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At least 469 records · Page 26

Two Phase Flow Mapping and Transition Under Microgravity Conditions

In this paper, recent microgravity two-phase flow data for air-water, air-water-glycerin, and air- water-Zonyl FSP mixtures are analyzed for transition from bubbly to slug and from slug to annular flow. It is found that Weber number-based maps are inadequate to predict flow-pattern transition, especially over a wide range of liquid flow rates. It is further shown that slug to annular flow transition is dependent on liquid phase Reynolds number at high liquid flow rate. This effect may be attributed to growing importance of liquid phase inertia in the dynamics of the phase flow and distribution. As a result a new form of scaling is introduced to present data using liquid Weber number based on vapor and liquid superficial velocities and Reynolds number based on liquid superficial velocity. This new combination of the dimensionless parameters seem to be more appropriate for the presentation of the microgravity data and provides a better flow pattern prediction and should be considered for evaluation with data obtained in the future. Similarly, the analysis of bubble to slug flow transition indicates a strong dependence on both liquid inertia and turbulence fluctuations which seem to play a significant role on this transition at high values of liquid velocity. A revised mapping of data using a new group of dimensionless parameters show a better and more consistent description of flow transition over a wide range of liquid flow rates. Further evaluation of the proposed flow transition mapping will have to be made after a wider range of microgravity data become available.

Parang, Masood↗

Resummation of QED radiative corrections in a strong constant crossed field

By considering radiative corrections of up to 3rd-loop order, Ritus and Narozhny conjectured that the proper expansion parameter for QED in a strong constant crossed field is $g=\alpha\chi^{2/3}$, where the dynamical quantum parameter $\chi=e\sqrt{-(Fp)^2}/m^3$ combines the particle momentum $p$ with the external field strength tensor $F$. Here we present and discuss the first non-perturbative result in this context, the resummed bubble-type polarization corrections to the electron self-energy in a constant crossed field. Our analysis confirms the relevance of the scaling parameter $g$ to the enhancement of bubble-type radiative corrections. This parameter actually represents the characteristic value of the ratio of the 1-loop polarization bubble to the photon virtuality. After an all-order resummation we identify and discuss two contributions to the self-energy with different formation regions and asymptotic behavior for $g\gg1$. Whereas the breakdown of perturbation theory occurs already for $g\gtrsim1$, the leading-order result remains dominant until the asymptotic regime $g\gg 1$ is reached. However, the latter is specific to processes like elastic scattering or photon emission and does not have to remain true for general higher-order QED processes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Computational Fluid Dynamics Simulations of Glass Vitrification Refractory Coupon Tests

The Waste Treatment and Immobilization Plant (WTP) at the Hanford site is nearing the start of the Direct-Feed Low-Activity Waste (DFLAW) operations. DFLAW is destined to convert a pretreated low activity waste portion of the 56 million gallons of tank waste into a stable solid glass. In the subsequent decade completion of the high-level waste (HLW) facility is anticipated. Sustained operational missions of both LAW and HLW melter facilities are expected over multiple decades. In high-temperature glass melters, the refractory lining corrodes over time, which could potentially be an issue for longer term operations, this refractory corrosion is higher at the level of the glass-air interface due to surface tension driven flow. The glass viscosity, melt pool temperature, and glass chemical composition can impact the rate at which the refractory corrodes. This rate is important to quantify for the various waste glasses to be produced at the WTP since the integrity of the refractory should not be a limiting factor affecting the lifetime of the melter. To this end, a series of glasses representative of the first batches of waste glass produced by the WTP will be melted in small-scale crucibles with Monofrax® K-3 coupons inserted. The corrosion of the K-3 will be measured in the melt and at the meltline (or neckline). A model for the corrosion rate will be constructed and implemented into a previously developed framework for a computational fluid dynamics (CFD) model of the full-scale WTP. To assist with experimental design and validate the implementation of the model in the full-scale melter, CFD simulations of the small-scale crucible tests were performed. The bubbling that occurs in the small-scale crucible is initially validated here with a model that uses silicone oil at room temperature. The viscosity of the oil ranges from 1 to 100 Pa•s, which corresponds to operating glass pool temperatures near 1150 °C down to idling temperatures near 950 °C. The simulation results show good agreement with the bubble sizes that form during experiments. CFD modeling of the crucible setup was used to determine bubbling characteristics to match the range of near-wall velocities expected in the full-scale WTP. This study presents the initial CFD modeling results, corrosion testing plan, and some preliminary corrosion samples with an outline for the next steps for the development of the corrosion model.

Abboud, Alexander W. [Idaho National Lab]↗

High-fidelity pool boiling simulations on multiple nucleation sites using interface capturing method

Boiling has proved to be one of the most efficient means for heat transfer and is a very important phenomenon during severe accident scenarios in light water reactors. High-fidelity pool boiling simulations can provide a numerical database for improving mechanistic boiling models by allowing for specific evaluation of interactions among bubbles. Previously published pool boiling simulations investigated two nucleation sites in which bubble growth at one site suppressed nucleation at the other site. Based on previous study results, more complicated interface-capturing simulations on pool boiling were conducted using PHASTA code with locally refined unstructured mesh. First, different boundary conditions (BCs) were assessed to support robustness and reproducibility of the boiling model. Then, a scale study was conducted at a larger domain with nine nucleation sites where either nine or four nucleation sites are activated. Involving more nucleation sites increased the complexity of bubble interactions from surrounding sites. Finally, bubble departure behavior influenced by wall heat flux was investigated. In this work, when heat flux was increased, the order of bubble departure changed, but diagonal bubbles always departed after one another. The departure time interval between the first and second bubble reduced as heat flux increased. The corresponding frequency was almost linearly proportional to the heat flux. In addition, bubble departure behavior was found to be greatly influenced by the nucleation site pattern. Multiple nucleation sites resulted in superimposed inhibitive effects from surrounding sites to each bubble, which extensively delayed the departure. This new observation was not discussed in previously published works. The work presented here provides new insight on the fundamental understanding of boiling phenomena, contributes to the development of a 3D multiphase computational fluid dynamics (M-CFD) model, and provides a more comprehensive database for data-driven pool boiling studies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Massive Stars and the Energy Balance of the Interstellar Medium: The Impact of an Isolated 60 M. Star - 1

We present results of numerical simulations carried out with a two-dimensional radiation hydrodynamics code in order to study the impact of massive stars on their surrounding interstellar medium. This first paper deals with the evolution of the circumstellar gas around an isolated 60 M. star. The interaction of the photo- ionized H II region with the stellar wind bubble forms a variety of interesting structures like shells, clouds, fingers, and spokes. These results demonstrate that complex structures found in H II regions are not necessarily relics from the time before the gas became ionized but may result from dynamical processes during the course of the H II region evolution. We have also analyzed the transfer and deposit of the stellar wind and radiation energy into the circumstellar medium until the star explodes as a supernova. Although the total mechanical wind energy supplied by the star is negligible compared to the accumulated energy of the Lyman continuum photons, the kinetic energy imparted to the circumstellar gas over the star s lifetime is 4 times higher than for a comparable windless simulation. Furthermore, the thermal energy of warm photoionized gas is lower by some 55%). Our results document the necessity to consider both ionizing radiation and stellar winds for an appropriate description of the interaction of OB stars with their circumstellar environment.

Freyer, Tim↗

Design Study for Bio-Oil Production from Biomass Using a Dual Fluidized-Bed Reactor

To evaluate the re-design and reconfiguration of a dual-fluidized bed (DFB) gasification system into a recirculating pyrolysis reactor, Computation Fluid Dynamic (CFD) simulations of the system were conducted. The Barracuda Virtual Reactor® computational particle fluid dynamic code was used to perform simulations of the pyrolysis process. Modeling of the chemical reaction kinetics for both gas phase and solid particle phase were included. The recirculating pyrolysis reactor shown in Fig. 1a is based on a bubbling-bed biomass pyrolyzer and a riser combustor to convert the remaining char. The operational differences in the re-configuration of the DFB gasification system into a recirculating pyrolysis system for the production of bio-oil are (1) replacement of a low-surface area inert bed material with a high-surface-area bed material that has acidic properties to provide catalytic activity for the production of bio-oil with reduced oxygen content, (2) lower temperature and residence time for bio-oil production from pyrolysis, (3) replacement of the fluidization gas in the bubbling bed pyrolyzer from steam to nitrogen, and (4) the reduction of pyrolyzer freeboard volume. The bed material used for catalytic pyrolysis is Sasol 300 (300-micron dia., bulk density 0.94 kg/l, and surface area 130 m2/g) and is a theta-alumina with mild acidity. This is in comparison with previous standard bed material Carbo HSP (430-micron dia., bulk density 2.01 kg/l, and surface area 0.03 m2/g) used for gasification. For bio-oil production, pyrolysis in the bubbling bed requires temperatures in the range of 550 C in comparison with gasification temperatures near 850 C. To attain this lower temperature requires management of the energy mass balances, with control of the bed material recirculation rate between bubbling bed pyrolyzer and riser combustor, the introduction of a nitrogen purge in the pyrolyzer, and adjusting the pressure balance between the two vessels. To extract bio-oil from the pyrolysis reactor with a snorkel, two different freeboard configurations were evaluated. In Fig. 1 b the existing high freeboard configuration is shown and in Fig. 1 c the reduced freeboard design is presented. The introduction of a nitrogen purge for the high free board configuration provided the highest bio-oil production from the CFD simulations. To decrease the bed-material circulation rate, primary and secondary air on the combustor side were reduced, and the pressure on the combustor was slightly increased. A portion of the biomass and bio-oil was observed to be transported to the combustor, leading to a smaller pyrolysis yield. The control of the pyrolyzer temperature is performed by controlling the circulation rate. Good fluidization of the bubbling bed and cascade PID control are required to keep the temperature from oscillating due to large time delay experienced when changing primary and secondary air. (a) (b) (c) Figure 1. (a) Dual Fluidized Bed pyrolysis system configuration, (b) mole fraction of nonpolar biooil in high freeboard configuration, and (c) mole fraction of nonpolar bio-oil in low freeboard configuration with nitrogen purge introduced in both configurations.

BASIC BIOLOGICAL SCIENCES,BIOMASS FUELS↗

Development of multi-scale computational frameworks to solve fusion materials science challenges

Over the past two decades, the US-DOE has funded multiple projects that rely on high-performance computing and exascale computing platforms to accelerate scientific discoveries and address grand scientific challenges, such as harnessing fusion energy. In this article, we review in detail one of these efforts aimed at enhancing our capability to model plasma-facing materials subject to plasma and high-energy ion/neutron irradiation. The plasma surface interactions project has built a multi-scale modeling framework where many of the plasma- and high-energy ion/neutron irradiation-induced effects occurring in tungsten are explored. Here, this knowledge is used to develop atomistically-informed, high-fidelity continuum and meso-scale models that can be validated against experiments. We review the developments within this project, with attention to experimental validation efforts, and specifically highlight activities associated with: helium bubble bursting and equation of state, and hydrogen-helium interactions in tungsten; atomistically-informed model development for beryllium-tungsten material mixing; coupling of scrape-of-layer plasma, sheath and material models; and coupling of stochastic cluster-dynamics and crystal plasticity models to address radiation effects in tungsten under stress. Finally, we present how the project is preparing for future computational architectures, for instance through efforts to adapt atomistic methods to exascale computing.

36 MATERIALS SCIENCE↗

Elastic Properties of Plasma-Exposed Tungsten Predicted by Molecular-Dynamics Simulations

We report results of systematic molecular-dynamics computations of the elastic properties of single-crystalline tungsten containing structural defects, voids and overpressurized He nanobubbles, related to plasma exposure of tungsten serving as a plasma- facing component (PFC) in nuclear fusion devices. Our computations reveal that the empty voids are centers of dilatation resulting in development of tensile stress in the tungsten matrix, whereas He-filled voids (nanobubbles) introduce compressive stress in the plasma-exposed tungsten. We find that the dependence of the elastic moduli of plasma-exposed tungsten, namely, the bulk, Young, and shear modulus, on its void fraction follows a universal exponential scaling relation. We also find that the elastic moduli of plasma-exposed tungsten soften substantially as a function of He content in the tungsten matrix, following an exponential scaling relation; this He-induced exponential softening is in addition to the softening caused in the matrix with increasing temperature. A systematic characterization of the dependence of the elastic moduli on the He bubble size reveals that He bubble growth affects significantly both the bulk modulus and the Poisson ratio of plasma-exposed tungsten, while its effect on the Young and shear moduli of the plasma-exposed material is weak. Our findings contribute directly to the development of a structure-properties database that is required for the predictive modeling of the dynamical response of PFCs in nuclear fusion devices.

36 MATERIALS SCIENCE↗

Beam dynamics challenges in linear colliders based on laser-plasma accelerators

In this paper we discuss design considerations and beam dynamics challenges associated with laser-driven plasma-based accelerators as applied to multi-TeV-scale linear colliders. Plasma accelerators provide ultra-high gradients and ultra-short bunches, offering the potential for compact linacs and reduced power requirements. We show that stable, efficient acceleration with beam quality preservation is possible in the nonlinear bubble regime of laser-plasma accelerators using beam shaping. Ion motion, naturally occuring for dense beams (i.e., low emittance and high energy) severely damps transverse beam instabilities. Coulomb scattering by the background ions is considered and it is shown that the strong focusing in the plasma strongly suppresses scattering-induced emittance growth. Finally, Betatron radiation emission from the transverse motion of the beam in the plasma will result in beam power loss and energy spread growth; however for sub-100 nm emittances, the beam power loss and energy spread growth will be sub-percent for multi-TeV-class plasma linacs.

47 OTHER INSTRUMENTATION↗

Anharmonic phonon behavior via irreducible derivatives: Self-consistent perturbation theory and molecular dynamics

Cubic phonon interactions are now regularly computed from first principles, and the quartic interactions have begun to receive more attention. Given this realistic anharmonic vibrational Hamiltonian, the classical phonon Green's function can be precisely measured using molecular dynamics, which can then be used to rigorously assess the range of validity for self-consistent diagrammatic approaches in the classical limit. Here we use the bundled irreducible derivative approach to efficiently and precisely compute the cubic and quartic phonon interactions of CaF 2 , systematically obtaining the vibrational Hamiltonian purely in terms of irreducible derivatives. We demonstrate that the 4-phonon sunset diagram has an important contribution to the optical phonon linewidths beyond T = 500 K. Reasonable results are obtained even at T = 900 K when performing self-consistency using the 4-phonon loop diagram and evaluating the 3-phonon bubble and 4-phonon sunset diagrams post-self-consistency. Further improvements are obtained by performing quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Finally, our irreducible derivative approach to self-consistent perturbation theory is a robust tool for studying anharmonic phonons in both the quantum and classical regimes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Atomic-scale mechanisms of void strengthening in tungsten

Neutron and heavy-ion irradiation of tungsten produces nanometer-size vacancy voids, gas-filled bubbles and dislocation loops. These defect features can affect mechanical properties and the impact can be quite significant because of their high density. Understanding the basic mechanisms of mechanical properties degradation is necessary for predicting radiation effects. Predictions can be made using discrete dislocation dynamics or/and finite element approaches which, however, need local interaction mechanisms as inputs. Such knowledge can be provided only by atomic-scale modeling. This paper reports the results of an extensive atomic-scale modeling study of the interactions between moving edge dislocations and voids in tungsten. Furthermore, the main focus is on the effects of the void size and ambient temperature. Critical resolved shear stress was calculated for voids up to 9 nm in diameter. Atomistic results are compared with the theoretical approach and with those obtained earlier for voids in body centered cubic (bcc) iron. An important role of the void surface has been revealed.

36 MATERIALS SCIENCE↗

Experiments on annular liquid jet instability and on the formation of liquid shells

An annular jet flow of liquid surrounding a flow of gas at its core is extremely unstable. Experiments are described in which such a flow is generated by an annular nozzle operated at fairly specific conditions. It is shown that periodic, axisymmetric oscillations arise spontaneously within the cylindrical sheet emerging from the nozzle and grow with such rapidity along the axial dimension that a sealing-off and encapsulation of the core gas occurs within a few jet diameters. This is closely followed by a pinchoff of the liquid between adjacent bubbles. The liquid shells set free thereby assume spherically symmetric form under capillary forces, and each contains a precisely uniform measure of gas and of liquid on account of the extremely high frequency-stability of the process. Description is given of the fluid dynamic processes by which the shells are formed, and mention is made of exploiting the instability for the production of rigid shells for technological applications.

Kendall, J. M.↗

Non-dilute helium-related defect interactions in the near-surface region of plasma-exposed tungsten

We report a systematic energetic analysis of helium-related defect interactions that mediate helium (He) segregation on surfaces of plasma-exposed tungsten at different levels of He ion implantation. We focus on high He fluences that increase the He content in the plasma-exposed material well beyond the dilute limit of He concentration and employ atomic configurations generated by large-scale molecular dynamics simulations of He-implanted tungsten. We perform systematic molecular statics computations of cluster– defect interaction energetics in the highly defect-rich near-surface region of plasma-exposed tungsten for small mobile helium clusters as a function of the cluster distance from the surface. In this region, mobile clusters are also subjected to the stress fields generated by defects such as helium bubbles and other clusters, which govern cluster–defect interactions in addition to the cluster–surface interaction. Based on systematic investigation of individual cluster–defect interactions, we develop a mathematical framework to describe the interaction energy landscapes consisting of elastic interaction potential perturbations to finite-width square-well potentials, where the potential well accounts for cluster trapping by the defect at close range and subsequent coalescence and the perturbation potential is parameterized according to elastic inclusion theory. Superposition of all the relevant interaction potentials provides a comprehensive description of the interaction energy landscape that would be experienced by a small mobile cluster along its migration path toward the plasma-exposed surface at high He fluence. Such descriptions are particularly important for developing atomistically-informed, hierarchical multi-scale models of helium cluster dynamics in plasma-facing materials.

36 MATERIALS SCIENCE↗

Evidence for Tropopause Layer Moistening by Convection During CRYSTAL-FACE

Measurements and analysis of the impact of deep convection on tropopause layer moisture are easily confounded by difficulties making precise observations with sufficient spatial coverage before and after convective events and difficulties distinguishing between changes due to local convection versus large-scale advection. The interactions between cloud microphysics and dynamics in the convective transport of moisture into the tropopause layer also result in a sufficiently complex and poorly characterized system to allow for considerable freedom in theoretical models of stratosphere-troposphere exchange. In this work we perform detailed large-eddy simulations with an explicit cloud microphysics model to study the impact of deep convection on tropopause layer moisture profiles observed over southern Florida during CRYSTALFACE. For four days during the campaign (July 11, 16, 28, and 29) we initialize a 100-km square domain with temperature and moisture profiles measured prior to convection at the PARSL ground site, and initiate convection with a warm bubble that produces an anvil at peak elevations in agreement with lidar and radar observations on that day. Comparing the moisture field after the anvils decay with the initial state, we find that convection predominantly moistens the tropopause layer (as defined by minimum temperature and minimum potential temperature lapse rate), although some drying is also predicted in localized layers. We will also present results of sensitivity tests designed to separate the roles of cloud microphysics and dynamics.

Ackerman, A.↗

Biochemical Process Modeling and Simulation (BPMS)

The Biochemical Process Modeling and Simulation project aims to reduce the cost and time of research by applying theory, modeling, and simulation to the most relevant bottlenecks in the biochemical process. We use molecular modeling, quantum mechanics, metabolic modeling, fluid dynamics, and reaction-diffusion methods in close collaboration with pretreatment, hydrolysis, upgrading, and TEA. The project's outcomes are increased yields and efficiency of the biochemical process, added value to products, and reduced price of fuels by specifically targeting catalytic efficiency, reactor design, enzyme efficiency, and microbial design. We work closely with experimental projects to identify problems and iterate with experiments to find and refine solutions. By working with experimentalists, we decide on problems that can be solved with simulation that could otherwise not be solved or would take too long with experiment alone to reach BETO's targets. Over the years, we have produced solutions that have resulted in determining the most likely fatty-acid derivative for passive transport out of bacteria that upgrade biomass, and we have also designed enzyme mutations for enhanced lignin upgrading. Metabolic models have been developed to tune the activity of 2,3 butanediol production for the 2030 target. A computational method to deliver understanding of how complex omics data can be interpreted in the metabolic pathways of organisms used in the Agile Biofoundry. We have found methods to overcome specific barriers and continue to develop those methods. Our reactor studies have guided the design of both the microbes and reactors for aerobic and micro-aerobic production at all scales and have been instrumental in improving the accuracy of techno-economic analysis models. This project is essential in the process of selecting the final processes for 2030 SAF production targets. More specifically, recently, we have: 1) Predicted the strength of the basic structural interactions in commodity plastics to provide guidance for plastics upcycling strategies. 2) Developed computational tool to improve the characterization of lignin-derived compounds 3) Developed new methodologies to enable Machine Learning-based Directed Evolution for protein engineering. 4) Developed Machine Learning methods to predict protein promiscuity and mutations to further improve microbial and enzymatic driven processes and demonstrated the utility of ML approaches to engineering proteins from sparse experimental datasets. 5) Developed new methods to enable high-fidelity simulation of aerobic fermentation at industrial scale and resolving mismatch of time scales through subcycling/operator splitting 7) Identified the difficulty in preventing local high-oxygen conditions in industrial bubble columns, which leads to less-desirable acetoin production, suggesting future research directions in alternative reactor configurations (e.g loop reactors, shallow-channel reactors).

BIOMASS FUELS↗

Open source implementation of glued sphere discrete element method and nonspherical biomass fast pyrolysis simulation

Here, in this research, a glued-sphere Discrete Element Method (DEM) method was implemented in the open-source, Computational Fluid Dynamics (CFD) software MFiX. The implementation was verified using a cylinder-wall collision and then validated by simulating the packing and fluidization of non-spherical particles. The validated code was applied to simulate fast pyrolysis of non-spherical biomass particles in a bubbling fluidized bed. The glued sphere occupancy ratio was proposed to quantify the quality of shape resolution using glued sphere. Shape resolution showed significant influence on the packing height in the simulation of particle packing and an occupancy ratio of 80 % was recommended. Its influence is minor in fully fluidized bed but can be 8 times higher in fixed fluidized bed. Three tested heat transfer models predicted similar yields of elongated biomass fast pyrolysis. The solver developed in this research can be used to simulate other multiphase reacting flows involving non-spherical particles.

42 ENGINEERING↗

Three-Dimensional Structure and Modeling of a Normal Bifurcated Shock Train from Experimental Measurements

An asymmetric, bifurcated normal shock train in a Mach 2 constant area, rectangular duct is investigated in the University of Michigan Direct Connect Isolator facility. High-speed schlieren imaging, wall static pressure measurements, surface oil flow visualization, and particle image velocimetry of a shock train are synthesized into a three-dimensional representation of shock train structure. This visualization is then used to inform the underlying flow physics of the distributed fluid dynamical processes along the structure. The detailed, three-dimensional morphology of the flow profile entering the shock train is shown to have a significant impact on the separated flow morphology of the shock train. This results in skewed supersonic core flow with alternating separation bubbles in the surrounding boundary layers. Finally, the efficacy of the prevailing pseudo-shock models in the literature is analyzed with the support of the available flow measurements. None are found to simultaneously model both the pressure and streamwise Mach number profile of the UMDCI pseudo-shock.

Hypersonics↗

Dynamics of Downdrafts Around a Growing Convective Cloud: A Numerical Study

We examine the dynamics of cloud-edge downdrafts over the growth phase of isolated cumuli, combining Eulerian and Lagrangian analyses. As in previous studies, our results show that growing cumuli are surrounded by downdrafts linked to cloud-scale quasi-toroidal circulations at all times at middle and upper cloud levels consistent with the thermal chain description of convective clouds. These toroidal circulations are responsible for the most intense cloud-edge downdrafts in our simulations. In the upper cloud half, roughly 30%–50% of the upward mass flux is typically compensated within a radius of about twice the updraft radius in quasi-laminar simulations forced by a warm bubble in an initially quiescent flow. In a turbulent cloud forced by surface fluxes, this compensation fraction is around 10%–30% over the same region. In contrast to the buoyancy-centered view of subsiding shells, Eulerian and Lagrangian vertical momentum budget analyses show that the most intense cloud-edge downdrafts in the turbulent setup, and after spin-up of the toroidal circulation in the quasi-laminar experiments, are predominantly mechanically forced (i.e., driven by dynamic pressure accelerations). This is consistent throughout the entire growth phase of the cumulus clouds and across tests with varying assumptions, including drier and moister environments. Despite dynamic pressure perturbations being the main driver of toroidal downdrafts, the downdraft speed (relative to the corresponding updraft velocity) exceeds the prediction of the non-buoyant Hill's spherical vortex—a simple model frequently used for cloud-scale circulations—by more than 30%.

Pardo, Lianet Hernández [Goethe Univ., Frankfurt (↗