Sample validation

ONERA M6 WING

The ONERA M6 wing [3] is a transonic wing test case for which detailed experimental data are available [4]. This test case is one of those used to validate the high-speed flow predictive capabilities of COSA. The COSA results presented in the remainder of this section were obtained using the 884,7360cell three-dimensional grid available at the web site of the NASA code CFL3D [5]. A view of the wing, its surface mesh and the grid on the symmetry plane are reported in the figure below. Only every second line line in each direction is reported for graphical clarity. Both computed results and experimental data refer to a freestream Mach number of 0.84, an angle of attack of 3.06 degrees, and a Reynolds number of 11.7 million based on a mean aerodynamic chord of 646 millimeters.

The comparison of measured and computed static pressure coefficients at 4 different spanwise positions along the blade is reported below, and it highlights an excellent agreement between the COSA predictions and the measured data [6[.

NACA4412 separated flow

In this test case, COSA was used to compute the turbulent flow field past the NACA4412 airfoil corresponding to the condition of maximum lift. The freestream Mach number is 0.2, and the angle of attack is 13.87 degrees. The Reynolds number based on the airfoil chord and the freestream velocity is 1.52 million. This regime is characterized by a flow reversal in the rear part of the airfoil suction side. Detailed hot-wire boundary layer measurements were performed at NASA Aimes and reported in [7]. The C-grid of the COSA simulation is that available on the web site of the NASA CFD code CFL3D [5], it consists of 20,480 cells, and the farfield boundaries are at about 20 chords from the airfoil. An enlarged view of the grid close to the airfoil is reported below.

The 4 plots below report the comparison between the measured and computed profiles of velocity component parallel to the wall measured along the local normal to the wall. The variable along the x-axis is the parallel velocity component normalized by the freestream velocity, and the variable along the y-axis is the normal distance from the airfoil surface normalized by the chord. A very good agreement between simulation and experimental data is observed.

1. M.M. Hand, D.A. Simms, L.J. Fingersh, D.W. Jager, J.R. Cotrell, S. Schreck, S.M. Larwood, Unsteady Aerodynamics Experiment Phase VI: Wind Tunnel Test Configuration and Available Data Campaigns, NREL/TP-500-29955, 2001.

2. J. Drofelnik, A. Da Ronch, M.S. Campobasso, Harmonic balance Navier-Stokes aerodynamic analysis of horizontal axis wind turbines in yawed wind, Wind Energy, Vol. 21, no. 7, 2018, pp. 515-530. DOI: 10.1002/we.2175. Download pre-peer reviewed article here.

3. ONERA M6 Wing, http://www.grc.nasa.gov/WWW/wind/valid/m6wing/m6wing.html, accessed on 5 July 2020.

4. Schmitt, V. and F. Charpin, "Pressure Distributions on the ONERA-M6-Wing at Transonic Mach Numbers," Experimental Data Base for Computer Program Assessment. Report of the Fluid Dynamics Panel Working Group 04, AGARD AR 138, May 1979.

5. CFL3D test cases, http://cfl3d.larc.nasa.gov/, accessed on 5 July 2020.

6. J. Drofelnik, Massively Parallel Time- and Frequency-Domain Navier-Stokes Computational Fluid Dynamics Analysis of Wind Turbines and Oscillating Wing Unsteady Flows, PhD Thesis, June 2017.

7. Wadcock AJ. Structure of the turbulent separated flow around a stalled airfoil. Contract report NASA CR-152263, NASA Aimes Research Center, Moffett Field, CA, USA; February 1979.