Showing papers on "Hele-Shaw flow published in 2016"

On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces

Abstract: Superhydrophobic surfaces can significantly reduce hydrodynamic skin drag by accommodating large slip velocity near the surface due to entrapment of air bubbles within their micro-scale roughness elements. While there are many Stokes flow solutions for flows near superhydrophobic surfaces that describe the relation between effective slip length and surface geometry, such relations are not fully known in the turbulent flow limit. In this work, we present a phenomenological model for the kinematics of flow near a superhydrophobic surface with periodic post-patterns at high Reynolds numbers. The model predicts an inverse square root scaling with solid fraction, and a cube root scaling of the slip length with pattern size, which is different from the reported scaling in the Stokes flow limit. A mixed model is then proposed that recovers both Stokes flow solution and the presented scaling, respectively, in the small and large texture size limits. This model is validated using direct numerical simulations of turbulent flows over superhydrophobic posts over a wide range of texture sizes from L+ ≈ 6 to 310 and solid fractions from ϕs = 1/9 to 1/64. Our report also embarks on the extension of friction laws of turbulent wall-bounded flows to superhydrophobic surfaces. To this end, we present a review of a simplified model for the mean velocity profile, which we call the shifted-turbulent boundary layer model, and address two previous shortcomings regarding the closure and accuracy of this model. Furthermore, we address the process of homogenization of the texture effect to an effective slip length by investigating correlations between slip velocity and shear over pattern-averaged data for streamwise and spanwise directions. For L+ of up to O(10), shear stress and slip velocity are perfectly correlated and well described by a homogenized slip length consistent with Stokes flow solutions. In contrast, in the limit of large L+, the pattern-averaged shear stress and slip velocity become uncorrelated and thus the homogenized boundary condition is unable to capture the bulk behavior of the patterned surface.

Fluid flow over and through a regular bundle of rigid fibres

Abstract: The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

The flow of a foam in a two‐dimensional porous medium

Abstract: Foams have been used for decades as displacing fluids for enhanced oil recovery and aquifer remediation, and more recently, for remediation of the vadose zone, in which case foams carry chemical amendments. Foams are better injection fluids than aqueous solutions due to their low sensitivity to gravity and because they are less sensitive to permeability heterogeneities, thus allowing a more uniform sweep. The latter aspect results from their peculiar rheology, whose understanding motivates the present study. We investigate foam flow through a two-dimensional porous medium consisting of circular obstacles positioned randomly in a horizontal transparent Hele-Shaw cell. The local foam structure is recorded in situ, which provides a measure of the spatial distribution of bubble velocities and sizes at regular time intervals. The flow exhibits a rich phenomenology including preferential flow paths and local flow nonstationarity (intermittency) despite the imposed permanent global flow rate. Moreover, the medium selects the bubble size distribution through lamella division-triggered bubble fragmentation. Varying the mean bubble size of the injected foam, its water content, and mean velocity, we characterize those processes systematically. In particular, we measure the spatial evolution of the distribution of bubble areas, and infer the efficiency of bubble fragmentation depending on the various control parameters. We furthermore show that the distributions of bubble sizes and velocities are correlated. This study sheds new light on the local rheology of foams in porous media and opens the way toward quantitative characterization of the relationship between medium geometry and foam flow properties. It also suggests that large-scale models of foam flows in the subsurface should account for the correlation between bubble sizes and velocities.

Stability of stratified two-phase flows in horizontal channels

Abstract: Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems the stratified flow with a smooth interface is stable only in confined zone of relatively low flow rates, which is in agreement with experiments, but is not predicted by long-wave analysis. Depending on the flow conditions, the critical perturbations can originate mainly at the interface (so-called "interfacial modes of instability") or in the bulk of one of the phases (i.e., "shear modes"). The present analysis revealed that there is no definite correlation between the type of instability and the perturbation wavelength.

Laminarisation of flow at low Reynolds number due to streamwise body force

Abstract: It is well established that when a turbulent flow is subjected to a non-uniform body force, the turbulence may be significantly suppressed in comparison with that of the flow of the same flow rate and hence the flow is said to be laminarised. This is the situation in buoyancy-aided mixed convection when severe heat transfer deterioration may occur. Here we report results of direct numerical simulations of flow with a linear or a step-change profile of body force. In contrast to the conventional view, we show that applying a body force to a turbulent flow while keeping the pressure force unchanged causes little changes to the key characteristics of the turbulence. In particular, the mixing characteristics of the turbulence represented by the turbulent viscosity remain largely unaffected. The so-called flow laminarisation due to a body force is in effect a reduction in the apparent Reynolds number of the flow, based on an apparent friction velocity associated with only the pressure force of the flow (i.e. excluding the contribution of the body force). The new understanding allows the level of the flow ‘laminarisation’ and when the full laminarisation occurs to be readily predicted. In terms of the near-wall turbulence structure, the numbers of ejections and sweeps are little influenced by the imposition of the body force, whereas the strength of each event may be enhanced if the coverage of the body force extends significantly away from the wall. The streamwise turbulent stress is usually increased in accordance with the observation of more and stronger elongated streaks, but the wall-normal and the circumferential turbulent stresses are largely unchanged.

Simulation of microscale gas flow in heterogeneous porous media based on the lattice Boltzmann method

Abstract: A microscale multi-relaxation-time lattice Boltzmann model with the regularization procedure is adopted to simulate gas flow in different porous media. The diffuse reflection boundary condition is used to deal with the random solid boundaries. Because of the complex geometry of the pores, the characteristic length is no longer a constant but a function of the pore locations for the porous media. A rational method is proposed to obtain the local characteristic lengths of the porous media for the microscale gas flow simulations. The simulation results show that gas flow characteristics in different flow regions are notably different. In the continuum flow region and slip flow region, the gas flow abilities in different pores are quite different. The effect of heterogeneity of the porous media on gas velocity distribution is very obvious. As the Knudsen number increases, the differences of gas flow abilities in different pores decrease. For gas flow in the strong transition flow region and free molecular flo...

Numerical and experimental analysis of local flow phenomena in laminar Taylor flow in a square mini-channel

Abstract: The vertically upward Taylor flow in a small square channel (side length 2 mm) is one of the guiding measures within the priority program “Transport Processes at Fluidic Interfaces” (SPP 1506) of the German Research Foundation (DFG). This paper presents the results of coordinated experiments and three-dimensional numerical simulations (with three different academic computer codes) for typical local flow parameters (bubble shape, thickness of the liquid film, and velocity profiles) in different cutting planes (lateral and diagonal) for a specific co-current Taylor flow. For most quantities, the differences between the three simulation results and also between the numerical and experimental results are below a few percent. The experimental and computational results consistently show interesting three-dimensional flow effects in the rear part of the liquid film. There, a local back flow of liquid occurs in the fixed frame of reference which leads to a temporary reversal of the direction of the wall shear stress during the passage of a Taylor bubble. Notably, the axial positions of the region with local backflow and those of the minimum vertical velocity differ in the lateral and the diagonal liquid films. By a thorough analysis of the fully resolved simulation results, this previously unknown phenomenon is explained in detail and, moreover, approximate criteria for its occurrence in practical applications are given. It is the different magnitude of the velocity in the lateral film and in the corner region which leads to azimuthal pressure differences in the lateral and diagonal liquid films and causes a slight deviation of the bubble from the rotational symmetry. This deviation is opposite in the front and rear parts of the bubble and has the mentioned significant effects on the local flow field in the rear part of the liquid film.

Dynamic unified RANS-LES simulations of high Reynolds number separated flows

Abstract: The development of hybrid RANS-LES methods is seen to be a very promising approach to enable efficient simulations of high Reynolds number turbulent flows involving flow separation. To contribute to further advances, we present a new, theoretically well based, dynamic hybrid RANS-LES method, referred to as DLUM. It is applied to a high Reynolds number flow involving both attached and separated flow regimes: a periodic hill flow is simulated at a Reynolds number of 37 000. Its performance is compared to pure LES, pure RANS, other hybrid RANS-LES (given by DLUM modifications), and experimental observations. It is shown that the use of this computational method offers huge cost reductions (which scale with Re/200, Re refers to the Reynolds number) of very high Reynolds number flow simulations compared to LES, it is much more accurate than RANS, and more accurate than LES, which is not fully resolved. In particular, this conclusion does also apply to the comparison of DLUM and pure LES simulations on rather c...

A pancake droplet translating in a Hele-Shaw cell: lubrication film and flow field

Abstract: We adopt a boundary integral method to study the dynamics of a translating droplet confined in a Hele-Shaw cell in the Stokes regime. The droplet is driven by the motion of the ambient fluid with the same viscosity. We characterize the three-dimensional (3D) nature of the droplet interface and of the flow field. The interface develops an arc-shaped ridge near the rear-half rim with a protrusion in the rear and a laterally symmetric pair of higher peaks; this pair of protrusions has been identified by recent experiments (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501) and predicted asymptotically (Burgess and Foster, Phys. Fluids A, vol. 2 (7), 1990, pp. 1105-1117). The mean film thickness is well predicted by the extended Bretherton model (Klaseboer et al., Phys. Fluids, vol. 26 (3), 2014, 032107) with fitting parameters. The flow in the streamwise wall-normal middle plane is featured with recirculating zones, which are partitioned by stagnation points closely resembling those of a two-dimensional droplet in a channel. Recirculation is absent in the wall-parallel, unconfined planes, in sharp contrast to the interior flow inside a moving droplet in free space. The preferred orientation of the recirculation results from the anisotropic confinement of the Hele-Shaw cell. On these planes, we identify a dipolar disturbance flow field induced by the travelling droplet and its $1/r^2$ spatial decay is confirmed numerically. We pinpoint counter-rotating streamwise vortex structures near the lateral interface of the droplet, further highlighting the complex 3D flow pattern.

A study of the rheology of planar granular flow of dumbbells using discrete element method simulations

Abstract: Granular materials handled in industries are typically non-spherical in shape and understanding the flow of such materials is important. The steady flow of mono-disperse, frictional, inelastic dumbbells in two-dimensions is studied by soft sphere, discrete element method simulations for chute flow and shear cell flow. The chute flow data are in the dense flow regime, while the shear cell data span a wide range of solid fractions. Results of a detailed parametric study for both systems are presented. In chute flow, increase in the aspect ratio of the dumbbells results in significant slowing of the flow at a fixed inclination and in the shear cell it results in increase in the shear stress and pressure for a fixed shear rate. The flow is well-described by the μ-I scaling for inertial numbers as high as I = 1, corresponding to solid fractions as low as ϕ = 0.3, where μ is the effective friction (the ratio of shear stress to pressure) and I is the inertial number (a dimensionless shear rate scaled with the time scale obtained from the local pressure). For a fixed inertial number, the effective friction increases by 60%-70% when aspect ratio is increased from 1.0 (sphere) to 1.9. At low values of the inertial number, there is little change in the solid fraction with aspect ratio of the dumbbells, whereas at high values of the inertial number, there is a significant increase in solid fraction with increase in aspect ratio. The dense flow data are well-described by the Jop-Forterre-Pouliquen model [P. Jop et al., Nature 441, 727–730 (2006)] with the model parameters dependent on the dumbbell aspect ratio. The variation of μ with I over the extended range shows a maximum in the range I ∈ (0.4, 0.5), while the solid fraction shows a faster than linear decrease with inertial number. A modified version of the JFP model for μ(I) and a power law model for ϕ(I) is shown to describe the combined data over the extended range of I.

Droplet migration in a Hele-Shaw cell: Effect of the lubrication film on the droplet dynamics

Abstract: Droplet migration in a Hele--Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are performed to investigate the problem. In order to reduce the computational cost, an adaptive mesh is employed and high mesh resolution is only used near the interface. Parametric studies are performed on the droplet horizontal radius and the capillary number. For droplets with an horizontal radius larger than half the channel height the droplet overfills the channel and exhibits a pancake shape. A lubrication film is formed between the droplet and the wall and particular attention is paid to the effect of the lubrication film on the droplet velocity. The computed velocity of the pancake droplet is shown to be lower than the average inflow velocity, which is in agreement with experimental measurements. The numerical results show that both the strong shear induced by the lubrication film and the three-dimensional flow structure contribute to the low mobility of the droplet. In this low-migration-velocity scenario the interfacial flow in the droplet reference frame moves toward the rear on the top and reverses direction moving to the front from the two side edges. The velocity of the pancake droplet and the thickness of the lubrication film are observed to decrease with capillary number. The droplet velocity and its dependence on capillary number cannot be captured by the classic Hele--Shaw equations, since the depth-averaged approximation neglects the effect of the lubrication film.

Droplet migration in a Hele–Shaw cell: Effect of the lubrication film on the droplet dynamics

Abstract: Droplet migration in a Hele–Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are performed to investigate the problem. In order to reduce the computational cost, an adaptive mesh is employed and high mesh resolution is only used near the interface. Parametric studies are performed on the droplet horizontal radius and the capillary number. For droplets with an horizontal radius larger than half the channel height, the droplet overfills the channel and exhibits a pancake shape. A lubrication film is formed between the droplet and the wall and particular attention is paid to the effect of the lubrication film on the droplet velocity. The computed velocity of the pancake droplet is shown to be lower than the average inflow velocity, which is in agreement with experimental measurements. The numerical results show that both the strong shear induced by the lubrication film and the three-dimensional flow structure contribute to the low mobility of the droplet. In this low-migration-velocity scenario, the interfacial flow in the droplet reference frame moves toward the rear on the top and reverses direction moving to the front from the two side edges. The velocity of the pancake droplet and the thickness of the lubrication film are observed to decrease with capillary number. The droplet velocity and its dependence on capillary number cannot be captured by the classic Hele–Shaw equations, since the depth-averaged approximation neglects the effect of the lubrication film.

Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring

Abstract: Liquid crystals (LCs) display many of the flow characteristics of liquids but exhibit long range orientational order. In the nematic phase, the coupling of structure and flow leads to complex hydrodynamic effects that remain to be fully elucidated. Here, we consider the hydrodynamics of a nematic LC in a hybrid cell, where opposite walls have conflicting anchoring boundary conditions, and we employ a 3D lattice Boltzmann method to simulate the time-dependent flow patterns that can arise. Due to the symmetry breaking of the director field within the hybrid cell, we observe that at low to moderate shear rates, the volumetric flow rate under Couette and Poiseuille flows is different for opposite flow directions. At high shear rates, the director field may undergo a topological transition which leads to symmetric flows. By applying an oscillatory pressure gradient to the channel, a net volumetric flow rate is found to depend on the magnitude and frequency of the oscillation, as well as the anchoring strength. Taken together, our findings suggest several intriguing new applications for LCs in microfluidic devices.

Modal instability of the flow in a toroidal pipe

Abstract: This work is concerned with the study of flow stability and turbulence control - two old but still open problems of fluid mechanics. The topics are distinct and are (currently) approached from different directions and with different strategies. This thesis reflects this diversity in subject with a difference in geometry and, consequently, flow structure: the first problem is approached in the study of the flow in a toroidal pipe, the second one in an attempt to reduce the drag in a turbulent channel flow.The flow in a toroidal pipe is chosen as it represents the common asymptotic limit between spatially developing and helical pipes. Furthermore, the torus represents the smallest departure from the canonical straight pipe flow, at least for small curvatures. The interest in this geometry is twofold: it allows us to isolate the effect of the curvature on the flow and to approach straight as well as helical pipes. The analysis features a characterisation of the steady solution as a function of curvature and the Reynolds number. The problem of forcing fluid in the pipe is addressed, and the so-called Dean number is shown to be of little use, except for infinitesimally low curvatures. It is found that the flow is modally unstable and undergoes a Hopf bifurcation that leads to a limit cycle. The bifurcation and the corresponding eigenmodes are studied in detail, providing a complete picture of the instability.The second part of the thesis approaches fluid mechanics from a different perspective: the Reynolds number is too high for a deterministic description and the flow is analysed with statistical tools. The objective is to reduce the friction exerted by a turbulent flow on the walls of a channel, and the idea is to employ a control strategy independent of the small, and Reynolds number-dependent, turbulent scales. The method of choice was proposed by Schoppa & Hussain [Phys. Fluids 10:1049-1051 (1998)] and consists in the imposition of streamwise invariant, large-scale vortices. The vortices are re-implemented as a volume force, validated and analysed. Results show that the original method only gave rise to transient drag reduction while the forcing version is capable of sustained drag reduction of up to 18%. An analysis of the method, though, reveals that its effectiveness decreases rapidly as the Reynolds number is increased.

A pancake droplet translating in a Hele-Shaw cell: lubrication film and flow field

Abstract: We adopt a boundary integral method to study the dynamics of a translating droplet confined in a Hele-Shaw cell in the Stokes regime. The droplet is driven by the motion of the ambient fluid with the same viscosity. We characterize the three-dimensional (3D) nature of the droplet interface and of the flow field. The interface develops an arc-shaped ridge near the rear-half rim with a protrusion in the rear and a laterally symmetric pair of higher peaks; this pair of protrusions has been identified by recent experiments (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501) and predicted asymptotically (Burgess & Foster, Phys. Fluids A, vol. 2 (7), 1990, pp. 1105–1117). The mean film thickness is well predicted by the extended Bretherton model (Klaseboer et al., Phys. Fluids, vol. 26 (3), 2014, 032107) with fitting parameters. The flow in the streamwise wall-normal middle plane is featured with recirculating zones, which are partitioned by stagnation points closely resembling those of a two-dimensional droplet in a channel. Recirculation is absent in the wall-parallel, unconfined planes, in sharp contrast to the interior flow inside a moving droplet in free space. The preferred orientation of the recirculation results from the anisotropic confinement of the Hele-Shaw cell. On these planes, we identify a dipolar disturbance flow field induced by the travelling droplet and its spatial decay is confirmed numerically. We pinpoint counter-rotating streamwise vortex structures near the lateral interface of the droplet, further highlighting the complex 3D flow pattern.

Mechanics of the Separating Surface for a Two-Phase Co-current Flow in a Porous Medium

Abstract: A mechanical description of an unsteady two-phase co-current flow in a porous medium is developed based on the analysis of the geometry and motion of the surface separating the two phases. It is demonstrated that the flow should be considered as essentially three-dimensional, even if the phase velocities are co-directed, since the phase interface is on average inclined to the direction of the flow. Kinematics of the flow is described, distinguishing between the average velocities of the bulk phases and their velocity near the interface between them. Dynamics of the flow is analyzed by means of the extended Maxwell-Stefan formalism, as in our previous paper (Shapiro 2015). Force balances are formulated in the directions parallel and orthogonal to the flow. A complete system of the flow equations, generalizing the traditional Buckley–Leverett and Rappoport–Leas system, is derived. Sample computations show that one of the main effects produced by the new system is sharpening of the displacement front, which otherwise would be washed out by the capillary forces, as in the solution of the Rappoport–Leas equation.

Numerical study of two-dimensional flow around two side-by-side circular cylinders at low Reynolds numbers

Abstract: Incompressible flows at low Reynolds numbers over two identical side-by-side circular cylinders have been investigated numerically using unstructured finite volume method. The gap between the cylinders (g) and Reynolds number (Re) considered in the study lies respectively in the range of 0.2 ≤ g/D ≤ 4.0 (D being the diameter of the cylinder) and 20 ≤ Re ≤ 160. Low Reynolds number steady flows are given considerable importance. Two types of wakes are observed in the steady flow regime; the first type is characterized by attached vortices as in the case of an isolated cylinder and the other type is identified by detached standing vortices in the downstream. Reynolds number at which flow turns unsteady is quantified for each gap width. Five different types of wake patterns are observed in the unsteady flow regime: single bluff body wake, deflected wake, flip-flopping wake, in-phase synchronized, and anti-phase synchronized wakes. Present simulations of the evolution of single bluff-body wake demonstrate presence of vortices in the gap side too. The very long time simulations show that below a limiting Re depending on the gap, there is a transition of fully developed initial anti-phase flow to the in-phase flow at a later time. The limiting Reynolds number for this phase bifurcation phenomenon is evaluated in the (Re, g/D) space. A properly calibrated reduced order model based stability analysis is carried out to investigate the phase transition.