Small-scale turbulence is a hallmark of countless natural and engineered flows. Its features are often described and modeled using the velocity gradient tensor (VGT), which is conventionally decomposed into the (symmetric) strain-rate tensor and the (antisymmetric) vorticity tensor. Although this symmetry-based decomposition has found use in areas such as vortex identification and closure modeling, it provides limited insight into local flow structure. A more refined description can be obtained by further distinguishing the normal and non-normal parts of the VGT. The resulting normality-based decomposition identifies contributions associated with normal straining (symmetric/normal), rigid rotation (antisymmetric/normal), and pure shearing (non-normal). We use this decomposition to identify flow features that are obscured by symmetry-based analyses yet have significant implications for efforts to understand and model turbulent flows.
\r\n\r\nWe first demonstrate that partitioning the strength of velocity gradients using our normality-based approach can distinguish between different regimes in various turbulent flows. In wall-bounded flows, the near-wall partitioning is dominated by shearing whereas the partitioning far from the wall collapses onto the partitioning associated with isotropic turbulence. In an unbounded vortex ring collision, our analysis distinguishes the initial vortex rings, which have a strong imprint from rigid rotation, from the decaying turbulent cloud produced by their collision, for which the partitioning is similar to that of isotropic turbulence. It also identifies enhanced shear\u2013rotation correlations as a distinctive fingerprint of the elliptic instability during transition, which can be interpreted using relevant geometric features of local streamlines. By deriving algebraic expressions for the partitioning constituents in terms of the invariants of the VGT and an additional parameter, which represents the alignment of shear vorticity with the local rotation axis, we identify a key facet of our analysis that goes beyond previous analyses of the VGT.
\r\n\r\nWe then apply our normality-based framework to filtered velocity gradients in direct and large-eddy simulations of isotropic turbulence. Our analysis enables shear layers, which are associated with shear vorticity, to be distinguished from vortex cores, which are associated with rigid rotation, in a multiscale setting. It reveals that filtering mitigates the relative contribution of shear layers in the subinertial range of the energy cascade. Moreover, it identifies crucial (yet perhaps overlooked) contributions from shear layers to fundamental energy transfer mechanisms, including strain self-amplification, vortex stretching, and backscatter associated with strain\u2013vorticity covariance. The dominant role of shear layers in the backscatter mechanism suggests that they contribute significantly to the bottleneck effect in the subinertial range of the cascade. Our analysis of large-eddy simulation data shows that they also amplify the artificial bottleneck effect produced by an eddy viscosity model in the inertial range. This reflects that the eddy viscosity model mimics an unfiltered direct numerical simulation at a lower Reynolds number. A mixed model can be used to mitigate the artificial bottleneck effect since it more accurately mimics a filtered direct numerical simulation.
", "doi": "10.7907/3py1-wj85", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:16619", "collection": "thesis", "collection_id": "16619", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:08072024-203148023", "primary_object_url": { "basename": "HeidtLiam_CaltechThesis.pdf", "content": "final", "filesize": 32563876, "license": "other", "mime_type": "application/pdf", "url": "/16619/1/HeidtLiam_CaltechThesis.pdf", "version": "v7.0.0" }, "type": "thesis", "title": "Modal Analysis of Harmonically Forced Turbulent Flows with Application to Jets", "author": [ { "family_name": "Heidt", "given_name": "Liam Frank Raven", "orcid": "0000-0003-1967-6847", "clpid": "Heidt-Liam-Frank-Raven" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909" } ], "thesis_committee": [ { "family_name": "Bae", "given_name": "H. Jane", "orcid": "0000-0001-6789-6209", "clpid": "Bae-H-J" }, { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Sader", "given_name": "John E.", "orcid": "0000-0002-7096-0627", "clpid": "Sader-J-E" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "GALCIT" }, { "literal": "div_eng" } ], "abstract": "Many turbulent flows exhibit time-periodic statistics. These include flows in turbomachinery, the wakes of bluff bodies, and flows exposed to harmonic actuation. However, many existing techniques for identifying and modeling coherent structures, most notably spectral proper orthogonal decomposition (SPOD) and resolvent analysis, assume statistical stationarity. In this thesis, we develop extensions to study turbulent flows with periodic statistics. We focus on the application of turbulent jets and jet noise reduction through harmonic actuation, which is of interest for both commercial and military aviation due to its success in reducing noise by up to 5dB.
\r\n\r\nTo analyze the coherent structures in harmonically forced flows, we develop the cyclostationary spectral proper orthogonal decomposition (CS-SPOD). We examine the resulting properties of CS-SPOD and develop a theoretical connection between CS-SPOD and harmonic resolvent analysis (HRA), thereby providing the theoretical basis for HRA to be used as a model for coherent structures of cyclostationary flows. We develop and validate a computationally efficient algorithm and then illustrate its efficacy using the linearized (complex) Ginzburg-Landau equation.
\r\n\r\nWe next employ cyclostationary analysis to investigate the impact of an axisymmetric acoustic harmonic forcing on the mean, turbulence, and coherent structures of a round turbulent jet with a Mach number of 0.4 and a Reynolds number of 450000. We perform large-eddy simulations for four cases at two forcing frequencies and amplitudes. Both low-frequency (Strouhal number of 0.3) and high-frequency (Strouhal number of 1.5) forcing is found to generate an energetic, nonlinear, tonal response consisting of the rollup of vortices via the Kelvin-Helmholtz mechanism. However, the impact of forcing on the broadband turbulence and coherent structures is limited, particularly at the low forcing amplitude associated with jet-noise-reduction devices. Additionally, the dominant coherent structures for the forced jets are similar in their energy, structure, and mechanism. At high forcing amplitudes, phase-dependent features arise in the dominant coherent structures and are associated with coupling to the high-velocity/shear regions of the mean. Overall, our results support the existing hypotheses that jet noise reduction can be associated with the deformation of the mean flow field rather than through direct interaction between the forcing and the turbulence. Lastly, we find that HRA predicts the dominant coherent structures well. This shows that HRA can be used to develop models of forced jets in a similar manner to how resolvent is employed for natural jets, which may be useful to guide future sound-source models of jets subjected to active control.
", "doi": "10.7907/e6fe-kz94", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:17083", "collection": "thesis", "collection_id": "17083", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03202025-173020131", "primary_object_url": { "basename": "Thesis_Hou.pdf", "content": "final", "filesize": 21073399, "license": "other", "mime_type": "application/pdf", "url": "/17083/1/Thesis_Hou.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Fast Algorithms for Spanwise Periodic Incompressible External Flows: From Simulation to Analysis", "author": [ { "family_name": "Hou", "given_name": "Wei", "orcid": "0000-0001-8023-6395", "clpid": "Hou-Wei" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Bae", "given_name": "H. Jane", "orcid": "0000-0001-6789-6209", "clpid": "Bae-H-J" }, { "family_name": "Sader", "given_name": "John E.", "orcid": "0000-0002-7096-0627", "clpid": "Sader-J-E" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "External flows over spanwise-homogeneous geometries are ubiquitous in science and engineering applications. In this thesis, we propose algorithms to simulate and analyze these flows using the lattice Green's function (LGF) approach. The LGF is the analytical inverse of a discrete elliptic operator that automatically incorporates exact far-field boundary conditions and minimizes computational expense by allowing snug computational regions encompassing only vortical flow regions. By combining LGFs with adaptive mesh refinement (AMR) and immersed boundary (IB) methods, we present two numerical algorithms specially designed for spanwise periodic incompressible external flows: one to directly solve the nonlinear equations of motion and one to compute stability and resolvent analyses.
\r\n\r\nFor these algorithms, the LGFs of the screened Poisson equation must be computed at runtime. To enable efficient flow simulation and analysis algorithms, we propose a fast numerical algorithm to tabulate these LGFs. We derive convergence results for the algorithms and show that they are orders of magnitude faster than existing algorithms. Armed with the LGF for the screened Poisson equation, we further develop algorithms to solve the Navier-Stokes equations and associated linearized eigenvalue problems.
\r\n\r\nWe present two applications of these algorithms. We perform simulations to validate the starting vortex theory proposed by Pullin and Sader (2021), and we perform stability analyses of flow past a rotating cylinder with a control cylinder in its wake.
", "doi": "10.7907/eygj-k325", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:16208", "collection": "thesis", "collection_id": "16208", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10162023-141935060", "primary_object_url": { "basename": "Spratt_Thesis.pdf", "content": "final", "filesize": 28877365, "license": "other", "mime_type": "application/pdf", "url": "/16208/1/Spratt_Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Numerical Simulations of Cavitating Bubbles in Elastic and Viscoelastic Materials for Biomedical Applications", "author": [ { "family_name": "Spratt", "given_name": "Jean-S\u00e9bastien Alexandre", "orcid": "0000-0002-1962-4214", "clpid": "Spratt-Jean-S\u00e9bastien-Alexandre" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Meiron", "given_name": "Daniel I.", "orcid": "0000-0003-0397-3775", "clpid": "Meiron-D-I" }, { "family_name": "Dabiri", "given_name": "John O.", "orcid": "0000-0002-6722-9008", "clpid": "Dabiri-J-O" }, { "family_name": "Austin", "given_name": "Joanna M.", "orcid": "0000-0003-3129-5035", "clpid": "Austin-J-M" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The interactions of cavitating bubbles with elastic and viscoelastic materials play a central role in many biomedical applications. This thesis makes use of numerical modeling and data-driven approaches to characterize soft biomaterials at high strain rates via observation of bubble dynamics, and to model burst-wave lithotripsy, a focused ultrasound therapy to break kidney stones.
\r\n\r\nIn the first part of the thesis, a data assimilation framework is developed for cavitation rheometry, a technique that uses bubble dynamics to characterize soft, viscoelastic materials at high strain-rates. This framework aims to determine material properties that best fit observed cavitating bubble dynamics. We propose ensemble-based data assimilation methods to solve this inverse problem. This approach is validated with surrogate data generated by adding random noise to simulated bubble radius time histories, and we show that we can confidently and efficiently estimate parameters of interest within 5% given an iterative Kalman smoother approach and an ensemble- based 4D-Var hybrid technique. The developed framework is applied to experimental data in three distinct settings, with varying bubble nucleation methods, cavitation media, and using different material constitutive models. We demonstrate that the mechanical properties of gels used in each experiment can be estimated quickly and accurately despite experimental inconsistencies, model error, and noisy data. The framework is used to further our understanding of the underlying physics and identify limitations of our bubble dynamics model for violent bubble collapse.
\r\n\r\nIn the second part of the thesis, we simulate burst-wave lithotripsy (BWL), a non- invasive treatment for kidney stones that relies on repeated short bursts of focused ultrasound. Numerical approaches to study BWL require simulation of acoustic waves interacting with solid stones as well as bubble clouds which can nucleate ahead of the stone. We implement and validate a hypoelastic material model, which, with the addition of a continuum damage model and calibration of a spherically- focused transducer array, enables us to determine how effective various treatment strategies are with arbitrary stones. We present a preliminary investigation of the bubble dynamics occurring during treatment, and their impact on damage to the stone. Finally, we propose a strategy to reduce shielding by collapsing bubbles ahead of the stone via introduction of a secondary, low-frequency ultrasound pulse during treatment.
", "doi": "10.7907/g34e-6p65", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:15083", "collection": "thesis", "collection_id": "15083", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01162023-041217909", "primary_object_url": { "basename": "Kamal_thesis_final.pdf", "content": "final", "filesize": 47336253, "license": "other", "mime_type": "application/pdf", "url": "/15083/1/Kamal_thesis_final.pdf", "version": "v7.0.0" }, "type": "thesis", "title": "Optimal Receptivity and the Generalization of the One-Way Navier-Stokes (OWNS) Equations to Complex High-Speed Boundary Layers and Jets", "author": [ { "family_name": "Kamal", "given_name": "Omar", "orcid": "0000-0002-3431-2964", "clpid": "Kamal-Omar" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Austin", "given_name": "Joanna M.", "orcid": "0000-0003-3129-5035", "clpid": "Austin-J-M" }, { "family_name": "Hussain", "given_name": "Fazle", "orcid": "0000-0002-2209-9270", "clpid": "Hussain-F" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Prediction of the linear amplification of disturbances in hypersonic boundary layers is challenging due to the presence and interactions of discrete modes (e.g. Tollmien-Schlichting and Mack) and continuous modes (entropic, vortical, and acoustic). While direct numerical simulations (DNS) and global analysis can be used, the large grids required make the stability calculations expensive, particularly when a large parameter space is required. At the same time, parabolized stability equations are non-convergent and unreliable for problems involving multi-modal and non-modal interactions. We therefore apply the One-Way Navier-Stokes (OWNS) Equations to study transitional hypersonic boundary layers. OWNS is based on a rigorous, approximate parabolization of the equations of motion that removes disturbances with upstream group velocity using a higher-order recursive filter. We extend the original algorithm by considering non-orthogonal curvilinear coordinates and incorporate full compressibility with temperature-dependent fluid properties. The generalized OWNS methodology is validated by comparing to DNS data for flat plates and a sharp cone, and to linear stability theory results for local disturbances on the centerline of the Mach 6 HIFiRE-5 elliptic cone. OWNS provides DNS-quality results for the former flows at a small fraction of the computational expense. We further demonstrate the capability of OWNS to track fully 3D instabilities by applying the algorithm to a complex Mach 6 finned-cone geometry as well as a 3D Mach 1.5 turbulent jet.
\r\n\r\nIt is often desirable, especially for design purposes, to compute worst-case disturbances, i.e. solving the inverse problem, otherwise known as resolvent or input-output analysis. While DNS and global analysis can be used to compute optimal forced responses, their large computational expense render these tools less practical for large design parameter spaces. We address this issue by modifying the original OWNS framework to find the optimal forcing and responses using Lagrangian multipliers via an iterative, adjoint-based, space-marching technique that appreciably reduces the computational burden compared to the global approach that uses singular value decomposition without sacrificing accuracy. The input-output OWNS model is validated against optimal forcings and responses of a Mach 4.5 flat-plate boundary layer from literature and a Mach 1.5 turbulent jet. We then apply these equations to study worst-case disturbances on the centerline of the Mach 6 HIFiRE-5 elliptic cone and on a highly cooled Mach 6 flat-plate boundary layer.
\r\n \r\nAlthough the worst-case forcings are theoretically informative, they are not physically realizable. In natural receptivity analysis, disturbances are forced by matching local solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic, and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with DNS of a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.
", "doi": "10.7907/haet-h558", "publication_date": "2023", "thesis_type": "phd", "thesis_year": "2023" }, { "id": "thesis:14489", "collection": "thesis", "collection_id": "14489", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02062022-203334930", "primary_object_url": { "basename": "Ben_Stevens_Thesis (4).pdf", "content": "final", "filesize": 5499929, "license": "other", "mime_type": "application/pdf", "url": "/14489/1/Ben_Stevens_Thesis (4).pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Applications of Machine Learning to Finite Volume Methods", "author": [ { "family_name": "Stevens", "given_name": "Benjamin Carter", "orcid": "0000-0002-3410-5922", "clpid": "Stevens-Benjamin-Carter" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Yue", "given_name": "Yisong", "orcid": "0000-0001-9127-1989", "clpid": "Yue-Yisong" }, { "family_name": "Anandkumar", "given_name": "Anima", "orcid": "0000-0002-6974-6797", "clpid": "Anandkumar-A" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The finite volume method (FVM) has been one of the primary tools of computational fluid dynamics (CFD) for many decades. This method allows for the approximate solution of a partial differential equation (PDE) to be determined by breaking up a problem with no analytical solution into smaller pieces that can be solved together to get a physically realistic simulation. These algorithms can even be used for PDEs with discontinuous solutions, though they must be carefully designed for those situations because they cannot assume any level of smoothness in the solution. An FVM that has been designed for PDEs with discontinuous solutions is referred to as a shock-capturing method. For most of their history, FVM algorithms have been developed using rigorous mathematical arguments to formally maximize the order of convergence of the solution as the grid is refined. However, these arguments depend on the solution to the PDE being smooth, and therefore do not apply to shock-capturing methods. Instead, shock-capturing methods have traditionally been designed using human intuition to create algorithms that then perform well empirically. In this thesis, we instead follow a data-driven approach to train neural networks to use for enhanced FVM methods.
\r\n\r\nBy including a neural network in our FVM, we can use empirical data to optimize the algorithm. We can also utilize ideas from traditional FVM algorithms to create hybrid methods that have tunable parameters and maintain convergence guarantees present in FVMs that have been designed by hand. We explore these hybrid methods in a variety of settings. First, we create a general-purpose shock-capturing method WENO-NN by hybridizing the popular shock-capturing method WENO-JS with a neural network. Additionally, we develop a network architecture, called FiniteNet, that can be used to learn a coarse-graining model associated with a specific PDE and embed it into an FVM scheme. Finally, we also explore the idea of using transfer learning to further improve the WENO-NN for specific problems and name the resulting algorithm WENO-TL. We demonstrate experimentally that this hybrid approach results in methods that can offer similar error levels as traditional FVMs at less computational cost. Although the neural network increases the computational cost of one evaluation of our hybrid FVM, these methods also allow the simulation to be carried out on a coarser grid, leading to a net reduction in both simulation time and memory usage.
", "doi": "10.7907/41qn-7n22", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14377", "collection": "thesis", "collection_id": "14377", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09282021-234035965", "primary_object_url": { "basename": "LeeMarcus_Thesis.pdf", "content": "final", "filesize": 35706257, "license": "other", "mime_type": "application/pdf", "url": "/14377/1/LeeMarcus_Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Instabilities in the Flow Over a Spinning Disk at Angle of Attack", "author": [ { "family_name": "Lee", "given_name": "Marcus Kuok Kuan", "orcid": "0000-0003-3972-843X", "clpid": "Lee-Marcus-Kuok-Kuan" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "McKeon", "given_name": "Beverley J.", "orcid": "0000-0003-4220-1583", "clpid": "McKeon-B-J" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "McKeon", "given_name": "Beverley J.", "orcid": "0000-0003-4220-1583", "clpid": "McKeon-B-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Micro air vehicles (MAVs) face stability issues, especially as they continue to decrease in size. A spinning disk is inherently robust to external disturbances due to its spin stabilization, and therefore is a potential design for stable MAV flight. However, controlled flight of a spinning disk requires a detailed understanding of the underlying flow structures that determine the aerodynamic behavior. A spinning disk acts to rotate and propel nearby flow tangentially outwards, while drawing in fluid from above. In this way, spin acts as an additional source of both angular and linear momentum from the disk's surface, which can alter the wake structure significantly. In this thesis, we explore how spin affects the aerodynamic forces on a disk and characterize several instabilities that occur. To this end, we use the immersed-boundary Lattice Green's function (IBLGF) method to simulate flow over a spinning disk at angle of attack for Reynolds numbers of O(102) and tip-speed ratios (non-dimensional spin rate) up to 3.
\r\n\r\nAt these Reynolds numbers, the steady flow first undergoes a bifurcation associated with wake instability, giving rise to vortex shedding. Increasing tip-speed ratio leads to monotonic increases in both lift and drag, although the lift-to-drag ratio remains fairly constant. We also identify several distinct wake regimes, including a region of vortex-shedding suppression, and the appearance of a distinct corkscrew-like short-wavelength instability in the advancing tip vortex. To understand the mechanism leading to suppression of vortex shedding, we study the streamlines and vortex lines in the wake. We show that the vorticity produced by the spinning disk strengthens the tip vortices, inducing a spanwise flow in the trailing edge vortex sheet. This helps to dissipate the vorticity, which in turn prevents roll up and thus suppresses vortex shedding. For the short-wavelength instability, we use spectral proper orthogonal decomposition (SPOD) to identify the most energetic modes and compare it to elliptic instabilities seen in counter-rotating vortex pairs with axial flow. The addition of vorticity from the disk rotation significantly alters the circulation and axial velocity in the tip vortices, giving rise to elliptic instability despite its absence in the non-spinning case. We also observe lock-in between the frequency of the elliptic instability and twice the spin frequency, indicating that disk rotation acts as an additional forcing for the elliptic instability. Many of these phenomena are consistent with observations in high Reynolds number studies and for other bluff body geometries. As a result, the mechanisms proposed here may serve as a basis for understanding and predicting the changing wake structures in more complex flow configurations.
", "doi": "10.7907/kmhn-7e49", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14253", "collection": "thesis", "collection_id": "14253", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06072021-162542722", "primary_object_url": { "basename": "Caltech_Thesis_Ke_Yu_final.pdf", "content": "final", "filesize": 13477246, "license": "other", "mime_type": "application/pdf", "url": "/14253/1/Caltech_Thesis_Ke_Yu_final.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Multi-Resolution Lattice Green's Function Method for High Reynolds Number External Flows", "author": [ { "family_name": "Yu", "given_name": "Ke", "orcid": "0000-0003-0157-4471", "clpid": "Yu-Ke" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Pullin", "given_name": "Dale Ian", "clpid": "Pullin-D-I" }, { "family_name": "Meiron", "given_name": "Daniel I.", "orcid": "0000-0003-0397-3775", "clpid": "Meiron-D-I" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This work expands the state-of-the-art computational fluid dynamics (CFD) methods for simulating three-dimensional, turbulent, external flows by further developing the immersed boundary (IB) Lattice Green's function (LGF) method. \r\nThe original IB-LGF method applies an exact far-field boundary condition using fundamental solutions on regular Cartesian grids and allows active computational cells to be restricted to vortical flow regions in an adaptive fashion as the flow evolves. The combination of spatial adaptivity and regular Cartesian structure leads to superior efficiency, scalability, and robustness, but necessitates uniform grid spacing. However, the scale separation associated with thin boundary layers and turbulence at higher Reynolds numbers favors a more flexible distribution of elements/cells, which is achieved in this thesis by developing a multi-resolution LGF approach that permits block-wise grid refinement while maintaining the important properties of the original scheme. We further show that the multi-resolution LGF method can be fruitfully combined with the IB method to simulate external flows around complex geometries at high Reynolds numbers. This novel multi-resolution IB-LGF scheme retains good efficiency, parallel scaling as well as robustness (conservation and stability properties). DNS of bluff and streamlined bodies at Reynolds numbers O(104) are conducted and the new multi-resolution scheme is shown to reduce the total number of computational cells up to 99.87%.
\r\n\r\nWe also extended this method to large-eddy simulation (LES) with the stretched-vortex sub-grid-scale model. In validating the LES implementation, we considered an isolated spherical region of turbulence in free space. The initial condition is spherically windowed, isotropic homogeneous incompressible turbulence. We study the spectrum and statistics of the decaying turbulence and compare the results with decaying isotropic turbulence, including cases representing different low wavenumber behavior of the energy spectrum (i.e. k2 versus k4). At late times the turbulent sphere expands with both mean radius and integral scale showing similar time-wise growth exponents. The low wavenumber behavior has little effect on the inertial scales, and we find that decay rates follow Saffman's predictions in both cases, at least until about 400 initial eddy turnover times. The boundary of the spherical region develops intermittency and features ejections of vortex rings. These are shown to occur at the integral scale of the initial turbulence field and are hypothesized to occur due to a local imbalance of impulse on this scale.
", "doi": "10.7907/wkc8-se35", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:14097", "collection": "thesis", "collection_id": "14097", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03022021-005902351", "type": "thesis", "title": "Resolvent Modeling of Turbulent Jets", "author": [ { "family_name": "Pickering", "given_name": "Ethan Marcus", "orcid": "0000-0002-4485-6359", "clpid": "Pickering-Ethan-Marcus" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "McKeon", "given_name": "Beverley J.", "orcid": "0000-0003-4220-1583", "clpid": "McKeon-B-J" }, { "family_name": "Dabiri", "given_name": "John O.", "orcid": "0000-0002-6722-9008", "clpid": "Dabiri-J-O" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Optimal control of turbulent flows requires a detailed prediction of the unsteady, three-dimensional turbulent structures that govern quantities of interest like noise, drag, and mixing efficiency. There is a need for physics-based, reduced-order models of turbulent structure for those cases where direct simulation of the flow would be computationally prohibitive. In this thesis, we explore resolvent analysis as a framework for such models. Based on a linearization about the turbulent mean flow field, the resolvent finds optimal (highest gain) forcing functions that give rise, through linear amplification mechanisms, to energetic coherent structures. The forcing functions represent the nonlinear interactions between the coherent structures as well as with background incoherent turbulence. While the high-gain structures capture many characteristics of the observed turbulent coherent structures in both wall-bounded and free-shear flows, closures for the forcing function are required to make these models predictive and thus utilize them for flow control.
\r\n\r\nIn the first part of this thesis, we examine a linear model for the resolvent forcing by adapting the concept of a turbulent (eddy) viscosity from classical Reynolds-Averaged Navier--Stokes (RANS) turbulence modeling. We present a data-driven approach to identify an optimal eddy-viscosity field that best matches the resolvent prediction to the most energetic coherent structure educed via spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We analyze the specific case of turbulent jets spanning a range of Mach numbers from subsonic to supersonic. We find the optimal eddy-viscosity field to be effective at matching both the shape and energy distribution of structures. More importantly, we find that calibrated eddy-viscosity fields predicted using standard eddy-viscosity models (utilizing only quantities available from RANS) yield results that are close to optimal.
\r\n\r\nWe use the resulting resolvent model together with the high-fidelity data to investigate the full spectrum of amplification mechanisms and coherent structures present in turbulent jets. The addition of a turbulence model provides a clear separation between two established mechanisms in turbulent jets (Kelvin-Helmholtz and Orr) and leads to the identification of a third mechanism known as lift-up. Lift-up becomes the dominant mechanism at low-frequency limits for nonzero azimuthal wavenumbers, generating elongated, streaky structures. We find these streaks to be the most energetic structures in the jet, and that their presence has implications for altering the mean flow and controlling noise.
\r\n\r\nFinally, we extend resolvent analysis to that of an acoustic analogy that relates the near-field forcing to the far-field acoustics 100 diameters from the nozzle. We again leverage high-fidelity data to produce an ensemble of realizations of the acoustic field and find that only a few resolvent modes are necessary for reconstruction. Ultimately, we find that a resolvent model based solely upon RANS quantities can reconstruct and predict the peak acoustic field at rank-1 to within 2 decibels for both the supersonic and transonic jets.
", "doi": "10.7907/szxb-f168", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:11181", "collection": "thesis", "collection_id": "11181", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09122018-201219035", "primary_object_url": { "basename": "Tosi_2018_Thesis.pdf", "content": "final", "filesize": 22012966, "license": "other", "mime_type": "application/pdf", "url": "/11181/1/Tosi_2018_Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Fluid-Structure Instability in an Internal Flow Energy Harvester", "author": [ { "family_name": "Tosi", "given_name": "Lu\u00eds Phillipe Costa Ferreira", "orcid": "0000-0002-0819-4765", "clpid": "Tosi-Lu\u00eds-Phillipe-Costa-Ferreira" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" }, { "family_name": "Hall", "given_name": "Jeffery", "orcid": "0000-0002-8835-2830", "clpid": "Hall-J-L" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Access to reliable power sources in remote locations is a recurring engineering challenge for both large and small applications. The developing world struggles with power connectivity in remote villages, while sensor networks strain with power limitations of batteries or short-lived turbines. Energy harvesting based on fluid-induced vibration provides a potential robust alternative for in-situ power generation, furnishing means for a decades long supply of power. Yet, one of the main challenges in the design of flow energy harvesters is understanding the mechanisms that drive their motion. Fluid-structure interaction problems often span a large parametric space and require considerable computational resources to resolve the necessary dynamic details for reliable designs.
\r\n\r\nThis thesis aims to address this challenge for a piezoelectric internal flow energy harvester developed in conjunction with NASA Jet Propulsion Laboratory for in-well, deepwater sensor and actuator systems. Through exploratory experimentation, a configuration consisting of a piezoelectric beam within a converging-diverging channel in axial flow generated considerable power at moderate flow velocities when compared to other devices of the same size. The current device, though adapted to a more robust configuration based on flextensional actuators, still maintains the same fluid-structure interaction: the instability that ensues forces the system into self-sustained oscillations that produces consistent power output for flow rates above a critical threshold.
\r\n\r\nTo understand and quantify this behavior, we develop an analytical framework based on a leakage-flow type instability, which curtails the shortcomings of expensive numerical simulations once verified. The formulation consists of a quasi one-dimensional simplification of coupled fluid-structure equations, which are linearized for classical stability analysis. The stability boundary and critical property predictions are verified through a set of fully coupled fluid-structure immersed boundary direct numerical simulations. Experiments are carried out in tandem to quantify the dynamics of the harvester, specifically targeting the critical flow rate threshold. The analytical framework is expanded to include flow in the spanwise direction of the beam, and results to a simplified geometry of the harvester compared with those from experiments. Agreement between predicted critical values suggest that leakage-flow may be the principal mechanism for fluid-induced vibration within our device. The model can serve as the foundation of initial exploration of design parameters, and perhaps more powerful devices in future endeavors.
", "doi": "10.7907/Y0KG-Y197", "publication_date": "2019", "thesis_type": "phd", "thesis_year": "2019" }, { "id": "thesis:11176", "collection": "thesis", "collection_id": "11176", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09072018-105527896", "type": "thesis", "title": "An EnKF-Based Flow State Estimator for Aerodynamic Problems", "author": [ { "family_name": "da Silva", "given_name": "Andre Fernando de Castro", "orcid": "0000-0002-8125-6010", "clpid": "da-Silva-Andre-Fernando-de-Castro" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "McKeon", "given_name": "Beverley J.", "orcid": "0000-0003-4220-1583", "clpid": "McKeon-B-J" }, { "family_name": "Stuart", "given_name": "Andrew M.", "orcid": "0000-0001-9091-7266", "clpid": "Stuart-A-M" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Regardless of the plant model, robust flow estimation based on limited measurements remains a major challenge in successful flow control applications. Aiming to combine the robustness of a high-dimensional representation of the dynamics with the cost efficiency of a low-order approximation of the state covariance matrix, a flow state estimator based on the Ensemble Kalman Filter (EnKF) is applied to two-dimensional flow past a cylinder and an airfoil at high angle of attack and low Reynolds number. For development purposes, we use the numerical algorithm as both the estimator and as a surrogate for the measurements. In a perfect-model framework, a reduced number of either pressure sensors on the surface of the body or sparsely placed velocity probes in the wake are sufficient to accurately estimate the instantaneous flow state. Because the dynamics of these flows are restricted to a low-dimensional manifold of the state space, a small ensemble size is sufficient to yield the correct asymptotic behavior. The relative importance of each sensor location is evaluated by analyzing how they influence the estimated flow field, and optimal locations for pressure sensors are determined.
\r\n\r\nHowever, model inaccuracies are ubiquitous in practical applications. Covariance inflation is used to enhance the estimator performance in the presence of unmodeled freestream perturbations. A combination of parametric modeling and augmented state methodology is used to successfully estimate the forces on immersed bodies subjected to deterministic and random gusts. The robustness of high-dimensional representation of the dynamics to the choice of parameters such as the Reynolds number is inherited by the estimator, which was shown to successfully estimate the reference Reynolds number on the fly. Spatial and temporal discretization can constitute a second source of errors which can render numerical solutions a biased representation of reality. Left unaccounted for, biased forecast and observation models can lead to poor estimator performance. In this work, we propose a low-rank representation for the bias whose dynamics are represented by a colored-noise process. System state and bias parameters are simultaneously tracked online with the Ensemble Kalman Filter (EnKF) algorithm. The proposed methodology is demonstrated to achieve a 70% error reduction for the problem of estimating the state of the two-dimensional low-Re flow past a flat plate at high angle of attack using an ensemble of coarse-mesh simulations and pressure measurements at the surface of the body, compared to a bias-blind estimator. Strategies to determine the bias statistics and to deal with nonlinear observation functions in the context of ensemble methods are discussed.
", "doi": "10.7907/W327-VF41", "publication_date": "2019", "thesis_type": "phd", "thesis_year": "2019" }, { "id": "thesis:11007", "collection": "thesis", "collection_id": "11007", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06012018-165819361", "primary_object_url": { "basename": "thesis_maeda.pdf", "content": "final", "filesize": 16816964, "license": "other", "mime_type": "application/pdf", "url": "/11007/1/thesis_maeda.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Simulation, Experiments, and Modeling of Cloud Cavitation with Application to Burst Wave Lithotripsy", "author": [ { "family_name": "Maeda", "given_name": "Kazuki", "orcid": "0000-0002-5729-6194", "clpid": "Maeda-Kazuki" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Brady", "given_name": "John F.", "orcid": "0000-0001-5817-9128", "clpid": "Brady-J-F" }, { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Shapiro", "given_name": "Mikhail G.", "orcid": "0000-0002-0291-4215", "clpid": "Shapiro-M-G" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Modeling, numerical simulations, and experiments are used to investigate the dynamics of cavitation bubble clouds induced by strong ultrasound waves.
\r\n\r\nA major application of this work is burst wave lithotripsy (BWL), recently proposed method of lithotripsy that uses pulses (typically 10 wavelengths each) of highintensity, focused ultrasound at a frequency of O(100) kHz and an amplitude of O(1) MPa to break kidney stones. BWL is an alternative to standard shockwave lithotripsy (SWL), which uses much higher amplitude shock waves delivered at a typically much lower rate. In both SWL and BWL, the tensile component of the pressure can nucleate cavitation bubbles in the human body. For SWL, cavitation is a significant mechanism in stone communition, but also causes tissue injury. By contrast, little is yet known about cavitation in BWL.
\r\n\r\nTo investigate cloud cavitation in BWL, two numerical tools are developed: a model of ultrasound generation from a medical transducer, and a method of simulating clouds of cavitation bubbles in the focal region of the ultrasound. The numerical tools enable simulation of the cavitation growth and collapse of individual bubbles, their mutual interactions, and the resulting bubble-scattered acoustics. The numerics are implemented in a massively parallel framework to enable large-scale, three-dimensional simulations. Next, the numerical tools are applied to bubble clouds associated with BWL. Additionally, laboratory experiments are conducted in vitro in order to calibrate and validate the simulations. A major feature of the resulting bubble clouds is that the cloud size is similar to the ultrasound wavelength. This results in an anisotropic structure where the bubbles closest to the wave source grow to larger size and oscillate more rapidly. A new scaling parameter is introduced to characterize the nonlinear bubble cloud dynamics that generalizes the cloud interaction parameter of d'Agostino and Brennen (1989) defined for weak (linearized), bubble cloud dynamics excited uniformly by long-wavelength pressure waves. The mechanisms leading to the observed bubble dynamics are identified. The results further show that bubble clouds can scatter a large portion of incident ultrasound and consequently shield distal regions, including kidney stones, from irradiation. This energy shielding is quantified, and the simulations show that even a thin layer of bubbles can scatter up to 90% of the incident wave energy. A strong correlation is identified between the magnitude of energy shielding and the amplitude of the bubble-scattered acoustics. The correlation may be of use to control cavitation in the human body in real time by ultrasound monitoring for better outcomes of BWL.
", "doi": "10.7907/N7JK-F529", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10509", "collection": "thesis", "collection_id": "10509", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10122017-095438989", "primary_object_url": { "basename": "goza_andres_2017.pdf", "content": "final", "filesize": 16239607, "license": "other", "mime_type": "application/pdf", "url": "/10509/1/goza_andres_2017.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Numerical Methods for Fluid-Structure Interaction, and their Application to Flag Flapping", "author": [ { "family_name": "Goza", "given_name": "Andres Jared", "clpid": "Goza-Andres-Jared" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Sader", "given_name": "John E.", "orcid": "0000-0002-7096-0627", "clpid": "Sader-J-E" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis is divided into two parts. Part I is devoted to the development of numerical techniques for simulating fluid-structure interaction (FSI) systems and for educing important physical mechanisms that drive these systems\u2019 behavior; part II discusses the application of many of these techniques to investigate a specific FSI system.
\r\n\r\nWithin part I, we first describe a procedure for accurately computing the stresses on an immersed surface using the immersed-boundary method. This is a key step to simulating FSI problems, as the surface stresses simultaneously dictate the motion of the structure and enforce the no-slip boundary condition on the fluid. At the same time, accurate stress computations are also important for applications involving rigid bodies that are either stationary or moving with prescribed kinematics (e.g., characterizing the performance of wings and aerodynamic bodies in unsteady flows or understanding and controlling flow separation around bluff bodies). Thus, the method is first formulated for the rigid-body prescribed-kinematics case. The procedure described therein is subsequently incorporated into an immersed boundary method for efficiently simulating FSI problems involving arbitrarily large structural motions and rotations.
\r\n\r\nWhile these techniques can be used to perform high-fidelity simulations of FSI systems, the resulting data often involves a range of spatial and temporal scales in both the structure and the fluid and are thus typically difficult to interpret directly. The remainder of part I is therefore devoted to extending tools regularly used for understanding complex flows to FSI systems. We focus in particular on the application of global linear stability analysis and snapshot-based data analysis (such as dynamic mode decomposition and proper orthogonal decomposition) to FSI problems. To our knowledge, these techniques had not been applied to deforming-body problems in a manner that that accounts for both the fluid and structure leading up to this work.
\r\n\r\nThroughout part I, our methods are derived in the context of fairly general FSI systems and are validated using results from the literature for flapping flags in both the conventional configuration (in which the flag is pinned or clamped at its leading edge with respect to the oncoming flow) and the inverted configuration (in which the flag is clamped at its trailing edge). In part II, we apply many of the techniques developed in part I to uncover new physical mechanisms about inverted-flag flapping. We identify the instability-driving mechanism responsible for the initiation of flapping and further characterize the large-amplitude and chaotic flapping regimes that the system undergoes for a range of physical parameters.
", "doi": "10.7907/Z95T3HPB", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:9658", "collection": "thesis", "collection_id": "9658", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04062016-223108239", "primary_object_url": { "basename": "liska_sebastian_2016_thesis.pdf", "content": "final", "filesize": 15551488, "license": "other", "mime_type": "application/pdf", "url": "/9658/1/liska_sebastian_2016_thesis.pdf", "version": "v7.0.0" }, "type": "thesis", "title": "Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains", "author": [ { "family_name": "Liska", "given_name": "Sebastian", "orcid": "0000-0003-4139-9364", "clpid": "Liska-Sebastian" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Meiron", "given_name": "Daniel I.", "orcid": "0000-0003-0397-3775", "clpid": "Meiron-D-I" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" } ], "local_group": [ { "literal": "GALCIT" }, { "literal": "div_eng" } ], "abstract": "In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green\u2019s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green\u2019s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.", "doi": "10.7907/Z9ZC80TG", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9361", "collection": "thesis", "collection_id": "9361", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01062016-163653523", "type": "thesis", "title": "Advancements in Jet Turbulence and Noise Modeling: Accurate One-Way Solutions and Empirical Evaluation of the Nonlinear Forcing of Wavepackets", "author": [ { "family_name": "Towne", "given_name": "Aaron S.", "orcid": "0000-0002-7315-5375", "clpid": "Towne-Aaron-S" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "McKeon", "given_name": "Beverley J.", "orcid": "0000-0003-4220-1583", "clpid": "McKeon-B-J" }, { "family_name": "Hussain", "given_name": "Fazle", "orcid": "0000-0002-2209-9270", "clpid": "Hussain-F" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.", "doi": "10.7907/Z99884XJ", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9764", "collection": "thesis", "collection_id": "9764", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05262016-092840941", "primary_object_url": { "basename": "JCMeng_Thesis_Final.pdf", "content": "final", "filesize": 98083728, "license": "other", "mime_type": "application/pdf", "url": "/9764/1/JCMeng_Thesis_Final.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Numerical Simulations of Droplet Aerobreakup", "author": [ { "family_name": "Meng", "given_name": "Jomela Chen-Chen", "clpid": "Meng-Jomela-Chen-Chen" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Shepherd", "given_name": "Joseph E.", "orcid": "0000-0003-3181-9310", "clpid": "Shepherd-J-E" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Austin", "given_name": "Joanna M.", "orcid": "0000-0003-3129-5035", "clpid": "Austin-J-M" } ], "local_group": [ { "literal": "GALCIT" }, { "literal": "div_eng" } ], "abstract": "The work presented in this thesis aims to bridge an existing gap in the state of droplet aerobreakup knowledge associated with the fundamental flow physics that govern the experimentally observable droplet morphologies. Using direct numerical simulations of the aerobreakup of water cylinders and droplets in the flow behind shock waves in air, we investigate the behavior of the surrounding gas flow to gain insight into the droplet\u2019s deformation and evolution in the stripping breakup regime. The compressible multicomponent Navier-Stokes equations are solved using the Multicomponent Flow Code \u2014 a high-order accurate structured finite-volume flow solver with shock- and interface-capturing. Following qualitative descriptions of the aerobreakup process, comparisons are made with available experimental data. In 2D, accurate measurements of the cylinder\u2019s center-of-mass acceleration across a range of incident shock Mach numbers allow characterization of the unsteady drag coefficient. Additionally, mass loss measurements from viscous simulations refute a well-known boundary layer stripping theory. The results of a 3D nonaxisymmetric aerobreakup simulation are presented with an emphasis on describing the intricate flow phenomena observable in the wake region. Subsequent analyses of the surface instabilities and a Fourier decomposition of the flow field reveal asymmetrical azimuthal modulations and broadband instability growth that result in the devolution of the wake region into chaotic flow.", "doi": "10.7907/Z9KW5D09", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9796", "collection": "thesis", "collection_id": "9796", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05272016-150613633", "primary_object_url": { "basename": "Hsieh-Chen_Tsai_thesis_2016_final.pdf", "content": "final", "filesize": 13168932, "license": "other", "mime_type": "application/pdf", "url": "/9796/1/Hsieh-Chen_Tsai_thesis_2016_final.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Numerical Investigation of Vertical-Axis Wind Turbines at Low Reynolds Number", "author": [ { "family_name": "Tsai", "given_name": "Hsieh-Chen", "clpid": "Tsai-Hsieh-Chen" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "McKeon", "given_name": "Beverley J.", "orcid": "0000-0003-4220-1583", "clpid": "McKeon-B-J" }, { "family_name": "Dabiri", "given_name": "John O.", "orcid": "0000-0002-6722-9008", "clpid": "Dabiri-J-O" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis is aimed at numerically investigating the aerodynamics and the starting of a vertical-axis wind turbine at low Reynolds number using the immersed boundary method. The influence of the Coriolis effect on dynamic stall is isolated by comparing the rotating airfoil to one undergoing an equivalent planar motion that is composed of surging and pitching motions that produce an equivalent speed and angle of attack variation over a cycle. At lower tip-speed ratios, the Coriolis force leads to the capture of a vortex pair which results in a significant decrease in lift when the angle of attack of a rotating airfoil begins to decrease in the upwind half cycle. In the absence of the wake-capturing, the equivalent planar motion is a good approximation to a rotating blade in a vertical-axis wind turbine.
\r\n\r\nAnalysis on the starting torque shows that when the turbine solidity is lower than about 0.5, the starting torque distribution can be well-modeled by considering a single blade at different orientations, and starting torque distributions for multi-bladed turbines can be constructed by linearly combining the torques at the respective positions of the blades. Using this model, optimal configurations to start a multi-bladed low-solidity vertical-axis wind turbine is proposed.
\r\n\r\nA preliminary study is made to determine an optimal blade pitch for a single-bladed motor-driven turbine using optimal control theory. When the input power is minimized directly, the solution seems to converge to only a local minimum due to a lower input power reduction than that obtained by maximizing the mean tangential force. After a transient, both controls converge to time-invariant pitch angles of about the same magnitude but with opposite signs. The wake-capturing phenomenon observed in the uncontrolled case necessitates large input power. Under active control, the disappearance of wake-capturing and attendant changes in the flow field collectively result in a reduction of required input power.
", "doi": "10.7907/Z9SF2T5R", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9808", "collection": "thesis", "collection_id": "9808", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05272016-220450949", "primary_object_url": { "basename": "Jeesoon Choi Caltech Thesis (Jun 10 2016).pdf", "content": "final", "filesize": 18192088, "license": "other", "mime_type": "application/pdf", "url": "/9808/1/Jeesoon Choi Caltech Thesis (Jun 10 2016).pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Unsteady Aerodynamics and Optimal Control of an Airfoil at Low Reynolds Number", "author": [ { "family_name": "Choi", "given_name": "Jeesoon", "clpid": "Choi-Jeesoon" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "McKeon", "given_name": "Beverley J.", "orcid": "0000-0003-4220-1583", "clpid": "McKeon-B-J" }, { "family_name": "Williams", "given_name": "David R.", "clpid": "Williams-D-R" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "As opposed to conventional air vehicles that have fixed wings, small birds and insects are known to flap their wings at higher angles of attack. The vortex produced at the tip of the wing, known as the leading-edge vortex (LEV), plays an important role to enhance lift during its flight. In this thesis, we analyze the influence of these vortices on aerodynamic forces that could be beneficial to micro-air vehicle performance and efficiency. The flow structures associated with simple harmonic motions of an airfoil are first investigated. The characteristics of the time-averaged and fluctuating forces are explained by analyzing vortical flow features, such as vortex lock-in, leading-edge vortex synchronization, and vortex formation time. Specific frequency regions where the wake instability locks in to the unsteady motion of the airfoil are identified, and these lead to significant changes in the mean forces. A detailed study of the flow structures associated with the LEV acting either in- or out-of-phase with the quasi-steady component of the forces is performed to quantify the amplification and attenuation behavior of the fluctuating forces. An inherent time scale of the LEV associated with its formation and detachment (LEV formation time) is shown to control the time-averaged forces. With these results, several optimal flow control problems are formulated. Adjoint-based optimal control is applied to an airfoil moving at a constant velocity and also to a reciprocating airfoil with no forward velocity. In both cases, we maximize lift by controlling the pitch rate of the airfoil. For the former case, the static map of lift at various angles of attack is additionally examined to find the static angle that provides maximum lift and also to confirm whether the optimizations perform according to the static map. For the latter case, we obtain a solution of the optimized motion of the flapping airfoil which resembles that of a hovering insect.", "doi": "10.7907/Z9J1014Q", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:8758", "collection": "thesis", "collection_id": "8758", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01222015-234921548", "type": "thesis", "title": "Simulation of Shock-Induced Bubble Collapse with Application to Vascular Injury in Shockwave Lithotripsy", "author": [ { "family_name": "Coralic", "given_name": "Vedran", "clpid": "Coralic-Vedran" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Shepherd", "given_name": "Joseph E.", "orcid": "0000-0003-3181-9310", "clpid": "Shepherd-J-E" }, { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" }, { "family_name": "Brady", "given_name": "John F.", "orcid": "0000-0001-5817-9128", "clpid": "Brady-J-F" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Shockwave lithotripsy is a noninvasive medical procedure wherein shockwaves are repeatedly focused at the location of kidney stones in order to pulverize them. Stone comminution is thought to be the product of two mechanisms: the propagation of stress waves within the stone and cavitation erosion. However, the latter mechanism has also been implicated in vascular injury. In the present work, shock-induced bubble collapse is studied in order to understand the role that it might play in inducing vascular injury. A high-order accurate, shock- and interface-capturing numerical scheme is developed to simulate the three-dimensional collapse of the bubble in both the free-field and inside a vessel phantom. The primary contributions of the numerical study are the characterization of the shock-bubble and shock-bubble-vessel interactions across a large parameter space that includes clinical shockwave lithotripsy pressure amplitudes, problem geometry and tissue viscoelasticity, and the subsequent correlation of these interactions to vascular injury. Specifically, measurements of the vessel wall pressures and displacements, as well as the finite strains in the fluid surrounding the bubble, are utilized with available experiments in tissue to evaluate damage potential. Estimates are made of the smallest injurious bubbles in the microvasculature during both the collapse and jetting phases of the bubble's life cycle. The present results suggest that bubbles larger than 1 \u03bcm in diameter could rupture blood vessels under clinical SWL conditions.", "doi": "10.7907/Z91N7Z26", "publication_date": "2015", "thesis_type": "phd", "thesis_year": "2015" }, { "id": "thesis:5539", "collection": "thesis", "collection_id": "5539", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01242010-111852941", "type": "thesis", "title": "Instability Wave Models of Turbulent Jets from Round and Serrated Nozzles", "author": [ { "family_name": "Gu\u00f0mundsson", "given_name": "Kristj\u00e1n", "clpid": "Gu\u00f0mundsson-Kristj\u00e1n" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Hussain", "given_name": "Fazle", "orcid": "0000-0002-2209-9270", "clpid": "Hussain-F" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" }, { "family_name": "Shepherd", "given_name": "Joseph E.", "orcid": "0000-0003-3181-9310", "clpid": "Shepherd-J-E" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis we study pressure fluctuations associated with large-scale coherent structures in turbulent round and serrated jets. Linear disturbances to the turbulent mean flow of the round jet are modeled via linear stability analysis and the Parabolized Stability Equations (PSE). We show that PSE provides better agreement with near-field microphone-array data at low frequencies than previous models based on linear stability theory. We examine the extent to which microphone data is contaminated by fluctuations uncorrelated with large-scale structures. By filtering out the uncorrelated fluctuations, via the proper orthogonal decomposition (POD), better agreement between data and theory is obtained. We next extend the linear stability analysis of round jets to include the effects of azimuthal inhomogeneities of serrated jets. We solve the resulting system of equations and find new modes, associated with the streamwise vorticity of the serrated-jet mean flow. All unstable modes of the serrated jet are stabilized, potentially explaining the noise reduction achieved by such jets. We also compare these predictions to POD-filtered microphone measurements, generally finding good agreement.\r\n", "doi": "10.7907/BQH9-G487", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5859", "collection": "thesis", "collection_id": "5859", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05272010-133830557", "primary_object_url": { "basename": "AndoCIT2010.pdf", "content": "final", "filesize": 2480169, "license": "other", "mime_type": "application/pdf", "url": "/5859/1/AndoCIT2010.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Effects of Polydispersity in Bubbly Flows", "author": [ { "family_name": "Ando", "given_name": "Keita", "orcid": "0000-0002-9572-8242", "clpid": "Ando-Keita" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Brennen", "given_name": "Christopher E.", "clpid": "Brennen-C-E" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Brennen", "given_name": "Christopher E.", "clpid": "Brennen-C-E" }, { "family_name": "Shepherd", "given_name": "Joseph E.", "orcid": "0000-0003-3181-9310", "clpid": "Shepherd-J-E" }, { "family_name": "Ravichandran", "given_name": "Guruswami", "orcid": "0000-0002-2912-0001", "clpid": "Ravichandran-G" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis concerns the dynamics of bubbly flows with a distribution of equilibrium bubble sizes. The main goal is to formulate the physical and numerical models of continuum bubbly flows that enable us to efficiently compute the average mixture dynamics. Numerical simulations are conducted to quantify the effects of bubble size distributions on the averaged dynamics for several model flows.
\r\n\r\nFirst, the ensemble-averaged conservation laws for polydisperse bubbly flows are derived. One-way-coupled flow computations are conducted to illustrate that the different-sized bubbles can oscillate with different frequencies. The resulting phase cancellations can be regarded as an apparent damping of the averaged dynamics of polydisperse flows. A high-order-accurate finite-volume method is then developed to compute the flow, paying special attention to issues of wave dispersion and stiffness.
\r\n\r\nNext, computations of one-dimensional shock propagation through bubbly liquids are performed. The numerical experiments reveal that the bubble size distribution has a profound impact on the averaged shock structure. If the distribution is sufficiently broad, the apparent damping due to the phase cancellations can dominate over the single-bubble-dynamic dissipation (due to thermal, viscous, and compressibility effects) and the averaged shock dynamics become insensitive to the individual bubble dynamics. One-dimensional cloud cavitation caused by fluid-structure interaction is also solved to investigate the collapse of cavitation clouds with both monodisperse and polydisperse nuclei. The phase cancellations among the cavitation bubbles with broad nuclei size distributions are found to eliminate violent cloud collapse in the averaged dynamics.
\r\n\r\nFinally, shock propagation through a bubbly liquid-filled, deformable tube is considered. The quasi-one-dimensional conservation law that takes into account structural deformation is formulated and steady shock relations are derived. The results are compared to water-hammer experiments; the present shock theory gives better agreement with the measured wave speeds than linear theory. This indicates that the gas-phase nonlinearity needs to be included to accurately predict the propagation speeds of finite-amplitude waves in a deformable tube filled with a bubbly liquid.
", "doi": "10.7907/SW8K-Y135", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5886", "collection": "thesis", "collection_id": "5886", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05282010-150032204", "primary_object_url": { "basename": "jjk_thesis_final.pdf", "content": "final", "filesize": 2429194, "license": "other", "mime_type": "application/pdf", "url": "/5886/1/jjk_thesis_final.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Numerical Simulation of Wave Focusing and Scattering in Shock Wave Lithotripsy", "author": [ { "family_name": "Krimmel", "given_name": "Jeffrey James", "clpid": "Krimmel-Jeffrey-James" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Brennen", "given_name": "Christopher E.", "clpid": "Brennen-C-E" }, { "family_name": "Dabiri", "given_name": "John O.", "orcid": "0000-0002-6722-9008", "clpid": "Dabiri-J-O" }, { "family_name": "Shepherd", "given_name": "Joseph E.", "orcid": "0000-0003-3181-9310", "clpid": "Shepherd-J-E" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this work we simulate shock wave focusing and scattering that occurs during shock wave lithotripsy, a noninvasive medical treatment for kidney stone disease. Shock waves are generated outside the body of the patient and are focused at the kidney stone with the intention of pulverizing the stone while it remains inside the patient. The patient can then ostensibly pass the debris naturally. We use a multidimensional second-order method of the Godunov type with slope limiters and shock capturing capability to solve the inviscid Euler equations. Because we begin with the fundamental statements of conservation of mass, momentum, and energy, we simulate all the relevant acoustics occurring during a typical treatment.
\r\n\r\nLithotripters, the machines that generate and focus shock waves, can be classified according to the mechanism of shock generation. In this work, we simulate three different types of lithotripters: electrohydraulic, piezoelectric, and electromagnetic. We choose one representative of each lithotripter type: the Dornier HM3, a research piezoelectric lithotripter array, and the XX-Es, respectively. We first study a model of the in vitro setting for each lithotripter, where shock waves are generated and focus in a bath of pure water. Next, we introduce different heterogeneous materials near the focus of the lithotripter to model the effect of the body of an actual patient, i.e., the in vivo condition. We use two approaches in this modeling effort. One approach is to use simple geometrical models for the body cavity and kidney that we created ourselves. The other approach is to import real anatomical data made available from the VOXEL-MAN Group.
\r\n\r\nIn studying the focal region acoustics, we specifically examine the maximum calculated pressures. These pressures represent the forces that will ultimately cause the kidney stone to break. We also study the pulse intensity integral, i.e., the energy density carried by the focusing shock wave. In addition to these pressures and energy densities, we are interested in investigating how soft tissue in the focal region may potentially be damaged by the resulting wavefields. We isolate two mechanisms that are thought to be important in soft tissue injury: shearing and cavitation. We calculate estimates for the maximum principal normal and shear strains in the focal region in addition to the corresponding strain rates and use these as metrics for the potential for damage via shearing. We study the calculated negative pressure fields in this region as a surrogate for potential damage caused by cavitation.
\r\n\r\nWe find that our simple geometrical anatomical models cause little deviation from the acoustics observed in a water bath. However, when the real anatomical data of the VOXEL-MAN Group is used, the fields of the various relevant flow quantities become more highly oscillatory and produce secondary extrema that could produce damage not predicted from the water bath case. In addition to the conclusions from our own work, we discuss how our results motivate future studies that will hopefully help elucidate specific mechanisms by which kidney stones break and soft tissue becomes damaged.
", "doi": "10.7907/XWED-RZ95", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5928", "collection": "thesis", "collection_id": "5928", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06072010-131025711", "primary_object_url": { "basename": "JoeCaltechThesis2010.pdf", "content": "final", "filesize": 77167886, "license": "other", "mime_type": "application/pdf", "url": "/5928/1/JoeCaltechThesis2010.pdf", "version": "v6.0.0" }, "type": "thesis", "title": "Optimized Feedback Control of Vortex Shedding on an Inclined Flat Plate", "author": [ { "family_name": "Joe", "given_name": "Won Tae", "clpid": "Joe-Won-Tae" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Hussain", "given_name": "Fazle", "orcid": "0000-0002-2209-9270", "clpid": "Hussain-F" }, { "family_name": "MacMynowski", "given_name": "Douglas G.", "clpid": "MacMynowski-D-G" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" }, { "family_name": "McKeon", "given_name": "Beverley J.", "orcid": "0000-0003-4220-1583", "clpid": "McKeon-B-J" }, { "family_name": "Blanquart", "given_name": "Guillaume", "orcid": "0000-0002-5074-9728", "clpid": "Blanquart-G" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis examines flow control and the potentially favorable effects of feedback, associated with unsteady actuation in separated flows over airfoils. The objective of the flow control is to enhance lift at post-stall angles of attack by changing the dynamics of the wake vortices. We present results from a numerical study of unsteady actuation on a two-dimensional flat plate at post-stall angles of attack at Reynolds number (Re) of 300 and 3000. At Re=300, the control waveform is optimized and a feedback strategy is developed to optimize the phase of the control relative to the lift with either a sinusoidal or the optimized waveform, resulting in a high-lift limit cycle of vortex shedding. Also at Re=3000, we show that certain frequencies and actuator waveforms lead to stable (high-lift) limit cycles, in which the flow is phase locked to the actuation.
\r\n\r\nFirst, a two-dimensional flat plate model at a high angle of attack at a Re of 300 is considered. We design the feedback to slightly adjust the frequency and/or phase of actuation to lock it to a particular phase of the lift, thus achieving a phase-locked flow with the maximal period-averaged lift over every cycle of actuation.
\r\n\r\nWith the sinusoidal forcing and feedback, we show that it is possible to optimize the phase of the control relative to the lift in order to achieve the highest possible period-averaged lift in a consistent fashion. However, continuous sinusoidal forcing could be adding circulation when it is unnecessary, or undesirable. Thus we employ an adjoint-based optimization in order to find the waveform (time history of the jet velocity) that maximizes the lift for a given actuation amplitude. The adjoint of the linearized perturbed equations is solved backwards in time to obtain the gradient of the lift to changes in actuation (the jet velocity), and this information is used to iteratively improve the controls.
\r\n\r\nOptimal control provides a periodic control waveform, resulting in high lift shedding cycle with minimal control input. However, if applied in open loop, the flow fails to phase lock onto the optimal waveform, degrading the lift performance. Thus, the optimized waveform is also implemented in a closed-loop controller where the control signal is shifted or deformed periodically to adjust to the (instantaneous) frequency of the lift fluctuations. The feedback utilizes a narrowband filter and an Extended Kalman Filter to robustly estimate the phase of vortex shedding and achieve phase-locked, high lift flow states. Feedback control of the optimized waveform is able to reproduce the high-lift limit cycle from the optimization, but starting from an arbitrary phase of the baseline limit cycle.
\r\n\r\nFinally, we apply the tools developed and knowledge gained at Re=300 to a Re of 3000 on a thin airfoil with a thickness-to-chord ratio of 4%, which were chosen to match the experimental studies of Greenblatt et al. (2008). We consider more detailed time-dependent aspects of the lift and corresponding flow fields, particularly the flow structures at the minimum and maximum lift, and the phase of pulses relative to the lift, in order to more precisely compare different actuated flow fields and distinguish the differences responsible for higher or lower instantaneous lift, along with identifying different vortex evolutions. We consider two representative angles of attack, 10 and 20 degrees, and investigate the lift enhancement and which combinations of forcing frequency and duty cycle lead to phase-locked flow. Finally, we show that for certain frequencies and actuator waveforms, there occur stable limit cycles in which the flow is phase locked to the actuation.
", "doi": "10.7907/6D11-2Y92", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5221", "collection": "thesis", "collection_id": "5221", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06022009-183247", "primary_object_url": { "basename": "Thesis_Franck.pdf", "content": "final", "filesize": 3520640, "license": "other", "mime_type": "application/pdf", "url": "/5221/1/Thesis_Franck.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Large-Eddy Simulation of Flow Separation and Control on a Wall-Mounted Hump", "author": [ { "family_name": "Franck", "given_name": "Jennifer Ann", "clpid": "Franck-Jennifer-Ann" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Dabiri", "given_name": "John O.", "orcid": "0000-0002-6722-9008", "clpid": "Dabiri-J-O" }, { "family_name": "Hunt", "given_name": "Melany L.", "orcid": "0000-0001-5592-2334", "clpid": "Hunt-M-L" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Active flow control techniques such as synthetic jets have been successful in increasing the performance of naturally separating flows on post-stall airfoils, bluff body shedding, and internal flows such as wide-angle diffusers. However, in order to implement robust control techniques there is a need for accurate computational tools capable of predicting unsteady separation and control at high Reynolds numbers. This thesis developed a compressible large-eddy simulation (LES) and validated it by simulating the turbulent flow over a wall-mounted hump. The flow is characterized by an unsteady, turbulent recirculation region along the trailing edge of the geometry, and is simulated at a Reynolds number of 500,000. Active flow control is applied just before the natural separation point via steady suction and zero-net mass flux oscillatory forcing. The addition of control is shown to be effective in decreasing the size of the separation bubble and pressure drag. LES baseline and controlled results are validated against previously performed experiments by Seifert and Pack and those performed for the NASA Langley Workshop on Turbulent Flow Separation and Control. Three test cases are explored to determine the effect of explicit filtering and the Smagorinsky subgrid scale model on the average flow and turbulent statistics. The flow physics and the control effectiveness are investigated at two Mach numbers, M=0.25 and M=0.6. Compressibility is shown to increase the separation bubble length in the baseline case, but does not significantly change the effectiveness of the control. In terms of decreasing drag on the wall-mounted hump model, steady suction is more effective than oscillatory control, but both control techniques are effective in reducing the separation bubble length. Two-dimensional direct numerical simulations (DNS) of the wall-mounted hump flow are also presented, and the results show different baseline flow features than the 3D LES. However the controlled 2D flow gives an indication of the most receptive actuation frequencies around twice that of the natural shedding frequency. Two regimes of reduced actuation frequency are also explored with the 3D LES. It is found that the low frequency actuation is successful in reducing the separation bubble length, but high frequency actuation produces an average flow comparable to the baseline case, and does not result in drag or separation bubble length reduction.\r\n", "doi": "10.7907/DH38-D592", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:1712", "collection": "thesis", "collection_id": "1712", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05092008-171346", "primary_object_url": { "basename": "johnsen2007.pdf", "content": "final", "filesize": 7026493, "license": "other", "mime_type": "application/pdf", "url": "/1712/1/johnsen2007.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Numerical Simulations of Non-Spherical Bubble Collapse with Applications to Shockwave Lithotripsy", "author": [ { "family_name": "Johnsen", "given_name": "Eric", "orcid": "0000-0001-9530-408X", "clpid": "Johnsen-Eric" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Brennen", "given_name": "Christopher E.", "clpid": "Brennen-C-E" }, { "family_name": "Brady", "given_name": "John F.", "orcid": "0000-0001-5817-9128", "clpid": "Brady-J-F" }, { "family_name": "Shepherd", "given_name": "Joseph E.", "orcid": "0000-0003-3181-9310", "clpid": "Shepherd-J-E" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Shockwave lithotripsy (SWL) is a non-invasive medical procedure in which shockwaves are focused on kidney stones in an attempt to break them. Because the stones are usually immersed in liquid, cavitation occurs during the process. However, the stone comminution mechanisms and the bubble dynamics of SWL are not fully understood. In the present thesis, numerical simulations are employed to study axisymmetric Rayleigh collapse and shock-induced collapse of a single gas bubble in a free field and near a wall. A high-order accurate, quasi-conservative, shock- and interface-capturing scheme is developed to solve the multicomponent Euler equations.
\r\n\r\nThe primary contributions of the present work are the development of a new numerical framework to study compressible multicomponent flows, the characterization of the dynamics of non-spherical bubble collapse, and quantitative measurements of wall pressures generated by bubble collapse. Because of asymmetries in the flow field, a re-entrant jet develops and generates a large water-hammer pressure upon impact onto the distal side. Jet properties are calculated and, as an indication of potential damage, wall pressures are measured; pressures on the order of 1 GPa are achieved locally. In shock-induced collapse, the wall pressure is amplified by the presence of bubbles within several initial radii from the wall. Thus, the pressure generated by the bubble collapse is larger than the incoming shock. The results extended to SWL show that shock-induced collapse has tremendous potential for damage along the stone surface. Furthermore, the simulations are coupled to an elastic wave propagation code to show that bubble collapse may cause damage within kidney stones as well.
\r\n", "doi": "10.7907/WPQB-2W24", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:1990", "collection": "thesis", "collection_id": "1990", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05232008-124342", "primary_object_url": { "basename": "Taira_thesis.pdf", "content": "final", "filesize": 7582318, "license": "other", "mime_type": "application/pdf", "url": "/1990/3/Taira_thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "The Immersed Boundary Projection Method and Its Application to Simulation and Control of Flows Around Low-Aspect-Ratio Wings", "author": [ { "family_name": "Taira", "given_name": "Kunihiko (Sam)", "orcid": "0000-0002-3762-8075", "clpid": "Taira-Kunihiko-Sam" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Dabiri", "given_name": "John O.", "orcid": "0000-0002-6722-9008", "clpid": "Dabiri-J-O" }, { "family_name": "Hunt", "given_name": "Melany L.", "orcid": "0000-0001-5592-2334", "clpid": "Hunt-M-L" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" } ], "local_group": [ { "literal": "GALCIT" }, { "literal": "div_eng" } ], "abstract": "First, we present a new formulation of the immersed boundary method that is algebraically identical to the traditional fractional step algorithm. This method, called the immersed boundary projection method, allows for the simulations of incompressible flows over arbitrarily shaped bodies under motion and/or deformation in both two and three dimensions. The no-slip condition along the immersed boundary is enforced simultaneously with the incompressibility constraint through a single projection. The boundary force is determined implicitly without any constitutive relations for the rigid body formulation, which in turn allows the use of high CFL numbers in our simulations compared to past methods.
\r\n\r\nNext, the above immersed boundary projection method is used to analyze three-dimensional separated flows around low-aspect-ratio flat-plate wings. A number of simulations highlighting the unsteady nature of the separated flows are performed for Re = 300 and 500 with various aspect ratios, angles of attack, and planform geometries. The aspect ratio and angle of attack are found to have a large influence on the stability of the wake profile and the force experienced by the low-aspect-ratio wing. At early times, following an impulsive start, topologies of the wake vortices are found to be the same across different aspect ratios and angles of attack. Behind low-aspect-ratio rectangular plates, leading-edge vortices form and eventually separate as hairpin vortices following the start-up. This phenomenon is found to be similar to dynamic stall observed behind pitching plates. The detached structure would then interact with the tip vortices, reducing the downward velocity induced by the tip vortices acting upon the leading-edge vortex. At large time, depending on the aspect ratio and angles of attack, the wakes reach one of the three states: (i) a steady state, (ii) a periodic unsteady state, or (iii) an aperiodic unsteady state. We have observed that the tip effects in three-dimensional flows can stabilize the flow and also exhibit nonlinear interaction with the shedding vortices.
\r\n\r\nAt last, we apply steady blowing to separated flows behind the low-aspect-ratio rectangular wings. The objective of the flow control is to enhance lift at post-stall angles of attack by changing the dynamics of the wake vortices. This controller strengthens the tip vortices by engulfing the trailing-edge vortex sheet to increase the downward thrust and the downward induced velocity onto the leading-edge vortices. The tip vortices that are traditionally considered as an aerodynamic nuisance, have been used favorably to increase lift in post-stall flows for the considered low-aspect-ratio wings.
", "doi": "10.7907/VSDD-P465", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:1515", "collection": "thesis", "collection_id": "1515", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-04262007-095945", "primary_object_url": { "basename": "GBres_Thesis.pdf", "content": "final", "filesize": 11080622, "license": "other", "mime_type": "application/pdf", "url": "/1515/13/GBres_Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Numerical Simulations of Three-Dimensional Instabilities in Cavity Flows", "author": [ { "family_name": "Br\u00e8s", "given_name": "Guillaume Alain", "orcid": "0000-0003-2507-8659", "clpid": "Br\u00e8s-Guillaume-Alain" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Brennen", "given_name": "Christopher E.", "clpid": "Brennen-C-E" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" }, { "family_name": "Shepherd", "given_name": "Joseph E.", "orcid": "0000-0003-3181-9310", "clpid": "Shepherd-J-E" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Direct numerical simulations are performed to investigate the stability of compressible flow over three-dimensional open cavities for future control applications.
\r\n\r\nFirst, the typical self-sustained oscillations, commonly referred as shear-layer (Rossiter) modes, are characterized for two-dimensional cavities over a range of flow conditions. A linear stability analysis is then conducted to search for three-dimensional global instabilities of the 2D mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of cavity configurations. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately 1 cavity depth and oscillates with a frequency about an order-of-magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities reported in flows over backward-facing steps, lid-driven cavity flows, and Couette flows.
\r\n\r\nResults from three-dimensional simulations of the nonlinear compressible Navier-Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. These results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.
", "doi": "10.7907/Z96W988B", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:2513", "collection": "thesis", "collection_id": "2513", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06082004-151101", "primary_object_url": { "basename": "thesis_HongyuRan.pdf", "content": "final", "filesize": 22723806, "license": "other", "mime_type": "application/pdf", "url": "/2513/1/thesis_HongyuRan.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Numerical Study of the Dynamics and Sound Generation of a Turbulent Vortex Ring", "author": [ { "family_name": "Ran", "given_name": "Hongyu", "clpid": "Ran-Hongyu" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" }, { "family_name": "Hunt", "given_name": "Melany L.", "orcid": "0000-0001-5592-2334", "clpid": "Hunt-M-L" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the present study, Direct Numerical Simulations (DNS) of the fully compressible, three-dimensional Navier-Stokes equations are used to generate an axisymmetric vortex ring to which three-dimensional stochastic disturbances are added. The radiated acoustic field is computed directly in the near field, and by solving the wave equation in a spherical coordinate system in the far field.
\r\n\r\nAt high Reynolds number, a vortex ring will undergo an instability to azimuthal waves. The instability produces higher azimuthal modes and induces nonlinear interaction between the modes, and will cause the vortex ring to break down and transition to turbulence. The early stages of the simulation agree well with the linear instability theory. Nonlinear stage of instability, transition, formation of axial flow and streamwise vorticity are analyzed and compared with experimental results. After turbulent transition, the evolution of statistical quantities becomes independent of viscosity and the initial geometry, and the flow become self-similar. The temporal evolution of quantities including total circulation, axial velocity profile, vortex ring displacement and vorticity profile agrees well with the self-similarity law. Turbulent energy spectrum, Reynolds stresses and turbulence production are also presented.
\r\n\r\nThe unsteady vorticity field generates acoustic waves with higher azimuthal modes, each mode with a distinctive spectrum and directivity. The ensemble averaged peak frequency, bandwidth, and the sound pressure level agrees qualitatively with reported experimental results. The directivity of each azimuthal mode is compared with predictions of vortex sound theory. The sound generation consists of three stages. The first is a deterministic stage when linear instability waves emerge and grow and generate relatively weak sound. The second stage is nonlinear interaction and vortex breakdown; at this stage the sound pressure level reaches a peak value. The third stage is the turbulent asymptotic decay of the acoustic field. Based on the self-similar decay of the turbulent near field, the self-similar decay of the sound field is investigated. Connection between the acoustic field and the vortex ring oscillations is also studied with vortex sound theory. Finally, we note some similarities between the sound radiated by a train of de-correlated vortex rings and turbulent jet noise. The sound pressure level, spectrum, and directivity of the train of vortex rings is similar to the sound field from a jet with similar Reynolds number and Mach number.
", "doi": "10.7907/ASHK-JV07", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:2188", "collection": "thesis", "collection_id": "2188", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05282004-130028", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 29774773, "license": "other", "mime_type": "application/pdf", "url": "/2188/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Computation of Bubbly Cavitating Flow in Shock Wave Lithotripsy", "author": [ { "family_name": "Tanguay", "given_name": "Michel", "clpid": "Tanguay-Michel" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" }, { "family_name": "Brady", "given_name": "John F.", "orcid": "0000-0001-5817-9128", "clpid": "Brady-J-F" }, { "family_name": "Crum", "given_name": "Lawrence A.", "clpid": "Crum-L-A" }, { "family_name": "Hunt", "given_name": "Melany L.", "orcid": "0000-0001-5592-2334", "clpid": "Hunt-M-L" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Lithotripsy is at the forefront of treatment of kidney stones. By firing shock waves at the stone, it can be broken down into small fragments. Although the treatment is non-invasive, both short- and long-term side effects occur. In order to understand and rectify these shortcomings, lithotripsy has been the subject of ongoing research. Based on in vitro experiments, it has been ascertained that the cloud of cavitating bubble produced in the wake of the shock wave is a crucial element in the stone comminution process.
\r\n\r\nVarious solutions designed to maximize stone comminution and/or decrease tissue damage have been proposed over the years. However, the particulars of the comminution mechanism(s) are still undetermined. In this work, a numerical model of the two-phase flow inside an electrohydraulic lithotripter was used to provide additional insight in the behavior of the bubble cloud. The numerical model is based on an ensemble averaged two-phase flow model for a compressible liquid. The differential equations were discretized following the WENO shock capturing scheme in prolate spheroidal and cylindrical coordinate systems. The initial conditions for the flow field are estimated based on empirical observations and then validated by comparing the predicted pressure measurements and bubble cloud behavior against experimental values.
\r\n\r\nIn order to gain additional insight in the mechanism for stone comminution, a variety of relevant initial conditions were modeled. The following lithotripter configurations were analyzed: free-field, dual-pulse and single-pulse with an artificial stone at the focus. The impact of parameters such as the intensity of the initial shock wave and the pulse rate frequency (PRF) has been investigated. Based on an energy argument, conclusions regarding the efficiency of stone comminution are presented. In addition, based on these conclusions, avenues for improvement of the numerical model are highlighted.
", "doi": "10.7907/VQXV-Y948", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:5040", "collection": "thesis", "collection_id": "5040", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12182003-150738", "primary_object_url": { "basename": "twosided.pdf", "content": "final", "filesize": 5778819, "license": "other", "mime_type": "application/pdf", "url": "/5040/2/twosided.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Modeling Heat and Mass Transfer in Bubbly Cavitating Flows and Shock Waves in Cavitating Nozzles", "author": [ { "family_name": "Preston", "given_name": "Alastair Thomas", "clpid": "Preston-Alastair-Thomas" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Acosta", "given_name": "Allan J.", "clpid": "Acosta-A-J" }, { "family_name": "Brennen", "given_name": "Christopher E.", "clpid": "Brennen-C-E" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Two problems are considered in this thesis: the modeling of heat and mass diffusion effects on the dynamics of spherical bubbles, and the computation of unsteady, bubbly cavitating flows in nozzles. The goal of Part I is to develop a reduced-order model that is able to accurately and efficiently capture the effect of heat and mass transfer on the dynamics of bubbles. Detailed computations of forced and oscillating bubbles including heat and mass diffusion show that the assumptions of polytropic behavior, constant vapor pressure, and an effective liquid viscosity do not accurately account for diffusive damping and thus do not accurately capture bubble dynamics. While the full bubble computations are readily performed for single bubbles, they are too expensive to implement into continuum models of complex bubbly flows where the radial diffusion equations would have to be solved at each grid point. Therefore reduced-order models that accurately capture diffusive effects are needed.
\r\n\r\nWe first develop a full bubble computation, where the full set of radial conservation equations are solved in the bubble interior and surrounding liquid. This provides insight as to which equations, or terms in equations, may be able to be neglected while still accurately capturing the bubble dynamics. Motivated by results of the full computations, we use constant heat and mass transfer coefficients to model the transfer at the bubble wall. In the resulting reduced-order model the heat and mass diffusion equations are each replaced by a single ordinary differential equation. The model is therefore efficient enough to implement into continuum computations. Comparisons of the reduced-order model to the full computations over a wide range of parameters indicate agreement that is superior to existing models.
\r\n\r\nIn Part II we investigate the effects of unsteady bubble dynamics on cavitating flow through a converging-diverging nozzle. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady state solutions exist, and those where steady state solutions diverge at the so-called flashing instability. These latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. An approximate analytical expression is developed to predict the critical back pressure for choked flow. The results agree with previous barotropic models for those flows where bubble dynamics are not important, but show that in many instances the neglect of bubble dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shock free flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. In the model, damping of the bubble radial motion is restricted to a simple \"effective\" viscosity to account for diffusive effects. However, many features of the nozzle flow are shown to be independent of the specific damping mechanism. This is confirmed by the implementation of the more sophisticated diffusive modeling developed in Part I.
", "doi": "10.7907/ZHSN-D849", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:4742", "collection": "thesis", "collection_id": "4742", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12032004-075012", "primary_object_url": { "basename": "cwr_thesis.pdf", "content": "final", "filesize": 10860896, "license": "other", "mime_type": "application/pdf", "url": "/4742/1/cwr_thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Modeling, Simulation, and Control of Cavity Flow Oscillations", "author": [ { "family_name": "Rowley", "given_name": "Clarence Worth, III", "clpid": "Rowley-Clarence-Worth-III" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" }, { "family_name": "Marsden", "given_name": "Jerrold E.", "clpid": "Marsden-J-E" }, { "family_name": "Murray", "given_name": "Richard M.", "orcid": "0000-0002-5785-7481", "clpid": "Murray-R-M" }, { "family_name": "Brennen", "given_name": "Christopher E.", "clpid": "Brennen-C-E" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis involves the modeling of self-sustained oscillations in the flow past a rectangular cavity. The emphasis is on developing low-dimensional models that are suitable for analysis using tools from dynamical systems and control theory. Two-dimensional direct numerical simulations are performed, and indicate the presence of a \u201cwake mode,\u201d which has been observed previously in experiments, but which is much less well understood than the \u201cshear-layer mode\u201d usually observed. We characterize the flow in both shear-layer mode and wake mode, and provide a criterion for predicting the onset of wake mode, as a function of the various geometrical and flow-related parameters. We focus on the modeling of shear-layer mode, and employ two distinct modeling approaches: first, we use the method of Proper Orthogonal Decomposition (POD) and Galerkin projection to reduce the Navier-Stokes equations to a lowdimensional system of ordinary differential equations (ODEs). We extend the method to compressible flows, using approximations that are valid for cold flows at moderate Mach number. In a compressible flow, both the kinematic and thermodynamic variables contribute to the total energy, and an inner product is introduced which respects this, and allows one to use vector-valued POD modes for the Galerkin projection. We obtain models in the form of ODEs with between 2 and 60 states, and compare models based on scalar-valued and vector-valued POD modes. All of the models work well for short times (a few periods of oscillation), but the models based on scalar-valued modes deviate for longer times, while in general the models based on vector-valued modes retain qualitatively correct dynamical behavior. In the second modeling approach, we model the underlying physical mechanisms separately (shear-layer amplification, acoustic scattering, acoustic propagation), and obtain linear models that are suitable for control design and analysis. We design a controller which stabilizes the model, and implement a similar control law on an experiment, demonstrating significant reduction in the amplitude of the oscillations, but revealing some limitations of feedback control.", "doi": "10.7907/G4ZX-KH73", "publication_date": "2002", "thesis_type": "phd", "thesis_year": "2002" }, { "id": "thesis:5147", "collection": "thesis", "collection_id": "5147", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12282004-113953", "primary_object_url": { "basename": "jeffthesis.pdf", "content": "final", "filesize": 3360828, "license": "other", "mime_type": "application/pdf", "url": "/5147/1/jeffthesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "A Dilating Vortex Particle Method for Compressible Flow with Applications to Aeroacoustics", "author": [ { "family_name": "Eldredge", "given_name": "Jeffrey D.", "orcid": "0000-0002-2672-706X", "clpid": "Eldredge-Jeffrey-D" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" } ], "thesis_committee": [ { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Pullin", "given_name": "Dale Ian", "clpid": "Pullin-D-I" }, { "family_name": "Hunt", "given_name": "Melany L.", "orcid": "0000-0001-5592-2334", "clpid": "Hunt-M-L" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Vortex methods have become useful tools for the computation of incompressible fluid flow. In the present work, a vortex particle method for the simulation of unsteady two-dimensional compressible flow is developed and applied to several problems. The method is the first Langrangian simulation method for the full compressible Navier-Stokes equations. By decomposing the velocity into irrotational and solenoidal parts, and using particles that are able to change volume and that carry vorticity, dilation, enthalpy, entropy, and density, the equations of motion are satisfied. A general deterministic treatment of spatial derivatives in particle methods is developed by extending the method of particle strength exchange through the construction of higher-order-accurate, non-dissipative kernels for use in approximating arbitrary differential operators. The application of this technique to wave propagation problems is thoroughly explored. A one-sided operator is developed for approximating derivatives near the periphery of particle coverage; the operator is used to enforce a non-reflecting boundary condition for the absorption of acoustic waves at this periphery. Remeshing of the particles and the smooth interpolation of their strengths are addressed, and a criterion for the frequency of remeshing is developed on the principle axes of the rate-of-strain tensor. The fast multipole method for the fast summation of the velocity field is adapted for use with compressible particles. The new vortex method is applied to co-rotating and leapfrogging vortices in compressible flow, with the acoustic field computed using a two-dimensional Kirchoff surface, and the results agree will with those of previous work or analytical prediction. The method is also applied to the baroclinic generation of vorticity, and to the steepening of waves in the one-dimensional Burgers\u2019 equation, with favorable results in both cases.
", "doi": "10.7907/7EYY-0S65", "publication_date": "2002", "thesis_type": "phd", "thesis_year": "2002" }, { "id": "thesis:6121", "collection": "thesis", "collection_id": "6121", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10082010-114955709", "primary_object_url": { "basename": "Mohseni_k_2000.pdf", "content": "final", "filesize": 5587886, "license": "other", "mime_type": "application/pdf", "url": "/6121/1/Mohseni_k_2000.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "A: Universality in Vortex Formation. B: Evaluation of Mach Wave Radiation Mechanisms in a Supersonic Jet", "author": [ { "family_name": "Mohseni", "given_name": "Kamran", "clpid": "Mohseni-Kamran" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" } ], "thesis_committee": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" }, { "family_name": "Brennen", "given_name": "Christopher E.", "clpid": "Brennen-C-E" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis two distinct features of coherent structures are investigated. In Part I a model for the pinch-off process in vortex ring formation is developed. The predicted nondimensional stroke length L/D (referred to as \"formation number\") satisfactorily matches experimental observations. The model introduces two nondimensional parameters that govern the limiting value of the formation number: a nondimensional energy and circulation, E_(nd) and \u0393_(nd), respectively. The predicted value of E_(nd) also matches well with the experimental data. The limiting value for the new nondimensional circulation is predicted to be in the range 1.77 \u2272 \u0393_(nd) \u2272 2.07. We perform detailed computations of vortex ring formation by nonconservative forcing. The validity of the assumptions in our model is verified in these computations. Some techniques for generating fat rings are successfully investigated, resulting in generation of vortex rings with Hill's like properties. We consider thermodynamics of the vorticity density field (w/r), and we develop a statistical equilibrium theory for axisymmetric flows. It is shown that the statistical equilibrium of an axisymmetric flow is the state that maximizes an entropy functional constrained to the invariants of motion. Furthermore, it is shown that the final equilibrium state satisfies a variational principle similar to Kelvin's variational principle. In Part II Mach wave radiation mechanisms in a fully expanded supersonic jet is studied. We compare a direct numerical simulation (DNS) of a 1.92 Mach number jet with a linearized Navier-Stokes (LNS) simulation. The numerical integration technique, inflow boundary conditions, and grid distributions are the same in both simulations. We found that the generated noise in the DNS calculation is dominated by the first two azimuthal modes, and contributions from all other azimuthal modes were limited to less than 1.5 dB in the acoustic field. The total directivity of the sound field in the LNS matches reasonably well with the sound field of the DNS data. At the peak Strouhal frequency, particularly for the azimuthal mode n = 1, the amplification of flow variables in the LNS closely matches that of the DNS data. However, for frequencies away from the peak Strouhal number the DNS data shows amplification rates comparable to those of the peak Strouhal number, while in the LNS data any disturbances away from the peak Strouhal number are highly damped. These extra noise sources in the DNS data have the characteristics of a nonlinear interaction among various modes. The noise generated by the first two modes in the linearized computation is substantially weaker than in the DNS. For example, in the near acoustic field, at a distance of 6 jet diameters from the jet centerline, the sound pressure level in the linearized computation is as much as 8 db smaller than the DNS results. We observed that the maximum amplification rate for the DNS data occurs at an axial location further downstream than for the LNS data, which corresponds to regions around and beyond the end of the potential core. Our results indicate that the missing sound generation mechanisms in the LNS computation at the frequencies considered in this study can be attributed to the non-linear sound generation mechanisms, that are not captured in linear theories.", "doi": "10.7907/MB7E-7950", "publication_date": "2000", "thesis_type": "phd", "thesis_year": "2000" } ]