Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Conditional Normalizing Flow”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Acute and chronic head-down tail suspension diminishes cerebral perfusion in rats

The purpose of this study was to test the hypothesis that regional brain blood flow and vascular resistance are altered by acute and chronic head-down tail suspension (HDT). Regional cerebral blood flow, arterial pressure, heart rate, and vascular resistance were measured in a group of control rats during normal standing and following 10 min of HDT and in two other groups of rats after 7 and 28 days of HDT. Heart rate was not different among conditions, whereas mean arterial pressure was elevated at 10 min of HDT relative to the other conditions. Total brain blood flow was reduced from that during standing by 48, 24, and 27% following 10 min and 7 and 28 days of HDT, respectively. Regional blood flows to all cerebral tissues and the eyes were reduced with 10 min of HDT and remained lower in the eye, olfactory bulbs, left and right cerebrum, thalamic region, and the midbrain with 7 and 28 days of HDT. Total brain vascular resistance was 116, 44, and 38% greater following 10 min and 7 and 28 days of HDT, respectively, relative to that during control standing. Vascular resistance was elevated in all cerebral regions with 10 min of HDT and remained higher than control levels in most brain regions. These results demonstrate that HDT results in chronic elevations in total and regional cerebral vascular resistance, and this may be the underlying stimulus for the HDT-induced smooth muscle hypertrophy of cerebral resistance arteries.

Non-NASA Center↗

Investigation of Aerodynamic and Icing Characteristics of Water-Inertia-Separation Inlets for Turbojet Engines

The results of an investigation of several internal water-inertia-separation inlets consisting of a main duct and an alternate duct designed to prevent automatically the entrance of large quantities of water into a turbojet engine in icing conditions are presented. Total-pressure losses and icing characteristics for a direct-ram inlet and the inertia-separation inlets are compared at similar aerodynamic and simulated icing conditions. Complete ice protection for inlet guide vanes could not be achieved with the inertia-separation inlets investigated. Approximately 8 percent of the volume of water entering the nacelles remained. In the air passing into the compressor inlet. Heavy alternate-duct-elbow ice formations caused by secondary inertia separation resulted in rapid total-pressure losses and decreases in mass flow. The duration in an icing condition for an inertia-separation- inlet, without local surface heating, was increased approximately four times above that for a direct-ram inlet with a compressor-inlet screen. For normal nonicing operation, the inertia-separation- inlet total-pressure losses were comparable to a direct-ram installation. The pressure losses and the circumferential uniformity of the mass flow in all the inlets were relatively independent of angle of attack. Use of an inertia-separation inlet would in most cases require a larger diameter nacelle than a direct-ram inlet in order to obtain an alternate duct sufficiently large to pass the required engine air flow at duct Mach numbers below 1.0 at the minimum area.

VonGlahn, Uwe↗

Smoke-Point Properties of Non-Buoyant Round Laminar Jet Diffusion Flames

The laminar smoke-point properties of non-buoyant round laminar jet diffusion flames were studied emphasizing results from long-duration (100-230 s) experiments at microgravity carried out in orbit aboard the space shuttle Columbia. Experimental conditions included ethylene- and propane-fueled flames burning in still air at an ambient temperature of 300 K, pressures of 35-130 kPa, jet exit diameters of 1.6 and 2.7 mm, jet exit velocities of 170-690 mm/s, jet exit Reynolds numbers of 46-172, characteristic flame residence times of 40-302 ms, and luminous flame lengths of 15-63 mm. Contrary to the normal-gravity laminar smoke point, in microgravity, the onset of laminar smoke-point conditions involved two flame configurations: closed-tip flames with soot emissions along the flame axis and open-tip flames with soot emissions from an annular ring about the flame axis. Open-tip flames were observed at large characteristic flame residence times with the onset of soot emissions associated with radiative quenching near the flame tip: nevertheless, unified correlations of laminar smoke-point properties were obtained that included both flame configurations. Flame lengths at laminar smoke-point conditions were well correlated in terms of a corrected fuel flow rate suggested by a simplified analysis of flame shape. The present steady and non-buoyant flames emitted soot more readily than non-buoyant flames in earlier tests using ground-based microgravity facilities and than buoyant flames at normal gravity, as a result of reduced effects of unsteadiness, flame disturbances, and buoyant motion. For example, present measurements of laminar smoke-point flame lengths at comparable conditions were up to 2.3 times shorter than ground-based microgravity measurements and up to 6.4 times shorter than buoyant flame measurements. Finally, present laminar smoke-point flame lengths were roughly inversely proportional to pressure to a degree that is a somewhat smaller than observed during earlier tests both at microgravity (using ground-based facilities) and at normal gravity.

Urban, D. L.↗

Charge exchange recombination spectroscopy at Wendelstein 7-X

The Charge Exchange Recombination Spectroscopy (CXRS) diagnostic has become a routine diagnostic on almost all major high temperature fusion experimental devices. For the optimized stellarator Wendelstein 7-X (W7-X), a highly flexible and extensive CXRS diagnostic has been built to provide high-resolution local measurements of several important plasma parameters using the recently commissioned neutral beam heating. This paper outlines the design specifics of the W7-X CXRS system and gives examples of the initial results obtained, to include typical ion temperature profiles for several common heating scenarios, toroidal flow and radial electric field derived from velocity measurements, beam attenuation via beam emission spectra, and normalized impurity density profiles under some typical plasma conditions.

47 OTHER INSTRUMENTATION↗

Modelling and simulation of brinicle formation

Below the Arctic sea ice, under the right conditions, a flux of icy brine flows down into the sea. The icy brine has a much lower fusion point and is denser than normal seawater. As a result, it sinks while freezing everything around it, forming an ice channel called a brinicle (also known as ice stalactite). In this paper, we develop a mathematical model for this phenomenon, assuming cylindrical symmetry. The fluid is considered to be viscous and quasi-stationary. The heat and salt transport are weakly coupled to the fluid motion and are modelled with the corresponding conservation equations, accounting for diffusive and convective effects. Finite-element discretization is employed to solve the coupled system of partial differential equations. We find that the model can capture the general behaviour of the physical system and generate brinicle-like structures while also recovering dendrite composition, which is a physically expected feature aligned with previous experimental results. This represents, to our knowledge, the first complete model proposed that captures the global structure of the physical phenomenon even though it has some discrepancies, such as brine accumulation.

97 MATHEMATICS AND COMPUTING↗

Hanford Waste Treatment Plant Effluent Management Facility Stack Effluent Monitoring: Sampling Probe Location Qualification Evaluation

The Hanford Tank Waste Treatment and Immobilization Plant Effluent Management Facility (EMF) stack monitor location was qualified using a combination of scale model stacks to mitigate the risk of identifying that the sampling location does not meet the qualification criteria on the full-scale stack. The LV-S1 scale model stack was used as a baseline, augmented by the LB-S1 and LV-S2 scale model stacks to address the Direct Feed Low Activity Waste Effluent Management Facility Vessel Vent Process (DVP) injection into the main Active Confinement Ventilation (ACV) system duct. As required by the American National Standards Institute/Health Physics Society (ANSI/HPS) N13.1-1999 standard, the scale model and its sampling locations were geometrically similar to the actual stack, and the Reynolds numbers for both the actual and model stacks were >10,000. An additional criterion is that the product of the hydraulic diameter and mean velocity (DV) of the full-scale stack must be between 1/6 DV and 6 DV of the scale model stack tests. The LV-S1, LB-S1, and LV-S2 scale model stack tests have met the criteria of the ANSI/HPS N13.1-1999 standard to demonstrate the stack sampling locations are well mixed. Verification tests of the EMF stack were performed at normal operating conditions. The minimum 1/6 DV value and the maximum 6 DV value from the scale model testing determine the range of stack flow rates for which the full-scale stack may be operated while remaining in compliance with the stack verification criterion. A practical range for the full-scale stack qualification uses the average DV through 6 DV from the scale model tests to compute the corresponding flow rates. Table S1 lists the operating flow rate along with the average and maximum qualified stack flow rate based on the LV-S1 scale model DV values. The operating flow is below the maximum qualified stack flow, which means that the scale model test results are acceptable for stack qualification. The remaining criteria for the stack verification to be considered valid involve the flow angle and velocity uniformity results. First, the flow angle at the full-scale stack must be ≤20°. Second, the velocity uniformity at the full-scale stack must be ≤20% coefficient of variance (COV). Finally, the velocity uniformity results for the actual and scale model stack tests must agree within 5% COV. These criteria were met through the full-scale stack test at the EMF. Flow angle results were <5°; all flow angle results were within the ≤20° criterion. The velocity uniformity results for each test condition ranged between 2.2% COV and 4.3% COV, all of which were within the range of the target % COV values from the scale model tests on the LV-S1, LB-S1, and LV S2 scale models. Based on these stack verification test results, the EMF filtered exhaust stack sampling location meets the qualification criteria provided in the ANSI/HPS N13.1-1999 standard for all planned fan operating configurations. This includes each combination of ACV fans with DVP exhausters. Further changes to the system configuration or operating conditions that are outside the qualified flow rates described in this report may require additional tests or analyses to determine compliance with the standard.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

The relative merits of several numerical techniques for solving the compressible Navier-Stokes equations

Four explicit finite difference techniques designed to solve the time-dependent, compressible Navier Stokes equations are compared. These techniques are: (1) MacCormack, (2) modified Du Fort-Frankel, (3) modified hopscotch, and (4) Brailovskaya. The comparison was made numerically by solving the quasi-one dimensional Navier Stokes equations for the flow in a converging-diverging nozzle. Solutions with and without standing normal shock waves were computed for unit Reynolds numbers (based on total conditions) ranging from 45374 to 2269. The results indicate that all four techniques are comparable in accuracy; however, the modified hopscotch scheme is two to three times faster than the Brailovskaya and MacCormack schemes and three to six times faster than the modified Du Fort-Frankel scheme.

Holst, T. L.↗

Three-dimensional compressible stability-transition calculations using the spatial theory

The e(exp n)-method is employed with the spatial amplification theory to compute the onset of transition on a swept wing tested in transonic cryogenic flow conditions. Two separate eigenvalue formulations are used. One uses the saddle-point method and the other assumes that the amplification vector is normal to the leading edge. Comparisons of calculated results with experimental data show that both formulations give similar results and indicate that the wall temperature has a rather strong effect on the value of the n factor.

Niethammer, R.↗

NASA Microgravity Combustion Science Program

Combustion has been a subject of increasingly vigorous scientific research for over a century, not surprising considering that combustion accounts for approximately 85% of the world's energy production and is a key element of many critical technologies used by contemporary society. Although combustion technology is vital to our standard of living, it also poses great challenges to maintaining a habitable environment. A major goal of combustion research is production of fundamental (foundational) knowledge that can be used in developing accurate simulations of complex combustion processes, replacing current "cut-and-try" approaches and allowing developers to improve the efficiency of combustion devices, to reduce the production of harmful emissions, and to reduce the incidence of accidental uncontrolled combustion. With full understanding of the physics and chemistry involved in a given combustion process, including details of the unit processes and their interactions, physically accurate models which can then be used for parametric exploration of new combustion domains via computer simulation can be developed, with possible resultant definition of radically different approaches to accomplishment of various combustion goals. Effects of gravitational forces on earth impede combustion studies more than they impede most other areas of science. The effects of buoyancy are so ubiquitous that we often do not appreciate the enormous negative impact that they have had on the rational development of combustion science. Microgravity offers potential for major gains in combustion science understanding in that it offers unique capability to establish the flow environment rather than having it dominated by uncontrollable (under normal gravity) buoyancy effects and, through this control, to extend the range of test conditions that can be studied. It cannot be emphasized too strongly that our program is dedicated to taking advantage of microgravity to untangle complications caused by gravity, allowing major strides in our understanding of combustion processes and in subsequent development of improved combustion devices leading to improved quality of life on Earth. Fire and/or explosion events aboard spacecraft could be devastating to international efforts to expand the human presence in space. Testing to date has shown that ignition and flame spread on fuel surfaces (e.g., paper, wire insulation) behave quite differently under partial gravity and microgravity conditions. In addition, fire signatures-i.e., heat release, smoke production, flame visibility, and radiation-are now known to be quite different in reduced gravity environments; this research has provided data to improve the effectiveness of fire prevention practices, smoke and fire detectors, and fire extinguishment systems. The more we can apply our scientific and technological understanding to potential fire behavior in microgravity and partial gravity, the more assurance can be given to those people whose lives depend on the environment aboard spacecraft or eventually on habitats on the Moon or Mars.

King, Merrill K.↗

Cross-Stream PIV Measurements of Jets With Internal Lobed Mixers

With emphasis being placed on enhanced mixing of jet plumes for noise reduction and on predictions of jet noise based upon turbulent kinetic energy, unsteady measurements of jet plumes are a very important part of jet noise studies. Given that hot flows are of most practical interest, optical techniques such as Particle Image Velocimetry (PIV) are applicable. When the flow has strong azimuthal features, such as those generated by chevrons or lobed mixers, traditional PIV, which aligns the measurement plane parallel to the dominant flow direction is very inefficient, requiring many planes of data to be acquired and stacked up to produce the desired flow cross-sections. This paper presents PIV data acquired in a plane normal to the jet axis, directly measuring the cross-stream gradients and features of an internally mixed nozzle operating at aircraft engine flow conditions. These nozzle systems included variations in lobed mixer penetration, lobe count, lobe scalloping, and nozzle length. Several cases validating the accuracy of the PIV data are examined along with examples of its use in answering questions about the jet noise generation processes in these nozzles. Of most interest is the relationship of low frequency aft-directed noise with turbulence kinetic energy and mean velocity.

Bridges, James↗

Radiative Extinction of Gaseous Spherical Diffusion Flames in Microgravity

Radiative extinction of spherical diffusion flames was investigated experimentally and numerically. The experiments involved microgravity spherical diffusion flames burning ethylene and propane at 0.98 bar. Both normal (fuel flowing into oxidizer) and inverse (oxidizer flowing into fuel) flames were studied, with nitrogen supplied to either the fuel or the oxygen. Flame conditions were chosen to ensure that the flames extinguished within the 2.2 s of available test time; thus extinction occurred during unsteady flame conditions. Diagnostics included color video and thin-filament pyrometry. The computations, which simulated flow from a porous sphere into a quiescent environment, included detailed chemistry, transport and radiation, and yielded transient results. Radiative extinction was observed experimentally and simulated numerically. Extinction time, peak temperature, and radiative loss fraction were found to be independent of flow rate except at very low flow rates. Radiative heat loss was dominated by the combustion products downstream of the flame and was found to scale with flame surface area, not volume. For large transient flames the heat release rate also scaled with surface area and thus the radiative loss fraction was largely independent of flow rate. Peak temperatures at extinction onset were about 1100 K, which is significantly lower than for kinetic extinction. One observation of this work is that while radiative heat losses can drive transient extinction, this is not because radiative losses are increasing with time (flame size) but rather because the heat release rate is falling off as the temperature drops.

Santa, K. J.↗

Sensory Bias Predicts Postural Stability, Anxiety, and Cognitive Performance in Healthy Adults Walking in Novel Discordant Conditions

We designed a gait training study that presented combinations of visual flow and support surface manipulations to investigate the response of healthy adults to novel discordant sensorimotor conditions. We aimed to determine whether a relationship existed between subjects visual dependence and their scores on a collective measure of anxiety, cognition, and postural stability in a new discordant environment presented at the conclusion of training (Transfer Test). A treadmill was mounted to a motion base platform positioned 2 m behind a large visual screen. Training consisted of three walking sessions, each within a week of the previous visit, that presented four 5-minute exposures to various combinations of support surface and visual scene manipulations, all lateral sinusoids. The conditions were scene translation only, support surface translation only, simultaneous scene and support surface translations in-phase, and simultaneous scene and support surface translations 180 out-of-phase. During the Transfer Test, the trained participants received a 2-minute novel exposure. A visual sinusoidal roll perturbation, with twice the original flow rate, was superimposed on a sinusoidal support surface roll perturbation that was 90 out of phase with the scene. A high correlation existed between normalized torso translation, measured in the scene-only condition at the first visit, and a combined measure of normalized heart rate, stride frequency, and reaction time at the transfer test. Results suggest that visually dependent participants experience decreased postural stability, increased anxiety, and increased reaction times compared to their less visually dependent counterparts when negotiating novel discordant conditions.

Brady, Rachel A.↗

Supersonic coaxial jet noise predictions

Predictions are made for the noise radiation from supersonic, coaxial jets. These predictions are based on the assumption that the noise radiation in the downstream direction of supersonic jets is dominated by sound generated by instability waves with supersonic phase velocities relative to ambient. Since the analysis requires a known mean flow and the coaxial jet mean flow is not described easily in terms of analytical functions, a numerical prediction is made for its development. The compressible, Reynolds averaged, boundary layer equations are solved with a modified mixing length turbulence model. The model has been calibrated to account for compressibility and temperature effects on the rate of mixing. Both normal and inverted velocity profile jets are considered. Predictions are made for the differences between the noise radiated by coaxial jets with difference operating conditions and a single reference jet with the same thrust, mass flow, and exit area. The effects of area ratio changes and simulated enhanced mixing on noise radiation are also considered.

Dahl, Milo D.↗

Transient cryogenic liquid discharge in normal and micro-gravity

Transient discharge of liquid cryogens from partially filled tanks under microgravity is considered. The discharge is made to a low-pressure site through a straight tube. The ultimate objective of the study is to predict the transient mass flow rate. In addition, the pressure history in the tank is of interest, since the pressure falls below the triple point toward the end of the dump, causing solidification in the tank and/or the discharge line. As first steps, experiments have been performed in normal gravity and attempts are made to predict the transient rate and pressure history under this condition. Experiments are performed with liquid nitrogen dumped to sites with pressures below the triple point. Homogeneous equilibrium and nonequilibrium two-phase critical flow models are compared to the experimental results. Equilibrium and nonequilibrium tank pressure history models are also compared to experimental data.

Purwin, T. P.↗

Effect of pressure anisotropy and flow velocity on Kelvin-Helmholtz instability of anisotropic magnetized plasma using generalized polytrope laws

The effect of pressure anisotropy and flow velocity on the Kelvin-Helmholtz (KH) instability of two magnetized anisotropic pressure plasmas flowing relative to each other is investigated using generalized polytrope laws. The anisotropic pressure with the generalized polytrope laws is considered with three-dimensional perturbations in the description of plasma using relevant magnetohydrodynamic (MHD) set of equations. The magnetic field is assumed in the x-direction and parallel to the direction of the flow of plasma streams. A complete polytrope model is given for the considered system in terms of pressure components, magnetic field, and density of the fluids to discuss the condition of KH instability, stability, and overstability. The problem is solved using the normal mode analysis and the general dispersion relation is obtained by applying the appropriate boundary conditions. The case of nonvanishing wavenumber transverse to the direction of the stream is obtained, which represents the stationery configuration without excitation of KH instability. The longitudinal mode of propagation is discussed with conditions of KH instability, stability, and overstability for collisionless (anisotropic) double-adiabatic Chew-Goldberger-Low (CGL) and collisional (isotropic) MHD media, depending on various values of polytrope indices. The effects of pressure anisotropy, different flow velocities, and magnetic field are also discussed on the growth rate of KH instability. We observe that the presence of flow velocity and pressure anisotropy of the plasmas has a destabilizing influence on the growth rate of the system. The growth rate is found larger for MHD set of equations in comparison to the CGL set of equations. The presence of magnetic field has a stabilizing role on the growth rate of the considered system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Low-Density Aerodynamics of the Stardust Sample Return Capsule

The aerodynamics of the Stardust Sample Return Capsule are analyzed in the low- density, transitional flow regime using free-molecular, Direct Simulation Monte Carlo, Navier-Stokes, and Newtonian methods to provide inputs for constructing a transitional flow bridging relation. The accuracy of this bridging relation in reconstructing the aero- dynamic coefficients given by the more exact methods is presented for a range of flight conditions and vehicle attitudes. There is good agreement between the various prediction methods, and a simple sine-squared bridging relation is shown to provide a reasonably good description of the axial force, normal force, and pitching moment over a range of Knudsen numbers from 0.001 to 10. The predictions show a static instability of the Star- dust capsule in the free-molecular regime that persists well into the transitional flow. The addition of a thin disk to the base of the capsule is shown to remove this static instability. However, the extremely high entry velocity of 12.6 km/s for the proposed trajectory introduces difficult design issues for incorporating this disk caused by the high aerothermal loads that occur even under relatively rarefied conditions.

Wilmoth, Richard G.↗

TESTING OF THE DUAL ROTARY FILTER SYSTEM

The Savannah River National Laboratory (SRNL) installed and tested two hydraulically connected SpinTek rotary microfilter (RMF) units to determine the behavior of a multiple filter system. Both units were successfully controlled by a control scheme written in DELTA-V architecture by Savannah River Remediation (SRR) Process Control Engineering personnel. The control system was tuned to provide satisfactory response to changing conditions during the operation of the multi-filter system. Stability was maintained through the startup and shutdown of one of the filter units while the second was still in operation. The installation configuration originally proposed by the Small Colum Ion Exchange (SCIX) project of independent filter and motor mountings may be susceptible to vibration. Significant stiffening of the filter and motor mounts was required to minimize the vibration. Alignment of the motor to the filter was a challenge in this test configuration. The deployment configuration must be easy to manipulate and allow for fine adjustment. An analysis of the vibration signature of the test system identified critical speeds. Whether it corresponds to the resonance frequency of a rotor radial vibration mode that was excited by rotor unbalance is uncertain based upon the measurements. A relative motion series should be completed on the filter with the final shaft configuration to determine if the resonances exist in the final filter design. The instrumentation selected for deployment, including the concentrate discharge control valve and flow meters, performed well. Automation of the valve control integrated well with the control scheme and when used in concert with the other control variables, allowed automated control of the dual RMF system. The one area of concern with the instrumentation was the condition resulting when the filtrate flow meter operated with less than three gpm. This low flow was at the lower range of performance for the flow meter. This should not be an issue in deployment where the desired flow rate will be within the normal operating range of the meter. Testing demonstrated that the use of a flexible line for the filtrate discharge is highly desired at the outlet of the rotary union to transition to the system piping. Isolating the vibration from the rotary union will significantly improve the lifetime of the seals. Methods to monitor and isolate individual filters should be considered during deployment. The ability to diagnose issues and isolate individual filters would allow isolation prior to failure. Thus, filters may be cleaned or repaired instead of requiring complete replacement if the condition were to continue unnoticed. Isolating the filtrate line of each filter during startup will minimize the premature buildup of solids on the filter disks. Several tests have shown that the method of filter startup can improve performance lifetime of the filters. The installation must factor in an air inlet for the draining of a filter that does not involve a reverse flow through the filter disks. The reverse flow may cause deformation of the disks or may damage other components of the filters themselves.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Quantifying the uncertainty of kinetic-theory predictions of clustering. Final Report covering 21 September 2011 - 20 September 2014

Previous work has indicated that inelastic grains undergoing homogeneous cooling may be unstable, giving rise to the formation of velocity vortices and particle clusters for sufficiently large systems. Such instabilities are observed in industrial coal and biomass gasifiers and are known to influence gas-solid contact area, mixing dynamics, and heat/mass transfer rates. However, the driving mechanisms that lead to vortices and clusters are not well understood. Discrete-particle simulations provide a well-established method for understanding such mechanisms but are not a feasible technique for predicting the behavior of large-scale systems. Kinetic-theory-based continuum models offer an effective means of describing such flows, and instabilities present a stringent test of such models due to the transient, three-dimensional nature of instabilities and the large range of time and length scales over which these mechanisms occur.This work begins with the study, via a combination of continuum models and discrete- particle simulations, of a relatively simple flow and includes additional complexities in a stepwise manner to assess various driving mechanisms. Comparisons with discrete-particle simulations, which offer detailed, well-established (but computationally limited) descriptions of particle flows, indicate the ability of continuum models to accurately incorporate each mechanism. Specifically, the critical length scale for velocity vortices and/or particle clusters are studied via direct numerical simulation, molecular dynamics simulations, linear stability analyses of the continuum model, and transient simulations of the continuum model in a range of flow complexities, including moderate dissipation and particle concentration, frictional particles collisions, high gradients, and gas-solid flows. Strong agreement between kinetic-theory-based continuum models and discrete-particle simulations is found for a range for conditions. Furthermore, discrete-particle simulations offer insight into the relative importance of various mechanisms for instability in both granular and gas-solid flows. Normal inelasticity and friction are both found to be important in granular flows. Particle collisions, thermal drag, and mean drag are found to be important in gas-solid flows.

42 ENGINEERING↗