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DOE OSTI2020

Electrolyte-Assisted Hydrogen Cycling in Lithium and Sodium Alanates at Low Pressures and Temperatures

An investigation of electrolyte-assisted hydrogen storage reactions in complex aluminum hydrides (LiAlH4 and NaAlH4) reveals significantly reduced reaction times for hydrogen desorption and uptake in the presence of an electrolyte. LiAlH4 evolves ~7.8 wt% H2 over ~3 h in the presence of a Li-KBH4 eutectic at 130 °C compared to ~25 h for the same material without the electrolyte. Similarly, NaAlH4 exhibits 4.8 wt% H2 evolution over ~4 h in the presence of a diglyme electrolyte at 150 °C compared to 4.4 wt% in ~15 h for the same material without the electrolyte. These reduced reaction times are composed of two effects, an increase in reaction rates and a change in the reaction kinetics. While typical solid state dehydrogenation reactions exhibit kinetics with rates that continuously decrease with the extent of reaction, we find that the addition of an electrolyte results in rates that are relatively constant over the full desorption window. Fitting the kinetics to an Avrami-Erofe’ev model supports these observations. The desorption rate coefficients increase in the presence of an electrolyte, suggesting an increase in the velocities of the reactant-product interfaces. In addition, including an electrolyte increases the growth parameters, primarily for the second desorption steps, resulting in the observed relatively constant reaction rates. Similar effects occur upon hydrogen uptake in NaH/Al where the presence of an electrolyte enables hydrogenation under more practical low temperature (75 °C) and pressure (50 bar H2) conditions.

25 ENERGY STORAGE↗

DOE OSTI2022

CFD simulations of electric motor end ring cooling for improved thermal management

Proper thermal management of an electric motor for vehicle applications extends its operating range. One cooling approach is to impinge Automatic Transmission Fluid (ATF) onto the rotor end ring. Increased ATF coverage correlates to enhanced heat transfer. Computational Fluid Dynamics (CFD) analytical tools provide a mechanism to assess motor thermal management prior to hardware fabrication. The complexity of the fluid flow (e.g., jet atomization, interface tracking, wall impingement) and heat transfer makes these simulations challenging. Computational costs are high when solving these flows on high-speed rotating meshes. Typically, a Volume-of Fluid (VOF) technique (i.e., two-fluid system) is used to resolve ATF dynamics within this rotating framework. Suitable numerical resolution of the relevant physics for thin films under strong inertial forces at high rotor speeds is computationally expensive, further increasing the run times. In this work, a numerical study of rotor-ring cooling by ATF is presented using a patent automated Cartesian cut-cell based method coupled with Automatic Mesh Refinement (AMR). This approach automatically creates the Cartesian mesh on-the-fly and can effectively handle complex rotating geometries by adaptively refining the mesh based on local gradients in the flow field which results in better resolution of the air-ATF interface. A Single non-inertial Reference Frame (SRF) approach is used to account for the rotating geometry and to further improve the overall computational efficiency. Quasi-steady state conditions are targeted in the analysis of the results. Important physics such as ATF jet structure, velocity detail near the air-jet interface, ATF coverage/accumulation on the ring surface, and cooling capacity are presented for a low-resolution Reynolds averaged Navier-Stokes (RANS), high-resolution RANS, and high-resolution Large-Eddy Simulation (LES) models. Computations are scaled over hundreds of cores on a supercomputer to maximize turnaround time. Each numerical approach is shown to capture the general trajectory of the oil jet prior to surface impingement. The high-resolution LES simulation, however, is superior in capturing small scale details and heat transfer between the free jet and surrounding air.

42 ENGINEERING↗

DOE OSTI2025

Phase-field model of alloy solidification far from chemical equilibrium at the solid-liquid interface

We further develop a recently introduced phase-field model of far-from-equilibrium alloy solidification under additive manufacturing conditions [K. Ji et al., Phys. Rev. Lett. 130, 026203 (2023)]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and timescales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be nontrivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. The results validate the important role of latent heat rejection at the interface and extend the limited predictions of linear stability analysis [A. Karma and A. Sarkissian, Phys. Rev. E 47, 513 (1993)] and sharp-interface 1D simulations to fully nonlinear regimes. Furthermore, 3D simulations, carried out using a computationally tractable axisymmetric cellular/dendritic interface shape, demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations, in turn, reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Sharp front tracking with geometric interface reconstruction

Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.

42 ENGINEERING↗

DOE OSTI2023

Human-in-the-Loop Motion Control of a Two-DOF Hydraulic Backhoe Powered by the Hybrid Hydraulic Electric Architecture (HHEA)

Abstract The Hybrid Hydraulic-Electric Architecture (HHEA) combines the respective power density and control advantages of hydraulic and electric actuation to save energy for off-road vehicles. It uses a set of selectable common pressure rails to transmit the majority of power and electric actuation to modulate that power. As it is critical that off-road vehicles can perform tasks dexterously and exactly as commanded by the operator, the switchings between discrete pressure rails pose a potential challenge for smooth and precise motion. A control strategy consisting of a backstepping nominal control and least norm transition control has previously been developed to address this issue. It has been tested on 1 degree of freedom (DOF) testbeds where known trajectories were able to be tracked precisely. This paper presents the implementation of the HHEA motion control strategy on a 2-DOF backhoe operated by a human operator via a 2-DOF joystick. Unlike previous studies, the duty cycle is unknown beforehand and the decision to change pressure rails is taken in real-time. The efficacy of the motion control strategy has been validated experimentally. Several strategies to improve the user interface: control in workspace coordinates, pressure feedback, and velocity field-based task specification, have also been implemented and demonstrated to make operating the multiple DOF, HHEA actuated machine more intuitive to novice operators.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Interfacial Nanostructure and Hydrogen Bond Networks of Choline Chloride and Glycerol Mixtures Probed with X-ray and Vibrational Spectroscopies

The molecular distribution at the liquid-vapor interface and evolution of the hydrogen bond interactions in mixtures of glycerol and choline chloride are investigated using X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy. Nanoscale depth profiles of supersaturated deep eutectic solvent (DES) mixtures up to ~2 nm measured by ambient-pressure XPS show the enhancement of choline cation (Ch + ) concentration by a factor of 2 at the liquid-vapor interface compared to the bulk. In addition, Raman spectral analysis of a wide range of DES mixtures reveals the conversion of gauche-conformer Ch + into the anti-conformer in relatively lower ChCl concentrations. Finally, the depletion of Ch + from the interface (probing depth = 0.4 nm) is demonstrated by aerosol-based velocity map imaging XPS measurements of glyceline and water mixtures. The nanostructure of liquid-vapor interfaces and structural rearrangement by hydration can provide critical insight into the molecular origin of the deep eutectic behavior and gas-capturing application of DESs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

A Conservative Finite-Volume Based Interface-Tracking Algorithm Using the Signed Distance Function

Methods for tracking an interface between two fluid phases are developed to ensure desired fluid properties, conservation, and stability are preserved in a finitevolume (FV) discretization. Here, the interface is tracked using a level set method where the signed distance function implicitly defines the interface. Marching methods are used to evaluate the value of the signed distance function, including a novel initialization method to initialize any implicit function to the signed distance function around sharp corners in the level set. Global conservation and consistency with a set of governing equations is enforced by a compression coefficient that measures the volumetric compression or expansion due to inaccuracies in the level set evaluation. A redistribution method is integrated into the volume correction to eliminate the small-cell instability while maintaining global conservation. This suite of methods is implemented and tested using static uniform velocity, and potential flow cases with multiple interface geometries. Results show these methods achieve up to second order accuracy, and are conservative. The application for these methods is intended to track the interface of a 3D printing filament in a finite-volume discretization of the all-speed Navier-Stokes equations.

42 ENGINEERING↗

DOE OSTI2021

Vortex-sheet modeling of hydrodynamic instabilities produced by an oblique shock interacting with a perturbed interface in the HED regime

In this work, we consider hydrodynamic instabilities produced by the interaction of an oblique shock with a perturbed material interface under high-energy-density (HED) conditions. During this interaction, a baroclinic torque is generated along the interface due to the misalignment between the density and pressure gradients, thus leading to perturbation growth. Our objective is to understand the competition between the impulsive acceleration due to the normal component of the shock velocity, which drives the Richtmyer–Meshkov instability, and the shear flow across the interface due to the tangential component of the shock velocity, which drives the Kelvin–Helmholtz instability, as well as its relation to perturbation growth. Since the vorticity resulting from the shock-interface interaction is confined to the interface, we describe the perturbation growth using a two-dimensional vortex-sheet model. We demonstrate the ability of the vortex-sheet model to reproduce roll-up dynamics for non-zero Atwood numbers by comparing to past laser-driven HED experiments. We determine the dependence of the interface dynamics on the tilt angle and propose a time scaling for the perturbation growth at early time. Eventually, this scaling will serve as a platform for the design of future experiments. This study is the first attempt to incorporate into a vortex-sheet model the time-dependent interface decompression and the deceleration (as well as the corresponding Rayleigh–Taylor instability) arising from laser turn-off.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Peak states of molybdenum single crystals shock compressed to high stresses

In this work, to determine crystal anisotropy effects at high stresses, peak states behind the plastic shock waves were examined in BCC single crystals. Using plate impact experiments, molybdenum (Mo) single crystals were shock compressed up to 190 GPa elastic impact stress along [100], [110], and [111] orientations. Laser interferometry was used to measure wave velocities and particle velocity profiles at the Mo–LiF window interface. These data were analyzed to obtain in-material quantities in the peak states. The Hugoniots for [100] and [110] orientations were comparable, but the Hugoniot for the [111] orientation was different from the other two orientations. Also, these Mo single crystal Hugoniots display differences from the polycrystalline Mo Hugoniots. Although none of the differences can be considered large, the present results demonstrate that, unlike FCC metal single crystals (Cu, Al), some anisotropy is preserved in Mo single crystal Hugoniots even at high stresses.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Charge Carrier Lifetime Determination in Graded Absorber Solar Cells Using Time‐Resolved Photoluminescence Simulations and Measurements

Thin‐film photovoltaic device efficiencies are limited by carrier recombination, thus understanding recombination mechanisms is critical for performance improvements. Bulk minority carrier lifetime ( τ bulk ) is a critical parameter for solar cells but is difficult to determine in P–N junction devices, especially for high doping. As doping ≥10 16 cm −3 is required for efficient drift‐charge‐carrier‐collection devices, a method for τ bulk determination in doped P–N junction devices is necessary. This work utilizes time‐resolved photoluminescence (TRPL) simulations to quantify bulk and interface recombination properties in highly doped, graded absorber CdSeTe structures. The two methods developed here for τ bulk determination include utilization of an instantaneous lifetime representation to guide TRPL fitting and direct comparison between measured and simulated decays. Simulations verified that both methods are valid for state‐of‐the‐art device architectures which include graded bandgap absorbers, graded doping, and graded lifetimes. Shifts in the dominant recombination mechanism are identified for sufficiently long τ bulk , where front and back interface quality plays a more prominent role. Evaluation of surface recombination velocities and conduction band offset illustrate electro‐optical advantages of a positive conduction band offset and highlight the necessity of improved interfaces as bulk quality in photovoltaic devices improves.

14 SOLAR ENERGY↗

DOE OSTI2023

Linear analysis of the Kelvin–Helmholtz instability in relativistic magnetized symmetric flows

ABSTRACT We study the linear stability of a planar interface separating two fluids in relative motion, focusing on the symmetric configuration where the two fluids have the same properties (density, temperature, magnetic field strength, and direction). We consider the most general case with arbitrary sound speed cs, Alfvén speed vA, and magnetic field orientation. For the instability associated with the fast mode, we find that the lower bound of unstable shear velocities is set by the requirement that the projection of the velocity on to the fluid-frame wavevector is larger than the projection of the Alfvén speed on to the same direction, i.e. shear should overcome the effect of magnetic tension. In the frame where the two fluids move in opposite directions with equal speed v, the upper bound of unstable velocities corresponds to an effective relativistic Mach number $M_{\rm re}\equiv v/v_{\rm {f}\perp }\sqrt{(1-v_{\rm {f}\perp }^2)/(1-v^2)} \cos \theta =\sqrt{2}$, where $v_{\rm {f}\perp }=[v_{\rm {A}}^2+c_{\rm s}^2(1-v_{\rm {A}}^2)]^{1/2}$ is the fast speed assuming a magnetic field perpendicular to the wavevector (here, all velocities are in units of the speed of light), and θ is the laboratory-frame angle between the flow velocity and the wavevector projection on to the shear interface. Our results have implications for shear flows in the magnetospheres of neutron stars and black holes – both for single objects and for merging binaries – where the Alfvén speed may approach the speed of light.

Astronomy & Astrophysics↗

DOE OSTI2023

A numerical solver for investigating the space charge effect on the electric field in liquid argon time projection chambers

This paper reports the development of a numerical solver aimed to simulate the interaction between the space charge (i.e. ions) distribution and the electric field in liquid argon time projection chamber (LArTPC) detectors. The ion transport equation is solved by a time-accurate, cell-centered finite volume method and the electric potential equation by a continuous finite element method. The electric potential equation updates the electric field which provides the drift velocity to the ion transport equation. The ion transport equation updates the space charge density distribution which appears as the source term in the electric potential equation. The interaction between the space charge distribution and the electric field is numerically simulated within each physical time step. The convective velocity in the ion transport equation can include the background flow velocity in addition to the electric drift velocity. The numerical solver has been parallelized using the Message Passing Interface (MPI) library. Numerical tests show and verify the capability and accuracy of the current numerical solver. It is planned that the developed numerical solver, together with a Computational Fluid Dynamics (CFD) package which provides the flow velocity field, can be used to investigate the space charge effect on the electric field in large-scale particle detectors.

42 ENGINEERING↗

DOE OSTI2020

Remote Fiber Based Velocimeter For Interface Strength Measurements

The understanding of the performance of nuclear reactor plate fuels is essential when developing new fuel systems. The condition of pre and post irradiated plate fuels must be characterized effectively and efficiently prior to irradiation and then post irradiation within a high rad environment. The post characterization work must be performed remotely and in an environment hostile to instrumentation. Laser based characterization methods provide the capability to be remote and robust within a hot-cell environment. Laser based characterization can provide high spatial resolution appropriate for scanning and imaging large areas. The INL is currently developing a laser shock system for Post Irradiation Examination (PIE) station for use in the Hot Fuel Examination Facility (HFEF) at the INL. The laser shock system is designed to characterize fuel to cladding and cladding to cladding interface strength. The laser shock-technique induces large amplitude shock waves to mechanically characterize interfaces such as the fuel-clad interface. The shock wave propagates as a compressional wave through the fuel plate to the free (unconfined) backside surface and is reflected back through the test plate as a rarefaction (tensile) wave. This rarefaction wave is the physical mechanism that produces internal delamination failure. The focus or this paper is on the accurate measurement of surface velocity to quantify the amount of energy traveling through the interfaces to the back surface of the fuel plate. The original fiber based velocimeter design was biased by parasitic back reflections. This paper will discuss the discovery of the back-reflection issue and the design changes to resolve the issue. Supporting data will be presented.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Internal structure of the San Jacinto fault zone at the Ramona Reservation, north of Anza, California, from dense array seismic data

SUMMARY We image the internal structure of the San Jacinto fault zone (SJFZ) near Anza, California, with seismic data recorded by two dense arrays (RA and RR) from ∼42 000 local and ∼180 teleseismic events occurring between 2012 and 2017. The RA linear array has short aperture (∼470 m long with 12 strong motion sensors) and recorded for the entire analysed time window, whereas the RR is a large three-component nodal array (97 geophones across a ∼2.4 km × 1.4 km area) that operated for about a month in September–October 2016. The SJFZ at the site contains three near-parallel surface traces F1, F2 and F3 from SW to NE that have accommodated several Mw > 6 earthquakes in the past 15 000 yr. Waveform changes in the fault normal direction indicate structural discontinuities that are consistent with the three fault surface traces. Relative slowness from local events and delay time analysis of teleseismic arrivals in the fault normal direction suggest a slower SW side than the NE with a core damage zone between F1 and F2. This core damage zone causes ∼0.05 s delay at stations RR26–31 in the teleseismic P arrivals compared with the SW-most station, and generates both P- and S-type fault zone trapped waves. Inversion of S trapped waves indicates the core damaged structure is ∼100 m wide, ∼4 km deep with a Q value of ∼20 and 40 per cent S-wave velocity reduction compared with bounding rocks. Fault zone head waves observed at stations SW of F3 indicate a local bimaterial interface that separates the locally faster NE block from the broad damage zone in the SW at shallow depth and merges with a deep interface that separates the regionally faster NE block from rocks to the SW with slower velocities at greater depth. The multiscale structural components observed at the site are related to the geological and earthquake rupture history at the site, and provide important information on the preferred NW propagation of earthquake ruptures on the San Jacinto fault.

Geochemistry & Geophysics↗

DOE OSTI2020

Hugoniot states and optical response of soda lime glass shock compressed to 120 GPa

In contrast to relatively pure silica glass (fused silica-FS), commercial silica-rich glasses contain significant fractions of additional oxide components. In particular, soda-lime glass (SLG) consists of approximately 71% SiO 2 by weight, which raises the question: what is the effect of additional cations on the shock compression response of silica-rich glasses? To address this concern, plate impact experiments were conducted to determine the high-pressure Hugoniot states for shocked SLG (37 to 120 GPa) and compared with recently reported results on FS. Using laser interferometry, particle velocity profiles were measured at the impact surface and the SLG/LiF window interface. In all experiments, the transmitted profiles show a single shock wave, with no features indicative of a phase transformation. The Hugoniot states determined from the wave profiles are described well using a linear shock velocity–particle velocity relation. Interferometry measurements (using 1550-nm wavelength laser) at the impact surface show that SLG is transparent when shocked to 55 GPa, transparent for tens of nanoseconds after impact between 55 and 81 GPa, and opaque beyond 81 GPa. From impact surface measurements, a linear relationship between the apparent and true particle velocity was observed, resulting in a linear relationship between the refractive index (at 1550 nm) and density. At 120 GPa, the SLG density is nearly twice its ambient value, indicating that SLG can achieve highly dense amorphous states. When compared to FS, shocked SLG is much less compressible and likely does not transform to a crystalline phase. A plausible explanation for this difference is indicated.

58 GEOSCIENCES↗

DOE OSTI2022

Ambient Noise Attenuation Tomography Reveals an Asymmetric Damage Zone Across San Jacinto Fault Near Anza, California

Here, we perform seismic attenuation tomography of the shallow structure for the San Jacinto Fault in the Ramona Reservation of southern California. The study uses ambient seismic noise recorded by a linear array of 65 3-C sensors across the fault. We extract amplitude decay information, with uncertainty, from noise interferometry functions. To account for strong heterogeneities in the complex shallow fault zone structure, we apply a frequency-dependent amplitude correction for focusing/defocusing effects using inverted phase velocity maps obtained by solving the transport equation. We then estimate the attenuation structure based on the linear station-triplet method for both Love and Rayleigh waves. The attenuation tomography indicates strong attenuation correlated with known San Jacinto Fault surface traces. The Love wave attenuation tomography reveals an asymmetric damage zone that exists primarily on the fault side with faster seismic velocity, consistent with earthquake ruptures on a fault bimaterial interface with preferred propagation direction to the northwest.

58 GEOSCIENCES↗

DOE OSTI2024

Electromagnetic Inhomogeneous-Energy-Density-Driven Instability in the UCLA Large Plasma Device (EM-IEDDI in LAPD) (Final Technical Report)

Using the Large Plasma Device (LAPD), the electromagnetic signatures associated with the inhomogeneous-energy-density-driven (IEDD) instability were targeted for documentation in a lab experiment. Exploitable features of LAPD are the extreme-length, high-beta, low-collisionality, and excellent reproducibility. The signatures of interest were mode amplitude, mode structure, frequency spectrum, phase velocity, and excitation threshold. The abrupt inhomogeneity at the interface between two coaxial plasma columns, that have disparate space potential values, were expected to generate a strong, localized, transverse, dc electric field and form a strong ExB-flow inhomogeneity that was expected to trigger broadband, intermediate-frequency waves that propagate many gyroradii beyond the interfacial source region. WVU was unable to destabilize the IEDDI mode in LAPD. Experimental limitation of three different parameters conspire to prevent IEDDI-favorable conditions even though Alfven-favorable conditions are met. Electron-neutral collision frequency is too high, Structuring of the radial profile of the radial electric field is negligible and the control of that structure is minimal, and the Magnetic field is too large for some purposes and too small for other purposes. WVU designed a new antenna and relied on externally-driving the IEDDI (instead of spontaneous destabilization). The antenna operation failed for unforeseen reasons and lack of electrician time and availability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗