On creeping drag flow of a viscoplastic fluid past a circular cylinder: wall effects

The creeping drag flow of a Bingham plastic past a circular cylinder kept symmetrically between parallel plates was analyzed via numerical simulations with the finite element method. Different gap/cylinder diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient for a wide range of Bingham numbers. The present results extend previous analyses for creeping drag flow past a cylinder in an infinite medium based on variational principles and provide calculations of the drag coefficient around a cylinder in the case of wall effects.     

Two-dimensional unsteady flow of power-law fluids over a cylinder

The unsteady flow of incompressible power-law fluids over an unconfined circular cylinder in cross-flow arrangement has been studied numerically. The two-dimensional (2-D) field equations have been solved using a finite volume method based solver (FLUENT 6.3). In particular, the effects of the power-law index (0.4?n?1.8) and Reynolds number (40?Re?140) on the detailed kinematics of the flow (streamline, surface pressure and vorticity patterns) and on the macroscopic parameters (drag and lift coefficients, Strouhal number) are presented in detail. The periodic vortex shedding and the evolution of detailed kinematics with time are also presented to provide insights into the nature of flow. The two-dimensional flow transits from steady to unsteady behaviour at a critical value of the Reynolds number Re∼(40-50) and the von-Karman vortex street is observed beyond the critical Reynolds number (Re). Obviously, both the lift coefficient and Strouhal number values are zero for the steady flow, but their values increase with the increasing Reynolds number (Re) in the unsteady flow regime. For highly shear-thickening fluids (n=1.8), the flow becomes unsteady at Re=40 and unsteadiness in the flow appears at Re=50 for all values of power-law index (n). As expected, the evolution of the kinematics and vortex shedding show a complex dependence on the flow parameters near the transition in the flow. For a fixed value of the Reynolds number (Re), the drag coefficient increases and lift coefficient decreases with increasing value of the power-law index (n). For a fixed value of the power-law index (n), the drag coefficient gradually increases with the Reynolds number (Re). Similar to the drag coefficient, lift coefficient also shows a complex dependence on the power-law index (n) near the transition zone. The value of the Strouhal number (St) decreases with the increasing value of the power-law index (n) at a fixed value of the Reynolds number (Re).     

Experimental study of drag reduction by a polymeric additive in slug two-phase flow of crude oil and air in horizontal pipes

In this study the effect of the presence of a drag reducing agent (DRA) on the pressure drop in cocurrent horizontal pipes carrying slug two-phase flow of air and crude oil is investigated. An experimental set-up is erected. The test section of the experimental set-up is consisted of: a smooth pipe of polycarbonate with 10.3 m long and 2.54 cm ID, a rough pipe of galvanized iron with 8.8 m long and 2.54 cm ID and a rough pipe of galvanized iron with 8.8 m long and 1.27 cm ID. The employing DRA is a Polyalpha-olefin (Polyisobutylene). The percent drag reduction (%DR) is calculated using the obtained experimental data, in presence of the DRA. The results show that addition of DRA could be effective up to some doses of DRA after which the pressure drop is kept constant. A %DR of about 40 is obtained for some experimental conditions.     

Viscoelastic flow past a confined cylinder: Instability and velocity inflection

The flow of the Oldroyd-B fluid past a circular cylinder in a channel is simulated by a parallelized finite volume method (FVM) using fine unstructured meshes. Convergent solutions are obtained up to a high Deborah number of De=1.6 with a high aspect ratio mesh, while it can only be obtained for De=0.6 with a more or less equi-lateral mesh. The governing equations are re-written using the discrete elastic viscous split stress formulation together with an independent interpolation of the vorticity (DEVSS-ω). The numerical procedure is based on the semi-implicit method for pressure-linked equations revised (SIMPLER) algorithm, using a collocated FVM discretization. To enhance the numerical accuracy, mixed meshes (structured and unstructured) are used and adapted to the geometry and the flow physics. The results show that an instability featuring stress oscillations on the top of the cylinder is produced at a critical De number (De≈0.6). This critical value is in agreement with the experiments in the literature. The oscillation generated in the shear layer on the cylinder surface at high De number is convected downstream into the wake behind the cylinder. This feature of flow oscillation agrees well with experiments reported in the literature. The mechanism of these phenomena can be explained reasonably by a boundary layer analysis. The key finding is that the instability is due to an inflectional velocity profile, near the cylinder, generated by normal stress on the cylinder surface at high De number, which can only be captured with fine meshes. According to a newly proposed theory (so called energy gradient theory), inflectional velocity profile leads to flow instability and consequently allows the convection of the oscillatory flow within the shear layer downstream of the wake and results in the flow pulsation in the spanwise direction. Therefore, the origin of the instability for the flow around a cylinder is in the shear layer on the cylinder and not in the wake itself. In addition, it seems that the increasing rate of numerical perturbation is related to the mesh aspect ratio. Computing using thin-long meshes could get convergence even if the flow is oscillatory, while the computing is prohibited by the inflectional instability when equi-lateral triangular meshes are used.     

Drag on two co-axial rigid spheres moving normal to a plane: Newtonian and Carreau fluids

The boundary effect and the presence of a nearby entity on the drag of a rigid entity is investigated by considering the movement of two identical, rigid, coaxial spheres normal to a plane in both a Newtonian and a Carreau fluid at a low to medium large Reynolds number. The parameters key to the phenomenon under consideration, including the nature of the fluid, the separation distance between two spheres, the distance between the near sphere and the plane, and the Reynolds number, on the drag coefficient are discussed. We show that the influence of a boundary on the drag coefficient is more important than that of the nature of a fluid and that of the separation distance between two spheres. The variation of the drag coefficient as a function of Reynolds number for a Carreau fluid is similar to that for a Newtonian fluid. Due to the shear-thinning nature of the former the drag coefficient in the former is smaller than that in the latter. The influence of the index parameter of a Carreau fluid becomes appreciable only if the Carreau number is sufficiently large. Correlations between the drag coefficient and the key parameters of a system are developed for the case when the Reynolds number is smaller than l.     

Nonrecirculating flow of a yield stress fluid around a circular cylinder in a poiseuille flow

Although yield stress fluids are very present today in everyday life and in industry, their flow behavior is still poorly understood and the databases are incomplete at this time. The present experimental and numerical study focuses on laminar nonrecirculating flows of an elastoviscoplastic model fluid in a rectangular duct. An original experimental set‐up has been developed. The Particle Image Velocimetry method is used for analyzing the kinematical fields. Results provided concern the morphology of the flow and the evolution of the velocity field around a cylindrical obstacle. Information is provided on the size of the rigid zones where the fluid behaves as a solid. The experimental data are compared with numerical results involving a regularized Herschel–Bulkley viscoplastic model. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4554–4563, 2016     

A numerical study of the Dufour and Soret effects on unsteady natural convection flow past an isothermal vertical cylinder

The Dufour and Soret effects on the unsteady laminar free convective flow with mass transfer flow past a semi-infinite isothermal vertical cylinder were studied numerically. The governing partial differential equations were converted into a non-dimensional form and solved numerically by applying a Crank-Nicolson type of implicit finite-difference method with a tri-diagonal matrix manipulation and an iterative procedure. For the hydrogen-air mixture, which is a non-chemical reacting fluid, the profiles of the unsteady dimensionless velocity, temperature and concentration are shown graphically for the different values of thermal and mass Grashof numbers, thermal diffusion parameters (Soret numbers) and diffusion-thermo parameters (Dufour numbers). Finally, the simulated values of the average skin-friction coefficient, the average Nusselt number and the average Sherwood number are presented. The numerical results reveal that for an increasing Soret number or decreasing Dufour number, the time to reach the temporal maximum and the steady-state decreases for the flow variables. As the Soret number increases or the Dufour number decreases, both the skin friction and the Sherwood number increase, whereas the Nusselt number decreases.     

Drag force on a circular cylinder midway between two parallel plates at very low Reynolds numbers—Part 1: Poiseuille flow (numerical)

At very low Reynolds numbers, we calculate the drag force exerted on a circular cylinder in cross flow fixed midway between two parallel plane walls which are fixed while the fluid experiences a Poiseuille profile at upstream and downstream. The drag wall correction factor is numerically investigated from a very weak interaction to the lubrication regime. The Navier-Stokes and continuity equations are expressed in the stream function and vorticity formulation and are rewritten in an orthogonal system of curvilinear co-ordinates. These equations are solved with using a finite differences method. The generation of the grid was carried out by the singularities method. We calculated the separate contributions of the pressure and viscous forces numerically. At very weak interactions, our numerical results are in good agreement with those obtained analytically by Harrison (Trans. Camb. Phil. Soc. 23 (1924) 71) and Faxèn (Proc. Roy. Swed. Acad. Eng. Sci. 187 (1946) 1). In the lubrication regime these numerical calculations are in very good agreement with those we carried out by asymptotic expansion. So that, the accuracy of the numerical code is tested. This analysis allowed us to show how that the pressure term prevails over the viscosity term in the lubrication regime. At very weak interaction, these forces have the same value.     

非等温黏弹流体圆柱绕流的数值模拟(英文)

A collocated finite volume method on unstructured meshes is introduced to simulate the viscoelastic flow of the polymer melt with viscous dissipation past a confined cylinder. The constitutive equation for the simulations is non-isothermal FENE-P model, which is derived from the molecular theories. The temperature effect on the macroscopic fields (e.g., velocity, stress) and microscopic fields (e.g., molecular orientation, deformation, stretch) is investigated by comparison of isothermal and non-isothermal situations. This investigation indicates that temperature rise caused by viscous dissipation should not be neglected since it has significant effect on the macroscopic and microscopic properties of the polymer melt.     

微细圆管及扁平管内液-液Taylor流动特性的数值研究

微细通道内Taylor流动广泛应用于能源化工领域,为分析其相界面及阻力特性,利用相对坐标系的方法,研究了竖直圆管及扁平管内的液-液Taylor流动,讨论了通道宽高比、Reynolds数（Re）及分散相体积分数对液膜厚度和两相压降的影响。结果表明：圆管内液滴头部和尾部可以膨胀至近似球形,而扁平管内壁面的限制作用较强,液滴呈现扁平状。随Reynolds数增大,两相界面逐渐收缩,液膜厚度逐渐上升。圆管内液膜厚度比较均匀,扁平管内液膜在通道顶部较薄,而圆弧部分较厚。两相压降随Re和宽高比的增大而增大,随分散相体积分数的增大而降低。相比连续相和分散相压降,界面压降所占的比重最高,并依据模拟结果,提出了圆管及扁平管内液-液Taylor流动的压降预测公式。     

Drag force on a floc in a flow field: two-layer model

The behavior of a floc in a flow field is analyzed theoretically; in particular, the force it experienced is estimated. Here, a floc is simulated by an entity having a two-layer type of structure, and its porous nature mimicked by varying the relative magnitudes of the permeability of its inner layer and that of its outer layer. The results of numerical simulation reveal that, for the same volume-averaged permeability, the drag coefficient of a floc with a heterogeneous structure is always much larger than that of a floc with a homogeneous structure. This is true regardless of the relative magnitudes of the permeability of the inner layer and that of the outer layer. The drag coefficient of a floc is mainly determined by the part having a less porous structure. We show that for the same volume-averaged permeability, the more heterogeneous the structure of a floc is, the easier for the relation between the drag coefficient and the Reynolds number to deviate from a Stokes’ law-like correlation.     

多排平直翅片管换热器表面气液降膜流动特性的三维数值模拟

基于VOF模型建立了考虑重力、表面张力及界面摩擦力源项的多排平直翅片管换热器表面气液两相降膜流动三维瞬态CFD模型。不同气流速度下液膜厚度模拟结果与文献中试验值吻合较好,最大偏差小于5%,表明所建立CFD模型是可靠的。通过研究壁面接触角为30°时不同气液Reynolds数下液膜流动特性,结果表明：翅片管表面满膜流的临界Reynolds数Re_l为239,临界喷淋密度为0.06 kg/(m·s);在239 ≤ Re_l ≤ 995内,其平均液膜厚度较Nusselt理论解高16.8%～35.1%;气液逆流和顺流时气相Reynolds数Re_g应分别小于2190.7和3286.0,其主要原因在于过高的Re_g会导致气液界面摩擦力快速增大,从而引发液膜破裂和液滴脱落等现象恶化设备性能。总之,气液顺流更有利于在较高气相Reynolds数下实现翅片管表面的较薄满膜流动。     

Determination of shear viscosity and shear rate from pressure drop and flow rate relationship in a rectangular channel

In this study, we present a unique approach to calculate the shear viscosity and shear rate with the pressure drop and flow rate data from a channel having a rectangular cross-section with a height-to-width ratio (H/W) of close to one. The derived equation was verified with experimental data from rectangular dies whose height-to-width ratio (H/W) ranges from 0.1 to 1. It was confirmed that the proposed approach is reliable for the calculation of the shear viscosity and shear rate from the flow data in a rectangular channel.     

Cluster-based drag coefficient model for simulating gas-solid flow in a fast-fluidized bed

Drag coefficient is of essential importance for simulation of heterogeneous gas-solid flows in fast-fluidized beds, which is greatly affected by their clustering nature. In this paper, a cluster-based drag coefficient model is developed using a hydrodynamic equivalent cluster diameter for calculating Reynolds number of the particle phase. Numerical simulation is carried out in a gas-solid fast-fluidized bed with an Eulerian-Lagrangian approach and the gaseous turbulent flow is simulated using large eddy simulation (LES). A Lagrange approach is used to predict the properties of particle phase from the equation of motion. The collisions between particles are taken into account by means of direct simulation Monte Carlo (DSMC) method. Compared with the drag coefficient model proposed by Wen and Yu, results predicted by the cluster-based drag coefficient model are in good agreement with experimental results, indicating that the cluster-based drag coefficient model is suitable to describe various statuses in fast-fluidized beds.     

非牛顿流体搅拌流场的数值模拟研究进展

对非牛顿流体搅拌流场数值模拟过程中的控制方程、旋转桨叶的处理以及数值计算方法三个方面进行了综合论述。阐述了广义牛顿流体模型形式简单、计算量低,在非牛顿流体搅拌流场数值模拟过程中应用广泛;黏弹性流体本构方程具有高度的非线性,采用计算流体力学(CFD)方法对其搅拌流场进行数值模拟难度较高,目前仍处于起步阶段;通过合理简化黏弹性流体本构方程以及采用恰当的数值离散方法,有助于在黏弹性流体的搅拌流场数值模拟中取得进展。     

An experimental study of drag reduction by nanofluids through horizontal pipe turbulent flow of a Newtonian liquid

This study investigates the effect of nanofluid injection as a drag reducing agent into horizontal pipes under turbulent flow conditions of water. An experimental apparatus was set up. The test section of the apparatus consisted of a smooth unique pipe and four galvanized iron pipes with the same length. Nanofluids were injected through pipes. Results showed that drag reduction in rough pipes was more than that in smooth pipes at the same flow conditions and it increased as the relative roughness increased. Also, drag reduction rose with increasing the nanofluid concentration up to about 24% in some tests.     

Wall effects on the velocities of a single sphere settling in a stagnant and counter-current fluid and rising in a co-current fluid

Experimental results were obtained on the steady settling of spheres in quiescent media in a range of cylindrical tubes to ascertain the wall effects over a relatively wide range of Reynolds number values. For practical considerations, the retardation effect is important when the ratio of the particle diameter to the tube diameter (λ) is higher than about 0.05. A new empirical correlation is presented which covers a Reynolds number range Re = 53-15,100 and a particle to tube diameter ratio λ < 0.88. The absolute mean deviation between the experimental data and the presented correlation was 1.9%. The well-known correlations of Newton, Munroe and Di Felice agree with the presented data reasonably well. For steady settling of spheres in a counter-current water flow, the slip velocity remains practically the same as in quiescent media. However, for rising spheres in a co-current water flow, the slip velocity decreases with increasing co-current water velocity, i.e., the wall factor decreases with increasing co-current water velocity. Consequently, the drag coefficient for rising particles in co-current water flow increases with increasing water velocity.     

An experimental study of motion of cylinders in newtonian fluids: Wall effects and drag coefficient

The terminal velocity of several cylinders (of glass, perspex and stainless steel) falling with their axis parallel to the direction of motion has been measured in a series of Newtonian fluids embracing a 40-fold variation in liquid viscosity. The measurements have been carried out in fall tubes of four different diameters to elucidate the importance of wall effects. The experimental results encompass the following ranges of conditions: cylinder to fall tube diameter ratio: 0.08 to 0.4; length to diameter ratio: 0.05 to 2 and Reynolds number varied from 0.2 to 180. The wall effects are discussed in a manner analogous to those for spherical particles. Terminal velocity data are analysed using two approaches, namely, drag coefficient-Reynolds number relationship and a dimensionless velocity ratio denoting the departure from the behaviour of an equivalent sphere. Predictive equations have been developed using both schemes.     

Tomography images to analyze the deformation of the cavern in the continuous‐flow mixing of non‐Newtonian fluids

Tomography, an efficient nonintrusive technique, was employed to visualize the flow in continuous‐flow mixing and to measure the cavern volume (V_c) in batch mixing. This study has demonstrated an efficient method for flow visualization in the continuous‐flow mixing of opaque fluids using two‐dimensional (2‐D) and 3‐D tomograms. The main objective of this study was to explore the effects of four inlet‐outlet configurations, fluid rheology (0.5–1.5% xanthan gum concentration), high‐velocity jet (0.317–1.660 m s^?1), and feed flow rate (5.3 × 10^?5?2.36 × 10^?4 m³ s^?1) on the deformation of the cavern. Dynamic tests were also performed to estimate the fully mixed volume (V_{fully mixed}) for the RT, A310, and 3AM impellers in a continuous‐flow mixing system, and it was found that V_{fully mixed} was greater than V_c. Incorporating the findings of this study into the design criteria will minimize the extent of nonideal flows in the continuous‐flow mixing of complex fluids and eventually improve the quality of end‐products. © 2013 American Institute of Chemical Engineers AIChE J, 60: 315–331, 2014