Numerical simulation of transition layer at a fluid-porous interface (original) (raw)
Related papers
2013
The objective of this thesis is to get new equations with out empirical constants to estimate discharge through porous medium for laminar, turbulent and transition flow regimes using easily measurable parameters in the field. It is necessary to analyze the relation between various flow parameters, connected with flow through porous media in parallel flow, to study in depth the various forms of friction equations and the behavior of Darcy and Non-Darcy parameters with physical properties of the media.
Fluid mechanics of the interface region between two porous layers
Applied Mathematics and Computation, 2002
Flow through and over a fluid-saturated porous layer is investigated. The flow through a porous channel (which is assumed to be governed by Forchheimer equation) is terminated by a porous layer possessing a different structure (the flow through which is governed by the Brinkman equation). At the interface between the physical regions, matching conditions on the velocity and shear stress are imposed. The flow through this configuration admits solutions which are linear combinations of polynomial and exponential functions. The effect of the Reynolds number and the Darcy numbers on the interface velocity is presented in this work. Ó
Verification of the boundary condition at the porous medium–fluid interface
We study the hydrodynamic stability of liquid flowing down over the inclined layer of uniform porous medium and compare the results obtained in the different frameworks. The flow in porous medium is described by the Brinkman model and by the Darcy model with corresponding boundary conditions at the interface between the homogeneous fluid and porous medium. It is shown the critical Reynolds number is calculated for the Darcy model much lower than in case of the Brinkman model, while the flow velocity is the same in the both models. It is a pure mathematical effect, which can be used to verify the models and to determine the empirical coefficients in the boundary conditions from an experimental study of flow instability.
Simulation of less‐mobile porosity dynamics in contrasting sediment water interface porous media
Hydrological Processes, 2018
Considering heterogeneity in porous media pore size and connectivity is essential to predicting reactive solute transport across interfaces. However, exchange with less-mobile porosity is rarely considered in surface water/groundwater recharge studies. Previous research indicates that a combination of pore-fluid sampling and geoelectrical measurements can be used to quantify lessmobile porosity exchange dynamics using the time-varying relation between fluid and bulk electrical conductivity (EC). For this study we use macro-scale (10s of cm) advection-dispersion solute transport models linked with electrical conduction in COMSOL Multiphysics to explore less-mobile porosity dynamics in two different types of observed sediment water interface porous media. Modeled sediment textures contrast from strongly layered streambed deposits to poorly sorted lakebed sands and cobbles. During simulated ionic tracer perturbations a lag between fluid and bulk EC, and the resultant hysteresis, is observed for all simulations indicating differential loading of pore spaces with tracer. Less-mobile exchange parameters are determined graphically from these tracer time series data without the need for inverse numerical model simulation. In both sediment types effective lessmobile porosity exchange parameters are variable in response to changes in flow direction and fluid flux. These observed flow-dependent effects directly impact local less-mobile residence times and associated contact time for biogeochemical reaction. The simulations indicate that for the sediment textures explored here less-mobile porosity exchange is dominated by variable rates of advection through the domain, rather than diffusion of solute, for typical low-to-moderate rate (approximately 3-40 cm d-1) hyporheic fluid fluxes. Overall our model-based results show that less-mobile porosity may be expected in a range of natural hyporheic sediments, and that changes in flowpath orientation and magnitude will impact less-mobile exchange parameters. These temporal dynamics can be assessed with the geoelectrical experimental tracer method applied at laboratory and field scales.
A Study of Flow through a Channel Bounded by a Brinkman Transition Porous Layer
Journal of Applied Mathematics and Physics, 2018
Flow through a channel bounded by a porous layer is considered when a transition layer exists between the channel and the medium. The variable permeability in the transition layer is chosen such that Brinkman's equation governing the flow reduces to a generalized inhomogeneous Airy's differential equation. Solution to the resulting generalized Airy's equation is obtained in this work and solution to the flow through the transition layer, of the same configuration, reported in the literature, is recovered from the current solution.
NUMERICAL ANALYSIS OF THE STRESS JUMP INTERFACE CONDITION FOR LAMINAR FLOW OVER A POROUS LAYER
Numerical Heat Transfer Part A-applications, 2003
A number of natural and engineering systems can be characterized by some sort of porous structure through which a working fluid permeates. Boundary layers over tropical forests and spreading of chemical contaminants through underground water reservoirs are examples of important environmental flows that can benefit form appropriate mathematical treatment. For hybrid media, involving both a porous structure and a clear flow region, difficulties arise due to the proper mathematical treatment given at the interface. The literature proposes a jump condition in which stresses at both sides of the interface are not of the same value. The objective of this article is to present a numerical implementation for solving such a hybrid medium, considering here a channel partially filled with a porous layer through which fluid flows in laminar regime. One unique set of transport equations is applied to both regions. Numerical results are compared with available analytical solutions in the literature for two cases, namely, with and without the nonlinear Forchheimer term. Results are presented for the mean velocity across both the porous structure and the clear region. The influence of medium properties, such as porosity and permeability, is discussed.
Transition layer thickness at a fluid-porous interface
Physics of Fluids, 2005
The length scale of the transition region between a porous layer and its overlying fluid layer is experimentally studied. The experimental setup consists of a rectangular channel, in which a fluid layer flows over a porous bed. Using particle image velocimetry and refractive index matching, two-dimensional velocity measurements in the interfacial region were performed. The thickness of this transition layer, defined by the height below the permeable interface up to which the velocity decreases to the Darcy scale, is measured and compared with the permeability and the matrix grain size. It was observed that the thickness of the transition zone, δ, is of the order of the grain diameter, and hence, much larger than the square root of the permeability as predicted by previous theoretical studies. The Reynolds number and the fluid height over the porous substrate were found to affect the gradient of the horizontal velocity component at the interfacial region while the length scale of the...
Velocity Pulse Model for Turbulent Diffusion from Flowing Water into a Sediment Bed
Journal of Environmental Engineering, 2008
The "velocity pulse model" simulates the transfer of turbulence from flowing water into a sediment bed, and its effect on the diffusional mass transfer of a solute ͑e.g., oxygen, sulfate, or nitrate͒ in the sediment bed. In the "pulse model," turbulence above the sediment surface is described by sinusoidal variations of vertical velocity in time. It is shown that vertical velocity components dampen quickly inside the sediment when the frequency of velocity fluctuations is high and viscous dissipation is strong. Viscous dissipation ͑͒ inside the sediment is related to the apparent viscosity depending on the structure of the sediment pore space, i.e., the porosity and grain diameter, as well as inertial effects when the flow is turbulent. A value / 0 between 1 and 20 ͑ 0 is kinematic viscosity of water͒ has been considered. Turbulence penetration into the sediment is parametrized by the Reynolds number Re= UL/ and the relative penetration velocity W / U, where Uϭamplitude of the velocity pulse; and Wϭpenetration velocity; L = WTϭwave length of the velocity pulse; and T is its period. Amplitudes of vertical velocity components inside the sediment and their autocorrelation functions are computed, and the results are used to estimate eddy viscosity inside the sediment pore system as a function of depth. Diffusivity in the sediment pore system is inferred by using turbulent or molecular Schmidt numbers. Turbulence penetration from flowing water can enhance the vertical diffusion coefficient in a sediment bed by an order of magnitude or more. Penetration depth of turbulence is higher for low frequency velocity pulses. Vertical diffusivity inside the pore system is shown to decrease more or less exponentially with depth below the sediment/water interface. Vertical diffusivities in a sediment bed estimated by the "velocity pulse model" can be used in pore water quality models to describe vertical transport from or into flowing surface water. The analysis has been conducted for a conservative material, but source and sink terms can be added to the vertical transport equation.
Water Resources Research, 2009
A model of pore water flow induced by pressure fluctuations from a turbulent boundary layer flow over a permeable sediment bed is presented. The bed has a smooth or rough flat surface without bed forms. Pressure and velocity fluctuations that penetrate from the sediment/water interface into the sediment pore system and affect mass (solute) transfer are described as periodic in space and time. The amplitude (p0) is determined from a study of the turbulent kinetic energy balance for wall turbulence; the wave number (chi) and the period (T) are given as functions of the shear velocity (U*) based on the near-bed coherent motions. The flow field in the sediment is described by the continuity equation and Darcy's law. Simulation results show that pore water velocity is faster when the shear velocity (U*) on the sediment bed and/or the permeability of the sediment bed (k) are increased. Accordingly, the exchange velocity of water or solute transfer rate across the sediment/water interface (V0) becomes larger when (U*) and (k) are increased. However, the penetration depth of pore water velocity fluctuations into the sediment bed becomes smaller when (U*) is larger, i.e., when the period of fluctuating pressure is short. Overall, this paper provides new and quantitative information on the enhancement of pore water flow in a flat sediment bed over which a turbulent current is flowing.
Interface between turbulent flows above and within rough porous walls
Acta Geophysica, 2008
This paper explores the concept of a macroscopic boundary between turbulent flows above and within rough permeable walls. The macroscopic boundary and the associated conditions for macroscopic flow variables have been thoroughly investigated for laminar, but not for turbulent flows. The literature on laminar flows follows two main conceptual models of the boundary: sharp boundary with step changes in macroscopic variables and gradual boundary with smooth changes of variables. The former approach is usually associated with the twodomain simulation models and the latter one with the single-domain models. This paper presents the derivation of the step conditions for velocity and shear stress at the macroscopic boundary between turbulent boundary layer and turbulent porous media flows. The physical meaning of the main terms in the shear stress condition is discussed in order to clarify the relationship between two-domain and single-domain simulation models.