Showing papers on "Hele-Shaw flow published in 2007"

Global stability of base and mean flows : a general approach and its applications to cylinder and open cavity flows

Abstract: This article deals with the first Hopf bifurcation of a cylinder flow, and more particularly with the properties of the unsteady periodic Karman vortex street regime that sets in for supercritical Reynolds numbers Re > 46. Barkley (Europhys. Lett. vol.75, 2006, p. 750) has recently studied the linear properties of the associated mean flow, i.e. the flow which is obtained by a time average of this unsteady periodic flow. He observed, thanks to a global mode analysis, that the mean flow is marginally stable and that the eigenfrequencies associated with the global modes of the mean flow fit the Strouhal to Reynolds experimental function well in the range 46 < Re < 180. The aim of this article is to give a theoretical proof of this result near the bifurcation. For this, we do a global weakly nonlinear analysis valid in the vicinity of the critical Reynolds number Rec based on the small parameter e = Rec−1 − Re−1 ≪ 1. We compute numerically the complex constants λ and μ′ which appear in the Stuart-Landau amplitude equation: dA/dt = e λA − eμ′ A|A|2. Here A is the scalar complex amplitude of the critical global mode. By analysing carefully the nonlinear interactions yielding the term μ′, we show for the cylinder flow that the mean flow is approximately marginally stable and that the linear dynamics of the mean flow yields the frequency of the saturated Stuart-Landau limit cycle. We will finally show that these results are not general, by studying the case of the bifurcation of an open cavity flow. In particular, we show that the mean flow in this case remains strongly unstable and that the frequencies associated with the eigenmodes do not exactly match those of the nonlinear unsteady periodic cavity flow. It will be demonstrated that two precise conditions must hold for a linear stability analysis of a mean flow to be relevant and useful.

Stability of a Jet in Confined Pressure-Driven Biphasic Flows at Low Reynolds Numbers

Abstract: Motivated by its importance for microfluidic applications, we study the stability of jets formed by pressure-driven concentric biphasic flows in cylindrical capillaries. The specificity of this variant of the classical Rayleigh-Plateau instability is the role of the geometry which imposes confinement and Poiseuille flow profiles. We experimentally evidence a transition between situations where the flow takes the form of a jet and regimes where drops are produced. We describe this as the transition from convective to absolute instability, within a simple linear analysis using lubrication theory for flows at low Reynolds number, and reach remarkable agreement with the data.

Role of the elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries

Abstract: We explore the interplay of fluid inertia and fluid elasticity in planar entry flows by studying the flow of weakly elastic solutions through micro-fabricated planar contraction geometries. The small characteristic lengthscales make it possible to achieve a wide range of Weissenberg numbers (0.4 < Wi < 42) and Reynolds numbers (0.03 < Re < 12), allowing access to a large region of Wi-Re space that is typically unattainable in conventional macroscale entry flow experiments. Experiments are carried out using a series of dilute solutions (0.78 < clc* < 1.09) of a high molecular weight polyethylene oxide, in which the solvent viscosity is varied in order to achieve a range of elasticity numbers, 2.8 < El = WilRe < 68. Fluorescent streak imaging and micro-particle image velocimetry ([L-PIV) are used to characterize the kinematics, which are classified into a number of flow regimes including Newtonian-like flow at low Wi, steady viscoelastic flow, unsteady diverging flow and vortex growth regimes. Progressive changes in the centreline velocity profilt are used to identify each of the flow regimes and to map the resulting stability boundaries in Wi-Re space. The same flow transitions can also be detected through measurements of the enhanced pressure drop across the contraction/expansion which arise from fluid viscoelasticity. The results of this work have significant design implications for lab-on-a-chip devices, which commonly contain complex geometric features and transport complex fluids, such as those containing DNA or proteins. The results also illustrate the potential for using micro-fabricated devices as rheometric tools for measuring the extensional properties of weakly elastic fluids. (C) 2007 Elsevier B.V. All rights reserved.

Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows

Abstract: The approach to determine pressure fields and integral loads from planar velocimetry data is discussed, in relation to the implementation for incompressible and compressible flows around two-dimensional objects. The method relies upon the application of control-volume approaches in combination with the deduction of the pressure field from the experimental data, by making use of the flow constitutive equations. In this paper the implementation for two specific application areas is addressed. The first is time-mean pressure field and force evaluation from velocity ensemble statistics, as obtained from time-uncorrelated PIV acquisition, for incompressible flow. Two test cases are considered for this flow regime: the unsteady vortical flow around a square section cylinder at incidence, as well as the force characterization of a low-speed airfoil. The second topic considers the extension of the method to steady compressible flow, with the supersonic flow around a bi-convex airfoil as experimental test case. As in this flow regime the density appears as an extra unknown in the momentum equation, additional flow equations need to be invoked. A convenient approach for this was found, using the gas law and the adiabatic flow condition, with which the pressure-integration procedure becomes essentially the same as for the incompressible case.

Analytical solution of the depth-averaged flow velocity in case of submerged rigid cylindrical vegetation

Abstract: A new model for the depth-averaged velocity for flow in presence of submerged vegetation is developed. The model is based on a two-layer approach, where flow above and through the vegetation layer is described separately. Vegetation is treated as a homogeneous field of identical cylindrical stems, and the flow field is considered stationary and uniform. It is demonstrated that scaling considerations of the bulk flow field can be used to avoid complications associated with smaller scale flow processes and that still the behavior of depth-averaged flow over vegetation is described accurately. The derived scaling expression of the average flow field is simple in form, it follows fundamental laws of fluid flow, and it shows very good agreement with laboratory flume experiments. The new model can be used for quick evaluation of a river’s hydraulic response in cases where vegetated floodplains are inundated.

Visualizations of the flow inside an open cavity at medium range Reynolds numbers

Abstract: The interaction between a laminar boundary layer and an open cavity is investigated experimentally for medium range Reynolds numbers. Flow visualizations are carried out for three different observation directions in order to understand the spatial development of dynamical structures. In particular, synchronized visualizations in two parallel planes picture the transverse development of the flow. The study is conducted by changing the cavity aspect ratio, the Reynolds number and therefore the flow patterns inside the cavity. The issue is to emphasize the 3-D development of the flow. In particular, we show that the dynamical structures are not due to secondary shear layer instabilities.

Statistical analysis of coherent structures in transitional pipe flow

Abstract: Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about $\mathrm{Re}=2200$, and it decreases to about 20% for $\mathrm{Re}=2500$. The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.

Gas-liquid two-phase flow across a bank of micropillars

Abstract: Adiabatic nitrogen-water two-phase flow across a bank of staggered circular micropillars, 100μm long with a diameter of 100μm and a pitch-to-diameter ratio of 1.5, was investigated experimentally for Reynolds number ranging from 5 to 50. Flow patterns, void fraction, and pressure drop were obtained, discussed, and compared to large scale as well as microchannel results. Two-phase flow patterns were determined by flow visualization, and a flow map was constructed as a function of gas and liquid superficial velocities. Significant deviations from conventional scale systems, with respect to flow patterns and trend lines, were observed. A unique flow pattern, driven by surface tension, was observed and termed bridge flow. The applicability of conventional scale models to predict the void fraction and two-phase frictional pressure drop was also assessed. Comparison with a conventional scale void fraction model revealed good agreement, but was found to be in a physically wrong form. Thus, a modified physically ...

Dynamo action at low magnetic Prandtl numbers: mean flow versus fully turbulent motions

Abstract: We compute numerically the threshold for dynamo action in Taylor- Green (TG) swirling flows. Kinematic dynamo calculations, for which the flow field is fixed to its time average, are compared to dynamical runs, with the Navier- Stokes and induction equations jointly solved. The dynamo instability for the kinematic calculations is found to have two branches. The dynamical dynamo threshold at low Reynolds numbers lies within the low branch, while at high Reynolds numbers it gets closer to the high branch. Based on these results, the effect of the mean flow and of the turbulent fluctuations in TG dynamos are discussed.

Computational issues related to iterative coupling of subsurface and channel flows

Abstract: We consider solution techniques for the coupling of Darcy and Stokes flow problems. The study was motivated by the simulation of the interaction between channel flow and subsurface water flow for realistic data and arbitrary interfaces between the two different flow regimes. Here, the emphasis is on the efficient iterative solution of the coupled problem based on efficient solvers for the discrete Stokes and Darcy problems.

A parameterization of flow separation over subaqueous dunes

Abstract: Flow separation plays a key role in the development of dunes, and modeling the complicated flow behavior inside the flow separation zone requires much computational effort. To make a first step toward modeling dune development at reasonable temporal and spatial scales, a parameterization of the shape of the flow separation zone over two-dimensional dunes is proposed herein, in order to avoid modeling the complex flow inside the flow separation zone. Flow separation behind dunes, with an angle-of-repose slip face, is characterized by a large circulating leeside eddy, where a separation streamline forms the upper boundary of the recirculating eddy. Experimental data of turbulent flow over two-dimensional subaqueous bed forms are used to parameterize this separation streamline. The bed forms have various heights and height to length ratios, and a wide range of flow conditions is analyzed. This paper shows that the shape of the flow separation zone can be approximated by a third-order polynomial as a function of the distance away from the flow separation point. The coefficients of the polynomial can be estimated, independent of flow conditions, on the basis of bed form shape at the flow separation point and a constant angle of the separation streamline at the flow reattachment point.

Fluid dynamics with a computational perspective

Abstract: 1. Introduction to viscous flow 2. Elements of computational analysis 3. Creeping flow 4. Intermediate Reynolds numbers 5. High Reynolds number and boundary layer 6. Turbulent flow 7. Compressible flow 8. Interfaces.

Eddy structures in a transitional backward-facing step flow

Abstract: In the present study, flow simulation has been carried out in a backward-facing step channel defined by an expansion ratio of 2.02 and a spanwise aspect ratio of 8 to provide the physical insight into the longitudinal and spanwise flow motions and to identify the presence of Taylor-Gvortices. The Reynolds numbers have been taken as 1000 and 2000, which fall in the category of transitional flow. The present simulated results were validated against the experimental and numerical data and the comparison was found to be satisfactory. The simulated results show that the flow becomes unsteady and exhibits a three-dimensional nature with the Kelvin-Helmholtz instability oscillations and Taylor-Glongitudinal vortices. The simulated data were analysed to give an in-depth knowledge of the complex interactions among the floor and roof eddies, and the spiralling spanwise flow motion. Destabilization of the present incompressible flow system, with the amplified Reynolds number due to the Kelvin-Helmholtz and Taylor-G¨ ortler instabilities, is also highlighted. A movie is available with the online version of the paper.

Unsteady simulations of the flow around a short surface-mounted cylinder

Abstract: The flow around a surface-mounted circular cylinder, of height/diameter ratio 1 with a free end, is simulated using large-eddy simulation (LES) and detached-eddy simulation (DES) at a Reynolds number based on diameter of 200 000. A comparison is made between the abilities of the two models to capture flow features observed in particle image velocimetry (PIV) experiments carried out by the authors. The flow contains three interacting features formed from the junction flow between the cylinder and the ground, separation from the cylinder wall and resultant turbulent wake, and the flow over the free-end of the cylinder. Both LES and DES overpredict the length of the recirculation region by 30%, but the turbulence quantities are close to the measured values. The topology of the flow over the free-end is confirmed as consisting of an arch or 'mushroom' vortex. Due to the high Reynolds number the grid resolution is insufficient to resolve the approaching ground-plane boundary layer flow with LES, leading to inaccuracies in the horseshoe vortex system. The DES model improves this area, though still has grid induced separation effects.

Fluxes and energy dissipation in thermal convection and shear flows

Abstract: We expose analogies between turbulence in a fluid heated from below (Rayleigh-Benard (RB) flow) and shear flows: The unifying theory for RB flow (see Grossmann S. and Lohse D., J. Fluid Mech., 407 (2000) 27 and subsequent refinements) can be extended to the flow between rotating cylinders (Taylor-Couette flow) and pipe (Poiseuille) flow. We identify "wind" dissipation rates and momentum fluxes that are analogous to the dissipation rate and heat flux in RB flow. The proposed unifying description for the three cases is consistent with the experimental data.

Flow in microchannels with rough walls: flow pattern and pressure drop

Abstract: In this paper perturbation methods are introduced to study the laminar flow in microchannels between two parallel plates with rough wall surfaces. By a coordinate transformation, the physical domain of the microchannel is transformed into the computational one. The relative roughness as a small parameter presents the governing equations resulting from the coordinate transformation. The equations are linearized through applying the perturbation method, and the spectral collocation method is employed to solve the perturbation equations. Furthermore, the boundary perturbation method is used to analyze the spatially-averaged pressure drop of the microchannel. The numerical results show that flow in microchannels with rough surfaces is quite different from Poiseuille flow: there exist apparent fluctuations and periodic variations of vorticity along the flow direction in the flow field; flow is viscously dominant under the conditions of a low Reynolds number and the flow separations happen in the troughs of wavy walls at a high Reynolds number. The spatially-averaged pressure drop being subject to the invariable flow rate could be greater than, equal to or even less than the theoretical value, which is qualitatively consistent with the results of the microfluidic experiments.

Computation of Mean Flow and Thermal Characteristics of Incompressible Turbulent Offset Jet Flows

Abstract: Two-dimensional, steady, incompressible, forced convection turbulent flow at high Reynolds number is considered. Mean velocity and thermal characteristics are presented for the wall and offset jet flows. The standard k–ϵ model is used. Finite volume-based SIMPLE algorithm is followed and the powerlaw scheme is used for the convective terms. The developed code is tested for offset flow and compared with the experimental results. Computational details of various mean flow and turbulent parameters (k, ϵ, ν t) are presented and explained for different offset ratios (OR).

Variable-density miscible displacements in a vertical Hele-Shaw cell: linear stability

Abstract: A computational study based on the Stokes equations is conducted to investigate the effects of gravitational forces on miscible displacements in vertical Hele-Shaw cells. Nonlinear simulations provide the quasi-steady displacement fronts in the gap of the cell, whose stability to spanwise perturbations is subsequently examined by means of a linear stability analysis. The two-dimensional simulations indicate a marked thickening (thinning) and slowing down (speeding up) of the displacement front for flows stabilized (destabilized) by gravity. For the range investigated, the tip velocity is found to vary linearly with the gravity parameter. Strongly stable density stratifications lead to the emergence of flow patterns with spreading fronts, and to the emergence of a secondary needle-shaped finger, similar to earlier observations for capillary tube flows. In order to investigate the transition between viscously driven and purely gravitational instabilities, a comparison is presented between displacement flows and gravity-driven flows without net displacements. The linear stability analysis shows that both the growth rate and the dominant wavenumber depend only weakly on the P´ eclet number. The growth rate varies strongly with the gravity parameter, so that even a moderately stable density stratification can stabilize the displacement. Both the growth rate and the dominant wavelength increase with the viscosity ratio. For unstable density stratifications, the dominant wavelength is nearly independent of the gravity parameter, while it increases strongly for stable density stratifications. Finally, the kinematic wave theory of Lajeunesse et al. (J. Fluid Mech. vol. 398, 1999, p. 299) is seen to capture the stability limit quite accurately, while the Darcy analysis misses important aspects of the instability.

Experimental studies of multi-layer flows using a visco-plastic lubricant

Abstract: In a core-annular pipe flow, if the outer lubricating fluid has a yield stress, it is possible for the flow to be both linearly and nonlinearly stable; see Frigaard [I.A. Frigaard, Super-stable parallel flows of multiple visco-plastic fluids, J. Non Newtonian Fluid Mech. 100 (2001) 49–76] or Moyers-Gonzalez et al. [M.A. Moyers-Gonzalez, I.A. Frigaard, C. Nouar, Nonlinear stability of a visco-plastically lubricated viscous shear flow, J. Fluid Mech. 506 (2004) 117–146]. In this paper we provide an experimental demonstration that such flows can be observed in a laboratory setting. Approximately 120 experiments using Xanthan and Carbopol solutions have been carried out and show that stable axisymmetric flows can be established and persist stably over many hundreds of diameters. Via control of the individual fluid flow rates, it is also possible to vary the inner fluid radius over a significant range, which suggests utility for various industrial processes.

Heat transfer and fluid flow around semi-circular tube in cross flow at different orientations

Abstract: Fluid flow and heat transfer characteristics around a semi-circular tube in cross flow were experimentally and numerically investigated. Three different tube-flow arrangements were considered. Firstly, the flat surface of the tube was placed parallel to the freestream flow; secondly, the flat surface of the tube was facing the upstream flow and thirdly, the curved surface of the tube was facing the upstream flow. For the second and the third arrangements, different angles of attack were studied. Flow visualization was carried out to illustrate streamlines around the tube and to verify flow patterns obtained from the numerical calculations. It was found that: (1) for any angle of attack, the arrangement of the curved surface facing the flow gave higher average Nusselt number than the arrangement of the flat surface facing the flow and (2) for all tube-flow arrangements, increasing the angle of attack slightly increases the average Nusselt number. Correlations of Nusselt numbers in terms of Reynolds number and angle of attack were deduced from the experimental results for the three arrangements. The comparisons between the experimental data, correlations’ predictions and numerical results showed reasonable agreements.

Numerical study of transonic cavity flows using large-eddy and detached-eddy simulation

Abstract: Numerical analysis of the flow in weapon bays modelled as open rectangular cavities of length-to-depth (L/D) ratio of 5 and width-to-depth (W/D) ratio of 1 with doors-on and doors-off is presented. Flow conditions correspond to Mach and Reynolds numbers (based on cavity length) of 0.85 and 6.783m respectively. Results from unsteady Reynolds-averaged Navier-Stokes (URANS), large-eddy simulation (LES) and detached-eddy simulation (DES) are compared with the simulation methods demonstrating the best prediction of this complex flow. It was found that URANS was not able to predict the change of flow characteristics between the doors-on and doors-off configurations. In addition, the energy content of the cavity flow modes was much better resolved with DES and LES. Further, the DES was found to be quite capable for this problem giving accurate results (within 3dB of) experiments and appears to be a promising alternative to LES for modelling massively separated flows.

Geometric evolution equations in critical dimensions

Abstract: We make a qualitative comparison of phenomena occurring in two different geometric flows: the harmonic map heat flow in two space dimensions and the Yang–Mills heat flow in four space dimensions. Our results are a regularity result for the degree-2 equivariant harmonic map flow, and a blow-up result for an equivariant Yang–Mills-like flow. The results show that qualitatively differing behaviours observed in the two flows can be attributed to the degree of the equivariance.

Adiabatic Flow Boiling in Fractal-Like Microchannels

Abstract: Fractal-like branching channels are proposed for a number of microscale applications, including heat sinks, heat exchangers, absorbers, desorbers, and micro-mixers. Based on model predictions, the benefit of fractal-like channel designs is a lower pressure drop than parallel straight channels for a given flow rate, when compared to an equal channel surface area basis with the terminal channel cross-section of the fractal-like network used to define the parallel channel geometry. The fractal-like flow networks are a unique geometry that follows fractal bifurcation patterns, in this case mimicking the flow patterns found in nature. Two-phase flow applications require an understanding of how the geometric constraints impact the flow characteristics during multiphase flow. One-dimensional modeling predictions are used in this study to asses the relative impact of flow network designs on pressure drop and void fraction distributions for adiabatic flow boiling. The characterization of the flow networks includes...