Unsteady Aerodynamics Modeling for Aircraft Maneuvers: a New Approach Using Time-Dependent Surrogate Modeling

A new approach for computing the unsteady and nonlinear aerodynamic loads acting on a maneuvering aircraft is presented. This approach is based on Duhamel’s superposition integral using indicial (step) response functions. The novelty of this approach relies on the development of a time-dependent surrogate model that fits the relationship between flight conditions (Mach number and angle of attack) and indicial functions calculated from a limited number of simulations (samples). The aircraft studied in the current paper exhibit highly nonlinear roll moment and therefore a very large number of step functions need to be calculated to accurately predict the aerodynamic behavior at each instant of time spent in aircraft maneuvers. The reduced order model, along with the surrogate model, provide a mean for rapid calculation of step functions and predicting aerodynamic forces and moments during maneuvering flight. The maneuvers are generated using a time-optimal prediction code with the feasible solutions based on the vehicle control and state constraints. Results presented show that the developed surrogate model aids in reducing the overall computational cost to develop cost-effective reduced-order models. It is also demonstrated that the reduced order model used can accurately predict timemarching solutions of maneuvering aircraft, but with an advantage that reduced order model predictions only require on the order of a few seconds of computational time.

[1]  M. Tobak.  On nonlinear longitudinal dynamic stability , 1966 .

[2]  Daniella E. Raveh.  Reduced order models for nonlinear unsteady aerodynamics , 2000 .

[3]  Patrick Reisenthel,et al.  Extraction of nonlinear indicial and critical state responses from experimental data , 1999 .

[4]  Michel van Tooren,et al.  Investigation over CFD-based models for the identification of nonlinear unsteady aerodynamics responses , 2006 .

[5]  Walter A. Silva,et al.  Development of Reduced-Order Models for Aeroelastic Analysis and Flutter Prediction Using the CFL3Dv6.0 Code , 2002 .

[6]  J. R. Chambers,et al.  Accomplishments of the Abrupt-Wing-Stall Program , 2005 .

[7]  J. Betts.  Survey of Numerical Methods for Trajectory Optimization , 1998 .

[8]  James D. Baeder,et al.  Direct Calculation of Three-Dimensional Indicial Lift Response Using Computational Fluid Dynamics , 1997 .

[9]  Deutsche Forschungsanstalt für Luft und Raumfahrt,et al.  Aerospace science and technology , 1997 .

[10]  Hendrikus G. Visser,et al.  Optimal Turn-Back Maneuver After Engine Failure in a Single-Engine Aircraft During Climb-Out , 2007 .

[11]  A. Da Ronch,et al.  Framework for establishing the limits of tabular aerodynamic models for flight dynamics analysis , 2009 .

[12]  Russell M. Cummings,et al.  Integrated Computational/Experimental Approach to Unmanned Combat Air Vehicle Stability and Control Estimation , 2012 .

[13]  K. Popp,et al.  System Dynamics and Mechanical Vibrations: An Introduction , 2010 .

[14]  Philip S. Beran,et al.  Reduced-order modeling - New approaches for computational physics , 2001 .

[15]  Clinton P. T. Groth,et al.  Assessment of Riemann solvers for unsteady one-dimensional inviscid flows for perfect gases , 1988 .

[16]  Patrick Reisenthel,et al.  A nonlinear indicial prediction tool for unsteady aerodynamic modeling , 1998 .

[17]  Gamal N. Elnagar,et al.  The pseudospectral Legendre method for discretizing optimal control problems , 1995, IEEE Trans. Autom. Control..

[18]  James R. Forsythe,et al.  Detached-eddy simulation of fighter aircraft at high alpha , 2002 .

[19]  W. F. Ballhaus,et al.  Computation of unsteady transonic flows by the indicial method , 1977 .

[20]  Patrick Reisenthel,et al.  Data-based aerodynamic modeling using nonlinear indicial theory , 1999 .

[21]  Russell M. Cummings,et al.  Unsteady Aerodynamic Modeling of Aircraft Control Surfaces by Indicial Response Methods , 2013 .

[22]  C. E. Manglano-Villamarin,et al.  Three-dimensional indicial response of finite aspect ratio yawed wings , 2007 .

[23]  P. Beran,et al.  Reduced-order modeling: new approaches for computational physics , 2004 .

[24]  L. B. Schiff,et al.  On the formulation of the aerodynamic characteristics in aircraft dynamics , 1976 .

[25]  Russell M. Cummings,et al.  An Integrated Computational/Experimental Approach to UCAV Stability & Control Estimation: Overview of NATO RTO AVT-161 , 2010 .

[26]  Earl H. Dowell,et al.  Reduced-order modelling of unsteady small-disturbance flows using a frequency-domain proper orthogonal decomposition technique , 1999 .

[27]  Scott A. Morton,et al.  Comparisons of CFD Solutions of Static and Maneuvering Fighter Aircraft with Flight Test Data , 2007 .

[28]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[29]  C. Canuto.  Spectral methods in fluid dynamics , 1991 .

[30]  J. G. Leishman,et al.  Indicial lift approximations for two-dimensional subsonic flow as obtained from oscillatory measurements , 1993 .

[31]  Mehdi Ghoreyshi,et al.  Accelerating the Numerical Generation of Aerodynamic Models for Flight Simulation , 2009 .

[32]  J. Forsythe,et al.  Unsteady Computations of Abrupt Wing Stall Using Detached-Eddy Simulation , 2005 .

[33]  Russell M. Cummings,et al.  Aerodynamics Modeling of A Maneuvering Aircraft Using Indicial Functions , 2012 .

[34]  Ken Badcock,et al.  Assessment of the Limits of Tabular Aerodynamic Models for Flight Dynamics Analysis using the SACCON UCAV Configuration , 2010 .

[35]  Bandu N. Pamadi,et al.  Performance, Stability, Dynamics, and Control of Airplanes , 2015 .

[36]  Russell M. Cummings,et al.  CFD Calculation of Aerodynamic Indicial Functions for a Generic Fighter Configuration , 2012 .

[37]  Vladislav Klein,et al.  Modeling of aircraft unsteady aerodynamic characteristics. Part 2: Parameters estimated from wind tunnel data , 1995 .

[38]  Russell M. Cummings,et al.  Aerodynamic Analysis of a Generic Fighter Using Delayed Detached-Eddy Simulation , 2009 .

[39]  Russell M. Cummings,et al.  Improved Methodologies for Maneuver Design of Aircraft Stability and Control Simulations , 2010 .

[40]  Robert M. Hall,et al.  Historical Review of Uncommanded Lateral-Directional Motions at Transonic Conditions , 2004 .

[41]  Jens Neumann,et al.  Numerical Simulation of Maneuvering Aircraft by Aerodynamic, Flight Mechanics and Structural Mechanics Coupling , 2007 .

[42]  Herbert Wagner.  Über die Entstehung des dynamischen Auftriebes von Tragflügeln , 1925 .

[43]  R. Liebe.  A challenge to engineering design , 2007 .

[44]  Vladislav Klein,et al.  Modeling of aircraft unsteady aerodynamic characteristics. Part 1: Postulated models , 1994 .

[45]  Russell M. Cummings,et al.  Computational Investigation into the Use of Response Functions for Aerodynamic-Load Modeling , 2012 .

[46]  J. Leishman,et al.  State-space representation of unsteady airfoil behavior , 1990 .

[47]  J. G. Leishman,et al.  Subsonic unsteady aerodynamics caused by gusts using the indicial method , 1996 .

[48]  Russell M. Cummings,et al.  SACCON Static and Dynamic Motion Flow Physics Simulations Using COBALT , 2010 .

[49]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[50]  R. Cummings,et al.  Detached-eddy simulation with compressibility corrections applied to a supersonic axisymmetric base flow , 2002 .

[51]  Lakshmi N. Sankar,et al.  An implicit algorithm for solving time dependent flows on unstructured grids , 1997 .

[52]  J. R. Chambers,et al.  Overview of the abrupt wing stall program , 2004 .

[53]  Robert Tomaro,et al.  The defining methods of Cobalt-60 - A parallel, implicit, unstructured Euler/Navier-Stokes flow solver , 1999 .

[54]  Mikhail Goman,et al.  State-Space Representation of Aerodynamic Characteristics of an Aircraft at High Angles of Attack , 1994 .

[55]  Dan D. Vicroy,et al.  SACCON Static Wind Tunnel Tests at DNW-NWB and 14'x22' NASA LaRC , 2010 .

[56]  J. G. Leishman,et al.  A Semi-Empirical Model for Dynamic Stall , 1989 .

[57]  Klein Vladislav,et al.  Estimation of Aircraft Nonlinear Unsteady Parameters From Wind Tunnel Data , 1998 .

[58]  Walter A. Silva,et al.  Development of Reduced-Order Models for Aeroelastic Analysis and Flutter Prediction Using the CFL3Dv6.0 Code , 2002 .

[59]  Russell M. Cummings,et al.  CFD Modeling for Trajectory Predictions of a Generic Fighter Configuration , 2011 .

[60]  A. Gaitonde,et al.  Reduced order state‐space models from the pulse responses of a linearized CFD scheme , 2003 .

[61]  Russell M. Cummings,et al.  Comparisons of computational fluid dynamics solutions of static and manoeuvring fighter aircraft with flight test data , 2009 .

[62]  D. Hull.  Conversion of optimal control problems into parameter optimization problems , 1996 .

[63]  L. B. Schiff,et al.  Mathematical modeling of the aerodynamic characteristics in flight dynamics , 1984 .

[64]  Dean G. Duffy,et al.  Advanced Engineering Mathematics with MATLAB , 2016 .

[65]  Murray Tobak,et al.  On the use of the indicial-function concept in the analysis of unsteady motions of wings and wing-tail combinations , 1954 .

[66]  Patrick C. Murphy,et al.  Prediction of Unsteady Aerodynamic Coefficients at High Angles of Attack , 2001 .

[67]  A. Da Ronch,et al.  Computation of Dynamic Derivatives Using CFD , 2010 .

[68]  A. Da Ronch,et al.  Computation and evaluation of dynamic derivatives using CFD , 2010 .

[69]  Scott A. Morton,et al.  Detached-Eddy Simulations and Reynolds-Averaged Navier-Stokes Simulations of Delta Wing Vortical Flowfields , 2002 .

[70]  Cristina H. Amon,et al.  Multi-Stage Bayesian Surrogates for the Design of Time-Dependent Systems , 2004 .

[71]  Neal M. Chaderjian,et al.  Automation of a Navier-Stokes S&C database generation for the Harrier in ground effect , 2002 .

[72]  Gary T. Chapman,et al.  Nonlinear problems in flight dynamics involving aerodynamic bifurcations , 1985 .

[73]  M. Goman,et al.  State-space representation of aerodynamic characteristics of an aircraft at high angels of attack , 1992 .

[74]  Lars Tysell,et al.  Hybrid grid generation for complex 3D geometries , 2010 .

[75]  Russell M. Cummings,et al.  Challenges in the aerodynamics modeling of an oscillating and translating airfoil at large incidence angles , 2012 .

[76]  Bernard Etkin,et al.  Dynamics of Atmospheric Flight , 1972 .