1. Coarse grained velocity derivatives Beat Lüthi & Jacob Berg Søren Ott Jakob Mann Risø National Laboratory Denmark

2. Motivation1 Technical4 Properties6 Multi particles4 Energy flux5 Flux modelling5 Conclusion1 Ã ij properties LES context What can 3D-PTV contribute? so far: HPIV, 2D PIV, DNS Motivation

3. Motivation1 Technical1/4 Properties6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 How to get à ij from points?

4. Motivation 1 Technical2/4 Properties6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 Particle seeding, scales?  =? How fast can we record?? How dense can we track??  L current seeding range: ½-1½ L current Re : 170, L/  ~200

5. Motivation 1 Technical3/4 Properties5 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 How many points?

6. Motivation 1 Technical4/4 Properties6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 Convergence If we take more than 12 particles then it is ok

7. Motivation 1 Technical4 Properties1/6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 Orientation of à ij as f(  )

8. Motivation 1 Technical4 Properties2/6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 Time scale t * r     r>    r 2/3

9. Motivation 1 Technical4 Properties3/6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 Eigenvalues of strain is positive strain production

10. Motivation 1 Technical4 Properties4/6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 Vorticity alignment with strain, f(  )? Ref to porter paper  switches from 2 to 1 ! similar observation:

11. Motivation 1 Technical4 Properties5/6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 RQ

12. Motivation 1 Technical4 Properties6/6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 RQ in mean strain

13. Motivation 1 Technical4 Properties6 Multi particles1/4 Energy flux5 Flux modelling5 Conclusion 1 g1g1 g2g2 g3g3 g i =eigenvalues of moment of inertia tensor g ab g1g1 g2g2 g3g3 I 2 =g 2 /R 2 w=2A/R 2 Multi particle constellations

14. Motivation 1 Technical4 Properties6 Multi particles2/4 Energy flux5 Flux modelling5 Conclusion 1 Description of shape evolution

15. Motivation 1 Technical4 Properties6 Multi particles3/4 Energy flux5 Flux modelling5 Conclusion 1 Alignment to strain

16. Motivation 1 Technical4 Properties6 Multi particles4/4 Energy flux5 Flux modelling5 Conclusion 1 Significant small scale contribution Significant contribution from small scales! total large scales total large scales

17. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux1/5 Flux modelling5 Conclusion 1 Definition of SGS TKE production rate 1, or ’energy flux’ Also referred to as: energy flux SGS dissipation

18. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux2/5 Flux modelling5 Conclusion 1 Energy flux from DNS

19. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux3/5 Flux modelling5 Conclusion 1 Energy flux from Experiment None homogeneous forcing

20. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux4/5 Flux modelling5 Conclusion 1 Alignment of  ij with s ij compressing: producing SGS stretching: backscattering

21. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux5/5 Flux modelling5 Conclusion 1 Alignm. of  ij with s ij for ’backscatter’ compressing: producing SGS stretching: backscattering

22. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux5 Flux modelling1/5 Conclusion 1 Smagorinsky, non-linear, mixed, … scalar eddy viscosity: related to strain no backscatter possible stable tensor eddy viscosity: related to strain and vorticity production allows for ’backscatter’ is instable

23. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux5 Flux modelling2/5 Conclusion 1 Testing the non-linear model for flux DNSExperiment

24. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux5 Flux modelling3/5 Conclusion 1 RQ mapping of energy flux

25. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux5 Flux modelling4/5 Conclusion 1 RQ mapping for error too little backscatter too much backscatter

26. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux5 Flux modelling5/5 Conclusion 1 Alternative mapping: Q-sss and s 2 -sss

27. Motivation 1 Technical4 Properties6 Multi particles4 Energy flux5 Flux modelling5 Conclusion 1 Conclusion perform more experiments measure à ij and  ij influence of complex mean strain? because with 3D-PTV we can