International audienceIn this work a vortex method is used to simulate and control an incompressible two-dimensional transitional flow over a backward-facing step. Two different control strategies are implemented to modify the shedding, the recirculation zone behind the step and the transport in the channel. The first technique consists in using a pulsing inlet velocity and the second one is based on local oscillating jets implemented on the step vertical wall. The influence of these controls on the flow behavior is carefuly investigated. Both, open-loop and closed-loop active control approaches are performed

Creusé, Emmanuel

Giovannini, André

Mortazavi, Iraj

In this work a vortex method is used to simulate and control an incompressible two-dimensional transitional flow over a backward-facing step. Two different control strategies are implemented to modify the shedding, the recirculation zone behind the step and the transport in the channel. The first technique consists in using a pulsing inlet velocity and the second one is based on local oscillating jets implemented on the step vertical wall. The influence of these controls on the flow behavior is carefuly investigated. Both, open-loop and closed-loop active control approaches are performed

CREUSÉ, Emmanuel

GIOVANNINI, André

MORTAZAVI, Iraj

Oskar Bordeaux

Active control of transitional channel flows with pulsed and synthetic jets using vortex methods

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HAL Id: inria-00346979https://hal.inria.fr/inria-00346979Submitted on 13 Dec 2008HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Active control of transitional channel flows with pulsedand synthetic jets using vortex methodsEmmanuel Creusé, A. Giovannini, Iraj MortazaviTo cite this version:Emmanuel Creusé, A. Giovannini, Iraj Mortazavi. Active control of transitional channel flows withpulsed and synthetic jets using vortex methods. ICCFD (International Conference on ComputationalFluid Dynamics), Jul 2008, Seoul, South Korea. ￿inria-00346979￿Active control of transitional channel flowswith pulsed and synthetic jets using vortexmethodsEmmanuel Creusé1, André Giovannini2, and Iraj Mortazavi31 LAMAV & INRIA Lille Nord Europe, Université de Valenciennes, 59313Valenciennes Cedex 09, France. ecreuse@univ-valenciennes.fr2 IMFT UMR CNRS, 118, route de Narbonne, 31062 Toulouse, France.giova@imft.fr3 IMB & INRIA Université Bordeaux I, 351, cours de la Libération, 33405Talence, France. Iraj.Mortazavi@math.u-bordeaux1.frKeywords : Vortex method, closed and open-loop active control, backward-facing step.Abstract: In this work a vortex method is used to simulate and control anincompressible two-dimensional transitional flow over a backward-facing step.Two different control strategies are implemented to modify the shedding, therecirculation zone behind the step and the transport in the channel. The firsttechnique consists in using a pulsing inlet velocity and the second one is basedon local oscillating jets implemented on the step vertical wall. The influence ofthese controls on the flow behavior is carefuly investigated. Both, open-loopand closed-loop active control approaches are performed.1 Context and aim of the studyThe aim of the present work is to develop two different active control strategiesto manipulate the flow characteristics inside a backward-facing step channelwith a transitional flow regime: 1) using pulsed inlet velocities, with open andclosed-loop frequency choices; 2) implementing two jets to the vertical stepwall with open-loop or closed-loop action into the lower and upper levels ofthe step. This work follows the primary results obtained by the authors in aprevious paper for laminar flows [3]. Here, the impact of the control on severalflow characteristics like vorticity, energy, fluctuations, velocity gradients etc.is carefully analysed. Reynolds numbers are Re = 500 and Re = 2000.2 Emmanuel Creusé, André Giovannini, and Iraj Mortazavi2 Numerical schemeThe numerical simulations are performed using a Vortex-In-Cell method [2].In VIC calculations, an Eulerian grid is implemented in order to computeefficiently the velocity field on the Lagrangian particles. The goal is to ob-tain a fast computation of the particle velocities in regular bounded domains.Here, fast Poisson solvers enable fast velocity evaluations. Compared withpure finite-difference methods, VIC methods offer the advantage of a robustand accurate treatment of the convective part of equations with time steps notconstrained by convective CFL conditions [1]. The simulations are validated,comparing them to existing experimental and numerical literature and gridconvergence analysis ensured. Appropriate sets of space and time numericalparameters are selected in order to achieve accurate control strategies [4].3 Control strategiesThe control is performed either by taking an oscillating inlet velocity u(t) =(uin(t), 0)T , instead of the uncontrolled uniform velocity boundary conditionsimulation (Fig. 1, Control1), or by two small jets implemented on the upperand lower parts of the step (Fig. 1, Control2). Both, open and closed-loopcontrols are used and compared. The open loop studies are performed for awide range of parameters to get the most efficient ones. These values are thencompared to the closed-loop control to verify its efficiency.        SensorControl2Control1xyFig. 1. Control devices on the step geometry.The control effect is focused on the vortex shedding, transport phenomenaand the step recirculation zone behavior. One of the main targets is to reducethe recirculation area and length, then to decrease the trapped particles and toimprove the transport of vortices [5]. In order to quantify this control, severaltime dependent fonctionals are studied [4]. These functionals are the recircu-lation area length Lr(t), the total enstrophy in the domain that measures theTitle Suppressed Due to Excessive Length 3vorticity of the flowfield and the near wall recirculation area intensity thatcorresponds to the level of shear forces.4 Numerical results4.1 First control typeThe first control (Fig. 1, Control1) is achieved oscillating the inlet velocityprofile uin(t) = 1.0 + A cos(2 π f t). The frequency f and the amplitude Aof this oscillating flow are obtained either by an extensive parametric study(open-loop control OLC) or implementing the dominant frequencies of thevorticity formation and transport in the pulsing flow as the reference value(closed-loop control CLC).For the open-loop control an extremum value for each time-averaged func-tional for a frequency nearly equal to the basic fundamental frequency of theflow, namely f ≈ 0.14 is achieved (see Fig. 2). On the other hand, the effi-ciency of the control almost linearly increases with the increasing values ofthe amplitude until a ”plateau”.The closed-loop control consists in using the fundamental frequencies offlow shedding or transport in order to fit the oscillation frequency. The fre-quency measuring sensors may be implemented on the wall (non-intrusivesensors) or inside the flow field (intrusive sensors). The main advantage ofthe closed-loop control is that the control frequency is taken directly fromthe principal flow frequencies and avoids the heuristic trial and error ap-proaches with high computational cost needed for open-loop methods. In thenon-intrusive closed-loop control the quantity ∂2u/∂y2 is connected to thewall tangent pressure gradient. The closed-loop control consists in takinguin(t) = 1.0 + M(∂2u/∂y2(t))Sn, where Sn is a point on the bottom wall(see the location of the sensor on Fig. 1), and M = 2.5.10−3 is chosen to makevary the inlet velocity in the same range as for the open loop case.The results show that the closed-loop control is efficient since each ob-tained functional value as well as average and instantaneous fields are close tothe best results achieved by the open-loop control. As the figure 3 shows theaveraged recirculation zones are remarquably reduced and concentrated in asmall area behind the step using this closed-loop control.These results are then compared to those obtained using intrusive sensor.More precisely, we now induce at the entry of the domain the velocity :uin(t) = 1.0 + M (uSi(t) − uSi) ,4 Emmanuel Creusé, André Giovannini, and Iraj MortazaviRecirculation area lenght Lr EnstrophyNear-wall recirculation area intensityf ffFig. 2. Value of the functionals. Top left : Recirculation area lenght. Top right :Enstrophy. Bottom left : Near-wall recirculation intensity. In dashed-blue line : Thevalue corresponding to uncontrolled flow.Fig. 3. Mean streamlines for uncontrolled (up) and non-intrusive CLC (down)regimes.where uSi(t) is the horizontal velocity at a given point inside the flow, uSiits time-averaged value recorded during an uncontrolled simulation, and Ma parameter chosen to tune the amplitude of the signal (which has to bethe same as in the non intrusive case). It shows the higher efficiency of theintrusive control compared to non intrusive one : the time-averaged value Lris respectively equal to 2.71 in the non intrusive case and 2.38 in the intrusiveone (4.51 for the uncontrolled flow). Indeed, in the intrusive configuration theTitle Suppressed Due to Excessive Length 5sensors are placed inside the flow that is less perturbated by the wall effects.This can be understood by looking at the value of uin(t) in both cases (seeFig. 4).280 300 320 340 360 380 400 4200.80.911.11.21.3280 300 320 340 360 380 400 4200.80.911.11.21.3Fig. 4. Signal of uin(t) for closed-loop control : with non intrusive sensor (top) andwith intrusive sensor (bottom).4.2 Second control typeIn the second type of control, two small jets are implemented on the upperand lower parts of the vertical step (Figure 1, Control2). The main target ofthis approach is to influence directly the vortex shedding and the recircula-tion zone: the upper jet changes the shedding dynamics and the lower oneperturbates and pushes away the recirculation zone. The actuators placed inthe close vicinity of the bottom and the top of the step, blow or expell anhorizontal flow inside the flow.In this study, different possibilities as steady open-loop, active open-loopand active closed-loop actuators are applied to this configuration and theirefficiency is verified. The inlet velocity is taken equal to unity; uju and ujbcorrespond to the uniform jet velocities respectively on the top and the bot-tom of the step. Then, the oscillation, according to the control technique, isimposed to these velocities. Moreover, the computations are performed withboth pulsed and synthetic jets. In the first case, in both devices the jet variesbetween 0 and |2A|, with a negative jet in the upper side of the step and apositive one in the lower part. In the second, the jet varies between −A and Aand there is no absolutely positive or negative device, even they never coincideto each other.6 Emmanuel Creusé, André Giovannini, and Iraj MortazaviFor this kind of control, as the figure 5 shows, the best closed-loop re-sults are achieved, taking (uju, ujb) = (−1.0, 0.5) as the initial conditions andimplementing the pulsed jets. A lot of detailed results are available in [4].Fig. 5. Mean streamlines for uncontrolled (up) and CLC with pulsed step jets(down) regimes.5 ConclusionIn this work, both open and closed-loop control methods were applied to con-trol a backward-facing step flow using a Vortex-In-Cell method. Two controlconfigurations the first one correponding to a pulsing inlet flow and the sec-ond one to jets introduced into the lower and upper parts of the step werestudied, . The first strategy showed that the natural fundamental frequencyof the flow offers the characteristic value to tune the pulsing frequency. Thecontrol is therefore based on this value whatever the used devices. We alsoobserved the efficiency of implementing the intrusive sensors. For the secondstrategy, the best control is achieved with a high velocity negative upper jetcompared to a positive bottom jet. This result was also true for oscillatingjets. It was verified that an automatic closed-loop approach can provide acontrol as efficient as the best open-loop control.References1. Cottet, G-H. and Koumoutsakos, P: Vortex methods, Cambridge Univ.Press. (2000)2. Christiansen, J.P: Numerical Simulation of Hydrodynamics by theMethod of Point Vortices. J. Comp. Phys., 13, 363–379 (1971)3. Creusé, E. and Mortazavi, I.: Simulation of low Reynolds number flowcontrol over a backward-facing step using pulsed inlet velocities. AppliedMath. Research Express, 4, 133-152 (2004)4. Creusé, E., Giovannini, A. and Mortazavi, I.: Vortex simulation of activecontrol strategies for transitional backward-facing step flows. Computersand Fluids, (2008) in press.5. Kaiktsis, L. and Monkewitz, P.: Global destabilization of flow over abackward-facing step. Phys. Fluids, 15, 3647-3658 (2003)

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Active control of transitional channel flows with pulsed and synthetic jets using vortex methods

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