Modelling Ehd Actuation with a Slip Velocity. A. Gronskis, R. Sosa, and G. Artana

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1 Joint ESA/IEEE-IAS/IEJ/SFE/IEA Conference - > Poster Session 2-Paper2.19< 1 Modelling Ehd Actuation with a Slip Velocity A. Gronskis, R. Sosa, and G. Artana Abstract The introduction of an electro-hydrodynamic (EHD) force in high performance numerical simulation may pose some problems as a consequence of the large differences between time or spatial scales of the physics of the discharge and those of interest for the fluid flow description. In this paper, we try to simplify this problem by looking for a correspondence between the global flow modifications produced by an EHD actuation and the one obtained by imposing locally a moving body surface. Thus direct numerical simulations (DNS) of the flow with slip velocities in correspondence with electrodes placements are performed. For a flow regime corresponding to Reynolds number based on the cylinder diameter and free-stream velocity of the flow of 125 (wake-transition regime), the simulations allow us to make a comparison with particle image velocimetry (PIV) measures of the flow induced by a dielectric barrier discharge (DBD) plasma actuator suitable disposed on the cylinder surface. The results obtained from the analysis of mean velocity fields show that the time-averaged vortical structures in the two cases enable us to establish a good analogy between actuations produced by both mechanisms. This kind of formulation enables the analysis of effects of actuators placement and distribution. Index Terms Flow control, Plasma actuators, Dielectric barrier devices, Particle image velocimetry, Direct numerical simulation I. INTRODUCTION Electro-hydrodynamic (EHD) actuators for flow control with aims to improve aerodynamic design have been receiving special attention in the last years [1, 2, 3]. Through the ionization of the flowing air close to the surface of a body, EHD devices produce a modification of the condition of the flow at the wall proximity. The charged particles present in the ionized air (plasma) experience an electric force that is transmitted through particle collision to the neutrals of the flowing air. The expression of this force on the fluid depends on the discharge characteristics, and in some cases there exists a two-way interaction created by electric forces as they elicit a mechanical response that, in turn, alters the fields. The implementation of this force in numerical flow simulations is of interest, as it could be used to optimize the design and Manuscript received April 17th, This work was supported in part by the ANPCYT under Grant PICT and University of Buenos Aires under Grant I023. A, Gronskis is with the Fluidynamics Laboratory, University of Buenos Aires (aleg@ fi.uba.ar). R Sosa., is with the CONICET and the Fluidynamics Laboratory, University of Buenos Aires (rsosa@ fi.uba.ar) G. Artana is with the CONICET and the Fluidynamics Laboratory, University of Buenos Aires, (gartana@ fi.uba.ar) placement of plasma actuators for different applications for flow control. Detailed studies on how to implement the electric force coupling in validated codes of computational fluid mechanics as direct numerical simulations (DNS) have been reported for the relative simple cases of classic corona discharges [4]. For the specific case of dielectric barrier device (DBD) actuators, which we study here, efforts have been also reported recently by different researchers [1, 2, 5]. Corke et al. (2005) derived a simplified expression for the body force distribution and implemented it in the numerical flow solver CFL3D [6] to estimate the aerodynamic coefficients involved in the control of leading-edge separation on wing sections. Miles et al. [7] developed a more detailed physical model for DBD in air, and noted the computational difficulties of plasma numerical simulation over large time and spatial scales. They concluded that in general, the cell size for the rectangular grid has to be chosen according to the characteristics of plasma and voltage scales and geometrical size (on the order of 10 microns); this in turns requires an extremely high number of computational points in order to perform calculations in large scale geometries (i.e., beyond the domain which is next to the electrode configuration). The other difficulty in plasma-effects simulations is the choice of time step. Because the time step should allow for the resolution of plasma formation and streamer propagation dynamic time (which is of the order of nanoseconds), this time scale must be several orders of magnitude smaller than the time scale over which the plasma is producing an effect on the surrounding air. Therefore, both factors rend prohibitive an easy approach to detailed plasma actuation over large spatiotemporal scale using DNS. A more recent computational exploration has been conducted by Visbal et al. (2006) [3] using large-eddy simulation approaches at a Reynold s number Re 10 4 in order to capture the effects of the local forces of the DBD device on turbulent, separated flows. Unfortunately, these researches also concluded that further work is still needed in order to construct detailed models for the spatio-temporal distribution of the plasma-induced body forces suitable for incorporation into flow simulations. We propose here to examine the global effect produced by a DBD actuation on a cylinder wake by adding an equivalent tangential velocity to the surface of the body in correspondence with electrodes placement. From this point of view, we consider the possible analogy of the global effects produced by a DBD actuation to those of a local moving surface. We concentrate our analysis on the case of disposing actuators on the surface of a cylinder arranged in such a way that their global action can have similarities with the rotation of a cylinder about its axis. In a previous work [8] we explored the possibility of undertaking this kind of analysis trying to

2 Joint ESA/IEEE-IAS/IEJ/SFE/IEA Conference - > Poster Session 2-Paper2.19< 2 refer the EHD actuated flow to the one of a spinning cylinder. Here we refine this strategy and test the adequacy of this approach to find the correspondence between localized slip velocity and EHD actuation. II. EXPERIMENTAL SETUP A. Wind tunnel and flow actuation The experimental configuration used in this work consisted of a flow imposed around a circular cylinder at low Reynolds number: Re=125. The velocity field measurements were undertaken with the cylinder placed in a closed loop wind tunnel with an 18-cm x 18-cm test section. The cylinder axis was placed perpendicular to the main flow (U 0 ). The EHD actuators were mounted on the surface of a D =14 mm diameter polymethyl methacrylate cylinder (length L = 18 cm in the spanwise direction). On the surface of the solid cylinder was fixed a Kapton film (thickness 50 m) which was used as a dielectric barrier for the electrodes of the DBD discharge. The asymmetric DBD plasma actuator used in our configuration consisted of four pairs of flat aluminum-foil electrodes (50 μm thickness, spanwise length 16 cm) disposed in the span around the cylinder surface, as shown in Figure 1. For each electrode pair, the electrode exposed to the air (electrode 1, width 3 mm) was electrically stressed while the other, separated by the dielectric material (electrode 2, width 5 mm), was grounded and was not in contact with the flow. The electrodes in a given pair were overlapped by a small amount (of the order of 0.5 mm). The actuators were disposed in the spanwise direction parallel to the cylinder axis and oriented such that the each pair of electrodes (i.e. each pair of DBD actuators) were equally spaced. As is shown in the figure the actuators were located with the edge of electrode (1) at positions: θ = 0º (the front stagnation point), θ = 90º, θ = 180 (the rear stagnation point) and θ = 270º. With θ the angle measured with respect to the main flow (U 0 ). In order to force the flow with only one border per electrode pair, the edge that forced the flow was left nude meanwhile the others that could introduce spurious forces were isolated with Teflon tape. By doing this, we assured that the plasma discharge was produced only in the regions indicated in Figure 1. The EHD forcing was produced by stressing the air-exposed electrode with a sinusoidal function. The AC sine voltage power supply (frequency: f = 8 khz, zero mean value; peak to peak voltage V AC up to 20 kv) was applied to electrodes (1). The AC power supply consisted in a function generator coupled to an audio amplifier (of 150 watt) that fed a high voltage transformer coil [9]. The electric current flowing in the system, I DBD (t) was measured with shunt resistances ( R = 50Ω ) connected to an oscilloscope with 60 MHz of analogical bandwidth and 1Gs/s of sampling rate. The AC voltage applied to electrodes (1), was measured with a HV probe (1000 / 3.0 pf / 100M). By setting the oscilloscope in the average acquisition mode, an average waveform of the current signal (I DBD ) over 128 samples was acquired. A typical signal of voltage and current vs time can be observed on Figure 2. V AC (kv) 2,0 1,5 1,0 0,5 0,0-0,5-1,0-1,5 V AC (t) I DBD (t) -2, ,15-0,10-0,05 0,00 0,05 0,10 0,15 t (ms) Figure 2: Typical waveforms of V(t) and I DBD for : V AC = 1.8 kv. By undertaking this type of excitation, the plasma actuator operation ensured the following: - Excitations were not extremely high for the Reynolds number in which the DNS code was validated and - Almost "steady" excitations were produced, as the input driving frequency was well above the fluid response frequency (taking into account a Strouhal number St 0.2, the characteristic length D = 14 cm, and the vortex shedding frequency of about 1Hz). The associated electrical power was about 5Watts I DBD (ma) Figure 1. Scheme of the electrode arrangement (not in scale) B. Velocity field measurements of a DBD actuated cylinder wake flow The velocity fields of DBD actuated flows have been measured using a PIV technique. These experiments were conducted using a camera having a resolution of 640x480 pixels, 1/100 s of inter-frame intervals. A green, 150-mW laser and a rotating polyhedric mirror were used to provide illumination of the test section. The algorithms used in this work belong to GPIV software [10] which is under GNU General Public License. We have

3 Joint ESA/IEEE-IAS/IEJ/SFE/IEA Conference - > Poster Session 2-Paper2.19< 3 considered for our images a two-step grid refinement; hence the final interrogation size is 16x16 pixels with 50% overlap. The time resolution was suitable to recover the flow dynamics, and the vortex shedding frequencies were much lower than the acquisition frequency. III. NUMERICAL SIMULATION A. General characteristics of the simulation code The Incompact3d code [11-15] was used to perform the DNS studies under the assumption of two dimensional flow. This code solves the continuity and momentum equations which are discretized using a finite difference method on a uniform cartesian grid. Spatial discretization is performed with a sixth-order, compact-centered, finite difference scheme, while temporal discretization is performed using a third-order low-storage Runge-Kutta method. The boundary condition on the cylinder surface is imposed using the virtual boundary technique. The simulations were performed using grid points in x and y directions respectively. The domain size was L x =19D, L y =12D, and the cylinder center was located at X c =8D, Y c =6D. The grid resolution was 144 points per diameter. These parameters were considered based on the previous validation attained for the case Re=200 [11, 15] and departures from non slip condition out of the actuation region. B. Governing equations Mass and momentum conservation principles are represented by the Navier-Stokes equations, which have the following form for an incompressible fluid r u r = 0 (1) r u r r r r r = p ω u + ν 2 u + f (2) t where ν is the kinematic viscosity, p( x r, t) the dynamic 1 r 2 pressure field P + ρ u, u r ( x r, t) the velocity field 2 and r ω ( x r, t) ( r ) the vorticity field r u. The external r r volumetric force field f ( x, t) is used here to impose the boundary condition on the cylinder surface. Figure 3 Boundary conditions at inflows and outflows contours The boundary conditions on cylinder surface have been r b b v = u u = v sinθ, v cosθ (3) ( ) ( ) x, y t t yb θ = arctg x (4) b where ( x b, y b ) the coordinates of the boundary points of the cylinder with respect to its axis and v t is the tangential velocity of the cylinder with θ θ p i θ θ i ( ) = t1 t 2 vt θ A 1 e e i with θ i [0, π/2, π, 3/2π]. The link between the parameters A, t1, t2 and p of this function with parameters Ap, Q1, Q2 and TOL of Figure 4 that can be established with a simple analysis of the pulse function. C. Boundary conditions and Parameters Figure 3 shows a schematic view of the boundary conditions over the inflow, lateral and outflow regions of the domain. At the outflow domain it is consider a non reflective condition in which it is consider a convective velocity U conv equal to the spatial mean velocity at the outflow We consider a pulsed type excitation in correspondence with electrodes in order to approximate the velocity profiles observed close to the wall when still air is actuated [16-17] Figure 4 Boundary conditions in correspondence with electrode placement

4 Joint ESA/IEEE-IAS/IEJ/SFE/IEA Conference - > Poster Session 2-Paper2.19< 4 IV. SLIP VELOCITY AND EHD ACTUATION The usual Karman vortex street was observed either in simulations and experiments for actuated and non actuated cases. In these last situations vortices shedded alternately and the flow achieved a temporally periodic state. The actuation introduced an asymmetry in the strength and location of the positive and negative vortices. An increase in actuation was accompanied by an increase in the upward deflection of the wake. We can observe on Figures 5 a comparison between experiments and simulations for the actuated cases at different streamwise positions. We compare the mean velocity profiles of the wake measured with PIV for the EHD experiments with the data obtained from simulations. It is well known that blockage effects modify the wake patterns characteristics. In our case we have had to introduce corrections of the experimental streamwise positions to account for this effect. In simulations we consider different values of the amplitude Ap of the pulse. The values of Q1 and Q2 were adopted D/7 and 4/7D meanwhile the parameter TOL was fixed to 1*10-4. Q1 was adopted in correspondence with typical values the plasma extension meanwhile Q2 length was adopted considering typical length of diffusion phenomena.. x/d=2 3 A =0 p 2 A =1 p y/d y/d < ux > x/d= < ux > =3 =5 EHD =0 =1 =3 =5 EHD Figure 5 Mean velocity profiles observed with simulations and experiments at different streamwise positions a)x=2.0d, b)x=2..5d a) b) From these figures we can deduce that either in simulations or in physical experiments it is observed that the shapes of the profiles are quite similar. The best correspondence in this case occurs for values of Ap close to 5. At the streamwise positions close to the cylinder and for y/d close to 1, it is observed a more important velocity deficit in experiments than in simulations. We associate this effect to experimental artifacts like differences in simultaneous actuation intensity between the different pair of electrodes. This effect however dissipates downstream. Thus assuming that the validation of the model of representation of EHD actuation with a local slip velocity for the case under study is good enough when Ap=5 we next show other results of simulations that are difficult to be captured with experimental procedures considering this value fixed. V. LOCALIZED OR UNIFORM ACTUATION It is of interest to analyze how does a discrete localized actuation differ from a more distributed one. To this end we analyze the flow induced by a localized slip velocity and the one of a uniform spinning cylinder. The instantaneous streamlines that we show on Figures 6 show that for the localized slip velocity case the evolution of the near wake fields seems quite similar than the one we can observe for a spinning cylinder immersed in a uniform flow [14]. In both cases as a consequence of actuation the frontal stagnation point moves around cylinder surface and the wake looses its horizontal symmetry. As the stagnation point position depends on the spinning velocity of the cylinder, from this position we can infer with a rough estimation that the actuation produced is analogous to spin the cylinder with a rotation parameter (ratio of tangential velocity at the wall and freestream velocity) of a value close to 1.0. A better insight can however obtained when one analyses the mean Reynolds stresses distribution appearing on Figure 7. With both kind of analysis it results that the mean recirculation region is shortened and tilted when actuation is activated. However the approach with localized slip velocity produce wake patterns with some differences than the one observed for the case of a spinning cylinder. For the simulations undertaken considering localized slip velocities the fluctuations in the wake result more intense. Also the wake pattern is less deflected at somewhat far downstream positions. Depending on the aim of actuation one should choose the more smooth effects associated to a relative uniform actuation (that could be achieved with a large number of actuators) or the more mixing one that could be produced with strong actuations and less uniform distributed actuators.

5 Joint ESA/IEEE-IAS/IEJ/SFE/IEA Conference - > Poster Session 2-Paper2.19< 5 a) a) b) b) c) Figure 6: Instantaneous streamlines att different instants of a period of vortex shedding a) T/8 b)3/8 T c) 5/8 T and d)7/8t. d) c) Figure 7 Mean Reynolds stresses a) non actuated cases b) spinning cylinder with α=1 c) actuated with local slip velocity for Ap=5.

6 Joint ESA/IEEE-IAS/IEJ/SFE/IEA Conference - > Poster Session 2-Paper2.19< 6 VI. CONCLUSION In this work, we show that a correspondence between the wake modifications from an electro-hydrodynamic (EHD) actuation and those obtained from a local moving body surface is possible. The main structural features of wake flows excited with dielectric barrier discharge (DBD) actuators are satisfactorily recovered numerically through direct numerical simulation (DNS) when actuation is represented as a tangential velocity at the wall. It seems adequate to simplify the analysis of the actuated flow with the one in which local pulsed slip velocities are imposed. Results of this research gives tools useful for optimization problems related to electrode placement and amplitude of actuations. However further investigations are necessary in order to improve this correspondence by refinements on numerical simulations and also validations in other situations like those in which the incidence of three dimensional effects may be of importance. [17] E. Moreau, R. Sosa and G. Artana, Electric wind produced by surface plasma actuators: a new dielectric barrier discharge based on a threeelectrode geometry, J. Phys. D: Appl. Phys 41, No 11, 12pp. (2008) A. GronskisA. Gronskis was born at Buenos Aires in He received the M.S. and Ph.D. degrees in Engineering from the University of Buenos Aires, in 2000 and 2009 respectively. Since 2004, he has been a researcher with the Fluidynamics Laboratory, Faculty of Engineering, University of Buenos Aires. His current research interests are flow control and computational fluid dynamics R. Sosa was born in Buenos Aires, Argentine in He received the M.S. and Ph.D. degrees in Engineering from Buenos Aires University, Buenos Aires, Argentina, in 2002 and 2007, respectively. Since 2000, he has been a researcher with the Fluidynamics Laboratory, Faculty of Engineering, University of Buenos Aires. His current research interests are plasma flow control and non-thermal high-pressure plasmas. Since 2008, he has been a researcher with CONICET. REFERENCES [1] Boeuf J.P. and Pitchford L.C.. Electrohydrodynamic force and aerodynamic flow acceleration in surface dielectric barrier discharge. J. Appl. Phys. 97, (2005). [2] Font G.I. and Morgan W.L.. Plasma discharges in atmospheric pressure oxygen for boundary layer separation control. AIAA Paper 4632, [3] Visba M.R. l,. Gaitonde D.V and Roy S.. Control of transitional and turbulent flows using plasma-based actuators. AIAA Paper , [4]. Soldati A and. Banerjee. S Turbulence modification by large-scale organized electrohydrodynamic flows. Phys. Fluids 10(7), , (1998). [5] Corke T.C. and Post M.L.. Overview of plasma flow control: concepts, optimization and applications. AIAA Paper , [6] NASA Langley Research Center, [7] Likhanskii A.V., Schneider, M.N. Macheret S.O. and Miles R.B.. Modeling of interaction between weakly ionized near-surface plasmas and gas flow. AIAA Paper , [8] Gronskis A., D Adamo J:,. Artana G, Cammillieri A., Silvestrini J., Coupling mechanical rotation and EHD actuation in flow past a cylinder, Journal of Electrostatics, 66(1), 1-7, (2008) [9] Manish Y 2005 Pitot tube and wind tunnel studies of the flow induced by one atmosphere uniform glow discharge (oaugdp ) plasma actuators using a conventional and an economical high voltage power supply MS Thesis Department of Physics University of Tennessee [10] G. van der Graaf, GPIV software, [11] Gronskis A., D Adamo J., Artana G. and Silvestrini J.. Direct numerical simulation of flow past a rotating cylinder. In Anais da 5a EPTT ABCM, Rio de Janeiro, Brasil, Set , [12] Lamballais, E., Silvestrini, J., Direct numerical simulation of interactions between a mixing layer and a wake around a cylinder. J. Turbul. 3, 028. [13] Silvestrini, J.H., Lamballais, E., Direct numerical simulation of wakes with virtual cylinders. Int. J. Comp. Fluid Dynam. 16 (4), [14] Ribeiro, P. Desprendimento de vortices e controle em esteira de cilindros por simulacao numerica direta. Master s thesis, Instituto de Pesquisas Hidraulicas - IPH/UFRGS, [15] Vitola, M., Influencia de um contorno plano sobre o desprendimento de vortices ao redor de um cilindro circular. PhD thesis, Instituto de Pesquisas Hidraulicas - IPH/UFRGS, [16] Moreau E 2006, Airflow control by non-thermal plasma actuators J. Phys. D: Appl. Phys G. Artana was born at Buenos Aires in He obtained his degree of Enginner of the University of Buenos Aires in 1989 and in 1995 his PhD at the University of Poitiers. Since 1997 is a researcher of CONICET and at present is professor of the Department of Mechanical Engineering and head of the Fluidynamics Laboratory of the University of Buenos Aires. Research areas of interest are flow control and continuum electromechanics.