Efficient Aero-Acoustic Simulation of the HART II Rotor with the Compact Pade Scheme Gunther Wilke DLR AS-HEL Sept 6th nd ERF Lille, France
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1 Chart 1 Efficient Aero-Acoustic Simulation of the HART II Rotor with the Compact Pade Scheme Gunther Wilke DLR AS-HEL Sept 6th nd ERF Lille, France
2 Chart 2 Overview - Motivation - Theory of Compact Pade Scheme (and JST Scheme) - Simulation Setup - Results - Prescribed vs computed motion - Grid sensitivity study - Alternative approaches - Conclusions
3 Chart 3 Motivation - Simulation of blade tip vortices and vortex structure - BVI noise in descent flight - Interaction aerodynamics, for example tail shake - Difficulties with State of the Art Tools - 2nd order too dissipative - Plenty of grid points and still not there - Problems with higher order schemes - Stability - Efficiency
4 Chart 4 -Theory
5 Chart 5 Howto get f '? Pade-Scheme - Higher order finite difference scheme implemented by Stefan Enk in FLOWer referred to as FLOWer4-4th order spatial discretization with 3rd order boundaries - 4th to 8th order filtering with down to 2nd order boundaries - Line implicit - Grid transformation from arbitrary to Cartesian grid - Not (yet) suitable for transonic flows Ansatz f 'i f 'i f 'i + f 'i 1 + f 'i 2 = c b f i + 3 f i 3 6h + 4h + f i + 2 f i 2 c f i + 1 f i 1 2h Solution through LU-decomposition (Thomas algorithm)
6 Chart 6 Jameson vs Pade-Scheme Jameson Finite Volume d +G dv + F ds =0 W S dt V Pade Finite Differences F i G d W ( ) d t J + i ξi + J = 0 RES = ΔVt [ t F t (W ) S t + G ] Flux Average RES = Δ t [J ( i Fi ξ i +W t ( 1J ))+ G ] Difference of Fluxes
7 Chart 7 Simulation Setup
8 Chart 8 Numerical Setup - Dual-Time Stepping with 1, 1/4, 1/8 degrees timesteps - Residual Smoothing - 2V Multigrid on JST blocks - 6th order Pade Filter with 4th order at the boundaries
9 Chart 9 Grids RANS Blade Mesh - C-H topology - Blunt root, tip and tab - Outer cell layer matching trickier - Point distribution (chordwise x spanwise x normal) = ( ( * 41) x ( ) x 73 ) = 2.6 mio - Y+ = 1 fulfilled on blade, not on blunt surfaces, (Y + = 2/4 on level 2/3) Level 3 shown
10 Chart 10 Grid Fuselage Mesh - Required for displacement effects - Simplified geometry, no hub included - Point distribution (axial x radial x normal) = ( 257 x 241 x 65 ) = 3.9 mio - Y+ = 1 on finest level Level 3 shown
11 Chart 11 Grid Background Mesh - Continuous, cartesion mesh of inner and outer region - Laplacian smoothed for Pade scheme - Inner region points: (inflight x lateral x vertical)= (554 x 422 x 210) = 49 mio - Total point distribution (inflight x lateral x vertical)= (641 x 481 x 289) = 88 mio
12 Chart 12 Grid Summary coarse medium fine blade 40k 323k 2.6 Mio fuselage 61k 490k 3.9 Mio background 1.4 Mio 11 Mio 88 Mio total 1.6 Mio 13 Mio 103 Mio
13 Chart 13 HART II + Pade Scheme = Results!
14 Chart 14 Comparison of Prescribed vs Computed Motion Lag Flap θo Torsion θc θs experiment computed
15 Chart 15 Comparison of Prescribed vs Computed Motion - Motion agrees on a fair level for the computed case - Loads agree better continuing with coupled simulation thrust req. power experiment 3300 N 18.7 kw prescribed 3825 N 25.5 kw simulated 3304 N 22.0 kw
16 Chart 16 Grid Sensitivity Study (JST vs Pade) JST Hybrid-Pade
17 Chart 17 Grid Sensitivity Study (JST vs Pade) JST Hybrid-Pade
18 Chart 18 Grid Sensitivity Study (JST vs Pade) medium fine medium JST Hybrid-Pade Cost increase about 50% fine
19 Chart 19 Alternative Simulation Techniques isolated rotor Runtime factor inviscid viscous +fuselage inviscid 63% viscous 76% fuselage 100%
20 Chart 20 Conclusions!
21 Chart 21 Conclusions - Established a hybrid simulation environment within FLOWer with the a 4th order compact Pade scheme - Computed motion results better than prescribed motion still discrepancies in the HOST+FLOWer coupling - Hybrid simulation with Pade scheme significantly improved vortex conservation better loads correlation better acoustic correlation - Medium mesh setup almost as good as fine mesh setup when using Hybrid over classical JST - For design purposes the viscosity as well as the fuselage can be neglected ~ 37% runtime improvement
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