arXiv subjects

Armin Zare

Publications and source records attributed to Armin Zare.

13 recordsLinked to original sources

arXiv2025

Turbulence modeling over riblets via domain transformation

Numerical and experimental studies have demonstrated the drag-reducing potential of carefully designed streamwise-elongated riblets in lowering skin-friction drag. To support the systematic design of such surface corrugations, recent efforts have integrated simplified versions of the governing equations with innovative methods for representing the effects of rough boundaries on flow dynamics. Notably, the statistical response of the eddy-viscosity-enhanced linearized Navier-Stokes equations has been shown to effectively capture the ability of riblets in suppressing turbulence, quantify the influence of background turbulence on the mean velocity, and reproduce established drag-reduction trends. In this paper, we enhance the flexibility and computational efficiency of this simulation-free approach by implementing a domain transformation for surface representation, along with a perturbation analysis on a small geometric parameter of the riblets. While domain transformation complicates the differential equations, it provides accurate boundary representations and facilitates the analysis of complex riblet shapes at high Reynolds numbers by enabling perturbation analysis to simplify the dimensional complexity of the governing equations. Our method successfully predicts drag reduction trends for triangular and scalloped riblets, consistent with existing literature. We further utilize our framework to investigate flow mechanisms influenced by riblets and extend our study to channel flows with friction Reynolds numbers up to 2003. Our findings reveal the emergence of K-H rollers over large and sharp scalloped riblets, contributing to the degradation of drag reduction in these geometries. Additionally, we examine the impact of riblets on near-wall flow structures, focusing on their suppression of streamwise-elongated structures in flows over large riblets.

physics.flu-dyn↗

arXiv2024

Short-term wind forecasting via surface pressure measurements: stochastic modeling and sensor placement

We propose a short-term wind forecasting framework for predicting real-time variations in atmospheric turbulence based on nacelle-mounted anemometer and ground-level air-pressure measurements. Our approach combines linear stochastic estimation and Kalman filtering algorithms to assimilate and process real-time field measurements with the predictions of a stochastic reduced-order model that is confined to a two-dimensional plane at the hub height of turbines. We bridge the vertical gap between the computational plane of the model at hub height and the measurement plane on the ground using a projection technique that allows us to infer the pressure in one plane from the other. Depending on the quality of this inference, we show that customized variants of the extended and ensemble Kalman filters can be tuned to balance estimation quality and computational speed 1-1.5 diameters ahead and behind leading turbines. In particular, we show how synchronizing the sign of estimates with that of velocity fluctuations recorded at the nacelle can significantly improve the ability to follow temporal variations upwind of the leading turbine. We also propose a convex optimization-based framework for selecting a subset of pressure sensors that achieve a desired level of accuracy relative to the optimal Kalman filter that uses all sensing capabilities.

physics.flu-dyn↗

arXiv2022

Model-based spectral coherence analysis

Recent data-driven efforts have utilized spectral decomposition techniques to uncover the geometric self-similarity of dominant motions in the logarithmic layer, and thereby validate the attached eddy model. In this paper, we evaluate the predictive capability of the stochastically forced linearized Navier-Stokes equations in capturing such structural features in turbulent channel flow at $Re_τ=2003$. We use the linear coherence spectrum to quantify the wall-normal coherence within the velocity field generated by the linearized dynamics. In addition to the linearized Navier-Stokes equations around the turbulent mean velocity profile, we consider an enhanced variant in which molecular viscosity is augmented with turbulent eddy-viscosity. We use judiciously shaped white- and colored-in-time stochastic forcing to generate a statistical response with energetic attributes that are consistent with the result of direct numerical simulation (DNS). Specifically, white-in-time forcing is scaled to ensure that the two-dimensional energy spectrum is reproduced and colored-in-time forcing is shaped to match normal and shear stress profiles. We show that the addition of eddy-viscosity significantly strengthens the self-similar attributes of the resulting stochastic velocity field within the logarithmic layer and leads to an inner-scaled coherence spectrum. We use this coherence spectrum to extract the energetic signature of self-similar motions that actively contribute to momentum transfer and are responsible for producing Reynolds shear stress. Our findings support the use of colored-in-time forcing in conjunction with the dynamic damping afforded by turbulent eddy-viscosity in improving predictions of the scaling trends associated with such active motions in accordance with DNS-based spectral decomposition.

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arXiv2022

Stochastic dynamical wake modeling for wind farms

Low-fidelity analytical models of turbine wakes have traditionally been used for wind farm planning, performance evaluation, and demonstrating the utility of advanced control algorithms in increasing the annual energy production. In practice, however, it remains challenging to correctly estimate the flow and achieve significant performance gains using conventional low-fidelity models. This is due to the over-simplified static nature of wake predictions from models that are agnostic to the effects of atmospheric boundary layer turbulence and the complex aerodynamic interactions among wind turbines. To improve the predictive capability of low-fidelity models while remaining amenable to control design, we offer a stochastic dynamical modeling framework for capturing the effect of atmospheric turbulence on the thrust force and power generation as determined by the actuator disk concept. In this approach, we use stochastically forced linear models of the turbulent velocity field to augment the analytically computed wake velocity and achieve consistency with higher-fidelity models in capturing power and thrust force measurements. The power-spectral densities of our stochastic models are identified via convex optimization to ensure consistency with partially available velocity statistics or power and thrust force measurements while preserving model parsimony. We demonstrate the utility of our approach in capturing turbulence intensity variations behind wind turbines and estimating thrust force and power signals generated by large-eddy simulations of the flow over a cascade of turbines. Our results provide insight into the significance of sparse field measurements in recovering the statistical signature of wind farm turbulence using stochastic linear models.

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arXiv2022

Input-output analysis of stochastic base flow uncertainty

We adopt an input-output approach to analyze the effect of persistent white-in-time structured stochastic base flow perturbations on the mean-square properties of the linearized Navier-Stokes equations. Such base flow variations enter the linearized dynamics as multiplicative sources of uncertainty that can alter the stability of the linearized dynamics and their receptivity to exogenous excitations. Our approach does not rely on costly stochastic simulations or adjoint-based sensitivity analysis. We provide verifiable conditions for mean-square stability and study the frequency response of the flow subject to additive and multiplicative sources of uncertainty using the solution to the generalized Lyapunov equation. For small-amplitude base flow perturbations, we bypass the need to solve large generalized Lyapunov equations by adopting a perturbation analysis. We use our framework to study the destabilizing effects of stochastic base flow variations in transitional parallel flows, and the reliability of numerically estimated mean velocity profiles in turbulent channel flows. We uncover the Reynolds number scaling of critically destabilizing perturbation variances and demonstrate how the wall-normal shape of base flow modulations can influence the amplification of various length scales. Furthermore, we explain the robust amplification of streamwise streaks in the presence of streamwise base flow variations by analyzing the dynamical structure of the governing equations as well as the Reynolds number dependence of the energy spectrum.

physics.flu-dyn↗

arXiv2021

Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem

Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these approaches are often poorly understood because of the nonconvex nature of the underlying optimization problems and the lack of exact gradient computation. In this paper, we take a step towards demystifying the performance and efficiency of such methods by focusing on the standard infinite-horizon linear quadratic regulator problem for continuous-time systems with unknown state-space parameters. We establish exponential stability for the ordinary differential equation (ODE) that governs the gradient-flow dynamics over the set of stabilizing feedback gains and show that a similar result holds for the gradient descent method that arises from the forward Euler discretization of the corresponding ODE. We also provide theoretical bounds on the convergence rate and sample complexity of the random search method with two-point gradient estimates. We prove that the required simulation time for achieving $ε$-accuracy in the model-free setup and the total number of function evaluations both scale as $\log \, (1/ε)$.

math.OC↗

arXiv2020

Model-based design of riblets for turbulent drag reduction

Both experiments and direct numerical simulations have been used to demonstrate that riblets can reduce turbulent drag by as much as $10\%$, but their systematic design remains an open challenge. In this paper, we develop a model-based framework to quantify the effect of streamwise-aligned spanwise-periodic riblets on kinetic energy and skin-friction drag in turbulent channel flow. We model the effect of riblets as a volume penalization in the Navier-Stokes equations and use the statistical response of the eddy-viscosity-enhanced linearized equations to quantify the effect of background turbulence on the mean velocity and skin-friction drag. For triangular riblets, our simulation-free approach reliably predicts drag-reducing trends as well as mechanisms that lead to performance deterioration for large riblets. We investigate the effect of height and spacing on drag reduction and demonstrate a correlation between energy suppression and drag-reduction for appropriately sized riblets. We also analyze the effect of riblets on drag reduction mechanisms and turbulent flow structures including very large scale motions. Our results demonstrate the utility of our approach in capturing the effect of riblets on turbulent flows using models that are tractable for analysis and optimization.

physics.flu-dyn↗

arXiv2019

Stochastic dynamical modeling of turbulent flows

Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be constructed to reproduce structural and statistical features of turbulent flows, opening the way to the design of effective model-based flow control strategies. This review describes a framework for completing second-order statistics of turbulent flows by models that are based on the Navier-Stokes equations linearized around the turbulent mean velocity. Systems theory and convex optimization are combined to address the inherent uncertainty in the dynamics and the statistics of the flow by seeking a suitable parsimonious correction to the prior linearized model. Specifically, dynamical couplings between states of the linearized model dictate structural constraints on the statistics of flow fluctuations. Thence, colored-in-time stochastic forcing that drives the linearized model is sought to account for and reconcile dynamics with available data (i.e., partially known second order statistics). The number of dynamical degrees of freedom that are directly affected by stochastic excitation is minimized as a measure of model parsimony. The spectral content of the resulting colored-in-time stochastic contribution can alternatively be seen to arise from a low-rank structural perturbation of the linearized dynamical generator, pointing to suitable dynamical corrections that may account for the absence of the nonlinear interactions in the linearized model.

physics.flu-dyn↗

arXiv2019

Stochastic receptivity analysis of boundary layer flow

We utilize the externally forced linearized Navier-Stokes equations to study the receptivity of pre-transitional boundary layers to persistent sources of stochastic excitation. Stochastic forcing is used to model the effect of free-stream turbulence that enters at various wall-normal locations and the fluctuation dynamics are studied via linearized models that arise from locally parallel and global perspectives. In contrast to the widely used resolvent analysis that quantifies the amplification of deterministic disturbances at a given temporal frequency, our approach examines the steady-state response to stochastic excitation that is uncorrelated in time. In addition to stochastic forcing with identity covariance, we utilize the spatial spectrum of homogeneous isotropic turbulence to model the effect of free-stream turbulence. Even though locally parallel analysis does not account for the effect of the spatially evolving base flow, we demonstrate that it captures the essential mechanisms and the prevailing length-scales in stochastically forced boundary layer flows. On the other hand, global analysis, which accounts for the spatially evolving nature of the boundary layer flow, predicts the amplification of a cascade of streamwise scales throughout the streamwise domain. We show that the flow structures that can be extracted from a modal decomposition of the resulting velocity covariance matrix, can be closely captured by conducting locally parallel analysis at various streamwise locations and over different wall-parallel wavenumber pairs. Our approach does not rely on costly stochastic simulations and it provides insight into mechanisms for perturbation growth including the interaction of the slowly varying base flow with streaks and Tollmien-Schlichting waves.

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arXiv2019

Modeling mode interactions in boundary layer flows via the Parabolized Floquet Equations

In this paper, we develop a model based on successive linearization to study interactions between different modes in boundary layer flows. Our method consists of two steps. First, we augment the Blasius boundary layer profile with a disturbance field resulting from the linear Parabolized Stability Equations (PSE) to obtain the modified base flow; and, second, we draw on Floquet decomposition to capture the effect of mode interactions on the spatial evolution of flow fluctuations via a sequence of linear progressions. The resulting Parabolized Floquet Equations (PFE) can be conveniently advanced downstream to examine the interaction between different modes in slowly varying shear flows. We apply our framework to two canonical settings of transition in boundary layers; the H-type transition scenario that is initiated by exponential instabilities, and streamwise elongated laminar streaks that are triggered by the lift-up mechanism. We demonstrate that the PFE capture the growth of various harmonics and provide excellent agreement with the results obtained in direct numerical simulations and in experiments.

physics.flu-dyn↗

arXiv2018

Proximal algorithms for large-scale statistical modeling and sensor/actuator selection

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The first, in statistical modeling, seeks to reconcile observed statistics by suitably and minimally perturbing prior dynamics. The second seeks to optimally select a subset of available sensors and actuators for control purposes. To address modeling and control of large-scale systems we develop a unified algorithmic framework using proximal methods. Our customized algorithms exploit problem structure and allow handling statistical modeling, as well as sensor and actuator selection, for substantially larger scales than what is amenable to current general-purpose solvers. We establish linear convergence of the proximal gradient algorithm, draw contrast between the proposed proximal algorithms and alternating direction method of multipliers, and provide examples that illustrate the merits and effectiveness of our framework.

math.OC↗

arXiv2016

Color of turbulence

In this paper, we address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier-Stokes equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation sources. For the case where only a subset of velocity correlations are known, we develop a framework to complete unavailable second-order statistics in a way that is consistent with linearization around turbulent mean velocity. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. We develop models for colored-in-time forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization. We show that colored-in-time excitation of the Navier-Stokes equations can also be interpreted as a low-rank modification to the generator of the linearized dynamics. Our method provides a data-driven refinement of models that originate from first principles and captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization, and control design.

physics.flu-dyn↗

arXiv2016

Low-complexity modeling of partially available second-order statistics: theory and an efficient matrix completion algorithm

State statistics of linear systems satisfy certain structural constraints that arise from the underlying dynamics and the directionality of input disturbances. In the present paper we study the problem of completing partially known state statistics. Our aim is to develop tools that can be used in the context of control-oriented modeling of large-scale dynamical systems. For the type of applications we have in mind, the dynamical interaction between state variables is known while the directionality and dynamics of input excitation is often uncertain. Thus, the goal of the mathematical problem that we formulate is to identify the dynamics and directionality of input excitation in order to explain and complete observed sample statistics. More specifically, we seek to explain correlation data with the least number of possible input disturbance channels. We formulate this inverse problem as rank minimization, and for its solution, we employ a convex relaxation based on the nuclear norm. The resulting optimization problem is cast as a semidefinite program and can be solved using general-purpose solvers. For problem sizes that these solvers cannot handle, we develop a customized alternating minimization algorithm (AMA). We interpret AMA as a proximal gradient for the dual problem and prove sub-linear convergence for the algorithm with fixed step-size. We conclude with an example that illustrates the utility of our modeling and optimization framework and draw contrast between AMA and the commonly used alternating direction method of multipliers (ADMM) algorithm.

math.OC↗