侧墙对中等半径比同心旋转圆柱间Taylor-Couette流的影响——Ⅰ层流涡

对有限长中等半径比同心旋转圆柱间Taylor-Couette流进行了数值计算,以研究侧墙对Taylor-Couette流的影响。圆柱的半径比为0.83,形状比为6,泰勒数在0~357之间。内圆柱旋转,外圆柱静止。数值计算结果表明,在无滑移侧墙边界条件下,在泰勒数低于临界泰勒数时,在侧墙边界层的作用下侧墙附近出现侧墙涡,而在滑移侧墙边界条件下,直到泰勒数大于临界泰勒数,轴间才出现明显的涡流。当泰勒数处在89~112之间,侧墙静止和侧墙旋转时产生的最大径向速度分别约为内筒表面线速度的3%~4%和7%~10%。侧墙静止时,随着泰勒数的增加,边界层的厚度也随之递增。侧墙旋转时,边界层厚度基本不变。在泰勒数大于临界泰勒数时,随着泰勒数的增加,侧墙静止和侧墙旋转时侧墙涡的轴向长度分别增加和减少,在滑移边界条件下,侧墙涡的轴向长度约等于轴间距。在3种侧墙边界条件下,层流涡向波动涡转捩的临界泰勒数变大。     

Effect of Reynolds numbers on flow past four square cylinders in an in-line square configuration for different gap spacings

In this paper two-dimensional (2-D) numerical investigation of flow past four square cylinders in an in-line square configuration are performed using the lattice Boltzmann method. The gap spacing g = s/d is set at 1, 3 and 6 and Reynolds number ranging from Re = 60 to 175. We observed four distinct wake patterns: (i) a steady wake pattern (Re = 60 and g = 1); (ii) a stable shielding wake pattern (80 ≤ Re ≤ 175 and g = 1); (iii) a wiggling shielding wake pattern (60 ≤ Re ≤ 175 and g = 3) and (iv) a vortex shedding wake pattern (60 ≤ Re ≤ 175 and g = 6). At g = 1, the Reynolds number is observed to have a strong effect on the wake patterns. It is also found that at g = 1, the secondary cylinder interaction frequency significantly contributes for drag and lift coefficients signal. It is found that the primary vortex shedding frequency dominates the flow and the role of secondary cylinder interaction frequency almost vanish at g = 6. It is observed that the jet between the gaps strongly influenced the wake interaction for different gap spacing and Reynolds number combination. To fully understand the wake transformations the details vorticity contour visualization, power spectra of lift coefficient signal and time signal analysis of drag and lift coefficients also presented in this paper.     

低压差驱动下中等半径比内轴高旋圆柱间轴流量的数值计算

利用RSM湍流模型/标准壁面函数对低压差驱动下中等半径比内轴高旋圆柱间流场进行了数值模拟。圆柱的内半径为4.45 cm,外半径为5.25 cm,半径比为0.848,轴间距为0.8 cm,形状比分别为5,10,15,20,泰勒数比分别为500,625,750,875,1 000。模拟结果表明,RSM湍流模型/标准壁面函数对低压差驱动下中等半径比内轴高旋圆柱间流场有较强的预报能力。随着压差的增加,轴流量随之增加,随着压差的进一步增加,压力流的作用处于主导地位,压力流的增强最终导致涡胞消失,轴间流场特征主要表现为压力流。随着旋转速度的增加,内壁高旋产生的旋转效应增强,轴向压差对轴间流场的作用相对减弱,导致轴流量减少。随着形状比的增加,轴流量呈现逐步减小的趋势,而且随着形状比的进一步增加,轴流量减少的趋势变缓。     

Numerical study of fluid force reduction on a circular cylinder using tripping rods

A numerical investigation on the effects of small tripping rods on the fluid force reduction on a big structure has been carried out using finite volume method where a configuration of a circular cylinder with two small tripping rods symmetrically placed very near to its front surface is studied. The diameter ratio of the rods and the cylinder is set at 0.08, 0.10 and 0.12, and the gap between the rods and the cylinder is fixed at 0.08 of the cylinder diameter. The angular position of the rods varies from 20° to 60°. The effects of the tripping rods on force reduction, vortex shedding frequency and flow separation have been examined for various arrangements of the rods with Reynolds number focused on 200 for laminar flow and 5.5×10⁴ for a turbulent flow. The results reveal that there exits an optimum position where the time averaged force coefficients acting on the cylinder all reach their minimum values and at the same time Strouhal number meets its maximum. At the optimum position the drag coefficient is reduced by 18% for Re=200 and 59% for Re=5.5×10⁴. Further investigation with tripping rods placed near the separation points is also carried out for Re=5.5×10⁴ and a considerable drag reduction is found.     

Taylor Vortices–Induced Instability (Transition Flow) versus “Turbulence” in Concentric Cylinders Separated by Microscale Clearances

This paper is concerned with the relationship between the onset and the development of the Taylor instabilities and their treatment as turbulent flows in the most accepted turbulence models (Constantinescu (1); Ng-Pan (2); Hirs (3)) used with the Reynolds equation, in the range of 41.3√R/C < Re < 2000. The authors show that in between these limits there is a transition regime where the velocity and pressure profiles are fundamentally different from either a Couette flow or a fully developed turbulent flow. Thus the issue under consideration is whether the flow formations observed during Taylor instability regimes should be simulated using the widely accepted turbulence models as they presently are modeled in microscale clearance flows. We are considering the flow of light silicone oil in gaps varying from 3.302 mm (0.13 in.) to 0.127 mm (0.005 in.) between two concentric cylinders, with the inner cylinder rotating. The computational engine used in this study is a well-established and a tried software package: CFD-ACE+. It was found that the Taylor vortices (cells) begin to form at certain, but different, “critical” speeds, function of clearance size, and as the speed grows, the vortices become fully developed and evolve further into wavy vortices. Calculations show that both the 1st and 2nd critical Taylor numbers and Reynolds numbers are functions of the clearance size. The Taylor numbers decrease, while the Reynolds numbers increase with the decrease in clearance size. The onset of both instabilities is clearly characterized by the discontinuities in the Torque-√Ta (or Torque – Re) curve slope. The calculations presented here show that the slope changes in the above-mentioned graphs are due to the changes in the average velocity gradient on the outer cylinder and not to a change in the actual viscosity as it is implemented by the turbulence models mentioned above. Finally a comparison is made between present calculations and the data of Roberts (4), Cole (5), Walowit et al. (6), Weinstein (7), Koschmieder (8), and DiPrima (9).     

Experimental study on the vortex flow in a concentric annulus with a rotating inner cylinder

This experimental study concerns the characteristics of vortex flow in a concentric annulus with a diameter ratio of 0.52, whose outer cylinder is stationary and inner one is rotating. Pressure losses and skin friction coefficients have been measured for fully developed flows of water and of 0.4% aqueous solution of sodium carboxymethyl cellulose (CMC), respectively, when the inner cylinder rotates at the speed of 0-600 rpm. Also, the visualization of vortex flows has been performed to observe the unstable waves. The results of present study reveal the relation of the bulk flow Reynolds number Re and Rossby number Ro with respect to the skin friction coefficients. In somehow, they show the existence of flow instability mechanism. The effect of rotation on the skin friction coefficient is significantly dependent on the flow regime. The change of skin friction coefficient corresponding to the variation of rotating speed is large for the laminar flow regime, whereas it becomes smaller as Re increases for the transitional flow regime and, then, it gradually approach to zero for the turbulent flow regime. Consequently, the critical (bulk flow) Reynolds number Re_c decreases as the rotational speed increases. Thus, the rotation of the inner cylinder promotes the onset of transition due to the excitation of Taylor vortices.     

Conical whirl instability of turbulent flow hybrid porous journal bearings

An analysis of conical whirl instability of an unloaded rigid rotor supported in a turbulent flow hybrid porous journal bearing has been presented, following Constantinescu's turbulent lubrication theory. The effect of bearing feeding parameter (β), Reynolds number (Re), ratio of wall thickness to journal radius (H/R) and anisotropy of porous material on the stability of rotor-bearing system has been investigated. It is observed that higher values of β gives better stability and higher stability is predicted if the porous bush is considered to be isotropic.     

Numerical assessment of turbulent models at a critical regime on unstructured meshes

The present study mainly aims to investigate the performances of different turbulent models for the flow simulation around a circular cylinder at a critical Reynolds number regime (Re = 8.5×10⁵, Tu = 0.7%). A hybrid RANS/LES model (SAS model), a correlation-based transition model ( $\gamma - \widetilde{\operatorname{Re} }_{\theta t} $ model), and a fully turbulent RANS model (SST model) were used to simulate various flow features, such as laminar-turbulence transition inside the boundary layer and the unsteady vortex shedding in the wake region, and their feasibilities for the flow simulation at a critical Reynolds number regime were demonstrated. A vertex-centered finite-volume method was used to discretize the incompressible Navier-Stokes equations, and an unstructured mesh technique was used to discretize the computational domain. The inviscid fluxes were evaluated using 2^nd-order Roe??s flux difference splitting, and the viscous fluxes were computed based on central differencing. A dual time-stepping method and the Gauss-Seidel iteration were used for unsteady time integration. The parallelization strategy using METIS and MPI libraries was used to reduce computational costs. The unsteady characteristics and the time-averaged quantities of the flow fields were compared between turbulent models. The numerical results were also compared with experimental results. The turbulent models showed quite different results at the critical regime because of the different abilities of each model to predict various flow features, such as laminar-turbulence transition and unsteady vortex shedding.     

Electrohydrodynamic instability of dielectric liquid between concentric circular cylinders subjected to unipolar charge injection

In this paper, we demonstrate instability of dielectric liquid subjected to unipolar charge injection from a pair of cylindrical electrodes at high Scmidt and high Peclet numbers. The transport of charge density in the annulus is governed by the Nernst-Planck equation and the electric potential by the Poisson equation. The fluid flow is governed by the Navier-Stokes equation together with the continuity equation. The base solutions composed of the one-dimensional conduction state are obtained numerically and the temporal growth of their perturbations is determined from the normal-mode instability analysis by using numerical simulations. The critical values of the parameter for the onset of 2D convective motion are obtained and compared well with the results of full-2D calculation. At high injection, the system tends to be more unstable for the inner injection case and more stable for the outer injection case, as the radius of the inner cylinder is decreased; this trend is however reversed at low injection. It turns out that the critical angular wave number obtained from the flatplate case well predicts the one for an annulus for a wide range of the inner cylinder’s radius.     

Drag reduction for flow past a square cylinder through corner chamfering

This study investigates the unsteady incompressible flow around a square cylinder with different chamfer ratios (CRs) using a commercial finite volume code, ANSYS Fluent. CR ranges from 0.0 (sharp square cylinder) to 0.5 (diamond cylinder) with variable increments. Detailed analysis of flow characteristics is conducted at Reynolds number (Re) = 2100. Additionally, simulation is extended to cover Re, i.e., Re = 100, 500, and 10000. The simulation results show that cylinder with CR = 0.1 outperforms all other cases by enabling a drag reduction of about 60 % at Re = 10⁴. Drag has an inverse relationship with the wake closure length. Time-averaged coefficient of pressure, streamlines, and vorticity contours are also discussed to better understand near-wake features and the physics of drag reduction.

     

Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory(FSDT) and perturbation method

Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.     

Influence of corner radius on the near wake structure of a transversely oscillating square cylinder

The near wake flow field features of transversely oscillating square section cylinders with different corner radii were studied in an attempt to assess the influence of corner radius. The investigation was performed by using particle image velocimetry (PIV) technique in a water channel with a turbulence intensity of 6.5%. Five models were studied with r/B=0, 0.1, 0.2, 0.3 and 0.5 (r is the corner radius and B is the characteristic dimension of the body), and the body oscillation was limited to lock-in condition (at fe/fo=1.0; fe is the excitation frequency and fo is the vortex shedding frequency from a stationary cylinder at the same Re). The corner radius was found to significantly influence the flow features around the bodies. Except for r/B=0.5, for all the other cases of r/B ratios, cycle-to cycle variation in the mode of vortex shedding was observed in the case of oscillating cylinders inducing highly non-linear wake characteristics. Apart from variation in the shedding mode, changes in shedding cycle timing were also observed for sharp and rounded square cylinders. The hgher the r/B ratio, shedding in the near wake was found to be more uniform (lesser variation in shedding cycle timings). Another admissible shedding mechanism is newly identified to operate in the near wake of oscillating cylinders now being called as the ‘passive shedding’ mechanism. Results indicate that increasing the corner radius suppresses the possible instabilities of the cylinder.     

中等半径比内轴高旋圆柱间湍流场的大涡模拟

利用大涡模拟对中等半径比内轴高旋圆柱间湍流场进行了数值模拟。半径比为0.83,形状比为6,侧墙为静止侧墙、旋转侧墙及无剪切力侧墙3种边界条件。模拟结果表明,大涡模拟对该类问题有较强的预报能力。侧墙静止时,涡流始于靠近侧墙的左下方和右下方位置,然后涡心向上向中间移动,涡胞逐渐变大,外轴上形成众多小涡,小涡的涡心向下移动涡胞变大,最后涡胞混合在一起,充满整个轴间。侧墙旋转时,涡流始于靠近侧墙的左上方和右上方位置,然后涡心向上向中间移动,涡胞逐渐变大,外轴上形成众多小涡,小涡的涡心向下移动涡胞变大,最后涡胞混合在一起,充满整个轴间。在无剪切力侧墙边界条件,涡流场形成过程与侧墙旋转时形成过程相似。轴间流场最终形成固定数量的涡胞,且随着时间的推移,各个涡胞呈现此消彼长的局面,始终保持固定数涡胞的存在。在侧墙静止和无剪切力条件,流场最终形成8个涡胞;侧墙旋转时,流场最终形成6个涡胞。     

Measurement of noncircularity of cylinders freely rolling on directing supports or a smooth surface

A new optical method of measuring noncircularity of cylinders is experimentally justified. The method is based on measuring the horizontal projection of velocity of a rolling circular body and calculating the maximum deviation of the local radius periodically repeated in the course of motion. Results measured by the proposed method are compared with direct measurements by a micrometer. The new method allows estimating tolerances of noncircularity in the case of defects of cylinder generatrices and the maximum variations of the radius in the case of guideline noncircularity. The noncircularity measurement error (～1 µm) is experimentally verified.     

Numerical investigation of fluid flow past a square cylinder using upstream,downstream and dual splitter plates

A two-dimensional numerical study is carried out to analyze the drag reduction and vortex shedding suppression behind a square cylinder in presence of splitter plate arranged in upstream, downstream and both upstream and downstream location at low Reynolds number (Re = 160). Computations are performed using a Single relaxation time lattice Boltzmann method (SRT-LBM). Firstly, the code is validated for flow past a single square cylinder. The obtained results are compared to those available in literature and found to be in good agreement. Numerical simulations are performed in the ranges of 1 ≤ L ≤ 4 and 0 ≤ g ≤ 7, where L and g are the length of splitter plate and gap spacing between the splitter plate and main square cylinder, respectively. The effect of these parameters on the vortex shedding frequency, time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficient, vorticity contours visualization and force exerted on the cylinder are quantified together with the observed flow patterns around the main cylinder and within the gap spacings. The observed results are also compared with a single square cylinder without splitter plate. We found that at some combinations of L and g, the mean drag coefficient and Strouhal number reach either its maximum or minimum value. It is found that the drag is reduced up to 62.2 %, 13.3 % and 70.2 % for upstream, downstream and dual splitter plates, respectively as compared to a single square cylinder (without splitter plate). In addition, in this paper we also discussed the applications of SRT-LBM for suppression of vortex shedding and reduction of the drag coefficients.     

Stroboscopic two-dimensional ultrasonic velocity profiling for measuring flow transition in Taylor Couette systems

Flow characterization in a Taylor Couette system was made by investigating the radial velocity component with Ultrasonic Doppler Velocimetry based flow mapping. With the technique presented in this work, it is possible to measure the radial velocity components for variable axial position in a Couette cell within Taylor vortex flow (TVF), wavy vortex flow (WVF), modulated vortex flow (MVF) as well as spiral vortex domains in a conical shaped gap. The resulting maps for the different flow states show the location of vortices in the annular gap between the inner and outer cylinder. Cylindrical and conical concentrically rotating inner bodies were applied and respective flow patterns were analyzed. The method uses a stroboscopic triggering to synchronize flow measurements and rotational motion. The oscillation frequency f of unsteady motion in WVF, MVF, and spirals can be obtained from the power spectrum of velocity. The UVP transducer was preferably positioned in radial direction, perpendicular to the surface of the inner rotating body for measuring the radial velocity component. At the same time, the transducer was moved with constant velocity vertically along the outer cylinder height.     

Unsteady Lift and Drag Forces Acting on the Elliptic Cylinder

A parametric study has been accomplished to figure out the effects of elliptic cylinder thickness, angle of attack, and Reynolds number on the unsteady lift and drag forces exerted on the elliptic cylinder. A two-dimensional incompressible Navier-Stokes flow solver is developed based on the SIMPLER method in the body-intrinsic coordinates system to analyze the unsteady viscous flow over elliptic cylinder. Thickness-to-chord ratios of 0.2, 0.4, and 0.6 elliptic cylinders are simulated at different Reynolds numbers of 400 and 600, and angles of attack of 10°, 20°, and 30°. Through this study, it is observed that the elliptic cylinder thickness, angle of attack, and Reynolds number are very important parameters to decide the lift and drag forces. All these parameters also affect significantly the frequencies of the unsteady force oscillations.     

Miniaturized liquid film sensor (MLFS) for two phase flow measurements in square microchannels with high spatial resolution

Two miniaturized liquid film sensors (MLFS) based on electrical conductance measurement have been developed and tested. The sensors are non-intrusive and produced with materials and technologies fully compatible and integrable with standard microfluidics. They consist of a line of 20 electrodes with a purpose-designed shape, flush against the wall, covering a total length of 5.00 and 6.68 mm. The governing electronics achieve 10 kHz of time resolution. The electrode spacing of the two sensors is 230 μm and 330 μm, which allows measurements of liquid films up to 150 μm and 400 μm for sensors MLFS_A and MLFS_B, respectively. The sensor characteristics were obtained by imposing static liquid films of known thickness on top of the actual sensor. Further dynamic measurements of concurrent air-water flow in a horizontal microchannel were performed. The line of electrodes is placed across the flow direction with an angle of 3.53° from the direction of flow, allowing for a spatial resolution perpendicular to the flow of 14.2 μm for sensor MLFS_A and 20.5 μm for sensor MLFS_B. The high time and spatial resolution allows for fast and accurate detection of the presence of bubbles, and even measurement of film thickness and bubble velocity. Further information, such as the bubble shape, can be gathered based on the shape of the liquid layer underneath the bubble, which is particularly important for heat transfer studies in microchannels.     

Numerical simulation of the electro-convective onset and complex flows of dielectric liquid in an annulus

We conducted a numerical study on the onset of electro-convection as well as the complex flow phenomena of dielectric liquid subjected to unipolar autonomous charge injection in the annular gap between two concentric circular cylindrical electrodes. The Nernst-Planck equations governing the charge density transport, the Poisson equation for the electric potential and the Navier-Stokes equations for the fluid flow are solved numerically using the finite volume method. The developed code is validated by comparing the critical stability parameter values for the onset of electro-convection with those obtained from the linear stability analysis. We identify in a parameter space the stable hydrostatic state and the electro-convection state. The electro-convection is again divided into three regimes: stationary, oscillatory and chaotic. For inner cylinder radius r _i ≥ 1.0, we observed an increase in the number of charged plumes and vortex pairs with stability parameter T before the electro-convection becomes chaotic. For outer injection, although the onset of electroconvection starts at T higher than the inner injection, the onset of chaotic motion occurs at lower T.     

Unsteady viscous flow over elliptic cylinders at various thickness with different reynolds numbers

Two-dimensional incompressible Navier-Stokes equations are solved using SIMPLER method in the intrinsic curvilinear coordinates system to study the unsteady viscous flow physics over two-dimensional ellipses Unsteady viscous flows over various thickness-to-chord ratios of 06, 08, 10, and 1 2 elliptic cylinders are simulated at different Reynolds numbers of 200, 400, and 1,000 This study is focused on the understanding the effects of Reynolds number and elliptic cylinder thickness on the drag and lift forces The present numerical solutions are compared with available experimental and numerical results and show a good agicement Through this study, it is observed that the Reynolds number and the cylinder thickness affect significantly the frequencies of the force oscillations as well as the mean values and the amplitudes of the drag and lift forces