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

2. Motivation Ãij properties LES context What can 3D-PTV contribute?
so far: HPIV, 2D PIV, DNS
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1

3. How to get Ãij from points?
Motivation 1
Technical 1/4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1

4. Particle seeding, scales?
How dense
can we track??
How fast
can we record??
D=?
Motivation 1
Technical 2/4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1
current seeding range: ½-1½ L h L
current Rel : 170, L/ h ~200

5. How many points? Motivation 1 Technical 3/4 Properties 5
Multi particles 6
Energy flux 5
Flux modelling 7
Conclusion 1

6. Convergence If we take more than 12 particles then it is ok
Motivation 1
Technical 4/4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1
If we take more than 12 particles then it is ok

7. Orientation of Ãij as f(D)
Motivation 1
Technical 4
Properties 1/6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1

8. Time scale t* r~h t*~ t h r> h t*~r2/3 Motivation 1 Technical 4
Properties 2/6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1
r~h t*~ t h
r> h t*~r2/3

9. Eigenvalues of strain is positive strain production Motivation 1
Technical 4
Properties 3/6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1

10. Vorticity alignment with strain, f(D)?
w switches from l2 to l1!
Ref to porter paper
Motivation 1
Technical 4
Properties 4/6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1
similar
observation:

11. RQ Motivation 1 Technical 4 Properties 5/6 Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1

12. RQ in mean strain Motivation 1 Technical 4 Properties 6/6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1

13. Multi particle constellationsg1 g2 g3
I2=g2/R2 g1 g2 g3
w=2A/R2
Motivation 1
Technical 4
Properties 6
Multi particles 1/5
Energy flux 5
Flux modelling 7
Conclusion 1
gi=eigenvalues of
moment of inertia tensor gab

14. Growth Motivation 1 Technical 4 Properties 6 Multi particles 2/5
Energy flux 5
Flux modelling 7
Conclusion 1

15. Description of shape evolution
Motivation 1
Technical 4
Properties 6
Multi particles 3/5
Energy flux 5
Flux modelling 7
Conclusion 1

16. Alignment to strain Motivation 1 Technical 4 Properties 6
Multi particles 4/5
Energy flux 5
Flux modelling 7
Conclusion 1

17. Significant small scale contribution
total
total
large scales
large scales
Motivation 1
Technical 4
Properties 6
Multi particles 5/5
Energy flux 5
Flux modelling 7
Conclusion 1
Significant contribution from small scales!

18. Definition of SGS TKE production rate1, or ’energy flux’
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 1/5
Flux modelling 7
Conclusion 1
Also referred to as:
energy flux
SGS dissipation

19. Energy flux from DNS Motivation 1 Technical 4 Properties 6
Multi particles 5
Energy flux 2/5
Flux modelling 7
Conclusion 1

20. Energy flux from Experiment
None homogeneous forcing
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 3/5
Flux modelling 7
Conclusion 1

21. Alignment of tij with sij
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 4/5
Flux modelling 7
Conclusion 1

22. Alignm. of tij with sij for ’backscatter’
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5/5
Flux modelling 7
Conclusion 1

23. 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
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 1/7
Conclusion 1

24. Testing the non-linear model for flux
Experiment
DNS
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 2/7
Conclusion 1

25. RQ mapping of energy flux
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 3/7
Conclusion 1

26. RQ mapping for error Motivation 1 Technical 4 Properties 6
Multi particles 5
Energy flux 5
Flux modelling 4/7
Conclusion 1

27. Alternative mapping: wiwjsij-sijsjkski
How to find distinct regions for positive and negative fluxes?
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 5/7
Conclusion 1

28. Alternative mapping: wiwjsij-sijsjkski
How to find distinct regions for positive and negative fluxes?
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 6/7
Conclusion 1

29. Alternative mapping: Q-sss and s2-sss
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 7/7
Conclusion 1

30. Conclusion perform more experiments measure Ãij and tij
flows with complex mean strain
because with 3D-PTV we can
Motivation 1
Technical 4
Properties 6
Multi particles 5
Energy flux 5
Flux modelling 7
Conclusion 1