In this review, we present control methods for flow over a bluff body such as a circular cylinder, a 2D bluff body with a blunt trailing edge, and a sphere. We introduce recent major achievements in bluff-body flow controls such as 3D forcing, active feedback control, control based on local and global instability, and control with a synthetic jet. We then classify the controls as boundary-layer controls and direct-wake modifications and discuss important features associated with these controls. Finally, we discuss some other issues such as Reynolds-number dependence, the lowest possible drag by control, and control efficiency.

Control of Flow Over a Bluff Body

There are none." John Doyle, IEEE Transactions on Automatic Control, 1978 [86] The most well-developed theory of control generally applies to a linear system or to the linearization of a nonlinear system about a fixed point or a periodic orbit. Linear control theory has many applications in fluid dynamics, such as the stabilization of unstable laminar boundary layers. Although the governing equations may be nonlinear, successful stabilizing controllers will regulate the system to a neighborhood where the linearization is increasingly valid. In this chapter we introduce linear systems (Sec. 3.1) and explore H2 optimal control problems, including the linear quadratic regulator (LQR) in Sec. 3.2 and Kalman filters in Sec. 3.3. These problems are chosen because of their simplicity, ubiquitous application, well-defined quadratic cost-functions, and the existence of known optimal solutions. Next, linear quadratic Gaussian (LQG) control is introduced for sensor-based feedback in Sec. 3.4. Finally, methods of system linear system identification are provided in Sec. 3.5. This chapter is not meant to be an exhaustive primer on linear control theory, although key concepts from optimal control are introduced as needed to build intuition. Note that none of the linear system theory below is required to implement the machine learning control strategies in the remainder of the book, but they are instead included to provide context and demonstrate known optimal solutions to linear control problems. In many situations, H∞ robust control may be more desirable to balance the trade-off between robustness and performance in systems with uncertainty and unmodeled dynamics, and the MLC methods developed here may be generalized to other cost functions. For a more complete discussion of linear control theory, excellent books include [93, 251].

Machine Learning Control – Taming Nonlinear Dynamics and Turbulence

Numerical investigation of hydrodynamics and heat transfer of elongated bubbles during flow boiling in a microchannel

A review on numerical studies of slug flow hydrodynamics and heat transfer in microtubes and microchannels

Adjoint formulation is employed for the optimal control of flow around a rotating cylinder, governed by the unsteady Navier-Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time-dependent. Since the numerical control problem is ill-posed, regularization is employed. An empirical logarithmic law relating the regularization coefficient to the Reynolds number was derived for 60 ≤ Re ≤ 140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re = 60 to Re = 1000

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Suppression of vortex shedding for flow around a circular cylinder using optimal control

Forced streamwise oscillations of a circular cylinder: Locked-on modes and resulting fluid forces

The temporal development of two-dimensional viscous incompressible flow induced by an impulsively started circular cylinder which performs time-dependent rotational oscillations about its axis and translates at right angles to this axis is investigated. The investigation is based on the solutions of the unsteady Navier-Stokes equations. A series expansion for small times is developed. The Navier-Stokes equations are also integrated by a spectral-finite difference method for moderate values of time for both moderate and high Reynolds numbers. The numerical method is checked with the results of the analytical solution. The effects of the Reynolds number and of the forcing Strouhal number S on the laminar asymmetric flow structure in the near-wake region are studied. The lift and drag coefficients are also extracted from numerical results. An interesting phenomenon has been observed both in the flow patterns and in the behaviour of drag coefficients for S = π/2 at Reynolds number R = 500 and is discussed. For comparison purposes the start-up flow is determined numerically at a low Reynolds number and is found to be in good agreement with previous experimental predictions.

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The flow induced by a rotationally oscillating and translating circular cylinder

Thermal spreading resistance problems have been studied by many different researchers over the past six decades. In this paper, the literature on thermal spreading resistance from the past 50 years is chronologically presented, and the last decade of advances are specifically described. Focus is given to recent advances since much of the literature was reviewed in a handbook chapter published in 2003. For consistency throughout the paper, the rectangular slab and cylindrical disk heat spreader are referred to as flux channels and flux tubes, respectively. The thermal spreading resistance of compound rectangular flux channels and circular flux tubes with and without contact resistance are presented. The sink plane boundary condition is modeled using convective cooling with constant and/or variable heat transfer coefficient. Furthermore, the effects of discrete cooling in the heat-sink plane, orthotropic properties, and temperature-dependent thermal conductivity are also presented.

Review of Advances in Thermal Spreading Resistance Problems

A numerical method is developed for investigating the two-dimensional unsteady viscous flow over an inclined elliptic cylinder placed in a uniform stream of infinite extent. The direction of the free stream is normal to the cylinder axis and the flow field unsteadiness arises from two effects, the first is due to the flow field development following the start of the motion and the second is due to vortex shedding in the wake region. The time-dependent flow is governed by the full conservation equations of mass and momentum with no boundary layer approximations. The parameters involved are the cylinder axis ratio, Reynolds number and the angle of attack. The investigation covers a Reynolds number range up to 5000. The minor-major axis ratio of the elliptic cylinder ranges between 0.5 and 0.6, and the angle of attack ranges between 0° and 90°. A series truncation method based on Fourier series is used to reduce the governing Navier-Stokes equations to two coupled infinite sets of second-order differential equations. These equations are approximated by retaining only a finite number of terms and are then solved by approximating the derivatives using central differences

Serpil Kocabiyik

Papers

A review on numerical studies of slug flow hydrodynamics and heat transfer in microtubes and microchannels

Forced streamwise oscillations of a circular cylinder: Locked-on modes and resulting fluid forces

The flow induced by a rotationally oscillating and translating circular cylinder

Review of Advances in Thermal Spreading Resistance Problems

Numerical simulation of the unsteady flow over an elliptic cylinder at different orientations