Analysis and control of asymmetric vortex flows and supersonic vortex breakdown

The near-vortex-wakeflowofa largeaspect-ratio rectangularwing isaccuratelycomputed by using the thinlayerand fullNavier-Stokes(NS) equations.The chordwise section of the wing is a NACA-0012 airfoil and its tip is round. The computations have been carried out on a fine C-O grid using an implicit, upwind, flux-difference splitting, finite-volume scheme. The thin-layer NS results have been obtained with and without flux limiters and the full NS results have been obtained without flux limiters. Flow transition from laminar to turbulent is miraiced by turning-on the Baldwin-Lomax algebraic model at an experimentally prescribed chord-station locationof 0.05. Comparison of the computed results with each other and with the experimental data shows that the full NS results give the best resolution of the near-vortex-wake flow. Next, the strength of the wing-tip vortex has been reduced substantially without reducing the lift coefficient by using flow-injection from a slot along a portion of the wing tip. The flow injection is directed in the wing plane at 45* with the wing-tip chord. INTRODUCTION Recently, there has been an alarming rate of increase of the volume of air civil transport at many airports. With this status of air traffic congestion, the hazardous effect of wake vortices emanating from large aircraft on light aircraft, which pass through these vortices during landing and take-off operations, is becoming a vital concern for operations safety. These vortices are characterized with high intensity and turbulence, and may produce high roiling moments on trailing aircraft which could exceed the available roll control of the trailing aircraft. Moreover, the trailing aircraft, under the influence of these vortex trails, could suffer a loss of altitude or clhnb rate in additionto structural damages. These vorticesmay persistup toseveralmilesand forlong periodsof time before their decay, and therefore they play a major role in sequencing landing and take-off operations at busy airports. For example, a minimum safe-separation distance between aircraft is dictated depending on the vortex intensity, wind shear, atmospheric turbulence and temperature gradient; among others. Research Associate,Dept. of Mvclumicml EnS_ and Mvclumica, Member AIAA. " Professorand Eminent Scholar,Dept. of Medutmcal Engincaing and Mechanics, Associate Fellow AIAA. "" Group Leader, _etical Flow Phymics Branch, Auociate Fellow AIAA. The literature shows a few experimental and computational investigations that attempt to model and analyze wake vo_x interaction, merging, decay and their hazardous effects on nailing aircraft. Hallock and Eberle l presented a review of the state of the art of aircraft wake vortices covering the research efforts in the United States until the mid-seventies. Experimental wind tunnel and airport measurements of the vor_x wakes were conducted by Dee and Nicholas a Harvey and Perry 3, El-Rarely 4, Wood and McWilliamss,Oardoz_,ClilIoneand Lonzo7, Olwi and Ohazi m, Liu 9 and Liu et all0. Mathematical models and computational schemes were developed using inviscid analysis by Chorin and Bernard it, Hucket and Evans 12, Yate$13, Iversen and Bcnlstein14,and Rossow Is. Although an inviscidmodel cannot describe the wake aging including its diffusion, it is still capable of producing the wake shape and its dynamics. The mathematical modeling used in the above references were based on the use of the point vortex method to compute the motion of a finite number of point vortices which model the vorticity behind a wing. The first three-dimensional inviscid model was introduced by Kandil, el. aP e, where the nonlinear vortex-lattice, which was also developed by Kandil, et. all? was used to compute the interference flow between wings and the vortex wake hazardous effects. V'LSCOusmodeling of trailing vortices was first introduced by McCormick, et. al n. Viscous interactions in vortex wakes and the effects of bac_und turbulence, wind shear and ground on two-dime:nsional vortex pairs were presented by Bilanin, eL a119'20. Liu and his co-workers at'24 studied the interaction, merging and decay of vortices in two-dimensional space and of threedimensional vortex filaments. To estimate the effects of density slratitication, turbulence and Reynolds number on vortex wakes, an ai_roximate model was recently developed by Greene 25. Later on, Greene and his co-workers _ presentedselectedresultsof aircraftvorticeswhich include a juncture vortex, a lifting-wing vortex and a wake vortex. It is concluded from the above brief literature survey that the problem contains several vortex flow regions along with several critical parameters influencing the vortex wake flows. The vortex wake flow of interacting-wing problems can be divided into three regions. The first region includes the leading wing and its near-vortex-wake flow. The second region includes the interseting vortices in the wake. The third region includes the far-wake flow along with the wailing-wing flow. In Ref. 27, Kandil, Copyright @ 1992 by Professor Osama A. Kandil. Published by the Asnerican Institute of Aeronamicl and Astronautics, Inc. with Permission. Wong and Liu presented results of the near-vortex-wake flow for a Large-aspect-ratio rectangular wing using the thin-layer, Reynolds averaged, NS equations on a C-O grid.Next,a smallaspect-ratio rectangular wing was introducedin the near-wake of the leading wing and the problemwas recomputedtodemonstratethe hazardous effects ofthevortexwake flow.Two interference cases were considered.The first was calledthe"along-track penetration throughvortexcenter"and thesecondwas called the"along-track penetration betweenvortices", see Fig. I. Itwas demonstratedthatinthefirst case,the trailing wing experienced largerolling moments and in thesecondcasethetrailing wingexperienced lossoflift. In thepresentpaper,the ncar-vormx-wake flowis recomputedusinga finergridthanthegridusedinRef. 27. Moreover,thethin-layer and fullNS equations are usedalongwithan upwind scheme,whereintheflux limitcr ofthesolveristurnedon andoff.The goalofthis partofthepaperistoaccurately computethevortexwake flowand tostudytheeffect ofthenumerical dissipation ofthefluxlimiter on thecomputedresuRs.Inthesecond partof thepaper,alleviation f thestrength of thetip vortexwithoutreducingthelift forceisdemonstrated by usingdirected flowinjection froma slotalonga certain lengthof thewing tip. FORMULATION Full and Thin-Layer Navier-Stokes Equations The conservative formoftlmdimensionless, unsteady, compressible, fullNavier-Stokes equations in termsof time-independent, body-conformed coordinates _i _ and _3 is given by aQ 0(L). + Ot O_m 0_. where =0; m=l-3, s=1-3 (I) _m __ Cm(xl, X2, X3) (2) 4 1 (_= _ = _[p,pui,pus,pus,#e]' (3) Em= inviscid flux 1 . i_. k J = . _U,,,,puiU= + O_'p, pu2U,. + _'p, :u3O=+ 03Cp, (pc+ p)o. ]' (4) (E,), viscousand heatconductionflux int" direction = _[0,0i_,i_, 0_t"ri_,0kf',i3, OkC'(u._ _)]'; k = 1 3, n = 1 3 (5) u= = 0_C'u_ @) The three momentmn elements of Eq. (5) are given by • . 0uj +_ _ ; j=l-3 (7) The last element of Eq. (5) is given by o_t"( %rl, oa) -_ [(0_"0p_" 2 ,., 0ul +0_('01("up 0_ 1 o(a')l 1)p,ak ' -j;p = 1-3 (s) The single [hin-layer approximmions of the full NavicrStokes equmions demand that we only keep the derivatires inthenormaldirection to the body,{_, in the viscous m_dheatfluxuamsinEqs. (I),(7)and(8). Thus,we let s= 2 fortheterm_ inEq. (I)ands = 2-andn = 2 in eqs. (7) and (g). These equations reducem OQ OF-_u 0(E,)g : 0 (9) + 0_0__