Showing papers on "Hele-Shaw flow published in 1996"

On boundary conditions in lattice Boltzmann methods

Abstract: A lattice Boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. Numerical simulations, including two‐dimensional Poiseuille flow, unsteady Couette flow, lid‐driven square cavity flow, and flow over a column of cylinders for a range of Reynolds numbers, are carried out, showing that this scheme is of second order accuracy in space discretization. Applications of the method to other boundary conditions, including pressure condition and flux condition are discussed.

Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity

Abstract: A summary of experimental results on structure functions obtained using extended self-similarity in various flow configurations (jet, grid, mixing layer, duct flow, cylinder) at Reynolds numbers ranging between 30 and 5000 is presented.

Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step

Abstract: A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds number Re = 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability analysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalues of a base flow state. The distinction is made between convectively and absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up to Re = 2500 are time-independent in the absence of any external excitation, whereas the flow is convectively unstable, in a large portion of the flow domain, for Reynolds numbers in the range 700 [les ] Re [les ] 2500. Consequently, upstream generated small disturbances propagate downstream at exponentially amplified amplitude with a space-dependent speed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, selective sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two different types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from the shear layer frequency; and (ii) random noise. It is found that for small-amplitude monochromatic excitation the flow acquires a time-periodic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequency. On the other hand, for the random noise as input, an unsteady behaviour is obtained with a fundamental frequency close to the shear layer frequency.

On the stability of an axisymmetric rotating flow in a pipe

Abstract: The linear stability of an inviscid, axisymmetric and rotating columnar flow in a finite length pipe is studied. A well posed model of the unsteady motion of swirling flows with compatible boundary conditions that may reflect the physical situation is formulated. A linearized set of equations for the development of infinitesimal axially‐symmetric disturbances imposed on a base rotating columnar flow is derived. Then, a general mode of axisymmetric disturbances, that is not limited to the axial‐Fourier mode, is introduced and an eigenvalue problem is obtained. Benjamin’s critical state concept is extended to the case of a rotating flow in a finite length pipe. It is found that a neutral mode of disturbance exists at the critical state. In the case of a solid body rotating flow with a uniform axial velocity component, analytical solution of the eigenvalue problem is found. It is demonstrated that the flow changes its stability characteristics as the swirl changes around the critical level. When the flow is ...

Couette-Taylor Flow in a Dilute Polymer Solution

Abstract: We present experimental evidence of the striking influence of small additions of high molecular weight polymers on stability and pattern selection in Couette-Taylor flow. Two novel oscillatory flow patterns were observed. One of them is essentially due to the fluid elasticity. The other results from inertial instability modified by the elasticity.

Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers

Abstract: High-resolution numerical simulations (with up to 2563 modes) are performed for three-dimensional flow driven by the large-scale constant force fy = F cos(x) in a periodic box of size L = 2π (Kolmogorov flow). High Reynolds number is attained by solving the Navier-Stokes equations with hyperviscosity (-1)h+1Δh (h = 8). It is shown that the mean velocity profile of Kolmogorov flow is nearly independent of Reynolds number and has the ‘laminar’ form vy = V cos(x) with a nearly constant eddy viscosity. Nevertheless, the flow is highly turbulent and intermittent even at large scales. The turbulent intensities, energy dissipation rate and various terms in the energy balance equation have the simple coordinate dependence a + b cos(2x) (with a, b constants). This makes Kolmogorov flow a good model to explore the applicability of turbulence transport approximations in open time-dependent flows. It turns out that the standard expression for effective (eddy) viscosity used in K-[Escr ] transport models overpredicts the effective viscosity in regions of high shear rate and should be modified to account for the non-equilibrium character of the flow. Also at large scales the flow is anisotropic but for large Reynolds number the flow is isotropic at small scales. The important problem of local isotropy is systematically studied by measuring longitudinal and transverse components of the energy spectra and crosscorrelation spectra of velocities and velocity-pressure-gradient spectra. Cross-spectra which should vanish in the case of isotropic turbulence decay only algebraically but somewhat faster than corresponding isotropic correlations. It is verified that the pressure plays a crucial role in making the flow locally isotropic. It is demonstrated that anisotropic large-scale flow may be considered locally isotropic at scales which are approximately ten times smaller than the scale of the flow.

High Reynolds number flow simulations using the localized dynamic subgrid-scale model

Abstract: The localized dynamic subgrid-scale model introduced by Kirn & Menon (1995), has been used hi large-eddy simulations of decaying and forced isotropic turbulence, and temporally evolving turbulent mixing layer for high Reynolds numbers. In the simulations of isotropic turbulence, it is demonstrated that the low-resolution large-eddy simulation results accurately reproduce the characteristics of a realistic, high-Reynolds number turbulence such as the powerlaw decay (decaying case), and the velocity statistics and the development of the non-Gaussian statistics (forced case). From the large-eddy simulations of temporally evolving turbulent mixing layer, the tuneaccurate results, which agree very well with the existing high-resolution direct numerical simulation and experimental data, are obtained using a new scaling which is capable of separating the distinct effects of initial development on the self-similar stage of the mixing layer evolution.

Models of non-Newtonian Hele-Shaw flow

Abstract: One reason for the enduring interest in Newtonian fluid flow in Hele-Shaw cells is its close analogy to quasistatic solidification. The Saffman-Taylor ~ST! instability of the driven fluid-fluid interface plays the same role as the Mullins-Sekerka instability of the solidification front @1#. Features usually associated with solidification, such as the growth of stable dendritic fingers and sidebranching, have also been observed in fluids with an imposed anisotropy, say by scoring lines on the plates of the cell @2#. However, experiments using non-Newtonian or anisotropic fluids, such as liquid crystals, have shown that ‘‘solidification’’ structures can be induced by the bulk properties of the fluid itself @3‐5#. The precise mechanisms of generating such dendritic fingers with stable tips are unknown. One of our interests is in liquid crystal flows, which are characterized by complicated hydrodynamics @6#. We conjecture that stable tip propagation in these materials is a consequence of shear thinning associated with flow induced realignment of the liquid crystal director. In this paper we focus on this single property, and consider an expanding gas bubble in a radial HeleShaw cell containing a shear-thinning liquid. In recent work on polymeric fluids, Bonn and co-workers @7# proposed modeling the Hele-Shaw flow of a nonNewtonian fluid by positing the modified Darcy’s law

On the instability of pipe Poiseuille flow

Abstract: Stability of the flow of incompressible viscous fluid in a circular pipe is studied numerically. A perturbation consisting of finite‐amplitude two‐dimensional and infinitesimal three‐dimensional parts is imposed on the basic flow. The temporal evolution of the perturbation is analyzed by direct numerical calculation of the Navier–Stokes equations. The two‐dimensional disturbances are independent of the streamwise coordinate and initially take the form of streamwise rolls. It is shown that the nonlinear development of two‐dimensional perturbations results in substantial spanwise modulation of the streamwise velocity component manifesting itself as a formation of streaks and the occurrence of inflection points. The modulated mean flow is found to be highly unstable to the three‐dimensional perturbations which are localized spatially near these points. An instability mechanism that includes the modulation of the flow by growing two‐dimensional disturbances and the inflectional instability of the modulated flow to three‐dimensional perturbations is proposed.

Single fluid flow in porous media

Abstract: A comprehensive study on single fluid flow in porous media is carried out. The volume averaging technique is applied to derive the governing flow equations. Additional terms appear in the averaged governed equations related to porosity e, tortuosity τ, shear factor F and hydraulic dispersivity D h. These four parameters are uniquely contained in the volume averaged Navier-Stokes equation and not all of them are independent. The tortuosity can be related to porosity through the Brudgemann equation, for example, for unconsolidated porous media. The shear factor models are reviewed and some new results are obtained concerning high porosity cases and for turbulent flows. It is known that there are four regions of flow in porous media: pre-Darcy's flow, Darcy's flow, Forchheimer flow and turbulent flow. The transitions between these regions arc smooth. The first region, the pre-Darcy's flow region represents the surface-interactive flows and hence is strongly dependent on the porous media and the flowing fluid...

Stokes slip flow between corrugated walls

Abstract: Stokes flow between corrugated plates in microdomains has been analyzed using a perturbation method. This approach used the incompressible Navier-Stokes equations, but the velocity-slip is present along the solid-fluid interface. For the slip flow regime, if we introduce Knudsen number (Kn) herein, 0.01 ≤Kn≤ 0.1, the total flow rate is increasing as a ratio of 1 + 6Knto no-slip Stokes flow. If we consider fixedKncases, the corrugations still decrease the flow rate, consideringO(e2) terms, and the decrease is maximum as the phase shift becomes 180 °.

Stability of flow in a channel with a suddenly expanded part

Abstract: The stability of a two‐dimensional flow in a symmetric channel with a suddenly expanded part is investigated numerically and analyzed by using the method of the nonlinear stability theory. From results of the numerical simulation, it is shown that the flow is steady, symmetric and unique at very low Reynolds numbers, while the symmetric flow loses its stability at a critical Reynolds number resulting in an appearance of asymmetric flow. The transition from the steady symmetric flow to the steady asymmetric one is found to occur due to the symmetry breaking pitchfork bifurcation when the aspect ratio, the ratio of the length of the expanded part to its width, is large. It is also found that the bifurcated flow becomes symmetric again when the Reynolds number is increased and the resultant symmetric flow loses its stability becoming periodic in time as the Reynolds number is further increased. On the other hand, when the aspect ratio is small there occurs no pitchfork bifurcation and the direct transition from the steady symmetric flow to a periodic flow occurs due to a Hopf bifurcation. The critical aspect ratio is found to be about 2.3. The critical Reynolds numbers for these bifurcations are evaluated.

Study of the von Karman flow between coaxial corotating disks

Abstract: We report an experimental study of the swirling flow generated in the gap between two coaxial corotating disks. We use a free geometry, i.e., unshrouded disks in air, with moderate to high Reynolds numbers. When the relative rotation rate is varied, transitions in the flow can be observed by global power measurement and are related to the geometry of the external recirculating flow. The mean flow is studied in details with hot‐wire measurements using a boxcar‐type averaging technique. It involves a single turbulent vortex undergoing a slow precession motion. We show that statistical properties of the turbulent fluctuations are affected by the dynamics of the mean flow, which also displays a correlation with the global power fluctuations.

Free-surface flows with near-critical flow conditions

Abstract: Open channel flow situations with near-critical flow conditions are often characterised by the development of free-surface instabilities (i.e. undulations). The paper develops a review of several near-critical flow situations. Experimental results are compared with ideal-fluid flow calculations. The analysis is completed by a series of new experiments. The results indicate that, for Froude numbers slightly above unity, the free-surface characteristics are very similar. However, with increasing Froude numbers, distinctive flow patterns develop.

The development of asymmetry and period doubling for oscillatory flow in baffled channels

Abstract: We report experimental and numerical observations on the way initially symmetric and time-periodic fluid oscillations in baffled channels develop in complexity Experiments are carried out in a spatially periodic baffled channel with a sinusoidal oscillatory flow At modest Reynolds number the observed vortex structure is symmetric and time periodic At higher values the flow progressively becomes three-dimensional, asymmetric and aperiodic A two-dimensional simulation of incompressible Newtonian flow is able to follow the flow pattern at modest oscillatory Reynolds number At higher values we report the development of both asymmetry and a period-doubling cascade leading to a chaotic flow regime A bifurcation diagram is constructed that can describe the progressive increase in complexity of the flow

Fluid flow across mass fractals and self-affine surfaces

Abstract: We use a lattice-gas method to simulate the slow flow of a fluid in systems with fractal surfaces and volumes. Two systems are studied. One is flow in a single three-dimensional fracture with self-affine surfaces. The other is flow across a three-dimensional diffusion-limited aggregate. In both cases, significant deviations from classical results are observed.

Flow over an obstacle emerging from the wall of a channel

Abstract: Direct simulation of laminar flow over a rising obstacle (an actuator) reveals the presence of vortical structures identical to those found in flow over a stationary obstacle, intensified and stretched by the upward velocity of the boundary. Following deceleration of the actuator to a stationary position, this amplification leads to a vortex shedding event in the wake region as the flow evolves toward its steady state. Three obstacle shapes are analyzed: one is streamwise symmetric, and two are skew symmetric. The symmetric actuator is also raised into a higher Reynolds number flow and in a final test is raised at half-speed into the low Reynolds number flow. Results indicate that the time scale of the transient is independent of Reynolds number, depending primarily upon the rising time of the actuator and to a lesser degree its shape. A CTIVE control in the turbulent boundary layer of a wallbounded flow is an area of research that has significant implications for the air transport industry: substantial reductions in fuel costs may be achieved through small reductions in skin-friction drag; higher operating temperatures (and better efficiency) may be obtained in gas turbines through control of the heat transfer between exhaust gases from the combustor and the turbine blades. Different strategies for control include mass transfer through porous walls1 and so-called smart skins: an actuator on the wall responds to a flow by adjusting its height to steer the wall region dynamics (the bursting processes that are signatures of turbulent'flows and primary sources of momentum and heat transport).2 Critical to the success of active control is not only an understanding of near-wall turbulence (a great deal of research has been directed toward this over the past 30 years) but also an understanding of the phenomena that are to be used to effect control—the transient behavior of flow over a moving obstacle (concerning which little data are available). Flows over three-dimensional, stationary obstacles have been studied in the laboratory, in the physical domain, and through numerical simulation.3"6 In a comprehensive survey consisting of both experimental and computational tests, Mason and Morton7 have analyzed laminar, steady flows past a variety of stationary obstacles. As an extension of this body of work, focus is redirected toward transients associated with obstacles that emerge in time, utilizing an algorithm that simulates flow in a channel with three-dimensional, time-dependent wall geometries. The code has been verified using wall geometries for which there exist known steady and unsteady solutions8; this includes comparisons with data from Mason and Morton.7 Between these benchmark tests involving simpler flows and the control work involving turbulent flows fall intermediate analyses of transients associated with low and moderate Reynolds number laminar flows over rapidly emerging obstacles. To distinguish between the stationary and the rising obstacle, the latter shall be referred to as an actuator. Three actuator shapes have been selected, one streamwise symmetric and two skew symmetric. All are smooth functions, symmetric in the spanwise (crossflow) direction. As in the cases analyzed by Mason and Morton,7 Reynolds numbers have been chosen that lie below the value at which flow (over a stationary obstacle) becomes unsteady. Using a local Reynolds number (Ret), based on obstacle height and the mean velocity that would exist through the height interval

Spatio—temporal behaviour in a rotating annulus with a source—sink flow

Abstract: The axisymmetric flows arising in a rotating annulus with a superimposed forced flow are investigated with a pseudo-spectral numerical method. The flow enters the annulus at the inner radius with a radial velocity, then develops into a geostrophic flow azimuthally directed and flanked by two Ekman (nonlinear) boundary layers, and finally exits the outer radius, with a radially directed velocity. In this study the rotation rate of the cavity is fixed and very high. When the forced flow is weak, the flow is steady. On increasing the mass flow rate, the flow evolves to a chaotic temporal behaviour through several bifurcations, which perturbs the basic spatial configuration of the flow. The first bifurcation drives the steady state into an oscillatory regime, associated with a break of symmetry with respect to the midheight of the annulus. The entry flow travels radially through the cavity as in the steady flow, but it wavers and then is alternately sucked towards each Ekman layer. The frequency of this oscillation is close to the rotation rate frequency of the cavity, which is characteristic of inertial waves in rotating flows. A second transition to a quasi-periodic regime is characterized by the appearance of a second frequency. Further increases in the flow rate lead to a period-five state, via a locking of both frequencies, and then to a chaotic motion. This second frequency is of the order of the inverse of the Ekman spin-up characteristic time, suggesting that this instability is originated by the relaxation of the perturbations in the flow field. These perturbations of the unsteady flow field are corotating vortices along the rigid boundary walls. They are excited by the entry flow and their strength diminishes with increasing radius due to the low value of the Reynolds number. The parameters characterizing the unstable flows are also consistent with this explanation. The conclusion is that in this configuration, the origin of the described dynamical behaviour is not the instability of the Ekman boundary layers, as could be expected, but the instability of the entry flow. The reason is the importance of the nonlinear inertial terms in cavities with small radius of curvature.

Long range exhaustion : A mathematical model for the axisymmetric air flow of a local exhaust ventilation hood assisted by a turbulent radial jet

Abstract: Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art flanged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air flow to be reduced and provide a means of identifying and assessing the various parameters that control the air flow. The mathematical model is formulated in terms of the Stokes steam function, Ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained flow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions.

Compressible fluid flow in micron sized channels

Abstract: One-dimensional compressible flow models for isothermal and adiabatic flow in microchannels are developed and verified by comparison with a two-dimensional approximate model and available experimental results. The one-dimensional model was found to predict the mass flow rate of helium flow through a duct measuring 1.33 {micro}m by 52.25 {micro}m by 7,500 {micro}m to within 1% of those predicted by the two-dimensional model for specified inlet and outlet conditions. The results are also in good agreement with the experimental mass flow measurements. In addition, the important quantities in microflow analysis, i.e., Reynolds, Mach, and Knudsen numbers, as well as the channel hydraulic diameter, are analyzed via a parametric study. Finally, the effect of rarefaction on drag coefficient is compared with the experimental results. The comparison showed a decrease in drag coefficient for low Reynolds number flows in microchannels.

Distribution of particles suspended in convective flow in differentially heated cavity

Abstract: Our aim is to explore, both experimentally and theoretically, the cumulative effects of small particle–liquid density difference, where the particles are used as tracers in recirculating flow. As an example we take a flow field generated in a differentially heated cavity. The main flow structure in such a cavity consists in one or two spiraling motions. Long‐term observations of such structures with the help of tracers (small particles) indicated that accumulation of the particles may set in at some flow regions. For theoretical insight into the phenomenon, a simple analytical model of recirculating (rotating) flow was studied. It was assumed that particles are spherical and rigid, and their presence does not affect the flow field. The particle Reynolds number is negligibly small, hence only the effects of particle–liquid density difference are of importance. Besides buoyancy, the effects of Saffman’s force and the inertial forces are also taken into account when calculating particle trajectories. Both cases were analyzed, particles with density slightly higher and lower than the fluid. It was found that in our case the inertial forces are egligible. In the numerical experiment trajectories of particles were investigated. The particles were allocated at random in the flow field obtained by numerical solution of the natural convection in the differentially heated cavity. In the experimental part, behavior of a dilute particle suspension in the convective cell was explored. In the model‐analytical study of a simple spiraling motion, it was found that due to the interaction of the recirculating convective flow field and the gravity‐buoyancy force, the particles may be trapped in some flow regions, whereas the rest of the flow field becomes particle‐free. This prediction agrees fairly well with the numerical and experimental findings.

High-enthalpy, hypersonic compression corner flow

Abstract: The results of an experimental investigation of high-enthalpy, hypersonic flow over sharp leading-edge compression corners are presented and discussed. In particular, the possible effects of real gas behavior are examined. Measurements have been made of the heat transfer and pressure distributions for flat plate and compression corner flow. Some flow visualization data have also been obtained. Test flows were generated using a free-piston shock tunnel operating in the reflected mode. The reservoir enthalpy ranged from 3 to 19 MJ kg -1 , giving freestream speeds of 2.3-5.5 km s -1 . For these conditions, the flow remains laminar throughout. The flat plate data for both high- and low-enthalpy flows are in agreement with the reference enthalpy method for heat transfer and the weak interaction theory for pressure. Also, the measured flat plate boundary-layer thickness compares well with an expression strictly valid for perfect gas flows only. The high- and low-enthalpy compression corner flows have upstream influence and plateau pressure behavior similar to perfect gas flow. That is, real gas effects for the present flows appear to be negligible. This is consistent with the essentially chemically frozen viscous and inviscid flow upstream of the interaction.