An investigation was carried out on the current state of the art in bubble modelling for computational fluid dynamics, and comparisons made between the different methods for both polydisperse and monodisperse multiphase flows. A multigroup method for polydisperse bubbly flows with the bubbles binned in terms of mass was selected from the various alternatives, which included other multigroup models and moment methods. The latter of these involve the integration of moments of the bubble number density function and transport of these quantities. The equations from this multigroup solver were then changed to more accurately and efficiently model cases involving extremely small bubbles over significant amounts of time, as the original model which was subsequently adapted had, as its primary purpose, simulation of larger bubbles over shorter periods of time. This was done by decoupling the gas and liquid momentum equations and adding an empirical rise velocity term for the bubbles. This new model was then partially implemented into OpenFOAM. The functioning of this new solver was confirmed by comparisons between the results and basic analytical solutions to the problems, as well as by means of comparison with another similar multiphase CFD solver (pbeTransportFoam). Following this confirmation of its functionality, the bubble model was implemented into another solver specifically designed for modelling wakes. Finally, the newly created solver was used to run some cases of interest involving a submerged wake. / Master of Science / Bubbles in the ocean are significant for a number of reasons, ranging from mixing of the upper layer of the ocean to scavenging of biological matter, by which means they can also impact the state of the ocean's surface where they are present. They serve as an important mechanism by which air is dissolved in the ocean, and their breaking at the surface can cause particles or droplets to be ejected into the atmosphere. They can be created by a variety of sources, ranging from the movement of ship propellers and hulls to natural processes, both abiotic and from microorganisms or other living things. They can have exceedingly variable sizes, meaning bubbles behave very differently from one another in the same area. For these reasons, their study is both interesting and sometimes challenging. In this research, methods were developed to simulate the movement over a significant amount of time of a wide size variety of very small bubbles within the ocean. First, study was undertaken of preexisting methods of bubble simulation and the different cases they were intended to represent. One of these existing methods was selected for use and then changed to more accurately represent smaller bubbles, as well as including simplifications to allow the simulations to run faster. Lastly, these methods were implemented into OpenFOAM, an open-source set of solvers for computational fluid dynamics (CFD). These new methods for simulation were finally applied to some cases involving submerged bubbles in the ocean and the movement of bubbles in these cases studied.

This dissertation presents a formulation of the Continuous Sensitivity Equation Method (CSEM) applied to the Computational Fluid Dynamics (CFD) simulation of thermoacoustic instability problems. The proposed sensitivity analysis approach only requires a single run of the CFD simulation. Moreover, the sensitivities of field variables, pressure, velocity and temperature to boundary-condition parameters are directly obtained from the solution to sensitivity equations. Thermoacoustic instability is predicted by the Rayleigh criterion. The sensitivity of the Rayleigh index is computed utilizing the sensitivities of field variables. The application of the CSEM to thermoacoustic instability problems is demonstrated by two classic examples. The first example explores the effects of the heated wall temperature on the one-dimensional thermoacoustic convection. The sensitivity of the Rayleigh index, which is the indicator of thermoacoustic instabilities, is computed by the sensitivity of field variables. As the heat wall temperature increases, the sensitivity of the Rayleigh index decreases. The evolution from positive to negative sensitivity values suggests the transition from a destabilizing trend to stabilizing trend of the thermoacoustic system. Thermoacoustic instabilities in a self-excited Rijke tube are investigated following the relatively simple thermoacoustic convection problem. The complexity of simulating the Rijke tube increases in both dimensions and mechanisms which incorporate the species transport process and chemical reactions. As a representative model of the large lean premixed combustor, Rijke tube has been extensively studied. Quantitative sensitivity analysis sets the present work apart from previous research on the prediction and control of thermoacoustic instabilities. The effects of two boundary-condition parameters, i.e. the inlet mass flow rate and the equivalence ratio, are tested respectively. Small variations in both parameters predict a rapid change in sensitivities of field variables in the early stage of the total time length of 1.2s. The sensitivity of the Rayleigh index "blows up" at a specific time point of the early stage. In addition, variations in the inlet mass flow rate and the equivalence ratio lead to opposite effects on the sensitivity of the Rayleigh index. There exist some common findings on the application of the CSEM. For both thermoacoustic problems, the sensitivities of field variables and the Rayleigh index exhibit oscillatory nature, confirming that thermoacoustic instability is an overall effect of the coupling process between fluctuations of pressure and heat release rate. All the sensitivities of the Rayleigh index show rapid changes and "blow up" in the early stage. Although the numerical errors could influence the fidelity of computational results, it is believed that the rapid changes reflect the susceptibility to thermoacoustic instabilities in the studied systems. It should also be noted that the sensitivities are obtained for small variations in influential parameters. Therefore, the resulting sensitivities do not predict the occurrence of thermoacoustic instabilities under a condition that is far from the reference state determined by either CFD simulation results (employed in this dissertation) or experimental data. The sensitivity solver developed for the present research has the feature of flexibility. Additional mechanisms and more complicated instability criteria could be easily incorporated into the solver. Moreover, the sensitivity equations formulated in this dissertation are derived from the full set of nonlinear governing equations. Therefore, it is possible to extend the use of the sensitivity solver to other CFD problems. The developed sensitivity solver needs to be optimized to gain better performance, which is considered to be the primary future work of this research. / Ph. D.

Cardiovascular diseases (CVD) are the leading cause of death in the world. According to the World Health Organization (WHO) 17.3 million people died from cardiovascular disease in 2008, representing 30% of all global deaths. The most common modality of treatment of occluded arteries is the use of stents. Despite the widespread use of stents, the incidence of post-stent restenosis is still high. The study of stents in conditions that are similar to in-vivo conditions is limited. This work tries to address the behavior of stents in conditions similar to in-vivo conditions in a generalized framework, thus providing insights for stent design and deployment. Three dimensional, time accurate computational fluid dynamics (CFD) simulations in a pulsatile flow with fluid-structure interaction (FSI) were carried out in realistic coronary arteries, with physiologically relevant flow parameters and dynamics due to induced motion of the heart. In addition, the geometric effects of the stent on the artery were studied to point towards possible beneficial stent deployment strategies. The results suggest that discontinuities in compliance and dynamic geometry cause critical changes in local hemodynamics, namely altering the local pressure and velocity gradients. Increasing the stent length, reducing the transition length and increasing the overexpansion caused adverse flow conditions. From this work, detailed flow characteristics and hemodynamic characteristics due to the compliance mismatch and applied motion were obtained that gave insights towards better stent design and deployment. / Ph. D.

Currently, the surgical procedure followed by the majority of cardiac surgeons to address right ventricular dysfunction is the Fontan procedure, which connects the superior and inferior vena cava directly to the left and right pulmonary arteries bypassing the right atrium. However, this is not the most efficient configuration from a hemodynamics perspective. The goal of this study is to develop a patient-specific 4-way connector to bypass the dysfunctional right ventricle and augment the pulmonary circulation. The 4-way connector was intended to channel the blood flow from the inferior and superior vena cava directly to the right and left pulmonary arteries. By creating a connector with proper hemodynamic characteristics, one can control the jet flow interactions between the inferior and superior vena cava and streamline the flow towards the right and left pulmonary arteries. In this study, the focus was on creating a system that could identify the optimal configuration for the 4-way connector for patients from 1-20 years of age. A platform was created in ANSYS that utilized the design of experiments (DOE) function to minimize power-loss and blood damage propensity in the connector based on junction geometries. A CFD model was created to simulate the blood flow through the connector. Then the geometry of the bypass connector was parameterized for the DOE process. The selected design parameters included inlet and outlet diameters, radius at the intersection, and length of the connector pathways. The chosen range for each geometric parameter was based on the relative size of the patient’s arteries found in the literature. It was confirmed that as the patient’s age and artery size change, the optimal size and shape of the connector also changes. However, the corner radius did not decrease at the same rate as the opening diameters. This means that creating different sized connectors is not just a matter of scaling the original connector to match the desired opening diameter. However, it was found that power losses within the connector decrease and average and maximum blood traversal time through the connector increased for increasing opening radius. A follow up study was conducted to try to reduce or negate a consistent recirculation area found at the center of the connectors. To accomplish this a flow diverter was added to the center of the connector and optimized for each of the connectors found for the age groups used. From this study, it was found that the diverter did negate the recirculation area form the centers of the connectors. A separate Blood Damage Index (BDI) study was also run on this optimized connector with a diverter, the optimized connectors from the first study and a baseline connector. This showed a decrease in IVC sourced BDI for the optimized versions of the connector compared to the baseline geometries. This information could be used to create a more specific relationship between the opening radius and the flow characteristics. So in order to create patient specific connectors, either a new more complicated trend needs to be found or an optimization program would need to be run on each patient’s specific geometry when they need a new connector. / Master of Science / Currently, the surgical procedure followed by the majority of cardiac surgeons to address a nonfunctioning right portion of the heart is the Fontan procedure, which connects the two major inflow venous structures from the right side of the heart directly to the two major outflow venous structures, bypassing the right nonfunctioning right portion of the heart. However, this is not the most efficient configuration from a fluid flow perspective. The goal of this study is to develop a patient-specific 4-way connector to bypass the nonfunctioning right side of the heart and aid in overall circulation. Just like the Fontan procdure, the 4-way connector was intended to channel the blood flow from the two main inflow venous structures directly to the two major outflow venous structures. By creating a connector with proper fluid flow characteristics, one can control the flow interactions between the two inflows and streamline the flow towards the two outflow venous structures. In this study, the focus was on creating a system that could identify the optimal configuration for the 4-way connector for patients from 1-20 years of age. A platform was created in a modeling and simulation program, called ANSYS, that utilized the design of experiments (DOE) function to minimize power-loss and the likelihood of blood damage in the connector based on connector geometries. A CFD model was created to simulate the blood flow through the connector. Then the geometry of the bypass connector was parameterized for the DOE process. The selected design parameters included inlet and outlet diameters, radius at the intersection, and length of the connector pathways. The chosen range for each geometric parameter was based on the relative size of the patient’s arteries found in the literature. It was confirmed that as the patient’s age and artery size change, the optimal size and shape of the connector also changes. From the results of the first study showed a very decreasing relationship between the opening radius and the corner radius as the opening radius increased in size. It was also found that power losses within the connector decrease and average and maximum blood traversal time through the connector increased for increasing opening radius. A follow up study was conducted to try to reduce or negate a consistent recirculation area found at the center of the connectors. To accomplish this a flow diverter was added to the center of the connector and optimized for each of the connectors found for the age groups used. From this study, it was found that the diverter did negate the recirculation area form the centers of the connectors. A separate Blood Damage Index (BDI) study was also run on this optimized connector with a diverter, the optimized connectors from the first study and a baseline connector. This showed a decrease in BDI from the venous structure with the larger inlet flow for the optimized versions of the connector compared to the baseline geometries. This information could be used to create a more specific relationship between the opening radius and the flow characteristics. So in order to create patient specific connectors, either a new more complicated trend needs to be found or an optimization program would need to be run on each patient’s specific geometry when they need a new connector.

Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results are presented for the steady viscous Burgers' equation, unsteady viscous Burgers' equation, steady quasi-1D Euler equations, and unsteady 1D Euler equations when applied to a shock tube. Cases using either defect correction or ETE are shown to give higher orders of accuracy for the corrected discretization error estimates when compared to the discretization error of the primal solution. / Master of Science / Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is used to understand complex flows that are difficult to replicate using experimental techniques or by theoretical methods. It is important to have rigorous techniques to estimate the error produced when using CFD even when the exact solution is not available for comparison. This paper develops techniques to estimate discretization error for unsteady flows. Discretization error has one of the largest error magnitudes in CFD solutions. The exact physics dictates the use of continuous equations but to apply CFD techniques, the continuous equations have to be converted to discrete equations. Truncation error is, the error obtained when converting the continuous equations to discrete equations. This truncation error is in turn, the local source term for discretization error. To reduce the discretization error in the discrete equations, the exact or estimated truncation error is either added as a source term to the discrete equations or is used along with the error transport equation to get a better estimate of the solutions. A framework to obtain exact truncation error and estimated truncation error is also presented. The framework is first applied to the steady equations and is verified with results from previous studies and is then extended to the unsteady flows.

<div>Combustion instability due to thermo-acoustic interactions in high-speed propulsion devices such as gas turbines and rocket engines result from pressure waves with very large amplitudes propagating back and forth in the combustion chamber. Exposure to the pressure fluctuations over a long period of time can lead to a cataclysmic failure of engines. The underlying physics governing the generation of the thermo-acoustic instability is a complex interaction among heat release, turbulence, and acoustic waves. Currently, it is very difficult to accurately predict the expected level of oscillations in a combustor. Hence development of strategies and engineering solutions to mitigate thermo-acoustic instability is an active area of research in both academia and industry. In this work, we carry out numerical modeling of thermo-acoustic instability in a self-excited, laboratory scale, model rocket combustor developed at Purdue University. Two different turbulent combustion models to account for turbulence-chemistry interactions are considered in this study, the flamelet model and the transported probability density function (PDF) method. </div><div><br></div><div>In the flamelet modeling approach, detailed chemical kinetics can be easily incorporated at a relatively low cost in comparison to other turbulent combustion models and it also accounts for turbulence-chemistry interactions. The flamelet model study is divided into two parts. In first part, we examine the effect of different numerical approaches for implementing the flamelet model. In advanced modeling and simulations of turbulent combustion, the accuracy of model predictions is affected by physical model errors as well as errors that arise from the numerical implementation of models in simulation codes. Here we are mainly concerned with the effect of numerical implementation on model predictions of turbulent combustion. Particularly, we employ the flamelet/progress variable (FPV) model and examine the effect of various numerical approaches for the flamelet table integration, with presumed shapes of PDF, on the FPV modeling results. Three different presumed-PDF table integration approaches are examined in detail by employing different numerical integration strategies. The effect of the different presumed-PDF table integration approaches is examined on predictions of two real flames, a laboratory-scale turbulent free jet flame, Sandia Flame D and the self-excited resonance model rocket combustor. Significant difference is observed in the predictions both of the flames. The results in this study further support the claims made in previous studies that it is imperative to preserve the laminar flamelet structure during integration while using the flamelet model to achieve better predictions in simulations. In the second part of the flamelet modeling study, computational investigations of the coupling between the transient flame dynamics such as the ignition delay and local extinction and the thermo-acoustic instability developed in a self-excited resonance combustor to gain deep insights into the mechanisms of thermo-acoustic instability. A modeling framework that employs different flamelet models (the steady flamelet model and the flamelet/progress variable approach) is developed to enable the examination of the effect of the transient flame dynamics caused by the strong coupling of the turbulent mixing and finite-rate chemical kinetics on the occurrence of thermo-acoustic instability. The models are validated by using the available experimental data for the pressure signal. Parametric studies are performed to examine the effect of the occurrence of the transient flame dynamics, the effect of artificial amplification of the Damkohler number, and the effect of neglecting mixture fraction fluctuations on the predictions of the thermo-acoustic instability. The parametric studies reveal that the occurrence of transient flame dynamics has a strong influence on the onset of the thermo-acoustic instability. Further analysis is then conducted to localize the effect of a particular flame dynamic event, the ignition delay, on the thermo-acoustic instability. The reverse effect of the occurrence of the thermo-acoustic instability on the transient flame dynamics in the combustor is also investigated by examining the temporal evolution of the local flame events in conjunction with the pressure wave propagation. The above observed two-way coupling between the transient flame dynamics (the ignition delay) and the thermo-acoustic instability provides a plausible mechanism of the self-excited and sustained thermo-acoustic instability observed in the combustor.</div><div><br></div><div>The second turbulent combustion model considered in this study is the transported PDF method. The transported PDF method is one of the most attractive models because it treats the highly-nonlinear chemical reaction source term without a closure requirement and it is a generalized model for a wide range of turbulent combustion problems.</div><div>Traditionally, the transported PDF method has been used to model low-Mach number, incompressible flows where the pressure is assumed to be thermodynamically constant. Since there is significant pressure fluctuations in the model rocket combustor, the flow is highly compressible and it is necessary to account for this compressibility in the transported PDF method. In the past there has been very little work to model compressible reactive flows using the transported PDF and no effort has been made to model thermo-acoustic instability using the transported PDF method. There is a pressing need to further examine and develop the transported PDF method for compressible reactive flows to broaden our understanding of physical phenomenon like thermo-acoustic instability, interaction between combustion and strong shock and expansion waves, coupling between acoustic and heat release which are observed in high-speed turbulent combustion problems. To address this, a modeling framework for compressible turbulent reactive flows by the using the transported PDF method is developed. This framework is validated in a series of test cases ranging from pure mixing to a supersonic turbulent jet flame. The framework is then used to study the thermo-acoustic interactions in the self-excited model rocket combustor.</div>

Computational Fluid Dynamics (CFD) is one of the fields that has strongly developed since the recent development of faster computers and numerical modeling. CFD is also finding its way into chemical engineering on several levels. We have used CFD for detailed modeling of heat and mass transfer in a packed bed. One of the major questions in CFD modeling is whether the computer model describes reality well enough to consider it a reasonable alternative to data collection. For this assumption a validation of CFD data against experimental data is desired. We have developed a low tube to particle, structured model for this purpose. Data was gathered both with an experimental setup and with an identical CFD model. These data sets were then compared to validate the CFD results. Several aspects in creating the model and acquiring the data were emphasized. The final result in the simulation is dependent on mesh density (model detail) and iteration parameters. The iteration parameters were kept constant so they would not influence the method of solution. The model detail was investigated and optimized, too much detail delays the simulation unnecessarily and too little detail will distort the solution. The amount of data produced by the CFD simulations is enormous and needs to be reduced for interpretation. The method of data reduction was largely influenced by the experimental method. Data from the CFD simulations was compared to experimental data through radial temperature profiles in the gas phase collected directly above the packed bed. It was found that the CFD data and the experimental data show quantitatively as well as qualitatively comparable temperature profiles, with the used model detail. With several systematic variances explained CFD has shown to be an ample modeling tool for heat and mass transfer in low tube to particle (N) packed beds.

The DigIndy tunnel is an extension of the Indianapolis combined sewer system that stores the combined sewer overflow during heavy rain conditions. The tunnel system has several openings in and around the city of Indianapolis. Gasses emitted from the tunnel may create health concerns and affect the quality of life for nearby residents. Understanding the air circulation patterns provides valuable insight into where gases are likely to emerge from the tunnel and what steps may be taken to mitigate gas emissions in undesirable locations. The objective of the present work is to develop a computational fluid dynamics (CFD) model capable of predicting the air circulation patterns in the DigIndy tunnel under dry weather conditions. In order to inform and validate the CFD model, an experimental campaign was designed and executed to measure weather data and air flow rates within the DigIndy tunnel. Obtaining accurate results requires careful consideration of key physical phenomena to include in the model, geometric simplification strategies, mesh generation strategies, and numerical modeling strategies. Results showed that the seasonal effect, manifest by thermally-driven flow, plays a significant role in the air circulation patterns within the tunnel. Furthermore, results show that tunnel alignment affects the natural air circulation within the tunnel. Large diameter shafts, as the working and retrieval shafts, lead to significant circulation rates in the new tunnel alignments.

This work examines the detailed flow characteristics of direct measuring skin friction gages with computational methods. This type of device uses a small movable head mounted flush to a wall such that the head is assumed to be exposed to the same shear stress from the flow as the surrounding wall. The force caused by the action of the shear stress on the head deflects a flexure system monitored by instruments such as strain gages mounted at the base of a beam. The goal of the study was to develop an understanding of the effects that the geometric design and installation parameters of the sensor have on the surrounding flow and the ability of the sensor to reflect the undisturbed shear stress value. Disruption of the external flow due to poor design and/or improper installation of the sensor can take the form of intrusion into the flow, recession into the wall, and/or tilted alignment of the sensor such that the head is not flat in the plane of the wall, as well as flow into or out of the small gap surrounding the sensing head. Further, the performance of a direct measuring skin friction sensor in the presence of a pressure gradient has always been a concern. These effects are studied here with a three-dimensional, Navier-Stokes code based on a finite element method technique. Numerical solutions for cases in which one or more design parameters were varied are shown for a variety of flow situations. These situations include: (a) a laminar fully-developed channel flow at a low Reynolds number, (b) a turbulent flat plate boundary layer flow at a high Reynolds number, and (c) strong favorable and adverse pressure gradient turbulent boundary layer flows created by converging and diverging channels at high Reynolds number. Reported results for all cases include detailed flow visualization and stress field imagery, and total surface forces on the sensing head and gage flexure. Under ideal circumstances, these total forces should reflect as accurately as possible the average value of undisturbed shear stress times the exposed sensing head area (the friction force). Any deviation from this value was considered an "error" in the simulated measurement. The laminar channel flow case with a strong favorable pressure gradient showed the importance of proper alignment of the sensor. Protrusion or recession of the sensing head proved to be the dominant effect on resulting forces seen by the gage, changing the output by up to 15% for head protrusion and 10% for head recession for misalignments up to +/-1% of the head diameter. The thickness of the lip on the edge of the head also proved to have a significant effect on the output, with a smaller lip thickness generally showing better performance than a large one. Zero lip thickness indicated accuracy to within 1% of the desired wall shear result, since the pressure differences had little influence on the sensing head. Finally, the assumption of a linear pressure variation from the surface to the cavity along the lip as has been suggested in the past was investigated. The results indicate that the linear assumption works well only for large ratios of lip thickness to gap size, a fact which is correlated with previous experimental results. For the turbulent external flat plate case, misalignment remained the dominant effect on the sensor response. Results indicated that, in general, protrusion is more costly than the same level of recession, and a protrusion of +1% of the head diameter was shown to cause in excess of 100% error in indicated wall shear output. Both protrusion and recession produced large variations in both force and moment on the sensing flexure, but the outcome was that for protrusion the errors caused by these two effects tended to sum together, while for recession they tended to partially cancel out. The gap size played an increased role in the high Reynolds number boundary layer cases. Gap sizes of 1.67% up to 6.67% of the head diameter were studied and were shown to produce output errors between 4% and 22% (with larger errors corresponding to larger gap sizes), thus showing the importance of minimizing the gap for high Reynolds number flows. The lip was shown to have no significant effect for a flow without a pressure gradient. Finally, the favorable and adverse pressure gradient flows showed reasonable performance of the skin friction gage. Errors in output were shown to be -6% for the favorable pressure gradient case and 17% for the adverse pressure gradient case. Only the baseline gage design was studied for these situations, but the results from the two cases indicate that further reducing the lip thickness may not improve the performance of the gage. The error in output was caused almost entirely by applied moment for the adverse pressure gradient, while the applied force and applied moment had a cancellation effect in the favorable pressure gradient case. As a general result, the use of computational fluid dynamics has been shown to be an effective tool in the design and analysis of skin friction gages. Using a computational approach has the advantage of being able to resolve the small, confined gap regions of the gage, providing information that has been shown to be unavailable from previous experimental studies. This work has contributed to a much better understanding of the detailed flow over, in, and around skin friction gages. This will lead to improved gage design and reduced uncertainty in these important measurements. / Ph. D.

In the past two decades, a growing interest in alternative energy resources as a replacement to the non-renewable resources used now days. These alternatives include geothermal energy which can be used to generate power and reduce the demands on energy used to heat and cool buildings. Ground-coupled ventilation system is one of the many applications of the geothermal energy that have a lot of attention in the early 80's and 90's but all designs of the system where based on single case situations. On the other hand, computational fluid dynamics tools are used to simulate heat and fluid flow in any real life situation. They start to develop rapidly with the fast development of computers and processors. These tools provide a great opportunity to simulate and predict the outcome of most problems with minimum loss and better way to develop new designs. By using these CFD tools in GCV systems designing procedure, energy can be conserved and designs going to be improved. The main objective of this study is to find and develop a CFD modeling strategy for GCV systems. To accomplish this objective, a case study must be selected, a proper CFD tool chosen, modeling and meshing method determined, and finally running simulations and analyzing results. All factors that affect the performance of GCV should be taken under consideration in that process such as soil, backfill, and pipes thermal properties. Multiple methods of simulation were proposed and compared to determine the best modeling approach. / Master of Science