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Fuel cells are predicted to be the power delivery devices of the future. They have many advantages such as the wide fuel selection, high energy density, high efficiency and an inherent safety which explains the immense interest in this power source. The need for advanced designs has been limited by the lack of understanding of the transport processes inside the fuel cell stack. The reactant gases undergo many processes in a fuel cell that cannot be observed. Some of these processes include convective and diffusional mass transport through various types of materials, phase change and chemical reaction. In order to optimize these variables, an accurate mathematical model can provide a valuable tool to gain insight into the processes that are occurring. The goal of this dissertation is to develop a mathematical model for polymer electrolyte-based fuel cells to help contribute to a better understanding of fuel cell mass, heat and charge transport phenomena, to ultimately design more efficient fuel cells. The model is a two-phase, transient mathematical model created with MATLAB. The model was created by using each fuel cell layer as a control volume. In addition, each fuel cell layer was further divided into the number of nodes that the user inputs into the model. Transient heat and mass transfer equations were created for each node. The catalyst layers were modeled using porous electrode equations and the Butler-Volmer equation. The membrane model used Fick's law of diffusion and a set of empirical relations for water uptake and conductivity. Additional work performed for this dissertation includes a mathematical model for predicting bolt torque, and the design and fabrication of four fuel cell stacks ranging in size from macro to micro scale for model validation. The work performed in this dissertation will help improve the designs of polymer electrolyte fuel cells, and other polymer membrane-based fuel cells (such as direct methanol fuel cells) in the future.

Improved basic understanding, predictability, and controllability of vortex-dominated and unsteady aerodynamic flows are important in enhancement of the performance of next generation helicopters. The primary objective of this research project was improved understanding of the fundamental vorticity and turbulent flow physics for a dynamically stalling airfoil at realistic helicopter flight conditions. An experimental program was performed on a large-scale (C = 0.45 m) dynamically pitching NACA 0012 wing operating in the Texas A&M University large-scale wind tunnel. High-resolution particle image velocimetry data were acquired on the first 10-15% of the wing. Six test cases were examined including the unsteady (k>0) and steady (k=0) conditions. The relevant mechanical, shear and turbulent time-scales were all of comparable magnitude, which indicated that the flow was in a state of mechanical non-equilibrium, and the expected flow separation and reattachment hystersis was observed. Analyses of the databases provided new insights into the leading-edge Reynolds stress structure and the turbulent transport processes. Both of which were previously uncharacterized. During the upstroke motion of the wing, a bubble structure formed in the leading-edge Reynolds shear stress. The size of the bubble increased with increasing angle-of-attack before being diffused into a shear layer at full separation. The turbulent transport analyses indicated that the axial stress production was positive, where the transverse production was negative. This implied that axial turbulent stresses were being produced from the axial component of the mean flow. A significant portion of the energy was transferred to the transverse stress through the pressure-strain redistribution, and then back to the transverse mean flow through the negative transverse production. An opposite trend was observed further downstream of this region.

While shoaling from deepwater in a stratified ocean, an interfacial solitary wave (ISW) may experience waveform inversion on a continental margin. Although many oceanographers have believed that the inversion from depression to elevation may commence at the turning point where the upper and bottom layers are equal in depth, this phenomenon has not been fully verified in field observations nor in a laboratory. In this study, a series of laboratory experiments and numerical modeling were conducted on the evolution of an ISW of depression across uniform slope joining a horizontal plateau which resembles pseudo slope-shelf topography, in order to clarify this fascinating phenomenon and the variations of wave properties associated with the process. In the laboratory experiments, a depression ISW was produced by a collapse mechanism in a stratified two-layer fluid system within a steel-framed wave flume (12 m long, 0.7 m high by 0.5 m wide) at the National Sun Yat-sen University in Taiwan. The fluid density in the upper (fresh) and bottom (brine) layers was 996 and 1030 kg/m3, respectively. A series of experiments were conducted upon varying the magnitude of the most important physical factors (i.e., nominal thickness of pycnocline, depth ratio between upper and bottom layer, front gradient and shape of pseudo slope-shelf), from which the results are now discussed in four separate chapters in this thesis. Present laboratory results indicate that the process of waveform inversion took place after an ISW had experienced internal run-down, hydraulic jump, vortex motion and surge-up on the front slope, prior to its propagation onto the plateau. Moreover, the fundamental wave period of leading wave on the plateau was significantly smaller than that in the preceding sections on the front slope and the incident stage earlier, thus representing frequency downshift. Amongst the factors involved, the depth ratio between the upper and bottom layer was the most significant one for waveform inversion. Only when the upper layer was thicker than the bottom layer on the plateau of pseudo slope-shelf, waveform inversion could occur, besides the length of the plateau. On the other hand, the front gradient and shape of pseudo slope-shelf also affected the magnitude of the transmitted wave over the plateau as the wave across this specific topography. In the case of a steeper front gradient, waveform inversion became insignificant due to stronger wave reflection and intense energy dissipation caused by turbulent mixing while a depression ISW propagated over a slope-shelf; particularly against a submerged vertical cliff. As a depression ISW across pseudo slope-shelf with short plateau, intense wave breaking might occur again with vortex motion at its rear end as the newly inversed waveform reentering deep water. In this region, the upper layer was smaller than the bottom layer, hence it could not support the continuous existence of an ISW in elevation. Again, energy dissipation occurred due to turbulent mixing beyond the rear end of a short plateau. Finally, a different mode of ISW appeared within pycnocline, while its nominal thickness was larger than the amplitude of the incident wave. In addition to the laboratory investigations, numerical model was also adopted to study the variations in the flow field as an ISW propagated over a pseudo slope-shelf, in order to complement the experimental results. The results of numerical modeling revealed that the horizontal velocity in the bottom layer increased when the wave encountered the front slope, even if the depth of upper layer was thinner than that of the bottom layer on the plateau. Consequently, the velocity in the upper layer became less than that in the bottom layer when the former was thicker than that of the latter on the plateau. On the other hand, the vertical velocity within the self-generated vortex switched direction as waveform inversion commenced after the wave across the shoulder of pseudo slope-shelf where the local depth of the upper layer was larger than that of bottom part. Overall, the significance of the four pertinent factors (i.e., nominal thickness of pycnocline, water depth ratio, front slope, and plateau length) that affected a depression ISW across pseudo slope-shelf is discussed in detail in this thesis, as well as the variation of flow field calculated by the numerical mode presented.

Squeeze Film Dampers (SFDs) are employed in high-speed Turbomachinery, particularly aircraft jet engines, to provide external damping. Despite numerous successful applications, it is widely acknowledged that the theoretical models used for SFD design are either overly simplified or incapable of taking into account all the features such as cavitation, air entrainment etc., affecting the performance of a SFD. On the other hand, experimental investigation of flow field and dynamic performance of SFDs can be expensive and time consuming. The current work simulates the flow field inside the dynamically deforming annular gap of a SFD using the commercial computational fluid dynamics (CFD) code Fluent and compares the results to the experimental data of San Andrés and Delgado. The dynamic mesh capability of Fluent and a User Defined Function (UDF) was used to replicate the deforming gap and motion of the rotor respectively. Two dimensional simulations were first performed with different combinations of rotor whirl speed, operating pressures and with and without incorporating the cavitation model. The fluid used in the simulations was ISO VG 2 Mobil Velocite no. 3. After the successful use of the cavitation model in the 2D case, a 3D model with the same dimensions as the experimental setup was built and meshed. The simulations were run for a whirl speed of 50 Hz and an orbit amplitude of 74 μm with no through flow and an inlet pressure of 31kPa (gauge). The resulting pressures at the mid-span of the SFD land were obtained. They closely agreed with those obtained experimentally by San Andrés and Delgado.

Improved basic understanding, predictability, and controllability of vortex-dominated and unsteady aerodynamic flows are important in enhancement of the performance of next generation helicopters. The primary objective of this research project was improved understanding of the fundamental vorticity and turbulent flow physics for a dynamically stalling airfoil at realistic helicopter flight conditions. An experimental program was performed on a large-scale (C = 0.45 m) dynamically pitching NACA 0012 wing operating in the Texas A&M University large-scale wind tunnel. High-resolution particle image velocimetry data were acquired on the first 10-15% of the wing. Six test cases were examined including the unsteady (k>0) and steady (k=0) conditions. The relevant mechanical, shear and turbulent time-scales were all of comparable magnitude, which indicated that the flow was in a state of mechanical non-equilibrium, and the expected flow separation and reattachment hystersis was observed. Analyses of the databases provided new insights into the leading-edge Reynolds stress structure and the turbulent transport processes. Both of which were previously uncharacterized. During the upstroke motion of the wing, a bubble structure formed in the leading-edge Reynolds shear stress. The size of the bubble increased with increasing angle-of-attack before being diffused into a shear layer at full separation. The turbulent transport analyses indicated that the axial stress production was positive, where the transverse production was negative. This implied that axial turbulent stresses were being produced from the axial component of the mean flow. A significant portion of the energy was transferred to the transverse stress through the pressure-strain redistribution, and then back to the transverse mean flow through the negative transverse production. An opposite trend was observed further downstream of this region.

The goal of this thesis is the development of a fast and robust algorithm that is able to detect patterns in flow fields independent from their orientation and adequately visualize the results for a human user. This thesis is an interdisciplinary work in the field of vector field visualization and the field of pattern recognition. A vector field can be best imagined as an area or a volume containing a lot of arrows. The direction of the arrow describes the direction of a flow or force at the point where it starts and the length its velocity or strength. This builds a bridge to vector field visualization, because drawing these arrows is one of the fundamental techniques to illustrate a vector field. The main challenge of vector field visualization is to decide which of them should be drawn. If you do not draw enough arrows, you may miss the feature you are interested in. If you draw too many arrows, your image will be black all over. We assume that the user is interested in a certain feature of the vector field: a certain pattern. To prevent clutter and occlusion of the interesting parts, we first look for this pattern and then apply a visualization that emphasizes its occurrences. In general, the user wants to find all instances of the interesting pattern, no matter if they are smaller or bigger, weaker or stronger or oriented in some other direction than his reference input pattern. But looking for all these transformed versions would take far too long. That is why, we look for an algorithm that detects the occurrences of the pattern independent from these transformations. In the second part of this thesis, we work with moment invariants. Moments are the projections of a function to a function space basis. In order to compare the functions, it is sufficient to compare their moments. Normalization is the act of transforming a function into a predefined standard position. Moment invariants are characteristic numbers like fingerprints that are constructed from moments and do not change under certain transformations. They can be produced by normalization, because if all the functions are in one standard position, their prior position has no influence on their normalized moments. With this technique, we were able to solve the pattern detection task for 2D and 3D flow fields by mathematically proving the invariance of the moments with respect to translation, rotation, and scaling. In practical applications, this invariance is disturbed by the discretization. We applied our method to several analytic and real world data sets and showed that it works on discrete fields in a robust way.

Plug nozzle, a passive altitude adaptive nozzle, for futuristic SSTO applications, exhibits greater efficiency as compared to conventional nozzles over a wide range of altitudes. The plug nozzle comprises of a primary nozzle and a contoured plug; an under–expanded jet exiting the primary nozzle is allowed to further expand over the plug surface for altitude adaptation. At design condition the flow expands correctly to the ambient conditions on the full length plug surface, while at off design conditions the flow adapts to the ambient conditions through wave interactions within the nozzle core jet. Based on thrust to weight considerations, the full length plug is truncated and this results in a base flow rich in flow physics. In addition, the base flow exhibits an interesting transitional behaviour from open wake to a closed wake because of the wave interactions within the nozzle core jet. The plug surface flow can further exhibit flow complexities because of wave interactions resulting from the shear layer emanating from the splitter plates, in case of clustered plug flows. Considering these flow complexities, the design of the plug nozzles and analysing the associated flows can be a challenge to the aerodynamic community. An attempt has been made in understanding this class of flows in this thesis. This objective has been accomplished using both experimental and computational tools. In the present work, both the linear and annular plug nozzle geometries have been analysed for a wide range of pressure ratios spanning from 5to 80. The linear and annular nozzles have been designed for similar flow conditions and their respective design pressure ratios are 60and 66. From the experimental and computational results, it has been shown that the computational solver performs well in predicting the wave interactions on the plug surface. In addition the limitations of the computational solver in predicting the plug base flows in general has been brought out. This limitation in itself need not be considered as a serious handicap in the design and analysis of plug nozzle flows; this is because the plug base contribution to the thrust is very minimal, as has been brought out in this thesis. Apart from this the high quality experimental data generated is also of immense value to the CFD community as this also serves as a valuable data base for CFD code validation. For analysis, the plug flow field has been categorized into three different regimes based on the primary nozzle lip expansion fan extent. The flow field is categorised based on the reflection of the primary nozzle lip expansion fan from plug surface, base region shear layer and symmetry line downstream of the base region recirculation bubble. This flow division is particularly helpful in understanding the base wake characteristics with increasing pressure ratio. The base lip pressure and the base pressure variation have been discussed with respect to the primary nozzle lip expansion fan extent. In the open wake regime (or for low pressure ratios) the wave interactions within the core jet flow impinge on the base region shear layer. Because of these interactions it is difficult to propose an empirical model for open wake base pressure. In the closed wake regime (for higher pressure ratios), the base region recirculation bubble is completely under the shower of primary nozzle lip expansion fan. Hence the base lip pressure and base pressure are frozen with respect to stagnation conditions. Based on these insights it was possible to propose empirical models for linear and annular closed wake base pressure. Along with these, a mathematical model defining a reference pressure ratio PR∗, beyond which the closed wake base pressure is expected to be more than the ambient pressure has also been proposed. This is expected to serve as a good design parameter. In case of linear plug flows, this also serves the purpose of base wake transition, for the cases considered in this thesis. The flow expansion process or the primary nozzle lip expansion fan extent was also useful in understanding the differences between the linear and annular plug nozzle flow fields. In a linear plug nozzle, the flow expands only in the streamwise direction while in an annular plug nozzle the flow expands both along the streamwise and azimuthal directions. The flow expands at a faster rate in case of annular nozzle as against linear nozzle. Hence differences are observed between the linear and annular nozzle on plug and base surfaces. On the annular plug surface more wave interactions are observed because of faster expansion. With regard to base characteristics, faster expansion in annular plug nozzle, with respect to linear nozzle, results in a lower base lip pressure, lower base pressure and higher wake transition pressure ratio. The realistic cluster plug configurations have also been considered for the present studies. The effects of clustering on the plug nozzle flow field have been brought out by considering two different linear cluster nozzles and one annular cluster nozzle. The differences in the flow field of a simple and cluster plug nozzle has been discussed. In case of simple plug nozzle wave interactions are observed only in the stream wise direction, while in case of cluster plug nozzle three dimensional wave interactions are observed because of the splitter plates. Along the splitter plate differential end conditions introduce a curved recompression shock on the plug surface. This recompression shock in turn induces a streamwise vortex and also a secondary shock. It has been observed that differences between the simple and cluster plug surface pressure field are because of three dimensional wave interactions. Regarding the base pressure, differences between the simple and cluster geometries were observed for shorter truncation plug lengths (20% length plug). While for longer plug lengths (more than 34% length) the effects of clustering were reduced on the base pressure. Regarding the transition pressure ratio, differences were observed between simple and clustered plug nozzles for all the plug lengths considered. In addition, the performance of the plug nozzles has been carried out. From the analysis it was found that the primary nozzle and plug surface are major contributors towards thrust. The base surface contributes only about 2– 3% of the thrust at design condition. Hence, from a design point of view, a computational solver can be a useful tool considering its efficacy on the plug surface and in the primary nozzle.

Plug nozzle, a passive altitude adaptive nozzle, for futuristic SSTO applications, exhibits greater efficiency as compared to conventional nozzles over a wide range of altitudes. The plug nozzle comprises of a primary nozzle and a contoured plug; an under–expanded jet exiting the primary nozzle is allowed to further expand over the plug surface for altitude adaptation. At design condition the flow expands correctly to the ambient conditions on the full length plug surface, while at off design conditions the flow adapts to the ambient conditions through wave interactions within the nozzle core jet. Based on thrust to weight considerations, the full length plug is truncated and this results in a base flow rich in flow physics. In addition, the base flow exhibits an interesting transitional behaviour from open wake to a closed wake because of the wave interactions within the nozzle core jet. The plug surface flow can further exhibit flow complexities because of wave interactions resulting from the shear layer emanating from the splitter plates, in case of clustered plug flows. Considering these flow complexities, the design of the plug nozzles and analysing the associated flows can be a challenge to the aerodynamic community. An attempt has been made in understanding this class of flows in this thesis. This objective has been accomplished using both experimental and computational tools. In the present work, both the linear and annular plug nozzle geometries have been analysed for a wide range of pressure ratios spanning from 5to 80. The linear and annular nozzles have been designed for similar flow conditions and their respective design pressure ratios are 60and 66. From the experimental and computational results, it has been shown that the computational solver performs well in predicting the wave interactions on the plug surface. In addition the limitations of the computational solver in predicting the plug base flows in general has been brought out. This limitation in itself need not be considered as a serious handicap in the design and analysis of plug nozzle flows; this is because the plug base contribution to the thrust is very minimal, as has been brought out in this thesis. Apart from this the high quality experimental data generated is also of immense value to the CFD community as this also serves as a valuable data base for CFD code validation. For analysis, the plug flow field has been categorized into three different regimes based on the primary nozzle lip expansion fan extent. The flow field is categorised based on the reflection of the primary nozzle lip expansion fan from plug surface, base region shear layer and symmetry line downstream of the base region recirculation bubble. This flow division is particularly helpful in understanding the base wake characteristics with increasing pressure ratio. The base lip pressure and the base pressure variation have been discussed with respect to the primary nozzle lip expansion fan extent. In the open wake regime (or for low pressure ratios) the wave interactions within the core jet flow impinge on the base region shear layer. Because of these interactions it is difficult to propose an empirical model for open wake base pressure. In the closed wake regime (for higher pressure ratios), the base region recirculation bubble is completely under the shower of primary nozzle lip expansion fan. Hence the base lip pressure and base pressure are frozen with respect to stagnation conditions. Based on these insights it was possible to propose empirical models for linear and annular closed wake base pressure. Along with these, a mathematical model defining a reference pressure ratio PR∗, beyond which the closed wake base pressure is expected to be more than the ambient pressure has also been proposed. This is expected to serve as a good design parameter. In case of linear plug flows, this also serves the purpose of base wake transition, for the cases considered in this thesis. The flow expansion process or the primary nozzle lip expansion fan extent was also useful in understanding the differences between the linear and annular plug nozzle flow fields. In a linear plug nozzle, the flow expands only in the streamwise direction while in an annular plug nozzle the flow expands both along the streamwise and azimuthal directions. The flow expands at a faster rate in case of annular nozzle as against linear nozzle. Hence differences are observed between the linear and annular nozzle on plug and base surfaces. On the annular plug surface more wave interactions are observed because of faster expansion. With regard to base characteristics, faster expansion in annular plug nozzle, with respect to linear nozzle, results in a lower base lip pressure, lower base pressure and higher wake transition pressure ratio. The realistic cluster plug configurations have also been considered for the present studies. The effects of clustering on the plug nozzle flow field have been brought out by considering two different linear cluster nozzles and one annular cluster nozzle. The differences in the flow field of a simple and cluster plug nozzle has been discussed. In case of simple plug nozzle wave interactions are observed only in the stream wise direction, while in case of cluster plug nozzle three dimensional wave interactions are observed because of the splitter plates. Along the splitter plate differential end conditions introduce a curved recompression shock on the plug surface. This recompression shock in turn induces a streamwise vortex and also a secondary shock. It has been observed that differences between the simple and cluster plug surface pressure field are because of three dimensional wave interactions. Regarding the base pressure, differences between the simple and cluster geometries were observed for shorter truncation plug lengths (20% length plug). While for longer plug lengths (more than 34% length) the effects of clustering were reduced on the base pressure. Regarding the transition pressure ratio, differences were observed between simple and clustered plug nozzles for all the plug lengths considered. In addition, the performance of the plug nozzles has been carried out. From the analysis it was found that the primary nozzle and plug surface are major contributors towards thrust. The base surface contributes only about 2– 3% of the thrust at design condition. Hence, from a design point of view, a computational solver can be a useful tool considering its efficacy on the plug surface and in the primary nozzle.

The goal of this thesis is the development of a fast and robust algorithm that is able to detect patterns in flow fields independent from their orientation and adequately visualize the results for a human user. This thesis is an interdisciplinary work in the field of vector field visualization and the field of pattern recognition. A vector field can be best imagined as an area or a volume containing a lot of arrows. The direction of the arrow describes the direction of a flow or force at the point where it starts and the length its velocity or strength. This builds a bridge to vector field visualization, because drawing these arrows is one of the fundamental techniques to illustrate a vector field. The main challenge of vector field visualization is to decide which of them should be drawn. If you do not draw enough arrows, you may miss the feature you are interested in. If you draw too many arrows, your image will be black all over. We assume that the user is interested in a certain feature of the vector field: a certain pattern. To prevent clutter and occlusion of the interesting parts, we first look for this pattern and then apply a visualization that emphasizes its occurrences. In general, the user wants to find all instances of the interesting pattern, no matter if they are smaller or bigger, weaker or stronger or oriented in some other direction than his reference input pattern. But looking for all these transformed versions would take far too long. That is why, we look for an algorithm that detects the occurrences of the pattern independent from these transformations. In the second part of this thesis, we work with moment invariants. Moments are the projections of a function to a function space basis. In order to compare the functions, it is sufficient to compare their moments. Normalization is the act of transforming a function into a predefined standard position. Moment invariants are characteristic numbers like fingerprints that are constructed from moments and do not change under certain transformations. They can be produced by normalization, because if all the functions are in one standard position, their prior position has no influence on their normalized moments. With this technique, we were able to solve the pattern detection task for 2D and 3D flow fields by mathematically proving the invariance of the moments with respect to translation, rotation, and scaling. In practical applications, this invariance is disturbed by the discretization. We applied our method to several analytic and real world data sets and showed that it works on discrete fields in a robust way.