COMPUTATIONAL AEROELASTICITY in HIGH PERFORMANCE AIRCRAFT FLIGHT LOADS* Mike Love, Tony De La Garza, Eric Charlton, Dan Egle Lockheed Martin Aeronautics Company

ICAS 2000 CONGRESS COMPUTATIONAL AEROELASTICITY IN HIGH PERFORMANCE AIRCRAFT FLIGHT LOADS* Mike Love, Tony De La Garza, Eric Charlton, Dan Egle Lockheed Martin Aeronautics Company Keywords: computational aeorelasticity, CFD, flight loads Abstract A computational aeroelasticity method has been developed that combines a computational fluid dynamics (CFD) code based on a finite volume, Cartesian / prismatic grid scheme with automated unstructured grid creation and adaption with established structural finite element methods. This analysis is motivated by the need to develop an analysis capability for fighter-aircraft critical flight loads. Flight conditions for such often reside in transonic flow regimes and comprise nonlinear aerodynamics due to shocks, flow-separation onset, and complex geometry. The Multidisciplinary Computa- tional Environment, MDICE [1], is provid- Figure 1: Pressures and streamlines obtained from a ing for timely integration of Lockheed computational aeroelastic maneuver simulation Martin’s CFD software, SPLITFLOW [2] in in maneuver simulations. The Loads engi- a maintenance friendly, loosely coupled neer’s time is mostly consumed in the nonlinear analysis method. Analysis corre- assembly of accurate data for the maneuver lation with static aeroelastic wind tunnel simulation. Adequate characterization of data demonstrates potential. Analysis set-up vehicle aerodynamics is critical. Recent tool and results for a fighter aircraft with multi- and technology developments are facilitating ple control surfaces are demonstrated. the aerodynamic characterization task of integrating data from CFD methods, wind 1 Introduction tunnel testing and other aerodynamic methods to assemble an aerodynamic pressure Computational aeroelasticity, or computa- database [3, 4]. This database is augmented tional fluid dynamics (CFD) based aeroelas- by static aeroelastic analyses to account for ticity, is an emerging technology with high flexibility effects of the structure and inertial potential for the development of critical effects of the flight vehicle. These analyses flight loads (Figure 1). The structural design are performed at a distributed set of Mach of flight vehicles is highly dependent on the number and altitude combinations. Histori- timeliness of accurate design flight loads. cally, a linear static aeroelastic solution is Flight loads are typically derived by com- acquired for each nonlinear rigid aerody- bining aerodynamic loads, vehicle inertia, namic data set using linear aerodynamic structural flexibility, and flight control laws panel methods. Linear methods do not * Copyright © 2000 Lockheed Martin Corporation All rights reserved. Published by the International Council of Aeronautical Sciences with permission. 481.1 Love, De La Garza, Charlton, Egle capture nonlinear phenomenon such as flow flow, control surface, rotary rate, and accel- separation and moving shocks in the critical eration parameters, respectively. ∂ ∂ loads flight regime. += α + PP LL β Lift PL Figure 2 illustrates the construction and 0 ∂α ∂β topology of a database for fighter loads. ∂ ∂ ∂ + L δ + L δ + PPP L δ Literally thousands of aerodynamic pressure ∂δ E ∂δ A ∂δ R vectors are constructed over a distribution of E A R ∂P ∂P ∂P Mach numbers, altitudes, and control pa- + P + Q + LLL R (1) rameter angles. The database is considered ∂P ∂Q ∂R nonlinear because the integrated aerody- ∂P ∂P ∂P + L N + L N + L N ∂ X ∂ Y ∂ Z namic load coefficients (e.g., lift coefficient N X NY N Z due to angle of attack) are nonlinear with ∂P & ∂P & ∂P & respect to control parameters such as angle + P + Q + LLL R ∂P& ∂Q& ∂R& of attack, sideslip, delta-aileron and delta- horizontal-pitch-trim. These aerodynamic At the equilibrium state of the vehicle in vectors are used in determining the inte- a maneuver (e.g., 9g symmetrical pull-up or grated aerodynamic load corresponding to a 5.86g asymmetric rolling pullout), inertia given maneuver simulation. Maneuver forces are balanced with aerodynamic forces simulations are performed using a nonlinear at the current control parameter values. The iterative algorithm that computes control accuracy of the flight loads is highly depend- parameter angles necessary to satisfy equilib- ent on the accuracy of each component of rium conditions about the vehicle’s center of aerodynamic load. The Loads engineer gravity. The algorithm is iterative because it endeavors to create a database where each is interpolating on the aerodynamic pressure aerodynamic pressure vector is correlated to vectors representing the control parameter physically known quantities. The large states closest to the current trim parameter database provides an environment for prediction. An example integrated aerody- expedient computation of thousands of flight namic load is depicted in (1), where each maneuver simulations surveying the flight term represents the contribution of onset- envelope for critical component design loads. Nonlinear Rigid 2-D Loads Linear Flexible Pressure Data Integration Model Increment Pressure Aeroelastic Mapping Analysis Typical Nonlinear Aerodynamic Database # Simulations FLEXIBLE • Onset Flow Effects Only 250 NONLINEAR • 1st Order Control Surface Effects 4800 AERODYNAMIC 2nd Order CS Interaction Effects 60000 PRESSURE • DATABASE • Aeroelastic Increments For Each Case Figure 2: Construction and topology of a nonlinear aerodynamic database for fighter loads 481.2 COMPUTATIONAL AEROELASTICITY IN HIGH PERFORMANCE AIRCRAFT FLIGHT LOADS The flight loads regime for high per- tions in the literature have shown reliable formance fighter aircraft consists of moder- results for standard test-bed problems (lifting ately high angles of attack (8-15 degrees) in surfaces in transonic flows) [5-11]. Analysis transonic Mach numbers (0.8 – 1.2). Angles time for each of these codes must consider for control surfaces may range from +30 initial grid generation, and in the case of degrees to –30 degrees. The resulting aero- complex geometry, modeling may require dynamic flow regimes include complex significantly more time than the actual shock interactions, flow separation, and other solution. Recall that databases for the fighter nonlinear flow phenomena. aircraft include a large distribution of onset Conventional methods of static aero- flows multiplied by control surface settings. elasticity combine nonlinear rigid aerody- Each control surface survey may require a namic data (correlated to test) with linear change of geometry up to plus and minus flexible pressure increments derived using thirty degrees (transpiration methods are linear aerodynamic panel methods. These limited). Complex geometry considerations, computations are depicted in (2) and (3), such as external stores, may require over-set where the linear aerodynamics is introduced grids as well. through an aerodynamic influence coeffi- All of the mentioned codes rely on grid- cient matrix, [AIC], and corresponding moving techniques to couple the nonlinear spline matrices, [G], to allow solutions in the aeroelastic equations. Common techniques structural domain. Structural displacements, noted use interpolation and dynamic mesh {u}, are calculated in the equilibrium equa- (pseudo-structural) methods and are applied tion (2) combining mass, [M], stiffness, [K], to structured grid and unstructured grid and rigid nonlinear load {PNL}. The aero- codes. Geometric conservation laws are elastic increment is computed in (3) using incorporated to maintain energy in the total the resulting structural displacements. The system. These techniques allow for depend- depicted example pertains to a solution for a able regeneration of the aeroelastic solution. nonlinear pressure increment at angle of However, model re-gridding (e.g., grid attack. adaptation) may be necessary to capture true aeroelastic phenomena. []{}&& []KM {}−+ [ ][][dp ]{}uGAICGquu (2) A desire to rapidly capture aeroelastic = {}α PNL )( phenomena with full airframe geometry motivated a probe to incorporate Lockheed {}α)( −= [][]AICGqP [dp ]{}uG (3) Martin Aeronautics Company’s SPLIT- NL increment FLOW [1] into a loosely coupled aeroelastic Computational aeroelasticity enables a analysis method. SPLITFLOW (Figure 3) is departure from the linear static aeroelastic an unstructured Cartesian prismatic grid analysis process by removing the aerodynamic influence coefficient approximation. This should improve accuracy, reduce risk and cost through avoidance of repair or even redesign for aircraft components of the operational flight vehicle. Limiting factors such as computational cost and the learning curve with respect to applying the CFD solver in an aeroelastic solution preclude wholesale adoption of the method. Historically grid generation and regeneration impede the process for computa- Figure 3: SPLITFLOW solution demonstrating tional aeroelastic analysis. Several applica- automated and adaptive gridding 481.3 Love, De La Garza, Charlton, Egle code. The unstructured Cartesian grid is FLOW to a simple structural deflection primary, and is automatically generated module. The deflection tool was based on using recursive cell subdivision. This grid libraries and methods developed in another scheme enables rapid and dependable Euler effort linking NASA Langley's CDISC solutions for complex geometry. The secon- aerodynamic shape design to SPLITFLOW. dary grid system, using triangular prismatic The prototype capability provides for one elements, may be added for resolving the flexible surface. boundary layer region near surfaces

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