Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session M28: Flow Instability: Theory and Control 
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Chair: Lou Kondic, New Jersey Institute of Technology Room: Georgia World Congress Center B316 
Tuesday, November 20, 2018 8:00AM  8:13AM 
M28.00001: Local stability of single phase jet in crossflow – an impulse response analysis Srikumar Warrier, Gaurav Tomar, Santosh Hemchandra Jet in cross flow involves a jet exiting from an orifice and exchanging momentum with a cross flow. Transverse jets are used in devices such as in lean burn gas turbine combustors where fuel jets mix with an air cross flow ahead of the flame. It is therefore desirable to understand what conditions promote selfexcited instabilities in these jets to improve the homogeneity of fuel air mixing. We will present results from a 2D local stability analysis, carried out in a plane normal to the jet exit. We use an analytical baseflow model derived by Kelly and Alves (2008). We explore a parameter space spanned by the ratio of crossflow velocity to the jet velocity and the exit shear layer thickness of the jet. A spatiotemporal stability analysis is carried out by numerically evaluating the dispersion relation using a 2D Chebyshev collocation method. The aim is to determine qualitatively, the conditions under which local absolute instability occurs in the jet. The presence of these pockets promotes the occurrence of global instability in the flow and can be used to achieve better uniformity in mixing and hence lower levels of pollutant emissions from gas turbine systems. 
Tuesday, November 20, 2018 8:13AM  8:26AM 
M28.00002: Linear model of infinite dimensional viscous Mathieu system Jason Yalim, Bruno Welfert, Juan Lopez The linear stability analysis of the motion of a fluid inside a stably stratified square cavity under vertical harmonic oscillation leads to a damped Mathieu equation whose coefficients are spatial operators. We describe an ansatz for the modal effect of viscosity which still provides a correct estimate of critical parameter values from a superposition of standard modal damped Mathieu oscillators, despite the noncommutativity of the operators due to confinement. 
Tuesday, November 20, 2018 8:26AM  8:39AM 
M28.00003: A new novel fundamental formula for viscous parallel shear flows Harry Lee, Shixiao Wang A vorticitybased identity that is contrastingly different to the traditional energytype identities, such as the renowned ReynoldsOrr equation, has been recently derived. The identity is shown to be more general than the one derived by Synge (1938). Based on this identity, we were able to provide a new set of physical interpretations to different phases of stability in classical 2D parallel shear flows. Specifically, we studied the mechanisms of stability and instability in planar Couette and Poiseuille flows the two most important representatives of classical shear flow models. As one direct implementation of the new identity, we demonstrated an example on vorticity boundary control for the planar Poiseuille flow, and it turned out that the flow becomes stable with the addition of a small amount of vorticity control. We foresee the prospect of the applicability of such control scheme in the field of CFD. The study and application of the identity is only at a preliminary stage, but it has promising potential to be further exploited for unveiling the exact mechanism that governs the onset of turbulence in a wide range of shear flows a grand task that has remained incomplete to generations of fluid dynamists for over 130 years. 
Tuesday, November 20, 2018 8:39AM  8:52AM 
M28.00004: ReducedOrder Control of Transient Instabilities in HighDimensional Dynamical Systems Antoine Blanchard, Saviz Mowlavi, Themistoklis Sapsis Identification and control of transient instabilities in highdimensional dynamical systems remain a challenge because transient (nonnormal) growth cannot be captured by lowdimensional modal analysis. Here, we leverage the power of the optimally timedependent (OTD) modes, a timeevolving set of orthonormal modes that capture directions in phase space associated with transient and persistent instabilities, to formulate a control law capable of suppressing transient and asymptotic growth around any fixed point of the governing equations. The control law is derived from a reducedorder system resulting from projecting the linearized dynamics onto the OTD modes, and enforces that the instantaneous growth of perturbations in the OTDreduced tangent space be nil. We apply the proposed reducedorder control algorithm to infinitedimensional fluid flows dominated by strong transient instabilities, and demonstrate unequivocal superiority of OTD control over conventional modal control. 
Tuesday, November 20, 2018 8:52AM  9:05AM 
M28.00005: Resolventanalysisbased design of airfoil separation control ChiAn Yeh, Kunihiko Taira We leverage LES and resolvent analysis to design active separation control on a NACA 0012 airfoil. Spanwiseperiodic flows over the airfoil at Reynolds number of 23000 are considered at an AoA of 9 deg. Localized unsteady thermal actuation is introduced near the leading edge in an openloop manner. To provide guidance for effective control, we conduct resolvent analysis on the baseline turbulent mean flow to identify the actuation frequency and wavenumber that provide high energy amplification. The present study also considers the use of a temporal filter (discounting) to limit the time horizon for assessing the energy amplification to extend resolvent analysis for unstable base flows. We incorporate the amplification and response mode from resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. By comparing this metric from resolvent analysis and the LES results of controlled flows, we demonstrate that resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. In control cases that achieves full reattachment, we observe drag reduction by up to 49% and lift enhancement by up to 54%.

Tuesday, November 20, 2018 9:05AM  9:18AM 
M28.00006: Shape sensitivity of eigenvalues in hydrodynamic stability, with physical interpretation for the flow around a cylinder Jack Brewster, Matthew P Juniper Flows around or within objects can oscillate at welldefined frequencies. Engineers often want to eliminate these oscillations or alter their frequencies. Current methods, such as suction at the boundaries, can be impractical. The methods presented here control these oscillations by changing the object's shape, which is often more practical. The methods are based on a linear stability analysis about a steady baseflow and use adjoints, computing the sensitivities to all possible deformations in two calculations. We demonstrate the methods, physically interpreting the results for a cylinder flow at Reynolds number 50. This work shows that deformations affect hydrodynamic oscillations mainly by changing the steady baseflow, rather than by changing the unsteady feedback mechanisms. Deformations strongly affecting the baseflow are shown to strongly affect the oscillations, as expected. In addition, subtle deformations around the separation points are shown to exploit small baseflow changes that have disproportionately large influence on the growth rate. The physical mechanisms behind this is shown to be similar to the wellknown phenomenon of 'base bleed'. The method presented here is general and versatile, providing both gradient information and physical insight. 
Tuesday, November 20, 2018 9:18AM  9:31AM 
M28.00007: Active attenuation of a trailing vortex inspired by a parabolized stability analysis Adam Edstrand, Yiyang Sun, Peter Schmid, Kunihiko Taira, Louis Cattafesta To design a control strategy for attenuating a trailing vortex, we employ solving the parabolized stability equations (PSE) on a trailing vortex aft of a NACA0012 halfwing at an angle of attack of α=5° and a chord Reynolds number of 1000. For the initial condition of the PSE, we perform a parallel stability analysis at x/c = 0.25, finding numerous unstable modes. As the modes evolve downstream, the principal mode corotates with the base flow near the tip vortex region, resulting from the convective nature of the PSE. However, a subdominant mode displays nonmonotonic growth rate behavior, becoming unstable as the trailing vortex develops farther downstream, counterrotating around the tip vortex, which is indicative of a vortex instability. From these results, we hypothesize that the subdominant mode provides a pathway to excite the trailing vortex instability potentially resulting with its attenuation. Hence, we conduct DNS with trailingedge actuation based on the the principal and subdominant mode shape to attenuate the tip vortex. Although both controlled cases achieve trailing vortex attenuation, the subdominant mode exhibits attenuatation of the trailing vortex more effectively. 
Tuesday, November 20, 2018 9:31AM  9:44AM 
M28.00008: Controlling MultiComponent Flow Instabilities Using Adjoints Ali Kord, Jesse S Capecelatro Flow instabilities are ubiquitous in nature and industrial applications. Controlling such flows is critical for increasing the efficiency of engineering systems. In this talk, adjointbased optimization is used to control latetime nonlinear evolution of a Rayleigh–Taylor (RT) instability by systematically adjusting the initial interfacial perturbations. The adjoint governing equations for multicomponent fluids provide sensitivity of RT mixing or growth at different stages of the instability. Three surrogate objective functions are considered: (i) a mixing quantity based on mole fraction variance; (ii) an energy norm based on the velocity normal to the interface; and (iii) a norm based on the deviation of mole fraction from an initially unperturbed state. Sensitivity of these objective functions to initial interfacial perturbations are used in a gradientbased optimization framework that seeks to both enhance and suppress the RT instability while keeping the initial perturbation energy constant. The optimized perturbations are reported for each case and compared against results from linear stability theory. In addition, the effect of different objective functions and integration durations on the optimized solutions are discussed. 
Tuesday, November 20, 2018 9:44AM  9:57AM 
M28.00009: Numerical simulations of viscous fingering patterns in a HeleShaw cell whose geometry has been manipulated Scott W McCue, Liam C. Morrow, Timothy J Moroney A commonly used experimental tool for studying viscous fingering instabilities is the classical HeleShaw cell, which is an apparatus that is made up of two parallel plates held close together. Typically, when a less viscous fluid penetrates a more viscous fluid, the interface is unstable and fingering patterns and structures form. More recently, there is interest in manipulating the physical geometry of the HeleShaw cell with a view to promote or inhibit viscous fingering, for example by tapering the plates, making the gap thickness timedependent, or by replacing one of the plates with an elastic membrane. Here, we discuss fullynonlinear numerical simulations of some of these nonstandard scenarios, computed via a level set method. We shall summarise various control strategies that are derived from applying linear stability analysis and demonstrate how these strategies can be implemented numerically. 
Tuesday, November 20, 2018 9:57AM  10:10AM 
M28.00010: Experimental study of compound convection patterns in a layer of volatile fluid driven by a horizontal temperature gradient Joshua Barnett, Roman Grigoriev, Minami Yoda Stability of, and pattern formation in, liquid layers driven by a horizontal temperature gradient have been studied extensively in various limiting cases. In thin liquid layers, thermocapillary stresses dominate and the instability typically leads to hydrothermal waves traveling in the direction of thermal gradient. In thicker layers, when buoyancy and thermocapillary effects are comparable (i.e., dynamic Bond numbers Bo_{D}=O(1)), a stationary pattern of corotating convection cells is found instead. However, the intermediate range, i.e., the transition between these two states, is not as wellstudied. Linear stability analysis predicts that the emerging convection pattern should have hydrothermal waves on the cold side and stationary convection cells on the hot side. We discuss experimental particleimage velocimetry (PIV) studies of the flow in a liquid layer at Bo_{D} = O(0.1) driven by a horizontal temperature gradient and confined in a 4.85 cm × 1 cm × 1 cm test cell designed to test these predictions. 
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