Vita. / Digitized by Kansas Correctional Industries

Call number: LD2668 .T4 1984 V46 / Master of Science

Call number: LD2668 .T4 1985 H62 / Master of Science

The boiling of water droplets on hot metal surfaces is studied experimentally and mathematically in order to establish the conditions necessary for droplets to enter a film boiling mode. The subsurface temperature history within a plate undergoing droplet boiling on the surface is measured. A numerical model of the heat transfer in the plate is then used to deduce from these data the following characteristics of droplet boiling: (1) the effective heat transfer coefficient between water droplet and plate during the initial transient forming the spherical droplet, (2) the apparent time period needed to establish the droplet in the film boiling mode, and (3) the minimum plate surface temperature reached during the initial formation of the boiling droplet. The effective heat transfer coefficient, formation time, and minimum surface temperature are sufficient to develop a calculation method which predicts the minimum initial plate temperature necessary for a water droplet to enter film boiling. This numerical conduction model accounts for the influence of plate material, plate thickness, oxidation of the plate surface, the boundary condition on the plate lower surface, and the size of the droplet. The prediction method is successfully used to estimate the minimum film boiling temperature for brass, graphite, Pyrex, copper, aluminum, stainless steel, and Zircalloy II. The findings of the experiments and numerical studies are applied to the rewetting phase of a loss-of-coolant-accident in a light water reactor. This application, in turn, provides explanations for some of the phenomena observed in studies of the prequench heat transfer within rod bundles including the effect of multiple droplet impacts, and suggests possible reasons for some of the difficulties experienced in attempts to establish the effective rewetting temperature on reactor fuel rod surfaces.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Unsteady two-dimensional laminar flow of an incompressible viscous fluid over a periodically grooved wall is investigated by numerical simulation using two independent finite-difference methods. One is the vorticity-stream function method, and the other involves the vorticity-velocity induction law formulation. The fluid motion is initiated impulsively from rest and is assumed to be spatially periodic in the streamwise direction. The flow field, which includes the time development of the shear layer and the recirculating flow in the zone of separation, is examined in detail during the transient phase to the steady-state condition. The analytical and numerical formulations, which include the implementation of the boundary conditions, are derived in detail. The generation of vorticity at the solid surfaces is modelled differently in the two approaches. This vorticity production plays an important role in determining the surface-pressure distribution and the drag coefficient. Characteristics of the transient solution for a moderate Reynolds number in the laminar range are presented. Included with the graphical results are the temporal development of the constant stream function contours, including the dividing contour between the zone of separation and the main flow, and the constant vorticity contours. These latter contours show the interactions of separated vortices. The flow is found to approach a steady-state condition comprising an undisturbed uniform flow, a nonuniform irrotational flow, a shear layer adjacent to the grooved wall, and a recirculating vortex flow in the groove. Results also include the time development of the surface shear stress, surface pressure, drag coefficient and several typical velocity profiles, which characterize the flow in the recirculating region. Comparisons of the results obtained by the two numerical methods are made during the major development of the flow. The results showing the general features of the flow development including the time development of the shear layer, free shear layer and recirculating vortex flow are in good agreement. However, a significant deviation does exist at early times for the distribution of surface pressure, which accordingly has noticeable effect on the drag coefficient. Nevertheless, the gap between the distributions of surface pressure and drag coefficients dies out gradually as time progresses. The form of the stream function and vorticity contours at the steady state agrees well with those obtained from a recent numerical investigation of the steady flow in grooved channels.

A simulation program to study the three dimensional temperature distributions produced by hyperthermia in anatomically realistic inhomogeneous tissue models has been developed. The anatomical data for the inhomogeneous tissues of the human body are entered on a digitizing tablet from serial CT scans. The program not only predicts temperature distributions in regions dominated by blood perfusion (with large number of small capillaries), but it can also predict the temperatures inside of and at the vicinity of large blood vessels. The program can be used for different power deposition patterns from various heating modalities, but they must be calculated independently. In this study, the author's attention has been focused on ferromagnetic implants. The program has been used to comparatively evaluate two and three dimensional simulations in a series of parametric calculations based on simple tissue models for both uniform power deposition and ferromagnetic implants. The conclusions drawn from these studies are that two dimensional simulations can lead to significant errors in many situations, and therefore three dimensional simulations will be necessary for accurate patient treatment planning. The conclusion from the geometrically simple model is substantiated by the results obtained using the full 3D model for actual patient anatomical simulations. The program has also been used for several parametric studies. The effect of the thermal conductivity used in the models on the temperature field has been studied, and the results show that its value in the range of 0.4 to 0.6 W/m/°C (valid for most soft tissues) has only a slight effect on the resultant temperature fields. The heating ability of the ferromagnetic implants has also been investigated for different blood perfusions. The effects of the Curie point of the ferromagnetic seeds, and seed spacing are also studied. Finally, the impact of large blood vessels on the resultant temperatures are studied, and the results show that the effect is dramatic and therefore it must be included in the simulations in order to predict accurate temperature fields. Finally, the program has been used to analyze a previously performed dog experiment, and a previously performed clinical treatment. A comparison between the predicted temperatures and the measured ones show that good agreement has been achieved for the clinical treatment, but not for the dog experiment. These results are studied in detail, and the conditions under which this program can be used as a hyperthermia patient treatment planning tool is discussed.

Numerical investigations of heat transfer in single and multiple thick-walled pipes and countercurrent pairs are used to deduce relationships between fluid and solid temperatures needed to develop more accurate thermal models of living tissue in the extremities. A structural model of heat transfer in living tissue is developed using currently available anatomical and physiological data for the extremities. In order to improve the heat transfer basis of thermal modeling under in vivo conditions, four heat transfer problems based on structures found in the extremities are solved using in vivo parameters-the thick-walled pipe and countercurrent pair, and the multiple thick-walled pipes and countercurrent pairs-are studied. Low resolution numerical models are devised to approximate the thick-walled pipe and the non-concentric thick-walled countercurrent pair in square geometries. A constant heat transfer coefficient at the fluid-solid interface adequately approximates the fluid and solid temperatures for moderate flow conditions (Peclet number of 10 < °Pe < 1000). In the thick-walled countercurrent pair, countercurrent exchange and fluid-solid thermal interaction are found to act simultaneously, giving rise to imperfect countercurrent exchange. Fluid and solid temperatures in the multiple thick-walled pipes and pairs near the outer boundary resemble those of the single thick-walled pipes and pairs. The countercurrent pairs near the center also exhibit imperfect countercurrent exchange. In cylinders with L* > 1 containing multiple countercurrent pairs, the shapes of the temperature profiles cannot be distinguished from the temperature profile shapes of cylinders containing multiple thick-walled pipes. Fluid and solid temperatures in multiple parallel pipes may be approximated with a field equation which has the same form as the Pennes' bioheat equation. Unlike Pennes' equation, the coefficients for the blood thermal energy term quantify the dependence of the amount of thermal energy transferred between blood and tissue with the geometry of the blood the flow rate through the dimensionless axial length L*, and the dimensionless axial coordinate x* . Comparisons of structural model temperatures with available in vivo temperature studies show that blood and tissue temperatures are consistent with fluid and solid temperatures of either multiple unpaired pipes or multiple countercurrent pairs embedded in a solid cylinder. Further improvements of the basis for in vivo heat transfer modeling are crucially dependent upon more extensive comparison with three-dimensional in vivo studies.

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