Time Spectral Method for Rotorcraft Flow with Vorticity Confinement

This paper follows up on the authors’ recent paper. 1 It is shown here that it is possible to obtain reasonable improvement in the results utilizing Vorticity Confinement method. The previous paper has shown that using the Time Spectral method can increase convergence in forward flight calculations by up to two orders of magnitude compared to the traditional Backward Difference Formula (BDF). With the addition of a new boundary condition for the periodic planes, Euler and RANS forward flight calculations can now be done using only one sector of the blade, and thus further improve convergence by a factor of N for an N-bladed rotor,

[1]  A. Jameson,et al.  A nonoscillatory shock capturing scheme using flux limited dissipation , 1985 .

[2]  J. Steinhoff,et al.  Modification of the Euler equations for ‘‘vorticity confinement’’: Application to the computation of interacting vortex rings , 1994 .

[3]  Guo-Hua Xu,et al.  New hybrid method for predicting the flowfields of helicopter rotors , 2006 .

[4]  M. McMullen,et al.  The application of non-linear frequency domain methods to the Euler and Navier-Stokes equations , 2003 .

[5]  J. Baeder,et al.  Flowfield of a Lifting Rotor in Hover: A Navier-Stokes Simulation , 1992 .

[6]  Christian B Allen,et al.  An unsteady multiblock multigrid scheme for lifting forward flight rotor simulation , 2004 .

[7]  K. Ramachandran,et al.  Hover Performance Prediction Using CFD , 1994 .

[8]  F. X. Caradonna,et al.  The flow over a helicopter blade tip in the transonic regime , 1976 .

[9]  Ken Badcock,et al.  A CFD Framework for Analysis of Helicopter Rotors , 2005 .

[10]  J. Steger,et al.  Numerical simulation of unsteady, viscous, high-angle-of-attack flows using a partially flux-split algorithm , 1986 .

[11]  J. Cole,et al.  Calculation of plane steady transonic flows , 1970 .

[12]  Yonghu Wenren,et al.  Numerical vorticity confinement for vortex-solid body interaction problems , 1995 .

[13]  Christian Allen,et al.  Numerical simulation of multi-bladed rotors in lifting forward flight , 2003 .

[14]  Roger C. Strawn,et al.  Computational modeling of hovering rotors and wakes , 2000 .

[15]  Ronald Fedkiw,et al.  Visual simulation of smoke , 2001, SIGGRAPH.

[16]  Antony Jameson,et al.  Lower-upper implicit schemes with multiple grids for the Euler equations , 1987 .

[17]  Jeffrey P. Thomas,et al.  Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique , 2002 .

[18]  John M. Hsu,et al.  An Implicit-Explicit Hybrid Scheme for Calculating Complex Unsteady Flows , 2002 .

[19]  Terry Ford The European Rotorcraft Forum , 1997 .

[20]  W. J. Mccroskey,et al.  Numerical solutions of forward-flight rotor flow using an upwind method , 1989 .

[21]  J. Crank,et al.  A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , 1947, Mathematical Proceedings of the Cambridge Philosophical Society.

[22]  A. Jameson Solution of the Euler equations for two dimensional transonic flow by a multigrid method , 1983 .

[23]  A. Harten,et al.  The artificial compression method for computation of shocks and contact discontinuities. 3: Self-adjusting hybrid schemes , 1977 .

[24]  F. Caradonna,et al.  An experimental investigation of the parallel blade-vortex interaction , 1984 .

[25]  J. Gordon Leishman,et al.  Principles of Helicopter Aerodynamics , 2000 .

[26]  A. Jameson ANALYSIS AND DESIGN OF NUMERICAL SCHEMES FOR GAS DYNAMICS, 1: ARTIFICIAL DIFFUSION, UPWIND BIASING, LIMITERS AND THEIR EFFECT ON ACCURACY AND MULTIGRID CONVERGENCE , 1995 .

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

[28]  Peretz P. Friedmann,et al.  Rotary-wing aeroelasticity - Current status and future trends , 2001 .

[29]  Lakshmi N. Sankar,et al.  Euler solutions for self-generated rotor blade-vortex interactions , 1990 .

[30]  E. Oran Frontiers in Computational Fluid Dynamics , 1997 .

[31]  Lakshmi N. Sankar,et al.  Recent Improvements to a Hybrid Method for Rotors in Forward Flight , 2000 .

[32]  S. Obayashi,et al.  Numerical simulation of vortical flows using vorticity confinement coupled with unstructured grid , 2001 .

[33]  Christian Allen,et al.  Parallel Flow-Solver and Mesh Motion Scheme for Forward Flight Rotor Simulation , 2006 .

[34]  A. Jameson ANALYSIS AND DESIGN OF NUMERICAL SCHEMES FOR GAS DYNAMICS, 2: ARTIFICIAL DIFFUSION AND DISCRETE SHOCK STRUCTURE , 1994 .

[35]  Antony Jameson,et al.  Multigrid algorithms for compressible flow calculations , 1986 .

[36]  F. Caradonna,et al.  An experimental study of rotor-vortex interactions , 1988 .

[37]  R. Loehner,et al.  Vorticity confinement on unstructured grids , 2002 .

[38]  B. Grossman,et al.  Towards a Better Understanding of Vorticity Confinement Methods in Compressible Flow , 2001 .

[39]  Claudio Canuto,et al.  Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation) , 2007 .

[40]  Michael E. Tauber,et al.  Measurement and Prediction of Model-Rotor Flowfields , 1986 .

[41]  Ramesh K. Agarwal,et al.  Euler calculations for flowfield of a helicopter rotor in hover , 1986 .

[42]  Antony Jameson,et al.  Solution of the Euler equations for complex configurations , 1983 .

[43]  W. Dietz APPLICATION OF VORTICITY CONFINEMENT TO COMPRESSIBLE FLOW , 2004 .

[44]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[45]  Chi Yang,et al.  TRACKING VORTICES OVER LARGE DISTANCES USING VORTICITY CONFINEMENT , 2001 .

[46]  G. Dahlquist Convergence and stability in the numerical integration of ordinary differential equations , 1956 .

[47]  Francis Caradonna Developments and challenges in rotorcraft aerodynamics , 2000 .

[48]  Juan J. Alonso,et al.  Time-accurate simulation of helicopter rotor flows including aeroelastic effects , 1997 .

[49]  J. Steinhoff,et al.  Application of vorticity confinement to the prediction of flows over complex bodies - A survey of recent results , 2001 .

[50]  A. Gopinath,et al.  Efficient fourier-based algorithms for time-periodic unsteady problems , 2007 .

[51]  Antony Jameson,et al.  Time Spectral Method for Rotorcraft Flow , 2008 .

[52]  R. P. Fedorenko The speed of convergence of one iterative process , 1964 .

[53]  O. J. Boelens,et al.  Multitlme multlgrid convergence acceleration for periodic problems with future applications to rotor simulations , 2001 .

[54]  P. Moin Fundamentals of Engineering Numerical Analysis , 2001 .

[55]  Antony Jameson,et al.  Steady-State Solution of the Euler Equations for Transonic Flow , 1982 .

[56]  Christian B Allen,et al.  Convergence of steady and unsteady formulations for inviscid hovering rotor solutions , 2003 .

[57]  J. Steinhoff,et al.  Efficient Eulerian computation of realistic rotorcraft flows using Vorticity Confinement - A survey of recent results , 2001 .

[58]  O. J. Boelens,et al.  Accurate and efficient vortex-capturing for a helicopter rotor in hover , 2000 .

[59]  V. R. Murthy,et al.  Efficient rotor flow calculation using multiblade coordinate transformed CFD in frequency domain , 2008 .

[60]  Manish Kumar,et al.  Analysis of flow around multibladed rotor using CFD in the frequency domain , 2007 .

[61]  George N. Barakos,et al.  A framework for CFD analysis of helicopter rotors in hover and forward flight , 2006 .

[62]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[63]  F. X. Caradonna,et al.  Experimental and Analytical Studies of a Model Helicopter Rotor in Hover , 1980 .

[64]  J. Alonso,et al.  Acceleration of Convergence to a Periodic Steady State in Turbomachinery Flows , 2001 .

[65]  Earl H. Dowell,et al.  Computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors , 2008 .

[66]  Ken Badcock,et al.  Aerofoil-Vortex Interaction Using the Compressible Vorticity Confinement Method , 2005 .

[67]  Hubert Pomin,et al.  Navier-Stokes Analysis of Helicopter Rotor Aerodynamics in Hover and Forward Flight , 2002 .

[68]  H. Xu,et al.  Numerical Simulations of Unsteady Flows Past a Four- Bladed Rotor in Forward-Flight , 2005 .

[69]  W. K. Anderson,et al.  Comparison of Finite Volume Flux Vector Splittings for the Euler Equations , 1985 .

[70]  C. Allen Multi-Bladed Lifting Rotor Simulation in Hover, Forward Flight, and Ground Effect , 2004 .

[71]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[72]  G. Sod Numerical methods in fluid dynamics , 1985 .

[73]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

[74]  Hubert Pomin,et al.  Aeroelastic Analysis of Helicopter Rotor Blades on Deformable Chimera Grids , 2004 .

[75]  Massimo Biava,et al.  The Effect of Far-Field Boundary Conditions on Tip Vortex Path Prediction in Hovering , 2002 .

[76]  R. A. Nicolaides,et al.  On the observed rate of convergence of an iterative method applied to a model elliptic difference equation , 1978 .

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

[78]  Christian B Allen Parallel simulation of lifting rotor wakes in forward flight , 2007 .

[79]  J. Steinhoff,et al.  Numerical method for vorticity confinement in compressible flow , 2002 .

[80]  Francis X. Caradonna,et al.  Numerical Calculation of Unsteady Transonic Potential Flow over Helicopter Rotor Blades , 1975 .

[81]  A. Jameson Iterative solution of transonic flows over airfoils and wings, including flows at mach 1 , 1974 .

[83]  M. E. Tauber,et al.  Computation of transonic flow about helicopter rotor blades , 1986 .

[84]  Mahendra J. Bhagwat,et al.  Development of a New Potential Flow Based Model for Hover Performance Prediction , 2005 .

[85]  Juan J. Alonso,et al.  Demonstration of Nonlinear Frequency Domain Methods , 2006 .

[86]  Wolfgang Hackbusch,et al.  Multigrid Methods II , 1986 .

[87]  Michael A Robinson APPLICATION OF VORTICITY CONFINEMENT TO INVISCID MISSILE FORCE AND MOMENT PREDICTION , 2004 .

[88]  A. T. Conlisk,et al.  MODERN HELICOPTER AERODYNAMICS , 1997 .

[89]  A. Jameson,et al.  Revisiting the Vertical-Axis Wind-Turbine Design Using Advanced Computational Fluid Dynamics , 2005 .

[90]  A. Jameson,et al.  Three-dimensional unsteady multi-stage turbomachinery simulations using the harmonic balance technique , 2007 .

[91]  Earl P. N. Duque,et al.  Flowfield analysis of modern helicopter rotors in hover by Navier-Stokes method , 1993 .

[92]  Bernard Grossman,et al.  The computation of massively separated flows using compressible vorticity confinement methods , 2006 .

[93]  D. Holmes,et al.  A Three-Dimensional Euler Solver for Turbomachinery Blade Rows , 1985 .

[94]  A. Jameson Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

[95]  J. Steinhoff,et al.  Computation of Blunt Body Wake Flow By Vorticity Confinement , 2004 .

[96]  Mahendra J. Bhagwat,et al.  Hybrid CFD for Rotor Hover Performance Prediction , 2006 .

[97]  Meng Fan,et al.  Vorticity Confinement and Advanced Rendering to Compute and Visualize Complex Flows , 2006 .

[98]  Antony Jameson,et al.  Acceleration of transonic potential flow calculations on arbitrary meshes by the multiple grid method , 1979 .

[99]  G. Dahlquist Stability and error bounds in the numerical integration of ordinary differential equations , 1961 .

[100]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[101]  Juan J. Alonso,et al.  Application of a Non-Linear Frequency Domain Solver to the Euler and Navier-Stokes Equations , 2002 .

[102]  D. Durran Numerical Methods for Fluid Dynamics , 2010 .

[103]  W. Mccroskey,et al.  Euler Calculations of Unsteady Interaction of Advancing Rotor with a Line Vortex , 1993 .

[104]  Dimitri J. Mavriplis,et al.  Large-scale parallel viscous flow computations using an unstructured multigrid algorithm , 1999 .

[105]  Francis X. Caradonna,et al.  Subsonic and Transonic Potential Flow over Helicopter Rotor Blades , 1972 .

[106]  J. Zierep,et al.  Theorie der schallnahen und der Hyperschallströmungen , 1966 .

[107]  Antony Jameson,et al.  Transonic flow calculations for aircraft , 1985 .