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NASA NTRS1995

Reflection and transmission of GMIR shock at the heliopause and their relation to the 2- and 3-kHz radio emissions

We use Voyager 2 plasma and magnetic field data together with a one-fluid MHD model to study the interactions of the 1991 Global Merged Interaction Region (GMIR) shock with the heliopause. The 1991 GMIR is an extraordinarily large global solar wind structure in radial, longitudinal and latitudinal extents. It has a strong shock at the leading edge. After its penetration through the termination shock, the GMIR shock first propagates through the subsonic solar wind, then interacts with the heliopause. The interaction produces a transmitted shock propagating outward in the interstellar medium, and a reflected shock propagating backward in the subsonic solar wind. We identify the reflected shock and the transmitted shock as the possible source of the radio noise detected at Voyagers. The plasma frequency behind the reflected and the transmitted shock can be, respectively, responsible for the 2- and 3-kHz radio emissions. The two bands of radio noise are emitted from sources on both sides of the heliopause starting at about the same time. If the emission is generated by f(sub p)-radiation then the heliopause is located at R approximately 130 AU. If the emission is generated by 2f(sub p)-radiation the n R approximately 150 AU. Because the relative speed of the interstellar plasma with respect to the sun appears to be sub-Alfvenic, it is very unlikely there is a fast-bow shock of the heliosphere.

Whang, Y. C.↗

NASA NTRS1995

Structure of the magnetopause inferred from one-dimensional hybrid simulations

The structure of the magnetopause is investigated by studying the interaction between two plasmas with solar wind and magnetospheric properties. Both Hall-MHD and hybrid (particle ions and fluid electrons) simulations are performed to compare and contrast the nature of the solutions in the fluid and the kinetic limits. It is shown that, in accordance with previous studies, the fluid solutions consist of multiple discontinuities and waves such as slow shocks and waves, as well as contact and rotational discontinuities. In contrast, the kinetic solutions consist of fewer discontinuities and include non-MHD boundaries. The difference between the two types of solutions are attributed to the absence of contact surfaces in collisionless plasmas and the possible Landau damping of slow waves. The kinetic solutions are found to be in a much better agreement with magnetopause observations, which have shown little evidence for the presence of slow shocks or contact discontinuities. The results of kinetic calculations suggest that the presence of a small but finite normal component of the magnetic field allows for the mixing of magnetosheath and magnetospheric plasmas and may, in part, be responsible for the formation of the boundary layer even during the periods of northward interplanetary magnetic field. These results also show that the necessary changes in the fields and the plasma parameters across the magnetopause do not occur simultaneously (i.e., in the same spatial location). As such, the magnetopause cannot be viewed as a single boundary but instead is a region which includes both abrupt and gradual changes in the fields and plasma parameters.

Omidi, N.↗

DOE OSTI2021

ExaWind: Exascale Predictive Wind Plant Flow Physics Modeling

The scientific goal of the ExaWind project is to advance our fundamental understanding of the flow physics governing whole wind plant performance, including wake formation, complex terrain impacts, and turbine-turbine-interaction effects. The primary application codes in the ExaWind environment are Nalu-Wind, an unstructured-grid computational fluid dynamics (CFD) code, AMR-Wind, a structured-grid CFD code, and OpenFAST, a whole-turbine simulation code. In this poster we present our progress towards simulating the ExaWind challenge problem, which is a predictive simulation of a wind farm with tens of megawatt-scale wind turbines dispersed over an area of 50 square kilometers.

49 EE - Wind and Water Power Program - Wind (EE-4W↗

DOE OSTI2023

ExaWind: Then and Now

The scientific goal of the ExaWind project is to advance our fundamental understanding of the flow physics governing whole wind plant performance, including wake formation, complex terrain impacts, and turbine-turbine-interaction effects. The primary application codes in the ExaWind environment are Nalu-Wind, an unstructured-grid computational fluid dynamics (CFD) code, AMR-Wind, a structured-grid CFD code, and OpenFAST, a whole-turbine simulation code. In this poster we present the current status of the ExaWind software stack in the context of the modeling and simulation capabilities when the project started in 2016.

computational fluid dynamics↗

DOE OSTI2015

Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation

The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pair-level interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, many-body interactions must be considered. Prior analytical approaches to capturing such interactions such as mean-field approaches replace detailed interactions with averaged approximations. However, long-range coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261–290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16–29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for low-Reynolds-number hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375–400 (1972) and G. K. Batchelor, J. Fluid Mech. 74, 1–29 (1976)]. Toward extension of these functions to concentrated systems, here we present a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two hard spheres immersed in a suspension of arbitrary concentration, utilizing accelerated Stokesian dynamics simulations. These mobility functions provide precise, radially dependent couplings of hydrodynamic force and torque to particle translation and rotation, for arbitrary colloid volume fraction ϕ. The pair mobilities (describing entrainment of one particle by the disturbance flow created by another) decay slowly with separation distance: as 1/r, for volume fractions 0.05 ≤ ϕ ≤ 0.5. For the relative mobility, we find an initially rapid growth as a pair separates, followed by a slow, 1/r growth. Up to ϕ ≤ 0.4, the relative mobility does not reached the far-field value even beyond separations of many particle sizes. In the case of ϕ = 0.5, the far-field asymptote is reached but only at a separation of eight radii and after a slow 1/r growth. At these higher concentrations, the coefficients also reveal liquid-like structural effects on pair mobility at close separations. These results confirm that long-range many-body hydrodynamic interactions are an essential part of the dynamics of concentrated systems and that care must be taken when applying renormalization schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2004

Buoyancy Effects on Flow Structure and Instability of Low-Density Gas Jets

A low-density gas jet injected into a high-density ambient gas is known to exhibit self-excited global oscillations accompanied by large vortical structures interacting with the flow field. The primary objective of the proposed research is to study buoyancy effects on the origin and nature of the flow instability and structure in the near-field of low-density gas jets. Quantitative rainbow schlieren deflectometry, Computational fluid dynamics (CFD) and Linear stability analysis were the techniques employed to scale the buoyancy effects. The formation and evolution of vortices and scalar structure of the flow field are investigated in buoyant helium jets discharged from a vertical tube into quiescent air. Oscillations at identical frequency were observed throughout the flow field. The evolving flow structure is described by helium mole percentage contours during an oscillation cycle. Instantaneous, mean, and RMS concentration profiles are presented to describe interactions of the vortex with the jet flow. Oscillations in a narrow wake region near the jet exit are shown to spread through the jet core near the downstream location of the vortex formation. The effects of jet Richardson number on characteristics of vortex and flow field are investigated and discussed. The laminar, axisymmetric, unsteady jet flow of helium injected into air was simulated using CFD. Global oscillations were observed in the flow field. The computed oscillation frequency agreed qualitatively with the experimentally measured frequency. Contours of helium concentration, vorticity and velocity provided information about the evolution and propagation of vortices in the oscillating flow field. Buoyancy effects on the instability mode were evaluated by rainbow schlieren flow visualization and concentration measurements in the near-field of self-excited helium jets undergoing gravitational change in the microgravity environment of 2.2s drop tower at NASA John H. Glenn Research Center. The jet Reynolds number was varied from 200 to 1500 and jet Richardson number was varied from 0.72 to 0.002. Power spectra plots generated from Fast Fourier Transform (FFT) analysis of angular deflection data acquired at a temporal resolution of 1000Hz reveal substantial damping of the oscillation amplitude in microgravity at low Richardson numbers (~0.002). Quantitative concentration data in the form of spatial and temporal evolutions of the instability data in Earth gravity and microgravity reveal significant variations in the jet flow structure upon removal of buoyancy forces. Radial variation of the frequency spectra and time traces of helium concentration revealed the importance of gravitational effects in the jet shear layer region. Linear temporal and spatio-temporal stability analyses of a low-density round gas jet injected into a high-density ambient gas were performed by assuming hyper-tan mean velocity and density profiles. The flow was assumed to be non parallel. Viscous and diffusive effects were ignored. The mean flow parameters were represented as the sum of the mean value and a small normal-mode fluctuation. A second order differential equation governing the pressure disturbance amplitude was derived from the basic conservation equations. The effects of the inhomogeneous shear layer and the Froude number (signifying the effects of gravity) on the temporal and spatio-temporal results were delineated. A decrease in the density ratio (ratio of the density of the jet to the density of the ambient gas) resulted in an increase in the temporal amplification rate of the disturbances. The temporal growth rate of the disturbances increased as the Froude number was reduced. The spatio-temporal analysis performed to determine the absolute instability characteristics of the jet yield positive absolute temporal growth rates at all Fr and different axial locations. As buoyancy was removed (Fr . 8), the previously existing absolute instability disappeared at all locations establhing buoyancy as the primary instability mechanism in self-excited low-density jets.

Pasumarthi, Kasyap Sriramachandra↗

DOE OSTI2025

The Alamo multiphysics solver for phase field simulations with strong-form mechanics and block structured adaptive mesh refinement

Alamo is a high-performance scientific code that uses block-structured adaptive mesh refinement to solve such problems as: the ignition and burn of solid rocket propellant, plasticity, damage and fracture in materials undergoing loading, and the interaction of compressible flow with eroding solid materials. Alamo is powered by AMReX, and provides a set of unique methods, models, and algorithms that enable it to solve solid-mechanics problems (coupled to other physical behavior such as fluid flow or thermal diffusion) using the power of block-structured adaptive mesh refinement.

36 MATERIALS SCIENCE↗

DOE OSTI2014

The behavior of the electron plasma boundary in ultraintense laser–highly overdense plasma interaction

The structural stability of the laser/plasma interaction is discussed, for the case of a linearly polarized laser beam interacting with a solid at normal incidence. Using a semi-analytical cold fluid model, the dynamics of the electron plasma boundary (EPB), usually related to the high-order harmonic generation and laser absorption, are presented. While the well-known J × B plasma oscillations at two times the laser frequency are recovered by the model, several other periodic in time stable solutions exist for exactly the same value of the physical parameters. This novel behavior highlights the importance of the laser pulse history among other factors. Some important features, such as the synchronization between the incident laser and the EPB oscillation, depend on the solution under consideration. A description of the possible types of stable oscillations in a parametric plane involving plasma density and laser amplitude is presented. The semi-analytical model is compared with particle-in-cell and semi-Lagrangian Vlasov simulations. They show that, among all the stable solutions, the plasma preferentially evolves to a state with the EPB oscillating twice faster than the laser. The effect of the plasma temperature and the existence of a ramp in the ion density profile are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1985

Graphics and flow visualization in computational fluid dynamics

Techniques for displaying two- and three-dimensional flowfield solutions are described. Several methods of illustrating flow structure are addressed including particle tracing, simulated oil flow, and shock finding. These are incorporated into an interactive graphics program for CFD flowfields, called PLOT3D. Emphasis is made on the difficulty in visualizing three-dimensional flow features, and the importance of color, fast 3D image manipulation, and dynamic movie play-back in displaying such flows. The need for advanced algorithms to identify shock waves, vortices, and separation lines is pointed out. It is likely that the supercomputer will be needed for this process because of the size of 3D and/or unsteady CFD databases.

Buning, P. G.↗

NASA NTRSDate not supplied

Structure and Dynamics of Bleed-Controlled Impinging Shock/Turbulent-Boundary-Layer Interactions

Porous boundary-layer bleed is often employed to alleviate the detrimental effects of shock/turbulent-boundary-layer interactions (STBLI) in high-speed vehicles. However, outstanding questions remain on the underlying mechanisms through which bleed influences STBLI dynamics. This work addresses this knowledge gap by performing a scale-resolved Large-Eddy Simulation of an impinging STBLI controlled by discrete bleed holes. The simulation has a freestream Mach number of 2.5, an oblique shock generator angle of 8 degrees, and a Reynolds number based on the incoming momentum thickness of 2800. Bleed substantially reduces the separation size and upstream influence of the STBLI compared to the canonical, uncontrolled case. Consequently, the characteristic, low-frequency motion of STBLI-induced separation is mitigated, as revealed by wall-pressure spectra. Energy is shifted from the low frequency separation behavior to a higher-frequency signature caused by the bleed shocks and expansions. The scale-resolved simulations also reveal that these small, localized structures severely limit the turbulence production traditionally seen in the uncontrolled interaction.

computational fluid dynamics↗

NASA NTRS1995

Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics

The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.

Webb, G. M.↗

NASA NTRS1992

Structure of supersonic turbulent flow past a swept compression corner

The structure of the shock wave/turbulent boundary-layer interaction generated by a 3D swept compression corner has been investigated through a combined experimental and theoretical research program. The flowfield geometry is defined by the streamwise compression angle alpha and the sweep angle lambda of the corner. The present study examines two different configurations, namely (alpha, lambda) = (24 deg, 40 deg) and (24 deg, 60 deg) at Mach 3 and Re sigma infinity about 9 x 10 exp 5. The theoretical model is the 3D Reynolds-averaged compressible Navier-Stokes equations with turbulence incorporated using a turbulent eddy viscosity. The calculated flowfields display general agreement with experimental data for surface pressure and good agreement with experimental flowfield profiles of pitot pressure and yaw angle. The principal feature of the flowfield is a large vortical structure approximately aligned with the corner. The entrainment of incoming fluid into the vortical structure is strongly affected by the sweep angle lambda. Viscous (turbulent and molecular) effects appear to be important only in the immediate vicinity of the surface and in an isolated region within the interaction and near the corner.

Knight, Doyle D.↗

DOE OSTI2015

Energy dynamics and current sheet structure in fluid and kinetic simulations of decaying magnetohydrodynamic turbulence

Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfvén waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation, whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of k{sub ⊥}{sup −1.3}. The kinetic code shows a spectral slope of k{sub ⊥}{sup −1.5} for smaller simulation domain, and k{sub ⊥}{sup −1.3} for larger domain. We estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. This work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Architected mesoporous crystalline magnesium silicates with ordered pore structures

Novel approaches to harness earth abundant silicates as building blocks for carbon dioxide removal, capture, utilization, and storage are gaining increasing attention in the context of sustainable and low carbon energy and resource recovery. Advancing a calibrated understanding of these fluid-silicate interactions is essential for developing scalable processes. One of the challenges in developing predictive controls over these interactions is the compositional and morphological heterogeneity of naturally occurring, heterogeneous magnesium silicate minerals. To address this challenge, the synthesis of architected mesoporous crystalline magnesium silicate (Mg 2 SiO 4 ) is proposed. While synthesis routes for producing amorphous mesoporous magnesium silicates have been developed via sol-gel methods, approaches to synthesize crystalline magnesium silicates with well-controlled pore size distributions have not been explored. The conventional approaches of converting matter that is amorphous to crystalline states at elevated temperatures results in a heterogeneous pore size distribution. To develop controls on pore size distribution, amorphous mesoporous magnesium silicates are coated with carbon. This approach preserves the pore size distributions during the amorphous to crystalline transformations of Mg-silicates at elevated temperatures. The carbon coating is removed on heating. Magnesium silicate particles produced using this approach have highly ordered pores around 2.58 nm and a specific surface area of 124.25 m 2 /g. In this study, we report the chemical compositions, morphologies, phase transitions, and pore structures of the intermediate materials produced during the synthesis of crystalline mesoporous magnesium silicates. The transitions, and pore structures of the intermediate materials produced during the synthesis of crystalline mesoporous magnesium silicates. Furthermore, the synthesis routes discussed in this study can be applied translationally to produce metal silicates with ordered mesoporous structures.

36 MATERIALS SCIENCE↗

NASA NTRS2011

Computational Models of the Eye and their Applications in Long Duration Space Flight

Astronauts are exposed to cephalad fluid shift, increased carbon dioxide levels and other environmental factors during space flight. As a result of these conditions, it is believed that they are at risk of developing increased intracranial pressure (ICP) and intraocular pressure (IOP), which in turn may cause papilledema and other disorders of the eye that can lead to temporary or permanent changes in vision. However, the mechanisms behind this risk are not fully understood. Ground analog and flight studies pose challenges because there are limited non-invasive methods that can be used to study the eye and intracranial space. Therefore it is proposed that computational models can be applied to help address this gap by providing a low cost method for studying the effects of IOP, ICP and various properties of the eye on these diseases. The information presented by the authors provides a summary of several models found in literature that could potentially be augmented and applied to inform research. Specifically, finite element models of the optic nerve head, sclera and other structures of the eye can be readily adapted as potential building blocks. These models may also be integrated with a brain/cerebrospinal fluid (CSF) model which will take into account the interaction between the CSF fluid and its pressure on the optic nerve. This integration can enable the study of the effects of microgravity on the interaction between the vasculature system and CSF system and can determine the effects of these changes on the optic nerve, and in turn the eye. Ultimately, it can help pinpoint the influences of long-term exposure to microgravity on vision and inform the future research into countermeasure development. In addition to spaceflight, these models can provide deeper understanding of the mechanisms of glaucoma, papilledema and other eye disorders observed in terrestrial conditions.

Chen, Richard↗

NASA NTRS2012

TEMHD Effects on Solidification Under Microgravity Conditions

An unexplored potential exists to control microstructure evolution through the use of external DC magnetic fields. Thermoelectric currents form during solidification and interact with this external field to drive microscopic fluid dynamics within the inter-dendritic region. The convective heat and mass transport can lead to profound changes on the dendritic structure. In this paper the effect of high magnetic fields is demonstrated through the use of both 3-dimensional and 2-dimensional numerical models. The results show that the application of a magnetic field causes significant disruption to the dendritic morphology. Investigation into the underlying mechanism gives initial indicators of how external magnetic fields can either lead to unexpected growth behaviour, or alternatively can be used to control the evolution of microstructure in undercooled melts as encountered in levitated droplet solidification.

Kao, Andrew↗

DOE OSTI2018

Geophysical Imaging of Geothermal Systems Spanning Various Geologic Settings

Despite the wide range of geologic settings in which geothermal systems reside, many systems share characteristics that can be targeted by geophysical techniques. Over the last few years, the authors have used potential field and magnetotelluric (MT) methods to jointly image and characterize numerous geothermal systems in various geologic and tectonic settings. This includes systems in the Basin and Range, Washington Cascade Range, Northeastern Oregon, and the Snake River Plain. The principal geothermal targets are areas of elevated temperatures near fault interactions that promote permeability and fluid flow. Gravity, magnetic, and MT data are all sensitive to different physical parameters that together form a complementary set of tools for characterizing subsurface structure and identifying favorable geothermal targets. In general, potential fields delineate important geologic structures and MT locates fluids and zones of hydrothermal alteration. Joint interpretation of these complementary methods, along with other geologic information, provides a robust framework for geothermal prospecting and understanding a hydrothermal system. Specifically, common geothermal targets lie along potential field gradients and are associated with an electrically conductive anomaly that resides in the less-dense, less-magnetic material.

15 GEOTHERMAL ENERGY↗

DOE OSTI2019

Comprehensive study of the interactions between the critical dimensionless numbers associated with multiphase flow in 3D porous media

Multiphase flow in porous media is of signifcant interest in many engineering applications, such as geologic carbon sequestration, enhanced oil recovery, and groundwater contamination and remediation. In order to advance the fundamental understanding of multiphase flow in complex three-dimensional (3D) porous media, the interactions between the critical dimensionless numbers, including the contact angle, viscosity ratio, and capillary (Ca) number, were explored using X-ray micro-computed tomography (micro-CT) scanning and lattice Boltzmann (LB) modeling. In this study, the 3D pore structure information was extracted from micro-CT images and then used as interior boundary conditions of flow modeling in a pore-scale LB simulator to simulate multiphase flow within the pore space. A Berea sandstone sample was scanned and then two-phase flow LB simulations were performed based on the micro-CT images. The LB-simulated water/CO 2 distributions agreed well with the micro-CT scanned images. Simulation findings showed that a decreasing contact angle causes a decrease in wetting-fluid relative permeability and an increase in non-wetting fluid relative permeability. A rising Ca number increases both wetting and non-wetting fluid relative permeabilities. An increasing viscosity ratio (the ratio of non-wetting fluid viscosity to wetting fluid viscosity) facilitates the increase of non-wetting fluid relative permeability and mitigates the reduction of wetting fluid relative permeability, when the contact angle decreases continuously. The primary novel finding of this study is that the viscosity ratio affects the rate of change of the relative permeability curves for both phases when the contact angle changes continuously. To date, we believe it is the first time that comprehensive interactions between these dimensionless numbers are demonstrated in a sandstone sample based on real 3D structures. We also investigated the role of the changes of flow direction and sample location on relative permeability curves. Simulation results showed that the change in non-wetting fluid relative permeability was larger when the flow direction was switched from vertical to horizontal, which indicated that there was stronger anisotropy in larger pore networks that were primarily occupied by the non-wetting fluid.

42 ENGINEERING↗