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Results for “Critical Velocity”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Grey Galaxies’ as an endpoint of the Kerr-AdS superradiant instability

Kerr-AdS d+1 black holes for d ≥ 3 suffer from classical superradiant instabilities over a range of masses above extremality. We conjecture that these instabilities settle down into Grey Galaxies (GGs) — a new class of coarse-grained solutions to Einstein’s equations which we construct in d = 3. Grey Galaxies are made up of a black hole with critical angular velocity ω = 1 in the ‘centre’ of AdS, surrounded by a large flat disk of thermal bulk gas that revolves around the centre of AdS at the speed of light. The gas carries a finite fraction of the total energy, as its parametrically low energy density and large radius are inversely related. GGs exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their boundary stress tensor is the sum of a smooth ‘black hole’ contribution and a peaked gas contribution that is delta function localized around the equator of the boundary sphere in the large N limit. We also construct another class of solutions with the same charges; ‘Revolving Black Holes (RBHs)’. RBHs are macroscopically charged SO(d, 2) descendants of AdS-Kerr solutions, and consist of ω = 1 black holes revolving around the centre of AdS at a fixed radial location but in a quantum wave function in the angular directions. RBH solutions are marginally entropically subdominant to GG solutions and do not constitute the endpoint of the superradiant instability. Nonetheless, we argue that supersymmetric versions of these solutions have interesting implications for the spectrum of supersymmetric states in, e.g. N = 4 Yang-Mills theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Silicate Melting and Vaporization During Rocky Planet Formation

Collisions that induce melting and vaporization can have a substantial effect on the thermal and geochemical evolution of planets. However, the thermodynamics of major minerals are not well known at the extreme conditions attained during planet formation.We obtained new data at the Sandia Z Machine and use published thermodynamic data for the major mineral forsterite (Mg 2 SiO 4 ) to calculate the specific entropy in the liquid region of the principal Hugoniot.We use our calculated specific entropy of shocked forsterite, and revised entropies for shocked silica, to determine the critical impact velocities for melting or vaporization upon decompression from the shocked state to 1 bar and the triple points, which are near the pressures of the solar nebula.We also demonstrate the importance of the initial temperature on the criteria for vaporization. Applying these results to N-body simulations of terrestrial planet formation, we find that up to 20% to 40% of the total system mass is processed through collisions with velocities that exceed the criteria for incipient vaporization at the triple point. Vaporizing collisions between small bodies are an important component of terrestrial planet formation.

58 GEOSCIENCES↗
DOE OSTI2021

Corona splashing triggered by a loose monolayer of particles

In nature, high-speed raindrops often impact and spread on particulate surfaces (e.g., soil, plant leaves with spores or pollen). We study the dynamics of droplet impact on a loosely packed monolayer of particles by combining experimental and mathematical approaches. We find that the presence of mobile particles lowers the critical impact velocity at which the droplet exhibits corona splashing, as the particle area fraction is systematically increased. We rationalize this experimental observation by considering the jamming of frictional particles at the spreading rim. Elucidating the splashing transition of the drop on a particulate bed can lead to a better understanding of soil loss and erosion from falling raindrops

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Antiferromagnetic transitions of Dirac fermions in three dimensions

We use determinant quantum Monte Carlo simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the π-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-range AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)-dimensional Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in the birefringent Dirac fermion system. It is found that the critical interaction strength U c is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions and may be observed using ultracold atoms in an optical lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Effects of inter-pulse coupling on nanosecond pulsed high frequency discharge ignition in a flowing mixture

This work numerically investigates the effects of non-equilibrium nanosecond plasma discharge pulse rep- etition frequency, pulse number, and flow velocity on the critical ignition volume, minimum ignition energy, and chemistry in a plasma-assisted H 2 /air flow at 300 K and 1 atm using a multi-scale adaptive reduced chemistry solver for plasma assisted combustion (MARCS-PAC). The interactions between discharges/ignition kernels spanning decoupled, partially-coupled and fully-coupled regimes in a pulse train are studied. For a single pulse discharge, increased flow velocity increases the minimum ignition energy required due to the increase of convective heat loss and flame stretch. The results show that the minimum ignition kernel prop- agation speed at the critical ignition kernel volume increases with the flow velocity. The minimum critical ignition volume decreases with the increase of plasma discharge energy. For sequential two-pulse discharges, ignition fails at both decoupled and partially-coupled regimes even when the total discharge energy is above the minimum ignition energy, but succeeds only in the fully-coupled regime at a shorter inter-pulse time. Overlap of the OH radical pool between the sequential two-pulse discharges and the increase of the chemistry effect due to the increase of reduced electric field in the fully-coupled regime contribute to the ignition enhancement. In addition, for two-pulse discharges in the fully-coupled discharge regime, the mixture can be ignited at a total energy below the minimum ignition energy of a single pulse with the same flow conditions. Moreover, for a given total discharge energy with multiple pulsed discharges, the enhancement of the ignition kernel volume has a non-monotonic dependence on discharge frequency and pulse number. The effective ignition enhancement can be achieved with an optimal pulse repetition frequency and pulse number. Furthermore, this work provides a new understanding of the mechanism for repetitive plasma ignition and insights for the optimization of plasma ignition in a reactive flow.

42 ENGINEERING↗
DOE OSTI2020

Analytical Investigation of the Role of Lateral Mixing in the Evolution of Nonprecipitating Cumulus. Part I: Developing Clouds

Evolution of nonprecipitating cumulus clouds (Cu) at the developing stage under the influence of lateral entrainment and mixing is studied analytically using a minimalistic analytical model. We present a model of an ascending cloud volume (a model of developing Cu) whose structure is determined by the processes of droplet diffusion growth/evaporation and entrainment mixing in the horizontal direction. Spatial and time changes of liquid water content, the adiabatic fraction, droplet concentration, and the mean volume droplet radius are calculated. It is shown that the existence of a nondiluted core in a growing cumulus cloud significantly depends on the cloud width and vertical velocity. While at the updraft velocity of 2 m s −1 the core of a 400-m-wide cloud becomes diluted at distances of a few hundred meters above cloud base, the core of a cloud of 1000-m width remains nondiluted at distances up to 1500 m above cloud base. The explanation of this result is simple: the increase in cloud width and the decrease in the updraft velocity increase the time during which the cloud is diluted due to mixing. Since lateral mixing synchronously decreases both the cloud water content and droplet concentration, the variation of the mean volume droplet radius is low inside the cloud. The approximate quantitative condition for cloud formation in updraft is derived. It is shown that a cloud can arise when its vertical velocity exceeds a critical value. To produce clouds, narrow turbulent plumes should ascend at higher velocity as compared to wider plumes. High humidity of the environment air is favorable for formation of clouds from plumes. The comparison of the obtained results with previously published observational data indicates a reasonable agreement. The results can be useful for parameterization purposes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Dynamics of the O ( 4 ) critical point in QCD: Critical pions and diffusion in model G

We present a detailed study of the finite momentum dynamics of the O ( 4 ) critical point of QCD, which lies in the dynamic universality class of “model G.” The critical scaling of the model is analyzed in multiple dynamical channels. For instance, the finite momentum analysis allows us to precisely extract the pion dispersion curve below the critical point. The pion velocity is in striking agreement with the predictions relation and static universality. The pion damping rate and velocity are both consistent with the dynamical critical exponent ζ = 3 / 2 of model G. Similarly, although the critical amplitude for the diffusion coefficient of the conserved O ( 4 ) charges is small, it is clearly visible both in the restored phase and with finite explicit symmetry breaking, and its dynamical scaling is again consistent with ζ = 3 / 2 . We determine a new set of universal dynamical critical amplitude ratios relating the diffusion coefficient to a suitably defined order parameter relaxation time. We also show that in a finite volume simulation, the chiral condensate diffuses on the coset manifold in a manner consistent with dynamical scaling, and with a diffusion coefficient that is determined by the transport coefficients of hydrodynamic pions. Finally, the amplitude ratios (together with other nonuniversal amplitudes also reported here) compile all relevant information for further studies of model G both in and out of equilibrium. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Bound states and electromagnetic radiation of relativistically rotating cylindrical wells

Here, we compute the effect of rigid rotation on the non-relativistic bound states. The energy levels of the bound states increase with the angular velocity of rotation until at certain value of the angular velocity they are completely pushed out into the continuum which corresponds to dissociation of the bound states. When the angular velocity exceeds the critical value at which the ground state disappears into the continuum, no bound state is possible. This effect should have important consequences for the phenomenology of the quark-gluon plasma. One of the ways to study it experimentally is to observe the electromagnetic radiation emitted by a rotating bound state. We compute the corresponding intensity of electromagnetic radiation and show that it strongly depends on the angular velocity of rotation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Limiting current in a collisional crossed-field gap

Crossed-field devices are often used in pulsed power and high-power microwave applications. Previous studies derived closed-form solutions for the limiting current of a vacuum crossed-field system, corresponding to the maximum permissible current for laminar flow, below and above the Hull cutoff B H for magnetic insulation. We extend these studies by introducing collision frequency into the electron force law as a friction term to derive the limiting current in a collisional crossed-field gap. The resulting solution recovers the vacuum crossed-field case in the limit of no collisions and the collisional space-charge limited current with general initial velocity for magnetic field B → 0. In the limit of infinite collisions, we obtain a crossed-field equivalent to the Mott–Gurney law for the maximum current permissible in a collisional, nonmagnetic diode. When the collision frequency ν is less than the electron cyclotron frequency Ω, increasing initial velocity makes the critical current nonmonotonic with increasing ν with the critical current higher at B = B H for ν = Ω. As for a misaligned crossed-field gap where a component of the magnetic field was introduced parallel to the electric field across the gap, magnetic insulation is eliminated and the discontinuity at B = B H for limiting current observed in a vacuum crossed-field gap vanishes. As B → ∞, the limiting current approaches a constant that depends on the initial velocity and the collision frequency.

Breen, Lorin I.↗
DOE OSTI2024

A prediction model of failure threshold for shear deformation in a Zr-based bulk metallic glass

The failure of bulk metallic glasses (BMGs) during plastic deformation at room temperature is abrupt and instantaneous, while the analysis of precursor information based on avalanche events helps predict catastrophic failure. An acoustic emission (AE) signal can provide accurate precursor information for material failure, due to its sensitive and high fast calculation ability. In the current study, AE monitoring tests are carried out during uniaxial compression tests of BMGs at different strain rates. The AE experimental failure threshold, E max , is proposed on the basis of AE cumulative energy, which reflects the intensity of damage evolution at different loading conditions. Compared with the critical shear band velocity (CSBV) associated with stick-slip dynamics of serrated flow, E max is a more sensitive failure parameter since it is connected with the local microscopic changes that occur during the material response process. Here, the E max is obtained prior to reaching the CSBV since the calculation of these two avalanches analysis focuses on the different stages of shear band growth. In particular, AE events are related to the “dry” friction process in the first stage, however, the CSBV is responsible for the “viscous” glide in the second stage. Therefore, Emax is not affected by the complex interactions between the shear bands during the stick-slip process. The maximum avalanche of serrated flow, S max , is proposed as the experimental failure threshold, which depends on the applied strain rate as S max ~ $\dot{ε}$ –λ . According to the relationship of E max and S max , the theoretical failure threshold, E max , follows a criterion E max = 2545$\dot{ε}$ –λ - 4468, where λ is equivalent to 0.15 for this work. Finally, combining the different calculations and AE measurements, this model gives new insights to predict the deformation failure behavior of Zr-based BMGs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Towards higher frequencies in a compact prebunched waveguide THz-FEL

Free-electron-lasers fill a critical gap in the space of THz-sources as they can reach high average and peak powers with spectral tunability. Using a waveguide in a THz FEL significantly increases the coupling between the relativistic electrons and electromagnetic field enabling large amounts of radiation to be generated in a single passage of electrons through the undulator. In addition to transversely confining the radiation, the dispersive properties of the waveguide critically affect the velocity and slippage of the radiation pulse which determine the central frequency and bandwidth of the generated radiation. In this paper, we characterize the spectral properties of a compact waveguide THz FEL including simultaneous lasing at two different frequencies and demonstrating tuning of the radiation wavelength in the high frequency branch by varying the beam energy and ensuring that the electrons injected into the undulator are prebunched on the scale of the resonant radiation wavelength.

Experimental particle physics↗
DOE OSTI2023

Lagrangian and Eulerian Supersaturation Statistics in Turbulent Cloudy Rayleigh–Bénard Convection: Applications for LES Subgrid Modeling

Abstract Turbulent fluctuations of scalar and velocity fields are critical for cloud microphysical processes, e.g., droplet activation and size distribution evolution, and can therefore influence cloud radiative forcing and precipitation formation. Lagrangian and Eulerian water vapor, temperature, and supersaturation statistics are investigated in direct numerical simulations (DNS) of turbulent Rayleigh–Bénard convection in the Pi Convection Cloud Chamber to provide a foundation for parameterizing subgrid-scale fluctuations in atmospheric models. A subgrid model for water vapor and temperature variances and covariance and supersaturation variance is proposed, valid for both clear and cloudy conditions. Evaluation of phase change contributions through an a priori test using DNS data shows good performance of the model. Supersaturation is a nonlinear function of temperature and water vapor, and relative external fluxes of water vapor and heat (e.g., during entrainment-mixing and phase change) influence turbulent supersaturation fluctuations. Although supersaturation has autocorrelation and structure functions similar to the independent scalars (temperature and water vapor), the autocorrelation time scale of supersaturation differs. Relative scalar fluxes in DNS without cloud make supersaturation PDFs less skewed than the adiabatic case, where they are highly negatively skewed. However, droplet condensation changes the PDF shape response: it becomes positively skewed for the adiabatic case and negatively skewed when the sidewall relative fluxes are large. Condensation also increases correlations between water vapor and temperature in the presence of relative scalar fluxes but decreases correlations for the adiabatic case. These changes in correlation suppress supersaturation variability for the nonadiabatic cases and increase it for the adiabatic case. Implications of this work for subgrid microphysics modeling using a Lagrangian stochastic scheme are also discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

RELAP-7 Application and Enhancement for FLEX Strategies and ATF Behavior under Extended Loss of AC Power Conditions

This report summarizes the results of a three-year research project sponsored by the U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) to enhance and apply the RELAP-7 code by adding and improving several important components (e.g., a mechanistic Reactor Core Isolation Cooling (RCIC) system model) for thermal hydraulic studies of LWRs under ELAP conditions and evaluating the time available for transition to portable FLEX equipment. The project team included University of Massachusetts–Lowell, The Ohio State University, Texas A&M University, Idaho National Laboratory and Oak Ridge National Laboratory. In the Fukushima accident, it was found that the RCIC system played a crucial role in delaying core meltdown by almost three days in Fukushima Daiichi Unit 2, because of self-regulated operation of the steam driven RCIC turbine-pump injection system. Steam flow in the convergent-divergent nozzles of the RCIC Terry turbine is two-phase non-equilibrium transonic flow with homogenous nucleation condensation. To more accurately predict the dynamic process and behavior of the transonic compressible steam flow, a one-dimensional transient two-phase analytical model is presented. A simplified four-fluid model was employed in the present work with the consideration of four separate fluid fields: vapor, liquid film, entrained droplets and condensed droplets. The mass, momentum and energy interactions between the fluids were considered and modeled. An extended seven-equation non-equilibrium critical flow model was developed to obtain the critical pressure and velocities of each phase at the nozzle throat. To predict the wetness in the divergent section, a mechanistic nucleation condensation model was integrated in the nozzle analysis model, considering the generation and consequent growth of droplets. The governing differential equations on a staggered grid were discretized using the second-order Lax-Wendroff scheme with a flux limiter, and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm was employed to solve the discrete linear system. To demonstrate the predictability and reliability of the physical models and the numerical method proposed in the present work, three representative nozzles were modeled and simulated. The results show good agreement with the available experimental data, even for condensation shock. Then, the 1D nozzle model was employed to obtain nozzle flow tables of the Terry turbine nozzle for different working pressures which can cover the operation pressure range of the RCIC system. A mechanistic RCIC turbine-pump system model was developed and implemented in the system code TRACE to simulate dynamic responses of the RCIC system under Beyond Design Basis Accident (BDBA) conditions. The turbine-pump governing equations are based on the control volume approach of the angular momentum balance. The physics based mechanistic RCIC model was developed using the TRACE control system components (i.e., signal variables, control blocks, and tables), and incorporated into a TRACE boiling water reactor (BWR) model. The TRACE model in this report has a detailed nodalization of the reactor pressure vessel (RPV), and all of the major flow paths and system components, including the safety relief valves (SRVs) and the containment suppression pool and drywell. Based on the nozzle flow tables generated from the 1D nozzle model developed, the turbine drive torque can be calculated from table lookup. Since the detailed specifications of the RCIC pump are unavailable, the homologous curves for a Bingham pump were used in the current pump component. A station black-out (SBO) accident test problem was selected to demonstrate the TRACE RCIC model. The short-term SBO simulations were performed for two cladding materials: Zircaloy and FeCrAl, to demonstrate the effect of the accident tolerant fuel cladding on fuel heat-up under BDBA accident conditions. The wetwell plays a vital safety role in SBO and other BWR accident scenarios in that it can reduce containment pressure and supply additional core make-up water. The suppression pool temperature distribution has a very large impact on both RPV and containment pressure. Thus, another novel contribution of the project comes mainly from an improved, systems-level wetwell model which can capture buoyancy-induced thermal stratification effects due to steam injection and condensation. A two-zone stratified wetwell model has been implemented in RELAP-7 and some results from that model are presented. This wetwell model is capable of simulating thermal stratification due to a low steam mass injection rate. With a low mass flow rate, the model assumes that all the steam condenses within the pipe and the resulting plume can be approximated with a purely buoyant, heat-source driven model. The wetwell model developed with these assumptions is adequate to simulate slow transients such as extended SBO transients.

42 ENGINEERING↗
DOE OSTI2025

Multi-objective automatic discovery of optimized metamaterials for varying velocity impact protection

Mechanical metamaterials have demonstrated exceptional impact performance while remaining lightweight. Impact resistance has traditionally been investigated using quasi-static simulations, often with the assumption that performance will translate to high-velocity impact scenarios. However, critical crash protection parameters—such as peak stress and absorbed energy—are highly sensitive to impact velocity, leading to inconsistent performance under dynamic loading. To address this, we introduce a strain-rate-aware, active deep learning framework that enables multi-objective optimization of impact protection metrics across a wide range of impact velocities. Our framework captures the strain-rate sensitivity of architected lattices by learning to control spatial gradation in cellular metamaterials, resulting in over 200 % enhancement in impact protection relative to state-of-the-art designs such as Voronoi and re-entrant lattices. We demonstrate its practical utility by designing next-generation lattice structures for automotive bumper systems that satisfy multiple, velocity-specific safety criteria—capabilities beyond those of conventional designs. More than just a predictive tool, this framework marks the first step towards enabling adaptable impact-resistant structures across dynamic regimes.

Deep learning↗
DOE OSTI2020

Molecular dynamics study on interface formation and bond strength of impact-welded Mg-steel joints

It was recently demonstrated that the vaporizing foil actuator welding (VFAW) method can directly join immiscible magnesium and steel alloys without coating or a third chemical element based intermetallic compound layer. The VFAW Mg/steel joint exhibits a mixed interface layer of up to 200μm thickness consisting of Mg matrix and Fe particles. Computer simulations have suggested the formation of the interlayer is from the high-velocity frictional shearing between the Mg/steel substrates during the oblique impact in the VFAW process. This paper investigates the formation of Mg-Fe interlayer under VFAW condition with different shearing velocities using molecular dynamics (MD) model, and studies the bonding strength under different scenarios. Finally, the results elucidate the critical role of shearing velocity and surface roughness in achieving Mg/Fe joint.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Experimental analysis of convective drying of paper and board

Conventional multi-cylinder drying of paper and board involves a mixture of conductive drying from steam-heated dryer cylinders and convective drying by the flow of heated air over the surface of the paper web in the pockets. Pocket ventilation is a critical component in assisting heat and mass transfer during the drying process but is the primary contributor towards removing evaporated water from the web. Air temperature, velocity, and humidity are critical parameters involved in the convective drying process. This paper covers an experimental study involving the design and development of a small lab-scale setup for convective drying of various grades of paper and board, monitoring multiple parameters like paper temperature, moisture content, air humidity, temperature, and velocity measured in situ as the drying proceeds with continuous and accurate sampling capabilities for all parameters in the sample and the system. Instantaneous drying rates, heat, and mass transfer coefficients were also deduced for every time step till the paper completely dried. Furthermore, the coefficients obtained were also reported in the form of dimensionless correlations, and the results were compared against traditional correlations used in the modelling of paper drying. Furthermore, this data will be useful in process development, modelling, design, and the paper drying process simulation.

42 ENGINEERING↗
DOE OSTI2025

Kinematic Evidence for Bipolar Ejecta Flows in the Galactic Supernova Remnant W49B

W49B is a unique Galactic supernova remnant with centrally peaked, “bar”-like ejecta distribution, which was once considered evidence for a hypernova origin that resulted in a bipolar ejection of the stellar core. However, chemical abundance measurements contradict this interpretation. Closely connected to the morphology of the ejecta is its velocity distribution, which provides critical details for understanding the explosion mechanism. We report the first ever observational constraint on the kinematics of the ejecta in W49B using the Resolve microcalorimeter spectrometer on the X-ray Imaging and Spectroscopy Mission (XRISM). Using XRISM/Resolve, we measured the line-of-sight velocity traced by the Fe Heα emission, which is the brightest feature in the Resolve spectrum, to vary by ±300 km s −1 with a smooth east-to-west gradient of a few tens of kilometers per second per parsec along the major axis. Similar trends in the line-of-sight velocity structure were found for other Fe-group elements Cr and Mn, traced by the Heα emission, and also for intermediate-mass elements Si, S, Ar, and Ca, traced by the Lyα emission. The discovery of the east–west gradient in the line-of-sight velocity, together with the absence of a twin-peaked line profile or enhanced broadening in the central region, clearly rejects the equatorially expanding disk model. In contrast, the observed velocity structure suggests bipolar flows reminiscent of a bipolar explosion scenario. An alternative scenario would be a collimation of the ejecta by an elongated cavity sculpted by bipolar stellar winds.

High resolution spectroscopy↗
DOE OSTI2024

Estimating Scaled Cloud Height in Pulse Jet Mixed Vessels

To suspend and mix radioactive slurries without pumps or impellers, the performance of pulsed jet mixed vessels has been investigated. The slurry in the pulse tubes is expelled impinging upon the vessel floor and lifting solids to a “cloud height” in a cyclic process. Experiments measuring cloud height for a variety of waste simulants have been conducted for vessel configurations that varied vessel diameter, fill height and pulse tube number, volume, and nozzle diameter. The elevation to which suspended particles rise is termed the cloud height and derives from a balance between the fluid forces of the jet and the gravitational forces acting on the particle ensemble. Here we use scaling to estimate the cloud height based on conservation of mass and momentum and jet similarity. We find that the cloud height varies with the nozzle exit velocity to the 2/3 power in agreement with observations.

cloud height, effective cleaning radius, effective↗