Organizer: Jörg Schumacher (TU Ilmenau, Fak. Maschinenbau)
DFG-PP 1 : Turbulent Superstructures
Tuesday 14:00 - 16:00 Coudraystr. 9A, Lecture hall 6
Turbulent Superstructures - An Introduction
J. Schumacher (TU Ilmenau, Fak. Maschinenbau) 14:00
The classical picture of turbulence which has prevailed since the pioneering works by Kolmogorov is that turbulent fluid motion is characterized by a cascade of vortices and swirls of different sizes that give rise to a featureless and stochastic fluid motion. Our daily experience shows, however, that turbulent flows in nature and technology are often organized in prominent large-scale and long-living structures that can cause extreme fluctuations. When present, superstructures dominate the global transport of mass, heat and momentum, they act as barriers to transport, and they increase the variability and fluctuations in the flow. Given the importance of superstructures for turbulent flows, we know very little about their origins, their dynamics, and their impact on turbulent flow properties. Furthermore, their consequences for the statistical properties of turbulent flows, and their connection to the occurrence of extreme events are poorly understood.
The study of superstructures is now possible due to significant advances in measurement techniques, numerical simulation, and mathematical characterization. Tomographic laser-based measurement techniques can track the dynamics of turbulent structures with unprecedented resolution in space and time. Direct numerical simulations on massively parallel supercomputers have advanced to a level where turbulent flows in extended do-mains can be simulated at sufficiently high Reynolds numbers and in parameter ranges where superstructures emerge. Efficient methods to characterize dominant vortices and flow structures and to determine the transport across their boundaries as well as their dynamical evolution have been developed in applied mathematics. Computer science provides efficient algorithms for the visualization of structures in very large data sets.
The presentation will give a compact overview on planned program activities.
Spectral Analysis of Large Scale Structures in Fully Developed Turbulent Pipe Flow
C. Egbers (BTU Cottbus Senftenberg), A. Shahirpour (BTU Cottbus -Senftenberg), E. Öngüner (BTU Cottbus - -Senftenberg), E. Zanoun (BTU Cottbus - Senftenberg)
14:20
Over the last decades, experimental and computational studies have resulted in con-siderable insight into physics of wall-bounded turbulent flows and have provided large turbulence data sets. Nevertheless, fundamental questions regarding structure and scal-ing of wall turbulence and coherent structures are still under debate. Therefore, the present work focuses on spectral analysis of experimentally measured data in Cottbus Large Pipe (CoLaPipe) test facility for a wide range of Reynolds numbers at low Mach numbers.
Spectral analysis of the velocity field can help to reveal insightful information about the behavior of structures with different wavelengths. The pre-multiplied velocity spectrum that represents the energy distribution in the wave number space helps to follow the foot prints of such structures and provides an estimate of their energy content. At sufficiently high Reynolds numbers and at certain wall-normal locations, two peaks are observable in the outer region of the pre-multiplied spectra, which can be interpreted as signatures of Large Scale Motions (LSM) and Very Large Scale Motions (VLSM) (see, e.g., Rosenberg et al. 2013, Vallikivi et al. 2015).
In the same manner, the present study aims at describing the most energetic motions found in experimental data measured in CoLaPipe, in terms of their wave lengths, wall-normal locations and energy content and their scaling. Experiments are conducted, utilizing the CoLaPipe at bulk Reynolds numbers of 6× 104 < Reb < 10× 106, where Reb is based on the pipe diameter D and bulk velocity Ub, at Mach numbers M a < 0.23.
Measurements have been carried out using Hot Wire Anemometry (HWA) and Particle Image Velocimetry (PIV).
Acknowledgments: This project is funded inside the DFG-SPP (1881) ”Turbulence and Superstructures” under grant no. EG100/24-1.
Turbulent Superstructures in Controlled Flows
D. Gatti, A. Stroh, Y. Hasegawa, B. Frohnapfel 14:40
The term “turbulent superstructure” (TSS) is used to describe certain patterns observed in wall-bounded shear flows at very high Reynolds numbers. These patterns, e.g. con-nected regions of relatively low speed fluid, are typically very elongated in streamwise direction. They are often described through the premultiplied streamwise velocity spec-tra in which a second peak emerges at high Reynolds numbers. Since TSS are known to carry a large amount of the Reynolds shear stress - which represents the turbulent contribution to skin friction drag - it is speculated whether or not the potential control of such structures could lead to significant drag reduction. The present contribution aims at improving our understanding of the link between TSS and skin friction drag through a numerical experiment. DNS of a turbulent channel flow is carried out at
Re_-tau=1000. While this friction Reynolds number is fixed through a prescribed pressure gradient the turbulent flow is modified with different near-wall control techniques. In the present setting with a fixed friction Reynolds number these control techniques lead to an increased flow rate. We investigate how these changes reflect in the spectral repre-sentation of the streamwise velocity fluctuations (and hence TSS) and most importantly in the corresponding spectral representation of the Reynolds shear stress.
Trajectory-based computational study of coherent behavior in flows
K. Padberg-Gehle (Leuphana Universität Lüneburg) 15:00
The notion of coherence in time-dependent dynamical systems is used to describe mobile sets that do not freely mix with the surrounding regions in phase space. In particular, coherent behavior has an impact on transport and mixing processes in fluid flows. The mathematical definition and numerical study of coherent structures in flows has received considerable scientific interest for about two decades, see [1] for a recent review and comparison of different approaches. However, mathematically sound methodologies such as transfer-operator-based schemes [2] require full knowledge of the flow field or at least high resolution trajectory data, which may not be available in applications.
Recently, different computational methods have been proposed to identify coherent be-havior in flows directly from Lagrangian trajectory data, such as obtained from particle tracking algorithms. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data [3, 4, 5].
Inspired by these recent approaches, we consider an unweighted, undirected network with Lagrangian particle trajectories serving as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph algorithms are then employed to analyze the resulting network. In particular, spectral graph partitioning schemes allow us to identify coherent sets of the underlying flow. The proposed method is very fast to run and we demonstrate its applicability in a number of example systems. Furthermore, we point out theoretical links to other approaches.
[1] Allshouse, M. R. and Peacock, T.: Lagrangian based methods for coherent structure detection, Chaos, 25, 097617, 2015.
[2] Froyland, G. and Padberg-Gehle, K.: Almost-invariant and finite-time coherent sets:
directionality, duration, and diffusion, in: Bahsoun, W., Bose, C., and Froyland, G. (eds.): Ergodic Theory, Open Dynamics, and Coherent Structures, vol. 70 of Proceedings in Mathematics and Statistics, pp. 171–216, Springer, 2014.
[3] Froyland, G. and Padberg-Gehle, K.: A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data, Chaos, 25, 087406, 2015.
[4] Hadjighasem, A., Karrasch, D., Teramoto, H., and Haller, G.: Spectral-clustering approach to Lagrangian vortex detection, Phys. Rev. E, 93, 063 107, 2016.
[5] Banisch, R. and Koltai, P.: Understanding the geometry of trans-port: diffusion maps for Lagrangian trajectory data unravel coherent sets, https://arxiv.org/abs/1603.04709, 2016.
Symmetry induced new non-modal eigenfunctions in hydrodynamic stability theory and non-exponential growth rates
M. Oberlack (TU Darmstadt) 15:20
Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and NavierStokes equations: translation in space and time and scaling of the dependent variable -independent of the base flow, which is analyzed on its stability. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed. Some of the new non-modal eigenvalue problems have been solve analytically and first results will be presented.
Turbulent superstructures in thermal convection flows
A. Pandey (TU Ilmenau), J. Schumacher (TU Ilmenau) 15:40
When turbulent convection proceeds in horizontally extended layers large-scale patterns of the time-averaged velocity and temperature fields are formed. These patterns are termed turbulent superstructures and are studied here by means of three-dimensional direct numerical simulations in closed rectangular cells with an aspect ratio of 25:25:1.
A spectral element method is applied which uses Lagrangian interpolation polynomials on the basis of Legendre functions for the spectral expansion of the turbulent fields on each element. We present a series of simulations at three Prandtl numbers and differ-ent Rayleigh numbers. The Prandtl numbers are Pr=7 for convection in water, Pr=0.7 for convection in air and Pr=0.021 for convection in a liquid metal such as mercury.
Rayleigh numbers are chosen with values even and larger than Ra=1e5. The investiga-tion of instantaneous and time-averaged velocity and temperature patterns is reported as well as a statistical analysis of the typical spatial correlation scales and fluctuations.
Furthermore, it is reported how the global transport of heat and momentum across the fluid layer compares with previous simulations in other geometric configurations. This
work is supported by the Priority Programme SPP 1881 of the Deutsche Forschungsge-meinschaft.