The two-dimensional flow of viscous incompressible fluid in the domain between two concentric circles is investigated numerically. To solve the problem, the low-order Galerkin models are used. When the inner circle rotates fast enough, two axially asymmetric flow regimes are observed. Both regimes are the stationary flows precessing in azimuthal direction. First flow represents the region of concentrated vorticity. Another flow is the jet-like structure similar to one discovered earlier in Vladimirov's experiments.
The flow inside a precessing fluid cavity has been given particular attention since the end of the 19th century in geophysical and industrial contexts. The present study aims at shedding light on the underlying mechanism by which the flow inside a precessing cylindrical annulus transitions from laminar to multiple scale complex structures. We address this problem experimentally using ultrasonic Doppler velocimetry to diagnose the fluid velocity in a rotating and precessing cylindrical annulus. When precession is weak, the flow can be described as a superposition of forced inertial modes. Above…
The stability of two-dimensional diverging and converging flows in an annulus between two permeable cylinders is examined. The basic flow is irrotational and has both the radial and azimuthal components. It is shown that for a wide range of the parameters of the problem, the basic flow is unstable to small two-dimensional perturbations. The instability is inviscid and oscillatory and persists if the viscosity of the fluid is taken into consideration.
In this paper we solve the inviscid inertial wave solutions in a circular pipe or annulus rotating constantly about its axis with moderate angular speed. The solutions are constructed by the so-called helical wave functions. We reveal that the mean velocity profiles must satisfy certain conditions to accommodate the inertial waves at the bulk region away from boundary. These conditions require the axial and azimuthal components of the mean velocity take the shapes of the zeroth and first order Bessel functions of the first kind, respectively. The theory is then verified by data obtained from d…
In this paper we examine the interaction of convection, rotation and mean flows in a thermal annulus. In this system mean flows are driven by correlations induced by rotation leading to non-trivial Reynolds stresses. The mean flows act back on the convective turbulence acting as a barrier to transport. For this system we demonstrate that the Generalised Quasilinear Approximation (GQL) (Marston et al 2016) may provide a much better approximation to the complicated full nonlinear dynamics than the widely used Quasilinear Approximation (QL). This result will enable the construction of more accura…
In this paper, we investigate steady inviscid compressible flows with radial symmetry in an annulus. The major concerns are transonic flows with or without shocks. One of the main motivations is to elucidate the role played by the angular velocity in the structure of steady inviscid compressible flows. We give a complete classification of flow patterns in terms of boundary conditions at the inner and outer circle. Due to the nonzero angular velocity, many new flow patterns will appear. There exists accelerating or decelerating smooth transonic flows in an annulus satisfying one side boundary c…
Axial flow in an annulus between two concentric cylinders is commonly seen in various flow devices used in chemical processing industries and petroleum science and engineering. The flow state in the annulus strongly influences the performance of fluid transportation in the devices. Therefore, the determination of flow state which is laminar flow or turbulent flow is an important task to predict the performance of the flow devices. In previous works, we have proposed an energy gradient method for studying the flow instability and turbulent transition. In this method, it is shown that the flow i…
Zonal flows are often found in rotating convective systems. Not only are these jet-flows driven by the convection, they can also have a profound effect on the nature of the convection. In this work the cylindrical annulus geometry is exploited in order to perform nonlinear simulations seeking to produce strong zonal flows and multiple jets. The parameter regime is extended to Prandtl numbers that are not unity. Multiple jets are found to be spaced according to a Rhines scaling based on the zonal flow speed, not the convective velocity speed. Under certain conditions the nonlinear convection ap…
The dynamics of rigid particle suspensions in a wall-bounded laminar flow present several non-trivial and intriguing features, including particle ordering, lateral transport, and the appearance of stable, preferential locations like the Segré-Silberberg annulus. The formation of more than one annulus is a particularly puzzling phenomenon that is still not fully explained. Here, we present numerical simulation results of a dilute suspension of particles in (periodic) pipe flow based on the lattice Boltzmann and the discrete element methods (DEM). Our simulations provide access to the full radia…
We study the steady streaming between two infinitely long circular cylinders produced by small amplitude transverse vibrations of the inner cylinder about the axis of the outer cylinder. The Vishik-Lyusternik method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds numbers of order of unity. The effect of the Stokes drift of fluid particles is also studied. It is shown that it is nonzero not only within the boundary layers but also in higher order terms of the expansion of the averaged outer fl…
We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter-rotating as well as with co-rotating cylinders. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation and stability behavi…
We present numerical simulations of circular Couette flow in axisymmetric and fully three-dimensional geometry of a cylindrical annulus inspired by Princeton MRI liquid gallium experiment. The incompressible Navier-Stokes equations are solved with the spectral element code Nek5000 incorporating realistic horizontal boundary conditions of differentially rotating rings. We investigate the effect of changing rotation rates (Reynolds number) and of the horizontal boundary conditions on flow structure, Ekman circulation and associated transport of angular momentum through the onset of unsteadiness …
We study numerically the induction mechanisms generated from an array of helical motions distributed along a cylinder. Our flow is a very idealized geometry of the columnar structure that has been proposed for the convective motion inside the Earth core. Using an analytically prescribed flow, we apply a recently introduced iterative numerical scheme to solve the induction equation and analyze the flow response to externally applied fields with simple geometries (azimuthal, radial, etc.). Symmetry properties allow us to build selected induction modes whose interactions lead to dynamo mechanisms…
We consider direct statistical simulation (DSS) of a paradigm system of convection interacting with mean flows. In the Busse Annulus model zonal jets are generated through the interaction of convectively driven turbulence and rotation; non-trivial dynamics including the emergence of multiple jets and bursting `predator-prey' type dynamics can be found. We formulate the DSS by expanding around the mean flow in terms of equal-time cumulants and arrive at a closed set of equations of motion for the cumulants. Here, we present results using an expansion terminated at the second cumulant (CE2); it …
Inertia-gravity waves (IGWs) play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when propagating upwards. An open question is to which extent IGWs contribute to the total energy and to flattening of the energy spectrum observed at the mesoscale. In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atm…
Multiphase flow simulations were run in an eccentric annulus. The dimensions of the annulus were 0.1 and 0.05 m for the outer and inner cylinders, respectively, and the mixture velocities were between 1.2 and 4.2 m/s. The simulations were compared with fully eccentric and completely concentric experiments conducted at the Institute for Energy Technology. The purpose of this paper is to explore the effect of the holdup fraction and interior pipe's position on the pressure gradient and flow regime. The comparisons indicate that moving the pipe from an entirely eccentric to a partially eccentric …
A series of laboratory experiments has been carried out in a thermally driven rotating annulus to study the onset of baroclinic instability, using horizontal and uniformly sloping bottom topographies. Different wave flow regimes have been identified and their phase boundaries -- expressed in terms of appropriate non-dimensional parameters -- have been compared to the recent numerical results of \citet{thomas_slope}. In the flat bottom case, the numerically predicted alignment of the boundary between the axisymmetric and the regular wave flow regime was found to be consistent with the experimen…
We consider the stability of two-dimensional viscous flows in an annulus with permeable boundary. In the basic flow, the velocity has nonzero azimuthal and radial components, and the direction of the radial flow can be from the inner cylinder to the outer one or vice versa. In most earlier studies, all components of the velocity were assumed to be given on the entire boundary of the flow domain. Our aim is to study the effect of different boundary conditions on the stability of such flows. We focus on the following boundary conditions: at the inflow part if the boundary (which may be either in…
We discuss the static force characteristic of annular gaps resulting from an axial flow component. So far there is a severe lack of understanding of the flow inside the annulus. First, the state-of-the-art modelling approaches to describe the flow inside the annulus are recapped and discussed. The discussion focuses in particular on the modelling of inertia effects. Second, a new calculation method, the Clearance-Averaged Pressure Model (CAPM) is presented. The CAPM uses an integro-differential approach in combination with power law ansatz functions for the velocity profiles and a Hirs' model …
We derive an expression for the velocity profile of a pressure-driven yield-stress fluid flow-ing around a two-dimensional concentric annulus. This result allows the prediction of the effects of channel curvature on the pressure gradient required to initiate flow for given yield stress, and for the width of the plug region and the flux through the channel at different curvatures. We use it to validate numerical simulations of the flow from a straight channel into a curved channel which show how the fluid first yields everywhere before reaching the predicted velocity profile.
In our recent work [H. Zhang, F.X. Trias, A. Oliva, D. Yang, Y. Tan, Y. Sheng. PIBM: Particulate immersed boundary method for fluid-particle interaction problems. Powder Technology. 272(2015), 1-13.], a particulate immersed boundary method (PIBM) for simulating fluid-particle multiphase flow was proposed and assessed in both two- and three-dimensional applications. In this study, the PIBM was extended to solve thermal interaction problems between spherical particles and fluid. The Lattice Boltzmann Method (LBM) was adopted to solve the fluid flow and temperature fields, the PIBM was responsibl…
A part of non-Newtonian fluids are yield stress fluids. They require a minimum stress to flow. Below this minimum value, yield stress fluids remain solid. To date, 1D and 2D numerical models have been used predominantly to study free surface flows. However, some phenomena have three-dimensional behaviour such as the appearance of the limit between the liquid regime and the solid regime. Here the aim is to use a Computational Fluid Dynamics (CFD) to reproduce the properties of the free surface flow of yield stress fluids in an open channel. Modelling the behaviour of the yield stress fluid is a…
The article describes the CFD software tool FlowVision (OOO "Tesis", Moscow). The model equations used for this research are the set of Reynolds and continuity equations and equations of the standard k - e turbulence model. The aim of the paper was testing of FlowVision by comparing the computational results for a number of simple internal channel fluid flows with known experimental data. The test cases are non-swirling and swirling flows in pipes and diffusers, flows in stationary and rotating bends. Satisfactory correspondence of results was obtained both for flow patterns and respective qua…
We present a computational framework to address the flow of two immiscible viscous liquids which co-flow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions based on the shallow depth of the domain are used to reduce the governing equations to one of Hele-Shaw type. The distinctive feature of the numerical method is the accurate modeling of the capillary effects. A continuum approach coupled with a volume-of-fluid formulation for computing the interface motion and for modeling the interfacial tension in Hele-Shaw flows is fo…
The paper presents the results of computation of some simple internal flows of incompressible fluid with the software package CFX-5. In the previous paper of the author, the same flows were used for testing of another CFD software tool, FlowVision. The model equations used for this research are again the set of Reynolds and continuity equations and equations of the standard k - e turbulence model. The results of computation of a number of internal fluid flows in channels are presented and comparison with known experimental data is performed. Good correspondence of results was obtained both con…
Two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube, and a concentric circular annulus. Here we study peristaltic flow in a non-axisymmetric annular tube, where the flow is three dimensional, with azimuthal motions. This geometry is motivated by experimental observations of cerebrospinal fluid flow along perivascular spaces (PVSs) surrounding arteries in the brain, which is at least partially driven by peristaltic pumping. These PVSs are well matched, in cross-section, by an adju…
An intuitively necessary requirement of models used to provide forecasts of a system's future is the existence of shadowing trajectories that are consistent with past observations of the system: given a system-model pair, do model trajectories exist that stay reasonably close to a sequence of observations of the system? Techniques for finding such trajectories are well-understood in low-dimensional systems, but there is significant interest in their application to high-dimensional weather and climate models. We build on work by Smith et al. [2010, Phys. Lett. A, 374, 2618-2623] and develop a m…
Non-linear effects of the Navier-Stokes equations disappear under the Stokes regime of Newtonian fluid flows disallowing the fluid flow rectification. Here we show mathematically and experimentally that passive flow rectification of Newtonian fluids is obtainable under the Stokes regime of both compressible and incompressible flows by introducing nonlinearity into the otherwise linear Stokes equations. Asymmetric flow resistances arise in shallow nozzle/diffuser microchannels with deformable ceiling, in which the fluid flow is governed by a non-linear coupled fluid-solid mechanics equation. Fl…
The article describes various aspects of mathematical modeling of fluid flows, both in general and with reference to hydraulic machinery. The article reviews historical development of corresponding methods of mathematical modeling. Implementation of these aspects in modern commercial CFD software tools is described together with advantages and disadvantages of implemented methods. The conclusion is drawn concerning possibilities of computation of fluid flows nowadays.
We investigate quasi-two-dimensional relaxation, by surface tension, of a long straight stripe of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. Combining analytical and numerical solutions, we describe the emergence of a self-similar dumbbell shape and find non-trivial dynamic exponents that characterize scaling behavior of the dumbbell dimensions.
The article reviews fluid flow models implemented in the leading CFD software tools and designed for simulation of multi-component and multi-phase flows, compressible flows, flows with heat transfer, cavitation and other phenomena. The article shows that these software tools (CFX, Fluent, STAR-CD, etc.) allow for adequate simulation of complex physical effects of different nature, even for problems where performing of physical experiment is extremely difficult.
In this work, by considering an isentropic fluid-fluid interaction model with a large symmetric drag force, a commonly used simplified two-fluids flow model is justified as the asymptotic limit. Equations for each fluid component with an interaction term are identified in addition to the simplified two-fluids flow model, which can be used to resolve the density of one fluid specie based on information on density and the velocity of the other fluid specie, i.e., the testing flow.
Surface tension gradients induce Marangoni flow, which may be exploited for fluid transport. At the micrometer scale, these surface-driven flows can be more significant than those driven by pressure. By introducing fluid-fluid interfaces on the walls of microfluidic channels, we use surface tension gradients to drive bulk fluid flows. The gradients are specifically induced through thermal energy, exploiting the temperature dependence of a fluid-fluid interface to generate thermocapillary flow. In this report, we provide the design concept for a biocompatible, thermocapillary microchannel capab…
The exact analytic solution is built for the plane flow of incompressible fluid through the wheel with profiles of blades approximating logarithmic spirals.
The creeping flow of a generalized Newtonian fluid in a non--uniform pore throat is investigated analytically. The analytical solution determines the flow regimes and the transition point from Newtonian to the power law flow regime. As an application of the new model, a regular lattice--based pore network model is constructed to simulate the flows of shear--thinning and shear--thickening fluids through porous media. The pore throats have convergent--divergent geometries.
The Navier-Stokes equations and boundary conditions for viscous fluids of capillary size are formulated in curvilinear coordinates associated with a geometry of the fluid-gas interface. As a result, the fluid dynamics of drops and menisci can be described taking into account an influence of gravitational forces and flows on the surface shape. This gives a convenient basis for respective numerical studies. Estimations of the effects are presented for the case of an evaporating sessile drop.
We discuss the use of 3D printing to physically visualize (materialize) fluid flow structures. Such 3D models can serve as a refreshing hands-on means to gain deeper physical insights into the formation of complex coherent structures in fluid flows. In this short paper, we present a general procedure for taking 3D flow field data and producing a file format that can be supplied to a 3D printer, with two examples of 3D printed flow structures. A sample code to perform this process is also provided. 3D printed flow structures can not only deepen our understanding of fluid flows but also allow us…
Using a generalization of vector calculus for the case of non-integer dimensional space we consider a Poiseuille flow of an incompressible viscous fractal fluid in the pipe. Fractal fluid is described as a continuum in non-integer dimensional space. A generalization of the Navier-Stokes equations for non-integer dimensional space, its solution for steady flow of fractal fluid in a pipe and corresponding fractal fluid discharge are suggested.
A physically-based method to derive well-posed instances of the two-fluid transport equations for two-phase flow, from the Hamilton principle, is presented. The state of the two-fluid flow is represented by the superficial velocity and the drift-flux, instead of the average velocities of each fluid. This generates the conservation equations of the two principal motion modes naturally: the global center-of-mass flow and the relative velocity between fluids. Well-posed equations can be obtained by modelling the storage of kinetic energy in fluctuations structures induced by the interaction betwe…
The ability to monitore bottomhole flowing pressure in pumping oil wells provides important information regarding both reservoir and artificial lift performance. Converting surface pressure measurements to bottomhole is currently accomplished by locating the fluid level in the annulus using a sonic device and then applying a correlation to estimate the density of the gas-cut liquid column above the perforations. This work proposes a flowing bottomhole pressure calculation procedure from fluid level measurements. The model is developed from experimental work and from theoretical arguments. The …
We investigate the fully developed flow between two parallel plates and the film flow over a plate in an electrically conducting fluid under the action of a parallel Lorentz force. Exact analytical solutions are derived for velocity, flow rate and wall shear stress at the plates. The velocity results are presented in figures. All these flows are new and are presented for the first time in the literature.
Analytical expressions for the flow field as well as for the effective slip length of a shear flow over a surface with periodic rectangular grooves are derived. The primary fluid is in the Cassie state with the grooves being filled with a secondary immiscible fluid. The coupling of both fluids is reflected in a locally varying slip distribution along the fluid-fluid interface, which models the effect of the secondary fluid on the outer flow. The obtained closed-form analytical expressions for the flow field and effective slip length of the primary fluid explicitly contain the influence of the …
We derive the flow field disturbance produced by point viscosity variations in a heterogeneous fluid when subject to a background flow while neglecting fluid inertia. The disturbance flow field is found to be identical to that generated by a force-dipole called stresslet. Using a combination of theory and numerical simulations, we show how the hydrodynamics of an active rigid particle is altered due to the presence of point viscosity variations, and how this can be exploited to manipulate and steer them in microfluidic environments.
Through high-fidelity numerical simulation, the simple shear flow over regularly arranged micro pillars has been investigated. The essential issues to be addressed include the characteristics of a simple shear flow over quadrilateral array of micro pillars, the effect of fluid inertia on the basic flow pattern, and the decomposition of the complex surface friction. The results show that the flow is characterized by a series of microscale recirculating eddies in the gaps between the streamwise neighboring pillars. The recirculation of the micro eddies and the oscillation of the overhead flow cl…
As the first endeavour, we have analyzed the pulsatile flow of Oldroyd-B viscoelastic fluid where the combined effects of fluid elasticity and pulsation parameters on the flow characteristics are numerically studied at a low Reynolds number. Computations are performed using a finite-volume based open-source solver OpenFOAM by appending the log-conformation tensor approach to stabilize the numerical solution at high Deborah number. Significant flow velocity enhancement is achieved by increasing the viscoelastic behaviour of the fluid. High-velocity gradient zones and high polymeric stress regio…
We consider concepts centered around modal analysis, data science, network science, and machine learning to reveal the essential dynamics from high-dimensional fluid flow data and operators. The presentation of the material herein is example-based and follows the author's keynote talk at the 32nd Computational Fluid Dynamics Symposium (Japan Society of Fluid Mechanics, Tokyo, December 11-13, 2018). This talk was delivered as a compilation of some of the research activities undertaken by the author's research group.
We analyzed the effect of viscoelasticity on the dynamics of fluids in porous media by studying the flow of a Maxwell fluid in a circular tube, in which the flow is induced by a wave traveling on the tube wall. The present study investigates novelties brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. This problem has numerous applications in various branches of science, including stimulation of fluid flow in porous media under the effect of elastic waves. We have found that in the extreme non-Newtonian …
We analyze the steady non-Newtonian fluid-structure interaction between the flow of an Oldroyd-B fluid and a deformable channel. Specifically, we provide a theoretical framework for calculating the leading-order effect of the fluid's viscoelasticity on the flow rate-pressure drop relation and on the deformation of the channel's elastic wall. We first identify the characteristic scales and dimensionless parameters governing the fluid-structure interaction in slender and shallow channels. Applying the lubrication approximation for the flow and employing a perturbation expansion in powers of the …
