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Structure and dynamics of turbulent pipe flow

Describe… Model…. Andrew Duggleby Mechanical Engineering Texas A&M University Isaac Newton Institute 2008. Structure and dynamics of turbulent pipe flow. Collaborators: Ken Ball, Mark Paul Mechanical Engineering Virginia Tech Markus Schwaenen Mechanical Engineering

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Structure and dynamics of turbulent pipe flow

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  1. Describe… Model… Andrew Duggleby Mechanical Engineering Texas A&M University Isaac Newton Institute 2008 Structure and dynamics of turbulent pipe flow Collaborators: Ken Ball, Mark Paul Mechanical Engineering Virginia Tech Markus Schwaenen Mechanical Engineering Texas A&M University Paul Fischer Argonne National Lab. Predict…

  2. Structure and dynamics of turbulent pipe flow • Proper Orthogonal Decomposition • Translational invariance vs. method of snapshots • What POD is, and what it is not (3 misnomers) • Turbulent pipe flow (spectral element DNS) • Describe, Model, Predict • Applications to drag reduction

  3. Karhunen-Loève (KL) Decomposition is a powerful tool that generates an optimal basis set for dynamical data Proper Orthogonal Decomposition (POD) Empirical (or dynamical) Eigenfunctions • Optimally fast convergence • Maximizes “energy” • Originates as a variational problem

  4. In order to reduce the size of the problem, the translational invariance of the system is taken into account. • By translational invariance • The POD mode is then • And the Fredholm integral reduces to • POD modes are labeled by the triplet (m,n,q) with Misnomer 1: Thisisa mode (1,3,1)

  5. Method of Snapshots • Define c(t) and rewrite • Take inner product with velocity at a different time • Solve Fredholm equation for coefficient c(t)

  6. Translational invariance vs. snapshots for turbulent pipe flow

  7. Dimension vs. time for turbulent pipe flow

  8. Translational Invariance and Method of Snapshots agree at infinite time – shown using Rayleigh-Bénard convection Misnomer 2: The basis set is only optimal for “recorded events” Misnomer 3: The basis set is only optimal for energy dynamics "Goal-oriented, model-constrained optimization for reduction of large-scale systems“ T. Bui-Thanh, K. Willcox, O. Ghattas, B. van BloemenWaandersJ. of Comp. Phys. (2006)

  9. POD reduces the order of the system to a much more manageable level(from 107 to 104) whereby one can examine the system • Insight gained through examining: • The energy ordering of the modes • The structure of the modes • The dynamics of the modes (1,5,1) mode – travelling wave Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  10. Example modes (wall modes) (1,3,1) (1,5,1) (2,4,1) Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  11. …more modes (lift modes) (2,2,1) (3,2,1) (3,3,1) Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  12. …and yet even more modes (roll mode) (0,6,1) (0,5,1) (0,3,1) Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  13. Karhunen-Loève decomposition is a very powerful tool in helping to understand large scale energy dynamics. Travelling wave interpretation of turbulence = Streamwise Roll + Travelling wave packet

  14. Energy content of the modes 38.34% energy in structures >8R (m<2) Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  15. Model: to understand drag reduction, two sets of DNS calculations were analyzed, one with spanwise wall oscillation and one without.

  16. Wall mode (vorticity starts and stays near the wall) is pushed away from the wall in the presence of oscillation Non-oscillated Oscillated (1,2,1) (1,5,1) Duggleby et al., 2007, Phys. Fluids, Vol. 19, 125107

  17. Lift mode (vorticity starts near the wall and lifts away from the wall ) is also pushed away from the wall in the presence of oscillation Oscillated Non-oscillated (2,2,1) (3,2,1) Duggleby et al., 2007, Phys. Fluids, Vol. 19, 125107

  18. Roll mode (no spanwise dependence, “streamwise vortices”) is also pushed away from the wall due to spanwise wall oscillation Oscillated Non-oscillated (0,6,1) (0,2,1) Duggleby et al., 2007, Phys. Fluids, Vol. 19, 125107

  19. Model: Drag reduction mechanism Duggleby et al., 2007, Phys. Fluids, Vol. 19, 125107

  20. Prediction: Drag reduction by sectional rotation

  21. Conclusions • Describe: POD is a great way to visualize the large scale energy dynamics • Method of Snapshots and Translational invariance agree at late time • L=100D pipe simulations underway • Model: drag reduction model • Predict: Drag reduction • Experimental testing under way

  22. Acknowledgements • System X • Teragrid • Paul Fischer • Markus Schwaenen • Travis Thurber • Ken Ball • Mark Paul

  23. Appendix Top 15 POD modes for various flows

  24. Convergence for Re_tau=180 Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  25. Statistics Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  26. Stress Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  27. Mean velocity profile (Reτ=150) shows a 26.9% increase in the mean flow rate due to spanwise wall oscillation. 26.9% increase in mean flowrate Duggleby et al., Phys. Fluids (in review), 2007

  28. The peaks of root-mean-square velocity fluctutationsand Reynolds stress profiles shift due to the oscillation. Duggleby et al., Phys. Fluids (in review), 2007

  29. Turbulent Pipe Flow examinations • Pipe Flow: • L/D=10 • Reτ=150 • Total simulation time: • t+=16800 • 80 flow through times • Rayleigh-Benard • R=6000 • σ=1 • Γ=10 Red: hot rising fluid, Blue: cold falling fluid H.M. Tufoand P.F. Fischer, in Proc. Of the ACM/IEEE SC99 Conf. on High Performance Networking and Computing (IEEE Computer Soc., 1999), Gordon Bell winning paper

  30. Translational invariance vs. Snapshots First mode from method of snapshots First mode from translational invariance (18,1)

  31. Propagating Subclasses: Asymmetric mode (1,1,1) (2,1,1) (3,1,1) Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  32. Propagating Subclasses: Ring mode (1,0,1) (1,0,2) (2,0,1) Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  33. Effect of quantum number (2,6,3) (2,6,5) (6,2,3) (6,2,5) Duggleby et al., 2007, Journal of Turbulence, Vol. 8 no. 43

  34. Model & Prediction: relaminarization (?) Or L=10D is too short!

  35. Spectral Elements combines geometrical flexibility, efficient parallelization, and exponential convergence • Spectral Element • Legendre Lagrangianinterpolants • 3rd order in time • Jacobi w/ Schwarz multigrid and GMRES • Scalable • 1.26 TFLOPS on 2048 proc. (BG/L) • 108 GFLOPS on 128 proc. (SysX) • Avoids the singularity at the origin inpolar-cylindrical coordinates • tU/L=80 H.M. Tufo and P.F. Fischer, in Proc. Of the ACM/IEEE SC99 Conf. on High Performance Networking and Computing (IEEE Computer Soc., 1999), Gordon Bell winning paper

  36. Channel modes

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