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Microbubbles, currently employed in diagnostic ultrasound as a contrast agent, have a potential new application as vehicles for targeted drug delivery, which could revolutionise medicine by eliminating side-effects. A new device is developed which outperforms all existing devices in terms of minimum microbubble size:channel diameter ratio. A numerical model is established to describe the flow behaviour and it is determined that the flow regime and resulting microbubble size are dependent on the ratio of inner- to outer Weber number.

The probability of a fire occurring in space vehicles and facilities is amplified by the amounts of electrical equipment used. Additionally, the lack of egress for space personnel and irreplaceable resources used aboard space vehicles and facilities require a rapid response of a suppression system and quick extinguishment. Current experimental means that exist to gather data in space vehicles and facilities are limited by both size of the experiment and cost. Thus, more economical solutions must be considered. The aim of this research was to develop a reliable and inexpensive methodology for the prediction of flame extinction and suppression in any three-dimensional environment. This project was split into two parts. Part one included the identification and validation of a computational model for the prediction of gas dispersion. Part two involved the development of an analytical parameter for predicting flame extinction. For model validation, an experimental apparatus was constructed. The experimental apparatus was one-eighth of the volume of electronics racks found aboard typical space facilities. The experimental apparatus allowed for the addition of parallel plates to increase the complexity of the geometry. Data acquisition consisted of gas concentration measurements through planar laser induced fluorescence (PLIF) of nitrogen dioxide and velocity field measurements through particle image velocimetry (PIV). A theoretical framework for a generalized Damköhler number for the prediction of local flame extinction was also developed. Based on complexities in this parameter, the computational code FLUENT was determined to be the ideal means for predicting this quantity. The concentration and velocity field measurements provided validation data for the modelling analysis. Comparison of the modelling analysis with experimental data demonstrated that the FLUENT code adequately predicted the transport of gas to a remote location. The 5 FLUENT code was also used to predict gas transport at microgravity conditions. The model demonstrated that buoyancy decreases the time to achieve higher gas concentrations between the parallel plates. As an example of the use of this methodology for a combustion scenario, the model was used to predict flame extinction in a blow-off case (i.e., rapid increase in strain rate) and localized flame extinction (i.e., flame shrinking) in a low-strain dilution case with carbon dioxide over time. The model predictions demonstrated the potential of this methodology with a Damköhler number for the prediction of extinction in three-dimensional environments.

Abstract: Accurate assessment of urban drainage system is vital for municipalities. Stormwater catch basin (CB) inlets are critical linkages between the two dimensional (2-D) urban street flow and the 1-D underground sewer network flow. So far, extensive studies have been conducted to quantify the performance of various types of CB inlets, focusing mainly on CB inlet capacity and efficiency under clean conditions. However, in reality, CB inlets can be easily clogged by debris, garbage, leaves and others, largely reducing their capacity and efficiency. There has been no numerical study that investigates the clogging effect, despite there are a few limited experimental studies. This thesis was written as paper-based, including two pieces of work. The first piece of work (Chapter 2) is a comprehensive literature review on each of the three major types of CB inlets: grate inlets, curb-opening inlets and combination inlets. The second piece of work is a 3-D numerical modeling study using a commercial computational fluid dynamic (CFD) package, FLUENT, to assess hydraulics of CB grate inlets under different conditions: clean and clogging conditions, large water depth on street, vertical depression of grate inlets compared to street surface, and outflow through grate inlets due to surcharging of underground sewers. The CFD model was first calibrated with the physical experiments of CB grate inlets under both clean and clogging conditions, and the results showed that the model built with the RANS and RNG k- ϵ equations and the VOF approach can simulate grate inlet hydraulics satisfactorily. Based on the calibrated model, the clogging factor for the grate inlets was calculated to be 0 - 0.7, depending on the clogging area, approaching flow and road slopes. Generalized clogging patterns tend to overestimate grate inlet intercepted flow rate, compared to the real clogging patterns. During urban flooding, large water depth on streets generate near-constant clogging factor, independent of approaching flow rate; and a discharge coefficient of 0.6 can be used with the orifice flow equation to predict the inlet intercepted flow rate. If the grate inlet has a vertical depression of 2 cm (i.e., 2 cm lower than road surface), it will increase the inlet intercepted flow rate and efficiency and decrease the clogging factor, compared to the non-depressed case. When underground sewers are surcharging via CBs to road surface, it was found that road slopes (longitudinal and transverse slopes) have no impact on the discharge coefficient, but the approaching flow on road will decrease the discharge coefficient. The suggested value of the discharge coefficient, 0.6, would overestimate the outflow via the grate inlet. Moreover, based on the simulation results, new formulas were proposed in this study for CB grate inlet efficiency, clogging factor, and orifice discharge coefficient. The predicted results of the formulas agreed well with the simulated results. General conclusions and future research directions were provided at the end of the thesis.

Computational fluid mechanics were used to determine the optimal depth of a skirt baffle in a circular-type secondary clarifier. Three sets of simulations were performed. The first, set A, determined the better range of operation conditions; set B investigated the numerical stability of the simulations and served as a base for simulation and set C which analyzed the skirt baffle depth on the effluent suspended solids, recycle solids concentration and biosolids mass in the clarifier. The skirt baffle depth was evaluated for three sets of surface overflow conditions and ranged from 10% to 90% of the clarifier depth. Best clarifier performance occurred when the skirt baffle depth was approximately 70% of the clarifier depth. The analysis used Fluent� log files to create a less time-consuming approach for clarifier analysis.

Natural convection in laterally heated vertical cylindrical enclosures (LHVCE) has been studied in the past; however, few studies have thoroughly investigated the characteristic length scales. The studied parameters of this enclosure included: the heated and cooled length, diameter, aspect ratio, hot cold wall temperature difference, and the fluid properties. The characteristic length and form of two correction functions were derived from a logical set of assumptions based upon the enclosure configuration. Utilizing the derived dimensionless functions and length scale in conjunction with numerical simulation results, a best fit correlation was formed. The correlation, a first of its kind for this geometry, successfully predicted heat transfer and the flow regime changes from laminar to turbulence. The correlation and the underlying foundation from which it was formed showed to be in agreement with other similar studies. This study then proceeded from enclosures to internal reactor configurations containing baffles. The baffles were grouped into three geometries: rings, single hole openings, and a uniquely shaped (flow enhancing) baffle. The dimensions of each baffle were parametrically varied, typically by scaling the openings; and the velocity and temperature contour results of the simulations are presented. It was found that the central hole and shaped baffle exhibited more desirable flow patterns and thermal environments than the ring baffles.The final portion of the study investigated the effect of the porous media within the enclosure. The porous media cannot be studied independently, thus, two baffles from the previous investigation were utilized for the porous media. Three porous media configurations were studied: homogenous block, extruded concentric rings, and disks. Each of the basic configurations were laid out with a set of scaling parameters and were simulated parametrically in conjunction with the two baffles. The resistance of the porous media was shown to be a critical design parameter. The porous disks did not exhibit any substantial benefit over a single homogeneous block but the concentric rings allowed for fluid to pass through the media. It was shown that porous media penetration can be increased by reducing the resistance or by shaping channels into the media.

In recent years the development of rocket engines has been mainly focused on improving the engine cycle and creating new fuels. Rocket nozzle design has not been changed since the late 1960s. Recent needs for reliable and reusable rockets, as well as advancements in additive manufacturing, have brought new interest into the aerospike nozzle concept. This nozzle is a type of altitude adjusting nozzle that is up to 90% more efficient than bell nozzles at low altitudes and spends up to 30% less fuel. Since the nozzle body is submerged in the hot exhaust gasses it is difficult to keep the rocket body at a reasonable temperature. The purpose of this research is to investigate techniques commonly used on bell nozzle geometries and determine their effectiveness on the aerospike nozzle geometry. The techniques investigated are film cooling and transpiration cooling. The aerospike engine used for the analysis was simulated via ANSYS Fluent 2020 R2 and validated from experimental results. The simulation utilized the k-ε turbulence model and the eddy-dissipation combustion model to accurately simulate the combustion of the H2/O2 rocket engine. The film cooling study investigated the effects of inlet geometry and the coolant blowing ratio, while the transpiration study investigated the effects of the coolant inlet pressure. The film cooling inlet angle was varied from 15° to 30°, the inlet size varied from 1mm to 3mm, and the blowing ratio was varied from 0.25 to 2. The transpiration cooling inlet pressure was varied from 10,000 Pa to 100,000 Pa. The film cooling study results showed that the inclination of the coolant inlet, coolant inlet size, and blowing ratio all positively affected the film cooling efficiency, but subsequently reduced the overall nozzle efficiency. The larger angle and blowing ratios were strong enough to distort the exhaust flow and completely divert it from the nozzle wall. The transpiration cooling results showed that the low and high inlet pressures had a low efficiency while the inlet pressure near 50,000 Pa had the highest efficiency. Since the transpiration cooling allows for the flow to exit at all points along the nozzle wall and create a film it showed the lowest wall temperatures with the least reduction in efficiency. Overall, the results showed that film cooling and transpiration cooling, while commonly used on bell nozzles, are able to similarly cool the aerospike nozzle.

As global warming becomes a cause of serious concern worldwide, stricter and stricter emission regulations are being imposed on gas turbine engines. Flameless combustion is a novel combustion technique that offers a significant reduction in NOx and CO emissions. The presence of a flameless flame is indicated by uniform temperature distribution in the combustor, which leads to simultaneous reductions in NOx and CO emissions. Nick Overman conducted tests on a swirl stabilized flameless burner in the GDPL lab at the University of Cincinnati. A well-distributed flameless flame was observed for an overall equivalence ratio of 0.36. But as the equivalence ratio was increased, the flame in the combustor switched to a diffusion flame, and non-uniform temperature distribution was observed, which led to an increase in NOx emissions. The work in this thesis aims to improve the operational range of flameless combustion by modifying the swirl stabilized setup used by Nick Overman to include a cavity upstream of the swirler. ANSYS Fluent is used to numerically investigate the performance of such a cavity-swirler setup. The k-epsilon realizable and Laminar Finite Rate model is used to model turbulence and combustion, respectively. Multiple cavity designs which lead to a final successful design are described in detail in this thesis. The final successful design consists of 8 fuel injectors surrounded by 24 air injectors introducing fresh reactants to the cavity. Modifications were then made to this design to include 8 injectors in the second stage of the swirler. The cavity injectors aligned at an angle to the cavity also possess a swirl angle to impart a tangential component of velocity to the reactants being introduced in the cavity. The performance of two designs, the Swirler Reduced air and Swirler Fuel cases, are investigated at different equivalence ratios. Parameters such as temperature, OH distribution, NOx, CO, CO2, H2O, and combustion efficiency are used to compare the two designs. The swirler-cavity setups were able to extend the range of flameless combustion to an equivalence ratio of 0.55. At 0.65, transitional behavior was observed, and the flame switched back to a diffusion flame at an equivalence ratio of 0.70. For the swirler-cavity F=0.55 cases (Swirler Reduced air and Swirler Fuel), uniform temperature distribution was observed in the combustor with a simultaneous reduction in NOx and CO emissions. The Swirler Fuel case exhibited an overall improved performance in the flameless regime as compared to the Swirler Reduced Air cases. The Swirler Fuel case shows a lower centerline peak temperature, lower centerline OH peak, reduced NOx, and higher combustion efficiency than the Swirler Reduced Air case. Even though both the Swirler Reduced air and Swirler Fuel cases were able to extend the range of flameless combustion to 0.55, the Swirler Fuel case clearly is the better candidate to operate in the flameless regime.

Nuclear Thermal Propulsion (NTP) will be an enabling technology for future deep space exploration missions. The high energy density of a nuclear reactor allows for the hydrogen propellant to reach exit velocities much greater than what is possible with traditional chemical propulsion, but that high energy density also presents some issues that must be designed around. Most notably, the decay heat produced after shutdown needs to be removed by venting hydrogen through the core. This thesis attempts to determine the minimum amount of hydrogen propellant that must be spent in this way by computationally modelling a portion of the core to predict exactly what mass flowrate is necessary for keeping important components below critical temperatures. In addition, an investigation into the effectiveness of Auxiliary Heat Removal Systems (AHRSs) at reducing cool-down hydrogen usage is reported on. It is found that significant opportunities for cool-down hydrogen reduction exist, both through computational optimization of the flowrate profile and through the inclusion of an AHRS to remove heat by less wasteful means.

Studying human brains and spinal cords, or many other complex body parts for that matter, come with great challenges and risks when hoping to get accurate data, hopefully in real-time, in vivo, as opposed to in vitro or from a corpse. Of even more interest, are diseased members, since they possess unique traits that shine significant light into the medical community to help understand and treat countless disorders and pathologies. Having this information greatly improves the quality of life for the afflicted, but not to mention, the whole human race. Of particular interest here, is the cerebrospinal fluid flow, a water-like substance, that encases the spinal cord and pulses in and out of the brain’s intracranial spaces. Upon entrance into the brain cavity from the spinal cord, it first encounters the cerebellum, the posterior lobes at the bottom of the brain. A lot of studies have been done, in vivo and in vitro, to understand its impact on the movement of the cerebellum, specifically in relation to a Chiari malformation which is characterized by herniation of the cerebellar tonsils. Pahlavian et al shows data from magnetic resonance imaging where the cerebellum of healthy patients moves approximately 100 microns. The work herein uses numerical software tools to hypothesize the cause of the cerebellum’s movement. Sources vary widely about the actual material properties of the spinal cord and brain. But with the later data found from Klatt et al, estimates show material elasticity on the order of 1 kPa. With said material elasticity, numerical studies here concluded the cerebellum moves approximately 200 microns. Considering the broad variance among scientists about human tissue elasticities, fluid substance properties, geometry, etc., this was very close to Pahlavian’s conclusion, thus fruitful. Two main contributors can lead to cerebellum movement, pressure and wall shear. It was determined from these numerical studies that pressure is the main contributor, while wall shear plays a very secondary role in the cerebellum movement.

The primary objective of this research is to study the performance of a heat exchanger system with a bypass valve. At first a simplified double-pipe heat exchanger is considered and a computational fluid dynamic (CFD) code FluentTM 15.0 is used to analyze the heat exchanger performance. The geometry of the double-pipe heat exchanger is scaled down based on the prototypic heat exchanger design provided by Tenneco. Numerical computations are carried out for different inlet conditions provided by Tenneco. The results, including the pressure drop, thermal entrance length, and heat transfer coefficient are benchmarked against correlations available in the literature. Furthermore the performance of the heat exchanger system with a bypass valve is studied. In order to simplify the model, the heat exchanger is modeled using the porous media approach. In addition, the mal-distribution of the flow within the heat exchanger is investigated. The simulations are performed for a range of mass flow rate with both closed and open bypass valve positions. The results are compared with the values obtained using the in-house heat exchanger light tool. The ultimate goal of the thesis is to improve the performance of the overall heat exchanger system to minimize pressure losses and maximize the heat transfer efficiency. This goal could be achieved by optimizing the geometries of the bypass leg to improve the flow uniformity into the heat exchanger and optimizing the flow response dynamics for the open/closed valve positions.

Bluff body vehicle drag is dominated by pressure drag on the rear end of the body due to the effect of momentum causing the flow to detach from the body contour. This flow separation results in a pressure difference between the front and back end, making up the pressure drag. A friction force is also generated at the contact of air and solid body that contributes to the total drag, however in the case of bluff body flow this value is far outweighed by the pressure drag. The rear separation region is also dominated by complex time dependent vortices, of which this pressure drag is also dependent, thereby making the overall drag at least partially dependent on the strength and frequency of this shedding phenomena as well. In this study, both a two-dimensional and three-dimensional Ahmed model are used, however only the zero-slant angle case is studied to coincide with the majority of transportation trucks and buses that are on the road today.Numerical simulation experiments on vortex shedding and corresponding drag coefficients from a two-dimensional bluff body are performed over a range of Reynolds numbers from one to four million. The simulations are performed using ANSYS Fluent, specifically the turbulence model of k-epsilon RNG (Re-normalization Group). In order to enhance the accuracy of the shedding wake vortices, an enhanced non-equilibrium wall treatment is utilized. Active control is implemented on the body via velocity boundary conditions in the form of blowing and suction jets. These controls range in velocity from half to double the free-stream inlet velocity. An overall drag coefficient reduction in excess of 75\% is observed for maximum power input to the actuators. In addition, a trend of increasing Strouhal number for each successive increase in actuator power (and corresponding reduction in drag) is noted. Important physical mechanisms involving near-body wake flow are analyzed to determine optimal wake flow pattern and corresponding control schemes.Discoveries are then used to study similar controls on the three-dimensional bluff body based on those of the two-dimensional model. For the 3-D simulations the Large Eddy Simulation model is used for the calculation of flow field variables within Fluent, however an introductory RANS analysis is performed as well. Control schemes involving suction jets are investigated. Aspects of the flow pattern such as shedding and streamlines are studied in depth in an effort to determine the most efficient application of the suction controls. These schemes seek to reduce the aerodynamic drag without constraints on the basic design of the model itself. An average of 10\% drag reduction is recorded.

The primary objective of this study is to obtain the rate of Carbon deposition by chemical vapor deposition (CVD) process for material samples hanged in CVD reactor. The samples include net of bundles of fibers, semi-opened channel cut through rectangular sample and sample with circular holes. Momentum, continuity and transport equations for chemical species within gas phase and surface reactions have been solved numerically. For numerical solution by finite-volume method ANSYS FLUENT software and for geometric modeling and finite-volume meshing ANSYS Workbench software have been used. For numerical study two approaches have been taken. The first approach is a single-step solution where the flow field in reactor including flow field near and inside the sample have been resolved simultaneously. The second approach is a two-step solution, where the model has been divided into reactor-scale model and sample-scale model, where for each one a separate numerical mesh has been generated and a corresponding set of numerical parameters has been optimized separately for each model. The former process is a straightforward one that is applicable to a sample of any linear scale; however, the approach is computationally expensive relative to the latter one. The latter approach assumes that the scale of sample is small compared to the reactor scale and the two CFD models are solved sequentially. Results obtained by one-step and two- steps approaches are similar in terms of obtained CVD rates with some discrepancy caused by use of different numerical meshes and because in the latter model there is nofeedback on the reactor flow field by the sample. For fibrous samples, CVD rates are obtained at the range of volume fractions. Obtained CVD rates are near-uniform along the fiber circumference and mostly sensitive to temperature field in reactor. For rectangular model with channel samples, the CVD rate is obtained at vertical orientations of the sample along the reactor axis for suspended sample with circular holes, CVD rates are obtained along the length of the hole. Near both entrances of each circular hole, vortices are generated which block the flow entering inside the hole. Because of diminished flowrate and corresponding advection inside the hole, C deposition is lowest at the center of the hole. In terms of effect on deposition, C2H2 and CH4 plays more significant role than other species. As C2H2 directly participates in surface reactions, higher concentration of C2H2 assures higher growth rate of C. CH4 in one of the primary species with largest initial mass fraction, participates in gas-phase reactions and is responsible for production of other intermediate gas species. Higher depletion of CH4 assures higher production of C2H2 and corresponding higher C deposition. This observation is similar for all the substrates.

This thesis presents a novel core multiphysics coupling method and its application to geometries and thermal hydraulic operating conditions typical of U.S. PWRs. Monte Carlo based radiation transport from the MCNP6 package and finite volume thermal hydraulic (TH) packages provided by ANSYS-FLUENT are combined to produce results with intra-pin resolved spatial resolution equivalent to state-of-the-art reactor physics and multi-physics suites. The Virtual Environment for Reactor Applications (VERA) whose development is spearheaded at Oak Ridge National Laboratory is one such example package. Benchmark and validation tasks performed as an integral part of the development of VERA demand intra-pin resolved pin power distributions as well as finely spatially resolved fuel burnups. This level of detail is not provided by most other lattice physics code packages. Intra-pin powers, for example, are reconstructed from lower fidelity model results using empirically derived shape functions. In addition, data sets from operating PWRs are sparse, resolved only at the inter-pin level, and prone to experimental error. With the proposed MCNP-FLUENT model, it is possible to provide within-pin/channel resolved power, temperature and moderator density field data. MCNP-FLUENT iteratively solves for multiple physical fields: flow velocity, temperature, energy deposition rate, and neutron flux. It does so by repeatedly passing information between dedicated solvers which independently handle the neutron transport and thermal hydraulic physics. The codes are linked by a Picard iteration scheme. Doppler and moderator density feedbacks are explicitly treated. In contrast to preceding generations of MCNP-FLUENT coupling implementations, the coupling framework described employs the latest unstructured mesh capabilities of the MCNP v6.1 code to achieve a new level of geometric and mesh tally generation flexibility. The coupling is demonstrated by a suite of test cases spanning planar 2D geometry, singe pin and a 3x3 assembly at hot full power with TH feedbacks. Good power and eigenvalue agreement (+/-4%, 340[pcm] respectively) is achieved for the hot full power single pin case. Qualitative agreement in the predicted power profiles and fuel temperature distributions is seen in the 3x3 pin geometry.

The design and analysis of turbo-machinery are complex tasks due to the complexity of the geometry and the flow physics. The application of various computational tools to evaluate the performance of a specified geometry is commonly designated as a direct method. In a direct design approach designer's experience and talent are vital factors to reduce the number of trials while in an inverse design approach designer needs to prescribe the performance function as an input. It is often desirable to apply the inverse design approach, in which performance parameters are prescribed in the form of performance functions, the so called loading distribution, to obtain the corresponding geometry of pump as the result. At the start of an inverse design technique, the desired performance functions are prescribed as input quantities, and an initial, guessed shape of the impeller blade geometry is changed iteratively to arrive at the converged shape.The present study has developed a procedure for inverse design of a two-dimensional centrifugal pump impeller blades using the computational fluid dynamics (CFD) software, OpenFOAM (an open-source CFD software) and FLUENT. In the current work, the Gambit software is used for geometry development, domain decomposition, and grid generation. In this thesis, OpenFOAM is used to solve for the in-viscid flow in the passage formed by two adjacent blades of a pump. FLUENT is used to solve full Navier-Stokes equations to calculate blockage factor distribution along the meridional plane. The evolving blade shapes are computed by using flow tangency condition; the viscous effects in the mean flow are introduced indirectly by using the blockage effects from viscous simulations. Polynomial curve fitting techniques is used to generate the loading distribution of circulation. During each step of the current inverse design technique, the flow field analysis and blade shape calculations are performed alternately, while satisfying the boundary condition based on the loading distribution function at each step, until a fully converged solution is achieved. All the steps involved in the technique are automated by linking the individual codes in a Linux shell script. The blade shape and flow domain changes with each iteration, which means the grid also changes with each iteration. It is very time consuming to generate grid manually at each iteration, so a journal file is written in Gambit, which is executed automatically with each iteration and generates a mesh. The generated mesh is imported in OpenFOAM, where the flow analysis is done using the laplacianFOAM module of OpenFOAM, using boundary conditions based on the prescribed performance function. The tentative performance function is obtained using the circulation distribution, which is accommodated by modifying the laplacianFOAM solver. The viscous flow is solved between passages of two consecutive blades of the impeller to find the blockage factor distribution, using FLUENT. The current inverse design process is verified for a logarithmic spiral blade. Thus, the current work gives a good approach of incorporating blockage via viscous effects in the mean flow for an impeller geometry using OpenFOAM and FLUENT.

Contemporary tools for experimentation and computational modeling of unsteady reacting flow open new opportunities for engineering insight into dynamic phenomena. In the work presented here, a novel use of proper orthogonal decomposition (POD) is described to validate the structure of dominant heat release and flow features in the flame, shear-layer, and wake of a bluff-body-stabilized flame. A general validation process is presented which involves a comparison of experimental and computational results, beginning with single-point mean statistics and then extending to the dynamic modes of the data using POD to reduce the ensemble of instantaneous flow field snapshots. The results demonstrate the use of this technique by applying it to large eddy simulations of the bluff body stabilized premixed combustion experiment. Large-eddy simulations (LES) using both Fluent and OpenFOAM were conducted to reproduce experiments conducted in an experimental test rig which was built as part of this work to study the behavior of turbulent premixed flames stabilized by bluff bodies. Planar Particle-Image Velocimetry (PIV) and filtered chemiluminescence were used to characterize the flow in the experiment's reacting and non-reacting regimes respectively. While PIV measurements could be compared directly to the velocity field in the simulations, the chemiluminescence measurements represented a line-of sight signal which was not directly comparable to the LES model. To account for this, the heat release in the LES models was integrated along simulated lines of sight by solving an additional discretized differential equation with heat release as the source term. The results show generally good agreement between the dominant modes of the experiment with those of the numerical simulations. By isolating the dynamic modes from each other via the proper orthogonal decomposition, it was shown the models were able to accurately reproduce the size, shape, amplitude, and timescale of various dynamic modes which exist the experiment, some of which are dwarfed by the other flow features and are not apparent using time-averaging approaches or by inspection of instantaneous snapshots of the flow.

The present numerical study in FLUENT analyzes the fluid flow field within a solar powered reactor designed for syngas production. The thermochemical reactor is based on continuous cycling of cerium oxide (ceria) in a non-stoichiometric reduction/oxidation cycle. The reactor uses a hollow cylinder of porous ceria which rotates through a high-temperature zone, by exposure to concentrated sunlight and partially reduced in an inert atmosphere due to flow of the sweep gas (N2), and then through a lower temperature zone where the reduced ceria is re-oxidized with a flow of CO2 and/or H2O, to produce CO and/or H2. In terms of fluid flow modeling, the issue of crossover of species (leakage) within the reactor is critical for proper functioning of the reactor. The first part of the work relates to the geometry and placement of the inlet/outlet gas channels for the reactor optimized to minimize crossover of the species. This is done by conducting a parametric study of geometric variables associated with the inlet/outlet geometry. A simplified 2D fluid flow reactor model which incorporates multi-species flow is used for this study. Further, 2D and 3D reactor models which capture the internal structure more accurately are used to refine the inlet/outlet design. The optimized reactor model is found to have an O2 crossover of 2%-6% and oxidizer crossover of 8%-21% at different flow rates of the sweep gas and the oxidizer studied.In the second part of the work, the reactor model is simulated under varying test conditions. Different working conditions include morphologies of the reactive material, rotational speed of the ceria ring and the recuperator, flow rates of sweep gas and the oxidizer, types of oxidizer (CO2, H2O). The 3D reactor model is also tested using one, two and three discrete inlet/outlet ports and compared with slot configuration

Bluff bodies form ubiquitous components of many engineered structures. They are often exposed to turbulent flows, and the subsequent shedding of vortices gives rise to aerodynamic forces with large fluctuating components. As a result, significant oscillations are induced, which can lead to resonances and structural fatigue. To obviate these deleterious effects passive flow control mechanisms can be incorporated into the design of bluff bodies. However, to ensure the designs are effective and safe it is essential to understand and anticipate the behavior of the turbulent flows around bluff bodies.

This work is done as a small facet of a much larger study on efficient control of indoor air environments. Halton passive chilled beams are used to cool rooms and the focus of this work is to model the beams. This work also reviews the mesh making process in Gmsh. ANSYS Fluent was used throughout the entire research and this thesis describes the software and a careful description of the case study.

In the realm of CFD, simulations can be very time consuming and the ability to obtain a solution quickly to a given problem is extremely valuable. Specialized solvers that use structured grids often have a lot of time spent in preprocessing to generate a grid if the geometry is relatively complex. Alternative software exists that makes use of unstructured grids, but often are general solvers and may not be able to obtain as accurate of a solution. In an attempt to see how well an unstructured alternative solver would compare to a structured specialized solver, a verified solution taken from the structured MSU-TURBO turbomachinery code was duplicated in ANSYS Fluent with an unstructured grid. Despite some limitations with ANSYS Fluent's turbomachinery setup, a close, but not exact, solution was obtained and compared to the MSU-TURBO solution.

This work seeks to illustrate the potential benefits afforded by implementing aspects of fluid dynamics, especially the latest computational fluid dynamics (CFD) modeling approach, through numerical experimentation and the traditional discipline of physical experimentation to improve the calibration of the severe reactor accident analysis code, MELCOR, in one of several spent fuel pool (SFP) complete loss-of-coolant accident (LOCA) scenarios. While the scope of experimental work performed by Sandia National Laboratories (SNL) extends well beyond that which is reasonably addressed by our allotted resources and computational time in accordance with initial project allocations to complete the report, these simulated case trials produced a significant array of supplementary high-fidelity solutions and hydraulic flow-field data in support of SNL research objectives. Results contained herein show FLUENT CFD model representations of a 9x9 BWR fuel assembly in conditions corresponding to a complete loss-of-coolant accident scenario. In addition to the CFD model developments, a MATLAB based control-volume model was constructed to independently assess the 9x9 BWR fuel assembly under similar accident scenarios. The data produced from this work show that FLUENT CFD models are capable of resolving complex flow fields within a BWR fuel assembly in the realm of buoyancy-induced mass flow rates and that characteristic hydraulic parameters from such CFD simulations (or physical experiments) are reasonably employed in corresponding constitutive correlations for developing simplified numerical models of comparable solution accuracy.

A pneumatic particulate collection system harnesses the energy associated with the release of a compressed gas to transport particulate to a collection chamber. In an effort to improve the efficiency of a previously designed collection system, high speed imaging in conjunction with computational fluid dynamics (CFD) was utilized to highlight design deficiencies. Areas of recirculation within the collection device as well as impingement of the sampling surface were observed through the testing and CFD analysis. The basis of the improved collection system was conceived through research of pneumatic transport and the deficiencies found through testing and simulation. An improved rectangular-duct-styled system was designed in three main stages. A variety of filters used to contain the desired particulate were characterized through testing for use in simulations as well as fluids calculations. The improved system was then analyzed utilizing compressible and incompressible flow calculations and design iterations were conducted with CFD to determine the final parameters. The final design was simulated with a multiphase flow model to examine the particulate entrainment performance. The improved collection system efficiently expanded and developed the gas flow prior to the collection area to employ the particulate entrainment process. The final design was constructed with an additive manufacturing process and experimentally tested to validate the simulations and flow calculations. The testing proved that the final design operated purely on particulate entrainment and collected only the top layer of particles as simulated. The improved collection system eliminated all areas of flow recirculation and impingement of the particle bed to provide a more efficient sampling device.

Fluency has been a neglected part of the reading curriculum in the past. However, more recently, fluency has been shown to play a part in comprehension. It is believed that the more fluent a reader is, the more he/she will comprehend. This is believed to be due to the increased attention that can be allotted to comprehending as opposed to sounding out the words. The emphasis on fluency has led to a variety of instructional methods being researched and implemented. This study explored the method of repeated reading in the form of the Read Naturally program and its effect on fluency. Along with repeated reading, the effects of proper modeling and feedback on prosody were also studied. The Read Naturally program was tested with two treatment groups and a control group of first grade students. The program’s prescribed procedures were followed for the two treatment groups. However, for one treatment group, prosody was introduced to the class and feedback was given. Results suggested Read Naturally had an effect on fluency and prosody. Although there was not a significant change among scores between the three classes, there was visible improvement shown by many of the students.

The purpose of this thesis is to investigate the steady-state behavior of a pressurized wave bearing. The pressurized air wave journal bearing was analyzed using a commercial CFD software, Fluent. The 3D Navier Stokes compressible equations were integrated to simulate the flow. Turbulence effects were included in the computation. The real geometry of the wave bearing and of the supply holes were simulated by using a structured grid. The steps performed during the numerical simulation and the set-up of Fluent used in the thesis are presented in detail. The model was validated by comparing the flow rate obtained at different supply pressures for zero eccentricity and zero rotational speed to values of the flow rate obtained experimentally.The steady-state behavior of the bearing for eccentric positions is simulated using the “moving reference frame” method. The load capacity for different eccentricities and velocities at a constant supply pressure of 50 PSI were calculated.The advantage of the method used in this thesis is that it does not require a correction of the flow rate with an empirical discharge coefficient. Moreover, the method allows the calculation of the discharge coefficient based on the results of the simulation. In the present thesis, the discharge coefficients are calculated for different eccentricities and rotational speeds and supply pressures

As the populations and the economies of the world grow, the demand for electricity rises and necessitates an increase in the supply of electricity as the primary fuels that are used to generate electricity are finite and exhausting. Moreover, mounting concerns about carbon emissions and the current direction of environmental legislation are pushing for lower emissions and higher efficiencies of energy producing facilities. One approach to abate such dilemmas is to increase the efficiency of the modern steam cycle, which is used to generate most of the world's electricity. Improving the components of the steam cycle, or the boiler component in particular, can affect the overall efficiency of the steam cycle significantly. An integral constituent of the boiler is the boiler tube. There are several types of boiler tubes, and the helically-finned tube is one type that has proven to increase the efficiency of the boiler. However, insight to the internal flow within the helically-finned tube is still developing and incomplete. The objective of this study was to computationally model the internal flow and measure the friction factor of a helically-finned tube for which experimental data was already published. Using three different modeling techniques, the flow was solved numerically with Fluent, a computational fluid dynamics software package. With respect to the experimental data, the Fluent solutions reflected percent errors ranging between 14% and 27%. Although the results are acceptable, suggestions for future work are included.

The TurboPiston Pump was invented to make use of merits such as, high flow rates often seen in centrifugal pumps and high pressures associated with positive displacement pumps. The objective of this study is to manufacture a plastic model 12” TurboPiston Pump to demonstrate the working principle and a metal prototype for performance testing. In addition, this research includes the study of the discharge valve to estimate the valve closing time and fluid mass being recycled back into the cylinder through hand calculations. Furthermore, a transient simulation was performed in CFD using Fluent to provide a better estimate of what will happen in the actual pump while running. Additionally, an experimental rig was designed to investigate the performance of the first generation valve on the TurboPiston Pump known as the flapper valve. Means to improve the hydrodynamic performance of both valves have been identified for future study.

The lens molding process is a relatively new technique used to manufacture lenses, in particular, high precision aspheric lenses. In order to achieve the desired size and shape of the lens, the cooling process after pressing must be controlled precisely because of the time and temperature dependent viscoelastic behavior of glass near and below the molding temperature. This thesis gives a detailed description of a three-dimensional computational model for analyzing the cooling phase of the lens molding process. Conduction, convection and radiation are considered in the model by coupling a computational fluid dynamics analysis of the flow of nitrogen through the system and a transient heat transfer finite element analysis of the assembly. An iterative process between the fluid flow analysis and the thermal analysis is used to account for their interdependency. The model is calibrated and validated by direct comparison with the experimental results. Various parametric studies are performed to study the effect of several unknown parameters and design parameters on the accuracy of the numerical model. It was found that the model depends significantly on the unknown properties such as thermal contact conductance values and radiation properties, which should therefore be the subject of further investigation. This three-dimensional model can be used to extract the boundary conditions for a parallel study involving a more detailed two-dimensional axisymmetric sub-model of the lens and molds. The validity of two-dimensional axisymmetry assumption is verified from the results obtained through the three-dimensional model's simulations.

A conventional accumulator stores energy for hydraulic systems by compressing an enclosed mass of air, but this air takes up too much volume at low pressure to be practical in applications such as a hydraulic hybrid passenger vehicle. An open accumulator compresses air from the atmosphere to store energy, eliminating the need to store low-pressure air but creating large temperature swings if the heat transfer during compression and expansion is poor. This thesis investigates thermodynamic and heat transfer aspects of an open accumulator to assist in its design. A thermodynamic model was created to determine the efficiency and required heat transfer for open accumulator designs with a volume 1/5th that of a comparable conventional, or “closed,” accumulator. A heat transfer parameter, Z = hA/V, describes how easy it would be to implement the required heat transfer, with low required values of Z being desirable. A design with only one stage of compression and high wall temperature had a lower required value for Z than the high pressure stages in multi-stage designs. For an open accumulator that provides 20 kW of power in expansion and 840 kJ of energy storage at a pressure of 350 times atmospheric conditions, the volume target was 15.7 ℓ and the required Z values for compression and expansion were approximately 6.2×104 W/m3K. A computational fluid dynamics model using the program FLUENT was created to investigate whether the required Z could be achieved in a more practical, three-stage open accumulator design. The expansion case of the lowest-pressure stage was simulated, with a required Z value from the thermodynamic model of 3.83×104 W/m3K. The iv computational domain was a symmetrical, 3-D, diaphragm-bounded chamber of approximately 0.5 ℓ displaced volume, and a realizable k-ε model was used to model the effects of turbulence. The flow pattern generated during the air intake period dominated the flow during expansion, and peak local heat fluxes occurred where the intake flow patterns drew cold fluid next to the walls. The peak heat transfer for the simulation was 386 W. The mean Z value calculated was 9.79×103 W/m3K, around 1/4th of the required value.

The present study is a three-dimensional numerical investigation of the effectiveness of film cooling for a turbine blade leading-edge model with both a single and a three-hole cooling configuration. The model used has the same dimensions as those in the experimental investigation of Ou and Rivir (2006). It consists of a half cylinder with a flat after-body, and well represents the leading edge of a turbine blade. The single coolant hole is situated approximately at the spanwise center of the cylindrical model, and makes an angle of 21.5 degrees to the leading edge and 20 degrees to the spanwise direction. For the three-hole configuration, the center hole is positioned the same as the single hole in the single-hole configuration, with the adjacent holes located at a spanwise distance of 37.4 mm on either side of the center hole. Multi-block grids were generated using GridGen, and the flows were simulated using the flow solver Fluent. A highly clustered structured C-grid was developed around the leading edge of the model. The outer unstructured-grid domain represents the wind tunnel as used in the experimental study of Ou and Rivir (2006), and the leading-edge model is located at the center of the domain. Simulations were carried out for blowing ratios, M, ranging from 0.75 to 2.0. Turbulence was represented using the k-? shear-stress transport (SST) model, and the flow was assumed to have a free-stream turbulence intensity of 0.75%.Two types of boundary conditions were used to represent the blade wall: an adiabatic surface, and a conductive surface. The adiabatic-wall results over-predicted the film-cooling effectiveness in the far downstream region for low blowing ratios. Also, in the vicinity of the cooling hole, an increase in blowing ratio resulted in higher film cooling effectiveness than observed in the experiments. It should be noted that the steady RANS-based turbulence model used under-predicts the interaction between the coolant and mainstream flow near the cooling-pipe exit. The conductive-wall results show a much closer agreement with experimental data for film effectiveness as compared to the adiabatic-wall predictions. Simulations were also performed with higher values of turbulence intensity at the cooling-hole inlet, and these predicted the coolant-mainstream interaction and the film-cooling effectiveness more accurately.Finally, a novel concept of pulsing the coolant flow was implemented so as to achieve film-cooling effectiveness equivalent to that with constant cooling, but with reduced overall coolant air, thereby enhancing turbine efficiency. Pulsed cooling with pulsing frequency PF = 5 and 10Hz, and duty cycle DC = 50%, shows the greatest cooling effects. The three-hole cooling results indicate that the 49 mm spanwise distance used for computing the spanwise-averaged values for film-cooling effectiveness accounts for all of the film-coolant spreading provided by the single hole. Also, the neighboring cooling holes contribute little film cooling to the 49 mm spanwise distance. The most significant new finding in this work is that the inclusion of wall conductance is the main factor responsible for reproducing the experimental data.

In 1997, the United States Environmental Protection Agency strengthened its health protection standard for particulate matter by introducing the PM 2.5 standard. This standard has since lead to control of fine particulates with even more importance and better technology. Although, fabric filters and electrostatic precipitators on coal-burning facilities are successful in attaining standards, these technologies are relatively expensive, need a huge amount of space, and require longer downtimes for installation. The primary focus of this research is to use Fluent and Gambit software to simulate an electro cyclone technology with a novel slipstream idea aimed at reducing fine particulate matter efficiently, combined with a conventional PM control technology. The computer model, once validated appropriately using a bench-scale cyclone, would serve as a design tool to further improve the novel electro cyclone concept.

Biotechnology-derived protein drugs, usually referred as biologics, represent a significant part of the whole pharmaceutical market. Typically, biologics are produced in genetically modified animal cells, which are regarded by many engineers and practitioners in the pharmaceutical industry as extremely sensitive to hydrodynamic forces. Since during research or normal operation in the biopharmaceutical industry cells are exposed to a range of hydrodynamic forces, this "shear sensitivity" idea often leads to very mild, sub-optimal designing and operating conditions.To determine the actual levels of hydrodynamic stress capable of affecting the metabolism or viability of a cell line in bioprocessing or analytical devices, a microfluidic contracting-expanding device was developed in our group that exposes cells to controlled, well-defined hydrodynamic forces by means of keeping the flow in laminar conditions. Using this device, changes in cell behavior can be determined as a function of the local energy dissipation rate (EDR). EDR is a scalar value that is intrinsic to any moving fluid, is independent of the flow regime (turbulent/laminar) and accounts for both shear and extensional components of three-dimensional flow. It represents the rate at which work is done on a fluid element or a cell. If laminar flow is maintained, EDR can be reliably calculated using well-established equations for simple geometries or computational fluid dynamics (CFD) software for more complex problems.The microfluidic device, consisting of a micro-channel bored in a stainless steel sheet in sandwich between two polycarbonate plates, was used in different setups to imitate the environment cells will experience in both bioprocessing and analytical equipment. As a model for analytical devices, it was selected a Fluorescent Activated Cell Sorter (FACS), where cells are forced through a nozzle and interrogated by a laser beam. This instrument was mimicked by passing the cells once through the microfluidic device; on the other hand, as a model for bioprocessing equipment, the hydrodynamic forces a cell experiences in a bioreactor were simulated by recirculating the cells through the microchannel, in an intent to reproduce the cyclic passage of the cells through the high EDR zone around the impeller to zones of relative low EDR intensity away from it. Several cell lines of industrial, research and medical interest were tested using the just described methodology. For single passage, in every case the elicited response was mainly an increase of cell necrosis with larger EDR while only a small fraction of cells became apoptotic when exposed to the highest levels of EDR tested. Changes in medium composition or genetic modifications did not affect this behavior.The response to repeated, chronic exposure to moderate levels of EDR was case-specific. A research CHO cell line (CHO6E6) stopped growing at the lowest levels of chronic EDR evaluated (2.9x105 W·m-3) and started dying when the EDR intensity was increased. On the other hand, the growth curve of a GS-CHO industrial cell line that produces a fully human antibody was not affected at all even at the highest EDR tested (6.5x106 W·m-3), although the glycosylation pattern of the antibody suffered modifications. Single passage results for both cell lines showed a very similar behavior to previously tested cell lines. Interestingly, results showed that at least some medical cell lines (THP1) might have an EDR threshold lower than industrial or research cell lines (i.e., more "shear" sensitive), which suggest a possible selection of the tougher individuals after continuous manipulation. This conclusion seems to be also supported by the chronic exposure of the industrial GS-CHO cell line at the highest chronic EDR tested. If this is the case, the microfluidic device could even become a tool for selection of stronger clones in the pharmaceutical industry.

The first objective of this thesis is the analysis of the dominant mechanisms involved in the removal of particles using a Sieving Electrostatic Precipitator (SEP). The second objective concerns the study of the SEP pressure drop. The main collecting mechanisms in the SEP prevent the release of the bulk of the toxic substances passing through it into the ambient air. The influence of those mechanisms is studied separately in this thesis. This is accomplished by calculating the effect of Coulomb forces on the particle coagulation rate, collision frequency for particles in the laminar shear flow, collision frequency for particles in Brownian motion, and the collection of particles on a cylindrical obstacle. An important feature of this dust removal device, pressure drop, is simulated and analyzed for different screen configurations and different inlet velocities. This is carried out by utilizing the software FLUENT. In addition, user defined function (UDF) is used to enhance the FLUENT simulation resulting in more realistic results.

This project entails a study of a wind energy recovery system that utilizes a unique three-dimensional spiral structure to amplify wind speed and direct it toward pluralities of turbines. The system is comprised of an outer spiral shell, internal support structure, turbines, and mechanisms for positioning the turbines to face the prevailing wind. Computational Fluid Dynamics (CFD) analyses were conducted to determine the wind speed amplification factors as a result of a simulated wind flow around the spiral structure. To ensure accuracy of the results, state of the art CFD techniques were applied using Gambit 2.2.30 and Fluent 6.2.16. Specifically, wind speed amplification factors were determined for 25ft and 30ft radius spiral shells. The velocity profiles of the wind flow around both spiral structures were obtained under a postulated 10mph wind speed. This resulted in a turbulent flow with a Reynolds number of 5,596,819. All analyses were run using “standard k-ε” turbulence model with the “near wall treatment” option “standard wall function”. A “y+” value of 50 was held constant in all vi simulations. The affect of the grid size on the accuracy of the results was examined. Convergence criterion was satisfied in each case. The 25ft radius spiral structure yielded an average velocity amplification factor of 1.524; while the 30ft radius resulted in an average amplification factor of 1.539. This particular information can help the designer of the system to select an appropriate overall shell size based not only on the mechanical efficiency, but also considering the cost and economical factors.

Film cooling computations and experiments were performed to study heat transfer and adiabatic effectiveness for several geometries. Various assumptions commonly made in film cooling experiments were computationally simulated to test the validity of using these assumptions to predict the heat flux into conducting walls. The validity of these assumptions was examined via computational simulations of film cooling on adiabatic, heated, and conducting flat plates using the commercial code FLUENT. The assumptions were found to be reasonable overall, but certain regions in the domain suffered from poor predictions. Film cooling adiabatic effectiveness and heat transfer coefficients for axial holes embedded in a 1 [hole diameter] transverse trench on the suction side of a simulated turbine vane were experimentally investigated as well to determine the net heat flux reduction. Heat transfer coefficients were determined with and without upstream heating both with and without a tripped boundary layer approach flow. The net heat flux reduction for the trench was found to be much higher than for the baseline row of holes. Two transverse trench geometries and a baseline row of holes geometry were also simulated using FLUENT and the results were compared to experiments by Waye and Bogard (2006). Trends between simulated trench configurations and baseline cylindrical holes without a trench were found to be largely in agreement with experimental trends, suggesting that FLUENT can be used as a tool for studying new trench configurations.

The Micro Loop Heat Pipe (LHP) is a two-phase device that may be used to cool electronics, solar collectors and other devices in space applications. A LHP is a two-phase device with extremely high effective thermal conductivity that utilizes the thermodynamic pressure difference developed between the evaporator and condenser and capillary forces developed inside its wicked evaporator to circulate a working fluid through a closed loop. While previous experiments have shown reduction in chip temperature, maximum heat flux was less than theoretically predicted. This paper addresses the main problem with the past designs of top caps which has been the conduction of heat from the heat source to the primary wick. The new top cap design provides conduction pathways which enables the uniform distribution of heat to the wick. The provision of conduction pathways in the top cap increases the pressure losses and decreases the temperature drop. The feasible competitive designs of the top cap with conduction pathways from the fabrication point of view are discussed in detail. Calculation of pressure drop and temperature drop is essential for the determination of optimal solutions of the top cap. Approximate pressure drop was calculated for the top cap designs using simple 2-D microchannel principles. Finite element modeling was performed to determine the temperature drop in the conduction pathways. The conditions used for arriving at the optimal design solutions are discussed and presented. A trapezoidal slot top cap design and trapezoidal mesas top cap were chosen for fabrication as they were relatively easy to fabricate with available MEMS fabrication technologies. Geometry of the external vapor reservoir for the trapezoidal slot top cap was designed for optimum pressure drop. Variation of pressure drop in the top cap with respect to the porosity in the coherent porous silicon wick was discussed and analyzed in detail. The exact pressure drop calculations were performed numerically using a finite volume commercial flow solver FLUENT 6.1 with appropriate boundary conditions. The temperature drop calculations were performed using finite element modeling in ANSYS 6.1. It was assumed that all the pores have uniform mass flow rate and were at saturation conditions during the phase change. Obtained values of pressure drop and temperature drop for chosen geometries of trapezoidal slot and trapezoidal mesa top cap were found to be within the optimal limits and are ready to be fabricated.

Understanding the flow in stirred vessels can be useful for a wide number of industrial applications, like in mining, chemical and pharmaceutical processes. Remodeling and redesigning these processes may have a significant impact on the overall design characteristics, affecting directly product quality and maintenance costs. In most cases the flow around the rotating impeller blades interacting with stationary baffles can cause rapid changes of the flow characteristics, which lead to high levels of turbulence and higher shear rates. The flow is anisotropic and inhomogeneous over the entire volume. A better understanding and a detailed documentation of the turbulent flow field is needed in order to design stirred tanks that can meet the required operation conditions. This thesis describes efforts for accurate estimation of the velocity distribution and the turbulent characteristics (vorticity, turbulent kinetic energy, dissipation rate) in a cylindrical vessel agitated by a Rushton turbine (a disk with six flat blades) and in a tank typical of flotation cells. Results from simulations using FLUENT (a commercial CFD package) are compared with Time Resolved Digital Particle Image Velocimetry (DPIV) for baseline configurations in order to validate and verify the fidelity of the computations. Different turbulence models are used in this study in order to determine the most appropriate for the prediction of turbulent properties. Subsequently a parametric analysis of the flow characteristics as a function of the clearance height of the impeller from the vessel floor is performed for the Rushton tank as well as the flotation cell. Results are presented for both configurations along planes normal or parallel to the impeller axis, displaying velocity vector fields and contour plots of vorticity turbulent dissipation and others. Special attention is focused in the neighborhood of the impeller region and the radial jet generated there. This flow in this neighborhood involves even larger gradients and dissipation levels in tanks equipped with stators. The present results present useful information for the design of the stirring tanks and flotation cells, and provide some guidance on the use of the present tool in generating numerical solutions for such complex flow fields.

This study investigated 9 variables to determine their relationship to the frequency of use of "Play Therapy" or non- verbal counseling techniques by elementary school counselors as well as their relationship to counselor perceived self-efficacy when counseling children who speak a language in which the counselor is not fluent. The notion of placing an emphasis on "Play Therapy" or non- verbal counseling techniques with such a population has emerged as a possible therapeutic intervention when working with individuals from a cultural background which is different from that of the counselor. Researchers in counseling have noted the importance of providing adequate services to diverse populations including those who do not speak a language in which the counselor is fluent. This study was based on the concept that an elementary school counselor's effectiveness when counseling children who speak a language in which the counselor is not fluent is related to the counselor's level of training in non-verbal counseling techniques, level of training in multicultural counseling, years of counseling experience, professional membership affiliations, fluency in other languages, gender, and grade level in which the counselor works. Statistically significant relationships were found with several of the variables including level of training in play therapy, membership in the Association for Play Therapy and American School Counselor Association, and grade level in which the counselor works. Elementary school counselors and counselor educators can utilize the findings of this study to develop and implement programs that teach play therapy and other non-verbal counseling techniques to elementary school counselors. These experiences may help provide better services to diverse populations including those who speak a language in which the counselor is not fluent.