We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

A computational fluid dynamics (CFD) model is developed to simulate the flow and delivery of oxygen and other substances in a capillary network. A three-dimensional capillary network has been constructed to replicate the one studied by Secomb et al. (2000), and the computational framework features a non-Newtonian viscosity model of blood and the oxygen transport model including in-stream oxygen-hemoglobin dissociation and wall flux due to tissue absorption, as well as an ability to study delivery of drugs and other materials in the capillary streams. The model is first run to compute the volumetric flow rates from the velocity profiles in the segments and compared with Secomb’s work with good agreement. Effects of abnormal pressure and stenosis conditions, as well as those arising from different capillary configurations, on the flow and oxygen delivery are investigated, along with a brief look at the unsteady effects and drug dispersion in the capillary network. The current approach allows for inclusion of oxygen and other material transports, including drugs, nutrients, or contaminants based on the flow simulations. Also, three-dimensional models of complex circulatory systems ranging in scale from macro- to microvascular vessels, in principle, can be constructed and analyzed in detail using the current method.

Compaction waves traveling through porous cyclotetramethylene-tetranitramine (HMX) are computationally modeled using the Eulerian hydrocode CTH and validated with gas gun experimental data. The method employed use of a newly generated set of P-α parameters for granular HMX in a Mie-Gruneisen equation of state. The P-α model adds a separate parameter to differentiate between the volume changes of a solid material due to compression from the volume change due to compaction, void collapse in a granular material. Computational results are compared via five validation schema for two different initial-porosity experiments. These schema include stress measurements, velocity rise times and arrival times, elastic sound speeds though the material and final compaction densities for a series of two different percent Theoretical Maximum Density (TMD) HMX sets of experimental data. There is a good agreement between the simulations and the experimental gas gun data with the largest source of error being an 11% overestimate of the peak stress which may be due to impedance mismatch on the experimental gauge interface. Determination of these P-α parameters are important as they enable modeling of porosity and are a vital first step in modeling of precursory hotspots, caused by hydrodynamic collapse of void regions or grain interactions, prior to deflagration to detonation transition of granular explosives.

The exploration of environmentally friendly energy resources is one of the major challenges facing society today. The last decade has witnessed rapid developments in renewable energy engineering. Wind and solar power plants with increasing sizes and technological sophistication have been built. Amid this development, meteorological modeling plays an increasingly important role, not only in selecting the sites of wind and solar power plants but also in assessing the environmental impacts of those plants. The permanent land-use changes as a result of the construction of wind farms can potentially alter local climate (Keith et al. [1], Roy and Traiteur [2]). The reduction of wind speed by the presence of wind turbines could affect the preconstruction estimate of wind power potential (e.g., Adams and Keith [3]). Future anthropogenic greenhouse gas emissions are expected to induce changes in the surface wind and cloudiness, which would affect the power production of wind and solar power plants. To quantify these two-way relations between renewable energy production and regional climate change, mesoscale meteorological modeling remains one of the most efficient approaches for research and applications.

In previous work from this laboratory, it has been found that the urban heat island intensity (UHI) can be scaled with the urban length scale and the wind speed, through the time-dependent energy balance. The heating of the urban surfaces during the daytime sets the initial temperature, and this overheating is dissipated during the night-time through mean convection motion over the urban surface. This may appear to be in contrast to the classical work by Oke (1973). However, in this work, we show that if the population density is used in converting the population data into urbanized area, then a good agreement with the current theory is found. An additional parameter is the “urban flow parameter,” which depends on the urban building characteristics and affects the horizontal convection of heat due to wind. This scaling can be used to estimate the UHI intensity in any cities and therefore predict the required energy consumption during summer months. In addition, all urbanized surfaces are expected to exhibit this scaling, so that increase in the surface temperature in large energy-consumption or energy-producing facilities (e.g., solar electric or thermal power plants) can be estimated.