Donald D. Gray

A viscoplastic approach to model the flow of granular solids

The flow of granular solids within rigid walls is modeled using continuum mechanics. The problem is represented as a viscoplastic flow in which the discontinuity function is taken as in previous works by Gray and Stiles, while the flow rule is modeled by the von-Mises criterion. The resulting model is incompressible and based on non-associated viscoplasticity. The apparent viscosity results in a non-linear function of the second invariant of the symmetric rate of deformation tensor and of the pressure. Friction, cohesion and fluidity of the granular model are taken into account. The constitutive model has been implemented assuming steady-state, in which the granular material flows under a critical state (incompressible behavior). Discretization of the problem has been carried out by finite elements, with direct iteration techniques to solve the non-linear system of equations. The model has been applied to the massive flow of granular material stored in vertical silos and hoppers with axisymmetric or planar shape. Comparisons with experimental tests performed by other authors are presented, together with parametric investigations to identify the main variables affecting the response.

Probabilistic Design of a Near-Surface CO2 Leak Detection System

A methodology is developed for predicting the performance of near-surface CO(2) leak detection systems at geologic sequestration sites. The methodology integrates site characterization and modeling to predict the statistical properties of natural CO(2) fluxes, the transport of CO(2) from potential subsurface leakage points, and the detection of CO(2) surface fluxes by the monitoring network. The probability of leak detection is computed as the probability that the leakage signal is sufficient to increase the total flux beyond a statistically determined threshold. The methodology is illustrated for a highly idealized site monitored with CO(2) accumulation chamber measurements taken on a uniform grid. The TOUGH2 code is used to predict the spatial profile of surface CO(2) fluxes resulting from different leakage rates and different soil permeabilities. A response surface is fit to the TOUGH2 results to allow interpolation across a continuous range of values of permeability and leakage rate. The spatial distribution of leakage probability is assumed uniform in this application. Nonlinear, nonmonotonic relationships of network performance to soil permeability and network density are evident. In general, dense networks (with ∼10-20 m between monitors) are required to ensure a moderate to high probability of leak detection.

Influence of the Coulomb Force on Spray Cooling

Effects of the Coulomb electrical body force on heat transfer performance of an instrumented spray cooling experiment are reported. Heat transfer performance is documented for a range of spray volume flow rates and heater power levels using the dielectric liquids, FC‐72 and HFE‐7000, sprayed onto a Thick Film Resistor (TFR) heater; along with flow visualization results using a transparent Indium‐Tin Oxide (ITO) heater. Two Coulomb force electrode geometries show modest but consistent improvements in heat transfer (order of 5–15%), but only at heat fluxes where boiling of the liquid film occurs. Flow visualization shows a highly contorted liquid film forming on the heater surface. These flow visualization results are used to aid in the estimation of characteristic time scales governing the effects of surface tension, gravity, heating of the liquid film, and vaporization of the film. For the present dense liquid sprays, it is concluded that none of these time scales are as short as the average time between ...

Thermoconvective Instability of Paramagnetic Fluids in a Uniform Magnetic Field

The effect of a uniform oblique magnetic field on a laterally unbounded insulating paramagnetic fluid layer heated from below is studied using a linear stability analysis of the Navier–Stokes equations supplemented by Maxwell’s equations and the appropriate magnetic body force. Two-dimensional rolls in an arbitrary vertical plane are considered. Longitudinal rolls with axes parallel to the horizontal component of the field are the rolls most unstable to convection. The corresponding critical Rayleigh number and critical wavelength for the onset of such rolls are less than the well-known Rayleigh–Benard values in the absence of magnetic fields. Vertical fields maximize these deviations, which vanish for horizontal fields. Horizontal fields increase the critical Rayleigh number and the critical wavelength for all rolls except longitudinal rolls. These effects should be observable in careful experiments at high fields.

Two-dimensional magnetothermal plumes

Abstract The physics of the Kelvin body force and the “buoyancy” it creates is explained. It is demonstrated that, under the Boussinesq approximation, the Kelvin buoyancy can be cast in terms of a spatially variable gravity force. Using the boundary layer approximation, closed form and numerical similarity solutions for steady, laminar, two-dimensional plumes driven by the interaction of a line heat source and a non-uniform magnetic field are obtained and discussed.

Spray Cooling in Terrestrial and Simulated Reduced Gravity

Initial baseline 1‐g heat transfer results are reported for an instrumented spray cooling experiment, developed to study effects of electric body forces on spray cooling heat transfer in variable gravity conditions. Heat transfer performance in 1‐g for both vertical downward and horizontal spray impingement has been documented for spray volume flow rates of 4.8×10−6 m3/s ⩽ Q ⩽ 9.8×10−6 m3/s, and heater power levels from 10 W to 70 W using a Thick Film Resistor (TFR) heater. As flow rate is increased at fixed heater power the heat transfer effectiveness increases, as indicated by reduced heater surface temperatures. Heat transfer effectiveness for the vertical downward spray and horizontal spray configurations are nearly identical, but the horizontal spray has slightly better heat transfer performance when a confining cap is removed at the highest flow rate of 9.8×10−6 m3/s. A transparent Indium‐Tin‐Oxide (ITO) heater consistently has somewhat better performance than the TFR heater. The heat transfer coeff...

Darcy Flow in a Wavy Channel Filled with a Porous Medium

Flow in channels bounded by wavy or corrugated walls is of interest in both technological and geological contexts. This paper presents an analytical solution for the steady Darcy flow of an incompressible fluid through a homogeneous, isotropic porous medium filling a channel bounded by symmetric wavy walls. This packed channel may represent an idealized packed fracture, a situation which is of interest as a potential pathway for the leakage of carbon dioxide from a geological sequestration site. The channel walls change from parallel planes, to small amplitude sine waves, to large amplitude nonsinusoidal waves as certain parameters are increased. The direction of gravity is arbitrary. A plot of piezometric head against distance in the direction of mean flow changes from a straight line for parallel planes to a series of steeply sloping sections in the reaches of small aperture alternating with nearly constant sections in the large aperture bulges. Expressions are given for the stream function, specific discharge, piezometric head, and pressure.

Effects of Contact Charging on Spray Impingement Heat Transfer Performance and Spray Behavior

The effects of contact charging on the heat transfer performance of a full-cone spray of the dielectric coolant, HFE-7000, has been studied using a Thick Film Resistor (TFR) heater with an active surface area of 1.46 cm 2 at a nozzle-to-heater spacing of 13 mm. Tests have been conducted at coolant flow rates between 1.3 and 6.8 GPH (1.4 x 10 –6 to 7.1 x 10 –6 m 3 /s), for heater power ranging from 0 to 60 Watts, yielding heat fluxes between 0 and 400 kW/m 2 . Voltage levels applied to the brass spray nozzle to charge the spray range from 0 to 30 kV, using both negative and positive polarity. A dramatic change in the visual spray flow pattern is observed as the charging voltage exceeds approximately 15 kV in magnitude. Above this voltage, the spray changes from droplets and collections of clearly observable discrete sheets to what appears to primarily be a finer mist of smaller droplets between the spray nozzle and the heater surface. This is due to exceeding the Rayleigh limit for the maximum charge on the liquid droplets, resulting in electrostatic atomization to a smaller average droplet size. However, no significant change in the measured heat transfer performance is seen between the no voltage and the high voltage cases up to a maximum charging voltage of 30 kV.

Electrical Force Effects on Spray Cooling

Initial results are reported for the effects of electrical body forces on heat transfer performance of an instrumented spray cooling experiment. Heat transfer performance is documented for ranges of electrode voltage, spray volume flow rate, and heater power level using a Thick Film Resistor heater. The heat transfer coefficient increases with increased spray flow rate, and also increases somewhat versus heat flux. Without the electrical body forces, different brass and PVC spray nozzles show significant variation in spray cooling performance (order of ±5-15%) whenever the nozzle is realigned. Changing the nozzle-to-heater spacing results in similar performance variations. Initial Kelvin force electrode designs show no improvement in heat transfer performance using FC-72, while a Coulomb force electrode geometry and a second-generation Kelvin force electrode design both show modest but consistent improvements (order of 10% in heat flux; order of 5% for Nusselt number) using HFE-7000.

Drop Impingement on Wet and Dry Surfaces

2 creates a need for a heat transfer design model which incorporates enough physical detail to yield accurate predictions while being sufficiently simplified to allow its use in routine design computations. The spray cooling group at West Virginia University is pursuing a coordinated program of laboratory experiments and computational simulations to develop a Monte Carlo-based spray cooling model that will satisfy this requirement. This paper reports progress in both the laboratory and computational fluid dynamics (CFD) phases of this study, including comparisons between single droplet impact results at We values of 161 and 633 to validate the CFD simulations and experimental measurements. A key goal of the present work is to determine the thickness of the thin liquid layer remaining in the crater formed when a liquid droplet impacts a surface covered by a preexisting liquid film. The volume of liquid in this thin liquid film in the droplet impact crater is one factor that will influence the onset of critical heat flux (CHF). Based on the present data the preexisting static film thickness is observed to have more of an effect than the initial drop parameters on the minimum liquid volume under the crater, but the crater lifetime depends on the initial drop conditions. The comparisons between experiments and simulations for these two cases show promise, but more refinement in experimental and computational technique are needed to achieve more consistent determinations of the volume of liquid under a crater.