AIRFOIL AND DETECTION OF FLOW SEPARATION ... In this paper, we focus on the use of angled fluidic vortex generators (FVG) to suppress flow separation.
FLOW PHYSICS OF SEPARATED FLOW OVER A NACA 0015 AIRFOIL AND DETECTION OF FLOW SEPARATION J. P. Bonnet, W. L. Siauw, L. Cordier, J. Tensi Laboratoire d’Etudes Aérodynamiques, UMR CNRS 6609, ENSMA, Téléport 2, 1 Av. Clément Ader, BP 40109, 86961 Futuroscope Chasseneuil Cedex, France Bernd R. Noack Berlin Institute of Technology MB1 Straße des 17. Juni 135, D-10623 Berlin, Germany L. N. Cattafesta III Interdisciplinary Microsystems Group, University of Florida, Gainesville, FL, USA 32611
Mots clefs : Flow separation control ; dynamical systems 1 Introduction It is of great technological importance to improve the efficiency and performance of an aircraft in terms of lift enhancement and drag reduction. Depending on the type of aircraft (military/civil), it would have impact on the maneuverability, fuel consumption efficiency, gas emission and noise emission of an aircraft. In this paper, we focus on the use of angled fluidic vortex generators (FVG) to suppress flow separation and the study of the transient process of in wake which correspond to flow attachment over the airfoil surface. Fluidic vortex generator has been shown to produce longitudinal vortices [9] that negotiate along a surface. Such a system is desirable as it does not introduce parasitic drag as compared to passive mechanical vortex generators. The key to efficient control utilizing such a system depends on the sustainability of vortical coherence, strength of the vortices, proximity towards a wall surface and the relative proximity between vortices. All these depend on condition of its origin at the orifices: angle of the jet, jet peak velocity and momentum. These technical facts are well documented in [1][10][11][12]. From these studies, we have deduced and adopted a yaw angle (relative to free stream velocity direction) of 60 degrees and a pitch angle (relative to airfoil surface) of 30 degrees. The size of the orifice was sized at 1mm (of the order of the boundary layer thickness at test condition) so that efficient exchange of momentum can take place between free stream and the boundary layer. Concerning the study of the transient process of attachment/separation; Amitay and Glezer [2], Darabi and Wygnanski [15][16] and Mathis [17] respectively conducted studies on a modified 4-digit NACA airfoil (piezoelectric synthetic jets), generic flap (electrodynamic synthetic jets) and a beveled splitter plate (continuous jet controlled by high speed valve). From these authors, the ratio of the time taken for separation to attachment was found to vary between ~ 1.2 to 5 (at almost optimal Cµ of the control jets). In all cases, time taken for separation was always greater than the case for attachment. An evacuation of the separated region was also observed in their experiment. In view of implementing a close loop control system, reduced order modeling have been used by Ausseur et al [3] and Perret et al [13] to predict the evolution of the flow empirically. The procedures involve solving for the coefficients belonging to a set of dynamical equations which are hypothesized to describe a set of reduced order dynamics derived from the dominant POD modes of experimental data. Depending on the phenomenological behavior of the flow; the dynamical equations can be of the first or higher order type. In the current work, the two-point velocity correlation tensor has been used as the kernel for the POD which has been extensively used in the analysis of the mixing layer by Bonnet et al [5], Braud et al [6] and Druault et al [7]. Other kernel such as the correlation of velocity gradient has been applied by Ausseur et al [4] and Kostas et al [18] utilized correlation of vorticity as the kernel. Recently, pressure sensors array has been used to estimate flow fields by using the technique of linear stochastic estimation (LSE), work of Ausseur et al [3] and Glauser et al [8]; outlined and attempted such technique to a NACA4412 airfoil. In the case of Stalnov et al [14], they used signals from surface mounted hot-film array to estimate the structures in the wake of a D-shaped profile. Such methods, could be a control strategy for close-loop separation control. Reader can refer to literature [19][20][21] for application of LSE to a jet flow. The last section of this paper will present briefly on the estimation of wake flow structures of the NACA0015 using LSE with unsteady surface pressure as the conditional signal.
2. Experimental results The wind tunnel used for the study is a closed loop type, it has a test section size of 2.4m by 2.6m with a turbulence intensity of 0.5% at 40m/sec. In this facility, a NACA0015 model of chord length 0.35m with a span of 2.4m is installed. 80 microns carborandum grit was applied at a location corresponding to 0.4% of chord from the leading edge. Test condition corresponding to a Reynolds number of approximately 1 million was chosen. 44 Orifices are installed in the vicinity at the central one third portion of the airfoil. Each orifice has a diameter of 1mm and is pitched 30 degrees and yawed at 60 degrees, see Figure 1a. The peak velocity of the jet was set at ~200m/s. PIV measurement had been performed on a window perimeter as shown in Figure 2. The resolution of the camera was 1375 by 1039 pixels. Velocity vectors are calculated on an interrogation window of 16 by 16 pixels with a 50% overlap ratio.
2.2
Wake Survey and Integration of Mean Surface Pressure Measurement
Figure 3 shows the contour of St.E(St) in the wake at x/c=1 from the trailing edge of the airfoil. The Strouhal number before jet deployment was 0.29 and 0.34 when the jet was deployed. Moreover, a narrowing of the wake was also observed. The same conclusion can be drawn from Figure 4(a) which depicts the evolution of the wake before and after jet deployment. It should be noted that there was a momentary spike at T+~8. This corresponded to the signature of a passing structure and was not observed in the separation process which commenced at T+~190. The wake survey technique (calculation of the momentum deficit) was applied to the data, shown in Figure 4, to estimate the Cd. As shown in Figure 4(b), the Cd reduced from 0.0275 to 0.02. The Cl calculated from the integration of mean surface pressure measurement indicated an improvement of ~17% at incidence of 11degrees as shown in Figure 5.
2.3 Reduced Order Modeling from PIV Data The experiment was performed with the jet pulsed at 1Hz. This 1Hz signal, with a time delay, was used as a trigger to the PIV system. 54 time delays are used to resolve the change in flow structure in the wake. This change corresponded to a change of the separated state to fully attached state over the airfoil. The POD is performed on nsnap = 300 snap shots taken at each designated time delay. Thus, we use a total of 54 x 300 velocity fields. An ensemble average time history was constructed from each time delay, corresponding to phase averaging process. Then, to build a reduced order model the following steps were taken: (a) Perform POD on the ensemble average time history according to:
u ( X , t ) = U mean +
nsnap
∑a
(n)
(t )Φ ( n ) ( X )
(1)
n =1
(b) Decide on the number of modes based on the POD spectrum as shown in Figure 6. 4 modes (98% of the energy is captured) are used in this case. The first three spatial modes are presented in Figures 7(a)-(c). (c) We hypotheses that a linear dynamical model could represent the flow dynamics:
da ( i ) = C ij a ( j ) + Di bi dt
(2)
Constructing a low order model then reduce to solving for the coefficients Cij and Di. (d) To verify the quality of the model in (c), integrate equation (2) by using a fifth order Runge-Kutta scheme. The results, with comparison to temporal modes calculated from equation (1), are presented in Figure 8(a)-(d). It can be observed that a non-dimensional-time (T+) of 10 is required the wake to change state. For the process of separation (not presented), a T+~21 was deduced and in good agreement with the hotwire data.
2.4 Linear Stochastic Estimation of Wake Flow Using Pressure Sensors Mounted on Airfoil the Upper Surface of the Airfoil The results in this section, concerns the estimation of the passage of flow structures at a position of x/c=1 from the trailing edge of the airfoil. Data acquisition was performed simultaneously for 10 pressure sensors and a cross-wire at each point in the wake. Data acquisition rate of 10kHz with a cutoff frequency of 5kHz
was used. See Figure 1(b) for the relative position of the surface mounted pressure transducers. LSE was realized by correlating the pressure signal on the upper surface of the airfoil with a cross-wire according to:
p j (t ) p k (t ) bu , j ( x ' ) = u ( y ' , t ) p k (t )
(3)
p j (t ) p k (t ) bv , j ( x ' ) = v( y ' , t ) p k (t )
(4)
Solutions of equations (3) and (4) (values of bu j & bv j) were then used for estimating the fluctuating velocity components: N
u est ( y , , t ) = ∑ bu , j ( y ) p j (t )
(5)
j =1 N
vest ( y , , t ) = ∑ bv , j ( y ) p j (t )
(6)
j =1
Figure 9 shows the estimation of flow structures in the wake without jet deployment that serves as baseline. Figure 10 shows the response of the pressure signal during the process of flow attachment over the airfoil. The corresponding estimated flow structure in the wake is presented in Figure 11. It should be noted that the transition takes place via the passage of a large eddy which explains the abrupt contour that was observed in Figure 4(a) during the activation of the jet. For the reverse process (separation over airfoil) the passage of a large eddy is not present as shown in Figure 12. The transition is more gradual from small to large eddies.
3. Conclusion Results in this paper concern with the physics of the flow in the vicinity of the NACA0015 set an incidence of 11degrees. The Reynolds number of the flow is approximately 1 million. The physics of energizing the boundary layer was exemplified from the span survey above the airfoil surface. It showed the trace and spatial evolution of the longitudinal vortices which originate from the angled jets. Merging of these vortices occur as they traversed towards the trailing edge. A narrowing of the wake was observed when the deploying the jet. The associated Strouhal number deduced from the spectrum analysis in the wake at one chord length away from the trailing edge changed from 0.29 to 0.32 during deployment and removal of the jet respectively. Concerning the efficiency of the jet system at incidence of 11 degree, Cl improved by ~17% and Cd was reduced by ~37%. With this flow configuration, PIV measurement was performed in the wake to study the attachment process and a linear dynamical model was built using the data. 4 POD modes are used to calculate the coefficients associated with the linear model. Close agreement has been obtained between modelled and the POD calculated temporal modes. This gave the possibility to simulate other similar flow conditions with jet deployment. Finally, an estimation of the wake structure was attempted for both cases of the transient process of attachment and separation over the airfoil. The attachment process over the airfoil was characterized by the passage of a large eddy. However, this characteristic was not present for the separation process.
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