Time dependent adjoint-based optimization for coupled fluid-structure problems

A formulation for sensitivity analysis of fully coupled time-dependent aeroelastic problems is given in this paper. Both forward sensitivity and adjoint sensitivity formulations are derived that correspond to analogues of the fully coupled non-linear aeroelastic analysis problem. Both sensitivity analysis formulations make use of the same iterative disciplinary solution techniques used for analysis, and make use of an analogous coupling strategy. The information passed between fluid and structural solvers is dimensionally equivalent in all cases, enabling the use of the same data structures for analysis, forward and adjoint problems. The fully coupled adjoint formulation is then used to perform rotor blade design optimization for a four bladed HART2 rotor in hover conditions started impulsively from rest. The effect of time step size and mesh resolution on optimization results is investigated. A fully coupled unsteady aeroelastic sensitivity analysis formulation is given.Forward and adjoint sensitivity formulations are analogues of analysis formulation.Fluid-structure interface information is dimensionally equivalent in all solvers.A four bladed HART2 rotor shape is optimized in hover using the adjoint platform.The effect of time step size and mesh resolution on optimization results is investigated.

[1]  M. Giles,et al.  Algorithm Developments for Discrete Adjoint Methods , 2003 .

[2]  D. Mavriplis.  Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes , 2007 .

[3]  Carol D. Wieseman,et al.  A Summary of Data and Findings from the First Aeroelastic Prediction Workshop , 2012 .

[4]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[5]  Antony Jameson,et al.  Computational Fluid Dynamics for Aerodynamic Design: Its Current and Future Impact , 2001 .

[6]  B. Diskin,et al.  Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids , 2009 .

[7]  Boris Diskin,et al.  Discrete Adjoint-Based Design for Unsteady Turbulent Flows on Dynamic Overset Unstructured Grids , 2012 .

[8]  Juan J. Alonso,et al.  Adjoint-Based Sonic Boom Reduction for Wing-Body Configurations in Supersonic Flow , 2005 .

[9]  Dimitri J. Mavriplis,et al.  Adjoint-Based Sensitivity Formulation for Fully Coupled Unsteady Aeroelasticity Problems , 2009 .

[10]  Ranjan Ganguli,et al.  Correlation of helicopter rotor aeroelastic response with HART‐II wind tunnel test data , 2010 .

[11]  D. Mavriplis,et al.  Mesh deformation strategy optimized by the adjoint method on unstructured meshes , 2007 .

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

[13]  Graeme J. Kennedy,et al.  Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Adjoint Derivative Computations , 2014 .

[14]  R. M. Hicks,et al.  Wing Design by Numerical Optimization , 1977 .

[15]  Joaquim R. R. A. Martins,et al.  Multidisciplinary design optimization: A survey of architectures , 2013 .

[16]  Martin Otter,et al.  The DLR FlexibleBodies library to model large motions of beams and of exible bodies exported from nite element programs , 2006 .

[17]  Elizabeth M. Lee-Rausch,et al.  Adjoint-Based Design of Rotors in a Noninertial Reference Frame , 2010 .

[18]  Luis Santos,et al.  Aerodynamic shape optimization using the adjoint method , 2007 .

[19]  A. Jameson,et al.  Multi-Element High-Lift Configuration Design Optimization Using Viscous Continuous Adjoint Method , 2004 .

[20]  A. Jameson,et al.  Aerodynamic shape optimization techniques based on control theory , 1998 .

[21]  Dimitri J. Mavriplis,et al.  Helicopter Rotor Design using Adjoint-based Optimization in a Coupled CFD-CSD Framework , 2013 .

[22]  Juan J. Alonso,et al.  Design of Adjoint-Based Laws for Wing Flutter Control , 2011 .

[23]  D. Mavriplis.  Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes , 1997 .

[24]  Berend G. van der Wall,et al.  The HART-II Test: Rotor Wakes and Aeroacoustics with Higher-Harmonic Pitch Control (HHC) Inputs - The Joint German/French/Dutch/US Project , 2002 .

[25]  Dimitri J. Mavriplis,et al.  Time-depedent Adjoint-based Aerodynamic Shape Optimization Applied to Helicopter Rotors , 2014 .

[26]  D. Mavriplis.  Solution of the Unsteady Discrete Adjoint for Three-Dimensional Problems on Dynamically Deforming Unstructured Meshes , 2008 .

[27]  Dimitri J. Mavriplis,et al.  Results using NSU3D for the First Aeroelastic Prediction Workshop , 2013 .

[28]  M. Rumpfkeil,et al.  The optimal control of unsteady flows with a discrete adjoint method , 2010 .

[29]  W. K. Anderson,et al.  Recent improvements in aerodynamic design optimization on unstructured meshes , 2001 .

[30]  Dimitri J. Mavriplis,et al.  Unsteady Discrete Adjoint Formulation for Two-Dimensional Flow Problems with Deforming Meshes , 2008 .

[31]  Dimitri J. Mavriplis,et al.  Geometry Optimization in Three-Dimensional Unsteady Flow Problems using the Discrete Adjoint , 2013 .

[32]  Antony Jameson,et al.  Optimum Shape Design for Unsteady Flows with Time-Accurate Continuous and Discrete Adjoint Methods , 2007 .

[33]  E. Nielsen,et al.  Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables , 2005 .