow inside two parallel wavy plates for steady-laminar flow is investigated numerically in the present study. Governing equations are discretized using control volume based finite-volume method with collocated variable arrangement. SIMPLE algorithm is used and SIP solver is applied for solution of system of equations. Effect of surface waviness (defined by amplitude to average interwall spacing ratio, a/H) and aspect ratio (defined by wavelength to average interwall spacing ratio, w/H) on separation characteristics of fluid flow is presented. The present work has been carried out for surface waviness a/H=0-0.3, aspect ratio w/H=1.5-2.25. A critical Reynolds number (Re_c) is used to identify the appearance of first separation of fluid flow in the channel. Critical Reynolds (Re_c) number is calculated for wide range of surface waviness and aspect ratio. The structure of separation bubble depends strongly on waviness of the surface and aspect ratio for a particular Reynolds number and changes little with wave number (n). Finally pressure drop characteristics is presented in terms of average friction factor as a function of Reynolds number.     

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.     

Effect of rotation of the inner cylinder on the equilibrium condition of spherical particles in a turbulent ascending flow in an annular channel

The equilibrium condition of a solid spherical particle in a turbulent flow is considered. A relation between the rotational velocity of the inner cylinder and the critical velocity of the ascending flow in an annular channel is obtained for the range of Reynolds numbers 10³ –5 · · 10⁴.     

Numerical and experimental studies on laminar forced convective heat transfer in a channel with surface‐mounted heated blocks

Abstract

The steady separated flow due to heated blocks mounted on one principal wall of a two‐dimensional channel has been numerically and experimentally studied. Numerical solutions of the Navier‐Stokes equations using the finite‐difference and the power‐law techniques have been obtained up to a Reynolds number of 2600. The effects of the Reynolds number and the block spacing on the fluid flow and heat transfer are investigated in detail. Results show that there exists two different types of flow between blocks, the D‐type and the K‐type flows. Furthermore, the Nusselt number monotonously increases or decreases along every face of the blocks. The calculated results of the reattachment length behind the second block and the local Nusselt number distribution compare well with the results obtained by the LDV and the naphthalene sublimation measurements, respectively. Heat transfer correlating equations are presented in terms of the Reynolds number and the block spacing.     

Sand accumulation on a wall in flows around a near-wall circular cylinder

Summary The sand accumulation on a flat plate in flows around a near-wall circular cylinder has been mainly investigated by the method of numerical simulation at the sub-critical Reynolds number1200 (based on the diameter of the circular cylinder) and the gap ratio G/D (ratio of the gap between the circular cylinder and the plane wall to the diameter of the circular cylinder) 1.0, 0.5 and 0.25. The standard k− ε turbulent model and the vorticity-stream function formulation are adopted to analyze the wake characteristics. The lift and drag coefficients of the circular cylinder and the pressure pulsation on the wall are solved. The simulation of streak-lines for the flow visualization and PIV experiments are detailed carried out to analyze the sand accumulation phenomenon on the plane wall, and a possible mechanism has been proposed. Results of the numerical simulation indicate that the effect of the cylinder results in flow separation from the plane wall. Separations occur about 1 to 2 cylinder diameters behind the cylinder, where the particles in the flow near the plane wall accumulate gradually.     

Time‐dependent incompressible viscous flow past a circular cylinder

Abstract

In this study, numerical solutions of the equations governing time‐dependent, viscous, incompressible fluid flow past a circular cylinder are presented for Reynolds numbers 100, 200, and 500. These solutions are based on the use of body‐fitted coordinate systems having a coordinate line coinciding with the body contour regardless of its shape.

The implicit solution utilizes vorticity‐stream function formulation. All field equations are approximated using central differences and are solved simultaneously at each time step by SOR iteration. Numerical computations are carried out for flows of Reynolds number 100, 200, and 500, and the results of these numerical flow simulations illustrate the phenomenon that the vortices of the flow pattern shed alternately from the two sides of the cylinder and evolve toward a periodic configuration. These solutions also reveal the oscillatory character of the drag, the lift, and the torque that are experienced by the cylinder.     

Numerical simulation of buoyant drops suspended in Poiseuille flow at nonzero Reynolds numbers

Suspensions of two-dimensional buoyant drops in Poiseuille flow are studied at nonzero Reynolds numbers by numerical simulations. The flow is studied as a function of the Froude number, the Reynolds number, the Capillary number and the density ratio. First, the lateral migration of a drop is studied. Results agree with two-dimensional simulations of solid circular cylinders by Feng et al. (J Fluid Mech 261:95–134, 1994; J Fluid Mech 277:271–301, 1994) qualitatively. At a relatively large Reynolds number (120) and a moderate Froude number (43), a drop shows oscillations across the channel and does not obtain a stable equilibrium position. Simulations are also performed at low and moderate area fractions (0.22, 0.44). It is found that the effective viscosity strongly depends on the Froude number for heavy drops (α > 1). The effective viscosity changes with the Froude number for light drops as well (α < 1), but to a lower extent. The distribution and the fluctuation energy of drops across the channel are non-uniform for buoyant drops that depend on the Froude number. The density ratio also affects the distribution and fluctuation energy of drops across the channel. The effect of the Reynolds number on the effective viscosity of the suspension is also investigated.     

Steady flow of a power-law fluid past a cylinder

Summary Considered in this paper is the two-dimensional steady flow of a power-law fluid past a stationary circular cylinder. The governing nonlinear equations, expressed in terms of a stream function and vorticity, were solved by finite differences for Reynolds numbers (based on the radius of the cylinder)R=5,20, 40 for various power-law indices,n. Parameters such as the drag coefficient, separation angle, wake length and critical Reynolds number are presented and contrasted with those of a Newtonian fluid (n=1) to illustrate the non-Newtonian effects. For a given-Reynolds number a consistent behaviour withn was observed in the parameters for the ranges considered. The results obtained for the Newtonian case agree well with documented results.     

直径30cm圆柱的气动力参数和绕流特性研究

为研究光滑圆柱的气动力系数和绕流特性,在均匀流中进行不同风速下的测压风洞试验,试验获得了阻力系数、升力系数、表面风压分布、风压相关性系数、斯托罗哈数等随雷诺数的变化特征,并将试验结果与以往结果进行比较。研究表明:升力系数的脉动值大于阻力系数的脉动值,说明涡脱造成的横风向激励比顺风向紊流激励剧烈;雷诺数位于临界区域时,圆柱表面风压分布呈现出对称-不对称-对称的变化过程,反映了由层流分离转化为湍流分离的全过程;在雷诺数为352000时呈现一侧为层流分离、另一侧为湍流分离的临界流态,风压呈现出左右不对称的单边泡形式;获得层流分离和湍流分离时的表面风压相关性分布特征,层流分离时圆柱同一侧的风压测点均呈较强的正相关,而湍流分离时在分离点前的区域相关性较强,分离点之后的区域相关性较弱;层流分离的升力系数谱有显著的峰值,表明尾流是规则的漩涡脱落,而湍流分离的升力系数谱没有明显峰值,表明尾流是随机的漩涡脱落。     

Numerical simulation of planar shear flow passing a rotating cylinder at low Reynolds numbers

Two-dimensional shear flow over a rotating circular cylinder is investigated using lattice Boltzmann method. Simulations are performed at a fixed blockage ratio (B = 0.1) while the Reynolds number, nondimensional shear rate (K) and absolute rotational speed range as 80 ≤ Re ≤ 180, 0 ≤ K ≤ 0.2 and −2 ≤ β ≤ 2, respectively. To verify the simulation, the results are compared to previous experimental and numerical data. Quantitative information about the flow variables such as drag and lift coefficients, pressure coefficient and vorticity distributions on the cylinders is highlighted. It is found that, generally, with the increment in |β|, the absolute value of time average lift coefficient increases and time average drag coefficient decreases, and beyond a certain magnitude of β, the vortex shedding vanishes. It is also revealed that the drag coefficient decreases as the Reynolds number increases while the effect of the Reynolds number on lift is almost negligible. At the end, correlations for drag and lift coefficients ([`(C<sub>D</sub> )] ,[`(C_L )]){(\overline {C_D } ,\overline {C_L })} are extracted from the numerical data.     

Asymptotic analysis of the viscous micro/nano pump at low Reynolds number

The steady viscous parabolic flow past an eccentrically placed rotating cylinder is studied in the asymptotic limit of small Reynolds number. It is assumed that the flow around the rotating cylinder undergoes boundary slip described by the Navier boundary condition. This involves a single parameter to account for the slip, referred to as the slip length ?, and replaces the standard no-slip boundary condition at solid boundaries. The streamlines for ? > 0 are closer to the body than for ? = 0, and it is discovered that the loss of symmetry due to the rotation of the cylinder is significantly reduced by the inclusion of slip. This arises as a result of a balance between the rotation velocity and the slip velocity on that portion of the cylinder which rotates opposite to the free-stream flow. Streamline patterns for nonzero eccentricity partially agree with Navier–Stokes simulations of the viscous pump; the small discrepancy is primarily due to the fact that here wall effects are not explicitly considered. Expressions for the frictional drag and the torque on the cylinder are obtained. The expression for the torque agrees well with the lubrication solution for the flow past a rotating cylinder placed symmetrically in a fully developed channel flow. The results presented here may be used to validate numerical schemes developed to study the viscous pump.     

Experimental study of fluid flow and heat transfer from a square prism approaching the wall of a wind tunnel

Experimental investigations of fluid flow and heat transfer have been carried out to study the effect of wall proximity due to flow separation around square prisms. Experiments have been carried for Reynolds number equal to 2.6∙10⁴. The results are presented in the form of pressure coefficient, drag coefficient, and Nusselt numbers for various height ratios, blockage ratios, and angles of attack. The pressure coefficient distribution shows positive values on the front face, whereas on the rear face negative values are observed. The drag coefficient decreases with increase in angle of attack as the height ratio decreases, and its maximum value takes place at an angle of about 50°. Both the local and average Nusselt numbers decrease as the height ratio decreases.     

Numerical Simulations of Thermocapillary Flow of a Binary Mixture with the Soret Effect in a Shallow Annular Pool

In order to understand the characteristics of thermocapillary flow of a toluene/n-hexane mixture with the Soret effect in a shallow annular pool, a series of three-dimensional numerical simulations were carried out. The shallow annular pool was heated from the outer cylinder and cooled at the inner cylinder. The initial toluene concentration in the toluene/n-hexane mixture varied from 0 to 0.4467. Results indicate that the flow undergoes two transitions from the axisymmetric steady flow to the hydrothermal waves, and then to chaos with the increase of the thermocapillary Reynolds number. The critical thermocapillary Reynolds number for the incipience of the oscillatory flow decreases with the increase of the initial solute concentration. When the thermocapillary flow transits to a three-dimensional oscillatory flow, a concentration fluctuation is observed on the free surface, which is similar to the hydrothermal waves. However, compared with that of the temperature, the dimensionless fluctuation amplitude of the concentration is relatively weak. Furthermore, the fundamental oscillation frequency increases linearly with the initial solute concentration, but the wave number of the hydrothermal waves is almost unchangeable.     

Drag coefficients for a sphere rolling down an inclined channel

Abstract

Forces acting on a sphere rolling down an inclined smooth or rough channel include submerged weight of the sphere, fluid drag, fluid lift, and rolling resistance from the channel bed. When the acting forces are in equilibrium, the sphere rolls down the inclined channel with a terminal velocity. The steady movements of such a sphere rolling down smooth and rough channel beds with the terminal velocity are studied through laboratory experiments and a simplified theoretical analysis. A method is proposed to evaluate the rolling resistance that consists of collision and friction parts of resistance. The coefficients of rolling resistance and the drag coefficients are determined by regression analysis with experimental data. The relationships of the drag coefficients and the Reynolds numbers for a sphere rolling over smooth and rough channel beds are also obtained. It is found that at the same Reynolds number, the drag coefficient for a sphere rolling down a rough bed is larger than that for a sphere down a smooth one, and that both are much larger than that of a sphere in the free fall.     

串列多圆柱气动力干扰效应的试验研究

通过刚性模型测压风洞试验,在均匀流场中对比研究了不同数量和不同间距串列多圆柱气动力的干扰效应。串列多圆柱两相邻圆柱的中心距L与圆柱的直径D之比L/D的变化范围为1.2~12.0。圆柱数量的变化范围为1~4。试验的雷诺数为3.4×10⁴。试验结果发现:串列多圆柱发生流态切换的临界间距比(L/D)cr为3.5~4.0,在临界间距附近,前两个圆柱的时均阻力系数和脉动升力系数突升,其余圆柱则突降,所有圆柱的斯托罗哈数均突升;气动干扰对串列多圆柱时均阻力系数和斯托罗哈数的影响主要表现为减小效应;后方干扰圆柱数量的增加对上游第一个圆柱气动力的影响基本可以忽略;前方干扰圆柱数量的增加对下游最后一个圆柱的气动力影响显著。     

Computation of flow and thermal fields in a model CVD reactor

Mixing of coaxial jets within a tube in the presence of blockage has been numerically studied. This configuration is encountered during the modelling of flow and heat transfer in CVD (chemical vapour deposition) reactors. For the conditions prevailing in the reactor, the Reynolds numbers are low and flow can be taken to be laminar and incompressible. The unsteady forms of the governing equations have been solved by a finite volume method that can treat complex three-dimensional geometries. The algorithm is a two-step procedure, wherein the first step predicts the velocity field using an assumed pressure field. The second step corrects the fields using a Poisson equation to obtain the pressure corrections. Advection terms have been treated by a hybrid upwind-central difference technique. The computer code developed is fully three-dimensional, though most computations of the present study have been carried out for two-dimensional geometry. Results have been obtained in the form of velocity vector plots, wall shear stress variation on the block and the tube wall, isotherms and temperature profiles. The flow and heat transfer characteristics of jet mixing have been explored in terms of the Reynolds number, the jet velocity ratio, the axial position of the block, and the blockage ratio. The results obtained show that a proper combination of the process parameters can lead to an improved performance of the CVD reactor.