Browsing by Subject "Flow Control"

Now showing 1 - 2 of 2
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    Imposing Physical Structure within Input-Output Analysis of Fluid Flows: Methods and Applications
    (2023-07) Mushtaq, Talha
    Input-output (I/O) methods have recently been proposed as simulation-free methods for identifying and quantifying fluid flow instabilities. Recent developments in I/O methods have focused on imposing additional physical structure within the I/O framework by (i) accounting for the structure of the nonlinear terms (i.e., structured I/O), or (ii) promoting sparsity in the identified instability mechanisms (i.e., spatially-localized modal analysis). This dissertation contributes to the state of the art by formulating and applying I/O analysis algorithms that are both computationally efficient and impose this physical structure in a mathematically consistent manner. First, we propose algorithms for performing the structured I/O analysis, which involves computing structured singular value (SSV) bounds (worst-case gains) and mode shapes by exploiting the underlying mathematical structure of the convective nonlinearity in the incompressible Navier-Stokes equations (NSE). The analysis yields physical insights of the global flow mechanisms, which are useful for identifying flow instabilities. We demonstrate the analysis on a laminar channel flow, and a turbulent channel flow over riblets. For both models, we identify various relevant flow mechanisms that are consistent with the ones predicted in high-fidelity numerical simulations, e.g., Kelvin-Helmholtz (KH) vortices, lift-up effects and Near-Wall (NW) cycles. Second, we propose computationally efficient algorithms for spatially-localized modal analysis. Unlike state of the art methods that promote sparsity, the methods proposed here work to solve a cardinality-constrained optimization problem. The solution to the optimization are sparse modes that highlight most pertinent flow quantities for triggering instabilities. We demonstrate the analysis on a laminar channel flow, where the sparse modes identify various spatially-localized flow mechanisms that contribute to the kinetic energy growth of the flow, e.g., the lift-up effect and Tollmien-Schlichting instabilities.
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    Low-complexity stochastic modeling of wall-bounded shear flows
    (2016-12) Zare, Armin
    Turbulent flows are ubiquitous in nature and they appear in many engineering applications. Transition to turbulence, in general, increases skin-friction drag in air/water vehicles compromising their fuel-efficiency and reduces the efficiency and longevity of wind turbines. While traditional flow control techniques combine physical intuition with costly experiments, their effectiveness can be significantly enhanced by control design based on low-complexity models and optimization. In this dissertation, we develop a theoretical and computational framework for the low-complexity stochastic modeling of wall-bounded shear flows. Part I of the dissertation is devoted to the development of a modeling framework which incorporates data-driven techniques to refine physics-based models. We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate optimization problems to identify the dynamics and directionality of input excitation in order to explain and complete available covariance data. For problem sizes that general-purpose solvers cannot handle, we develop customized optimization algorithms based on alternating direction methods. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement. In Part II, we employ our modeling framework to account for statistical signatures of turbulent channel flow using low-complexity stochastic dynamical models. We demonstrate that white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics and develop models for colored-in-time forcing of the linearized Navier-Stokes equations. We also examine the efficacy of stochastically forced linearized NS equations and their parabolized equivalents in the receptivity analysis of velocity fluctuations to external sources of excitation as well as capturing the effect of the slowly-varying base flow on streamwise streaks and Tollmien-Schlichting waves. In Part III, we develop a model-based approach to design surface actuation of turbulent channel flow in the form of streamwise traveling waves. This approach is capable of identifying the drag reducing trends of traveling waves in a simulation-free manner. We also use the stochastically forced linearized NS equations to examine the Reynolds number independent effects of spanwise wall oscillations on drag reduction in turbulent channel flows. This allows us to extend the predictive capability of our simulation-free approach to high Reynolds numbers.