Inertial Flow Regime Research Articles

Lattice Boltzmann Simulation of Mass Transfer Coefficients for Chemically Reactive Flows in Porous Media

We present lattice Boltzmann (LB) simulations for the mass transfer coefficient from bulk flows to pore surfaces in chemically reactive flows for both ordered and disordered porous structures. The ordered porous structure under consideration consists of cylinders in a staggered arrangement and in a line arrangement, while the disordered one is composed of randomly placed cylinders. Results show that the ordered porous structure of staggered cylinders exhibits a larger mass transfer coefficient than ordered porous structure of inline cylinders does. It is also found that in the disordered porous structures, the Sherwood number (Sh) increases linearly with Reynolds number (Re) at the creeping flow regime; the Sh and Re exhibit a one-half power law dependence at the inertial flow regime. Meanwhile, for Schmidt number (Sc) between 1 and 10, the Sh is proportional to Sc0.8; for Sc between 10 and 100, the Sh is proportional to Sc0.3.

Biomechanics of swimming in developing larval fish.

Most larvae of bony fish are able to swim almost immediately after hatching. Their locomotory system supports several vital functions: fish larvae make fast manoeuvres to escape from predators, aim accurately during suction feeding and may migrate towards suitable future habitats. Owing to their small size and low swimming speed, larval fish operate in the intermediate hydrodynamic regime, which connects the viscous and inertial flow regimes. They experience relatively strong viscous effects at low swimming speeds, and relatively strong inertial effects at their highest speeds. As the larvae grow and increase swimming speed, a shift occurs towards the inertial flow regime. To compensate for size-related limitations on swimming speed, fish larvae exploit high tail beat frequencies at their highest speeds, made possible by their low body inertia and fast neuromuscular system. The shifts in flow regime and body inertia lead to changing functional demands on the locomotory system during larval growth. To reach the reproductive adult stage, the developing larvae need to adjust to and perform the functions necessary for survival. Just after hatching, many fish larvae rely on yolk and need to develop their feeding systems before the yolk is exhausted. Furthermore, the larvae need to develop and continuously adjust their sensory, neural and muscular systems to catch prey and avoid predation. This Review discusses the hydrodynamics of swimming in the intermediate flow regime, the changing functional demands on the locomotory system of the growing and developing larval fish, and the solutions that have evolved to accommodate these demands.

Lattice Boltzmann simulation of shear viscosity of suspensions containing porous particles

We present three-dimensional lattice Boltzmann simulations of dilute suspensions containing porous particles. The fluid flow around and inside a porous particle is described by the volume-averaged macroscopic equations in terms of intrinsic phase average. The energy dissipation of the suspended particle in a Couette flow is calculated to obtain the relative viscosity of the suspension. Results show that the relative viscosity of the suspension increases linearly with the particle volume fraction. A correlation equation is obtained for the intrinsic viscosity as a function of Darcy number. It is found that when the suspension is at the inertial flow regime, its intrinsic viscosity increases linearly with Reynolds number, and the increasing rate depends on Darcy number.

Hydraulic fracture conductivity: effects of rod-shaped proppant from lattice-Boltzmann simulations and lab tests

The goal of this study is to evaluate the conductivity of random close packings of non-spherical, rod-shaped proppant particles under the closure stress using numerical simulation and lab tests, with application to the conductivity of hydraulic fractures created in subterranean formation to stimulate production from oil and gas reservoirs. Numerical simulations of a steady viscous flow through proppant packs are carried out using the lattice Boltzmann method for the Darcy flow regime. The particle packings were generated numerically using the sequential deposition method. The simulations are conducted for packings of spheres, ellipsoids, cylinders, and mixtures of spheres with cylinders at various volumetric concentrations. It is demonstrated that cylinders provide the highest permeability among the proppants studied. The dependence of the nondimensional permeability (scaled by the equivalent particle radius squared) on porosity obtained numerically is well approximated by the power-law function: K/Rv2=0.204ϕ4.58 in a wide range of porosity: 0.3 ≤ ϕ ≤ 0.7. Lattice-Boltzmann simulations are cross-verified against finite-volume simulations using Navier–Stokes equations for inertial flow regime. Correlations for the normalized beta-factor as a function of porosity and normalized permeability are presented as well. These formulae are in a good agreement with the experimental measurements (including packings of rod-shaped particles) and existing laboratory data, available in the porosity range 0.3 ≤ ϕ ≤ 0.5. Comparison with correlations by other authors is also given.

Non-Darcian flow of shear-thinning fluids through packed beads: Experiments and predictions using Forchheimer's law and Ergun's equation

The flow of shear-thinning fluids through unconsolidated porous media is present in a number of important industrial applications such as soil depollution, Enhanced Oil Recovery or filtration of polymeric liquids. Therefore, predicting the pressure drop–flow rate relationship in model porous media has been the scope of major research efforts during the last decades. Although the flow of Newtonian fluids through packs of spherical particles is well understood in most cases, much less is known regarding the flow of shear-thinning fluids as high molecular weight polymer aqueous solutions. In particular, the experimental data for the non-Darcian flow of shear-thinning fluids are scarce and so are the current approaches for their prediction. Given the relevance of non-Darcian shear-thinning flow, the scope of this work is to perform an experimental study to systematically evaluate the effects of fluid shear rheology on the flow rate–pressure drop relationships for the non-Darcian flow through different packs of glass spheres. To do so, xanthan gum aqueous solutions with different polymer concentrations are injected through four packs of glass spheres with uniform size under Darcian and inertial flow regimes. A total of 1560 experimental data are then compared with predictions coming from different methods based on the extension of widely used Ergun's equation and Forchheimer's law to the case of shear thinning fluids, determining the accuracy of these predictions. The use of a proper definition for Reynolds number and a realistic model to represent the rheology of the injected fluids results in the porous media are shown to be key aspects to successfully predict pressure drop–flow rate relationships for the inertial shear-thinning flow in packed beads.

Lattice Boltzmann methods in porous media simulations: From laminar to turbulent flow

The lattice Boltzmann method has become a popular tool for determining the correlations for drag force and permeability in porous media for a wide range of Reynolds numbers and solid volume fractions. In order to achieve accurate and relevant results, it is important not only to implement very efficient code, but also to choose the most appropriate simulation setup. Moreover, it is essential to accurately evaluate the boundary conditions and collision models that are effective from the Stokes regime to the inertial and turbulent flow regimes. In this paper, we compare various no-slip boundary schemes and collision operators to assess their efficiency and accuracy. Instead of assuming a constant volume force driving the flow, a periodic pressure drop boundary condition is employed to mimic the pressure-driven flow through the simple sphere pack in a periodic domain. We first consider the convergence rates of various boundary conditions with different collision operators in the Stokes flow regime. Additionally, we choose different boundary conditions that are representatives of first- to third-order schemes at curved boundaries in order to evaluate their convergence rates numerically for both inertial and turbulent flow. We find that the multi-reflection boundary condition yields second order for inertial flow while it converges with third order in the Stokes regime. Taking into account the both computational cost and accuracy requirements, we choose the central linear interpolation bounce-back scheme in combination with the two-relaxation-time collision model. This combination is characterized by providing viscosity independent results and second-order spatial convergence. This method is applied to perform simulations of touching spheres arranged in a simple cubic array. Full- and reduced-stencil lattice models, i.e., the D3Q27 and D3Q19, respectively, are compared and the drag force and friction factor results are presented for Reynolds numbers in the range of 0.001 to 2,477. The drag forces computed using these two different lattice models have a relative difference below 3% for the highest Reynolds number considered in this study. Using the evaluation results, we demonstrate the flexibility of the models and software in two large scale computations, first a flow through an unstructured packing of spherical particles, and second for the turbulent flow over a permeable bed.

Internal and External Flow over Laser-Textured Superhydrophobic Polytetrafluoroethylene (PTFE).

In this work, internal and external flows over superhydrophobic (SH) polytetrafluoroethylene (PTFE) were studied. The SH surface was fabricated by a one-step femtosecond laser micromachining process. The drag reduction ability of the textured surface was studied experimentally both in microscale and macroscale internal flows. The slip length, which indicates drag reduction in fluid flow, was determined in microscale fluid flow with a cone-and-plate rheometer, whereas a pressure channel setup was used for macroscale flow experiments. The textured PTFE surface reduced drag in both experiments yielding comparable slip lengths. Moreover, the experimentally obtained slip lengths correspond well to the result obtained applying a semianalytical model, which considers the solid fraction of the textured surface. In addition to the internal flow studies, we fabricated SH PTFE spheres to test their drag reduction abilities in an external flow experiment, where the terminal velocities of the falling spheres were measured. These experiments were conducted at three different Reynolds numbers in both viscous and inertial flow regimes with pure glycerol, a 30% glycerol solution, and water. Surprisingly, the drag on the SH spheres was higher than the measured drag on the non-SH spheres. We hypothesize that the increase in form drag outweighs the decrease in friction drag on the SH sphere. Thus, the overall drag increased. These experiments demonstrate that a superhydrophobic surface that reduces drag in internal flow might not reduce drag in external flow.

Flow regime transitions in dense non-Brownian suspensions: rheology, microstructural characterization, and constitutive modeling.

Shear flow of dense non-Brownian suspensions is simulated using the discrete element method taking particle contact and hydrodynamic lubrication into account. The resulting flow regimes are mapped in the parametric space of the solid volume fraction, shear rate, fluid viscosity, and particle stiffness. Below a critical volume fraction ϕ(c), the rheology is governed by the Stokes number, which distinguishes between viscous and inertial flow regimes. Above ϕ(c), a quasistatic regime exists for low and moderate shear rates. At very high shear rates, the ϕ dependence is lost, and soft-particle rheology is explored. The transitions between rheological regimes are associated with the evolving contribution of lubrication to the suspension stress. Transitions in microscopic phenomena, such as interparticle force distribution, fabric, and correlation length are found to correspond to those in the macroscopic flow. Motivated by the bulk rheology, a constitutive model is proposed combining a viscous pressure term with a dry granular model presented by Chialvo et al. [Phys. Rev. E 85, 021305 (2012)]. The model is shown to successfully capture the flow regime transitions.

Modeling the hydrodynamics and the process of averaging a highly concentrated granular medium in a mixing hopper

The study of motion and mixing of a highly concentrated loose granular medium in a vertical mixing hopper in the inertial motion mode within the framework of the of fast granular flows are shown. This paper presents the study of motion and mixing of a highly concentrated loose granular medium in a vertical mixing hopper in the inertial motion mode (1) within the framework of the of fast granular flows. To describe the flow, a differential model based on continuum mechanics concepts and rheological properties of granular materials with an additional equation of chaotic energy transfer caused by pulsation of the granules (2) is used. Simulation of the mixing process is based on the transport equation of concentration of the primary and key components of the granular mixture. Energy of the stochastic motion of granules in the inertial flow regime is modeled by analogy with the theory of turbulence (3). Energy dissipation of the stochastic motion of the granular medium and determination of the viscosity of the model in the equations of momentum and energy transport are written by means of the Kolmogorov-Prandtl formula. Granular motion in the pulsating mode is limited due to the high concentration of the granular medium that allows, in the first approximation, to consider the length scale of the chaotic pulsation of the granules as a constant value. This paper focuses on the steady gravity flow of a highly concentrated granular medium in a vertical silo with horizontal plates inside for intensive mixing of the primary and key components of the mixture. A scheme of such a bunker is shown in Fig. 1. At the entrance to the channel an unmixed homogeneous (by its physical properties) granular medium is fed at a constant speed from the top. The process of averaging is due to convection and diffusion phenomena caused by the chaotic pulsation of the granules in the inertial flow mode when moving through the bunker. To describe the hydrodynamics and the averaging process of a highly concentrated granular medium in the inertial flow regime, a set of equations consisting of those of momentum transport, the continuity equation, the equation of stochastic energy of pulsating granular motion and the transport equation of

Hydrodynamic comparison of spherical and cylindrical particles in a gas–liquid–solid fluidized bed at elevated pressure and high gas holdup conditions

Experiments were carried out to validate the use of spheres in lieu of cylinders when investigating the global hydrodynamic features of a co-current gas–liquid–solid fluidized bed. Two sizes of glass spheres with diameters of 4 and 1.5mm were compared to aluminum cylinders with equivalent volume/surface area ratios (i.e., matching Sauter mean diameters). Lengths/diameters of the larger and smaller cylinders were 7.5/3.2mm and 3.1/1.2mm, respectively, which resulted in equal particle sphericity of 0.8 for both sizes. The particle properties of the larger particles led to the inertial settling flow regime (ReLT∞>500) in water while the smaller particles were in the intermediate regime (0.2<ReLT∞<500). High gas holdup conditions were obtained by increasing the system pressure to 6.5MPa and/or adding a surfactant. Atmospheric conditions were also studied for comparison. Experiments were conducted in a 101.6mm diameter column with tap water or a 0.5wt.% aqueous ethanol solution as the liquid phase while the gas phase was a combination of air and nitrogen. Global phase holdups measured from the dynamic pressure profiles characterized the hydrodynamic behavior of the fluidized bed and studied the impact of particle shape. Standard deviations of the mean holdups aided the comparison and also examined the fluctuations of the bed interface. Liquid–solid fluidized bed experiments demonstrated that equivalent Sauter mean diameters resulted in comparable bed porosities. Gas–liquid–solid fluidized bed dynamics of equivalent size spherical and cylindrical particles were similar in the dispersed bubble flow regime whereas differences were observed in the presence of larger coalescing bubbles.

Porous media properties of reticulated shape memory polymer foams and mock embolic coils for aneurysm treatment

BackgroundShape memory polymer (SMP) foams are being investigated as an alternative aneurysm treatment method to embolic coils. The goal of both techniques is the reduction of blood flow into the aneurysm and the subsequent formation of a stable thrombus, which prevents future aneurysm rupture. The purpose of this study is to experimentally determine the parameters, permeability and form factor, which are related to the flow resistance imposed by both media when subjected to a pressure gradient.MethodsThe porous media properties—permeability and form factor—of SMP foams and mock embolic coils (MECs) were measured with a pressure gradient method by means of an in vitro closed flow loop. We implemented the Forchheimer-Hazen-Dupuit-Darcy equation to calculate these properties. Mechanically-reticulated SMP foams were fabricated with average cell sizes of 0.7E-3 and 1.1E-3 m, while the MECs were arranged with volumetric packing densities of 11-28%.ResultsThe permeability of the SMP foams was an order of magnitude lower than that of the MECs. The form factor differed by up to two orders of magnitude and was higher for the SMP foams in all cases. The maximum flow rate of all samples tested was within the inertial laminar flow regime, with Reynolds numbers ranging between 1 and 35.ConclusionsThe SMP foams impose a greater resistance to fluid flow compared to MECs, which is a result of increased viscous and inertial losses. These results suggest that aneurysms treated with SMP foam will have flow conditions more favorable for blood stasis than those treated with embolic coils having packing densities ≤ 28%.

Ferromagnetic shape memory flapper for remotely actuated propulsion systems

Generating propulsion with small-scale devices is a major challenge due to both the domination of viscous forces at low Reynolds numbers as well as the small relative stroke length of traditional actuators. Ferromagnetic shape memory materials are good candidates for such devices as they exhibit a unique combination of large strains and fast responses, and can be remotely activated by magnetic fields. This paper presents the design, analysis, and realization of a novel NiMnGa shear actuation method, which is especially suitable for small-scale fluid propulsion. A fluid mechanics analysis shows that the two key parameters for powerful propulsion are the engineering shear strain and twin boundary velocity. Using high-speed photography, we directly measure both parameters under an alternating magnetic field. Reynolds numbers in the inertial flow regime (>700) are evaluated. Measurements of the transient thrust show values up to 40 mN, significantly higher than biological equivalents. This work paves the way for new remotely activated and controlled propulsion for untethered micro-scale robots.

Flow and axial dispersion in a sinusoidal-walled tube: Effects of inertial and unsteady flows

In this work, we consider a sinusoidal-walled tube (a three-dimensional tube with sinusoidally-varying diameter) as a simplified conceptualization of flow in porous media. Direct numerical simulation using computational fluid dynamics (CFD) methods was used to compute velocity fields by solving the Navier–Stokes equations, and also to numerically solve the volume averaging closure problem, for a range of Reynolds numbers (Re) spanning the low-Re to inertial flow regimes, including one simulation at Re=449 for which unsteady flow was observed. The longitudinal dispersion observed for the flow was computed using a random walk particle tracking method, and this was compared to the longitudinal dispersion predicted from a volume-averaged macroscopic mass balance using the method of volume averaging; the results of the two methods were consistent. Our results are compared to experimental measurements of dispersion in porous media and to previous theoretical results for both the low-Re, Stokes flow regime and for values of Re representing the steady inertial regime. In the steady inertial regime, a power-law increase in the effective longitudinal dispersion (DL) with Re was found, and this is consistent with previous results. This rapid rate of increase is caused by trapping of solute in expansions due to flow separation (eddies). One unsteady (but non-turbulent) flow case (Re=449) was also examined. For this case, the rate of increase of DL with Re was smaller than that observed at lower Re. Velocity fluctuations in this regime lead to increased rates of solute mass transfer between the core flow and separated flow regions, thus diminishing the amount of tailing caused by solute trapping in eddies and thereby reducing longitudinal dispersion. The observed tailing was further explored through analysis of concentration skewness (third moment) and its assymptotic convergence to conventional advection–dispersion behavior (skewness=0). The method of volume averaging was applied to develop a skewness model, and demonstrated that the skewness decreases as a function of inverse square root of time. Our particle tracking simulation results were shown to conform to this theoretical result in most of the cases considered.

Visualization of inertial flow in deterministic ratchets

Recently it was found that at moderate Reynolds numbers, Re>1, the displacement behavior of suspended particles in deterministic ratchets changes with increasing flow rates, resulting in superior separation at higher flow rates. This change was attributed to the inertial flow regime where the flow pattern strongly depends on Re. The objective of this study was to visualize the fluid streamlines of inertial flow in deterministic ratchets, using 2D flow field simulations and high speed camera images.Experimental investigation and numerical simulation of the flow field in two deterministic ratchet designs provided more insight in the improved separation efficiency. The most remarkable observation was the formation of vortices, which increased in size at higher flow rates. For cylindrical-shaped obstacles a pair of vortices developed at Re=9 and grew to 70% of the gap size between two consecutive obstacle rows at Re=30. For quadrilateral-shaped obstacles vortices developed at Re=2 and grew to 75% at Re=26. The expected effect of vortex formation on particle movement is preventing the ‘zigzag’ motion of particles by narrowing the gap between two consecutive obstacle rows. Another observation is the increase in the number of flow lanes at higher Re. This is explained by the asymmetry of the fluid velocity profile in the gaps, caused by the anisotropy of the obstacle arrays in combination with the development of vortices. The increase in number of flow lanes reduced the critical particle size for displacement by 14% for the design with cylindrical-shaped obstacles and 24% for the design with quadrilateral-shaped obstacles. This gives opportunities for new designs with larger gap sizes, which reduces the chance for clogging and lowers the pressure drop.The observations underline that anisotropy or asymmetry of the obstacles and the flow regime are both important parameters for the separation efficiency of deterministic ratchets.

Buoyant miscible displacement flows at moderate viscosity ratios and low Atwood numbers in near-horizontal ducts

We present results from a study of buoyant miscible displacements flows at moderate viscosity ratios in near-horizontal ducts. Low Atwood numbers are considered. Inertial effects are significant although the flow regimes are laminar. Pipe and plane channel geometries are considered using a mix of experimental, computational and analytical techniques. The main focus of the study is on the effects of the viscosity ratio between the fluids. We show that small viscosity ratios lead to more efficient displacements, as is intuitive. In each geometry we find a mix of viscous and inertial flows, in broadly the same pattern as for the iso-viscous displacements studied extensively in Taghavi et al. (submitted for publication). Predictive models are proposed for the viscous regime, in the case of the plane channel, and for the inertial exchange flow regime, in both geometries. We also study displacement flows with shear-thinning fluids, over a more restrictive range of parameters. We show that with an appropriate definition of the effective viscosity the scaled front velocities fit well with the results from the Newtonian displacements, in both pipe and plane channel geometries. The main role of ratio m of displaced fluid viscosity to displacing viscosity is in line with our intuition. For m > 1 displacement efficiencies are reduced and the front velocities are larger. However, the main increase in front velocity is achieved for modest viscosity ratios of 3 or 4 to 1, with little increase afterwards. The reverse situation, m < 1 , shows significant improvements in displacement efficiency, with front velocity V ^ f reduced down towards the imposed mean velocity V ^ 0 , as m decreases. A viscosity ratio of around 1–4 appears to achieve quite efficient displacements, and to be able to compensate for the effects of buoyancy (which in our case are always destabilising).

The Spectral Ice Habit Prediction System (SHIPS). Part IV: Box Model Simulations of the Habit-Dependent Aggregation Process

Abstract The purpose of this paper is to assess the prediction of particle properties of aggregates and particle size distributions with the Spectral Ice Habit Prediction System (SHIPS) and to investigate the effects of crystal habits on aggregation process. Aggregation processes of ice particles are critical to the understanding of precipitation and the radiative signatures of cloud systems. Conventional approaches taken in cloud-resolving models (CRMs) are not ideal to study the effects of crystal habits on aggregation processes because the properties of aggregates have to be assumed beforehand. As described in Part III, SHIPS solves the stochastic collection equation along with particle property variables that contain information about crystal habits and maximum dimensions of aggregates. This approach makes it possible to simulate properties of aggregates explicitly and continuously in CRMs according to the crystal habits. The aggregation simulations were implemented in a simple model setup, assuming seven crystal habits and several initial particle size distributions (PSDs). The predicted PSDs showed good agreement with observations after rescaling except for the large-size end. The ice particle properties predicted by the model, such as the mass–dimensional (m-D) relationship and the relationship between diameter of aggregates and number of component crystals in an aggregate, were found to be quantitatively similar to those observed. Furthermore, these predictions were dependent on the initial PSDs and habits. A simple model for the growth of a particle’s maximum dimension was able to simulate the typically observed fractal dimension of aggregates when an observed value of the separation ratio of two particles was used. A detailed analysis of the collection kernel indicates that the m-D relationship unique to each crystal habit has a large impact on the growth rate of aggregates through the cross-sectional area or terminal velocity difference, depending on the initial equivalent particle distribution. A significant decrease in terminal velocity differences was found in the inertial flow regime for all the habits but the constant-density sphere. It led to formation of a local maximum in the collection kernel and, in turn, formed an identifiable mode in the PSDs. Remaining issues that must be addressed in order to improve the aggregation simulation with the quasi-stochastic model are discussed.

Deposit architecture and dynamics of the 2006 block‐and‐ash flows of Merapi Volcano, Java, Indonesia

AbstractThe internal architecture of the 2006 block‐and‐ash flow deposits of Merapi volcano (Java, Indonesia) was investigated using data collected from 27 stratigraphic sections measured immediately after flow emplacement, and after one and two rainy seasons of erosion. Identification of different depositional units and their longitudinal and lateral facies variations provide detailed information about: (i) the distribution, volumes and sedimentological characteristics of the different units; (ii) flow types and mobility as inferred from associated deposits; and (iii) changes in the dynamics of the different flows and their material during emplacement. Two main types of block‐and‐ash flows (short‐runout to medium‐runout block‐and‐ash flows and long‐runout block‐and‐ash flows) are defined based on flow generation mechanism, flow volume, travel distance, deposit morphology, distribution, lithology and grain‐size distribution. Conceptual models for the transport and depositional mechanisms of these two types of block‐and‐ash flows are presented. Variations in the runout distances observed for short‐runout to medium‐runout block‐and‐ash flows are linked directly to different initial flow volumes, degree of fragmentation and material properties of the moving mass during transport, with the largest and finer grained flows having the greatest mobility. Deposition occurs only over a narrow range of basal inclinations close to the angle of repose for pyroclastic material, indicating that such flows behave in a similar way to granular‐free surface flows on unconfined planes. The flow mechanisms of long‐runout block‐and‐ash flows at Merapi are interpreted to be similar, in many respects, to unsteady, cohesionless grain flows with an inertial flow regime where collisional forces largely overcome frictional forces. Flow unsteadiness causes the main body to be segmented into different pulses that run closer to each other as the flow moves downslope. Deposition occurs stepwise, with rapid aggradation of stacked sub‐units from different parts of the major flow pulses. In such a model, the arrival of each flow pulse front at selected sites in the main river valley controls the generation and development of highly mobile, unconfined pyroclastic flows outside valley regions and their associated overbank deposits.

Modeling of unsteady and steady fluid flow, heat transfer and dispersion in porous media using unit cell scale

A unit cell scale computation of laminar steady and unsteady fluid flow and heat transfer is presented for a spatially periodic array of square rods representing two-dimensional isotropic or anisotropic porous media. In the model, a unit cell is taken as a representative elementary control volume and uniform heat flux boundary conditions are imposed on the solid–fluid interface. The governing equations are discretized by means of the finite volume approach; boundaries between adjacent cells are taken to be spatially periodic. Computations obtained using the SIMPLER algorithm, are made by varying the macroscopic flow direction from 0° to 90° relative to the unit cell, and varying the Reynolds number over the range 1–10 3 spanning the Darcian and the inertial flow regimes to construct a database of local flow and heat transfer resistances in terms of permeabilities, inertial coefficients, Nusselt numbers, and thermal dispersion coefficients. The resulting database is utilized in a system scale analysis of a serpentine heat exchanger, where these directional terms from the microscale analysis provide closure to the porous-continuum model.

Reconstruction of the Water Table from Self‐Potential Data: A Bayesian Approach

Ground water flow associated with pumping and injection tests generates self-potential signals that can be measured at the ground surface and used to estimate the pattern of ground water flow at depth. We propose an inversion of the self-potential signals that accounts for the heterogeneous nature of the aquifer and a relationship between the electrical resistivity and the streaming current coupling coefficient. We recast the inversion of the self-potential data into a Bayesian framework. Synthetic tests are performed showing the advantage in using self-potential signals in addition to in situ measurements of the potentiometric levels to reconstruct the shape of the water table. This methodology is applied to a new data set from a series of coordinated hydraulic tomography, self-potential, and electrical resistivity tomography experiments performed at the Boise Hydrogeophysical Research Site, Idaho. In particular, we examine one of the dipole hydraulic tests and its reciprocal to show the sensitivity of the self-potential signals to variations of the potentiometric levels under steady-state conditions. However, because of the high pumping rate, the response was also influenced by the Reynolds number, especially near the pumping well for a given test. Ground water flow in the inertial laminar flow regime is responsible for nonlinearity that is not yet accounted for in self-potential tomography. Numerical modeling addresses the sensitivity of the self-potential response to this problem.

Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes

We employ numerical simulation to investigate the hydrodynamic performance of anguilliform locomotion and compare it with that of carangiform swimming as the Reynolds number (Re) and the tail-beat frequency (Strouhal number, St) are systematically varied. The virtual swimmer is a 3-D lamprey-like flexible body undulating with prescribed experimental kinematics of anguilliform type. Simulations are carried out for three Reynolds numbers spanning the transitional and inertial flow regimes, Re=300, 4000 (viscous flow), and infinity (inviscid flow). The net mean force is found to be mainly dependent on the tail-beat frequency rather than the tail-beat amplitude. The critical Strouhal number, St, at which the net mean force becomes zero (constant-speed self-propulsion) is, similar to carangiform swimming, a decreasing function of Re and approaches the range of St numbers at which most anguilliform swimmers swim in nature (St approximately 0.45) only as Re increases. The anguilliform swimmer's force time series is characterized by significantly smaller fluctuations above the mean than that for carangiform swimmers. In stark contrast with carangiform swimmers, the propulsive efficiency of anguilliform swimmers at St is not an increasing function of Re but instead is maximized in the transitional regime. Furthermore, the power required for anguilliform swimming is less than that for the carangiform swimmer at the same Re. We also show that the form drag decreases while viscous drag increases as St increases. Finally, our simulations reinforce our previous finding for carangiform swimmers that the 3-D wake structure depends primarily on the Strouhal number.