Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel

This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically.     

Study on forced shear flow by a oscillating spoiler

In the present paper, numerical solution of the two-dimensional unsteady Navier-Stokes equations is used to study the forced shear flow induced by a spoiler's periodical up and down oscillation on a flat plate. The paper studies the evolution of growing, shedding, merging and decaying of vortices due to the spoiler's oscillation, particularly the dependence of the forced shear flow on the reduced frequency. Results show that the reduced frequency is a key factor in controlling the growing and the shedding of vortices in the shear layer. The instantaneous streamlines and the equi-vorticity contours, as well as the surface pressure distributions, have also been investigated. Numerical results agree well with corresponding experimental ones. The study is helpful for understanding the physical mechanism of shear flow control.     

Comparing vortex methods and finite difference methods in a homogeneous turbulent shear flow

The vortex method is applied to the calculation of a homogeneous shear turbulence, and compared with a finite difference code using identical calculation conditions. The core spreading method with spatial adaptation is selected as the viscous diffusion scheme of the vortex method. The shear rate is chosen so that it matches the maximum value observed in a fully developed channel flow. The isosurface, anisotropy tensors, and joint probability density functions reflect the ability of the present vortex method to quantitatively reproduce the anisotropic nature of strongly sheared turbulence, both instantaneously and statistically. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of span length and temperature on the 3-D confined flow around a vortex promoter

This article presents a numerical study on the influence of span length and wall temperature on the 3-D flow pattern around a square section vortex promoter located inside a micro-channel in the low Reynolds number regime. The first objective of the work is to quantify the critical Reynolds number that defines the onset of vortex shedding and to identify the different regimes that appear as a function of the channel aspect ratio (span to height ratio). We found that the critical Reynolds number for the onset of the Karman street regime increases as the aspect ratio decreases. In particular, for the aspect ratio of 1/2 the critical Reynolds number is nearly six times the critical Reynolds number of the 2-D problem. An intermediate oscillating regime between the steady and the Karman street solutions was also found to exist within a rather wide range of Reynolds numbers for small channel aspect ratios. The second objective was to investigate the influence of the vortex promoter wall temperature on both vortex shedding and flow pattern. This has practical engineering implications because the working fluid considered in the article is water that has a viscosity that depends significantly on temperature and promotes a strong coupling between the momentum and energy equations that influences the system behaviour. Results indicate that high surface temperature on the prism promotes the onset of the Karman street, suggesting design guidelines for micro-channel based heat sinks that make use of vortex promoters.     

Hydrodynamic interactions of dilute polymer solutions under shear flow in a narrow channel

Hydrodynamic interactions on dilute solutions of spherical beads under shear flow are calculated with the method of induced forces. The Navier-Stokes equation is considered in the Stokes approximation. Hydrodynamic interactions cause the drag to be anisotropic in space.Numerical solutions are obtained for the added stress, caused by polymeric molecules in solution in a narrow channel under shear flow. The polymeric molecules are considered as Hookean spring-dumbbells.Slip velocity and the effective viscosity are obtained taking different dumbbells' bead radii. Transversal migration in the channel is obtained for different bead radii.     

Investigation of fiber motion near solid boundaries in simple shear flow

In this paper, fiber motion near a planar wall was investigated using a planar shear flow apparatus. Fibers were placed (one at a time) perpendicular to the flow direction at various locations throughout the flow field. The location and orientation of each fiber versus time was measured, using an image processing system, until the fiber aligned with the flow direction. When the centroid of the fiber was located at distances greater than a fiber length from the wall, Jeffery's equations governing particle motion were verified. For distances less than a fiber length and greater than a fiber diameter from the wall, the fiber experienced an increased rate of rotation. In this regime, the motion of the fiber could be described by Jeffery's equations if an increased effective shear rate was used. The effective shear rate was found to increase logarithmically with decreasing separation distance. The wall effect was higher for longer aspect ratio fibers and was also a function of orientation; fibers oriented perpendicular to the wall rotated faster than those oriented parallel to the wall at the same separation distance. Once the fiber aligned with the flow direction, it ceased to rotate within the field of view. In this orientation, the wall had a stabilizing effect on the fiber. In efforts to relate the increase in shear rate to the aspect ratio of the fiber and the separation distance between the fiber and a solid wall, a translation model based on the work of De Mestre and Russel was explored. This model allows one to quantify the increase in shear rate experienced by the fiber due to the presence of a wall or obstruction in the flow field. However, the model has its limitations and care should be taken when applying this model outside its realm of validity. When compared to experimental data, the translation model provides a very good estimate of the increased shear rate experienced by the fiber when it is located less than 2/3 of a fiber length from a planar wall. Received: 20 April 2000 Accepted: 28 September 2000     

Non-linear behaviour of asphalts in steady and transient shear flow

Steady-state and transient shear stress and normal stress data were obtained for four asphalts with a modified Weissenberg Rheogoniometer. Interest was specially related to non-linear behaviour at high shear-rates. The time-temperature superposition principle was found to hold in non-linear behaviour. Moreover, steady-state and transient data could be plotted as master curves irrespective of the nature of the asphalts. In particular, the master curve of steady-state viscosity could be extended to results published in the literature. In the nonlinear region the shear stress relaxation after cessation of a steady shear rate becomes a function of t only and is related to the primary normal-stress coefficient, as predicted by the Yamamoto equation. In the shear stress growth experiment an overshoot is obtained at a constant strain close to 1.5, independent of the rate of strain.     

Numerical simulation of shear effect on vortex shedding behind a square cylinder

This paper is concerned with the numerical simulation of the flow structure around a square cylinder in a uniform shear flow. The calculations were conducted by solving the unsteady 2D Navier–Stokes equations with a finite difference method. The effect of the shear parameter K of the approaching flow on the vortex-shedding Strouhal number and the force coefficients acting on the square cylinder is investigated in the range K=0·0–0·25 at various Reynolds numbers from 500 to 1500. The computational results are compared with some existing experimental data and previous studies. The effect of shear rate on the Strouhal number and the force acting on the cylinder has a tendency to reduce the oscillation. The Strouhal number, mean drag and amplitude of the fluctuating force tend to decrease as the shear rate increases, but show no significant change at low shear rate. Increasing the Reynolds number decreases the Strouhal number and increases the force acting on the cylinder. At high shear rate the shedding frequencies of the fluctuating drag and lift coefficients are identical. © 1997 John Wiley & Sons, Ltd.     

Numerical simulation of an isolated vortex and shear flow interaction

A numerical solution for the Navier-Stokes equations in the unbounded region is considered for the interaction of an isolated vortex and shear flow. A Chebyshey collocation method in space and finite-difference method for temporal discretization are used. The results of the numerical experiments for the interaction are discussed. It is shown that shear flow can both increase and decrease the vortex dissipation rate.     

Computational analysis of exit conditions on the sound field of turbulent hot jets

A hybrid computational fluid dynamics (CFD) and computational aeroacoustics (CAA) method is used to compute the acoustic field of turbulent hot jets at a Reynolds number $Re=316,000$ and a Mach number $M=0.12$. The flow field computations are performed by highly resolved large-eddy simulations (LES), from which sound source terms are extracted to compute the acoustic field by solving the acoustic perturbation equations (APE). Two jets are considered to analyze the impact of exit conditions on the resulting jet sound field. First, a jet emanating from a fully resolved non-generic nozzle is simulated by solving the discrete conservation equations. This computation of the jet flow is denoted free-exit-flow (FEF) formulation. For the second computation, the nozzle geometry is not included in the computational domain. Time averaged exit conditions, i.e. velocity and density profiles of the first formulation, plus a jet forcing in form of vortex rings are imposed at the inlet of the second jet configuration. This formulation is denoted imposed-exit-flow (IEF) formulation. The free-exit-flow case shows up to 50% higher turbulent kinetic energy than the imposed-exit-flow case in the jet near field, which drastically impacts noise generation. The FEF and IEF configurations reveal quite a different qualitative behavior of the sound spectra, especially in the sideline direction where the entropy source term dominates sound generation. This difference occurs since the noise sources generated by density and pressure fluctuations are not perfectly modeled by the vortex ring forcing method in the IEF solution. However, the total overall sound pressure level shows the same qualitative behavior for the FEF and IEF formulations. Towards the downstream direction, the sound spectra of the FEF and IEF solutions converge.     

可渗透壁对翼型声涡相互作用下流场及声场的影响

由仿生学原理构建的可渗透翼型对湍流气动噪声抑制作用已展现良好的应用前景。对NACA 0012可渗透翼型和实体翼型进行了数值计算,得到了声涡相互作用下气动噪声声场和流场,分析了可渗透壁对翼型流场和声场的影响。研究表明,相对实体翼型,可渗透壁通过减小声源强度降低了主纯音噪声声压级幅值和远场总声压级,消除了高阶离散纯音,但对噪声的指向性没有较大改变。进一步的流场分析表明,可渗透壁对翼型气动性能影响不大的情况下能够降低边界层扰动和翼型后缘大尺度涡旋强度,并推迟分离泡转捩和再附位置。     

Remarks on orthogonal superposition of small amplitude oscillations on steady shear flow

The paper demonstrates that experimental data (Simmons, 1968) for orthogonal superposition of small amplitude oscillations on steady shear flow, coincide well enough with the theoretical predictions (Leonov et al., 1976) of simple multi-modal version of Leonov model (Leonov, 1976, 1987; Leonov et al., 1976). It was also shown that the recent theoretical calculations (Wong and Isayev, 1989) of the problem, which used the same Leonov model, are wrong.     

双柱状颗粒在线性剪切流场中的动力学分析

为研究柱状颗粒在线性剪切流场中的运动状态和受力情况,本文以颗粒长径比为2,颗粒之间的初始距离ΔS_Py=4D为例,基于直接力浸入边界法数值模拟了双柱状颗粒在三维线性剪切流场中的运动过程。根据模拟结果分析了柱状颗粒周围流场参数分布,在考虑壁面对颗粒的影响和颗粒之间相互影响的条件下,研究了颗粒的受力和运动的变化,探索了流体曳力导致柱状颗粒迁移和转动的规律。研究结果表明,双柱状颗粒在线性剪切流场中易向速度大的流体区域运动;前后两颗粒运动状态和轨迹不同,颗粒之间距离较近时,曳力会产生较大的波动;只有当颗粒在壁面附近时,滞后颗粒才能追上领先颗粒,两颗粒发生牵引、翻滚和分离过程。     

Large eddy simulation of bluff body wake in planar shear flow

Large eddy simulation of planar shear flow past a square cylinder has been investigated. Dynamic Smagorinsky model has been used to model subgrid scale stress. The shear parameter, K, namely the nondimensional streamwise velocity gradient in the lateral direction, is 0.0, 0.1 and 0.2. Reynolds number based on the centerline velocity is fixed at Re=21400. The time and span‐averaged velocity components, pressure coefficient, Reynolds stresses for uniform are in good agreement with the literature. In shear flow the calculated flow structure and mean velocity components are shown to be markedly different from those of the uniform flow. With increasing shear parameter, the cylinder wake is dominated by clockwise vortices. Both the velocity components in shear flow are compared with respective components in uniform flow. Comparison of normal and shear stresses between shear and no shear case have also been presented. Copyright © 2009 John Wiley & Sons, Ltd.     

Three‐dimensional vortex simulation of unsteady flow in hydraulic turbines

On the basis of the Helmholtz decomposition, a grid‐free numerical scheme is provided for the solution of unsteady flow in hydraulic turbines. The Lagrangian vortex method is utilized to evaluate the convection and stretch of the vorticity, and the BEM is used to solve the Neumann problem to define the potential flow. The no‐slip boundary condition is satisfied by generating vortex sticks at the solid surface. A semi‐analytical regularization technique is applied to evaluate the singular boundary surface integrals of the potential velocity and its gradients accurately. The fast multipole method was extended to evaluate the velocity and velocity gradients induced by the discretized vortex blobs in the Lagrangian vortex method. The successful simulation for the unsteady flow through a hydraulic turbine's runner has manifested the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Instability of the separated shear layer in flow past a cylinder: Forced excitation

The receptivity of the separated shear layer for Re = 300 flow past a cylinder is investigated by forced excitation via an unsteady inflow. In order to isolate the shear layer instability, a numerical experiment is set up that suppresses the primary wake instability. Computations are carried out for one half of the cylinder, in two dimensions. The flow past half a cylinder with steady inflow is found to be stable for Re = 300. However, an inlet flow with pulsatile perturbations, of amplitude 1% of the mean, results in the excitation of the shear layer mode. The frequency of the perturbation of the inlet flow determines the frequency associated with the shear layer vortices. For a certain range of forced frequencies the recirculation region undergoes a low‐frequency longitudinal contraction and expansion. An attempt is made to relate this instability to a global mode of the wake determined from a linear stability analysis. Interestingly, this phenomenon disappears when the outflow boundary of the computational domain is shifted sufficiently downstream. This study demonstrates the need of carefully investigating the effect of the location of outflow boundaries if the computational results indicate the presence of low‐frequency fluctuations. The effect of Re and amplitude of unsteadiness at the inlet are also presented. All computations have been carried out using a stabilized finite element formulation of the incompressible flow equations. Copyright © 2007 John Wiley & Sons, Ltd.     

On identification of flow separation and vortices in internal periodic flows

To permit simplified analysis of complex time-dependent flows, possible relationship between the near-wall flow, flow separation and vortices are studied numerically for a flow in a constricted two-dimensional channel. The pulsating incoming wave-form consists of a steady flow, followed by a half-sinus flow superimposed on the steady component. One pair of vortices is created in each cycle, one vortex near each wall. The vortices propagate downstream in the next cycles, promoting flow separation as they move. Existing flow separation criteria were not found to be uniformly valid. A relation between the near-wall flow and the vortical system exists only during the steady incoming flow phase of the cycle. It seems that local criteria of flow separation cannot be found for complex internal pulsating flow fields. However, the vorticity field can be utilized, even in complex time-periodic flows, for identifying vortices that have been formed by the roll-up of shear layers.     

Research on the effect of particle of two-dimensional shear flow

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Effect of confinement on droplet deformation in shear flow

The dynamics of a single droplet under shear flow between two parallel plates is investigated by using the immersed boundary method. The immersed boundary method is appropriate for simulating the drop-ambient fluid interface. We apply a volume-conserving method using the normal vector of the surface to prevent mass loss of the droplet. In addition, we present a surface remeshing algorithm to cope with the distortion of droplet interface points caused by the shear flow. This mesh quality improvement in conjunction with the volume-conserving algorithm is particularly essential and critical for long time evolutions. We study the effect of wall confinement on the droplet dynamics. Numerical simulations show good agreement with previous experimental results and theoretical models.     

Numerical simulation of free shear flows and far-field sound pressure directivity

An implicit spatial differencing technique with fourth-order accuracy has been developed based on the Pade compact scheme. A dispersion-relation-preserving concept has been incorporated into the numerical scheme. Two-dimensional Euler computation of a spatially developing free shear flow with and without external excitation has been performed to demonstrate the capability of the numerical scheme developed. Results are in good agreement with theory and experimental observation regarding the growth rate of the fluctuating velocity, the convective velocity and the vortex-pairing process. The far-field sound pressure generated by the computed shear flow solution using Lighthill's acoustic analogy shows a strong directivity with a zone of silence at the flow angle.