The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable. The emergence of linear instability by convection cells is excluded on the basis of a numerical solution of the linearised governing equations. This result extends to the annular geometry the well-known Gill's theorem regarding the impossibility of convective instability in a vertical porous plane slab whose boundaries are impermeable and isothermal with different temperatures. The extension of Gill's theorem to the annular domain is approached numerically by evaluating the growth rate of normal mode perturbations and showing that its sign is negative, which means asymptotic stability of the basic flow. A concurring argument supporting the absence of linear instability arises from the investigation of cases where the impermeability condition at the vertical boundaries is relaxed and a partial permeability is modelled through Robin boundary conditions for the pressure. With partially permeable boundaries, an instability emerges which takes the form of axisymmetric normal modes.
Since the liquid flow rate of the annular flow is closely related to the heat exchange efficiency, it has great significance to measure the liquid flow rate of the annular flow in vertical tee junction. In order to acquire the liquid flow rate of the annular flow in vertical tee junction, a measurement method has been designed, which implements the digital subtraction method to measure the thickness of the liquid film under the visible light and to apply the image feature matching algorithm to obtain the liquid velocity field. Moreover, the accuracy of the liquid film velocity field as well as…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid reservoirs. There exists a stationary parallel velocity field with a zero flow rate and pure conduction heat transfer. Its linear stability is analysed with normal mode perturbations of the pressure and temperature fields. The transition to convective instability is caused by the basic horizontal temperature gradient. Hence, its nature differs from that of the usual…
In the above paper the author treats the boundary layer flow of an electrically conducting, non-Newtonian fluid along a vertical plate embedded in a Darcy-Brinkman-Forchheimer porous medium. The fluid is under the action of a constant transverse magnetic field and the radiation is taken into account in the energy equation. The boundary layer equations are transformed into ordinary ones and subsequently are solved numerically. However, there is a fundamental error in this paper which is presented below:
The paper presents a theoretical study using the Karman-Pohlhausen method for describing the transient heat exchange between the boundary-layer free convection and a vertical flat plate embedded in a porous medium. The unsteady behavior is developed after the generation of an impulsive heat flux step at the right-hand side of the plate. Two cases are considered according to whether the plate has a finite thickness or no thickness. The time and space evolution of the interface temperature is evidenced.
In the above paper the author treats the boundary layer flow along a vertical flat plate, immersed in a Darcy Brinkman Forchheimer porous medium. The porosity and the permeability of the porous medium are variable across the boundary layer. In addition a magnetic field with constant strength is applied normal to the plate. The fluid temperature at the plate is constant and different from that of the ambient fluid. This temperature difference creates a buoyancy force and the flow is characterized as mixed convection. The partial differential equations of the boundary layer flow are transformed …
This paper discusses the convective heat transfer enhancement of non-condensing slug flows by using phase separation for local liquid circulations through a porous-tube insert. Numerical simulations were carried out to study the air-water slug flow and heat transfer without phase change (boiling and condensation) in a vertical upward flow. The governing equations of two-phase flow and heat transfer were numerically solved using the Volume of Fluid-Continuum Surface Force (VOF-CSF) method in a two-dimensional axisymmetric computational domain. The rear end (exit) of the porous tube was open to …
The buoyancy-induced parallel flow in a vertical cylindrical porous layer is analysed. A radial thermal gradient caused by a uniformly distributed heat source is assumed to induce the buoyant flow. The layer boundaries are modelled as isothermal and permeable to an external fluid reservoir. The onset of the convective instability is analysed by linearising the governing equations for the perturbations. The governing parameters driving the instability are the heat-source Rayleigh number and the ratio between the internal radius and the external radius. Neutral stability curves and the critical …
A fully-implicit solving approach to an adaptive multi-scale model -- coupling a vertical-equilibrium and full-dimensional model for compressible, multi-phase flow in porous media
Context: A radial temperature gradient together with an inhomogeneous radial electric field gradient is applied to a dielectric fluid confined in a vertical cylindrical annulus inducing thermal electro-hydrodynamic convection. Aims: Identification of the stability of the flow and hence of the line of marginal stability separating stable laminar free (natural) convection from thermal electro-hydrodynamic convection, its flow structures, pattern formation and critical parameters. Methods: Combination of different measurement techniques, namely the shadowgraph method and particle image velocimetr…
Buoyancy-driven exchange flows are common to a variety of natural and engineering systems ranging from persistently active volcanoes to counterflows in oceanic straits. Experiments of exchange flows in closed vertical tubes have been used as surrogates to elucidate the basic features of such flows. The resulting data have historically been analyzed and interpreted through core-annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natur…
The emerging instability of a forced throughflow in a fluid saturated horizontal porous duct of rectangular cross section is investigated. The duct is heated from below by assuming the horizontal boundaries to be at different temperatures. Both the horizontal and the vertical boundaries are impermeable and the basic flow is parallel to such boundaries. The porous medium is anisotropic with different permeabilities in the vertical and horizontal directions. The effect of the anisotropy on the onset of the buoyancy driven modal instability and absolute instability is analysed. The parametric con…
We explore the motion of an axisymmetric gravity current in an anisotropic porous medium in which the horizontal permeability is larger than the vertical permeability. It is well known that the classical axisymmetric gravity current supplied by a constant point source of fluid has an unphysical singularity near the origin. We address this by considering a pressure-dominated region near the origin which allows for vertical flow from the source, such that the current remains of finite depth, whilst beyond this region the flow is gravity-dominated. At early times the inner pressure-driven region …
The problem of steady mixed convection boundary-layer flow on a cooled vertical permeable circular cylinder embedded in a fluid-saturated porous medium is studied. Here, we evaluate the flow and heat transfer characteristics numerically for various values of the governing parameters and demonstrate the existence of dual solutions beyond a critical point.
Upscaling the effect of heterogeneities in porous media is crucial for macroscopic flow predictions, with widespread applications in energy and environmental settings. In this study, we derive expressions for the upscaled flow properties of a porous medium with a vertical heterogeneity, using a combination of asymptotic analysis and numerical simulations. Then, we use these upscaled expressions to describe the dynamic flooding of an aquifer, where the classic Buckley-Leverett formulation is modified to account for heterogeneities. In particular, we show that heterogeneities can modify flooding…
The temporal stability of an inviscid flow through cylindrical geometries with a porous wall subjected to non-axisymmetric perturbations is investigated in the present work using an unsteady Darcy equation for the porous layer. An expression for the perturbation energy exchange term between the fluid and porous layers is derived by integrating the perturbation equation for the porous layer which is then used to prove the propositions. The necessary and sufficient condition for the existence of the instability in flows through cylindrical geometries is shown to be $\frac{d}{dr} \left( \frac{r \…
We consider the axisymmetric displacement of an ambient fluid by a second input fluid of lower density and lower viscosity in a horizontal porous layer. If the two fluids have been vertically segregated by buoyancy, the flow becomes self-similar with the input fluid preferentially flowing near the upper boundary. We show that this axisymmetric self-similar flow is stable to angular-dependent perturbations for any viscosity ratio. The Saffman-Taylor instability is suppressed due to the buoyancy segregation of the fluids. The radial extent of the segregated current is inversely proportional to t…
We consider the slow flow of a viscous incompressible liquid in a channel of constant but arbitrary cross section shape, driven by non-uniform suction or injection through the porous channel walls. A similarity transformation reduces the Navier-Stokes equations to a set of coupled equations for the velocity potential in two dimensions. When the channel aspect ratio and Reynolds number are both small, the problem reduces to solving the biharmonic equation with constant forcing in two dimensions. With the relevant boundary conditions, determining the velocity field in a porous channels is thus e…
We report a numerical study of Rayleigh--Bénard convection through random porous media using pore-scale modelling, focusing on the Lagrangian dynamics of fluid particles and heat transfer for varied porosities $ϕ$. Due to the interaction between the porous medium and the coherent flow structures, the flow is found to be highly heterogeneous, consisting of convection channels with strong flow strength and stagnant regions with low velocities. The modifications of flow field due to porous structure have a significant influence on the dynamics of fluid particles. Evaluation of the particle displa…
In the present work, the mathematical description of a two-dimensional unsteady magneto-hydrodynamics slow flow with thermoelectric properties (TEMHD) on an infinite vertical partially hot porous plate is presented. The Laplace-Fourier transform technique is employed to simplify the field equations. For the steady-state heat transfer assumption, exact expressions for the temperature and stream function are analytically obtained for TEMHD flow on a wall with two infinite instantaneous hot suction lines. The results obtained are displayed graphically.
We present a numerical study of convection in a horizontal layer comprising a fluid-saturated porous bed overlain by an unconfined fluid layer. Convection is driven by a vertical, destabilising temperature difference applied across the whole system, as in the canonical Rayleigh-Bénard problem. Numerical simulations are carried out using a single-domain formulation of the two-layer problem based on the Darcy-Brinkman equations. We explore the dynamics and heat flux through the system in the limit of large Rayleigh number, but small Darcy number, such that the flow exhibits vigorous convection i…
In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dyna…
We develop a 3D porous medium model for sap flow within a tree stem, which consists of a nonlinear parabolic partial differential equation with a suitable transpiration source term. Using an asymptotic analysis, we derive approximate series solutions for the liquid saturation and sap velocity for a general class of coefficient functions. Several important non-dimensional parameters are identified that can be used to characterize various flow regimes. We investigate the relative importance of stem aspect ratio versus anisotropy in the sapwood hydraulic conductivity, and how these two effects im…
This investigation deals with the analysis of stagnation point heat transfer and corresponding flow features of hydromagnetic viscous incompressible fluid over a vertical shrinking sheet. The considered sheet is assumed to be permeable and subject to addition of stagnation point to control the generated vorticity in the boundary layer. The sheet is placed on the right side of the fluid saturated porous medium which is having permeability of specified form. Nonlinear convection waves in the flow field are realized due to the envisaged nonlinear relation between density and temperature. The equa…
The effect of the variations of the permeability tensor on the close-to-the-wall behaviour of a turbulent channel flow bounded by porous walls is explored using a set of direct numerical simulations. It is found that the total drag can be either reduced or increased by more than $20\%$ by adjusting the permeability directional properties. Drag reduction is achieved for the case of materials with permeability in the vertical direction lower than the one in the wall-parallel planes. This configuration limits the wall normal velocity at the interface while promoting an increase of the tangential …
When a fluid is injected into a porous medium saturated with an ambient fluid of a greater density, the injected fluid forms a plume that rises upwards due to buoyancy. In the near-field of the injection point the plume adjusts its speed to match the buoyancy velocity of the porous medium, either thinning or thickening to conserve mass. These adjustments are the dominant controls on the near-field plume shape, rather than mixing with the ambient fluid, which occurs over larger vertical distances. In this study, we focus on the plume behaviour in the near-field, demonstrating that for moderate …
Many key environmental, industrial, and energy processes rely on controlling fluid transport within subsurface porous media. These media are typically structurally heterogeneous, often with vertically-layered strata of distinct permeabilities -- leading to uneven partitioning of flow across strata, which can be undesirable. Here, using direct in situ visualization, we demonstrate that polymer additives can homogenize this flow by inducing a purely-elastic flow instability that generates random spatiotemporal fluctuations and excess flow resistance in individual strata. In particular, we find t…
We perform direct numerical simulations of a kerosene-water mixture in pipe flow under realistic experimental conditions by solving the Cahn-Hilliard-Navier-Stokes equations. We compute the linear stability of core-annular flow of kerosene and water in a vertical pipe and find that it is highly unstable. By performing DNS initialized with a slightly perturbed core-annular flow, we show that the system transitions to turbulence and finally relaxes into a turbulent slug flow regime provided that the pipe is sufficiently long. This configuration presents mild turbulence and large scale three-dime…
Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (1995) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical cont…
Deep saline aquifers used for CO$_2$ sequestration are commonly made of sedimentary formations consisting of several layers of distinguishable permeability. In this work, the effect of a non-monotonic, vertically varying permeability profile on the onset of convective instability is studied theoretically using linear stability analyses. The onset time depends on the interaction between the permeability profile and the location of the concentration perturbation peak beyond which the concentration of CO$_2$ decays. A thin low-permeability layer can either accelerate or delay the onset time of th…
We examine transient axial creeping flow in the annular gap between a rigid cylinder and a concentric elastic tube. The gap is initially filled with a thin fluid layer. The study focuses on viscous-elastic time-scales for which the rate of solid deformation is of the same order-of-magnitude as the velocity of the fluid. We employ an elastic shell model and the lubrication approximation to obtain a forced nonlinear diffusion equation governing the viscous-elastic interaction. In the case of an advancing liquid front into a configuration with a negligible film layer (compared with the radial def…
Comprehensive Study of 3D Liquid Flow Fields in Additive Manufactured Structures for SMART Reactors Using Large-Scale Vertical Magnetic Resonance Imaging and Computational Fluid Dynamics
Hamburg University of Technology（汉堡工业大学）；University Medical Center Hamburg-Eppendorf（汉堡-埃彭多夫大学医学中心）
Rigorous vertical averaging for pseudo-3D modeling of precipitation obstructed fluid flow
University of Stuttgart（斯图加特大学）；Stuttgart Center for Simulation Science, University of Stuttgart（斯图加特大学斯图加特模拟科学中心）；Helmholtz Centre for Environmental Research（亥姆霍兹环境研究中心）；Department Technical Biogeochemistry, Helmholtz Centre for Environmental Research（亥姆霍兹环境研究中心技术生物地球化学系）；Department of Chemical and Biological Engineering, Center for Biofilm Engineering, Montana State University（蒙大拿州立大学生物膜工程中心化学与生物工程学系）；Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart（斯图加特大学水力学及水系统建模系）
