Showing papers on "Hele-Shaw flow published in 2018"
TL;DR: In this paper, a linear instability of pressure-driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions, was shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow.
Abstract: Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure-driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions. The instability is shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow. Our results qualitatively explain experimental observations of transition to turbulence in pipe flow of dilute polymer solutions at flow rates where Newtonian turbulence is absent. The instability discussed here should form the first stage in a hitherto unexplored dynamical pathway to turbulence in polymer solutions. An analogous instability exists for plane Poiseuille flow.
76 citations
TL;DR: In this paper, the authors investigated the heat transfer characteristics of developing and fully developed flow in smooth horizontal tubes in the transitional flow regime at a constant heat flux, and found that the Reynolds number at which transition started was independent of axial position, and transition occurred at the same moment in time along the whole tube length.
62 citations
TL;DR: In this paper, the authors studied the viscous-fingering instability in a radial Hele-Shaw cell, where the top boundary has been replaced by a thin elastic sheet, and compared the experimental observations to the predictions from a theoretical model that is based on the solution of the Reynolds lubrication equations, coupled to the Foppl-von-Karman equations which describe the deformation of the sheet.
Abstract: We study the viscous-fingering instability in a radial Hele-Shaw cell in which the top boundary has been replaced by a thin elastic sheet. The introduction of wall elasticity delays the onset of the fingering instability to much larger values of the injection flow rate. Furthermore, when the instability develops, the fingers that form on the expanding air–liquid interface are short and stubby, in contrast with the highly branched patterns observed in rigid-walled cells (Pihler-Puzovic et al., Phys. Rev. Lett., vol. 108, 2012, 074502). We report the outcome of a comprehensive experimental study of this problem and compare the experimental observations to the predictions from a theoretical model that is based on the solution of the Reynolds lubrication equations, coupled to the Foppl–von-Karman equations which describe the deformation of the elastic sheet. We perform a linear stability analysis to study the evolution of small-amplitude non-axisymmetric perturbations to the time-evolving base flow. We then derive a simplified model by exploiting the observations (i) that the non-axisymmetric perturbations to the sheet are very small and (ii) that perturbations to the flow occur predominantly in a small wedge-shaped region ahead of the air–liquid interface. This allows us to identify the various physical mechanisms by which viscous fingering is weakened (or even suppressed) by the presence of wall elasticity. We show that the theoretical predictions for the growth rate of small-amplitude perturbations are in good agreement with experimental observations for injection flow rates that are slightly larger than the critical flow rate required for the onset of the instability. We also characterize the large-amplitude fingering patterns that develop at larger injection flow rates. We show that the wavenumber of these patterns is still well predicted by the linear stability analysis, and that the length of the fingers is set by the local geometry of the compliant cell.
53 citations
TL;DR: In this article, a literature review of work related to the two-phase flow patterns of vertical downward flow in plate heat exchangers with corrugated chevron plates is presented, and the preferred flow pattern map explains the transition of condensation mechanisms qualitatively when variations of mass flux and vapor quality are considered.
Abstract: This study presents a literature review of work related to the two-phase flow patterns of vertical downward flow in plate heat exchangers with corrugated chevron plates. An understanding of these flow patterns is crucial for developing accurate models of plate heat exchangers functioning as condensers or absorbers. Flow pattern maps of the previous studies are combined and translated to dimensionless forms. One of the proposed flow pattern maps is based on ReL versus F r T P , h o r / Λ 0.5 and performs better than other representations. This map is compared with the map of tubes and shows general agreements in terms of the pattern positions, but the separating lines between flow patterns fit poorly. Influencing factors of condensation mechanisms are presented, among which mass flux and vapor quality are dominant. The preferred flow pattern map explains the transition of condensation mechanisms qualitatively when variations of mass flux and vapor quality are considered. Recommendations are given to come to more uniform flow pattern maps in plate heat exchangers with chevron corrugations.
32 citations
24 citations
TL;DR: In this paper, the authors investigated the electroosmotic flow of a two-layer fluid through a slit microchannel where the wall shape as well as zeta potential may vary slowly and periodically with axial position.
23 citations
TL;DR: In this article, the results from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime were presented.
Abstract: The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime. In the analysis, the uniform flow profiles have been used to compare with those of the non-uniform flows to investigate their time-averaged spatial flow turbulence structure characteristics. The measured non-uniform velocity profiles are used to verify the von Karman constant κ and to estimate sets of log-law integration constant Br and wake parameter П, where their findings are also compared with values from previous studies. From κ, Br and П findings, it has been found that the log-wake law can sufficiently represent the non-uniform flow in its non-modified form, and all κ, Br and П follow universal rules for different bed roughness conditions. The non-uniform flow experiments also show that both the turbulence intensity and Reynolds stress are governed well by exponential pressure gradient parameter β equations. Their exponential constants are described by quadratic functions in the investigated β range. Through this experimental study, it has been observed that the decelerating flow shows higher empirical constants, in both the turbulence intensity and Reynolds stress compared to the accelerating flow. The decelerating flow also has stronger dominance to determine the flow non-uniformity, because it presents higher Reynolds stress profile than uniform flow, whereas the accelerating flow does not.
23 citations
TL;DR: In this paper, a flow accelerating from an initially turbulent state following the opening of a valve, together with large eddy simulations of the experiments and extended Stokes first problem solutions for the early stages of the flow, was shown to resemble an accelerating laminar flow superimposed on the original steady turbulent flow.
Abstract: We report new laboratory experiments of a flow accelerating from an initially turbulent state following the opening of a valve, together with large eddy simulations of the experiments and extended Stokes first problem solutions for the early stages of the flow. The results show that the transient flow closely resembles an accelerating laminar flow superimposed on the original steady turbulent flow. The primary consequence of the acceleration is the temporal growth of a boundary layer from the wall, gradually leading to a strong instability causing transition. This extends the findings of previous direct numerical simulations of transient flow following a near-step increase in flow rate. In this interpretation, the initial turbulence is not the primary characteristic of the resulting transient flow, but can be regarded as noise, the evolution of which is strongly influenced by the development of the boundary layer. We observe the spontaneous appearance of turbulent spots and discontinuities in the velocity signals in time and space, revealing rich detail of the transition process, including a striking contrast between streamwise and wall-normal fluctuating velocities.
22 citations
TL;DR: In this paper, the gap-averaged Navier-Stokes equations were used to obtain the stable standing wave with half frequency of the external forced vibration in a Hele-Shaw cell.
Abstract: We investigate Faraday waves in a Hele-Shaw cell via experimental, numerical, and theoretical studies. Inspired by the Kelvin-Helmholtz-Darcy theory, we develop the gap-averaged Navier-Stokes equations and end up with the stable standing waves with half frequency of the external forced vibration. To overcome the dependency of a numerical model on the experimental parameter of wave length, we take two-phase flow into consideration and a novel dispersion relation is derived. The numerical results compare well with our experimental data, which effectively validates our proposed mathematical model. Therefore, this model can produce robust solutions of Faraday wave patterns and resolve related physical phenomena, which demonstrates the practical importance of the present study.
15 citations
TL;DR: In this article, the authors consider the problem of initiation of motion of a single mobile particle resting on a surface populated by similar types of grains and being exposed to a linear shear flow and compute hydrodynamic forces and torques numerically by considering Stokes flow conditions and solving the governing equations using the boundary element method (BEM).
14 citations
TL;DR: In this article, the global meshless method of approximate Stokes particular solutions (MASPS) is used to solve a two-dimensional incompressible fluid flow in the presence of a uniform magnetic field, i.e., the Navier-Stokes equations with the Lorentz force as a source term in the momentum equations.
TL;DR: Three-dimensional transient flow fluctuation energy evolution and characteristic scale distribution based on wavelet analysis of air–water two-phase flow were presented, which revealed the structural features of each phase in two- phase flow.
Abstract: Two-phase flow widely exists in many industries. Understanding local characteristics of two-phase flow under different flow conditions in piping systems is important to design and optimize the industrial process for higher productivity and lower cost. Air–water two-phase flow experiments were conducted with a 16×16 conductivity wire-mesh sensor (WMS) in a horizontal pipe of a multiphase flow facility. The cross-sectional void fraction time series was analysed by the probability density function (PDF), which described the void fraction fluctuation at different flow conditions. The changes and causes of PDFs during a flow regime transition were analysed. The local structure and flow behaviour were characterized by the local flow spectrum energy analysis and the local void fraction distribution (horizontal, vertical and radial direction) analysis. Finally, three-dimensional transient flow fluctuation energy evolution and characteristic scale distribution based on wavelet analysis of air–water two-phase flow ...
TL;DR: In this article, the authors studied immiscible liquid-liquid parallel microflow in microchannels and found that the surface states of the solid walls were the dominant condition in controlling the flow patterns in many cases.
TL;DR: In this paper, a study on the fluid flow characteristics of a multi-scale fluidic network consisting of a number of elementary ladders is presented, where a special effort was made to improve the flow distribution uniformity among the 90 parallel mini-channels by inserting geometrically optimized perforated baffles.
Abstract: This paper presents an original study on the fluid flow characteristics of a multi-scale fluidic network consisting of a number of elementary ladders. Computational Fluid Dynamics (CFD) simulations were performed to characterize local fluid flow patterns and flow distribution properties in such a complex geometry. In parallel, flow visualizations using fast camera and tracers were carried out in a transparent prototype. A special effort was made to improve the flow distribution uniformity among the 90 parallel mini-channels by inserting the geometrically optimized perforated baffles. The global pressure losses of the multi-scale network with or without baffles were also measured experimentally so as to be compared with the numerical results. For the multi-scale fluid network, non-uniform flow distribution was observed even under very low flow-rate conditions (e.g., mean Rech = 10). For higher flow-rate conditions, significant flow non-uniformity seems inevitable. The insertion of optimized perforated baffles could provide a remarkable improvement on flow distribution uniformity, even under high flow-rate conditions (mean Rech up to 2000). Good agreements between numerical and experimental results are observed.
TL;DR: In this article, the authors studied the dynamics of fluid tori in slow viscous flow and found that the torus either collapses towards the axis of symmetry or expands indefinitely, depending on the initial conditions and the capillary number, Ca.
Abstract: Dynamics of fluid tori in slow viscous flow is studied. Such tori are of interest as future carriers of biological and medicinal substances and are also viewed as potential building blocks towards more complex particles. In this study the immiscible ambient fluid is subject to a compressional flow (i.e., bi-extensional flow), and it comprises a generalization of our earlier report on the particular case with viscosity ratio (see Zabarankin et al., J. Fluid Mech., vol. 785, 2015, pp. 372–400), where is the ratio between the torus viscosity and that of the ambient fluid. It is found that, for all viscosity ratios, the torus either collapses towards the axis of symmetry or expands indefinitely, depending on the initial conditions and the capillary number, Ca. During these dynamic patterns the cross-sections exhibit various forms of deformation. The collapse and expansion dynamic modes are separated by a limited deformation into a deformed stationary state which appears to exist in a finite interval of the capillary number, , and is unstable to axisymmetric disturbances, which eventually cause the torus either to collapse or to expand indefinitely. The characteristic dimensions and shapes of these unstable stationary tori and their dependence on the physical parameters Ca and are reported.
TL;DR: In this paper, the Saffman-Taylor instability of an immiscible quasilinear viscoelastic-Newtonian displacement in a Hele-Shaw cell is studied numerically for the first time.
Abstract: In this paper, the well-known Saffman-Taylor instability of an immiscible quasilinear viscoelastic-Newtonian displacement in a Hele-Shaw cell is studied numerically for the first time. The volume of fluid method is applied to predict the formation of two phases. Here, a quasilinear viscoelastic fluid is considered as the displacing fluid and a Newtonian fluid as the displaced fluid. The Oldroyd-B constitutive equation, which is physically useful for Boger liquids, is considered for the viscoelastic phase. The effect of dimensionless parameters, consisting of the viscosity ratio, the viscosity ratio of viscoelastic fluid, the elasticity number, and the capillary number on Saffman-Taylor instability are studied in detail. The results illustrate that increasing the capillary number, elasticity number, and the viscosity ratio of viscoelastic fluid stabilizes the displacement, while enhancing the viscosity ratio has a destabilizing effect on the displacement. As a main result, it is found that the elasticity of the displacing fluid has a stabilizing effect on the flow field in the presence of capillary forces, which can be attributed to enhancing the extensional viscosity that resists against the stretching of the fingers.
TL;DR: In this article, a comprehensive experimental study is presented to analyse the instabilities of a magnetic fluid drop surrounded by miscible fluid confined in a Hele-Shaw cell, and two distinct instabilities are induced by the external magnetic fields with different sweep rates: (i) labyrinthine fingering instability, where small fingerings emerge around the initial circular interface in the early period, and (ii) secondary waves in the later period.
Abstract: A comprehensive experimental study is presented to analyse the instabilities of a magnetic fluid drop surrounded by miscible fluid confined in a Hele-Shaw cell. The experimental conditions include different magnetic fields (by varying the maximum pre-set magnetic field strengths, , and sweep rates, , where is the instant magnetic field strength), gap spans, , and magnetic fluid samples, and are further coupled into a modified Peclect number to evaluate the instabilities. Two distinct instabilities are induced by the external magnetic fields with different sweep rates: (i) a labyrinthine fingering instability, where small fingerings emerge around the initial circular interface in the early period, and (ii) secondary waves in the later period. Based on 81 sets of experimental conditions, the initial growth rate of the interfacial length, , of the magnetic drop is found to increase linearly with , indicating that is proportional to the square root of the and at the onset of the labyrinthine instability. In addition, secondary waves, which are characterised by the dimensionless wavelength , can only be triggered when the three-dimensional magnetic microconvection is strong enough to make exceed a critical value, i.e. , where is the wavelength of the secondary wave. In this flow regime of high , the length scale of the secondary wave instability is found to be , corresponding to the Stokes regime; meanwhile, in the flow regime of low , the flow corresponds to the Hele-Shaw regime introduced by Fernandez et al. (J. Fluid Mech., vol. 451, 2002, pp. 239–260).
TL;DR: An analytically investigating Stokes flow over Reiner–Rivlin liquid sphere embedded in a porous medium filled with micropolar fluid using Brinkman’s model and assuming uniform flow away from the obstacle is reported.
TL;DR: Sarraf, Sofia Soledad, et al. as discussed by the authors presented a paper as discussed by the authors, in which they presented the work of the Consejo Nacional de Investigaciones Cientificas y Tecnicas, Argentina.
Abstract: Fil: Sarraf, Sofia Soledad. Universidad Nacional del Comahue. Facultad de Ingenieria. Departamento de Mecanica; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina
TL;DR: In this article, the normal components of the viscoelastic stresses are found analytically for a second order fluid up to numerical inversion for a cross-slot geometry for which the height of the channel is small compared to the other channel dimensions.
Abstract: In this paper a cross-slot geometry for which the height of the channel is small compared to the other channel dimensions is considered. The normal components of the viscoelastic stresses are found analytically for a second order fluid up to numerical inversion. The validity of the theoretical analysis was corroborated by comparison with numerical simulations based on a stabilized Galerkin least squares finite element method using an Oldroyd B fluid. Close agreement was found between numerical predictions and analytical results for Weissenberg numbers up to 0.2. An explicit expression is formulated for viscoelastic parameters in terms of the variation and strength of the first normal stress difference around the stagnation point. The analysis is generalized for the case where the inlet channel width is different from the outlet channel width. For such configurations it was found that uniformity of the elongation rate was reduced.
TL;DR: In this article, the characteristics of the flow and heat transfer in transitional flow are not clear and especially the lack of some reliable experimental data hinders the numerical study of the heat exchanger.
Abstract: The characteristics of the flow and heat transfer in transitional flow are not clear and especially the lack of some reliable experimental data hinders the numerical study of the heat exchanger. Ba...
TL;DR: In this paper, analytical expressions of wall and interface friction properties are derived for idealised three layered and two layered pressure driven stratified flow in a two-dimensional channel under the assumption of fully developed laminar viscous flow.
Abstract: Friction factors and associated friction velocities are important flow characteristics. Analytical expressions of wall and interface friction properties are derived for idealised three layered and two layered pressure driven stratified flow in a two-dimensional channel under the assumption of fully developed laminar viscous flow. Channel inclination is accounted for as well. The influence of flow and geometrical channel parameters is then concretely assessed for water/air and oil/air interfaces due to their potential relevance to two phase flows occurring in the human airways.
01 Jan 2018
TL;DR: In this paper, the authors prove existence of a solution Wε in the Bochner space L2(0, T ;H1 0 (Ω;Rm)) to a non-local in time semi-linear system of coupled PDEs of second order related to obstacle type problems, having explicit form −∆uε + (1− χDi 0 )βε(u i ε) (0.1)
Abstract: The one-phase Hele-Shaw flow has a long history and has been extensively studied from several point of views ranging from the fluid dynamical beginnings to complex analysis and integrable systems, see [5]. We prove existence, using the implicit function theorem, of a solution Wε in the Bochner space L2(0, T ;H1 0 (Ω;Rm)) to a non-local in time semi-linear system of coupled PDEs of second order related to obstacle type problems, having the explicit form −∆uε + (1− χDi 0 )βε(u i ε) (0.1)
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TL;DR: In this article, the complex potentials representing flows around a vertical plate semi-submerged in a uniform stream are derived in analytical forms by the reduction method, composed from the regular solution and a weak singular eigen eigen solution.
Abstract: The complex potentials representing flows around a vertical plate semi-submerged in a uniform stream are derived in analytical forms by the reduction method. They are composed from the regular solution and a weak singular eigen solution. The linear combinations of them represent some flows such as regular flow, zero-vertical flux flow, flow satisfying Kutta condition and wave-free flow. The wave resistances of the flows are also obtained in analytical forms. The analytical solution obtained by Bessho-Mizuno(1962) has a possibility that it does not satisfy the boundary condition on the plate.
TL;DR: The invariance in time of free boundary in the case of two-dimensional viscous fluid flows in Hele-Shaw cells under injection is studied by applying various results in the theory of univalent functions.
01 Jan 2018
TL;DR: In this paper, large-eddy simulations of the flow past a cylinder at Reynolds numbers in the range of 2.5\times 10^5{-}10^6 are performed.
Abstract: It is well known that the wake topology in the flow past a circular cylinder remains almost unchanged up to Reynolds number \(\sim 10^5\) Williamson (Annu Rev Fluid Mech 28(1), 477–539 (1996)) [1]. Then, at \(Re\sim 2\times 10^5\) major changes take place entailing flow separation, turbulence transition in the detached shear layers, reattachment of the flow and further separation of the boundary layer. In the present work, large-eddy simulations of the flow past a cylinder at Reynolds numbers in the range \(2.5\times 10^5{-}10^6\) are performed. This range includes both critical and super-critical Reynolds numbers (J Fluid Mech 10(3), 345–356 (1961)) [2]. Contradicting results about the wake configuration and structures are found in the literature.
17 Sep 2018
TL;DR: In this paper, an analytical investigation of the combined effect of through flow and magnetic field on the convective instability in an electrically conducting fluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory.
Abstract: In this paper, an analytical investigation of the combined effect of through flow and magnetic field on the convective instability in an electrically conducting fluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory. The Galarkin method is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability of the system is examined analytically as well as graphically. It is observed that the through flow and magnetic field have both stabilizing effects, while the Hele-Shaw number has destabilizing effect on the stability of system. It is also found that the oscillatory mode of convection possible only when the magnetic Prandtl number takes the values less than unity.