This thesis provides an experimental window into the duality between thrust production and energy harvesting by a flapping foil subject to unsteadiness in an oncoming flow. In particular, an airfoil is placed downstream of a circular cylinder, and allowed to interact with the vorticity shed in its wake to produce motions in both the transverse and streamwise directions. It is confirmed that under the right conditions, passive fluid-structure interactions arising from such a configuration give rise to simultaneous extraction of energy from the flow, coupled with net thrust larger than net drag experienced by the airfoil.
Measurements of forces acting on the airfoil and the motion that arises are presented, for cases where the flapping motion is both active (the foil is driven through a pre-planned trajectory) and fully passive (the foil is allowed to react to the fluid forcing it experiences). These are coupled with simultaneous Particle Image Velocimetry (PIV) measurements of the flow field in the region of the airfoil. These measurements allow for direct observation of fluid-structure interactions which give rise to both thrust production and power extraction potential, illuminating the mechanisms driving each. The dynamics of a fully passive flapping foil are largely determined by the mounting system used to facilitate its motion. It is shown that by leveraging Cyber-Physical Fluid Dynamics (CPFD) capabilities to tune these mounting parameters, the behaviour of a fully passive flapping foil can be made similar to that of a representative driven system. A framework based on a simplified linear model for mounting system dynamics is presented, to allow for the optimization of such a system for power extraction potential subject to relevant engineering constraints. The effects of nonlinearity on airfoil behaviour, particularly those due to friction in the mechanism(s) permitting passive flapping, are also explored. Finally, two-dimensional motion of a fully passive flapping foil is demonstrated, allowing for the foil to travel upstream against the oncoming flow solely due to forces induced by interactions with oncoming unsteadiness.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/kmhn-7e49, author = {Lee, Marcus Kuok Kuan}, title = {Instabilities in the Flow Over a Spinning Disk at Angle of Attack}, school = {California Institute of Technology}, year = {2022}, doi = {10.7907/kmhn-7e49}, url = {https://resolver.caltech.edu/CaltechTHESIS:09282021-234035965}, 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.
At 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.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, } @phdthesis{10.7907/sy44-d841, author = {Barthel, Benedikt}, title = {On the Variational Principles of Linear and Nonlinear Resolvent Analysis}, school = {California Institute of Technology}, year = {2022}, doi = {10.7907/sy44-d841}, url = {https://resolver.caltech.edu/CaltechTHESIS:03222022-135834919}, abstract = {Despite decades of research, the accurate and efficient modeling of turbulent flows remains a challenge. However, one promising avenue of research has been the resolvent analysis framework pioneered by McKeon and Sharma (2010) which interprets the nonlinearity of the Navier-Stokes equations (NSE) as an intrinsic forcing to the linear dynamics. This thesis contributes to the advancement of both the linear and nonlinear aspects of resolvent analysis (RA) based modeling of wall bounded turbulent flows. On the linear front, we suggest an alternative definition of the resolvent basis based on the calculus of variations. The proposed formulation circumvents the reliance on the inversion of the linear operator and is inherently compatible with any arbitrary choice of norm. This definition, which defines resolvent modes as stationary points of an operator norm, allows for more tractable analytical manipulation and leads to a straightforward approach to approximate the resolvent (response) modes of complex flows as expansions in any arbitrary basis. The proposed method avoids matrix inversions and requires only the spectral decomposition of a matrix of significantly reduced size as compared to the original system, thus having the potential to open up RA to the investigation of larger domains and more complex flow configurations. These analytical and numerical advantages are illustrated through a series of examples in one and two dimensions. The nonlinear aspects of RA are addressed in the context of Taylor vortex flow. Highly truncated and fully nonlinear solutions are computed by treating the nonlinearity not as an inherent part of the governing equations but rather as a triadic constraint which must be satisfied by the model solution. Our results show that as the Reynolds number increases, the flow undergoes a fundamental transition from a classical weakly nonlinear regime, where the forcing cascade is strictly down scale, to a fully nonlinear regime characterized by the emergence of an inverse (up scale) forcing cascade. It is shown analytically that this is a direct consequence of the structure of the quadratic nonlinearity of the NSE formulated in Fourier space. Finally, we suggest an algorithm based on the energy conserving nature of the nonlinearity of the NSE to reconstruct the phase information, and thus higher order statistics, from knowledge of solely the velocity spectrum. We demonstrate the potential of the proposed algorithm through a series of examples and discuss the challenges and potential applications to the study and simulation of turbulent flows.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/rhs5-yq49, author = {Shamai, Maysam}, title = {Complexity Reduction of Fluid-Structure Systems at Low Forcing Frequencies}, school = {California Institute of Technology}, year = {2021}, doi = {10.7907/rhs5-yq49}, url = {https://resolver.caltech.edu/CaltechTHESIS:05282021-215050622}, abstract = {This thesis addresses complexity reduction in periodic fluid-structure systems at low forcing frequencies. A novel quasi-steady time scaling framework is developed to relate the dynamics of a forced system to a corresponding unforced system.
Particle Image Velocimetry and dye flow visualization are used to study the streamwise-oscillating cylinder’s wake at a mean Reynolds number of 900. Forcing frequencies both one and two orders of magnitude below the stationary shedding frequency are considered. Forcing amplitudes are such that the instantaneous Reynolds number remains above the critical value at all times. It is shown that this forcing regime is synonymous with the development of both frequency and amplitude modulation in the wake. While frequency modulation is linked to vortex shedding, amplitude modulation arises due to symmetric reorganization of the wake at certain phases in the forcing cycle. Furthermore, Dynamic Mode Decomposition is used to extract underlying flow structures and quasi-steady time scaling is employed to relate dynamics to the corresponding unforced system. Specifically, forcing regimes where quasi-steady shedding can develop are identified and time is scaled to transform the system to resemble the stationary cylinder at the same mean Reynolds number.
Experimental flowfields are also used to analyze the wake of a surface mounted hemisphere subject to a highly pulsatile freestream, characterized by a forcing amplitude equal to the mean. Although this flow sees regular shedding of hairpin vortices in the unforced case, pulsatile forcing leads to significant deviations. For a nominal mean Reynolds number of 1000, analysis of the wake shows that forcing at a frequency much smaller than that associated with hairpin shedding can lead to frequency modulated shedding. Consequently, time scaling is employed to reduce system complexity associated with hairpin shedding and to relate wake dynamics to the analogous unforced system.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/me3y-te05, author = {Toedtli, Simon Silvio}, title = {Control of Wall-Bounded Turbulence Through Closed-Loop Wall Transpiration}, school = {California Institute of Technology}, year = {2021}, doi = {10.7907/me3y-te05}, url = {https://resolver.caltech.edu/CaltechTHESIS:05272021-055610816}, abstract = {Many wall-bounded flows of practical relevance are turbulent, including the flows past airplanes and ships. The turbulent motions enhance momentum mixing and, as a result, the drag force on the engineering surface increases, for transportation vessels typically by at least a factor of two compared to laminar flow. Turbulent flow control aimed at drag reduction therefore has the potential to deliver enormous energetic and economic savings, but many challenges remain despite active research for well over a century. The present thesis aims to contribute towards two open questions of the field: first, what are suitable controller design tools for high Reynolds number flows? And second, how does actuation through closed-loop wall transpiration change the flow physics? We investigate aspects of these questions through direct numerical simulation (DNS) and modal analyses of an example control scheme, which is applied to a low Reynolds number turbulent channel flow. The controller is a generalization of the opposition control scheme, and introduces a phase shift between the Fourier transformed sensor measurement and actuator response.
The first part of the thesis demonstrates that a low-order model based on the resolvent framework is able to approximate the drag reduction results of DNS over the entire parameter space considered. The model is about two orders of magnitude cheaper to evaluate than DNS at low Reynolds numbers, and we present a strategy based on subsampling of the wave number space and analytical scaling laws that enables model-based flow control design at technologically relevant Reynolds numbers. The second part of the thesis shows that the physics of the controlled flow can be understood from two distinct families of spatial scales, termed streamwise-elongated and spanwise-elongated scales, respectively. Wall transpiration with streamwise-elongated scales attenuates or amplifies the near-wall cycle and therefore leads to drag reduction or increase, depending on the phase shift. In contrast, wall transpiration with spanwise-elongated scales only leads to drag increase, which occurs at positive phase shifts and is due to the appearance of spanwise rollers which largely enhance momentum mixing. Both patterns are robust features of flows with closed-loop wall transpiration, and the present study offers a simple explanation of their origin in terms of phase relations at distinct spatial scales. The findings of this study may set the stage for a unifying framework for various forms of wall transpiration, and implications for future flow control design are discussed.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/wayx-eh75, author = {McMullen, Ryan Michael}, title = {Aspects of Reduced-Order Modeling of Turbulent Channel Flows: From Linear Mechanisms to Data-Driven Approaches}, school = {California Institute of Technology}, year = {2020}, doi = {10.7907/wayx-eh75}, url = {https://resolver.caltech.edu/CaltechTHESIS:05282020-161209039}, abstract = {This thesis concerns three key aspects of reduced-order modeling for turbulent shear flows. They are linear mechanisms, nonlinear interactions, and data-driven techniques. Each aspect is explored by way of example through analysis of three different problems relevant to the broad area of turbulent channel flow.
First, linear analyses are used to both describe and better understand the dominant flow structures in elastoinertial turbulence of dilute polymer solutions. It is demonstrated that the most-amplified mode predicted by resolvent analysis (McKeon and Sharma, 2010) strongly resembles these features. Then, the origin of these structures is investigated, and it is shown that they are likely linked to the classical Tollmien-Schichting waves.
Second, resolvent analysis is again utilized to investigate nonlinear interactions in Newtonian turbulence. An alternative decomposition of the resolvent operator into Orr-Sommerfeld and Squire families (Rosenberg and McKeon, 2019b) enables a highly accurate low-order representation of the second-order turbulence statistics. The reason for its excellent performance is argued to result from the fact that the decomposition enables a competition mechanism between the Orr-Sommerfeld and Squire vorticity responses. This insight is then leveraged to make predictions about how resolvent mode weights belonging to several special classes scale with increasing Reynolds number.
The final application concerns special solutions of the Navier-Stokes equations known as exact coherent states. Specifically, we detail a proof of concept for a data-driven method centered around a neural network to generate good initial guesses for upper-branch equilibria in Couette flow. It is demonstrated that the neural network is capable of producing upper-branch solution predictions that successfully converge to numerical solutions of the governing equations over a limited range of Reynolds numbers. These converged solutions are then analyzed, with a particular emphasis on symmetries. Interestingly, they do not share any symmetries with the known equilibria used to train the network. The implications of this finding, as well as broader outlook for the scope of the proposed method, are discussed.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/7RSR-3277, author = {Morgan, Jonathan Philip}, title = {Linear and Non-linear Interactions in a Rough-Wall Turbulent Boundary Layer}, school = {California Institute of Technology}, year = {2019}, doi = {10.7907/7RSR-3277}, url = {https://resolver.caltech.edu/CaltechTHESIS:04112019-234812867}, abstract = {This thesis explores the linear and non-linear interactions which take place in a rough-wall turbulent boundary through experiments and modeling. In order to derive physics-based models for the relation between roughness geometry and flow physics, two very simple periodic roughnesses were 3D printed and placed in a boundary layer wind tunnel for separate experiments. Hot-wire measurements were taken at a grid of points within a single period of the roughness in order to map the spatial variation of important flow statistics in way that allows correlation back to the roughness geometry. Time averaged streamwise velocity and the power spectrum of instantaneous streamwise velocity were both found to vary coherently with the roughness. The spatial variation of the time averaged velocity was identified as the linear result of the roughness, as it has identical wavenumber and frequency to the static roughness geometry. Modeling the time-averaged velocity field as a response mode of the linear resolvent operator was found to be reasonable for certain wavenumbers. The spatial distribution of the power spectrum was shown to be a non-linear effect of the roughness; the power spectrum only measures the energy of convecting modes, which necessarily have non-zero frequency and cannot correlate linearly to the static roughness. The spatial modulation of the power spectrum was found to be indicative of non-linear triadic interactions between the static velocity Fourier modes and pairs of convecting modes, as allowed by the Navier-Stokes equations. A low-order model for these interactions, and their effect on the power spectrum, was constructed using resolvent response modes to represent all velocity Fourier modes. The model was found to qualitatively predict the modulation of the power spectrum for several sets of wavenumbers. The success of such a simple model suggests that it presents a useful low-order understanding of non-linear forcing between scales in rough-wall boundary layers.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/A5PS-GT54, author = {Huynh, David Pham}, title = {Spatio-Temporal Response of a Compliant-Wall, Turbulent Boundary Layer System to Dynamic Roughness Forcing}, school = {California Institute of Technology}, year = {2019}, doi = {10.7907/A5PS-GT54}, url = {https://resolver.caltech.edu/CaltechTHESIS:04232019-162807004}, abstract = {This thesis investigates the interaction between an elastic compliant surface and a turbulent boundary layer exposed to dynamic roughness forcing. The goals are to explore a unique perspective of this fluid-structural problem through narrow-band forcing, and to further develop the understanding of dynamic roughness. Water tunnel experiments are designed with flow and surface measurements, both phase-locked to the roughness actuation. This enables a phase-averaged analysis, which leverages the deterministic input to isolate the temporally correlated components of the flow and surface response. Identifying the directly interacting velocity and deformation modes allows the complex, fluid-structural system to be studied in a more tractable, input-output manner.
The first experiment is conducted with a smooth-wall turbulent boundary layer forced by dynamic roughness, and contributes to the knowledge of this type of forcing through structure-resolved particle image velocimetry. This allows for the streamwise-spatial nature and the wall-normal velocity component (v) of the roughness-forced flow to be explored, which had not been previously studied. A spatial amplitude modulation is observed in the synthetic structure and investigated directly through the spatial spectra. Through a parametric study and an empirical fit, the forcing frequency may now be selected to target a particular streamwise length scale.
The second experiment implements a gelatin sample subject to an unforced turbulent boundary layer. The surface response is characterized and serves as a base case with which to identify the roughness-forced component of the deformations. This naturally leads to the third experiment, where the full compliant-wall, dynamic-roughness-forced turbulent boundary layer system is considered. The surface response to the synthetic flow structure is confirmed, which sets the stage for a comparison between the smooth-wall and compliant-wall data to study the effect of the compliant surface.
The smooth/compliant comparison is guided by a resolvent analysis, which predicts a virtual wall feature in the v velocity mode for the elastic material under consideration. Using this prediction to inform a conditional average, the virtual wall is revealed in the experimental data. Thus, the action of the elastic surface is interpreted as opposing the v velocity near the wall, in a manner similar to wall-jet opposition control. Previous experimental studies of viscoelastic compliant surfaces have demonstrated the potential for turbulent drag reduction, though either indirectly via the turbulence intensities or with relatively high skin friction measurement error. A common observation in these studies was the importance of the interaction between the surface and the coherent structures in the flow. To that end, this study has isolated and modeled the behavior of the fluid-structural system with a single spatio-temporal scale generated by dynamic roughness forcing. The results provide a physical interpretation of the effect of an elastic surface on turbulent boundary layer flow structures and informs the ongoing development of a reduced-order modeling tool in the resolvent analysis.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/Z9W0943P, author = {Saxton-Fox, Theresa Ann}, title = {Coherent Structures, their Interactions, and their Effects on Passive Scalar Transport and Aero-Optic Distortion in a Turbulent Boundary Layer}, school = {California Institute of Technology}, year = {2018}, doi = {10.7907/Z9W0943P}, url = {https://resolver.caltech.edu/CaltechTHESIS:11272017-152918929}, abstract = {This thesis focused on the characterization of coherent structures and their interactions in a turbulent boundary layer using data from particle image velocimetry (PIV) measurements performed at Caltech and from a direct numerical simulation (DNS) of Wu et al. (2017). Connections were identified between instantaneous and statistical descriptions of coherent velocity structures, through the analysis of representative models for their structures derived from the resolvent analysis of McKeon and Sharma (2010). The representative models were used in a novel conditional averaging technique to identify the average behavior of small scales about variations in the large-scale streamwise velocity field. Based upon the results of this analysis, a hypothesis for a scale interaction mechanism was proposed involving three-dimensional critical layers. The modeling and analysis methods were then applied to the aero-optic problem in which optical beams are observed to be distorted after passing through variable-density turbulent flows. Measurements using simultaneous PIV and an aero-optic sensor called a Malley probe (Malley, Sutton, and Kincheloe, 1992) were conducted in an incompressible, mildly-heated turbulent boundary layer with Prandtl number of 0.7. A conditional averaging analysis of the data identified that the nonlinear interaction of two scales was most correlated to the aero-optic distortion. The modeling of this interaction using resolvent modes led to new insights regarding the instantaneous relationship between the velocity and scalar fields over a range of Prandtl numbers.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/B4K7-K876, author = {Symon, Sean Pearson}, title = {Reconstruction and Estimation of Flows Using Resolvent Analysis and Data-Assimilation}, school = {California Institute of Technology}, year = {2018}, doi = {10.7907/B4K7-K876}, url = {https://resolver.caltech.edu/CaltechTHESIS:05302018-181049042}, abstract = {A flow reconstruction methodology is presented for incompressible, statistically stationary flows using resolvent analysis and data-assimilation. The only inputs necessary for the procedure are a rough approximation of the mean profile and a single time-resolved measurement. The objective is to estimate both the mean and fluctuating states of experimental flows with limited measurements which do not include pressure. The input data may be incomplete, in the sense that measurements near a body are difficult to obtain with techniques such as particle image velocimetry (PIV), or contaminated by noise. The tools developed in this thesis are capable of filling in missing data and reducing the amount of measurement noise by leveraging the governing equations. The reconstructed flow is capable of estimating fluctuations where time-resolved data are not available and solving the flow on larger domains where the mean profile is not known.
The first part of the thesis focuses on how resolvent analysis of the mean flow selects amplification mechanisms. Eigenspectra and pseudospectra of the mean linear Navier-Stokes (LNS) operator are used to characterize amplification mechanisms in flows where linear mechanisms are important. The real parts of the eigenvalues are responsible for resonant amplification and the resolvent operator is low-rank when the eigenvalues are sufficiently separated in the spectrum. Two test cases are studied: low Reynolds number cylinder flow and turbulent channel flow. The latter is studied by considering well-known turbulent structures while the former contains a marginally stable eigenvalue which drowns out the effect of other eigenvalues over a large range of temporal frequencies. There is a geometric manifestation of this dominant mode in the mean profile, suggesting that it leaves a significant footprint on the time-averaged flow that the resolvent can identify. The resolvent does not provide an efficient basis at temporal frequencies where there is no separation of singular values. It can still be leveraged, nevertheless, to identify coherent structures in the flow by approximating the nonlinear forcing from the interaction of highly amplified coherent structures.
The second part of the thesis extends the framework of Foures et al. (2014), who data-assimilated the mean cylinder wake at very low Reynolds numbers. The contributions presented here are to assess the minimum domain for successfully reconstructing Reynolds stress gradients, modifying the algorithm to assimilate mean pressure, determining whether weighting input measurements contributes to improved performance, and adapting the method to experimental data at higher Reynolds numbers. The results from data-assimilating the mean cylinder wake at low Reynolds numbers suggest that the measurement domain needs to coincide with the spatial support of the Reynolds stress gradients while point weighting has a minimal impact on the performance. Finally, a smoothing procedure adapted from Foures et al. (2014) is proposed to cope with data-assimilating an experimental mean profile obtained from PIV data. The data-assimilated mean profiles for an idealized airfoil and NACA 0018 airfoil are solved on a large domain making the mean profile suitable for global resolvent analysis. Data-assimilation is also able to fill in missing or unreliable vectors near the airfoil surface.
The final piece of the thesis is to synthesize the knowledge and techniques developed in the first two parts to reconstruct the experimental flow around a NACA 0018 airfoil. Preliminary results are presented for the case where α = 0° and Re = 10250. The mean profile is data-assimilated and used as an input to resolvent analysis to educe coherent structures in the flow. The resolvent operator for non- amplified temporal frequencies is forced by an approximated nonlinear forcing. The amplitude and phase of the modes are obtained from the discrete Fourier-transform of a time-resolved probe point measurement. The final reconstruction contains less measurement noise compared to the PIV snapshots and obeys the incompressible Navier-Stokes equations (NSE). The thesis concludes with a discussion of how elements of this methodology can be incorporated into the development of estimators for turbulent flows at high Reynolds numbers.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/PHDW-Z389, author = {Rosenberg, Kevin Thomas}, title = {Resolvent-Based Modeling of Flows in a Channel}, school = {California Institute of Technology}, year = {2018}, doi = {10.7907/PHDW-Z389}, url = {https://resolver.caltech.edu/CaltechTHESIS:06012018-114927289}, abstract = {This thesis concerns the continued development of the resolvent framework (McKeon and Sharma, 2010) to model wall-bounded turbulent flows. Herein, we introduce novel modifications and extensions of the framework to improve the compact representation of flows in a channel. In particular, inspired by ideas rooted in classical linear stability theory, we introduce a decomposition of the velocity field into Orr-Sommerfeld (OS) and Squire (SQ) modes in a nonlinear context via the resolvent operator. We demonstrate through the analysis of a number of exact coherent states (ECS) of the Navier-Stokes equations (NSE) in Couette and Poiseuille flow that this decomposition offers a significant improvement in the low-dimensional representation of these flows. With this efficient basis, we are able to develop through the notion of interaction coefficients a method to compute accurate, self-consistent solutions of the NSE with knowledge of only the mean velocity profile. We also highlight the role of the solenoidal component of the nonlinear forcing in the solution process. In addition, the resolvent framework is extended to the analysis of 2D/3C flows. This approach, again applied to ECS, sheds light on the underlying scale interactions which sustain these solutions. Notably, it reveals that lower branch ECS can be effectively described in their entirety with a single resolvent response mode. This discovery is leveraged to construct a method to compute accurate approximations of ECS starting from a laminar profile using a single parameter model. This thesis also utilizes a constant time-step DNS of a turbulent channel to perform a direct characterization of the nonlinear forcing terms. We compute power spectra and confirm that the nonlinear forcing has a non-trivial signature in the wavenumber-frequency domain. We also compute and analyze spectra for the OS/SQ vorticity and discuss the potential benefit of this decomposition technique to the study of fully turbulent flows as well.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/Z9Q52MN5, author = {Hufstedler, Esteban Antonio Lemus}, title = {Experimental Generation and Modeling of Vortical Gusts and Their Interactions with an Airfoil}, school = {California Institute of Technology}, year = {2017}, doi = {10.7907/Z9Q52MN5}, url = {https://resolver.caltech.edu/CaltechTHESIS:05232017-111820349}, abstract = {This thesis examines two methods of vortical gust generation and the interaction between these gusts and an airfoil. These flows were studied with both experiments at a Reynolds number of 20,000 and with potential-flow based simulations.
The standard method of generating a vortical gust has been to rapidly pitch an airfoil. A novel approach is presented: heaving a plate across the tunnel, and changing direction rapidly to release a vortex. This method is motivated by the desire to limit a test article’s exposure to the wake of the gust generator by moving it to the side of the tunnel.
A series of potential flow models were used to examine these flows: steady and unsteady thin airfoil theory, an extension of Tchieu and Leonard’s unsteady airfoil model, and an unsteady vortex panel method.
Experiments characterized the generated gusts and verified that the strength of the shed vortices approximately matched the theoretical predictions. The inviscid simulations were unable to predict viscous effects like the wakes of the generators. The pitching airfoil resulted in a persistent wake in the test section, whereas the wake of the heaving plate only temporarily disturbed the flow.
The vortex-wing interaction was examined using both mechanisms. When the wake of the generator was far from the wing, the unsteady simulations provided reasonable estimates for the early variation in lift. This demonstrated that the initial lift peak is due to inviscid effects. Each of the potential flow methods with wake models provided reasonable estimates of this lift. The simplicity of the unsteady thin airfoil theory model recommends its use for examining early vortex-wing interactions.
With the test article mounted at the midline of the tunnel, the wakes had substantial effects when the pitching generator was near the midline of the tunnel, or when the heaving plate passed the midline. The simulations were not able to capture the effects of the wakes or predict the effects of the airfoil’s angle of attack. This had the largest effect on the timescale of the post-gust approach to the final forces. With the airfoil at α=0°, this was 5-10 convective time units, which is characteristic of attached flows. The airfoil at α=10° needed double the time to approach its final state after perturbations due to its separated flow. The heaving plate’s withdrawal allowed for measurement of the resumption of vortex shedding, which was impossible with the pitching airfoil’s persistent wake.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/Z92Z13FX, author = {Dunne, Reeve}, title = {Dynamic Stall on Vertical Axis Wind Turbines}, school = {California Institute of Technology}, year = {2016}, doi = {10.7907/Z92Z13FX}, url = {https://resolver.caltech.edu/CaltechTHESIS:09042015-152813860}, abstract = {In this study the dynamics of flow over the blades of vertical axis wind turbines was investigated using a simplified periodic motion to uncover the fundamental flow physics and provide insight into the design of more efficient turbines. Time-resolved, two-dimensional velocity measurements were made with particle image velocimetry on a wing undergoing pitching and surging motion to mimic the flow on a turbine blade in a non-rotating frame. Dynamic stall prior to maximum angle of attack and a leading edge vortex development were identified in the phase-averaged flow field and captured by a simple model with five modes, including the first two harmonics of the pitch/surge frequency identified using the dynamic mode decomposition. Analysis of these modes identified vortical structures corresponding to both frequencies that led the separation and reattachment processes, while their phase relationship determined the evolution of the flow.
Detailed analysis of the leading edge vortex found multiple regimes of vortex development coupled to the time-varying flow field on the airfoil. The vortex was shown to grow on the airfoil for four convection times, before shedding and causing dynamic stall in agreement with ‘optimal’ vortex formation theory. Vortex shedding from the trailing edge was identified from instantaneous velocity fields prior to separation. This shedding was found to be in agreement with classical Strouhal frequency scaling and was removed by phase averaging, which indicates that it is not exactly coupled to the phase of the airfoil motion.
The flow field over an airfoil undergoing solely pitch motion was shown to develop similarly to the pitch/surge motion; however, flow separation took place earlier, corresponding to the earlier formation of the leading edge vortex. A similar reduced-order model to the pitch/surge case was developed, with similar vortical structures leading separation and reattachment; however, the relative phase lead of the separation mode, corresponding to earlier separation, necessitated that a third frequency to be incorporated into the reattachment mode to provide a relative lag in reattachment.
Finally, the results are returned to the rotating frame and the effects of each flow phenomena on the turbine are estimated, suggesting kinematic criteria for the design of improved turbines.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/Z9Z31WKP, author = {Duvvuri, Subrahmanyam}, title = {Non-Linear Scale Interactions in a Forced Turbulent Boundary Layer}, school = {California Institute of Technology}, year = {2016}, doi = {10.7907/Z9Z31WKP}, url = {https://resolver.caltech.edu/CaltechTHESIS:02292016-143116051}, abstract = {This thesis explores the dynamics of scale interactions in a turbulent boundary layer through a forcing-response type experimental study. An emphasis is placed on the analysis of triadic wavenumber interactions since the governing Navier-Stokes equations for the flow necessitate a direct coupling between triadically consist scales. Two sets of experiments were performed in which deterministic disturbances were introduced into the flow using a spatially-impulsive dynamic wall perturbation. Hotwire anemometry was employed to measure the downstream turbulent velocity and study the flow response to the external forcing. In the first set of experiments, which were based on a recent investigation of dynamic forcing effects in a turbulent boundary layer, a 2D (spanwise constant) spatio-temporal normal mode was excited in the flow; the streamwise length and time scales of the synthetic mode roughly correspond to the very-large-scale-motions (VLSM) found naturally in canonical flows. Correlation studies between the large- and small-scale velocity signals reveal an alteration of the natural phase relations between scales by the synthetic mode. In particular, a strong phase-locking or organizing effect is seen on directly coupled small-scales through triadic interactions. Having characterized the bulk influence of a single energetic mode on the flow dynamics, a second set of experiments aimed at isolating specific triadic interactions was performed. Two distinct 2D large-scale normal modes were excited in the flow, and the response at the corresponding sum and difference wavenumbers was isolated from the turbulent signals. Results from this experiment serve as an unique demonstration of direct non-linear interactions in a fully turbulent wall-bounded flow, and allow for examination of phase relationships involving specific interacting scales. A direct connection is also made to the Navier-Stokes resolvent operator framework developed in recent literature. Results and analysis from the present work offer insights into the dynamical structure of wall turbulence, and have interesting implications for design of practical turbulence manipulation or control strategies.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/BPEZ-VM28, author = {Bourguignon, Jean-Loup}, title = {Models of Turbulent Pipe Flow}, school = {California Institute of Technology}, year = {2013}, doi = {10.7907/BPEZ-VM28}, url = {https://resolver.caltech.edu/CaltechTHESIS:11272012-130849053}, abstract = {The physics of turbulent pipe flow was investigated via the use of two models based on simplified versions of the Navier-Stokes equations. The first model was a streamwise-constant projection of these equations, and was used to study the change in mean flow that occurs during transition to turbulence. The second model was based on the analysis of the turbulent pipe flow resolvent, and provided a radial basis for the modal decomposition of turbulent pipe flow. The two models were tested numerically and validated against experimental and numerical data.
Analysis of the streamwise-constant model showed that both non-normal and nonlinear effects are required to capture the blunting of the velocity profile, which occurs during pipe flow transition. The model generated flow fields characterized by the presence of high- and low-speed streaks, whose distribution over the cross-section of the pipe was remarkably similar to the one observed in the velocity field near the trailing edge of the puff structures present in pipe flow transition.
A modal decomposition of turbulent pipe flow, in the three spatial directions and in time, was performed, and made possible by the significant reduction in data requirements achieved via the use of compressive sampling and model-based radial basis functions. The application and efficiency of compressive sampling in wall-bounded turbulence was demonstrated.
Approximately sparse representations of turbulent pipe flow by propagating waves with model-based radial basis functions, were derived. The basis functions, obtained by singular value decomposition of the resolvent, captured the wall-normal coherence of the flow; and provided a link between the propagating waves and the governing equations, allowing for the identification of the dominant mechanims sustaining the waves, as a function of their streamwise wavenumber.
Analysis of the resolvent showed that the long streamwise waves are amplified mainly via non-normality effects, and are also constrained to be tall in the wall-normal direction, which decreases the influence of viscous dissipation. The short streamwise waves were shown to be localized near the critical-layer (defined as the wall-normal location where the convection velocity of the wave equals the local mean velocity), and thus exhibit amplification with a large contribution from criticality. The work in this thesis allows the reconciliation of the well-known results concerning optimal disturbance amplification due to non-normal effects with recent resolvent analyses, which highlighted the importance of criticality effects.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/H5WJ-RK31, author = {Jacobi, Ian}, title = {Structure of the Turbulent Boundary Layer under Static and Dynamic Impulsive Roughness Perturbation}, school = {California Institute of Technology}, year = {2013}, doi = {10.7907/H5WJ-RK31}, url = {https://resolver.caltech.edu/CaltechTHESIS:07102012-152431583}, abstract = {
The zero-pressure gradient turbulent boundary layer at Reynolds numbers (based on momentum thickness) ranging from 2700–4100 was perturbed using an impulsively short patch of two-dimensional, spanwise roughness elements. A spatial perturbation was considered in which the roughness patch was held statically on the flat-plate, and the flow downstream of the perturbation was measured by hotwire and particle-image velocimetry. A dynamic perturbation, in which the roughness patch was actuated periodically in time, was also studied, and additional measurements were taken by phase-locking to the dynamic actuation itself.
The static perturbation distorted the boundary layer through the generation of a `stress bore’ which modified the mean streamwise velocity gradient. The effect of this stress bore was observed in a modification of statistical and spectral measures of the turbulence, as well as a redistribution of coherent structures in the boundary layer. The characterization of the statically perturbed boundary layer provided a base flow from which to consider the dynamically perturbed flow. The dynamically perturbed flow manifested both effects analogous to the static perturbation, as well as a coherent, periodic, large-scale velocity fluctuation. The extent to which these two features could be treated as linearly independent was studied by a variety of statistical and spectral means. Moreover, the very large scale motion synthesized by the dynamic perturbation was isolated by phase-locked measurement, and its behavior was predicted with reasonable success by employing a resolvent operator approach to a forced version of the Orr-Sommerfeld equation.
The relationship between large-scale motions and an envelope of small-scale motions in the turbulent boundary layer was studied in both the unperturbed and perturbed flows. A variety of correlation techniques were used to interpret the interaction between the different scale motions in the context of a phase-relationship between large and small scales. This phase relationship was shown to provide a physically-grounded perspective on the relationship between the synthetic very large scale motion produced by the dynamic perturbation and the smaller scales in the flow, and was able to provide a foundation for thinking about new approaches to controlling turbulence through large-scale forcing.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/20CM-EV70, author = {LeHew, Jeffrey Allen}, title = {Spatio-Temporal Analysis of the Turbulent Boundary Layer and An Investigation of the Effects of Periodic Disturbances}, school = {California Institute of Technology}, year = {2012}, doi = {10.7907/20CM-EV70}, url = {https://resolver.caltech.edu/CaltechTHESIS:05232012-142127799}, abstract = {
The purpose of this study was to investigate the turbulent boundary layer to learn more about the dynamics of the flow and how it might be controlled through the input of spatially and/or temporally periodic disturbances. The first part of this work studies the structure of a zero-pressure-gradient turbulent boundary layer using time-resolved particle image velocimetry in both wall-normal and wall-parallel planes. Using data from wall-parallel measurements, a 3D spectrum over streamwise, spanwise, and temporal wavelengths was constructed for the first time, a major focus of this work. Among several uses, this spectrum allows the calculation of a scale-based convection velocity, that is, a convection velocity for each streamwise-spanwise scale pair present in the flow. This data set also provided a method for investigating the temporal evolution of coherent structures in the flow, of which, swirling coherent structures (SCS), indicative of vortices, and low-momentum regions were investigated thoroughly. The convection velocity and lifetime of the SCS were measured; using histograms of the SCS convection velocity in multiple wall-parallel planes, it was possible to statistically infer different SCS structures that could be categorized as attached'' ordetached’’ from the wall.
A study was also performed on the response of the turbulent boundary layer to a stationary periodic roughness inspired by the scale pattern on the sailfish. The roughness was relatively sparse with element spacing on the order of the boundary layer thickness allowing the measurement of turbulent statistics at different points along the roughness as well as below the crests of the roughness elements, a region not commonly accessible in rough-wall boundary layer studies. The streamwise turbulent statistics were studied using hotwire anemometry from which it was found that while the outer part of the flow remained similar, the near-wall region was perturbed by structures of size similar to the roughness spacing.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, month = {July}, advisor = {McKeon, Beverley J.}, } @phdthesis{10.7907/SED1-5250, author = {Norman, Adam Keith}, title = {Effect of Surface Morphological Changes on Flow Over a Sphere}, school = {California Institute of Technology}, year = {2010}, doi = {10.7907/SED1-5250}, url = {https://resolver.caltech.edu/CaltechTHESIS:05212010-124044645}, abstract = {An experimental investigation was undertaken to examine the effect of a morphing surface on the flow over a sphere in the Reynolds number range of 5x10⁴ to 5x10⁵. Here, a morphing surface is defined as a continuous surface that undergoes small amplitude changes in order to excite flow instabilities, rather than utilizing large mechanical changes to the overall shape as with traditional aerodynamic control surfaces. The sphere was chosen as an ideal geometry for testing morphing surfaces, because of the well-known sensitivity of the flow to small asymmetries on the surface. In this study, an approximation of a morphing surface was made by dynamically moving a small isolated roughness element along the sphere, thus producing small amplitude time-dependent changes to the surface shape. An experimental apparatus was designed that produced the actuation with an internal motor, which moved the roughness element via magnetic interaction. A three-component piezoelectric force sensor placed inside the sphere allowed for accurate, instantaneous measurements of the global effect of the actuator on the flow. It was found that the moving roughness could produce an instantaneous lateral force as large as the drag. Simultaneous force and particle image velocimetry measurements in the subcritical regime were used to show that there is a relatively long timescale associated with the instability growth, entrainment of fluid, and local change of the position of separation. This allowed the roughness to trip an extended region of the flow at once. It is shown that the three-dimensionality of the disturbance leads to the production of two helical counter-rotating vortices in the wake. In addition, it is demonstrated that a mean side force can be obtained by oscillating the roughness element about a point, producing a lateral force an order of magnitude larger than the force caused by a stationary roughness element. Finally, the results from the dynamic roughness were used to help interpret the underlying physical mechanisms that govern the forcing on a smooth sphere.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {McKeon, Beverley J.}, }