A validation of parallel TURBO, an unsteady RANS turbomachinery solver, is performed for Rotor 35. Comparisons of the rotor's operational range for computational and experimental data as well as comparisons of its spanwise performance characteristics for a single blade passage provide depth to the validation and show a very favorable agreement. Further operational and performance comparisons against experiment are used for multiple blade passage simulations. Multiple blade passage simulations are shown to demonstrate noticable gains over the single blade passage simulation in solution accuracy against experiment. Also demonstrated are the asymmetric flow features that develop at the near stall operating condition for multiple blade passages. These single and multiple blade passage simulations are presented as groundwork for future research examining the effect of periodic boundary conditions on the growth of computational stall cells within a rotor or stage configuration.

The purpose of this dissertation is to develop a methodology for designing active control laws in a computational aeroelasticity environment. The methodology involves employing a systems identification technique to develop an explicit state-space model for control law design from the output of a computational aeroelasticity code. The particular computational aeroelasticity code employed in this dissertation solves the transonic small disturbance equation using a time-accurate, finite-difference scheme. Linear structural dynamics equations are integrated simultaneously with the computational fluid dynamics equations to determine the time responses of the structural outputs. These structural outputs are employed as the input to a modern systems identification technique that determines the Markov parameters of an "equivalent linear system". The eigensystem realization algorithm is then employed to develop an explicit state-space model of the equivalent linear system. Although there are many control law design techniques available, the standard Linear Quadratic Guassian technique is employed in this dissertation. The computational aeroelasticity code is modified to accept control laws and perform closed-loop simulations. Flutter control of a rectangular wing model is chosen to demonstrate the methodology. Various cases are used to illustrate the usefulness of the methodology as the nonlinearity of the computational fluid dynamics system is increased through increased angle-of-attack changes. / Ph. D.

A numerical investigation of the performance of two candidate designs for injection into supersonic flow, including a comparison of two renormalized group theory (RNG) based k-epsilon turbulence models with a more conventional k-epsilon model. The chosen designs were an unswept ramp injector with four injection ports and a novel nine-hole injector array. The objectives of the investigation were to provide reliable computational solutions to the flowfields in question using both RNG and standard k-epsilon turbulence models and to compare the solutions to experiment, thereby to judge the relative performance of the turbulence models. A second objective of the investigation was to use the computed data to provide design insights for the nine-hole injector array. This investigation made use of GASP(tm) version 2.2, a commercial computational fluid dynamics code that was augmented by the addition of one RNG-based k-epsilon turbulence model derived by Zhou, et. al. and one variant of Zhou's model, which was derived by the author. Mesh sequencing studies were performed to measure solution quality, with the fine mesh for the injector array containing roughly one million grid nodes and the fine mesh for the ramp injector containing more than six million grid nodes. Results of these studies indicated that the injector-array solution was significantly under-resolved in the farfield, though the quality was better in the vicinity of the injector itself. The ramp-injector solution, while not perfectly grid-resolved, showed much better grid convergence in both the nearfield and farfield. Accordingly, comparison with experiment was better for the ramp injector than for the injector array. For both injectors, the differences between solutions generated with RNG-based k-epsilon and standard k-epsilon turbulence models were negligibly small." Despite inadequate grid resolution in the farfield, the computational investigation of the nine-hole injector array did yield several important design insights. Particularly, the significance to mixing and losses of the placement of the outer injectors of the second and third rows was determined. / Ph. D.

Several different time-integration algorithms for the Euler equations are investigated on two distributed-memory parallel computers using an explicit message-passing paradigm: these are classic Euler Explicit, four-stage Jameson-style Runge-Kutta, Block Jacobi, Block Gauss-Seidel, and Block Symmetric Gauss-Seidel. A finite-volume formulation is used for the spatial discretization of the physical domain. Both two- and three-dimensional test cases are evaluated against five reference solutions to demonstrate accuracy of the fundamental sequential algorithms. Different schemes for communicating or approximating data that are not available on the local compute node are discussed and it is shown that complete sharing of the evolving solution to the inner matrix problem at every iteration is faster than the other schemes considered. Speedup and efficiency issues pertaining to the various time-integration algorithms are then addressed for each system. Of the algorithms considered, Symmetric Block Gauss-Seidel has the overall best performance. It is also demonstrated that using parallel efficiency as the sole means of evaluating performance of an algorithm often leads to erroneous conclusions; the clock time needed to solve a problem is a much better indicator of algorithm performance. A general method for extending one-dimensional limiter formulations to the unstructured case is also discussed and applied to Van Albada’s limiter as well as Roe’s Superbee limiter. Solutions and convergence histories for a two-dimensional supersonic ramp problem using these limiters are presented along with computations using the limiters of Barth & Jesperson and Venkatakrishnan — the Van Albada limiter has performance similar to Venkatakrishnan’s. / Ph. D.

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.

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.

<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.

Master of Science / Department of Mechanical and Nuclear Engineering / Steven Eckels and Mohammad Hosni / This research presents results from experimental and numerical investigations of two-phase flow pattern analysis in a staggered tube bundle. Shell-side boiling tube bundles are used in a variety of industries from nuclear power plants to industrial evaporators. Fluid flow patterns in tube bundles affect pressure drop, boiling characteristics, and tube vibration. R-134a was the working fluid in both the experimental and computational fluid dynamics (CFD) analysis for this research. Smooth and enhanced staggered tube bundles were studied experimentally using a 1.167 pitch to diameter ratio. The experimental tube bundles and CFD geometry consist of 20 tubes with five tubes per pass. High speed video was recorded during the experimental bundle boiling. Bundle conditions ranged in mass fluxes from 10-35 kg/m[superscript]2.s and inlet qualities from 0-70% with a fixed heat flux. Classification of the flow patterns from these videos was performed using flow pattern definitions from literature. Examples of smooth and enhanced bundle boiling high speed videos are given through still images. The flow patterns are plotted and compared with an existing flow pattern map. Good agreement was found for the enhanced tube bundle while large discrepancies exist for the smooth tube bundle. The CFD simulations were performed without heat transfer with non-symmetrical boundary conditions at the side walls, simulating rectangular bundles used in this and other research. The two-phase volume of fluid method was used to construct vapor interfaces and measure vapor volume fraction. A probability density function technique was applied to the results to determine flow patterns from the simulations using statistical parameters. Flow patterns were plotted on an adiabatic flow pattern map from literature and excellent agreement is found between the two. The agreement between simulation results and experimental data from literature emphasizes the use of numerical techniques for tube bundle design.