Showing papers on "Hele-Shaw flow published in 2011"

Interface-resolved DNS of vertical particulate channel flow in the turbulent regime

Abstract: We have conducted a direct numerical simulation (DNS) study of dilute turbulent particulate flow in a vertical plane channel, considering thousands of finite-size rigid particles with resolved phase interfaces. The particle diameter corresponds to approximately 11 wall units and their terminal Reynolds number is set to 136. The fluid flow with bulk Reynolds number 2700 is directed upward, which maintains the particles suspended upon average. Two density ratios were simulated, differing by a factor of 4.5. The corresponding Stokes numbers of the two flow cases were O(10) in the near-wall region and O(1) in the outer flow. We have observed the formation of large-scale elongated streak-like structures with streamwise dimensions of the order of 8 channel half-widths and cross-stream dimensions of the order of one half-width. At the same time, we have found no evidence of significant formation of particle clusters, which suggests that the large structures are due to an intrinsic instability of the flow, triggered by the presence of the particles. It was found that the mean fluid velocity profile tends towards a concave shape, and the turbulence intensity as well as the normal stress anisotropy are strongly increased. The effect of varying the Stokes number while maintaining the buoyancy, particle size and volume fraction constant was relatively weak.

The wake of two side-by-side square cylinders

Abstract: Aerodynamic interference between two cylinders involves most of the generic flow features associated with multiple structures, thus providing an excellent model for gaining physical insight into the wake of multiple cylindrical structures. This work aims to provide an experimental systematic study of the flow behind two side-by-side square cylinders. The square cylinder is a representative model for bluff bodies with sharp corners, characterized by a fixed flow separation point, which are distinct from those of continuous curvature with oscillating separation points, typically represented by the circular cylinder. Experiments were performed at a Reynolds number Re of 4.7 × 10 4 and a cylinder centre-to-centre spacing ratio T/ d (d is the cylinder height) of 1.02–6.00. The flow was measured using different techniques, including hot wires, load cell, particle imaging velocimetry and laser-induced fluorescence flow visualization. Four distinct flow regimes and their corresponding T/ d ranges are identified for the first time on the basis of the flow structure and the Strouhal number. Physical aspects in each regime, such as interference between shear layers, gap flow deflection and changeover, multiple flow modes, entrainment, recirculation bubble, vortex interactions and formation lengths, are investigated in detail and are connected to the characteristics of the time-averaged and fluctuating fluid forces. The flow displays a marked difference in many facets from that behind two side-by-side circular cylinders, which is linked to their distinct flow separation natures. A crucial role played by the gap flow and its passage geometry in contributing to the observed difference is also unveiled.

Inertial migration of deformable capsules in channel flow

Abstract: Using three-dimensional computer simulations, we study the cross-stream inertial migration of neutrally buoyant deformable particles in a pressure-driven channel flow. The particles are modeled as elastic shells filled with a viscous fluid. We show that the particles equilibrate in a channel flow at off-center positions that depend on particle size, shell compliance, and the viscosity of encapsulated fluid. These equilibrium positions, however, are practically independent of the magnitude of channel Reynolds number in the range between 1 and 100. The results of our studies can be useful for sorting, focusing, and separation of micrometer-sized synthetic particles and biological cells.

Some aspects of aerodynamic flow control using synthetic-jet actuation.

Abstract: Aerodynamic flow control effected by interactions of surface-mounted synthetic (zero net mass flux) jet actuators with a local cross flow is reviewed. These jets are formed by the advection and interactions of trains of discrete vortical structures that are formed entirely from the fluid of the embedding flow system, and thus transfer momentum to the cross flow without net mass injection across the flow boundary. Traditional approaches to active flow control have focused, to a large extent, on control of separation on stalled aerofoils by means of quasi-steady actuation within two distinct regimes that are characterized by the actuation time scales. When the characteristic actuation period is commensurate with the time scale of the inherent instabilities of the base flow, the jets can effect significant quasi-steady global modifications on spatial scales that are one to two orders of magnitude larger than the scale of the jets. However, when the actuation frequency is sufficiently high to be decoupled from global instabilities of the base flow, changes in the aerodynamic forces are attained by leveraging the generation and regulation of 'trapped' vorticity concentrations near the surface to alter its aerodynamic shape. Some examples of the utility of this approach for aerodynamic flow control of separated flows on bluff bodies and fully attached flows on lifting surfaces are also discussed.

Quantitative prediction of flow patterns in liquid–liquid flow in micro-capillaries

Abstract: Flow patterns in microstructured reactors (or microchannels) play an important role in dictating the mass transfer rates. In the present work, experiments were carried out to investigate the two phase (liquids) flow patterns in microchannels with different cross sections and contacting geometries. The pattern formation was analysed and conditions were classified in the three regions: surface tension dominated (slug flow), transition (slug-drop and deformed interface flow) and inertia dominated region (annular or parallel flow). A criterion for liquid-liquid flow pattern transition was developed using Capillary and Reynolds numbers based on the work of Dessimoz et al. Ill for gas-liquid systems. Finally, it was applied to the literature data and good agreement was obtained. The criterion is suitable for capillaries with hydraulic diameter up to 3 mm independently of cross section form and is an important predictive tool for the rational design of micro reactors for liquid-liquid reactions. (C) 2011 Elsevier B.V. All rights reserved.

On the stationary macroscopic inertial effects for one phase flow in ordered and disordered porous media

Abstract: We report on the controversial dependence of the inertial correction to Darcy’s law upon the filtration velocity (or Reynolds number) for one-phase Newtonian incompressible flow in model porous media. Our analysis is performed on the basis of an upscaled form of the Navier-Stokes equation requiring the solution of both the micro-scale flow and the associated closure problem. It is carried out with a special focus on the different regimes of inertia (weak and strong inertia) and the crossover between these regimes versus flow orientation and structural parameters, namely porosity and disorder. For ordered structures, it is shown that (i) the tensor involved in the expression of the correction is generally not symmetric, despite the isotropic feature of the permeability tensor. This is in accordance with the fact that the extra force due to inertia exerted on the structure is not pure drag in the general case; (ii) the Forchheimer type of correction (which strictly depends on the square of the filtration velocity) is an approximation that does not hold at all for particular orientations of the pressure gradient with respect to the axes of the structure; and (iii) the weak inertia regime always exists as predicted by theoretical developments. When structural disorder is introduced, this work shows that (i) the quadratic dependence of the correction upon the filtration velocity is very robust over a wide range of the Reynolds number in the strong inertia regime; (ii) the Reynolds number interval corresponding to weak inertia, that is always present, is strongly reduced in comparison to ordered structures. In conjunction with its relatively small magnitude, it explains why this weak inertia regime is most of the time overlooked during experiments on natural media. In all cases, the Forchheimer correction implies that the permeability is different from the intrinsic one.

Large velocity fluctuations in small-Reynolds-number pipe flow of polymer solutions

Abstract: The flow of polymer solutions is examined in a flow geometry where a jet is used to inject the viscoelastic solution into a cylindrical tube. We show that this geometry allows for the generation of a "turbulentlike" flow at very low Reynolds numbers with a fluctuation level which can be as high as 30%. The fluctuations increase with an increase in solution polymer concentration and flow velocity. The turbulent fluctuations decay downstream for small flow velocities but persist for high velocities. The statistical properties of the generated fluctuations indicate that this turbulentlike flow is different from previously studied flows displaying elastic turbulence and shows a direct cascade of energy to small scales with practically no intermittency.

Onset of three-dimensionality in electromagnetically driven thin-layer flows

Abstract: Two-dimensional fluid flow is often approximated in the laboratory with thin electromagnetically forced fluid layers. The faithfulness of such an experimental model must be considered carefully, however, because the physical world is inherently three-dimensional. By adapting an analysis technique developed for oceanographic data, we divide velocity measurements from a thin-layer flow into two components: one that is purely two-dimensional and another that accounts for all out-of-plane flow. We examine the two- and three-dimensional components separately, finding that motion in thin-layer flows is nearly two-dimensional at low Reynolds numbers, but that out-of-plane flow grows quickly above a critical Reynolds number. This onset is likely due to a shear instability.

Numerical simulation of flow over two circular cylinders in tandem arrangement

Abstract: In this article, the 2-D unsteady viscous flow around two circular cylinders in a tandem arrangement is numerically simulated in order to study the characteristics of the flow in both laminar and turbulent regimes. The method applied alternatively is based on the finite volume method on a Cartesian-staggered grid. The great source term technique is employed to identify the cylinders placed in the flow field. To apply the boundary conditions, the ghost-cell technique is used. The implemented computational method is firstly validated through simulation of laminar and turbulent flows around a fixed circular cylinder. Finally, the flow around two circular cylinders in a tandem arrangement is simulated and analyzed. The flow visualization parameters, the Strouhal numbers, and drag and lift coefficients are comprehensively presented and compared for different cases in order to reveal the effect of the Reynolds number and gap spacing on the behavior of the flow. The obtained results have shown two completely distinct flow characteristics in laminar and turbulent regimes.

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

Abstract: We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow v.s. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque $G=T/ u^2L$, where $L$ is the cylinder length, scales with Reynolds number $R$ and gap width $\eta$, $G=1.46 \eta^{3/2} (1-\eta)^{-7/4}R^{3/2}$. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: $$ G=0.50\frac{\eta^{2}}{(1-\eta)^{3/2}}\frac{R^{2}}{\ln[\eta^2(1-\eta)R^ 2/10^4]^{3/2}}.$$ These predictions are found to be in excellent agreement with available experimental data. Predictions for scaling of velocity fluctuations are also provided.

Granular jets and hydraulic jumps on an inclined plane

Abstract: A jet of granular material impinging on an inclined plane produces a diverse range of flows, from steady hydraulic jumps to periodic avalanches, self-channelised flows and pile collapse behaviour. We describe the various flow regimes and study in detail a steady-state flow, in which the jet generates a closed teardrop-shaped hydraulic jump on the plane, enclosing a region of fast-moving radial flow. On shallower slopes, a second steady regime exists in which the shock is not teardrop-shaped, but exhibits a more complex ?blunted? shape with a steadily breaking wave. We explain these regimes by consideration of the supercritical or subcritical nature of the flow surrounding the shock. A model is developed in which the impact of the jet on the inclined plane is treated as an inviscid flow, which is then coupled to a depth-integrated model for the resulting thin granular avalanche on the inclined plane. Numerical simulations produce a flow regime diagram strikingly similar to that obtained in experiments, with the model correctly reproducing the regimes and their dependence on the jet velocity and slope angle. The size and shape of the steady experimental shocks and the location of sub- and supercritical flow regions are also both accurately predicted. We find that the physics underlying the rapid flow inside the shock is dominated by depth-averaged mass and momentum transport, with granular friction, pressure gradients and three-dimensional aspects of the flow having comparatively little effect. Further downstream, the flow is governed by a friction?gravity balance, and some flow features, such as a persistent indentation in the free surface, are not reproduced in the numerical solutions. On planes inclined at a shallow angle, the effect of stationary granular material becomes important in the flow evolution, and oscillatory and more general time-dependent flows are observed. The hysteretic transition between static and dynamic friction leads to two phenomena observed in the flows: unsteady avalanching behaviour, and the feedback from static grains on the flowing region, leading to lev�ed, self-channelised flows.

Fluid Flow and Heat Transfer from Circular and Noncircular Cylinders Submerged in Non-Newtonian Liquids

Abstract: Publisher Summary This chapter discusses the role of non-Newtonian flow characteristics of structured fluids—within the framework of continuum mechanics—on the hydrodynamic and convective heat and mass transport processes for bluff bodies of various shapes immersed in streaming (unconfined or confined) or quiescent fluids in different flow regimes. It focuses on the steady and laminar vortex shedding regimes of the flow over long cylinders of circular, elliptic, semicircular, square, and triangular cross sections. Within this framework, the flow invariably tends to be two-dimensional and laminar. The unconfined or free flow past a circular cylinder exhibits a rich variety of flow regimes depending upon the intrinsic nature of the flow. The simple flow is governed by the Reynolds number that is based upon the diameter of the cylinder, kinematic viscosity of the fluid, and the faraway uniform velocity. Most non-Newtonian fluids tend to be far more viscous than their Newtonian counterparts like air and water and, therefore, laminar flow conditions prevail more often in such fluids than that in Newtonian fluids like air. The chapter describes the flow regimes and fluid mechanical aspects related to circular, elliptical, semicircular, triangular, and square cylinders, together with the critical values of the Reynolds number denoting the transition from one flow regime to another. These values are strongly influenced not only by the rheological characteristics but also by the shape of the bluff body, its orientation with regard to the mean direction of flow, and its extent and type of confinement. The scaling considerations that are used to extract the pertinent dimensionless parameters which influence the detailed and macroscopic momentum and heat transfer characteristics for each shape of the bluff body have also been highlighted.

Control of the antisymmetric mode (m = 1) for high Reynolds axisymmetric turbulent separating/reattaching flows

Abstract: The separated flow over a three-dimensional axisymmetric step controlled by means of continuous jets is investigated numerically at a high subsonic regime using Zonal Detached Eddy Simulation (ZDES). The main objective is here to analyze the influence of two controlled devices acting in different regions of the separated flow, i.e., in the shear layer or in the recirculation area. Contrary to most flow control strategies that aim at reducing the drag, the final purpose of this study consists in controlling the antisymmetric azimuthal mode (m=1) responsible for side loads occurring on a massively separated afterbody. Thus, the design of controlled cases has been motivated both by a literature review which is detailed but especially by the previous identification of a potential area of receptiveness linked to an absolutely unstable area. The related achievement expected lies in increasing the three-dimensionality of the flow but decreasing its large scale coherence. For both controlled configurations, insta...

Resolving high Reynolds numbers in SPH simulations of subsonic turbulence

Abstract: Accounting for the Reynolds number is critical in numerical simulations of turbulence, particularly for subsonic flow. For Smoothed Particle Hydrodynamics (SPH) with constant artificial viscosity coefficient , it is shown that the effective Reynolds number in the absence of explicit physical viscosity terms scales linearly with the Mach number — compared to mesh schemes, where the effective Reynolds number is largely independent of the flow velocity. As a result, SPH simulations with = 1 will have low Reynolds numbers in the subsonic regime compared to mesh codes, which may be insufficient to resolve turbulent flow. This explains the failure of Bauer & Springel (2011, arXiv:1109.4413v1) to find agreement between the moving-mesh code AREPO and the GADGET SPH code on simulations of driven, subsonic (v 0:3cs) turbulence appropriate to the intergalactic/intracluster medium, where it was alleged that SPH is somehow fundamentally incapable of producing a Kolmogorov-like turbulent cascade. We show that turbulent flow with a Kolmogorov spectrum can be easily recovered by employing standard methods for reducing away from shocks.

Gravity-driven flow over heated, porous, wavy surfaces

Abstract: The method of weighted residuals for thin film flow down an inclined plane is extended to include the effects of bottom waviness, heating, and permeability in this study. A bottom slip condition is used to account for permeability and a constant temperature bottom boundary condition is applied. A weighted residual model (WRM) is derived and used to predict the combined effects of bottom waviness, heating, and permeability on the stability of the flow. In the absence of bottom topography, the results are compared to theoretical predictions from the corresponding Benney equation and also to existing Orr-Sommerfeld predictions. The excellent agreement found indicates that the model does faithfully predict the theoretical critical Reynolds number, which accounts for heating and permeability, and these effects are found to destabilize the flow. Floquet theory is used to investigate how bottom waviness influences the stability of the flow. Finally, numerical simulations of the model equations are also conducted and compared with numerical solutions of the full Navier-Stokes equations for the case with bottom permeability. These results are also found to agree well, which suggests that the WRM remains valid even when permeability is included.

Plane Poiseuille flow of miscible layers with different viscosities: instabilities in the Stokes flow regime

Abstract: We investigate the linear stability of miscible, viscosity-layered Poiseuille flow. In the Stokes flow regime, diffusion is observed to have a destabilizing effect very similar to that of inertia in finite-Reynolds-number flows. For two-layer flows, four types of instability can dominate, depending on the interface location. Two interfacial modes exhibit large growth rates, while two additional bulk modes grow more slowly. Three-layer Stokes flows give rise to diffusive modes for each interface. These two diffusive interface modes can be in resonance, thereby enhancing the growth rate. Furthermore, modes without inertia and diffusion are also observed, consistent with a previous long-wave analysis for sharp interfaces. In contrast to that earlier investigation, the present analysis demonstrates that instability can also occur when the more viscous layer is in the centre, at larger wavenumbers.

Manifold Design for Micro-Channel Cooling With Uniform Flow Distribution

Abstract: High-power electronic systems often require temperature uniformity for optimal performance. While many advanced cooling systems, such as micro-channels, result in significant heat removal, they are also susceptible to flow mal-distribution that can impact the local temperature variation on a device. By examining the pressure drops through each flow path in a multi-channel cooling system, an analytical model is predicted for the optimal manifold shape to produce uniform velocities. This is a simple power law, whose exponent depends on the flow regime in the manifold passages. The model is validated for laminar fully developed conditions using a series of computational simulations. With the power law design, the speeds in a parallel channel design are uniformly distributed at low Reynolds numbers, with a standard deviation of less than 3% of the overall mean channel speed. At higher Reynolds numbers, some mal-distribution is observed due to developing flow conditions, but it is not as significant as with typical untapered designs.

ODTLES simulations of wall-bounded flows

Abstract: ODTLES is a novel multi-scale model for 3D turbulent flow based on the one-dimensional-turbulence model of Kerstein [“One-dimensional turbulence: Model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows,” J. Fluid Mech. 392, 277 (1999)]. Its key distinction is that it is formulated to resolve small-scale phenomena and capture some 3D large-scale features of the flow with affordable simulations. The present work demonstrates this capability by considering four types of wall-bounded turbulent flows. This work shows that spatial profiles of various flow quantities predicted with ODTLES agree fairly well with those from direct numerical simulations. It also shows that ODTLES resolves the near-wall region, while capturing the following 3D flow features: the mechanism increasing tangential velocity fluctuations near a free-slip wall, the large-scale recirculation region in lid-driven cavity flow, and the secondary flow in square duct flow.

Flow past two rotating cylinders

Abstract: Flow past two uniformly rotating cylinders with the same rotation rates in a side-by-side configuration is studied experimentally. The experiments are carried out at Reynolds numbers, Re, of 100, 200, 300, 400, and 500 and nondimensional rotation rates, α, varying from 0 to 5. The spacing ratios, T/D, are 1.8, 2.5, 4.0, and 7.5. Two possibilities of rotations are considered with the cylinder surfaces in between the two cylinders moving upstream in one case (inward rotation case) and downstream in the other (outward rotation case). The diagnostics is done by flow visualization using hydrogen bubble technique and quantitative measurements using particle image velocimetry (PIV). We present, using extensive flow visualization, the global view of the wake structure at Re of 200 for various rotation rates, and two senses. Vortex shedding suppression is studied through flow visualization and/or PIV at various Re’s, T/D’s, and two senses. Vortex shedding is found to be suppressed in the inward rotation cases at a...

Global instabilities in diverging channel flows

Abstract: A global stability study of a divergent channel flow reveals features not obtained hitherto by making either the parallel or the weakly non-parallel (WNP) flow assumption. A divergent channel flow is chosen for this study since it is the simplest spatially developing flow: the Reynolds number is constant downstream, and for a theoretical Jeffery–Hamel flow, the velocity profile obeys similarity. Even in this simple flow, the global modes are shown to be qualitatively different from the parallel or WNP. In particular, the disturbance modes are often not wave-like, and the local scale, estimated from a wavelet analysis, can be a function of both streamwise and normal coordinates. The streamwise variation of the scales is often very different from the expected linear variation. Given recent global stability studies on boundary layers, such spatially extended modes which are not wave-like are unexpected. A scaling argument for why the critical Reynolds number is so sensitive to divergence is offered.

Viscous Swirling Flow over a Stretching Cylinder

Abstract: We investigate a viscous flow over a cylinder with stretching and torsional motion. There is an exact solution to the Navier—Stokes equations and there exists a unique solution for all the given values of the flow Reynolds number. The results show that velocity decays faster for a higher Reynolds number and the flow penetrates shallower into the ambient fluid. All the velocity profiles decay algebraically to the ambient zero velocity.