Browsing by Author "Collis, S. Scott"

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    Adjoint analysis for receptivity prediction
    (2003) Dobrinsky, Alexander Y.; Collis, S. Scott
    Physical knowledge of the laminar-turbulent transition process, prediction of the transition location, as well as the ability to control transition are essential in many engineering applications. However, control of the laminar-turbulent transition depends critically on various environmental sources and their ability to excite the instability waves in the flow, which are responsible for the laminar-turbulent transition. The process by which external disturbances are converted into instability waves is called receptivity. The research described in this thesis focuses on the receptivity of two- and three-dimensional boundary layers. The main objective of this research is to formulate, validate and apply adjoint analysis in order to predict receptivity. Adjoint analysis is a powerful approach for investigating the receptivity of different flows for arbitrary environmental sources. In this work, Adjoint Navier-Stokes (ANS) equations are formulated based on the sensitivity approach, and adjoint predictions are validated against Linearized Navier-Stokes (LNS) calculations. Further, Adjoint Parabolized Stability Equations (APSE) are derived as an approximation of ANS equations and compared against the ANS results. Our studies indicate that the APSE method should be constructed as an approximation to the ANS equations, not as the formal adjoint of the PSE. When implemented in this manner, we show that APSE is a viable method for receptivity prediction, even in highly nonparallel flows. The APSE is first applied to predict receptivity of weakly nonparallel two-dimensional boundary layer flows for a variety of parameters. We find that these flows are generally more receptivity to oblique disturbances although two-dimensional disturbances are less stable. We also find that favorable pressure gradient boundary layers are more receptive then adverse pressure gradient boundary layers, although adverse pressure gradients are destabilizing. The APSE are then applied to highly nonparallel three-dimensional boundary layers where we find that for the inviscidly unstable crossflow instability, stability effects typically dominate receptivity effects. Comparison of receptivity for stationary and unsteady crossflow instabilities shows that receptivity to both localized momentum sources and streamwise wall-velocity excitations is larger for unsteady modes, but that receptivity to wall-normal excitations is larger for stationary modes. Finally, we consider receptivity for the swept parabolic cylinder and observe that convex surface curvature tends to enhance receptivity to wall roughness, in agreement with prior studies. Utilizing the efficiency of adjoint methods, we also consider other excitations for the swept parabolic cylinder and show that convex surface curvature also enhances receptivity to streamwise momentum sources, but that receptivity to both normal and tangential velocity disturbances is slightly reduced.
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    Analysis of the SUPG Method for the Solution of Optimal Control Problems
    (2002-03) Collis, S. Scott; Heinkenschloss, M.
    We study the effect of the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method on the discretization of optimal control problems governed by linear advection-diffusion equations. We compare two approaches for the numerical solution of such optimal control problems. In the discretize-then-optimize approach the optimal control problem is first discretized, using the SUPG method for the discretization of the advection-diffusion equation, and then the resulting finite dimensional optimization problem is solved. In the optimize-then-discretize approach one first computes the infinite dimensional optimality system, involving the advection-diffusion equation as well as the adjoint advection-diffusion equation, and then discretizes this optimality system using the SUPG method for both the original and the adjoint equations. These approaches lead to different results. The main result of this paper is an estimates for the error between the solution of the infinite dimensional optimal control problem and their approximations computed using the previous approaches. For a class of problems prove that the optimize-then-discretize approach has better asymptotic convergence properties if finite elements of order greater than one are used. For linear finite elements our theoretical convergence results for both approaches are comparable, except in the zero diffusion limit where again the optimize-then-discretize approach seems favorable. Numerical examples are presented to illustrate some of the theoretical results.
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    Approximate models for optimal control of turbulent channel flow
    (2000) Chang, Yong; Collis, S. Scott
    Advances in high-performance computing and Large-Eddy Simulation (LES) have made it possible to obtain accurate solutions of complex, turbulent flows at moderate Reynolds numbers. With these advances, computational modeling of turbulent flows in order to develop, evaluate, and optimize active control strategies is feasible. In this thesis, we present approaches to numerical modeling of opposition control and optimal control of turbulent flows with attention to algorithms that utilize the dynamic subgrid-scale LES model. Approximately 25% drag reduction is achieved by opposition control using LES, which is in good agreement with previous DNS results at a low Reynolds number of Retau = 180. Based on this success, we have used our LES approach to extend opposition control to a high Reynolds number flow of Retau = 590. With the sensing location at y+ ≈ 15, which is the best sensing plane for Retau = 180, only 21% drag reduction can be achieved, suggesting that opposition control is less effective at higher Reynolds numbers. An optimal control scheme based on LES has been implemented successfully using an instantaneous control approach with a nonlinear conjugate gradient algorithm used to update the control. The flow sensitivity is computed from the adjoint LES equations which are presented herein, and LES results are compared to prior DNS results for optimal control under similar conditions at Retau = 100. These comparisons indicate that optimal control based on LES can relaminarize low Reynolds number turbulent channel flow similar to results obtained using DNS but with significantly lower computational expense. Optimal control is also explored for turbulent channel flow at Retau = 180. At this Reynolds number, our optimal control approach is not as effective as the results at Retau = 100, the flow eventually enters a statistically stable state with approximately 40% drag reduction. Some possible ways to improve the control effectiveness are discussed, including the use of the discrete adjoint equations. Results are also presented for a novel hybrid LES/DNS scheme in which the optimization iterations are performed using LES while the flow is advanced in time using DNS for flow at Retau = 100. These hybrid simulations retain the computational efficiency of LES and the accuracy of DNS. Results from hybrid simulations clearly demonstrate that the controls computed based on LES optimization are also viable in the context of DNS. In all cases, the agreement between LES, DNS, and hybrid LES/DNS indicates that reliable turbulence control strategies can be efficiently developed based on LES models. We conclude that LES can be used as a reduced order model for optimal control of turbulence and this conclusions is shown to hold for even low resolution LES. The control mechanisms for drag reduction using opposition control and optimal control are discussed. Opposition control creates a virtual wall that affects all scales of turbulent motions near the physical wall. In contrast, optimal control creates a virtual wall for the large scale roll mode of the turbulent flow. Since this virtual wall affects directly the scales of motion responsible for increased drag in a turbulent flow, the optimal control is able to achieve larger drag reductions.
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    Immersed boundary methods with applications to flow control
    (2001) Kellogg, Steven Michael; Collis, S. Scott
    While some engineers use computers as a first line of attack on design problems, others are persistently making computers and their software faster and more capable of solving realistic problems. The technology used to build the microscale electronic components that makes computers fast is also used to construct micron-scale electromechanical (MEMS) actuators ideal for use in control schemes to reduce drag in industrial flows, promising millions of dollars in cost savings. The Immersed Boundary Condition (IBC) developed here augments a common fractional step, pseudospectral method used with Large Eddy Simulation to inexpensively and more realistically simulate turbulent flow over MEMS-like actuators. This is done by augmenting the numerical method to simulate flow over unsteady, irregular boundaries with static, structured rectilinear grids. The method is validated and applied to evaluate actuator characteristics and simulate open and closed loop flow control with continuous and discrete, MEMS-like actuators.
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    Local variational multi-scale method for turbulence simulation
    (2005) Ramakrishnan, Srinivas; Collis, S. Scott
    Accurate and efficient turbulence simulation in complex geometries is a formidable challenge. Traditional methods are often limited by low accuracy and/or restrictions to simple geometries. We explore the merger of Discontinuous Galerkin (DG) with Variational Multi-Scale (VMS), termed Local VMS (LVMS), to overcome these limitations. DG spatial discretizations support arbitrarily high-order accuracy on unstructured grids amenable for complex geometries. Furthermore, high-order hierarchical representation within DG provides a natural framework for a priori scale separation crucial for VMS implementation, a promising approach to LES. We study the efficacy of LVMS for turbulence simulation using a fully-developed turbulent channel flow. First, a detailed spatial resolution study is undertaken to record the effects of the DG discretization on turbulence statistics. Here, the local hp-refinement capabilities of DG are exploited to obtain reliable low-order statistics efficiently. Then, we explore the effects of enforcing Dirichlet boundary conditions through numerical fluxes in DG that allows solution jumps (slip) at the channel walls. This feature of DG is effective in mitigating the high near-wall resolution requirements in the wall-normal direction that enables reasonable drag predictions even with moderate resolutions. However, using coarse resolutions leads to significant slip at the channel walls that affect drag predictions. Here, modifying the numerical viscous flux to regulate this slip through a penalty is found to improve drag predictions. Thus, demonstrating the potential of the numerical viscous flux to act as a rudimentary wall-model. Next, for reduced-order modeling, we evaluate the merits of Spectral Filtering (SF) and Polynomial Dealiasing (PD) for improving non-linear stability. While both approaches are successful, PD is found to be better suited for Sub-Grid Scales (SGS) modeling. Finally, a VMS model is implemented to account for SGS effects. Results in good agreement with reference are obtained demonstrating the effectiveness of LVMS for wall-bounded turbulence. The locality of DG provides the flexibility to specify model parameters individually on each element. This unique feature of LVMS can be exploited for surgical modeling in a wide range of turbulent flows.
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    Multi-model simulation for optimal control of aeroacoustics
    (2005) Chen, Guoquan; Collis, S. Scott
    Flow-generated noise, especially rotorcraft noise has been a serious concern for both commercial and military applications. A particular important noise source for rotorcraft is Blade-Vortex-Interaction (BVI) noise, a high amplitude, impulsive sound that often dominates other rotorcraft noise sources. In this thesis the research is to formulate and implement efficient computational tools for the development and study of optimal control and design strategies for complex flow/acoustic systems with emphasis on rotorcraft applications, especially BVI noise control problem. The main purpose of aeroacoustic computations is to determine the sound intensity and directivity far away from the noise source. However, the computational cost of using a high-fidelity flow-physics model across the full domain is usually prohibitive and it might also be less accurate because of the numerical diffusion and other problems. Taking advantage of the multi-physics and multi-scale structure of this aeroacoustic problem, we develop a multi-model, multi-domain (near-field/farfield) method based on a discontinuous Galerkin discretization. In this approach the coupling of multi-domains and multi-models is achieved by weakly enforcing continuity of normal fluxes across a coupling surface. For our interested aeroacoustics control problem, the adjoint equations that determine the sensitivity of the cost functional to changes in control are also solved with same approach by weakly enforcing continuity of normal fluxes across a coupling surface. Such formulations have been validated extensively for several aeroacoustics state and control problems. A multi-model based optimal control framework has been constructed and applied to our interested BVI noise control problem. This model problem consists of the interaction of a compressible vortex with Bell AH-1 rotor blade with wall-normal velocity used as control on the rotor blade surface. The computational domain is decomposed into the near-field and far-field. The near-field is obtained by numerical solution of the Navier-Stokes equations while far away from the noise source, where the effect of nonlinearities is negligible, the linearized Euler equations are used to model the acoustic wave propagation. The BVI wave packet is targeted by defining an objective function that measures the square amplitude of pressure fluctuations in an observation region, at a time interval encompassing the dominant leading edge compressibility waves. Our control results show that a 12dB reduction in the observation region is obtained. Interestingly, the control mechanism focuses on the observation region and only minimize the sound level in that region at the expense of other regions. The vortex strength and trajectory get barely changed. However, the optimal control does alter the interaction of the vortical and potential fields, which is the source of BVI noise. While this results in a slight increase in drag, there is a significant reduction in the temporal gradient of lift leading to a reduction in BVI sound levels. (Abstract shortened by UMI.)
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    Variational multiscale methods for turbulence control
    (2003) Ramakrishnan, Srinivas; Collis, S. Scott
    Large Eddy Simulation (LES) is an efficient computational tool for turbulence simulation. Variational Multiscale (VMS) is a new paradigm for LES that uses variational projection instead of spatial filtering that obviates many issues related to spatial filtering in traditional LES. VMS for a fully-developed turbulent channel flow using a constant coefficient Smagorinsky model is implemented in a hybrid-spectral code. Our implementation differs from prior VMS where we apply scale separation only in the homogeneous directions, i.e. in the planes. The results obtained are comparable to prior VMS implementations that show good agreement with Direct Numerical Simulation (DNS) and are superior to dynamic LES. The ability of the VMS method to simulate turbulence control is studied in the context of opposition control. The results show good agreement with DNS and dynamic LES making VMS an attractive method for turbulence control investigations.