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A new high-order method for direct numerical simulations of turbulent wall-bounded flows
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

A new method to perform direct numerical simulations of wall-bounded flows has been developed and implemented. The method uses high-order compact finite differences in wall-normal (for channel flow) or radial direction (for pipe flow) on a collocated grid, which gives high-accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid. The use of compact finite differences means that extreme clustering near the wall leading to small time steps in high-Reynolds number simulations is avoided. The influence matrix method is used to ensure a completely divergence-freesolution and all systems of equations are solved in banded form, which ensures an effcient solution procedure with low requirements for data storage. The method is unique in the sense that exactly divergence-free solutions on collocated meshes are calculated using arbitrary dffierence matrices.

The code is validated for two flow cases, i.e. turbulent channel and turbulent pipe flow at relatively low Reynolds number. All tests show excellent agreement with analytical and existing results, confirming the accuracy and robustness ofthe method. The next step is to eciently parallelise the code so that high-Reynolds number simulations at high resolution can be performed.

We furthermore investigated rare events occurring in the near-wall region of turbulent wall-bounded flows. We find that negative streamwise velocities and extreme wall-normal velocity uctuations are found rarely (on the order of 0:01%), and that they occur more frequently at higher Reynolds number. These events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall-bounded flows.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , xii, 40 p.
Keyword [en]
Incompressible wall-bounded flows, direct numerical simulations, high-order, compact finite differences, collocated grid, influence matrix method
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-142374OAI: oai:DiVA.org:kth-142374DiVA: diva2:700006
Public defence
2014-03-21, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20150303

Available from: 2014-03-03 Created: 2014-03-03 Last updated: 2014-03-03Bibliographically approved
List of papers
1. A new high-order method for the simulation of incompressible wall-bounded turbulent flows
Open this publication in new window or tab >>A new high-order method for the simulation of incompressible wall-bounded turbulent flows
2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 272, 108-126 p.Article in journal (Refereed) Published
Abstract [en]

A new high-order method for the accurate simulation of incompressible wall-bounded flows is presented. In the stream- and spanwise directions the discretisation is performed by standard Fourier series, while in the wall-normal direction the method combines high-order collocated compact finite differences with the influence matrix method to calculate the pressure boundary conditions that render the velocity field exactly divergence-free. The main advantage over Chebyshev collocation is that in wall-normal direction, the grid can be chosen freely and thus excessive clustering near the wall is avoided. This can be done while maintaining the high-order approximation as offered by compact finite differences. The discrete Poisson equation is solved in a novel way that avoids any full matrices and thus improves numerical efficiency. Both explicit and implicit discretisations of the viscous terms are described, with the implicit method being more complex, but also having a wider range of applications. The method is validated by simulating two-dimensional Tollmien-Schlichting waves, forced transition in turbulent channel flow, and fully turbulent channel flow at friction Reynolds number Re-tau = 395, and comparing our data with analytical and existing numerical results. In all cases, the results show excellent agreement showing that the method simulates all physical processes correctly.

Place, publisher, year, edition, pages
Academic Press, 2014
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-142392 (URN)10.1016/j.jcp.2014.04.034 (DOI)000336620900006 ()2-s2.0-84899836589 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20140702

Available from: 2014-03-03 Created: 2014-03-03 Last updated: 2017-12-05Bibliographically approved
2. A new high-order method for the simulation of incompressible wall-bounded turbulent pipe flow
Open this publication in new window or tab >>A new high-order method for the simulation of incompressible wall-bounded turbulent pipe flow
(English)Manuscript (preprint) (Other academic)
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-142395 (URN)
Note

QS 2014

Available from: 2014-03-03 Created: 2014-03-03 Last updated: 2014-03-03Bibliographically approved
3. Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence
Open this publication in new window or tab >>Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence
Show others...
2012 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 3, 035110- p.Article in journal (Refereed) Published
Abstract [en]

Rare negative streamwise velocities and extreme wall-normal velocity fluctuations near the wall are investigated for turbulent channel flow at a series of Reynolds numbers based on friction velocity up to Re-tau = 1000. Probability density functions of the wall-shear stress and velocity components are presented as well as joint probability density functions of the velocity components and the pressure. Backflow occurs more often (0.06% at the wall at Re-tau = 1000) and further away (up to y(+) = 8.5) from the wall for increasing Reynolds number. The regions of backflow are circular with an average diameter, based on ensemble averages, of approximately 20 viscous units independent of Reynolds number. A strong oblique vortex outside the viscous sublayer is found to cause this backflow. Extreme wall-normal velocity events occur also more often for increasing Reynolds number. These extreme fluctuations cause high flatness values near the wall (F(v) = 43 at Re-tau = 1000). Positive and negative velocity spikes appear in pairs, located on the two edges of a strong streamwise vortex as documented by Xu et al. [Phys. Fluids 8, 1938 (1996)] for Re-tau = 180. The spikes are elliptical and orientated in streamwise direction with a typical length of 25 and a typical width of 7.5 viscous units at y(+) approximate to 1. The negative spike occurs in a high-speed streak indicating a sweeping motion, while the positive spike is located in between a high and low-speed streak. The joint probability density functions of negative streamwise and extreme wall-normal velocity events show that these events are largely uncorrelated. The majority of both type of events can be found lying underneath a large-scale structure in the outer region with positive sign, which can be understood by considering the more intense velocity fluctuations due to amplitude modulation of the inner layer by the outer layer. Simulations performed at different resolutions give only minor differences. Results from experiments and recent turbulent boundary layer simulations show similar results indicating that these rare events are universal for wall-bounded flows. In order to detect these rare events in experiments, measurement techniques have to be specifically tuned.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-93942 (URN)10.1063/1.3696304 (DOI)000302224600037 ()2-s2.0-84859308655 (Scopus ID)
Funder
Knut and Alice Wallenberg FoundationSwedish e‐Science Research Center
Note

QC 20120503

Available from: 2012-05-03 Created: 2012-05-03 Last updated: 2017-12-07Bibliographically approved

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