Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session Q23: Control and Nonlinear DynamicsControl Nonlinear

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Chair: Serhiy Yarusevych, University of Waterloo Room: 710 
Tuesday, November 21, 2017 12:50PM  1:03PM 
Q23.00001: The effects of tonal and broadband acoustic excitation on the transition process within a laminar separation bubble Serhiy Yarusevych, John Kurelek, Marios Kotsonis The effects of controlled acoustic excitation on the transition process in a laminar separation bubble formed on the suction side of a NACA 0018 airfoil at a chord Reynolds number of 125,000 and an angle of attack of 4 degrees are studied experimentally. The investigation is carried out using timeresolved, planar, twocomponent Particle Image Velocimetry. Two types of excitation are considered: (i) tonal excitation at the frequency of the most unstable disturbances in the natural flow, and (ii) broadband excitation consisting bandpass filtered to the natural unstable frequency range, modelling two common types of airfoil selfnoise production. For equal energy input levels, the results show that tonal and broadband types of excitation have equivalent effects on the mean flow field. Specifically, both cause the streamwise extent and height of the bubble to decrease. However, further analysis reveals notable differences in the underlying physics. For the tonal case, the transition process is dominated by the growth of disturbances at the excitation frequency that damps the growth of all other disturbances, leading to the formation of strongly coherent vortices in the aft portion of the separation bubble. On the other hand, broadband excitation promotes more moderate growth of all disturbances within the unstable frequency band, producing less coherent shear layer structures that experience earlier breakdown. Thus, the frequency content of acoustic excitation has a strong influence on the transition process in laminar separation bubbles. [Preview Abstract] 
Tuesday, November 21, 2017 1:03PM  1:16PM 
Q23.00002: Control of threedimensional waves on thin liquid films. I  Optimal control and transverse mode effects Ruben Tomlin, Susana Gomes, Greg Pavliotis, Demetrios Papageorgiou We consider a weakly nonlinear model for interfacial waves on threedimensional thin films on inclined flat planes  the KuramotoSivashinsky equation. The flow is driven by gravity, and is allowed to be overlying or hanging on the flat substrate. Blowing and suction controls are applied at the substrate surface. In this talk we explore the instability of the transverse modes for hanging arrangements, which are unbounded and grow exponentially. The structure of the equations allows us to construct optimal transverse controls analytically to prevent this transverse growth. In this case and the case of an overlying film, we additionally study the influence of controlling to nontrivial transverse states on the streamwise and mixed mode dynamics. Finally, we solve the full optimal control problem by deriving the first order necessary conditions for existence of an optimal control, and solving these numerically using the forwardbackward sweep method. [Preview Abstract] 
Tuesday, November 21, 2017 1:16PM  1:29PM 
Q23.00003: Control of threedimensional waves on thin liquid films. II  Point actuated control Susana Gomes, Ruben Tomlin, Greg Pavliotis, Demetrios Papageorgiou We consider the application of point actuated blowing and suction controls in the twodimensional KuramotoSivashinsky equation; this is a weakly nonlinear model for interfacial waves of threedimensional thin films on inclined flat surfaces. The flow is driven by gravity, and is allowed to be overlying or hanging the flat substrate. In this talk, the controls are modelled using Dirac delta functions. We first study the case of proportional control, where the actuation at a point depends on the local interface height alone. Here, we study the influence of control strength and number/location of actuators on the possible stabilization of the zero solution. For hanging films, we observe that there are critical parameters above which we obtain bounded solutions, and in general there is another set of critical parameters above which the zero solution is stabilized exponentially. We also consider the full feedback problem, which assumes that we can observe the full interface and allow communication between actuators. Using these controls we can obtain exponential stability where proportional controls fail, and stabilize nontrivial solutions. [Preview Abstract] 
Tuesday, November 21, 2017 1:29PM  1:42PM 
Q23.00004: Airfoil stall interpreted through linear stability analysis Denis Busquet, Matthew Juniper, Francois Richez, Olivier Marquet, Denis Sipp Although airfoil stall has been widely investigated, the origin of this phenomenon, which manifests as a sudden drop of lift, is still not clearly understood. In the specific case of static stall, multiple steady solutions have been identified experimentally and numerically around the stall angle. We are interested here in investigating the stability of these steady solutions so as to first model and then control the dynamics. The study is performed on a 2D helicopter blade airfoil OA209 at low Mach number, $M\sim0.2$ and high Reynolds number, $Re\sim1.8 \times 10^6$. Steady RANS computation using a SpalartAllmaras model is coupled with continuation methods (pseudoarclength and Newton's method) to obtain steady states for several angles of incidence. The results show one upper branch (high lift), one lower branch (low lift) connected by a middle branch, characterizing an hysteresis phenomenon. A linear stability analysis performed around these equilibrium states highlights a mode responsible for stall, which starts with a low frequency oscillation. A bifurcation scenario is deduced from the behaviour of this mode. To shed light on the nonlinear behavior, a low order nonlinear model is created with the same linear stability behavior as that observed for that airfoil. [Preview Abstract] 
Tuesday, November 21, 2017 1:42PM  1:55PM 
Q23.00005: Ground effects on the stability of separated flow around an airfoil at low Reynolds numbers Wei He, Peng Yu, Larry K. B. Li We perform a BiGlobal stability analysis on the separated flow around a NACA 4415 airfoil at low Reynolds numbers ($Re=3001000$) and a high angle of attack $\alpha=20^\circ$ with a focus on the effect of the airfoil's proximity to a moving ground. The results show that the most dominant perturbation is the KelvinHelmholtz mode and that this traveling mode becomes less unstable as the airfoil approaches the ground, although this stabilizing effect diminishes with increasing Reynolds number. By performing a Floquet analysis, we find that this ground effect can also stabilize secondary instabilities. This numericaltheoretical study shows that the ground can have a significant influence on the stability of separated flow around an airfoil at low Reynolds numbers, which could have implications for the design of micro aerial vehicles and for the understanding of natural flyers such as insects and birds. [Preview Abstract] 
Tuesday, November 21, 2017 1:55PM  2:08PM 
Q23.00006: Shape optimisation for linear stability with a RANS baseflow Jack Brewster, Matthew Juniper A linear stability analysis of a steady flow yields a series of mode shapes and their corresponding growth rates and frequencies. The presence of modes with positive growth rates indicates that the flow will transition to another steady state or develop unsteady behaviour. Targeting the growth rate, we demonstrate shape optimisation for RANS flows. We examine the flow over a cylinder at a Reynolds number of 1000 with the SpalartAllmaras turbulence model. A linear stability analysis yields a mode shape analogous to the low Reynolds number vortex shedding mode. Through the introduction of an adjoint global mode and an adjoint baseflow we derive the Hadamard form, a surface integral representation of the shape gradient. This gradient information is then used to modify the shape and reduce the growth rate of the mode. The cost of this approach is independent of the number of parameters and equivalent to an additional eigenvalue problem together with a linear flow calculation. In addition to the model problem of flow over a cylinder an industrial application is also presented. [Preview Abstract] 
Tuesday, November 21, 2017 2:08PM  2:21PM 
Q23.00007: Role of anisotropy and inhomogeneity on the instability due to viscosity stratification of Poiseuille flow in a porous channel R Usha, Geetanjali Chattopadhyay, Severine Millet Understanding of stability characteristics of twofluids system in confined complex geometries is crucial in industrial applications and natural phenomena. This study is motivated by the necessity to understand possible drag reduction using superhydrophobic surfaces or liquidinfused surfaces or surfaces with complex features which can be modeled as porous substrates with appropriate properties. A linear stability analysis of Poiseuille flow of viscositystratified twolayer immiscible fluids system in a porous channel with anisotropic and inhomogeneous permeability is analyzed. The flow in the porous medium is governed by the generalized Darcy model with BeaversJoseph condition at the interface of the liquidporous layers. The resulting generalized eigenvalue problem is solved numerically and the temporal linear stability analysis shows the existence of three distinct modes of instability; a porous mode, an interface mode and a shear mode. The influence of the variations in anisotropic and inhomogeneous properties of the porous medium on the interface and shear mode instabilities is assessed.The study reveals a possibility of controlling instabilities in twolayer flows in a rigid channel by designing a wall of the channel as a porous surface with appropriate properties. [Preview Abstract] 
Tuesday, November 21, 2017 2:21PM  2:34PM 
Q23.00008: A weakly nonlinear approach to predict the dynamics of precession of vortex core in a strongly swirling flow Kiran Manoharan, Mark Frederick, Jacqueline O'Connor, Santosh Hemchandra Swirling flows at large swirl numbers, ie the ratio of the axial flux of tangential momentum to the axial flux of axial momentum, the central recirculation zone (CRZ) precesses about the streamwise normal axis causing precession of the vortex core (PVC). In the present study swirling flow field at various inflow swirl numbers are obtained from a variable swirl experimental facility. At large inflow swirl numbers, a PVC was observed from the experiment. We perform a weakly nonparallel linear stability analysis on the time averaged flow field at the different swirl numbers to identify all the unstable global modes. The linear stability analysis predicts that the flow becomes globally unstable through m=1 helical instability and eventually with the increase in swirl m=2 double helical mode also becomes unstable. A Fast Fourier Transform of the velocity time series data where PVC is present shows a dominant m=1 oscillation at 1060Hz. But the linear stability analysis predicts a globally unstable m=1 mode at the first subharmonic of the PVC frequency and globally unstable m=2 mode at the PVC frequency. Hence, in the present study, a weakly nonlinear model is developed to predict the PVC frequency and the amplitude variation due to nonlinear interaction of m=1 and m=2 modes. [Preview Abstract] 
Tuesday, November 21, 2017 2:34PM  2:47PM 
Q23.00009: Transverse acoustic forcing of a round hydrodynamically selfexcited jet Abhijit Kumar Kushwaha, Marek Mazur, Nicholas Worth, James Dawson, Larry K.B. Li Hydrodynamically selfexcited jets can readily synchronize with longitudinal acoustic forcing, but their response to transverse acoustic forcing is less clear. In this experimental study, we apply transverse acoustic forcing to an axisymmetric lowdensity jet at frequencies around its natural global frequency. We place the jet in a rectangular box containing two loudspeakers, one at each end, producing nominally onedimensional standing pressure waves. By traversing the jet across this box, we subject it to a range of acoustic modes, from purely longitudinal (streamwise) modes at the pressure antinode to purely transverse (crossstream) modes at the pressure node. Using timeresolved BackgroundOriented Schlieren (BOS) imaging and hotwire anemometry, we characterize the jet response for different forcing frequencies, amplitudes and mode shapes, providing new insight into the way transverse acoustic oscillations interact with axisymmetric hydrodynamic oscillations. [Preview Abstract] 
Tuesday, November 21, 2017 2:47PM  3:00PM 
Q23.00010: An intermittency route to global instability in lowdensity jets Meenatchidevi Murugesan, Yuanhang Zhu, Larry K. B. Li Above a critical Reynolds number ($Re$), a lowdensity jet can become globally unstable, transitioning from a steady state (i.e. a fixed point) to a selfexcited oscillatory state (i.e. a limit cycle) via a Hopf bifurcation. In this experimental study, we show that this transition can sometimes involve intermittency. When $Re$ is just slightly above the critical point, intermittent bursts of highamplitude periodic oscillations emerge amidst a background of lowamplitude aperiodic fluctuations. As $Re$ increases further, these intermittent bursts persist longer in time until they dominate the overall dynamics, causing the jet to transition fully to a periodic limit cycle. We identify this as TypeII PomeauManneville intermittency by quantifying the statistical distribution of the duration of the aperiodic fluctuations at the onset of intermittency. This study shows that the transition to global instability in lowdensity jets is not always abrupt but can involve an intermediate state with characteristics of both the initial fixed point and the final limit cycle. [Preview Abstract] 
Tuesday, November 21, 2017 3:00PM  3:13PM 
Q23.00011: Coherence resonance in lowdensity jets Yuanhang Zhu, Vikrant Gupta, Larry K.B. Li Coherence resonance is a phenomenon in which the response of a stable nonlinear system to noise exhibits a peak in coherence at an intermediate noise amplitude. We report the first experimental evidence of coherence resonance in a purely hydrodynamic system, a lowdensity jet whose variants can be found in many natural and engineering systems. This evidence comprises four parts: (i) the jet’s response amplitude increases as the Reynolds number approaches the instability boundary under a constant noise amplitude; (ii) as the noise amplitude increases, the amplitude distribution of the jet response first becomes unimodal, then bimodal, and finally unimodal again; (iii) a distinct peak emerges in the coherence factor at an intermediate noise amplitude; and (iv) for a subcritical Hopf bifurcation, the decay rate of the autocorrelation function exhibits a maximum at an intermediate noise amplitude, but for a supercritical Hopf bifurcation, the decay rate decreases monotonically with increasing noise amplitude. It is clear that coherence resonance can provide valuable information about a system’s nonlinearity even in the unconditionally stable regime, opening up new possibilities for its use in system identification and flow control. [Preview Abstract] 
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