SIMULATION OF THE DYNAMIC STALL OVER AN OSCILLATING AIRFOIL

In this paper, a method is presented for the simulation of the boundary layer separation of the flow over a pitching NACA-0012 airfoil in dynamic stall conditions. Computations are performed using a locally developed unsteady twodimensional Navier-Stokes flow solver. This solver utilizes the finite volume method and employs the upwind flux-differencesplitting (FDS) technique of Roe for the inviscid terms and the viscous terms are centrally differenced. Newton-type subiterations are employed to obtain accurate solutions on the moving mesh. The Baldwin-Barth turbulence model is implemented in conjunction with the transition model of Gostelow et al. to simulate realistic flow situations. The transition onset location can either be predicted with Michel’s criterion or specified as an input parameter. The accuracy of the developed solver is validated with good agreement against published experimental measurements. Furthermore, the developed flow solver is used to simulate the flow over the NACA 0012 airfoil exhibiting sinusoidal pitching movement in deep-stall conditions and the evolution of the dynamic stall phenomena is satisfactorily captured and investigated. NOMENCLATURE a Speed of sound c Airfoil chord e Total energy per unit volume f Parameter governing the temporal order of accuracy of the scheme k Reduced frequency n Spot generation rate p Static pressure po Stagnation pressure

[1]  L. Christopher,et al.  Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations , 1995 .

[2]  Ravi Ramamurti,et al.  Computational study of 3-D flapping foil flows , 2001 .

[3]  M. Akbari,et al.  Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method , 2003 .

[4]  N. Rott.  Unsteady viscous flow in the vicinity of a stagnation point , 1956 .

[5]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[6]  T. Pulliam.  Time accuracy and the use of implicit methods. [in CFD , 1993 .

[7]  W. Mccroskey,et al.  Analysis of the development of dynamic stall based on oscillating airfoil experiments , 1977 .

[8]  R. R. Brodeur,et al.  TRANSITION PREDICTION FOR A TWO DIMENSIONAL NAVIER-STOKES SOLVER APPLIED TO WIND-TURBINE AIRFOILS , 2000 .

[9]  D. Telionis,et al.  Boundary-layer separation in unsteady flow , 1975 .

[10]  T. Barth,et al.  A one-equation turbulence transport model for high Reynolds number wall-bounded flows , 1990 .

[11]  Marilyn J. Smith,et al.  Evaluation of CFD to Determine Two-Dimensional Airfoil Characteristics for Rotorcraft Applications , 2004 .

[12]  Robert T. Biedron,et al.  Efficiency and accuracy of time-accurate turbulent Navier-Stokes computations , 1995 .

[13]  James L. Thomas,et al.  Extension and applications of flux-vector splitting to unsteady calculations on dynamic meshes , 1987 .

[14]  P. Bradshaw,et al.  Momentum transfer in boundary layers , 1977 .

[15]  Ken Badcock,et al.  CFD Investigation of 2D and 3D Dynamic Stall , 2004 .

[16]  Avi Seifert,et al.  Oscillatory Excitation of Unsteady Compressible Flows over Airfoils at Flight Reynolds Numbers , 1999 .

[17]  W. Stepniewski,et al.  Rotary Wing Aerodynamics , 2022 .

[18]  D. Drikakis,et al.  An implicit unfactored method for unsteady turbulent compressible flows with moving boundaries , 1999 .

[19]  Marilyn J. Smith,et al.  Improving the CFD Predictions of Airfoils in Stall , 2005 .

[20]  Gregory J. Walker,et al.  Effects of Streamwise Pressure Gradient on Turbulent Spot Development , 1995 .

[21]  Philip L. Roe,et al.  A comparison of numerical flux formulas for the Euler and Navier-Stokes equations , 1987 .