Validation of vortex-lattice method for loads on wings in lift-generated wakes

Vernon J. ROSSOW*NASA Ames Research Center, Moffett Field, California 94035-1000A study is described that evaluates the accuracy of vortex-lattice methods when they are used to computethe loads induced on aircraft as they encounter lift-generated wakes. The evaluation is accomplished by the useof measurements made in the 80 by 120 ft Wind Tunnel of the lift, rolling moment, and downwash in the wakeof three configurations of a model of a subsonic transport aircraft. The dnwnwash measurements are used asinput for a vortex-lattice code in order to compute the lift and rolling moment induced on wings that have aspan of 0.186, 0.510, or 1.022 times the span of the wake-generating model. Compartsun of the computed resultswith the measured lift and rolling-moment distributions the vortex-lattice method is very reliable as long asthe span of the encountering or following wing is less than about 0.2 of the generator span. As the span of thefollowing wing increases above 0.2, the vortex-lattice method continues to correctly predict the trends andnature of the induced loads, but it overpredicts the magnitude of the loads by increasing amounts.Nomenclatureb = wingspanC_. = lift coefficient, L/qSC_ = rolling-moment coefficient, M/qSbc = wing chordfp = natural frequency in pitchfr = natural frequency in rollL = liftM = rolling momentq = dynamic pressure, pU_/2r = radiusr,. = radius of vortex coreS = wing planform areat = timeU_ = freestream velocityu, v, w = velocity components in x, y, zdirectionsx = distance in flight directionY = y/bgy = distance in spanwise directionZ = z/b_z = distance in vertical directionF = bound circulationy = wake vorticityp = air densitySubscriptsav = averaged over timef = following modelg = wake-generating modelmax = maximum for one side of wakemi = local minimummx = local maximumReceived April 5, 1994; presented as Paper 94-1839 at the AIAA12th Applied Aerodynamics Conference, Colorado Springs, CO, June20-23, 1994; revision received March 23, 1995; accepted for publi-cation May 15, 1995. Copyright © 1995 by the American Institute ofAeronautics and Astronautics, Inc. No copyright is asserted in theUnited States under Title 17, U.S. Code. The U.S. Government hasa royalty-free license to exercise all rights under the copyright claimedherein for Governmental purposes. All other rights are reserved bythe copyright owner.*Senior Scientist. Associate FeIlow AIAA.1254IntroductionHROUGHOUTistration(FAA) wake-vortexthe NASA Federalresearch Aviationprogram, Admin-efforthas been directed at the development of reliable models andtools for the representation and prediction of the structureand dynamics of vortex wakes and their interaction with air-craft. As a part of this effort, the study reported here wascarried out in order to obtain an improved understanding ofthe current capability to calculate loads on lifting surfacesembedded in the rotary flowfields of vortex wakes. It wasreasoned that the method to be studied must be easy to applyto a large variety of configurations because the number ofaircraft configurations in the subsonic transport fleet is large.Another reason for simplicity is that the method must not usemuch computer time (i.e., it should be fast), so that a largenumber of solutions can be obtained quickly for spatial anal-yses and for simulation of the dynamics of aircraft-wake en-counters. Along with the foregoing requirements, the methodshould also be accurate enough so that, given a reliable ve-locity field as input, the computed lift and rolling momentfall within the scatter of the values measured in the windtunnel.A method that possibly fulfills these requirements is thesame vortex-lattice method used in previous wake-vortexstudies, t--"A validation of the method requires that up- anddownwash velocity distributions are available in the same lo-cations in the vortex wake as are the measurements of the liftand rolling moment on following wings of various sizes. Inorder to reduce the uncertainties in the comparisons to bemade, both the measured velocity field and the measured liftand rolling moment are taken from the same wind-tunneltest? With the measured velocity distribution in the wakeused as a boundary condition, the vortex-lattice code is usedto compute lift and rolling moment on the following wing.The computed values are then compared with the measuredvalues to assess the validity of the method, in t_his way thevortex-lattice method to be tested is the_ only theoretical linkin the comparisons to be made. The comparisons to be dis-cussed also provide an evaluation of the experimental tech-niques used in the experiment.A variety of theoretical methods could have been tested asthe link between the computed and measured lift and rollingmoments. Only the vortex-lattice method is used in the com-parisons because it is simple to apply and has the capabilityto include a variety of wing shapes and vortex structures.