Delta wing with sharp leading edge Johan Kok

Delta wing with sharp leading edge Johan Kok (NLR) Go 4 Hybrid kick-off meeting CFDB, Berlin, 10– 11 October 2011 Nationaal Lucht- en Ruimtevaartlaboratorium – National Aerospace Laboratory NLR

Characterization of flow Shear layer separates from sharp leading edge and rolls up into primary vortex At high Reynolds, shear layer becomes unstable and turbulent vortex is formed At high angle of attack, primary vortex breaks down (high axial velocity in core drops to zero) Possible secondary, pressure-induced separation (between primary vortex and leading edge) Grey areas: shear layers emanating from leading edges initial vortex near apex Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 2

Test case definition NASA delta wing Chu & Luckring (1996) 65° leading-edge sweep sharp leading edge used in VFE-2 Stepping Stone in ATAAC Selected flow condition vortex breakdown M = 0. 07, Remac = 1· 106, Ao. A = 23° Experiment by TU München includes pressure and velocity fluctuations Furman & Breitsamter (2008, 2009) Partners: CFDB, NLR (coordinator) Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 3

Geometry definition analytic definition includes sting Chu & Luckring (1996) Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 4

Grids Common multi-block structured grid 6. 3 Mcells (mandatory) 21. 4 Mcells (fine) mesh size ≈ 0. 003 to 0. 011 cmac far field: 3 root chords (standard) 15 root chords (extended) conical structure: refined towards apex Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 5

Computational guidelines Time step of 3. 75· 10 -4 CTU used by most partners in ATAAC implies convective CFL = 1/8 suitable for 4 th-order spatial scheme plus 2 nd-order implicit time integration use for other numerical schemes as well (consistency) 1, 333 time steps period of dominant frequency (St = 2) Time sample of 15 CTU to compute flow statistics Initial solution: steady RANS solution transient approximately 7 CTU Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 6

Available reference data Experiment of TU München: Steady surface pressure at five chord stations: x/cr = 0. 2, 0. 4, 0. 6, 0. 8, and 0. 95 Unsteady surface pressure at four chord stations: x/cr = 0. 4, 0. 6, 0. 8, and 0. 95 Stereo-PIV (mean velocity field) at five chord stations: x/cr = 0. 2, 0. 4, 0. 6, 0. 8, and 0. 95 HWA (fluctuating velocity field) at three chord stations: x/cr = 0. 4, 0. 6, and 0. 8 Oil flow visualization Christian Breitsamter of TU München has provided the experimental data to the ATAAC project Availability to Go 4 Hybrid to be checked Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 7

Some experiences from ATAAC Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 8

Grey Area Mitigation X-LES Q criterion Stochastic SGS model High-pass filtered SGS model Old grid Stochastic X-LES Stochastic HPF X-LES Resolved TKE Standard X-LES Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 9

Grid sensitivity Common grid vs. old grid Common grid Old: uniform grid in x-direction need to maintain isotropic grid towards apex Resolved turbulent kinetic energy Old grid Q criterion Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 10

Grid sensitivity Common grid vs. fine grid fine: mesh width and time step 2/3 of common grid differences negligible relative to model/code differences Common grid Cross section x/c = 0. 4 Fine grid Mean pressure coefficient RMS of pressure coefficient Resolved turbulent kinetic energy Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 11

Sensitivity to time sample Statistics taken over varying time sample statistical convergence for about 16 CTU smallest time sample (6. 6 CTU) also acceptable 6. 6 CTU Cross section x/c = 0. 4 21 CTU Mean pressure coefficient RMS of pressure coefficient Resolved turbulent kinetic energy Go 4 Hybrid kick-off meeting, Berlin 10 -11/10/2013 12