<div>Quantifying the dynamics and rheology of soft biological suspensions such as red blood cells, vesicles, or capsules is paramount to many biomedical and computational applications. These systems are multiphase flows that can contain a diverse set of deformable cells and rigid bodies with complex wall geometries. For this thesis, we are performing several numerical simulations using boundary element methods (BEM) for biological suspensions in biomedically relevant conditions. Each simulation is devised to answer fundamental questions in modeling these systems.</div><div><br></div><div><br></div><div>Part of this thesis centers around the fluid mechanics of giant unilamellar vesicles (GUVs), fluid droplets surrounded by a phospholipid bilayer. GUVs are important to study because they mimic the dynamics of anuclear cells and are commonly used as a basis for artificial cells. The dynamics of vesicles in simple shear or extensional flows have been extensively studied. However the conditions seen in microfluidic devices or industrial processing are not always described by steady shear or extensional flows alone, and require more investigation. In our first study, we investigate the shape stability of osmotically deflated vesicles in a general linear flow (i.e., linear combinations of extensional and rotational flows). We modeled the vesicles as a droplet with an incompressible interface with a bending resistance. We simulated a range of flow types from purely shear to purely extensional at viscosity ratios ranging from 0.01 to 5.0 and reduced volumes (measured asphericity, higher is more spherical) from 0.60 to 0.70. The vesicle's viscosity ratio appears to play a minimal role in describing its shape and stability for many mixed flows, even in cases when significant flows are present in the vesicle interior. We find in these cases that the bending critical capillary number for shape instabilities collapse onto similar values if the capillary number is scaled by an effective extensional rate. These results contrast with droplet studies where both viscosity ratio and flow type have significant effects on breakup. Our simulations suggest that if the flow type is not close to pure shear flow, one can accurately quantify the shape and stability of vesicles using the results from an equiviscous vesicle in pure extension. Only when the flow type is nearly shear flow, do we start to see deviations in the observations discussed above. In this situation, the vesicle's stationary shape develops a shape deviation, which introduces a stabilizing effect and makes the critical capillary number depend on the viscosity ratio.</div><div><br></div><div><br></div><div>Continuing with our research on single vesicle dynamics, we have performed simulations and experiments on vesicles in large amplitude oscillatory extensional (LAOE) flows. By using LAOE we can probe the non-linear extension and compression of vesicles and how these types of deformation affect dilute suspension microstructure in time-dependent flows through contractions, expansions, or other complex geometries. Our numerical and experimental results for vesicles of reduced volumes from 0.80 to 0.95 have shown there to be three general dynamical regimes differentiated by the amount of deformation that occurs in each half cycle. We have termed the regimes: symmetrical, reorienting, and pulsating in reference to the type of deformation that occurs. We find the deformation of the quasispherical vesicles in the microfluidic experiments and boundary element simulations to be in quantitative agreement. The distinct dynamics observed in each regime result from a competition between the flow frequency, flow time scale, and membrane deformation timescale. Using the numerical results, we calculate the particle coefficient of stresslet and quantify the nonlinear relationship between average vesicle stress and strain rate. We additionally present some results on the dynamics of tubular vesicles in LAOE, showing how the experiments suggest the vesicles undergo a shape transformation over several strain rate cycles. Broadly, our work provides new information regarding the transient dynamics of vesicles in time-dependent flows that directly informs bulk suspension rheology.</div><div><br></div><div><br></div><div>Our most recent project deals with the accuracy of discretized double layer integrals for Stokes flow in the boundary element method.</div><div>In the fluid mechanics literature, the chosen parameterization, meshing procedure, and singularity handling are often selected arbitrarily or based on a convergence study where the number of elements is decreased until the relative error is sufficiently low.</div><div>A practical study on the importance of each of these parameters to the accurate calculation of physically relevant results, such as the particle stresslet, could alleviate some of the guesswork required. The analytical formulas for the eigenfunctions/eigenvalues of the double layer operator of an ellipsoidal particle in a quadratic flow were recently published¹, providing an analytical basis for testing boundary element method discretization accuracy.</div><div>We use these solutions to examine the local and global errors produced by changing the interpolation order of the geometry and the double-layer density. The results show that the local errors can be significant even when the global errors are small, prompting additional study on the distribution of local errors. Interestingly, we find that increasing the interpolation orders for the geometry and the double layer density does not always guarantee smaller errors. Depending on the nature of the meshing near high curvature regions, the number of high aspect ratio elements, and the flatness of the particle geometry, a piecewise-constant density can exhibit lower errors than piecewise-linear density, and there can be little benefit from using curved triangular elements. Overall, this study provides practical insights on how to appropriately discretize and parameterize three-dimensional (3D) boundary-element simulations for elongated particles with prolate-like and oblate-like geometries.</div><div><br></div>

<p>The objective of this work is to provide a computational baseline for modelling the flow physics in the tip region of a transonic fan. A transonic fan was donated by Honeywell Aerospace to the Purdue University High-Speed Compressor Research Laboratory for the purposes of studying casing treatments and inlet distortion under the Office of Naval Research Power and Propulsion Program. The purpose of casing treatment is to extend the stall margin of the fan without being detrimental to fan efficiency. Hence, before an effective casing treatment can be designed, understanding the instabilities that lead to stall or surge and understanding the flow field near the rotor tip at different operating conditions is necessary. </p> <p>The behavior of the flow field was studied at design speed using steady simulations for near stall, peak efficiency, and choke operating conditions. The details of the passage shock, tip leakage vortex, and the shock-vortex interaction were investigated. The passage shock moves forward in the rotor passage as the loading increases, until eventually becoming unstarted near stall. The tip leakage vortex convects from the rotor tip leading edge to the pressure side of the adjacent blade, and its trajectory becomes parallel to the rotor inlet plane as the loading increases. The shock-vortex interaction does not cause the tip leakage vortex to breakdown, although distortion of the shock front and diffusion of the tip leakage vortex is significant near stall.</p> <p>To validate this computational model, steady simulations were used to conduct a grid convergence study. A single passage mesh of 8 million elements is sufficient to capture the flow qualitatively, but a mesh of at least 22 million elements is recommended to lower discretization error if quantitative details are important. A brief comparison of turbulence models is made, and the SST model was found to predict stronger radial flows than the BSL-EARSM and BSL-RSM models. However, the SST model still captures the flow features qualitatively, and the more complex models would be too costly for iterative design simulations.</p> <p>The importance of unsteady effects was also considered for a point near peak efficiency. Near peak efficiency, the effect of shock oscillations near the rotor shroud are small. Compared to steady simulations, the unsteady simulation predicts a slightly stronger horseshoe vortex at the hub and a passage shock closer to the rotor leading edge. The tip leakage vortex trajectory appears to be the same between the steady and unsteady simulations.</p> <p>The modelling decisions made in this research are currently only based on comparison between simulations. This model will be calibrated with experimental data in the future to provide a more accurate view of the flow physics inside this transonic fan.</p>

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This analysis calculates the velocity profile and recirculation ratio in the aspirator region of an enhanced once-through steam generator of the Babcock & Wilcox design. This information is important to the development of accurate RELAP5 models, steam generator level calculations, steam generator downcomer models, and flow induced vibration analyses. The OpenFOAM CFD software package was used to develop the three-dimensional model of the EOTSG aspirator region, perform the calculations, and post-process the results. Through a series of cases, each improving upon the modeling accuracy of the previous, insight is gained into the importance of various modeling considerations, as well as the thermal-hydraulic behavior in the steam generator downcomer. Modeling the tube support plates and tube nest is important for the accurate prediction of flow rates above and below the aspirator port, but has little affect on the aspirator region itself. Modeling the MFW nozzle has minimal influence on the incoming steam velocity, but does create a slight azimuthal asymmetry and alter the flow pattern in the downcomer, creating recirculation patterns important to inter-phase heat transfer. Through the development of a two-phase solution that couples the aspirated steam and liquid feedwater, it was found that the ratio of droplet surface area to volume plays the most important role in determining the rate of aspiration. Calculations of the velocity profile and recirculation ratio are compared against those of historical calculations, demonstrating the possibility that these parameters were previously underpredicted. Such a conclusion can only be confidently made once experimental data is made available to validate the results of this analysis. / Master of Science

Traditional methods of closing the Boussinesq-based Reynolds-averaged Navier-Stokes equations are considered, and suggestions for improving two-equation turbulence models are made. The traditional smooth-wall boundary conditions are shown to be incorrect, and the correct boundary conditions are provided along with sample solutions to traditional models. The correct boundary condition at a smooth wall for dissipation-based turbulence models is that which forces both the turbulent kinetic energy and its first derivative to zero. Foundations for an energy-vorticity model suggested by Phillips are presented along with the near-smooth-wall behavior of the model. These results show that at a perfectly smooth wall, the turbulent kinetic energy may approach the wall at a higher order than is generally accepted. The foundations of this model are used in the development of a k-λ model for fully rough pipe flow. Closure coefficients for the model are developed through gradient-based optimization techniques. Results of the model are compared to results from the Wilcox 1998 and 2006 k-ω models as well as four eddy-viscosity models. The results show that the Phillips k-λ model is much more accurate than other models for predicting the relationship between Reynolds number and friction factor for fully rough pipe flow. However, the velocity profiles resulting from the model deviate noticeably from the law of the wall.

Indiana University-Purdue University Indianapolis (IUPUI) / While computed tomographic angiography (CTA) has emerged as a powerful noninvasive option that allows for direct visualization of arterial stenosis(AS), it cant assess the hemodynamic abnormality caused by an AS. Alternatively, trans-stenotic pressure gradient (TSPG) and fractional flow reserve (FFR) are well-validated hemodynamic indices to assess the ischemic severity of an AS. However, they have significant restriction in practice due to invasiveness and high cost. To fill the gap, a new computational modality, called InVascular has been developed for non-invasive quantification TSPG and/or FFR based on patient's CTA, aiming to quantify the hemodynamic abnormality of the stenosis and help to assess the therapeutic/surgical benefits of treatment for the patient. Such a new capability gives rise to a potential of computation aided diagnostics and therapeutics in a patient-specific environment for ASs, which is expected to contribute to precision planning for cardiovascular disease treatment. InVascular integrates a computational modeling of diseases arteries based on CTA and Doppler ultrasonography data, with cutting-edge Graphic Processing Unit (GPU) parallel-computing technology. Revolutionary fast computing speed enables noninvasive quantification of TSPG and/or FFR for an AS within a clinic permissible time frame. In this work, we focus on the implementation of inlet and outlet boundary condition (BC) based on physiological image date and and 3-element Windkessel model as well as lumped parameter network in volumetric lattice Boltzmann method. The application study in real human coronary and renal arterial system demonstrates the reliability of the in vivo pressure quantification through the comparisons of pressure waves between noninvasive computational and invasive measurement. In addition, parametrization of worsening renal arterial stenosis (RAS) and coronary arterial stenosis (CAS) characterized by volumetric lumen reduction (S) enables establishing the correlation between TSPG/FFR and S, from which the ischemic severity of the AS (mild, moderate, or severe) can be identified. In this study, we quantify TSPG and/or FFR for five patient cases with visualized stenosis in coronary and renal arteries and compare the non-invasive computational results with invasive measurement through catheterization. The ischemic severity of each AS is predicted. The results of this study demonstrate the reliability and clinical applicability of InVascular.

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No description available.

A comprehensive survey of available numerical methods and models was performed on the open source computational fluid dynamics solver OpenFOAM version 2.0 for incompressible turbulent bluff body flows. Numerical methods are illuminated using source code for side-by-side comparison. For validation, the accuracy of flow predictions over a sphere in the subcritical regime and delta wing with sharp leading edge is assessed. Solutions show mostly good agreement with experimental data and data obtained from commercial software. A demonstration of the numerical implementation of a dynamic hybrid RANS/LES framework is also presented, including results from test studies.

When an explosive detonates above ground, air is principally the only material involved in the transmission of shock waves that can result in damage. Hydrodynamic codes that simulate these explosions use equations of state (EOSs) for modeling the behavior of air at these high-pressure, high-velocity conditions. An investigation is made into the effect that the EOS selection for air has on the calculated overpressure-time waveforms of a blast event. Specifically, the ideal gas, Doan-Nickel, and SESAME EOSs in the SHAMRC code were used to reproduce experiments conducted at the Blast Load Simulator (BLS), a large-scale shock tube operated by the U.S. Army Engineer Research and Development Center, that consisted of subjecting an instrumented rigid box at three angles of orientation inside the BLS to a blast environment. Numerical comparisons were made against experimentally-derived confidence intervals using peak values and several error metrics, and an attempt was made to rank the EOS based on performance. Issues were noted with the duration of decay from maximum pressure to negative phase that resulted in a general underprediction of the integrated impulse regardless of EOS, while the largest errors were noted for gages on faces at 45 to 90 degrees from the initial flow direction. Although no significant differences were noticed in the pressure histories from different EOSs, the ideal gas consistently ranked last in terms of the error metrics considered and simultaneously required the least CPU hours. Similarly, the Doan-Nickel EOS slightly performed better than SESAME while requiring additional wallclock time. The study showed that the Doan-Nickel and SESAME EOSs can produce blast signatures with less errors and more matches in peak pressure and impulse than the ideal gas EOS at the expense of more computational requirements.