Delta Wing with Sharp Leading Edge
ST08 Delta wing with sharp leading edge
Main objective of this test case is the prediction of vortex breakdown. A sharp leading edge is preferred over a round one, so that the separation location is fixed and the focus can be on predicting vortex breakdown, not separation.
As test case the delta wing from the Second International Vortex Flow Experiment (VFE-2) is chosen:
- NASA delta wing with analytic definition of geometry (Figure 1):
Chu,J. and Luckring, J. M.: Experimental surface pressure data obtained on 65°delta wing across Reynolds number and Mach number ranges. NASA TM 4645 (1996). - 65° leading-edge sweep,
- four leading edges: one sharp and three round edges,
- only sharp leading edge will be used,
- geometry includes sting,
- large set of experiments and numerical results, see
The most detailed experiments within VFE-2 are the experiments of TU München, which include measurements of velocity fluctutations:
- Furman, A. and Breitsamter, Ch.: Turbulent and unsteady flow characteristics of delta wing vortex systems. AIAA Paper 2008-0381, 2008.
The most extensive set of data is available at the flow conditions: M = 0.07, Remac = 1·106, α = 13/18/23°. Experiments have also been peformed at M = 0.14, but velocity fluctuations are only available at M = 0.07. Therefore, the following conditions are proposed for the numerical computations:
- M = 0.07, Remac = 1·106, α = 23° (vortex breakdown),
- M = 0.07, Remac = 1·106, α = 18° (optional; no vortex breakdown).
The second condition is optional and can serve as reference before vortex breakdown.
The experiments of TU München include the following measurements:
- Steady surface pressure measurements at five chord stations:
x/cr = 0.2, 0.4, 0.6, 0.8, and 0.95. - Unsteady surface pressure measurements at four chord stations:
x/cr = 0.4, 0.6, 0.8, and 0.95. - Stereo particle image velocimetry (stereo-PIV) (mean velocity field) at five chord stations:
x/cr = 0.2, 0.4, 0.6, 0.8, and 0.95. - Hot-wire anemometry (HWA) (fluctuating velocity field)at three chord stations:
x/cr = 0.4, 0.6, and 0.8. - Oil flow visualization.
- (Laser light sheet visualization has also been performed, but only at M = 0.035, Remac = 0.5·106.)
Christian Breitsamter of TU München has agreed in principal to make the experimental data available to the ATAAC project. Details (precise data, format, etc.) still have to be worked out.
It is proposed to use the following computational results for cross-plotting and comparison with experiment:
- mean and RMSof surface pressure at the five chord stations (x/cr = 0.2, 0.4, 0.6, 0.8, and 0.95),
- mean velocity field and resolved Reynolds stresses at cross planes at the five chord stations,
- mean surface streamlines,
- surface pressure spectra at the locations of the unsteady pressure sensors:
x/cr = 0.4, 0.6, 0.8, 0.95,
2y/bl = 0.25, 0.4, 0.5, 0.575, 0.625, 0.675, 0.725, 0.775, 0.825, 0.875, 0.925, 0.975,
(a selection will be made based on experimental and computational results).
NLR will generate a multi-block structured grid, suitable for hybrid RANS–LES, and make it available.
Open for discussion is whether we also want to perform computations at higher Mach numbers. In particular, experimental results are also available from DLR Göttingen (PIV and PSP) at M = 0.4/0.8, Remac = 2·106/3·106, and α = 10 – 25°:
- Konrath, R., Klein, C., and Schröder, A.: PSP and PIV Investigations on the VFE-2 Configuration in Sub- and Transonic Flow. AIAA Paper 2008-379, 2008.
These measurements do not include fluctuating velocities.
The M = 0.8 case would be challenging as shock-vortex interaction comes into play, influencing the vortex-breakdown location. See, e.g.,
- Schiavetta, L.A.et al.: Shock Effects on Delta Wing Vortex Breakdown. AIAA Paper 2008-395, 2008.
In the literature (see VFE2 website), hybrid RANS–LES computations have been performed for vortex breakdown for this delta wing, however, for a round leading edge and at higher Mach numbers.
Figure 1Geometry of VFE2 delta wing