Showing papers on "Hele-Shaw flow published in 1994"

Flow structure in a three‐dimensional bubble column and three‐phase fluidized bed

Abstract: Macroscopic flow structures of 3-D bubble columns and gas-liquid-solid fluidization systems under various operating conditions are studied using particle image velocimetry. Flow visualization is also conducted with the aid of a laser sheeting technique. The refractive index matching technique is used to eliminate the opaqueness of solid particles occurring in the visualization study of gas-liquid-solid fluidization. Three flow regimes (dispersed bubble, vortical-spiral flow, and turbulent flow) are identified. The flow structure is investigated for various operating variables including liquid velocity, gas velocity, and particle holdups. Four flow regions (descending flow, vortical-spiral flow, fast bubble flow, and central plume) can generally be characterized in the vortical-spiral flow regime where the gross circulation pattern occurs. A conceptual model for the flow structure in the vortical-spiral flow regime is discussed. The transition of the flow regimes and structure in the vortical-spiral flow regime is postulated to be related to the Taylor instability for flow between two concentric rotating cylinders. Similarities between the flow structures of 2- and 3-D beds are also discussed.

Reynolds Number Effects in Wall-Bounded Turbulent Flows

Abstract: This paper reviews the state of the art of Reynolds number effects in wall-bounded shear-flow turbulence, with particular emphasis on the canonical zero-pressure-gradient boundary layer and two-dimensional channel flow problems. The Reynolds numbers encountered in many practical situations are typically orders of magnitude higher than those studied computationally or even experimentally. High-Reynolds number research facilities are expensive to build and operate and the few existing are heavily scheduled with mostly developmental work. For wind tunnels, additional complications due to compressibility effects are introduced at high speeds. Full computational simulation of high-Reynolds number flows is beyond the reach of current capabilities. Understanding of turbulence and modeling will continue to play vital roles in the computation of high-Reynolds number practical flows using the Reynolds-averaged Navier-Stokes equations. Since the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed towards the low Reynolds numbers, the key question in such high-Reynolds number modeling as well as in devising novel flow control strategies is: what are the Reynolds number effects on the mean and statistical turbulence quantities and on the organized motions? Since the mean flow review of Coles (1962), the coherent structures, in low-Reynolds number wall-bounded flows, have been reviewed several times. However, the Reynolds number effects on the higher-order statistical turbulence quantities and on the coherent structures have not been reviewed thus far, and there are some unresolved aspects of the effects on even the mean flow at very high Reynolds numbers. Furthermore, a considerable volume of experimental and full-simulation data have been accumulated since 1962. The present article aims at further assimilation of those data, pointing to obvious gaps in the present state of knowledge and highlighting the misunderstood as well as the ill-understood aspects of Reynolds number effects.

Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion

Abstract: A direct numerical simulation, based on spectral methods, has been used to compute the time-dependent, axisymmetric viscous flow past a rigid sphere. An investigation has been made for oscillatory flow about a zero mean for different Reynolds numbers and frequencies. The simulation has been verified for steady flow conditions, and for unsteady flow there is excellent agreement with Stokes flow theory at very low Reynolds numbers. At moderate Reynolds numbers, around 20, there is good general agreement with available experimental data for oscillatory motion. Under steady flow conditions no separation occurs at Reynolds number below 20; however in an oscillatory flow a separation bubble forms on the decelerating portion of each cycle at Reynolds numbers well below this. As the flow accelerates again the bubble detaches and decays, while the formation of a new bubble is inhibited till the flow again decelerates. Steady streaming, observed for high frequencies, is also observed at low frequencies due to the flow separation. The contribution of the pressure to the resultant force on the sphere includes a component that is well described by the usual added-mass term even when there is separation. In a companion paper the flow characteristics for constant acceleration or deceleration are reported.

Transition to chaos in converging–diverging channel flows: Ruelle–Takens–Newhouse scenario

Abstract: Direct numerical simulations of the transition process from laminar to chaotic flow in converging–diverging channels are presented. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic self‐sustained flow regimes. The numerical experiments reveal three distinct bifurcations as the Reynolds number is increased, each adding a new fundamental frequency to the velocity spectrum. In addition, frequency‐locked periodic solutions with independent but synchronized periodic functions are obtained. A scenario similar to the Ruelle–Takens–Newhouse scenario of the onset of chaos is verified in this forced convective open system flow. The results are illustrated for different Reynolds numbers using time‐velocity histories, Fourier power spectra, and phase space trajectories. The global structure of the self‐sustained oscillatory flow for a periodic regime is also discussed.

Measurement of the scaling of the dissipation at high Reynolds numbers

Abstract: We present experimental results from a mechanically driven turbulent flow in helium gas at low temperature. A large range of Reynolds numbers, extending over three decades (up to 5000 for ${\mathit{R}}_{\ensuremath{\lambda}}$) is investigated. We perform torque measurements and determine the dissipation locally by two methods, using the third-order structure function and the energy spectrum. Related quantities, such as the Kolmogorov and Taylor scales, are determined. Both methods give consistent measurements for ${\mathit{R}}_{\ensuremath{\lambda}}$g1000 but differences are observed at lower values. The scaling of the dissipation is determined by using a single power law to fit the whole range of Reynolds numbers; we recover the classical value (exponent equal to 3) when dissipation is calculated by using a third-order structure function, while a significantly lower value is obtained when a spectral method is used. The question of the viscosity dependence of the dissipation is thus left open. Several issues, such as the anisotropy, homogeneity of the flow, and Taylor hypothesis are discussed.

Large-Eddy Simulation of Turbulent Flow through a Straight Square Duct and a 180° Bend

Abstract: LES is expected to become a powerful tool for turbulent flow calculations of practical interest in the near future. The paper is concerned with the development and first applications of a finite-volume method based on curvilinear body-fitted grids suitable to simulate flows in or around complex geometries. Two different subgrid-scale models are implemented and tested. Because the near-wall region cannot be resolved for high-Reynolds-number flows, two different wall function approaches are applied. The turbulent flow through a straight duct at two different Reynolds numbers (Re = 4410/56690) and a 180° bend (Re = 56690) is investigated. While for the low-Reynolds-number flow the results are in close agreement with DNS and other LES data, the higher Reynolds number computations are not yet satisfactory when compared with available measurements. However, the main features of the flows like Prandtl’s secondary motion of first and second kind are reasonably predicted by LES.

Flows induced in a cylinder with both end walls rotating

Abstract: The flow field inside a cylindrical container induced by the rotation of the top and bottom end walls with a fixed sidewall is described. For this problem, this paper shows that stagnation points occur along the axis of rotation between the midplane of symmetry and the rotating end walls for appropriate values of the characteristic parameters, viz., the Reynolds number and the aspect ratio of the container. Aspect ratios of 0.5, 0.8, 1.0, and 1.5 were examined over a range of Reynolds numbers from 100 to 2000. As the Reynolds number increased beyond a critical value a recirculation zone surrounding a columnar vortex core in the meridional‐plane flow pattern is predicted to occur near the midplane. This toroidal vortex is different from the type B vortex breakdown phenomenon that occurs in cylindrical containers with only one end wall rotating.

Periodic steady vortices in a stagnation-point flow

Abstract: A stagnation point flow of the form U = (0, Ay, - Az) is unstable to three-dimensional disturbances. It has been shown that the vorticity components of such a disurbance that are perpendicular to the direction of the diverging flow will decay, and that the parallel component of vorticity can grow. We augment these findings by showing that fully nonlinear steady-state deviations from this flow exist that consist of a periodic distribution of counter-rotating vortices whose axes lie parallel to the direction of the diverging flow. These solutions have two independent parameters : the dimensionless strength of the converging flow, and the intensity of the vortices. We examine the structure of these vortices in the asymptotic limits of large strain rate of the converging flow, and of large amplitude of the vortices. In this paper we look at three-dimensional steady perturbations (which need not be small) to a steady two-dimensional stagnation point flow, or extensional flow, of the form U = (0, Ay, - Az) with A > 0. Originally motivated by a desire for a simple model of mixing between converging streams of gases, we considered the possible existence of steady-state solutions to the Navier-Stokes equation that are perturbations to this stagnation-point flow. With this geometry it is easy to show that any nonlinear perturbation to this stagnation-point flow that initially has no y-dependence will retain this property throughout its evolution. We exploit this feature by looking for solutions to the steady problem that consist of perturbations with no y-dependence. We find solutions to the governing equations that consist of a periodic row of steady counterrotating vortices, with axes parallel to the y-axis. The vortices found are reminiscent of the vortex in an axisymmetric converging flow found by Burgers (1948). In both cases the persistent state of the vortices is due to a balance between the intensification of the vorticity due to the stretching of the vortex lines by the diverging flow parallel to the vortex axes, and the dissipation of the vorticity due to viscosity. As with the Burgers vortex the vortices found here can have arbitrary strength. Although this problem was initially investigated as a theoretical exercise, the flows found do have application to real fluid flow phenomena. The undisturbed background flow considered here is good approximation to the flow in a ‘four-roll mill’ used by Taylor (1934) in his study of droplet breakup. The stability of this two-dimensional flow has received little theoretical attention. Pearson (1959) found that, in the context of homogeneous turbulence, the extensional flow was always unstable. Aryshev, Golovin & Ershin (1981) looked at the linear stability of an inviscid fluid in such a regime, while Lagnado, Phan-Thien & Leal (1984), as a special case in their investigation of the stability of general two-dimensional linear flows, found an explicit expression for the temporal and spatial evolution of an arbitrary linear disturbance to

Low-dimensional description of the dynamics in separated flow past thick airfoils

Abstract: Results are presented for the numerical simulation of unsteady viscous incompressible flow past thick airfoils. Specifically, flow past a NACA 4424 at an angle of attack of 2.5 deg and Reynolds numbers in the range of 1700-4000 has been simulated using the spectral element method. At these conditions the flow is separatedd and an unsteady wake is formed. Application of the method of empirical eigenfunction reveals the structure of the most energetic components of the flow. These are found to occur in pairs that, through phase exchange, are responsible for the vortex shedding. A set of ordinary differential equations is obtained for the amplitudes of these eigenfunctions by a Galerkin projection of the Navier-Stokes equations. The solutions of the model system are compared with the full simulation. The work is of relevance to the transition process and observed routes to chaos in airfoil wakes.

Feedback control to delay or advance linear loss of stability in planar Poiseuille flow

Abstract: By using linear stability theory, we demonstrate theoretically that the critical Reynolds number for the loss of stability of planar Poiseuille flow can be significantly increased or decreased through the use of feedback control strategies which enhance or suppress disturbance dissipating mechanisms in the flow. The controller studied here consists of closely packed, wall mounted, shear stress sensors and thermoelectric actuators. The sensors detect flow instabilities and direct the actuators to alter the fluid’s viscosity by modulating the adjacent wall temperature in such a way as to suppress or enhance flow instabilities. Results are presented for water and air flows.

Applied fluid mechanics

Abstract: 1. Introduction to Fluid Mechanics. 2. Fluid Statics. 3. Mass, Energy, and Momentum Balances. 4. Viscous Flow and Friction: Confined, Open, Free Stream, and Porous Media Flows. 5. Introduction to Differential Fluid Mechanics. 6. Unidirectional Flows. 7. Two-dimensional Laminar Flows: Creeping, Potential, and Boundary Layer Flows. 8. Nearly Unidirectional Flows: Lubrication and Stretching Flows. 9. Rheology and Flows of Non-Newtonian Liquids. 10. Turbulent Flow and Mixing. Appendices. Index.

The motion of particles in the Hele-Shaw cell

Abstract: The force and torque on a particle that translates, rotates, or is held stationary in an incident flow within a channel with parallel-sided walls, are considered in the limit of Stokes flow. Assuming that the particle has an axisymmetric shape with axis perpendicular to the channel walls, the problem is formulated in terms of a boundary integral equation that is capable of describing arbitrary three-dimensional Stokes flow in an axisymmetric domain. The method involves: (a) representing the flow in terms of a single-layer potential that is defined over the physical boundaries of the flow as well as other external surfaces, (b) decomposing the polar cylindrical components of the velocity, boundary surface force, and single-layer potential in complex Fourier series, and (c) collecting same-order Fourier coefficients to obtain a system of one-dimensional Fredholm integral equations of the first kind for the coefficients of the surface force over the traces of the natural boundaries of the flow in an azimuthal plane. In the particular case where the polar cylindrical components of the boundary velocity exhibit a first harmonic dependence on the azimuthal angle, we obtain a reduced system of three real integral equations. A numerical method of solution that is based on a standard boundary element-collocation procedure is developed and tested. For channel flow, the effect of domain truncation on the nature of the far flow is investigated with reference to plane Hagen–Poiseuille flow past a cylindrical post. Numerical results are presented for the force and torque exerted on a family of oblate spheroids located above a single plane wall or within a parallel-sided channel. The effect of particle shape on the structure of the flow is illustrated, and some novel features of the motion are discussed. The numerical computations reveal the range of accuracy of previous asymptotic solutions for small or tightly fitting spherical particles.

Three-dimensional finite element analysis of polymeric fluid flow in an extrusion die. Part I: Entrance effect

Abstract: The Galerkin finite element method has been applied to study the three-dimensional flow field of power-law fluids inside an extrusion die. Two inlet designs, i.e., center-fed and end-fed, have been considered. The effects of inertial force as represented by the Reynolds number Re, inlet geometry, and the power-law index n on lateral flow uniformity and vortex formation in the entrance region have been examined. A flow visualization technique has been carried out to experimentally verify the theoretical prediction of the three-dimensional flow field inside a die. It has been found that increasing Re or decreasing n will deteriorate flow uniformity. Depending on the direction of the inlet jet stream, the inertial force may create a flow peak in the central region of a center-fed die, or the maximum flow rate will appear close to the end of the die for an end-fed die. For highly shear-thinning fluids, lower flow rates are always observed close to the end of the dies. It is concluded that creating a plug flow in the inlet tube of the extrusion die is advantageous for both center-fed and end-fed designs.

Circular Couette flow with pressure-driven axial flow and a porous inner cylinder

Abstract: In a rotating filter separator a suspension is introduced at one end of the annulus between a rotating porous inner cylinder and a fixed impermeable outer cylinder. The filtrate is removed through the inner cylinder and the concentrate is removed from the opposite end of the annulus from which the suspension entered. The flow in a rotating filter separator is circular Couette flow with a pressure-driven axial flow and a suction boundary condition at the inner cylinder. Flow visualization was used to determine the effect of the Taylor number, axial Reynolds number, and radial Reynolds number on the types of flows present in the annulus. A rich variety of secondary vortical flows appear, depending upon the flow parameters. The radial inflow at the inner cylinder delays the appearance of supercritical circular Couette flow and prevents the appearance of certain flow regimes that have a helical vortex structure. Nevertheless, the average azimuthal velocity measured using laser Doppler velocimetry indicates that the velocity profile is nearly the same for all supercritical flow regimes.

Advances in control-volume-based finite-element methods for compressible flows

Abstract: Recent developments in the application of a control-volume-based finite-element method, that has proven successful in solving incompressible flow problems, to the solution of compressible flow problems are presented. The finite Element Differential Scheme (FIELDS) is demonstrated to retain the pressure checker boarding problem for the case of Euler flow under certain conditions of flow. The source of this is investigated and remedies are provided that surmount this problem for all flows including Euler flows. Success is demonstrated for incompressible flow and a formulation is provided for extension to compressible flows. One dimensional testing on a supersonic converging-diverging nozzle exhibits extremely high accuracy of flow prediction including both shock strength and sharpness of resolution.

Free-surface Taylor vortices

Abstract: The hydrodynamic instability of a viscous incompressible flow with a free surface is studied both numerically and experimentally. While the free-surface flow is basically two-dimensional at low Reynolds numbers, a three-dimensional secondary flow pattern similar to the Taylor vorticies between two concentric cylinders appears at higher rotational speeds. The secondary flow has periodic velocity components in the axial direction and is characterized by a distinct spatially periodic variation in surface height similar to a standing wave. A numerical method, using boundary-fitted coordinates and multigrid methods to solve the Navier–Stokes equations in primitive variables, is developed to treat two-dimensional free-surface flows. A similar numerical technique is applied to the linearized three-dimensional perturbation equations to treat the onset of secondary flows. Experimental measurements have been obtained using light sheet techniques to visualize the secondary flow near the free surface. Photographs of streak lines were taken and compared to the numerical calculations. It has been shown that the solution of the linearized equations contains most of the important features of the nonlinear secondary flows at Reynolds number higher than the critical value. The experimental results also show that the numerical method predicts well the onset of instability in terms of the critical wavenumber and Reynolds number.

The Development of the Mean Flow and Turbulence Structure in an Annular S-Shaped Duct

Abstract: This paper describes an investigation of the mean and fluctuating flow field within an annular S-shaped duct which is representative of that used to connect the compressor spools of aircraft gas turbine engines. Data was obtained from a fully annular test facility using a 3-component Laser Doppler Anemometry (LDA) system. The measurements indicate that development of the flow within the duct is complex and significantly influenced by the combined effects of streamwise pressure gradients and flow curvature. In addition CFD predictions of the flow, using both the k-e and Reynolds stress transport equation turbulence models, are compared with the experimental data. Whereas curvature effects are not described properly by the k-e model, such effects are captured more accurately by the Reynolds stress model leading to a better prediction of the Reynolds shear stress distribution. This, in turn, leads to a more accurate prediction of the mean velocity profiles, as reflected by the boundary layer shape parameters, particularly in the critical regions of the duct where flow separation is most likely to occur.© 1994 ASME

On the Unsteady and Turbulent Characteristics of the Three-Dimensional Shear-Driven Cavity Flow

Abstract: The three-dimensional shear-driven cavity flow is numerically investigated at Reynolds numbers of 5000 and 10000. This investigation focuses on the unsteadiness and turbulent characteristics of the flow. At the moderate Reynolds number (Re=5000) where the cauity flow is fully laminar, a direct numerical simulation (DNS) is used whereas large-eddy simulation (LES) methodology is adopted to predict the cavity flow at the higher Reynolds number (Re=10000). Establishing a suitable form for the subgrid scale (SGS) turbulence model in this complex flow is guided by the DNS results at Re=5000. Additionally, the SGS model is verified against DNS results at Re=7500 where the cavity flow is known through experimentation to be locally transitional

Non-linear and unsteady flow analysis of flow in a viscous flowmeter

Abstract: An experimental and theoretical investigation has been undertaken on a viscous flowmeter, with both steady and unsteady flow. The steady flow analysis quantifies the nonlinear effects of entry and exit losses, development length effects and compressibility effects. The steady flow analysis and experiments show that the pressure drop has a quadratic response to flowrate, but that for practical applications a linear approximation will lead to an error of less than 1%.The unsteadyflow experiments show that it is necessary to integrate the instantaneous flow over a whole number of cycles, in order to obtain reliable values of the mean flow. An analysis of unsteady viscous flow has been used to show how the instantaneous pressure difference measured across the viscous flowmeter can be analysed to give the instantaneous volume flow rate.

A numerical study of the viscous supersonic flow past a flat plate at large angles of incidence

Abstract: A numerical study of the viscous supersonic flow past a flat plate is presented. The objective is to investigate the supersonic flow at high angles of incidence where large flow gradients occur. The effect of the angle of incidence and the Reynolds number (Re) in the flow structure especially in the formation of the separation region is investigated. The study is based on the solution of the full Navier–Stokes equations by high resolution schemes, and it focuses on the supersonic flow over the plate at Re≤105. Results on fine computational grids are presented for flow angles up to 20°. The calculations reveal that the flow remain attached for angles of incidence less than a=5°. For a=5° and Re=105, separation of the flow at the trailing edge appeared. Increasing the flow angle (a≳5°) moves the separation point upstream while a reverse flow region forms for the entire range of the Reynolds numbers used in this study. The results reveal that for large angles of incidence, the variation of the Reynolds numbe...

The effects of flow split ratio and flow rate in manifolds

Abstract: This paper reports a combined experimental and numerical investigation of three-dimensional steady turbulent flows in inlet manifolds of square cross-section. Predictions and measurements of the flows were carried out using computational fluid dynamics and laser Doppler anemometry techniques respectively. The flow structure was characterized in detail and the effects of flow split ratio and inlet flow rate were studied. These were found to cause significant variations in the size and shape of recirculation regions in the branches, and in the turbulence levels. It was then found that there is a significant difference between the flow rates through different branches. The performance of the code was assessed through a comparison between predictions and measurements. The comparison demonstrates that all important features of the flow are well represented by the predictions.

Near-wake characteristics of various V-shaped bluff bodies

Abstract: Mechanism of vortex shedding and turbulent flow features of the near-wake flow behind regular/irregular v-shaped bluff bodies are experimentally investigated at various airflow speeds between 10-60 m/s. With the aid of schlieren photography and a three-beam, two-component backward-scattering LDA system, the phenom- ena of vortex shedding and flow recirculation behind the flameholder are well illustrated. Results show Strouhal numbers, based on vortex shedding frequencies, being independent of gutter shape and within a range of 0.23- 0.25. A similar flow structure of flow exists among near wake flows of v-gutters with different span angles. Increase of Reynolds number monotonically reduces the size of the recirculation zone. Variation in attack angle only slightly changes mean flow features, but enhances normalized Reynolds shear stresses in the near-wake. NTRODUCING a t?luff body into the airstream is an ef- fective way of holding the flame in ramjet combustors and thrust augmenters. Ample evidence has shown aerodynamic characteristics of the near-wake flow behind a v-gutter having crucial influence on flame structures and flameholding mech- anisms. This type of flow, however, is associated with com- plicated phenomena such as separation and recirculation, mass entrainment through the shear layers, and vortex shedding. Many of these detailed mechanisms have not yet been well understood. Extensive research1"4 was conducted on ranges of fuel con- centration, flow velocity, fuel air ratio, and blockage ratio with the flame stably sustained. Nicholson and Field5 com- pared various experimental methodologies; they also used a high-speed camera for recording the wake flow patterns. Longwell6 and William et al.7 investigated effects of the mixing on oscillation of flow velocity and pressure. Rao and Lefebvre8 and Stwalley and Lefebvre9 measured effects of flameholder shape on limits of stabilization . Previous research primarily focused on overall performance of flame stabilization of the gutter and flame stability limits. Little research concentrated on aerodynamical aspect. Vortex shedding process in shear layers supposedly has a close interaction with wake flow structures. Roshko10 used a hot wire anemometer and a pitot tube in investigating the flow past a circular cylinder at a very high Reynolds number of 10 7. Strouhal number increased with Reynolds number when the Reynolds number was less than 3.5 x 10 6. Future research on recirculation zone was proposed. Mechanism of formation and shedding of vortices in wake region were stud- ied by Gerrad.11 He used wake width as the characteristic length, determining the dimensionless vortex shedding fre- quency. Unal and Rockwell12 used a water channel in ex- ploring the wake flow with Reynolds number less than 5000. Good quality photographs of wake flow pattern at a low Rey- nolds number were obtained, reporting Strouhal number as remaining at 0.2, while the Reynolds number was higher than '1000.

A High-Resolution Finite Difference Scheme for Supersonic Wet-Stream Flows.

Abstract: A high-resolution finite difference method to simulate the gas-liquid two-phase flow is proposed taking account of the apparent compressibility which characterizes high -speed two -phase flow phenomena. The speed of sound and the total energy for the gas-liquid two-phase fluid flows are re-estimated based on the assumption of homogeneous and the thermodynamic relations. Here, the homogeneous two-phase flow model assuming a local equilibrium is adopted. The basic equations for the two-phase mixture flow similar to those of the ordinary single-phase compressible gas flow are solved using the upwind finite difference scheme based on the theory of characteristics. To elucidate the applicability of the present scheme, some numerical calculations of wet-steam nozzle flows with condensation were implemented. The calculated results are in good agreement with the existing experimental data.