A method for solving compressible flow equations in an unsteady free stream

Abstract The paper presents a method to increase the computational accuracy by preserving additional constraints on the numerical solution. The new technique can noticeably increase the precision of a standard finite-volume flow solver by a modification to the flux computation procedure without changing its essential features. The efficiency of this method is demonstrated by application to the prediction of sound from high-speed helicopter blades. Several open domain boundary conditions for this application are also developed and compared for a model problem of a two-dimensional transonic aerofoil in an unsteady free stream.

[1]  C. Hirsch.  Numerical Computation of Internal and External Flows, Volume 2: Computational Methods for Inviscid and Viscous Flows , 1990 .

[2]  Roger C. Strawn,et al.  Computational Modeling of Hovering Rotor and Wake Aerodynamics , 2001 .

[3]  Michael B. Giles,et al.  Nonreflecting boundary conditions for Euler equation calculations , 1990 .

[4]  F. Hu.  On Absorbing Boundary Conditions for Linearized Euler Equations by a Perfectly Matched Layer , 1995 .

[5]  Ann P. Dowling,et al.  The aeroacoustics of transonic helicopter blades , 2002 .

[6]  S. Tsynkov,et al.  An Application of the Difference Potentials Method to Solving External Problems in CFD , 1997 .

[7]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[9]  Tim Colonius,et al.  MODELING ARTIFICIAL BOUNDARY CONDITIONS FOR COMPRESSIBLE FLOW , 2004 .

[10]  Thomas L. Geers.  IUTAM Symposium on Computational Methods for UnBound Domains , 1998 .

[11]  Duck-Joo Lee,et al.  Generalized Characteristic Boundary Conditions for Computational Aeroacoustics, Part 2 , 2000 .

[12]  C. B. Allen,et al.  The reduction of numerical entropy generated by unsteady Shockwaves , 1997, The Aeronautical Journal (1968).

[13]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .

[14]  Manuel Torrilhon,et al.  Locally Divergence-preserving Upwind Finite Volume Schemes for Magnetohydrodynamic Equations , 2005, SIAM J. Sci. Comput..

[15]  Ken Badcock,et al.  An unfactored implicit moving mesh method for the two-dimensional unsteady N-S equations , 1996 .

[16]  C. Tam,et al.  RADIATION AND OUTFLOW BOUNDARY CONDITIONS FOR DIRECT COMPUTATION OF ACOUSTIC AND FLOW DISTURBANCES IN A NONUNIFORM MEAN FLOW , 1996 .

[17]  S. Obayashi,et al.  Numerical solutions of forward-flight rotor flow using an upwind method , 1989 .

[18]  Gareth D. Padfield,et al.  Helicopter Flight Dynamics , 2000 .

[19]  Tom Hynes,et al.  OPEN BOUNDARY CONDITIONS OF PREDICTOR-CORRECTOR TYPE FOR EXTERNAL FLOWS , 2002 .

[20]  Siegfried Wagner,et al.  Euler procedure for calculation of the steady rotor flow with emphasis on wake evolution , 1990 .

[21]  R Hixon,et al.  Evaluation of boundary conditions for computational aeroacoustics , 1995 .

[22]  J. Baeder,et al.  TURNS - A free-wake Euler/Navier-Stokes numerical method for helicopter rotors , 1993 .

[23]  K. Thompson.  Time-dependent boundary conditions for hyperbolic systems, II , 1990 .

[24]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[25]  C. Rowley,et al.  Discretely Nonreflecting Boundary Conditions for Linear Hyperbolic Systems , 2000 .

[26]  Ning Qin,et al.  Unsteady flow around helicopter rotor blade sections in forward flight , 1999, The Aeronautical Journal (1968).

[27]  F. Hu.  A Stable, perfectly matched layer for linearized Euler equations in unslit physical variables , 2001 .

[28]  Andrea Crivellini,et al.  A Three-Dimensional Parallel Discontinuous Galerkin Solver for Acoustic Propagation Studies , 2003 .

[29]  B. Zhong,et al.  Non-inertial multiblock Navier-Stokes calculation for hovering rotor flowfields using relative velocity approach , 2001, The Aeronautical Journal (1968).

[30]  On the Accuracy of Direct Noise Calculations Based on the Euler Model , 2004 .

[31]  Tom Hynes,et al.  Transonic Helicopter Noise , 2003 .

[32]  K. Pahlke,et al.  Navier-Stokes Prediction of Helicopter Rotor Performance in Hover Including Aeroelastic Effects , 2001 .

[33]  Aeroacoustic Predictions Using High-Order Shock-Capturing Schemes , 2003 .