Heating and cooling needs have been highly demanded as the extreme weathers become increasingly frequent and global warming becomes well-founded. Because ground temperature keeps relatively constant at 20-30 feet below the surface, using the earth as a thermal mass for temperature conditioning and thermal management creates an energy-efficient and environmentally beneficial approach to surface heating and cooling, which has been used in self-heated pavement, greenhouse, and building integrated photovoltaic thermal systems. Inspired by the human body wherein a blood circulation system keeps skin nearly at a constant temperature under environmental changes, a thermal fluid circulation system is introduced to the geothermal well system. Through bi-directional heat exchange between surface space with the ground, heat harvested at high temperatures can be stored underground for utilization at low temperatures, so that the surface temperature variations can be significantly reduced for daily and yearly cycles minimizing the heating/cooling needs. Understanding the heat transfer under the ground and thermal stress of the heat exchange systems induced by the temperature changes is critical for system design, performance prediction and optimization, and system control and operation. This dissertation studies heat transfer and thermomechanical problems for different geothermal systems. The temperature field of the earth can be calculated given the heat source and ambient temperature. Due to nonuniform thermal expansion caused by temperature differences or material mismatches, thermal stress will be induced. Its interaction with surface mechanical load and displacement constraint will be investigated for the design and failure analysis of the fluid circulation and heat exchange system. In the theoretical study, the earth is approximated as a semi-infinite domain. Green's function technique has been used in the analysis of heat conduction, elastic, and thermoelastic problems respectively. The semi-infinite domain with a surface boundary condition can be considered a special case of two semi-infinite domains with a perfectly bonded interface, which forms an infinite bi-material domain. For a Dirichlet boundary value problem with a constant temperature or displacement, the top semi-infinite domain can be considered with infinitely large conductivity or stiffness, respectively; for a Neumann boundary value problem with zero flux or traction, the top semi-infinite domain can be considered with a zero conductivity or stiffness, respectively. The general Green's functions of an infinite bi-material domain can recover the classic solutions for Boussinesq's problem, Mindlin's problem, Kelvin's problem, etc. The three-dimensional (3D) problems can be used to recover the corresponding two-dimensional (2D) problems by an integral of Green's function in one dimension through the Hadamard regularization. Firstly, the heat transfer problem in an infinite bi-material is introduced and the Green's function is formulated for the temperature change caused by a point heat source in the material. It is used to simulate heat transfer for a spherical heat exchanger embedded underground in geothermal energy applications. The temperature field of the spherical inhomogeneity embedded in an infinite bi-material subjected to a uniform far-field steady-state or sinusoidal heat flux is determined by solving the boundary value problem. Eshelby’s equivalent inclusion method (EIM) is used to consider the mismatch of the thermal conductivities of the particle from the matrix, which is simulated by a prescribed temperature gradient. When the material of one semi-infinite domain exhibits zero or infinite thermal conductivity, the above solution can be used for a semi-infinite domain containing a heat source with heat insulation or constant temperature on the boundary, respectively. The analytical solution has been verified with the finite element method. The formulation is used to simulate a spherical heat source embedded in a semi-infinite domain. The method can be immediately applied to the design of geothermal energy systems for heat storage and harvesting. When the heat exchanger is a long horizontal pipe, a similar procedure can be conducted for the corresponding 2D problem. If the temperature exhibits a cyclic change, such as daily variation, the formulation is extended to the harmonic transient heat conduction problems. Secondly, a similar formulation has been introduced for the elastic problem of an infinite bi-material. The Green's function is formulated for the displacement caused by a point force in the bi-material. It is used to simulate the stress transfer for a spherical heat exchanger embedded underground in geothermal energy applications. The formulation of the heat transfer problem is extended to the corresponding elastic problem. How a surface mechanical load is transferred to the underground heat exchanger is illustrated. The interactions between a heat exchanger and the surface load are investigated. Finally, the thermoelastic problem of an infinite bi-material is introduced and the Green's function is formulated for the displacement field caused by a point heat source in the material. It can be straightforwardly used to derive the thermoelastic stress caused by a distributed heat source by volume integrals. However, when the thermal conductivity and elasticity of the heat exchanger are different from the earth in actual geothermal energy applications, the Green's function cannot be directly used. By analogy to Eshelby's equivalent inclusion method, a dual equivalent inclusion method (DEIM) is introduced to address the dual material mismatch in thermal and elastic properties. The fundamental solutions of a bi-material for thermal, elastic, and thermoelastic problems are versatile and recover the ones of the single material domain for both 2D and 3D problems. The equivalent inclusion method is successfully extended to the thermoelastic problems to simulate the material mismatch. The formulation can be used in designing a geothermal heat exchanger for heat storage and supply for energy-efficient buildings as well as other geothermal applications. Future work will extend the fundamental solutions to time-dependent thermomechanical load and investigate the daily and seasonal heat exchange with the ground using different configurations of the pipelines. The algorithms will be integrated into the inclusion-based boundary element method (iBEM) for geothermal system design and analysis.

No description available.

A mathematical model is presented for the problem of determining the two-dimensional temperature distribution resulting from the discharge of a heated effluent into a shallow, quiescent receptacle. The physical model of the problem is the two-dimensional jet augmented by an imposed condition of viscous drag due to bottom friction effects. By virtue of the assumption that the physical properties of the effluent are independent of temperature over the operational temperature range of the plume, the analysis separates the total problem into a flow problem and a temperature problem. Solution of the temperature distribution is accomplished both analytically and numerically. Analytically, the temperature distribution is found through sequential integral solution of the equations defining the mathematical model, under the physical assumptions of a Gaussian flow distribution and the following relationship between the velocity and temperature distributions: [formula] where the subscript (max) denotes conditions along the jet centerline. Numerically, the equations defining the mathematical model are solved by a finite differencing technique implemented with the aid of an I.B.M. 360 digital computer. Comparison of the predictions of the model with the classical two-dimensional momentum jet indicate that the model is a reasonable approximation of the real physical problem. In addition, there is seen to be a critical dependence of the flow in the plume on the depth of the receptacle.

As crucial infrastructure systems remain in service up to and beyond their originally intended service lives, there has been a significant increase in efforts to quantify their current strength and remaining life span. Suspension bridges are of particular concern due to their impact on commerce, low repairability, and high replacement cost. As such, quantification of the performance of suspension bridge main cables at elevated temperatures is necessary for a holistic safety assessment. These cables are the primary load-carrying members, and are susceptible to vehicular fires near the midspan and anchorage where the cable sweeps low to the deck. Due to the dearth of empirical data regarding the thermomechanical properties of main cables, previous studies were forced to rely on thermomechanical properties derived for different materials, geometries, and scales. It is the chief goal of this dissertation to fill this void in high-temperature empirical data. First, the high temperature stress-strain behavior of the constituent ASTM A586 wires is examined. The coldworked wires are highly susceptible to recovery at elevated temperatures, which has the power to undo the primary strengthening mechanism. Large decreases in elastic modulus, yield stress, and ultimate stress are observed at elevated temperature. The high temperature stress-strain curves are fully parameterized, and a procedure for generating stress-strain curves at temperatures between 22°C and 724°C is provided. Next, the post-fire performance of the wire is quantified. Wires are heated to various temperatures up to 842°C and then allowed to cool before being tensile tested. The results of this testing show that a significant portion of the high-temperature strength-loss observed in the in-situ tests persists after cool-down. Exposure to elevated temperatures reduces strength and fundamentally alters the shape of the stress-strain curves of the heated and cooled wires. These post-fire stress-strain curves are fully parameterized, and a procedure for recreating them between 22°C and 842°C is provided. Next, the metallurgical underpinnings for the observed changes in mechanical behavior at and after high-temperature exposure are explored using neutron diffraction techniques. Two engineering beamline experiments generate peak-narrowing data that sheds light on the evolving dislocation density and crystallite size in this wire during and after heating. Results confirm that the decreases in wire strength that persist after cool-down are the product of recovery; temperatures in excess of 700°C decrease wire dislocation density to values similar to those of undeformed structural materials. Finally, the thermal conductivity of the main cable is addressed. The air voids and point contacts between the wires create a complex (and anisotropic) heat transfer situation within main cables. A one-to-one, 8200 kg mock-up of a panel of a suspension bridge main cable is constructed, instrumented, and heated. The data provided by the internal temperature sensors is used to tune the thermal conductivity of a representative finite element via a gradient descent algorithm. The resulting temperature-dependent thermal conductivity function allows the complex internal heat transfer of the main cable to be accurately approximated by a monolithic section with conductivity tuned to the measured behavior of a physical main cable. Cumulatively, the results of these studies shows that the thermomechanical properties of main cables are not well represented by previous approximations that are based on other materials and applications. The properties derived herein will facilitate more accurate performance estimates of suspension bridges subjected to fires than previously possible.

The mechanism by which convective heat transfer is augmented by freestream turbulence in the stagnation region was studied experimentally. Previous work has suggested that the primary mechanism for the observed augmentation is the amplification of vorticity into strong vortices which dominate the flow field near the surface. Therefore, two separate experimental investigations were performed to further study this phenomenon. In the first, the spatiotemporal convection from a heated surface was measured during the normal collision of a vortex ring. The convection was observed to increase dramatically in areas where vortices forced outer fluid through the natural convection boundary layer to the surface. Regions where fluid was swept along the surface experienced much smaller increases in convection. These observations led to the development of a mechanistic model which predicted the heat transfer based on the amount of time that fluid remained within the thermal boundary layer prior to reaching the surface. In subsequent testing, the model was able to accurately predict the time-resolved convection based solely on the transient properties of the vortex present. In the second investigation, the model was applied to the vortices which form in a stagnating turbulent flow. Three turbulence conditions were tested which changed the properties of the vortices produced. Again, the model was successful in predicting the time-resolved convection over much of the experimental measurement time. The work of designing and calibrating the heat flux sensor used is also reported. A new sensor was developed specifically for the convection research performed herein as no existing sensor possessed the required spatiotemporal resolution and underwater capabilities. Utilizing spot-welded foils of thermoelectric alloys resulted in a very robust and sensitive sensing array which was thoroughly analyzed and calibrated. In the final section, the hybrid heat flux (HHF) method is presented which significantly increases the performance of existing heat flux sensors. It is shown (both numerically and experimentally) that by combining the spatial and temporal temperature measurements from a standard sensor, the time response increases by up to a factor of 28. Also, this method causes the sensor to be insensitive to the material to which it is mounted. / Ph. D.

One way to increase cycle efficiency of a gas turbine engine is to operate at higher turbine inlet temperature (TIT). In most engines, the turbine inlet temperatures have increased to be well above the metallurgical limit of engine components. Film cooling of gas turbine components (blades and vanes) is a widely used technique that allows higher turbine inlet temperatures by maintaining material temperatures within acceptable limits. In this cooling method, air is extracted from the compressor and forced through internal cooling passages within turbine blades and vanes before being ejected through discrete cooling holes on the surfaces of these airfoils. The air leaving these cooling holes forms a film of cool air on the component surface which protects the part from hot gas exiting the combustor. Design optimization of the airfoil film cooling system on an engine scale is a key as increasing the amount of coolant supplied yields a cooler airfoil that will last longer, but decreases engine core flow—diminishing overall cycle efficiency. Interestingly, when contemplating the physics of film cooling, optimization is also a key to developing an effective design. The film cooling process is shown to be a complex function of at least two important mechanisms: Increasing the amount of coolant injected reduces the driving temperature (adiabatic wall temperature) of convective heat transfer—reducing heat load to the airfoil, but coolant injection also disturbs boundary layer and augments convective heat transfer coefficient due to local increase in freestream turbulence. Accurate numerical modeling of airfoil film cooling performance is a challenge as it is complicated by several factors such as film cooling hole shape, coolant-to-freestream blowing ratio, coolant-to-freestream momentum ratio, surface curvature, approaching boundary layer state, Reynolds number, Mach number, combustor-generated high freestream turbulence, turbulence length scale, and secondary flows just to name a few. Until computational methods are able to accurately simulate these factors affecting film cooling performance, experimental studies are required to assist engineers in designing effective film cooling schemes. The unique contribution of this research work is to experimentally and numerically investigate the effects of coolant injection rate or blowing ratio and exit Reynolds number/Mach number on the film cooling performance of a showerhead film cooled first stage turbine vane at high freestream turbulence (Tu = 16%) and engine representative exit flow conditions. The vane was arranged in a two-dimensional, linear cascade in a heated, transonic, blow-down wind tunnel. The same facility was also used to conduct experimental and numerical study of the effects of freestream turbulence, and Reynolds number on smooth (without film cooling holes) turbine blade and vane heat transfer at engine representative exit flow conditions. The showerhead film cooled vane was instrumented with single-sided platinum thin film gauges to experimentally determine the Nusselt number and film cooling effectiveness distributions over the surface from a single transient-temperature run. Showerhead film cooling was found to augment Nusselt number and reduce adiabatic wall temperature downstream of injection. The adiabatic effectiveness trend on the suction surface was also found to be influenced by a favorable pressure gradient due to Mach number and boundary layer transition region at all blowing ratio and exit Mach number conditions. The experimental study was also complimented with a 3-D CFD effort to calculate and explain adiabatic film cooling effectiveness and Nusselt number distributions downstream of the showerhead film cooling rows of a turbine vane at high freestream turbulence (Tu = 16%) and engine design exit flow condition (Mex = 0.76). The research work presents a new three-simulations technique to calculate vane surface recovery temperature, adiabatic wall temperature, and surface Nusselt number to completely characterize film cooling performance in a high speed flow. The RANS based v2-f turbulence model was used in all numerical calculations. CFD calculations performed with experiment-matched boundary conditions showed an overall good trend agreement with experimental adiabatic film cooling effectiveness and Nusselt number distributions downstream of the showerhead film cooling rows of the vane. / Ph. D.

The mechanism of heat transfer augmentation due to freestream turbulence in classic Hiemenz stagnation flow was studied experimentally for the first time using time-resolved digital particle image velocimetry (TRDPIV) and a new thin film heat flux sensor called the Heat Flux Array (HFA). Unique measurements of simultaneous, time-resolved velocity and surface heat flux data were obtained along the stagnation line on a simple, rectangular flat plate model mounted in a water tunnel facility. Identification and tracking of coherent structures in the stagnation region lends support to the theory that coherent structures experience stretching and amplification of vorticity by the mean flow strain rate upon approaching the stagnation surface. The resulting flow field in the near-wall region is comprised primarily of high strength, counter-rotating vortex pairs with decreased integral length scale relative to the imposed freestream turbulence. It is hypothesized that the primary mechanism of heat transfer augmentation is the movement of cooler freestream fluid into the heated near-wall region by these coherent structures. Furthermore, the level of heat transfer augmentation is dictated by the integral length scale, circulation strength, and core-to-surface distance of the coherent structures. To test this hypothesis, these properties were incorporated into a mechanistic model for predicting the transient, turbulent heat transfer coefficient. The model was successful in predicting the shape and magnitude of the measured heat transfer coefficient over much of the experimental measurement time. In a separate yet related set of studies, heat flux sensors and calibration methods were examined. The High Temperature Heat Flux Sensor (HTHFS) was designed and developed to become one of the most durable heat flux sensors ever devised for long duration use in high temperature, extreme environments. Extensive calibrations in both conduction and convection were performed to validate the performance of the sensor near room temperature. The measured sensitivities in conduction and convection were both very close to the predicted sensitivity using a thermal resistance model of the HTHFS. The sensor performance was unaffected by repeated thermal cycling using kiln and torch firing. Finally, the performance of Schmidt-Boelter heat flux sensors were examined in both shear and stagnation flow using two custom designed convection calibration facilities. Calibration results were evaluated using an analytical sensitivity model based on an overall sensor thermal resistance from the sensor to the heat sink or mounting surface. In the case of convection the model included a term for surface temperature differences along the boundary layer. In stagnation flow the apparent sensitivity of the Schmidt-Boelter sensors decreased non-linearly with increasing heat transfer coefficient. Estimations of the sensor's internal thermal resistance were obtained by fitting the model to the stagnation calibration data. This resistance was then used with the model to evaluate the effects of non-uniform surface temperature on the shear flow sensitivity. A more pronounced non-linear sensitivity dependence on heat transfer coefficient was observed. In both cases the main result is that convection sensitivity varies a great deal from standard radiation calibrations. / Ph. D.

Investigation of momentum and heat transfer between the fluid and solid phase is critical to the study of fluid-particle systems. Dense suspensions are characterized by the solid fraction (ratio of solid volume to total volume), the particle Reynolds number, and the shape of the particle. The behavior of non-spherical particles deviates considerably from spherical particle shapes which have been studied extensively in the literature. Momentum transfer, to first-order, is driven by drag forces experienced by the particles in suspension, followed by lift and lateral forces, and also through the transmission of fluid torque to the particles. The subject of this thesis is a family of prolate ellipsoidal particle geometries of aspect ratios (AR) 2.5, 5.0 and 10.0 at nominal solid fractions (φ) between 0.1 and 0.3, and suspensions of cylinders of AR=0.25. The nominal particle Reynolds number (Re) is varied between 10 to 200, representative of fluidized beds. Fluid forces and heat transfer coefficients are obtained numerically by Particle Resolved Simulations (PRS) using the Immersed Boundary Method (IBM). The method enables the calculation of the interstitial flow and pressure field surrounding each particle in suspension leading to the direct integration of fluid forces acting on each particle in the suspension. A substantial outcome of the research is the development of a new drag force correlation for random suspensions of prolate ellipsoids over the full range of geometries and conditioned studied. In many practical applications, especially as the deviation from the spherical shape increases, particles are not oriented randomly to the flow direction, resulting in suspensions which have a mean preferential orientation. It is shown that the mean suspension drag varies linearly with the orientation parameter, which varies from -2.0 for particles oriented parallel to the flow direction to 1.0 for particles normal to the flow direction. This result is significant as it allows easy calculation of drag force for suspension with any preferential orientation. The heat transfer coefficient or Nusselt number is investigated for prolate ellipsoid suspensions. Significantly, two methods of calculating the heat transfer coefficient in the literature are reconciled and it is established that one asymptotes to the other. It is also established that unlike the drag force, at low Reynolds number the suspension mean heat transfer coefficient is very sensitive to the spatial distribution of particles or local-to-particle solid fractions. For the same mean solid fraction, suspensions dominated by particle clusters or high local solid fractions can exhibit Nusselt numbers which are lower than the minimum Nusselt number imposed by pure conduction on a single particle in isolation. This results from the dominant effect of thermal wakes at low Reynolds numbers. As the Reynolds number increases, the effect of particle clusters on heat transfer becomes less consequential. For the 0.25 aspect ratio cylinder, it was found that while existing correlations under predicted the drag forces, a sinusoidal function F_(d,θ)=F_(d,θ=0°)+(F_(d,θ=90°)-F_(d,θ=0°) )sin⁡(θ) captured the variation of normalized drag with respect to inclination angle over the range 10≤Re≤300 and 0≤φ≤0.3. Further the mean ensemble drag followed F_d=F_(d,θ=0°)+1/2(F_(d,θ=90°)-F_(d,θ=0°)). It was shown that lift forces were between 20% to 80% of drag forces and could not be neglected in models of fluid-particle interaction forces. Comparing the pitching fluid torque to collision torque during an elastic collision showed that as the particle equivalent diameter, density, and collision velocities decreased, fluid torque could be of the same order of magnitude as collisional torque and it too could not be neglected from models of particle transport in suspensions. / Doctor of Philosophy / Momentum and heat exchange between the fluids (air, water…) and suspensions of solid particles plays a critical role in power generation, chemical processing plants, pharmaceuticals, in the environment, and many other applications. One of the key components in momentum exchange are the forces felt by the particles in the suspension due to the flow of the fluid around them and the amount of heat the fluid can transfer to or from the particles. The fluid forces and heat transfer depend on many factors, chief among them being the properties of the fluid (density, viscosity, thermal properties) and the properties of the particles in the suspension (size, shape, density, thermal properties, concentration). This introduces a wide range of parameters that have the potential to affect the way the fluid and particles behave and move. Experimental measurements are very difficult and expensive to conduct in these systems and computational modeling can play a key role in characterization. For accuracy, computational models have to have the correct physical laws encoded in the software. The objective of this thesis is to use very high-fidelity computer models to characterize the forces and heat transfer under different conditions to develop general formulas or correlations which can then be used in less expensive computer models. Three basic particle shapes are considered in this study, a sphere, a disk like cylindrical particles, and particles of ellipsoidal shapes. More specifically, Particle Resolved Simulations of flow through suspensions of ellipsoids with aspect ratio of 2.5, 5, 10 and cylinders with aspect ratio of 0.25 are performed. The Reynolds number range covered is [10, 200] for ellipsoids and [10, 300] for cylinders with solid fraction range of [0.1, 0.3]. New fluid drag force correlations are proposed for the ellipsoid and cylinder suspensions, respectively, and heat transfer behavior is also investigated.

The simultaneous estimation of multi-mode heat transfer properties, conductive and radiative, is investigated for materials that include significant heat transfer by radiation. The focus is on insulative type materials with a relatively large optical thickness. Two basic models were developed for the combined conduction and radiation heat transfer: a diffusion solution and a more exact absorbing and isotropically scattering solution. Both solutions were written for one-dimensional heat transfer in gray, isotropically scattering materials. Different experimental setups were compared through a sensitivity analysis of the parameters to determine the best experiment for estimating the properties. An experiment was performed to collect real data to verify estimation procedures. The material used for the experiment was Styrofoam and the experiment consisted of a heat flux supplied by a thin film heater on one boundary and a constant temperature on the other boundary. The thermal capacitance of the heater proved to have an effect on the temperature measurements at the heated surface and had to be incorporated into the model. The estimation procedure involved the use of two methods, the modified Box Kanemasu algorithm and a genetic algorithm. Difficulties were encountered in simultaneously estimating all the properties due to correlation between the thermal conductivity and the radiation parameters, as well as some correlation between the heat capacity of the Styrofoam and the heat capacity of the heater. However, the genetic algorithm did provide fairly narrow and well-defined property ranges and confirmed that radiation transfer was significant in the Styrofoam. / Ph. D.

The relationship of time-resolved surface heat flux to the turbulent free-stream flow over a turbine blade is investigated. Measurements are made in a transonic linear cascade with a modem high pressure turbine blade profile. Time-resolved direct heat transfer measurements are made with Heat Flux Microsensor (HFM) inserts along the pressure side, and with one HFM directly deposited on the suction surface near the leading edge. Simultaneous velocity measurements are made above the heat flux sensors using miniature hot-wire probes. Grids are used to produce two turbulence fields of constant inlet turbulence intensity, Tu = 5%, but significantly different integral length scales (Ax). Results are compared with a low free-stream turbulence baseline condition. Special emphasis is given to frequency domain analysis of the data via coherence function magnitude and phase, energy spectra, and time auto- arid cross-correlations. Results are presented for both mean and fluctuating velocity and heat flux. Mean heat transfer is highest for the smaller length scale grid, but inlet integral length scale appears of limited use in predicting surface heat flux interactions with the observed complex passage flow. While free-stream rms velocity, u', and surface rms heat flux, q', show some correlation with mean heat transfer in the laminar region near the leading edge, no such correlation is seen on the pressure side. Instead, u' decreases along the pressure side while low frequency transitional activity causes q' to increase. Application of laminar heat transfer correlations to the near leading edge region shows some success. However, application of laminar and turbulent heat transfer correlations along the pressure side gives poor results which are likely due to the transitional state of the boundary layer and complex flow. Frequency domain analysis allowed estimation of scales, frequency, and time lag across the boundary layer of passing flow structures. Coherence between free-stream velocity and surface heat flux was found useful for determining the scale and frequency range of free-stream turbulent structures interacting with the surface heat flux, but did not correlate with mean heat transfer. Suction side coherence was low relative to the pressure side and isolated to a narrow frequency band. Pressure side coherence was broadband with significant low frequency energy near the leading edge. This low frequency energy (larger structures) decayed along the pressure side while higher frequency coherent structures were seen to grow. / Ph. D.