Characterization of the Noise Generation from Biological and Bio-Inspired Swimmers with a Novel Fluid-Acoustic Numerical Framework

An unsteady potential flow boundary element method (BEM) is coupled to a transient acoustic BEM to gain insight into the hydrodynamic and acoustic characteristics of fish swimming. The transient acoustic BEM formulation features the novel application of

Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver

International audienceThe response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated

Boundary element simulation of oscillating foil with leading-edge separation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (leaves 107-110).In this thesis, we develop a numerical model to account for the leading-edge separation for the boundary element simulation of the oscillating foil with potential flow assumption. Similar to the trailing-edge separation, the leading-edge separation is modeled by a thin shear layer. Because the leading edge is rounded which is different from the sharp trailing edge, the location for leading-edge separation is extremely difficult to predetermine especially when the flow is unsteady. For unsteady flows, the position of the leading-edge separation may vary with time. However, we present a criterion that is related to the adverse pressure gradient to predict the location for the leading-edge separation. Because of the Lagrange scheme of the wake relaxation in the boundary element simulation, the leading-edge wake sheet goes into or through the thin foil easily. In order to solve the problem of the wake penetration into the foil, we present an algorithm to deal with the penetration of the leading-edge wake into the foil body. We simulate the oscillating foil in heaving-pitching motions with our leading-edge model by the boundary element method to compare with the experiments.(cont.) Without accounting for leading-edge separation, the predictions of the thrust coefficient and the propulsion efficiency of a heaving-pitching foil are good only when the Strouhal number or the maximum angle of attack is small. With our model of the leading-edge separation, the predictions are improved significantly at a larger range of Strouhal numbers or maximum angles of attack because leading-edge separation becomes significant at large Strouhal numbers or maximum angles of attack. Further possible improvements of this leading-edge separation model are discussed.by Xiaoxia Dong.S.M

Relaxation oscillations in slow-fast systems beyond the standard form

Relaxation oscillations are highly non-linear oscillations, which appear to feature many important biological phenomena such as heartbeat, neuronal activity, and population cycles of predator-prey type. They are characterized by repeated switching of slow and fast motions and occur naturally in singularly perturbed ordinary differential equations, which exhibit dynamics on different time scales. Traditionally, slow-fast systems and the related oscillatory phenomena -- such as relaxation oscillations -- have been studied by the method of the matched asymptotic expansions, techniques from non-standard analysis, and recently a more qualitative approach known as geometric singular perturbation theory. It turns out that relaxation oscillations can be found in a more general setting; in particular, in slow-fast systems, which are not written in the standard form. Systems in which separation into slow and fast variables is not given a priori, arise frequently in applications. Many of these systems include additionally various parameters of different orders of magnitude and complicated (non-polynomial) non-linearities. This poses several mathematical challenges, since the application of singular perturbation arguments is not at all straightforward. For that reason most of such systems have been studied only numerically guided by phase-space analysis arguments or analyzed in a rather non-rigorous way. It turns out that the main idea of singular perturbation approach can also be applied in such non-standard cases. This thesis is concerned with the application of concepts from geometric singular perturbation theory and geometric desingularization based on the blow-up method to the study of relaxation oscillations in slow-fast systems beyond the standard form. A detailed geometric analysis of oscillatory mechanisms in three mathematical models describing biochemical processes is presented. In all the three cases the aim is to detect the presence of an isolated periodic movement represented by a limit cycle. By using geometric arguments from the perspective of dynamical systems theory and geometric desingularization based on the blow-up method analytic proofs of the existence of limit cycles in the models are provided. This work shows -- in the context of non-trivial applications -- that the geometric approach, in particular the blow-up method, is valuable for the understanding of the dynamics of systems with no explicit splitting into slow and fast variables, and for systems depending singularly on several parameters

Understanding the Role of Morphology and Kinematics in Bio-Inspired Locomotion

Inspired by the advanced capabilities of fish and other aquatic swimmers, in this thesis, a greater understanding of fish-like propulsion has been sought in terms of morphology and kinematics. Unsteady potential flow simulations on real cetacean flukes reveal that the effect of shape and gait on the swimming performance are not intertwined and are in fact independent. There is one fluke shape that maximizes the propulsive efficiency regardless of the gait and vice versa. It is also determined that the shape and the gait of the fluke have a considerable influence on the wake topology and in turn the Strouhal number. Evolutionary optimization is used to isolate the shape effects and study optimum conditions when the kinematic features of the animals are varied. Searching the optimum swimmer in terms of swimming gait is performed by considering the three main aspects of the swimming performance: swimming speed, swimming range, and efficiency. Optimum conditions are found when i) the swimmer keeps the duty cycle low and uses sinusoidal-like motion by maintaining higher pitching amplitudes to provide higher thrust and swimming range; ii) the swimmer uses square-like waveform shapes by increasing the duty cycle and using small pitching amplitudes which decrease the swimming range but increase the swimming speed. In all combinations, swimming efficiency is maintained at the maximum achievable level. Scaling laws are presented to predict thrust production and power consumption of the swimmers by accounting for three-dimensionality with shape and gait variations. The scaling laws presented here provide insight into the flow physics that drive thrust production, power consumption, and efficient swimming when the morphology and kinematics are varied

Método de vórtices discretos e multipolos rápidos aplicados em escoamentos não-estacionários

Orientadores: William Roberto Wolf, Alex Mendonça BimbatoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: O método de vórtices discretos (DVM) não necessita de malhas por ser uma descrição lagrangiana da equação do transporte de vorticidade. Esta, por sua vez, é separada em termos difusivos e convectivos. Esta equação é resolvida pela discretização do campo de vorticidade em N vórtices discretos. Diversos métodos podem ser usados para modelar os efeitos da difusão; pode-se citar o método do passo aleatório, método do crescimento do núcleo, método da troca de intensidade, entre outros. Os termos de convecção são resolvidos pela utilização da derivada material para evitar termos não-lineares. Assim, cada vórtice discreto é convectado pelo campo local de velocidade, que é calculado pela contribuição do escoamento livre, superfícies sólidas e pela solução da lei de Biot-Savart que rege a interação entre vórtices. Entretanto, esta última contribuição exige um dispendioso passo de convolução com O(N 2 ) operações, que impõe restrição no uso do método para a solução de problemas típicos de engenharia. Assim, métodos alternativos são necessários para acelerar a solução do DVM. O método de multipolos rápidos, FMM, considerado um dos 10 melhores algoritmos do século 20, foi proposto por Greengard and Rokhlin (1987) para a solução da interação gravitacional entre N corpos. O algoritmo consiste no agrupamento da influência de elementos próximo entre si, e então calcula-se a interação em regiões distantes, como por exemplo o centro de outro agrupamento. Esta operação tem custo computacional de ordem O(N) para um número N suficientemente grande. Assim, a influência entre grupos distantes de elements é calculada mais eficientemente do que a ordem O(N 2 ) para calcular diretamente a lei de Biot-Savart. Neste trabalho, nós usamos um esquema não-adaptativo multi-nível do FMM com melhorias para acelerar o preprocessamento bem como os cálculos de interação no FMM. O acoplamento dos métodos é investigado para três diferentes problemas: a simulação de um cilindro abruptamente acelerado e a evolução temporal de uma esteira de aeronave assim como de uma camada de mistura. Uma comparação do custo computacional do método acelerado é comparado com a solução usando apenas a lei de Biot-Savart. Finalmente, como uma camada de mistura requer condições de contorno periódicas, o estudo de uma série alternativa para o cerne do FMM é feito com a investigação da precisão e do tempo computacionalAbstract: The Discrete Vortex Method (DVM) is a meshless numerical method based on a Lagrangian description of the vorticity transport equation, which is split into diffusive and convective effects. In order to solve this equation, the vorticity field is discretized in N vortex-particles. Several formulations can be used to model the diffusive effects, e.g., the random walk method, the core spreading method, the particle strength exchange, etc. The convection term can be treated using a material derivative to avoid the solution of a non-linear term. Therefore, each vortex is convected with the fluid velocity field, which is evaluated by the contributions from the incident flow, the perturbation due to the body, and the vortex-vortex interactions calculated by the Biot-Savart law. However, the last contribution requires an expensive convolution step of O(N 2 ) calculations, which imposes a heavy limitation on the usage of the method to solve engineering problems. With that in mind, alternative ways are required to accelerate the DVM simulations. The Fast Multipole Method is listed as one of the top 10 algorithms of the twentieth century, and it was developed by Greengard and Rokhlin (1987) for the solution of N -body gravitational problems. The algorithm consists of clustering the influence of elements close to each other, and then evaluating their interaction at distant locations, i.e., the center of far away clusters, with computational cost O(N) for a large number N . This way, the influence among different groups of particles is computed faster than the O(N 2 ) operations required by the direct Biot-Savart law. Here, we use the non-adaptive multi-level FMM with an optimization in the pre-processing steps, along with several techniques to speed up both pre-processing and FMM steps. The coupling of DVM and FMM is investigated in the present work, in three different problems: the simulation of the flow past an impulsively started cylinder and the temporal evolution of both an aircraft wake as well as a mixing layer. For these problems, there is a comparison of the computational time used by both the DVM-FMM and solely by the DVM. Finally, as the temporal evolution of a mixing layer requires periodic boundary conditions, a solution of an alternative kernel for the FMM is also employed in order to solve the problem, followed by the investigation of its precisionMestradoTermica e FluidosMestre em Engenharia Mecânica33003017CAPE

Emergence of Coherent Localized Structures in Shear Deformations of Temperature Dependent Fluids

Shear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. The latter is a nonlinear effect and its analysis is the main objective of this article. We consider a model that captures the main mechanisms observed in high strain-rate deformation of metals, and describes shear motions of temperature dependent non-Newtonian fluids. For a special dependence of the viscosity on the temperature, we carry out a linearized stability analysis around a base state of uniform shearing solutions, and quantitatively assess the effects of the various mechanisms affecting the problem: thermal softening, momentum diffusion and thermal diffusion. Then, we turn to the nonlinear model, and construct localized states -in the form of similarity solutions -that emerge as coherent structures in the localization process. This justifies a scenario for localization that is proposed on the basis of asymptotic analysis in [10]

Lagrangian simulation of transverse jets with a distribution-based diffusion scheme

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaves 248-255).Transverse jets form a dominant group of flow fields arising in many applications of modern energy utilization, including propulsion and effluent dispersion. Furthermore, they form canonical examples where the flow field is dominated by large-scale and small-scale vortical structures, whose inter-related dynamics is a challenging subject in modern fluid mechanics. This study seeks a mechanistic understanding of the vortical structures of the transverse jet and their evolution. A set of massively parallel three-dimensional vortex simulations of high-momentum transverse jets at intermediate Reynolds number, utilizing a discrete filament representation of the vorticity field to capture stretching and tilting of vorticity, is performed. A diffusion scheme to treat viscosity at intermediate Reynolds number is formulated and analyzed in a distribution-based description. The implementation of the diffusion scheme is achieved by performing interpolation, which is a process that has been widely used to regularize particle distributions in vortex simulations, with a new set of interpolation kernels. These kernels provide an accurate and efficient way to simulate vorticity diffusion in transverse jets. An improved formulation of the vorticity flux boundary conditions is rigorously derived.(cont.) This formulation includes separation of the wall boundary layer and feedback from the jet to the wall boundary layer, and describes detailed near-field jet structures. The results present the underlying mechanisms by which vortical structures evolve. Transformation of the jet shear layer emanating from the nozzle starts with jet streamwise lift-up of its lee side to form sections of counter-rotating vorticity aligned with the jet trajectory. Periodic rollup of the shear layer, which is similar to the Kelvin-Helmholtz instability in free shear layers, accompanies this deformation. A sudden breakdown of these coherent structures into dense vortical structures of smaller scales is observed. This breakdown to small-scale structures is due to the interaction of counter-rotating vortices and rolled-up shear layer. With a separated wall boundary layer, strong near-wall counter-rotating vortices are observed. This observation substantiates the importance of including the full interaction between the wall boundary layer and the jet shear layer in the investigation of transverse jet dynamics.by Daehyun Wee.Sc.D