Showing papers on "Hele-Shaw flow published in 2009"

On vortex shedding from an airfoil in low-Reynolds-number flows

Abstract: Development of coherent structures in the separated shear layer and wake of an airfoil in low-Reynolds-number flows was studied experimentally for a range of airfoil chord Reynolds numbers, 55 × 10 3 ≤ Re c ≤ 210 × 10 3 , and three angles of attack, α = 0°, 5° and 10°. To illustrate the effect of separated shear layer development on the characteristics of coherent structures, experiments were conducted for two flow regimes common to airfoil operation at low Reynolds numbers: (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results demonstrate that roll-up vortices form in the separated shear layer due to the amplification of natural disturbances, and these structures play a key role in flow transition to turbulence. The final stage of transition in the separated shear layer, associated with the growth of a sub-harmonic component of fundamental disturbances, is linked to the merging of the roll-up vortices. Turbulent wake vortex shedding is shown to occur for both flow regimes investigated. Each of the two flow regimes produces distinctly different characteristics of the roll-up and wake vortices. The study focuses on frequency scaling of the investigated coherent structures and the effect of flow regime on the frequency scaling. Analysis of the results and available data from previous experiments shows that the fundamental frequency of the shear layer vortices exhibits a power law dependency on the Reynolds number for both flow regimes. In contrast, the wake vortex shedding frequency is shown to vary linearly with the Reynolds number. An alternative frequency scaling is proposed, which results in a good collapse of experimental data across the investigated range of Reynolds numbers.

A Phase Diagram for Turbulent, Transitional, and Laminar Clay Suspension Flows

Abstract: New phase diagrams for the dynamic structure of clay-laden open-channel flows are proposed. These diagrams can be used to distinguish between turbulent Newtonian, transitional, and laminar non-Newtonian flow behavior, on the basis of the balance between turbulent forces (approximated by the horizontal components of flow velocity and turbulence intensity) and cohesive forces (approximated by the suspended clay concentration and rheology). Stability regimes for five different flow types are defined using a comprehensive series of laboratory flume experiments at depth-averaged flow velocities ranging from 0.13 m s−1 to 1.47 m s−1, and at volumetric kaolinite clay concentrations ranging from 0.03% (= 0.8 g L−1) to 16.7% (= 434 g L−1). As clay concentration increases, five flow types can be distinguished: turbulent flow, turbulence-enhanced transitional flow, lower and upper transitional plug flow, and quasi-laminar plug flow. The turbulent properties of transitional flows are shown to be considerably more complex than the common notion of gradual turbulence damping. Turbulence-enhanced transitional flows display higher turbulence intensity than turbulent flows of similar velocity, with such enhancement originating from development of a highly turbulent basal internal shear layer within ~ 0.01 m of the bed. In lower transitional plug flows, the basal internal shear layer separates a lower region of high vertical gradient in horizontal velocity and strong turbulence from an upper region of plug flow with a much gentler velocity gradient and lower turbulence intensity. Kelvin-Helmholtz shear instabilities within the highly turbulent shear layer are expressed as distinct second-scale oscillations in the time series of downstream velocity. Turbulence damping dominates upper transitional plug flows, because strong cohesive forces, inferred to be caused by gelling of the high-concentration clay suspension, start to outbalance turbulent forces. In quasi-laminar plug flows, gelling is pervasive and turbulence is fully suppressed, apart from some minor residual turbulence near the base of these flows. With very few exceptions, all flows pass through the same development stages as clay concentration increases, regardless of their velocity, but the threshold concentrations for turbulence enhancement, gelling, and development of internal shear layers and plug flows are proportional to flow velocity. At flow velocities below ~ 0.5 m s−1, only low concentrations (< 0.75%) of kaolinite are required to induce transitional flow behavior, thus potentially affecting many slow-moving and decelerating clay flows in natural sedimentary environments. However, at flow velocities above 1 m s−1, clay concentrations of at least 6% are required in order for flows to enter the transitional flow phase, but even at these velocities the transitional flow phases make up a significant proportion of the flow phase space. By converting the experimental data to nondimensional Froude number (momentum term) and Reynolds number (cohesive term), it is shown that each boundary between the turbulent, transitional, and laminar flow phases can be described by a specific narrow range of Reynolds numbers. Within the duration of the experiments, settling of clay particles occurred only in plug flows of low flow velocity (and low Froude number), when the flows lacked the strength to support the entire clay suspension load.

Droplet formation and stability of flows in a microfluidic T-junction

Abstract: Flow regimes obtained as a consequence of two immiscible fluids interacting at a T-junction are presented for high Capillary numbers and different flow rates of the continuous and dispersed phases. Through lattice Boltzmann based simulations, a regime map is created that distinguishes parallel flows from droplet flows. Simulations show the dependence of flow rates and viscosity ratio on the volume of droplets formed, which is compared with existing experimental data. At high Capillary numbers, the transition zone which separates parallel and droplet flows shrinks, and is influenced by the viscosity ratio as well.

Coupled Generalized Nonlinear Stokes Flow with Flow through a Porous Medium

Abstract: In this article, we analyze the flow of a fluid through a coupled Stokes-Darcy domain. The fluid in each domain is non-Newtonian, modeled by the generalized nonlinear Stokes equation in the free flow region and the generalized nonlinear Darcy equation in the porous medium. A flow rate is specified along the inflow portion of the free flow boundary. We show existence and uniqueness of a variational solution to the problem. We propose and analyze an approximation algorithm and establish a priori error estimates for the approximation.

Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels

Abstract: We investigate the stability of steady planar stagnation flows of a dilute polyethylene oxide (PEO) solution using T-shaped microchannels. The precise flow rate control and well-defined geometries achievable with microfluidic fabrication technologies enable us to make detailed observations of the onset of elastically driven flow asymmetries in steady flows with strong planar elongational characteristics. We consider two different stagnation flow geometries; corresponding to T-shaped microchannels with, and without, a recirculating cavity region. In the former case, the stagnation point is located on a free streamline, whereas in the absence of a recirculating cavity the stagnation point at the separating streamline is pinned at the confining wall of the microchannel. The kinematic differences in these two configurations affect the resulting polymeric stress fields and control the critical conditions and spatiotemporal dynamics of the resulting viscoelastic flow instability. In the free stagnation point flow, a strand of highly oriented polymeric material is formed in the region of strong planar extensional flow. This leads to a symmetry-breaking bifurcation at moderate Weissenberg numbers followed by the onset of three-dimensional flow at high Weissenberg numbers, which can be visualized using streak-imaging and microparticle image velocimetry. When the stagnation point is pinned at the wall this symmetry-breaking transition is suppressed and the flow transitions directly to a three-dimensional time-dependent flow at an intermediate flow rate. The spatial characteristics of these purely elastic flow transitions are compared quantitatively to the predictions of two-dimensional viscoelastic numerical simulations using a single-mode simplified Phan-Thien–Tanner (SPTT) model.

Computational and experimental study of gas flows through long channels of various cross sections in the whole range of the Knudsen number

Abstract: A computational and experimental study has been performed for the investigation of fully developed rarefied gas flows through channels of circular, orthogonal, triangular, and trapezoidal cross sections. The theoretical-computational approach is based on the solution of the Bhatnagar-Gross-Krook kinetic equation subject to Maxwell diffuse-specular boundary conditions by the discrete velocity method. The experimental work has been performed at the vacuum facility “TRANSFLOW,” at Forschungszentrum Karlsruhe and it is based on measuring, for assigned flow rates, the corresponding pressure differences. The computed and measured mass flow rates and conductance are in all cases in very good agreement. In addition, in order to obtain some insight in the flow characteristics, the reference Knudsen, Reynolds, and Mach numbers characterizing the flow at each experimental run have been estimated. Also, the pressure distribution along the channel for several typical cases is presented. Both computational and experimental results cover the whole range of the Knudsen number.

Two-dimensional unsteady laminar flow of a power law fluid across a square cylinder

Abstract: The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ R e ≤ 160 and 0.5 ≤ n ≤ 2.0 . Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The global quantities such as drag coefficients, Strouhal number and the detailed kinematic variables like stream function, vorticity and so on, have been obtained for the above range of conditions. While, over this range of Reynolds number, the flow is known to be periodic in time for Newtonian fluids, a pseudo-periodic flow regime displaying more than one dominant frequency in the lift is observed for shear-thinning fluids. This seems to occur at Reynolds numbers of 120 and 140 for n = 0.5 and 0.6, respectively. Broadly speaking, the smaller the value of the power law index, lower is the Reynolds number of the onset of the pseudo-periodic regime. This work is concerned only with the fully periodic regime and, therefore, the range of Reynolds numbers studied varies with the value of the power law index. Not withstanding this aspect, in particular here, the effects of Reynolds number and of the power law index have been elucidated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening fluid behaviour delays this separation and shows the lowering of the drag coefficient with the Reynolds number. Also, the preliminary results suggest the transition from the steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thinning fluids than that in Newtonian fluids.

A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations

Abstract: In the present paper, three non-Newtonian models for blood are used in a lattice Boltzmann flow solver to simulate non-Newtonian blood flows. Exact analytical solutions for two of these models have been derived and presented for a fully developed 2D channel flow. Original results for the use of the K-L model in addition to the Casson and Carreau-Yasuda models are reported for non-Newtonian flow simulations using a lattice Boltzmann (LB) flow solver. Numerical simulations of non-Newtonian flow in a 2D channel show that these models predict different mass flux and velocity profiles even for the same channel geometry and flow boundary conditions. Which in turn, suggests a more careful model selection for more realistic blood flow simulations. The agreement between predicted velocity profiles and those of exact solutions is excellent, indicating the capability of the LB flow solver for such complex fluid flows.

Pressure-driven miscible two-fluid channel flow with density gradients

Abstract: We study the effect of buoyancy on pressure-driven flow of two miscible fluids in inclined channels via direct numerical simulations. The flow dynamics are governed by the continuity and Navier–Stokes equations, without the Boussinesq approximation, coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity and density. The effect of varying the density ratio, Froude number, and channel inclination on the flow dynamics is examined, for moderate Reynolds numbers. We present results showing the spatiotemporal evolution of the flow together with an integral measure of mixing.

High-speed unsteady flows around spiked-blunt bodies

Abstract: This paper presents a detailed investigation of unsteady supersonic and hypersonic flows around spiked-blunt bodies, including the investigation of the effects of the flow field initialization on the flow results. Past experimental research has shown that if the geometry of a spiked-blunt body is such that a shock formation consisting of an oblique foreshock and a bow aftershock appears, then the flow may be unsteady. The unsteady flow is characterized by periodic radial inflation and collapse of the conical separation bubble formed around the spike (pulsation). Beyond a certain spike length the flow is ‘stable’, i.e. steady or mildly oscillating in the radial direction. Both unsteady and ‘stable’ conditions have been reported when increasing or decreasing the spike length during an experimental test and, additionally, hysteresis effects have been observed. The present study reveals that for certain geometries the numerically simulated flow depends strongly on the assumed initial flow field, including the occurrence of bifurcations due to inherent hysteresis effects and the appearance of unsteady flow modes. Computations using several different configurations reveal that the transient (initial) flow development corresponds to a nearly inviscid flow field characterized by a foreshock–aftershock interaction. When the flow is pulsating, the further flow development is not sensitive to initial conditions, whereas for an oscillating or almost ‘steady’ flow, the flow development depends strongly on the assumed initial flow field.

Hairpin vortex solution in planar couette flow: a tapestry of knotted vortices.

Abstract: A numerical continuation method has been carried out seeking solutions for two distinct flow configurations, planar Couette flow (PCF) and laterally heated flow in a vertical slot (LHF). We found that the spanwise vortex solution in LHF identifies a new solution in PCF. The vortical structure of our new solution has the shape of a hairpin observed ubiquitously in high-Reynolds-number turbulent flow, and we believe this discovery may provide the paradigm for a hierarchical organization of coherent structures in turbulent shear layers.

Flow regimes and parameter dependence in nanochannel flows.

Abstract: Nanoscale fluid flow systems involve both microscopic and macroscopic parameters, which compete with each another and lead to different flow regimes. In this work, we investigate the interactions of four fundamental parameters, including the fluid-fluid, fluid-wall binding energies, temperature of the system, and driving force, and their effects on the flow motion in nanoscale Poiseuille flows. By illustrating the fluid flux as a function of a dimensionless number, which represents the effective surface effect on the fluid, we show that the fluid motion in nanochannels falls into different regimes, each of which is associated with a distinct mechanism. The mechanisms in different situations reveal the effects of the parameters on the fluid dynamics.

System and method to control flowfield vortices with micro-jet arrays

Abstract: The present invention provides a system and method for actively manipulating and controlling aerodynamic or hydrodynamic flow field vortices within a fluid flow over a surface using micro-jet arrays. The system and method for actively manipulating and controlling the inception point, size and trajectory of flow field vortices within the fluid flow places micro-jet arrays on surfaces bounding the fluid flow. These micro-jet arrays are then actively manipulated to control the flow behavior of the ducted fluid flow, influence the inception point and trajectory of flow field vortices within the fluid flow, and reduce flow separation within the primary fluid flow.

Exploration of a Potential-Flow-Based Compact Model of Air-Flow Transport in Data Centers

Abstract: This paper summarizes an exploration of a compact model of air flow and transport in data centers developed from potential flow theory. Boundaries for the airflow in the data center are often complex due to the numerous rows of servers and other equipment in the facility, and there are generally multiple air inlets and outlets, which produce a fairly complex three-dimensional flow field in the air space in the data center. The general problem of airflow and convective transport in a data center requires accurate treatment of a turbulent flow in a complex flow passage with some buoyancy effects. As a result, full CFD thermofluidic models tend to be time-consuming and tedious to set up for such complex flow circumstances. In this initial study, we formulated an approximate model that retains only the most basic physical mechanisms of the flow. The resulting model of air flow in the data center is based on potential flow theory, which is exact for irrotational inviscid flow. The temperature field resulting from server heat input is determined by solving the convective energy transport equation along potential flow streamlines. This innovative approach, which takes advantage of the irrotational character of the modeled flow, provides a fast computational method for determining the temperature field and convective transport of thermal energy in the data center. Computations to predict the three-dimensional flow and temperature fields with the model typically require less than 60 seconds to complete on a laptop computer. Flow and temperature field results predicted by the model for typical data center flow circumstances are presented and limitations of the model are assessed. Features of an intuitive graphical user interface for the model that simplifies input of the data center design parameters are also described. Results for case studies indicate low sensitivity to mesh size and convergence criteria. Although the flow and temperature field models developed here are more approximate than full CFD methods, they are good first approximations that provide the means to rapidly explore the parameter space for the data center design. This model can be used to quickly identify the optimal region of the design space, whereupon a more detailed CFD modeling can be used to fine-tune an optimal design. The results of this investigation demonstrate that this type of fast compact model can be a very useful tool when used as a precursor to full CFD modeling in data center design optimization.© 2009 ASME

Three‐dimensional numerical simulation of compound meandering open channel flow by the Reynolds stress model

Abstract: Turbulent flow in a compound meandering open channel with seminatural cross sections is one of the most complicated turbulent flows as the flow pattern is influenced by the combined action of various forces, such as centrifugal force, pressure, and shear stresses. In this paper, a three-dimensional (3D) Reynolds stress model (RSM) is adopted to simulate the compound meandering channel flows. Governing equations of the flow are solved numerically with finite-volume method. The velocity fields, wall shear stresses, and Reynolds stresses are calculated for a range of input conditions. Good agreement between the simulated results and measurements indicates that RSM can successfully predict the complicated flow phenomenon.

Part load flow in radial centrifugal pumps

Abstract: Centrifugal pumps are required to sustain a stable operation of the system they support under all operating conditions. Minor modifications of the surfaces defining the pump's water passage can influence the tendency to unstable system operation significantly. The action of such modifications on the flow are yet not fully understood, leading to costly trial and error approaches in the solution of instability problems. The part-load flow in centrifugal pumps is inherently time-dependent due to the interaction of the rotating impeller with the stationary diffuser (Rotor-Stator Interaction, RSI). Furthermore, adverse pressure gradients in the pump diffuser may cause flow separation, potentially inducing symmetry-breaking non-uniformities, either spatially stationary or rotating and either steady or intermittent. Rotating stall, characterized by the presence of distinct cells of flow separation on the circumference, rotating at a fraction of the impeller revolution rate, has been observed in thermal and hydraulic turbomachines. Due to its complexity, the part-load flow in radial centrifugal pumps is a major challenge for numerical flow simulation methods. The present study investigates the part-load flow in radial centrifugal pumps and pump-turbines by experimental and numerical methods, the latter using a finite volume discretization of the Reynolds-averaged Navier-Stokes (RANS) equation. Physical phenomena of part load flow are evidenced based on three case studies, and the ability of numerical simulation methods to reproduce part-load flow in radial centrifugal pumps qualitatively and quantitatively is assessed. A numerical study of the flow in a high specific speed radial pump-turbine using steady approaches and the hypothesis of angular periodicity between neighboring blade channels evidences the relation of sudden flow topology changes with an increase of viscous losses, impacting on the energy-discharge characteristic, and thus increasing the risk of unstable operation. When the flow rate drops below a critical threshold, the straight through-flow with flow separation zones attached to the guide vanes changes to an asymmetrical flow. Energy is drawn off the mean flow and dissipated in a large vortex-like structure. Besides flow separation in some diffuser channels, time-dependent numerical simulations of the flow in a double suction pump evidence a flow rate imbalance between both impeller sides interacting with asymmetric flow separation in the diffuser. Viscous losses increase substantially as this imbalance occurs, the resulting segment of positive slope in the energy-discharge characteristic is found for a flow rate sensibly different from measurements. Different modes of rotating stall are identified by transient pressure measurements in a low-specific-speed pump-turbine, showing 3 to 5 zones of separated flow, rotating at 0.016 to 0.028 times impeller rotation rate, depending on discharge. For operating conditions where stall with 4 cells is most pronounced, velocity is measured by Laser-Doppler methods at locations of interest. The velocity field is reconstructed with respect to the passage of stall cells by definition of a stall phase obtained from simultaneous transient pressure measurements. Time-dependent numerical simulation predicting rotating stall with 4 cells shows velocity fields that are in reasonable agreement with the measured velocity fields, but occurring at a sensibly higher flow rate than found from experiments. In consideration of the quantitative shortcomings of the numerical simulation, a novel modelling approach is proposed: Replacing the costly 3-dimensional simulation of the major part of the impeller channels by a 1-dimensional model allows a significant economy in computational resources, allowing an improved modeling for the remainder of the domain at constant computational cost. The model is validated with the challenging cases of rotating stall and impeller side flow rate imbalance. The satisfying coherence of the results with the simulation including the entire impeller channels qualifies this approach for numerous turbomachinery applications. It could also provide improved, time-dependent boundary conditions for draft tube vortex rope simulations at reasonable computational cost. Parameter studies modifying deliberately some quantities of mean flow and turbulence at the modeled boundary surfaces can be implemented in the framework of the method.

Viscous potential flow analysis of radial fingering in a Hele-Shaw cell

Abstract: The problem of radial fingering in two phase gas/liquid flow in a Hele-Shaw cell under injection of gas is studied here. The fingers arise as an instability of a time-dependent flow. The instability is analyzed as a viscous potential flow, in which potential flow analysis of Paterson [L. Paterson, J. Fluid Mech. 113, 513 (1981)] and others is augmented to account for the effects of viscosity on the normal stress at the gas/liquid interface. The addition of these new effects brings our theory into a much better agreement with experiments of Maxworthy [T. Maxworthy, Phys. Rev. A 39, 5863 (1989)] than other theories.

Route to a chaotic state in fluid flow past an inclined flat plate.

Abstract: We present the results of a numerical study of flow past an inclined flat plate and reveal a route of the transition from steady to chaotic flow. We find that the chaotic flow regime can be reached through the sequential occurrence of successive period-doubling bifurcations and various incommensurate bifurcations. The results provide physical insight into the understanding of fundamental flow behaviors underlying in this flow system and complement the transition phenomenon from steady to chaotic flow.