Efficient Computation of Dynamic Stability Datawith a Linearized Frequency Domain Solver.

Determination of aeroelastic stability boundaries for full aircraft configu- rations by solving the time-accurate unsteady Reynolds-averaged Navier-Stokes (RANS) equations is recognized as extremely computationally expensive or impractical. This is due to the wide range of flight conditions, frequencies, and structural deformation mode shapes that must be examined to ensure a configuration is free from flutter. Nonetheless there is an increasing demand within the aerospace industry for accurate utter analysis in the transonic regime, which can only be satisfied with the use of high-fidelity RANS codes. Hence we are motivated to seek a more efficient numerical method. By assuming that perturbations to the ow are small and harmonic, we can derive an efficient alternative method by linearization of the RANS equations, a linearized frequency domain (LFD) solver. With this approach the unsteady simulation reduces to a single non-linear steady computation followed by a single linear simulation in the frequency-domain. This method is not new, but has principally been applied to turbomachinery so far. The contribution of this paper twofold: firstly to show that LFD is sufficiently accurate and reliable for applications to aeroelastic problems that occur in external aerodynamics, and secondly to demonstrate the speed-up that can be expected over full unsteady computations. Viscous transonic analysis is carried out on complex geometries in three-dimensions. The results show good agreement with full unsteady simulation and experiment, and a reduction in computational costs up to one order of magnitude is demonstrated.

[1]  R. Voß,et al.  TDLM - A Transonic Doublet Lattice Method for 3D Potential Unsteady Transonic Flow Calculation. , 1992 .

[2]  R. Dwight,et al.  Efficient and robust algorithms for solution of the adjoint compressible Navier–Stokes equations with applications , 2009 .

[3]  Stefan Görtz,et al.  Evaluation of the Recursive Projection Method for Efficient Unsteady Turbulent CFD Simulations , 2004 .

[4]  R. Dwight.  Efficiency Improvements of RANS-Based Analysis and Optimization using Implicit and Adjoint Methods on Unstructured Grids , 2006 .

[5]  T. Gerhold,et al.  Calculation of Complex Three-Dimensional Configurations Employing the DLR-tau-Code , 1997 .

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

[7]  Andreas-René Hübner,et al.  Integrated Experimental and Numerical Research on the Aerodynamics of Unsteady Moving Aircraft , 2007 .

[8]  Antony Jameson,et al.  Time Spectral Method for Periodic Unsteady Computations over Two- and Three- Dimensional Bodies , 2005 .

[9]  Richard P. Dwight,et al.  Efficient Algorithms for Solution of the Adjoint Compressible Navier-Stokes Equations with Applications , 2006 .

[10]  J. P. Giesing,et al.  Subsonic Unsteady Aerodynamics for General Configurations. Part 1. Volume I. Direct Application of the Nonplanar Doublet-Lattice Method , 1971 .

[11]  Boris Laschka,et al.  Small Disturbance Navier-Stokes Method: Efficient Tool for Predicting Unsteady Air Loads , 2006 .

[12]  Michael B. Giles,et al.  Stabilization of linear flow solver for turbomachinery aeroelasticity using Recursive Projection method , 2004 .

[13]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[14]  G. Golub,et al.  Gmres: a Generalized Minimum Residual Algorithm for Solving , 2022 .

[15]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[16]  R. Voß,et al.  Transonic flutter calculations for a low wing transport aircraft using the Transonic Doublet Lattice Method , 2001 .

[17]  R. Dwight,et al.  Eect of Various Approximations of the Discrete Adjoint on Gradient-Based Optimization , 2006 .

[18]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[19]  Andreas Bergmann,et al.  Experimental and Numerical Investigations of Unsteady Force and Pressure Distributions of Moving Transport Aircraft Configurations , 2009 .

[20]  Ralf Heinrich,et al.  The DLR TAU-Code: Recent Applications in Research and Industry , 2006 .

[21]  W. Rodden,et al.  A doublet-lattice method for calculating lift distributions on oscillating surfaces in subsonic flows. , 1969 .

[22]  Gautam M. Shroff,et al.  You have printed the following article : Stabilization of Unstable Procedures : The Recursive Projection Method , 2007 .

[23]  W. S. Clark,et al.  Aerodynamic Damping Predictions Using a Linearized Navier-Stokes Analysis , 1999 .

[24]  Kenneth C. Hall,et al.  A Time-Linearized Navier–Stokes Analysis of Stall Flutter , 2000 .

[25]  R. G. Wells,et al.  Predicting Bladerow Interactions Using a Multistage Time-Linearized Navier-Stokes Solver , 2003 .

[26]  Kenneth C. Hall,et al.  A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery , 1993 .