Coarse grained velocity derivatives

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
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
Motivation 1 Technical 4 Properties 2/6 Multi
particles 5 Energy flux 5 Flux
modelling 7 Conclusion 1
rh t t h rgt h tr2/3
9
Eigenvalues of strain
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 constellations
w2A/R2
Motivation 1 Technical 4 Properties 6 Multi
particles 1/5 Energy flux 5 Flux
modelling 7 Conclusion 1
gieigenvalues 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
DNS
Experiment
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