Session G14: Flow Control II

Low Reynolds Number Flow Dynamics of a Thin, Flat Airfoil with Elastically Mounted Leading Edge Actuator

Direct numerical simulations are performed to investigate the effect of an elastically mounted leading edge actuator on the unsteady flow at high angles of attack over a flat, thin airfoil at Reynolds number of 14700 based on the chord length. The leading edge actuator is mounted with a torsion spring at one-third the chord length allowing dynamic variations in the effective angle of attack through flow-induced oscillations. The goal is to investigate potential benefits of flow induced flapping motion of the leading edge actuator to the lift and drag characteristics of thin airfoils. The structural model for the rigid actuator is based on a torsional spring-mounted compound pendulum. A fictitious-domain based finite volume approach [(Apte et al. (JCP 2009)] is used to compute this fluid-structure interaction problem on a fixed background mesh. It is shown that a lock-in region leading to limit cycle oscillations of the leading edge actuator can be achieved for certain spring parameters leading to improvements in mean lift-to-drag ratio.   

Passive control of the flow in a symmetric channel with a sudden expansion based on linear stability analysis

In the present work we investigate the stability properties of the flow in a 2D-plane channel with a symmetric sudden expansion, which is a possible schematization of a plane diffuser. The laminar flow in 2D diffusers may produce either symmetric or nonsymmetric steady solutions, depending on the value of the Reynolds number $Re$ as compared with some critical value $Re_c$. The stability properties of the flow are studied in the context of linear theory, characterizing the sensitivity of the instability to both a structural perturbation of the linearized flow equations and a perturbation of the base flow. The information provided by the two kinds of analysis is used to propose a passive flow control strategy, obtained by the introduction of a small cylinder in the channel, aimed at stabilizing the symmetric solution at $Re>Re_c$. The effectiveness of this control strategy in the nonlinear case is investigated, and ultimately verified by numerical simulations of the flow in which a real control cylinder is introduced. The robustness of the control is also tested by numerical simulations in which the position of the cylinder is slightly changed with respect to the optimal one given by the sensitivity analysis.   

Simultaneous achievement of drag reduction and heat transfer augmentation in wall turbulence by optimal control theory

The analogy concept between momentum and heat transfer, which is based upon the similarity between the Navier-Stokes and energy transport equations, has been widely used for analyzing turbulent transport phenomena. This fact implies inherent difficulty in enhancing heat transfer with pumping power reduced or not increased as much as heat transfer. We consider a fully developed turbulent channel flow with uniform heat generation in the fluid, so that the averaged transport equations have an identical form. The problem thus posed offers the most difficult challenge to achieve dissimilar momentum and heat transfer. Even under such a difficult condition, we demonstrate that the dissimilar control is possible if we exploit the continuity constraint on the velocity field. In order to optimize the control input, i.e., wall blowing/suction, the optimal control theory developed by Bewley et al. (2001) is applied. By defining the cost functional as a weighted sum of the intensity of the wall blowing/suction and the analogy factor, i.e., the ratio of wall heat flux and skin friction, the analogy factor increases more than double beyond that in the uncontrolled flow. It is also found that the resultant optimized control input exhibits a downstream traveling wave-like property.   

Robustness of reduced-order observer-based controllers in transitional 2D Blasius boundary layers

In this work, we seek to delay transition in the Blasius boundary layer. We trip the flow with an upstream disturbance and dampen the growth of the resulting structures downstream. The observer-based controllers use a single sensor and a single localized body force near the wall. To formulate the controllers, we first find a reduced-order model of the system via the Eigensystem Realization Algorithm (ERA), then find the $H_2$ optimal controller for this reduced-order system. We find the resulting controllers are effective only when the sensor is upstream of the actuator (in a feedforward configuration), but as is expected, are sensitive to model uncertainty. When the sensor is downstream of the actuator (in a feedback configuration), the reduced-order observer-based controllers are not robust and ineffective on the full system. In order to investigate the robustness properties of the system, an iterative technique called the adjoint of the direct adjoint (ADA) is employed to find a full-dimensional $H_2$ optimal controller. This avoids the reduced-order modelling step and serves as a reference point. ADA is promising for investigating the lack of robustness previously mentioned.   

Turbulent drag reduction by transverse wall oscillations

Skin-friction drag reduction by transverse wall oscillations has received significant attention in the last two decades. Both experiments and simulations have demonstrated that oscillations with properly selected amplitude and frequency can reduce turbulent drag by as much as 40 percent. For a turbulent channel flow, we develop a model-based approach to design oscillations that suppress turbulence. We show that judiciously selected linearization of the flow with control can be used to determine turbulent eddy viscosity in a computationally efficient way. The resulting correction to the turbulent mean velocity is then used to identify optimal frequency of oscillations, which is in close agreement with previously conducted experimental and numerical studies. This demonstrates the predictive power of our simulation-free approach to controlling turbulent flows.   

A computational framework for adjoint-based study of flapping wings

The study of flapping wings has provided many challenges for numerical simulation and experimental measurement by the problem's unsteadiness, nonlinearity, moving boundary, fluid-structure interaction, and other factors. However, even with perfect flow field from perfect numerical simulation, there is still limited understanding of fundamental flying mechanism. The sensitivity information, as a higher order quality, shows sometimes the mechanism often hidden in direct numerical simulation and experiments. Adjoint-based method, by its nature, suits the best for solving sensitivity problems with large input space and small output space. The work presented here is to provide a general framework to apply adjoint-based method to solve the sensitivity of flapping-wing problems. Immersed boundary technique is used in dealing with the moving boundaries in both physical and adjoint spaces.   

Control Performance of Input Shaping to Reduce Liquid Sloshing in a Horizontally Accelerating Container

Input shaping was originally developed to suppress the structural vibrations and many successful results have been reported so far. Its applicability can be extended to fluid vibrations such as liquid sloshing, which occurs when a partially filled container experiences acceleration for fast positioning control. However, its performance for sloshing suppression has not been assessed by solving the governing equations for unsteady two-phase fluid motions. Therefore, the objective of this study is to numerically investigate the performance of input shaping to reduce liquid sloshing in a horizontally accelerating container. In this study, three different input shapers (ZV, ZVD, convolved ZV shapers) are considered to eliminate the sloshing completely. With all of the shapers investigated, liquid sloshing is successfully suppressed but the control effects are quite dependent on the input shaper. In the cases of ZV(Zero Vibration) and ZVD(Zero Vibration and Derivative) shapers, liquid sloshing is suppressed to some extent, but residual vibrations still remain. On the other hand, liquid sloshing is almost eliminated with a two-mode convolved ZV shaper, which is designed to suppress the most energetic (first and third) modes.   

Flow past a moderately heated horizontal cylinder at low Reynolds number

In the present work, the influence of heat on vortex shedding and the wake structure in a flow cylinder is analyzed. Flow past a heated two dimensional cylinder in the laminar regime is investigated in the range of Reynolds numbers 25 to 100 under varying buoyancy conditions, $0\le Ri\le 1.0$ (where $Ri$ is the Richardson number, indicates the relative dominance of the inertial and buoyant effects). A hybrid FEM-FVM method is used to solve Navier-Stokes and energy equations. The vortex shedding frequency defined non-dimensionally as Strouhal number is observed to be increasing with heating. Vortex shedding behind heated cylinder exhibit asymmetry in wake region due to stable and unstable density stratification below and above the cylinder respectively. A negative lift is generated due to heating, in an otherwise symmetric zero time-averaged lift configuration, due to skewness in vortex shedding towards the direction of buoyancy. We also note that the heating brings down the drag slightly for the cases considered here. We also note here that at large Ri, the drag coefficient ($C_D$) decrease by $\sim 30\%$ at $Re=25$, percentage of decrease being less pronounced at higher Re (=100).   

On the evaluation of control performance in drag reducing flows

Performance of drag reduction control for internal flows is customarily evaluated under two flow conditions, i.e., constant mass flow rate or constant pressure gradient. In the former, the drag reduction rate, i.e. the reduction of the pumping power, is used for evaluating control performance, while the increase rate of the mass flow rate indicates successful control in the latter. Considering real applications, however, the optimization problem of flow control is essentially formulated by the interplay between energy saving and achieved flow rate, that can be interpreted as money on one side, and time or convenience on the other side. Based on this idea, we derive two dimensionless parameters which quantify the costs of total energy consumption and convenience for transportation of fluid through a given duct. We reevaluate the control performances of existing strategies in the present framework and also show that this evaluation can easily be extended to external flows.   

A reduced order interaction model for flow control via a poroelastic carpet of compliant actuators

A passive actuation technique that consists of covering the suction side of an airfoil with a coating of porous, compliant actuators (analogous to a class of flight feathers known as ``coverts''), has in the recent past been shown to be effective in controlling its wake. A feature in the case of an airfoil (as opposed to the case of a cylinder) is that two flow frequencies are observed under many conditions. Such wake control is highly sensitive to whether or not the frequency of the structure's dynamics synchronizes with one of these frequencies. Possible transitions from non-chaotic to chaotic vortex shedding regimes have also been observed. To determine the physics governing this complex fluid-structure interaction problem, a reduced order model is developed, by coupling an oscillator model for the structure with a van der Pol-like nonlinear oscillator model for the vortex shedding of the airfoil (a form with which the vortex-shedding from many canonical structures has been represented). In the case of a cylinder, the limit cycle of the unsteady lift coefficient for the coupled system is seen to lie within that of the plain vortex-shedding oscillator, indicating that the poroelastic coating is capable of yielding drag reduction, arising from a stabilization of the wake.