1. EULER Code for Helicopter Rotors EROS - European Rotorcraft Software Romuald Morvant March 2001

2. PLAN 1- Presentation of the EROS project 2- The numerical SCHEMES 3- FUN & UNFACtored methods - RESULTS 4- CONCLUSIONS 5- FUTURE WORK

3. OBJECTIVES Accurate prediction of the Aerodynamic Load distribution along the blades. 1- Reduce pilot control-loads 2- Increase speed 3- Identify and quantify the aerodynamic noise sources

4. GEROS - GRID GENERATOR Adapted for Multi-blade calculations Various topologies in the framework of CHIMERA overlapping grids

5. EROS - INVISCID EULER solver A- Cell-centred FINITE VOLUME method B- SPATIAL discretisation scheme C- DUAL-TIME implicit scheme D- TIME-STEPPING scheme

6. Finite volume method 1- Closed surface 2- Rigid motion of the blade 3- Geometric Conservation Law

7. Calculations of the surface fluxes

8. IMPLICIT DUAL-TIME METHOD Redefinition of the Residual term Spatial discretisation Time discretisation

9. Time-stepping SCHEME 1- Multi-stage Runge-Kutta scheme 2- Unfactored-factored method Use of acceleration techniques CFL number

10. RESULTS from previous reports  JAMESON - Runge-Kutta  ROE - FUN method Preference for the ROE-FUN method: - BETTER respect of the physic (convection) - FASTER convergence

11. FUN METHOD Factorisation in the spanwise direction 2 LINEAR SYSTEMS

12. ANALYSES of the FUN method  SMALL SIZE of the matrices  LARGE NUMBER of pseudo-time steps to get a high convergence. Problems to damp out the small errors frequencies

13. Objectif: SPEED the code UP 1- CODING 2- ALGORITHM UNFACtored method

14. CODING UNROLLING of repetitive operations Transformation of the matrices (5x5) into a vector (25x1)

15. ALGORITHM Implementation of the UNFACtored method Modification of the LHS block matrix size where the flow variables are stored Consideration of the 3 Dimensions

16. REFERENCE TESTS - LANN WING : unsteady case (3D) - EC/ONERA 7A 4-bladed Model Rotor Model Rotor in transonic hover flight Single block grid

17. UNSTEADY Case - LANN wing y/b=0.475 y/b=0.825 Sectional Force Coefficients Pitching moment coeff.

18. UNSTEADY Case - LANN wing y/b=0.475 y/b=0.825 Mean Steady PressureFirst Harmonic Pressure

19. Convergence behaviour STEADY run UNSTEADY run

20. Periodic OH grid, 84 x 60 x 32 7A Model Rotor in hover flight

21. Pressure Coefficient distribution, Normal force Coeff.

22. CONVERGENCE Behaviour

23. COMMENTARIES UNFACtored method  Higher CFL number  Faster convergence Higher average computing time / iterations

24. FINAL RESULTS

25. CONCLUSIONS  GOOD agreement with the FUN method  Calculations 5 times faster This method requires some other tests. It looks ATTRACTIVE for the unsteady cases

26. FUTURE WORK  Use of the UNFACtored method for the CHIMERA grid  Implementation of the WENO method relevant to a future AEROACOUSTIC module: Blade Vortex Interaction (BVI)  MPI implementation to enable the studies of large and important cases.