Summary of Research ( Final Report ) Simulation of Flow Control Using Deformable Surfaces

Thegoalof this investigationis to numericallysimulatetheeffectsof oscillatory actuatorsplacedon theleadingedgeof anairfoil, andto quantifytheeffectsof oscillatory blowing onanairfoil stall behavior. It hasbeendemonstratedexperimentallythatperiodic blowing candelayflow separationat highangleof attack. Thecomputationsareto beperformed for aTAU 0015airfoil atahigh Reynoldsnumberof 1 x 106 with turbulent flow conditions. The two-equation Wilcox k (o turbulence model has been shown to provide reliable descriptions of transition and turbulence at high Reynolds numbers. The results are to be compared to Seifert's experimental data. Introduction Studies indicate that when periodic flow excitation is applied to airfoils, it can effectively delay flow separation. There have been several approaches introduced to reduce flow separation, namely, deformation of the leading edge of an airfoil, steady blowing and several different methods of oscillatory blowing applied to the airfoil. This research is focused on steady or oscillatory blowing on the leading edge of an airfoil. Studies have indicated that oscillatory/periodic blowing is significantly more efficient than steady suction or steady blowing at controlling separation, t_'2'31 Not only that, the implementation of a controlled periodic excitation is more feasible than steady blowing. Experiments on a NACA 0015 airfoil with low Reynolds number have shown that the incompressible maximum lift coefficient, Cl,m,x, can be increased by more than 15%. In addition, the post-stall lift can be increased by as much as 50% and post-stall drag can be reduced by more than 50%. [4] The airfoil that is currently being investigated is the TAU 0015, which was tested in a low-speedwind tunnelat Tel-Aviv University (TAU). Finally, experimentsperformedovera wide rangeof ReynoldsandMachnumbersshowedthatperiodicexcitationcaneffectivelydelay turbulentboundarylayerseparationandreattachflows. E_'2'31 Furtherresearchin activecontrol hasshownthatReynoldsnumberscorrespondingto ajetliner at takeoffconditionwere successfullyapplied.E21Thenumericalmodelbeingusedis thecompressibleNavier-Stokes OSC2Dcodeimplementingthetwo-equationWilcox k-to turbulence model. Predictions will be compared with the experimental results produced by Seifert TMas well as with the computational results from Joslin et al. [61and Donovan et al. _71. Airfoil Geometry A common practice in experiments is to use a blunt or finite thickness trailing edge. However, for computational and grid generation purposes we implement a sharp trailing edge. The NACA 00xx airfoils with a finite thickness trailing edge are described by c-[ 0.20 __ O[ c ) + at + a2 4 +as c +a4 7 (1) where t/_c is the thickness-chord ratio (e.g., t/_c:O.15 for a NACA 0015 airfoil). The constant coefficients for the equation (1) are: ao = 0.2969, al = -0.1260, a2 = -0.3516, as = 0.2843 and a4 = -0.1015. [81 The coefficient of the x2 component is changed to a2 = -0.3537, to convert the NACA 00xx airfoil from a blunt trailing edge to a sharp trailing edge. The coordinate data for the TAU 0015 airfoil provided by Seifert includes a notch at the leading edge, a notch at x/_c ---0. 76 on the upper surface, and a finite thickness trailing edge. The notch on the upper surface will be ignored in this study. By using a similar approach to that describedabove,theTAU 0015dataprovidedby Seifertwasconvertedto a sharptrailingedge by thetransformations Y = Yd,,_ -0.001575('71 )2 (2) where . 71 =(x+0"003281 is a function ofthe specified length for the upper surface of the t,)l. 00328 airfoil, and Y = Yd,,, + 0.001570( .72 )2 (3) where . 72 = (x + 0.00656 _ is a function of the specified length for the lower surface of the , 1.00656 ) airfoil. The difference between equations (2) and (3) is due to the definition of points on the trailing edge at the upper and lower surfaces. Now, by modifying the NACA 0015 equation we can closely match the values produced the equations above with y = Y//fc° and x = _c ° , and let co = 1.0 for comparison purposes. from First, the upper surface of the airfoil is described by y, =O.75(ao xg + alx + a2x 2 + a3x3 + a4x4 ), for 0.3 <_x<_l. O (4.a) and Yt2 = O. 75(aoXl _ + alx I + a2xl 2 + a3xl J + a4xl 4 ), for 0.00328 < x < 0.3 0.3 ) where, xt = (x + 0.00328 0.3 --328 " The lower surface is described by and ybt =-O.75(aoXk_ + alx + a2 x2 + a3x 3 + a4x4 ), for 0.3