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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗
DOE OSTI2022

Frictional Behavior Downdip Along the Subduction Megathrust: Insights From Laboratory Experiments on Exhumed Samples at In Situ Conditions

Subduction megathrusts exhibit a spectrum of slip modes, including catastrophic earthquakes. Although the mechanical and frictional properties of materials sampled from subduction zones have been studied extensively, few datasets have been collected for compositions and at pressure and temperature conditions representative of those in situ. The Nankai subduction zone in southwest Japan is a well-studied margin, and abundant data provide an opportunity to advance our understanding of fault and earthquake physics. Here, we use samples exhumed in the Shimanto and Sanbagawa Belts on Shikoku Island of southwest Japan that represent analogs for materials along the present-day megathrust at depths of ~5–>25 km, and we shear these at their peak in situ pressure-temperature (P-T) conditions. Effective normal stresses range from 28 to 192 MPa, and temperatures from 105°C to 470°C. We used pore fluid pressures of 45–240 MPa, corresponding to fluid overpressure ratios λ of 0.65 and 0.90. Slip velocities of 0.1–100 μm/s were used, in order to focus on the nucleation of instability and earthquakes. We found predominantly velocity-strengthening (inherently stable) behavior under all conditions for λ = 0.65. For λ = 0.90, velocity-weakening behavior was observed at 350°C, with velocity-strengthening behavior at lower and higher temperatures. The rate/state frictional stability parameter (a-b) increases with slip velocity at temperatures up to ~200°C and remains constant or decreases with slip velocity at higher temperatures. Altogether, our results demonstrate the potentially important roles of both temperature and slip velocity in controlling the distribution of stress and frictional rheology along subduction thrusts.

58 GEOSCIENCES↗
DOE OSTI2020

Velocity Measurements in Channel Gas Flows in the Slip Regime by means of Molecular Tagging Velocimetry

Direct measurements of the slip velocity in rarefied gas flows produced by local thermodynamic non-equilibrium at the wall represent crucial information for the validation of existing theoretical and numerical models. In this work, molecular tagging velocimetry (MTV) by direct phosphorescence is applied to argon and helium flows at low pressures in a 1-mm deep channel. MTV has provided accurate measurements of the molecular displacement of the gas at average pressures of the order of 1 kPa. To the best of our knowledge, this work reports the very first flow visualizations of a gas in a confined domain and in the slip flow regime, with Knudsen numbers up to 0.014. MTV is cross-validated with mass flowrate measurements by the constant volume technique. The two diagnostic methods are applied simultaneously, and the measurements in terms of average velocity at the test section are in good agreement. Moreover, preliminary results of the slip velocity at the wall are computed from the MTV data by means of a reconstruction method

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Shape effects on the local dynamics of suspensions of spheroidal particles

The effect of shape on the dynamics of suspensions of non-spherical heavy particles is examined by fully resolved numerical simulations of oblate and prolate spheroids, as well as spheres, for a density ratio of ten, volume fractions ranging from 0.5% to 5%, and Reynolds numbers between 20 and 30. The dynamics is determined both by the interactions of the particles with the fluid as well as by collisions, with the number and importance of collisions increasing with volume fractions. A single isolated oblate or prolate spheroid falling under gravity generally falls broadside on, for the governing parameters examined here, and at low-volume fractions, the majority of particles in a suspension fall that way. At higher-volume fractions, the orientation is more random. The slip velocity decreases as the volume fraction increases for all shapes, as expected, but the effect of the shape is much less than seen for a single particle. Furthermore, this seems to be due to two effects. For all volume fractions, the most deformed particles cluster more than spheres and less deformed particles, which increases their slip velocity. As the concentration increases, the increased particle interactions also causes more particles to fall short side-on, which reduces the frontal area and the resulting drag, increasing the slip velocity. This second effect is, of course, absent for spherical particles.

42 ENGINEERING↗
DOE OSTI2023

Foreshock properties illuminate nucleation processes of slow and fast laboratory earthquakes

Understanding the connection between seismic activity and the earthquake nucleation process is a fundamental goal in earthquake seismology with important implications for earthquake early warning systems and forecasting. We use high-resolution acoustic emission (AE) waveform measurements from laboratory stick-slip experiments that span a spectrum of slow to fast slip rates to probe spatiotemporal properties of laboratory foreshocks and nucleation processes. We measure waveform similarity and pairwise differential travel-times (DTT) between AEs throughout the seismic cycle. AEs broadcasted prior to slow labquakes have small DTT and high waveform similarity relative to fast labquakes. We show that during slow stick-slip, the fault never fully locks, and waveform similarity and pairwise differential travel times do not evolve throughout the seismic cycle. In contrast, fast laboratory earthquakes are preceded by a rapid increase in waveform similarity late in the seismic cycle and a reduction in differential travel times, indicating that AEs begin to coalesce as the fault slip velocity increases leading up to failure. These observations point to key differences in the nucleation process of slow and fast labquakes and suggest that the spatiotemporal evolution of laboratory foreshocks is linked to fault slip velocity.

58 GEOSCIENCES↗
DOE OSTI2020

Dissolution of Fluoride Salts in Hanford Tank Waste

The Direct Feed High-Level Waste (DFHLW) strategy seeks to bypass the Hanford Waste Treatment and Immobilization Plant Pretreatment Facility while retaining some processing functions to maximize waste feed loading and minimize high-level waste (HLW) waste volume. The DFHLW flowsheet needs leaching, washing, and solids concentration operations either in new or existing tanks. The effectiveness and efficiency of sludge washing has a substantial impact on DST space, mission duration, and the evaporation and low-activity waste (LAW) treatment operations required by these large wash-water additions. One target species requiring washing is fluoride. The HLW glass composition limits for fluorine drive operations to dissolve fluoride-bearing salts into the LAW fraction and thereby maximize waste loading in HLW glass. The fluoride in many high-level wastes at Hanford is predominantly in the form of fluoride-salt precipitates: villiaumite (NaF), kogarkoite (Na 3 FSO 4 ), and natrophosphate (Na 7 F(PO 4 ) 2 ·19H 2 O). Fluoride produces melter off-gas that creates corrosion risk in the off-gas system piping, while the sulfate and phosphate in the fluoride double salts kogarkoite and natrophosphate can be detrimental to glass waste loading. Fluoride salts are sparingly soluble, with solubilities ranging from approximately 40 to 130 kg per kL of pure water, and the dissolution kinetics of the three fluoride salts are not well known. Unexpected delays in a tank dissolution process could be encountered as a result of the lack of information about dissolution rates. In addition, if the double salts show transient non-stoichiometric dissolution of fluoride versus phosphate or sulfate, unexpectedly high concentrations of one of these other constituents could be produced. Washington River Protection Solutions authorized Pacific Northwest National Laboratory to collect the available data for fluoride salt dissolution rate, provide a scoping estimate of dissolution time if possible, and identify gaps in the understanding and predictive capability for estimating dissolution time. Open literature and Hanford reports were reviewed to document, understand, and (where possible) evaluate limitations on fluoride salt equilibria and dissolution kinetics, including both mass transport and surface reaction rate. Scoping estimates of dissolution time were made for mass-transfer-controlled dissolution of spherical particles of fluoride salts suspended in liquid. This is not the only potential governing mechanism; dissolution could be substantially slower if the surface reaction rate (the rate of release of ions from the surface) is the controlling mechanism. When the minimum amount of water for complete dissolution is used and the slip velocity between the liquid and suspended particles is less than or equal to the terminal settling velocity, the estimated mass-transfer rates allow 0.1 mm particles of fluoride salt to dissolve in minutes at 25 °C in water containing no other dissolved salts. Much larger solids, such as the 6-mm chunks that have been seen in heels, could take a few hours to more than a week to dissolve. The actual dissolution times will depend strongly on the actual slip velocity, the extent of particle suspension, constraint by surface reaction rates, the ratio of solvent to solid, and the presence of common ions that shift the solubility equilibria to restrict dissolution of fluoride salts.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Frequency–Magnitude Statistics of Laboratory Foreshocks Vary With Shear Velocity, Fault Slip Rate, and Shear Stress

Understanding the nucleation phase of earthquakes is key for advancing earthquake hazard assessment and improving earthquake early warning systems. However, little progress has been made in this area due to a poor understanding of nucleation processes and incomplete seismic and fault zone measurements. The ability to integrate measured fault zone properties with seismic data could significantly improve our understanding of how earthquakes begin and whether there are systematic variations in seismic properties preceding failure. In this work, we use high-resolution laboratory measurements of fault zone properties along with acoustic emission data to document temporal variations of foreshock properties. Our data show that foreshock size increases with shear stress, loading rate, and fault slip rate. We propose that the preseismic fault slip rate and fault zone thickness (i.e., porosity) work in concert to modulate foreshock properties.

15 GEOTHERMAL ENERGY↗
DOE OSTI2020

Pore-scale simulation of gas flow in microscopic permeable media with complex geometries

Lattice Boltzmann method (LBM) is an efficient tool to perform direct numerical simulation of gas flow in micro-size pores. Despite great advances in LBM and its use in describing gas flow in micro-size channels in slip and transitional flow regimes, exploring formulations that are able to capture flow behavior in domains with complex boundary geometries remains a challenging task. As a result, the impact of complexities in pore structures on gas flow may not be fully explored using LBM. In this study, we propose to use the combined bounce-back and Maxwellian diffusive reflection scheme to capture the slip velocity with a new set of slip coefficients. Optimal values of slip coefficients are determined using a gradient based method, where the results from the linearized Boltzmann equation is used as the reference solution. The proposed formulation is further validated against predictions from molecular dynamics simulation in the presence of complex geometries by introducing obstacles of different shapes in straight channels. LBM with the proposed boundary treatment is then used to investigate gas flow in a synthetic microscopic permeable medium. Here, results indicate that gas exhibits different flow configurations as Knudsen number varies, and apparent gas permeability appears to have up to a second-order dependency on the reciprocal mean pressure in slip and transitional flow regimes.

03 NATURAL GAS↗
DOE OSTI2022

The High-Frequency Signature of Slow and Fast Laboratory Earthquakes

Tectonic faults fail through a spectrum of slip modes, ranging from slow aseismic creep to rapid slip during earthquakes. Understanding the seismic radiation emitted during these slip modes is key for advancing earthquake science and earthquake hazard assessment. In this work, we use laboratory friction experiments instrumented with ultrasonic sensors to document the seismic radiation properties of slow and fast laboratory earthquakes. Stick-slip experiments were conducted at a constant loading rate of 8 μm/s and the normal stress was systematically increased from 7 to 15 MPa. We produced a full spectrum of slip modes by modulating the loading stiffness in tandem with the fault zone normal stress. Acoustic emission data were recorded continuously at 5 MHz. We demonstrate that the full continuum of slip modes radiate measurable high-frequency energy between 100 and 500 kHz, including the slowest events that have peak fault slip rates <100 μm/s. The peak amplitude of the high-frequency time-domain signals scales systematically with fault slip velocity. Stable sliding experiments further support the connection between fault slip rate and high-frequency radiation. Experiments demonstrate that the origin of the high-frequency energy is fundamentally linked to changes in fault slip rate, shear strain, and breaking of contact junctions within the fault gouge. Our results suggest that having measurements close to the fault zone may be key for documenting seismic radiation properties and fully understanding the connection between different slip modes.

58 GEOSCIENCES↗
DOE OSTI2023

Scalable simulation of coupled adsorption and transport of methane in confined complex porous media with density preconditioning

The growing significance of shales and tight formations in the transition to less carbon-intensive and clean energy drives the research endeavor to understand the physics of gas flow within these systems. However, shales are composed of massively heterogeneous physical and chemical features. Most nano-sized pores connect to millimeter-scale fractures, leading to multiscale transport. These nano-scale pore throats demonstrate non-classical flow behavior, such as non-negligible slip velocities and adsorbed gas layers at the boundary. As a result, classical computational fluid dynamics models do not capture the physics. In this work, we develop a coupling scheme for the multiple-relaxation-time (MRT) lattice Boltzmann (LB) method that integrates the Peng-Robinson equation of state into a pseudo-potential interaction model to capture the physics of methane flow in irregular networks of channels that represent nano-scale porous media. We use atomistic simulations to calibrate and validate our model in slit nano-channels. We propose a preconditioning scheme to initialize the coupled transport and adsorption simulation of methane in complex porous media. The results of this implementation of LB agree with Direct Simulation Monte Carlo (DSMC) and Molecular Dynamics (MD) simulations. We then scale up the LB implementation through vectorization and indirect addressing. We parallelize it using Message Passing Interface (MPI) and OpenMP frameworks to simulate transport and adsorption in complex media with a million lattices. Additionally, we analyze the differences between coupled and transport-only simulations in two case studies and show that considering phase behavior, i.e., adsorption, can significantly change the flow behavior. This work constitutes an important step towards bridging the gap between molecular flow and system-scale behavior of complex disordered porous media.

42 ENGINEERING↗
DOE OSTI2022

Reciprocal swimming at intermediate Reynolds number

In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number of recent works have investigated dimer models that swim reciprocally at intermediate Reynolds numbers Re≈1–1000. These show interesting results (e.g. switches of the swim direction as a function of inertia) but the results vary and seem to be case specific. Here, in this work, we introduce a general model and investigate the behaviour of an asymmetric spherical dimer of oscillating length for small-amplitude motion at intermediate Re. In our analysis we make the important distinction between particle and fluid inertia, both of which need to be considered separately. We asymptotically expand the Navier–Stokes equations in the small-amplitude limit to obtain a system of linear partial differential equations. Using a combination of numerical (finite element) and analytical (reciprocal theorem, method of reflections) methods we solve the system to obtain the dimer's swim speed and show that there are two mechanisms that give rise to motion: boundary conditions (an effective slip velocity) and Reynolds stresses. Each mechanism is driven by two classes of sphere–sphere interactions, between one sphere's motion and (1) the oscillating background flow induced by the other's motion, and (2) a geometric asymmetry induced by the other's presence. We can thus unify and explain behaviours observed in other works. Our results show how sensitive, counterintuitive and rich motility is in the parameter space of finite inertia of particles and fluid.

42 ENGINEERING↗
DOE OSTI2021

Development of a Filtered CFD-DEM Drag Model with Multiscale Markers Using an Artificial Neural Network and Nonlinear Regression

Here, the accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R 2 values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Correlating Interlayer Spacing and Separation Capability of Graphene Oxide Membranes in Organic Solvents

Membranes synthesized by stacking two-dimensional graphene oxide (GO) hold great promise for applications in organic solvent nanofiltration. However, the performance of a layer-stacked GO membrane in organic solvent nanofiltration can be significantly affected by its swelling and interlayer spacing, which have not been systematically characterized. In this study, the interlayer spacing of the layer-stacked GO membrane in different organic solvents was experimentally characterized by liquid-phase ellipsometry. To understand the swelling mechanism, the solubility parameters of GO were experimentally determined and used to mathematically predict the Hansen solubility distance between GO and solvents, which is found to be a good predictor for GO swelling and interlayer spacing. Solvents with a small solubility distance (e.g., dimethylformamide, N-methyl-2-pyrrolidone) tend to cause significant GO swelling, resulting in an interlayer spacing of up to 2.7 nm. Solvents with a solubility distance larger than 9.5 (e.g., ethanol, acetone, hexane, and toluene) only cause minor swelling and are thus able to maintain an interlayer spacing of around 1 nm. Correspondingly, GO membranes in solvents with a large solubility distance exhibit good separation performance, for example, rejection of more than 90% of the small organic dye molecules (e.g., rhodamine B and methylene blue) in ethanol and acetone. Additionally, solvents with a large solubility distance result in a high slip velocity in GO channels and thus high solvent flux through the GO membrane. Finally, the GO membrane performs better in solvents that are unlike GO, i.e., solvents with large solubility distance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Transient evolution of permeability and friction in a slowly slipping fault activated by fluid pressurization

The mechanisms of permeability and friction evolution in a natural fault are investigated in situ. During three fluid injection experiments at different places in a fault zone, we measured simultaneously the fluid pressure, fault displacements and seismic activity. Changes in fault permeability and friction are then estimated concurrently. Results show that fault permeability increases up to 1.58 order of magnitude as a result of reducing effective normal stress and cumulative dilatant slip, and 19-to-60.8% of the enhancement occurs without seismic emissions. When modeling the fault displacement, we found that a rate-and-state friction and a permeability dependent on both slip and slip velocity together reasonably fit the fault-parallel and fault-normal displacements. This leads to the conclusion that the transient evolution of fault permeability and friction caused by a pressure perturbation exerts a potentially dominant control on fault stability during fluid flow.

58 GEOSCIENCES↗
DOE OSTI2025

Charges on a suspended silicon nitride membrane under a high-energy electron beam

Thin silicon nitride (SiN x ) membranes are widely used in gas and liquid phase transmission electron microscopy (TEM) and as phase plates to enhance imaging contrast. SiN x contains trap sites for both positive and negative charges, which can be manipulated by high-energy electron irradiation, external potential biasing, or light exposure. Charge accumulation on the membrane can significantly affect in situ TEM processes, including chemical and electrochemical reactions, nanoparticle dynamics, and catalytic activity, or introduce unwanted phase shifts when used as a phase plate. Here, in this study, charge accumulation on suspended SiN x membranes was investigated using off-axis electron holography combined with model-free charge analysis, supported by custom finite element analysis (FEA) simulations. An average residual positive charge density of approximately 2.8 × 10 −4 C m −2 was measured. Localized and stable regions of both positive and negative charges were identified on the membrane. The global positive and localized positive/negative charges give rise to strong electric fields and electroosmotic slip velocities at the membrane surface, which are sufficient to induce non-Brownian particle behavior and directional fluid flow, offering a physical explanation for previously observed anomalies in particle dynamics, nucleation, and growth during gas and liquid phase TEM experiments. These results provide a benchmark for understanding charge behavior at SiNx interfaces in gas and liquid phase TEM. Furthermore, the FEA simulations establish a framework for future investigations into charge distribution, electrostatic potentials, and electrical double layers at solid–liquid interfaces, particularly in complex geometries and chemically dynamic environments.

Suspended silicon↗
DOE OSTI2021

Suppression of electroconvective and morphological instabilities by an imposed cross flow of the electrolyte

Electroconvective (EC) instability and its influence on surface morphological perturbations (Morph) are important in many applications, including electrodialysis, batteries, and fuel cells. In this work, we study the effects of a two-dimensional channel flow on the EC and Morph instabilities using two approaches. In the bulk analysis, we derive the asymptotic solutions for small and large wave numbers by neglecting the space charge layer and imposing a second kind electroosmosis slip velocity boundary condition on the electroneutral bulk region. In the full analysis, the instability of the entire region of the liquid electrolyte is analyzed using the ultraspherical spectral method. Both studies show that the flow significantly affects the EC instability. The imposed flow distorts the concentration field, causing a sheltering effect which hinders the ion transport from low- to high-concentration regions, and therefore suppresses the EC instability below a certain wave number. In combination with the viscous stabilization of the high wave number modes by the space charge layer, a sufficiently strong imposed flow can fully suppress the EC instability. The increment in the critical voltage for the instability onset is roughly proportional to the square root of the product of imposed velocity and double layer thickness. The imposed flow has a smaller effect on the Morph instability, except that it may remove the morphological modes resulting from the EC instability and thereby change the wave number of the most unstable mode.

42 ENGINEERING↗
DOE OSTI2023

Utah FORGE: Fault Shear Reactivation Experimental Data for Fluid Injection-Rate Controls on Seismic Moment

Included are experimental data recorded from shear experiments that specifically explore the link between fluid-injection rate and seismic moment resulting from shear reactivation of laboratory faults. Raw mechanical data from three experiments are included alongside corresponding MATLAB scripts that import and plot the data, as well as use it to calculate shear and normal stress. Experiments are performed on 2.5-3 inch long granitoid cores from the Utah FORGE EGS demonstration site, containing a single inclined fracture with small-scale roughness added to the fracture surface. The raw data included here were recorded from an aluminum triaxial pressure vessel (TEMCO) configured with three independent servo-controlled pumps, with distilled water used as the working fluid. The pumps control confining pressure, upstream pore pressure, and axial pressure, with each pump connected to a LabView interface to record applied pressures, cumulative injected water volumes, and pump flow rates. The downstream outlet from the fracture is closed to allow pressurization, which is measured by an external pressure transducer. A linear variable differential transformer (LVDT) attached to the axial piston measures axial displacement, from which we calculate shear displacement along the fracture. Additionally, P-wave transducers are used to record acoustic signatures, where acoustic emission events and maximum amplitudes are compared against seismic moment and shear slip velocity. Fluid injection rates range between 0.05 mL/min, 0.25 mL/min, and 0.75 mL/min for each experiment. Along-fault pressure distributions are progressively less uniform as injection rates increase, representing a switch from steady-state to transient conditions. Triggered shear displacement is used as a proxy for seismic moment and is indexed against cumulative injection volume and rate. Each experiment is performed under constant shear stress conditions, and the sample is fully saturated with DI water. Axial and confining stresses are applied to 3 MPa through pressure-stepping in 500 kPa increments. The pore pressure is held constant at 200 kPa prior to initiating the experiment, and initial axial displacement is recorded. The axial stress is then increased to initiate shear mobilization during the loading phase (run-in) until a peak steady state is achieved. The initial shear stress is reduced to approximately 80% of the peak shear stress by decreasing the axial stress, then held constant for the duration of each experiment.

15 GEOTHERMAL ENERGY↗
DOE OSTI2020

Radial Wall Jet Flow Over Sigmoidal Surfaces

Radial wall jet flows across flat smooth surfaces have been studied for decades. These studies show that the radial velocity of these jets decays inversely with distance from the nozzle with modest contribution from friction (Poreh, et al., 1967; Rajaratnam, 1976). However, the extent to which flat surface results apply to curved surfaces remains unclear. In this article we explore the influence of settled particle bed slope on these velocity profiles. We model the step change in thickness as a sigmoidal curve of variable steepness and use conservation of momentum to evaluate the velocity profile. We show that the velocity profile attenuates because of curvature. Next, we evaluate the influence of surface curvature on radial wall jet flow. Jet flows over particle beds often introduce curvature in the particle bed profile but the influence of the developed curvature on the velocity profile has not been explored. Here we develop a solution for steady fixed beds based on conservation of momentum. We find that surface curvature has a significant influence on the velocity decay coefficients and celerity of radial wall jets, provided there is velocity slip in the vicinity of the particle bed interface, which is strictly true for particle surfaces. Conservation of momentum predicts conditions where the forward momentum of the flow is directed completely upward. The solution identifies two new dimensionless groups that determine whether a curved surface is sufficient to block radial flow and force flow vertically.

Surface curvature, jet flow, multiphase flow↗