Far-Field Analysis of the Aerodynamic Force by Lamb Vector Integrals

A new far-field method is proposed for the analysis of the aerodynamic force acting on an airfoil in subsonic unsteady flow conditions given a numerical solution of the flowfield. For this purpose, a recent theory proposed by Wu et al. (Wu, J.-Z., Ma, H.-Y., and Zhou, M.-D., Vorticity and Vortex Dynamics, Springer, New York, 2006), relating the aerodynamic force acting on a body to the Lamb vector (the cross product ofthe vorticity by the velocity) in case of unsteady Navier-Stokes flow, has been extended to the analysis of high-Reynolds-number turbulent flows governed by the Reynolds-averaged Navier-Stokes equations. The applications showed here concern the analysis of numerical solutions around an airfoil in steady flow and in pitching oscillations including a dynamic-stall condition. Both lift and drag coefficients have been computed by means of Lamb vector integrals and have been compared with the reference near-field results (stress integration on the body). The method allows for the decomposition of the aerodynamic force in a contribution associated with the bound vorticity on the body and a contribution related to the free vorticity developing in the airfoil wake.

[1]  Edward N. Tinoco,et al.  Abridged Summary of the Third AIAA Computational Fluid Dynamics Drag Prediction Workshop , 2008 .

[2]  Kazuhiro Nakahashi,et al.  Aerodynamic Design Optimization Using the Drag-Decomposition Method , 2008 .

[3]  Philippe R. Spalart,et al.  On the far wake and induced drag of aircraft , 2008, Journal of Fluid Mechanics.

[4]  Xi-Yun Lu,et al.  Integral force acting on a body due to local flow structures , 2007, Journal of Fluid Mechanics.

[5]  Dilek Funda Kurtulus,et al.  Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV , 2007 .

[6]  Renato Tognaccini,et al.  Drag Computation and Breakdown in Power-on Conditions , 2005 .

[7]  D. Destarac,et al.  Drag/thrust analysis of jet-propelled transonic transport aircraft; Definition of physical drag components , 2004 .

[8]  Tim Lee,et al.  Investigation of flow over an oscillating airfoil , 2004, Journal of Fluid Mechanics.

[9]  Luigi Paparone,et al.  Computational Fluid Dynamics-Based Drag Prediction and Decomposition , 2003 .

[10]  Edward N. Tinoco,et al.  Data Summary from Second AIAA Computational Fluid Dynamics Drag Prediction Workshop , 2003 .

[11]  Johan C. Kok,et al.  Resolving the Dependence on Freestream Values for the k- Turbulence Model , 2000 .

[12]  C. P. van Dam,et al.  Recent experience with different methods of drag prediction , 1999 .

[13]  F. Noca,et al.  A COMPARISON OF METHODS FOR EVALUATING TIME-DEPENDENT FLUID DYNAMIC FORCES ON BODIES, USING ONLY VELOCITY FIELDS AND THEIR DERIVATIVES , 1999 .

[14]  Jiezhi Wu,et al.  Turbulent force as a diffusive field with vortical sources , 1999 .

[15]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[16]  Jayanta Panda,et al.  Experimental investigation of the flow field of an oscillating airfoil and estimation of lift from wake surveys , 1994, Journal of Fluid Mechanics.

[17]  W J McCroskey,et al.  A critical assessment of wind tunnel results for the NACA 0012 airfoil , 1987 .

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

[19]  J. Wu.  Theory for Aerodynamic Force and Moment in Viscous Flows , 1981 .

[20]  T. Kármán.  General aerodynamic theory. Perfect fluids , 1963 .