Rotation einer ebenen turbulenten Kanalströmung um die Hauptströmungsrichtung
Final Report Abstract
DNS of streamwise rotating channel flow at Re = 560 was performed for different rotation rates Ro = 4, 10, 14, 20. In this work the turbulent channel flow with streamwise rotation has been investigated by means of an analytical and a numerical method. The appearance of a cross flow in the spanwise direction is the most obvious difference compared to the classical spanwise rotating channel flow. It was shown that all six components of the Reynolds stress tensor are non-zero. The influence of the rotation was studied at three different Reynolds numbers (Reτ = 180, 270, 560) and at a variety of different rotation rates. The last Reynolds number was the main objective of this project. The first two lower Reynolds numbers where studied in the previous project. Both the induced cross flow and the fact that the six components of the Reynolds stress tensor are non-zero could be verified. In addition a significant decay of the streamwise maximum velocity between Ro = 5.2 and 10 was noticed. At the same time the cross flow reaches a maximum at about Ro = 10 and then decreases for higher rotation rates. These observations are called rotation drag effect. A better understanding of transition to turbulence in a three-dimensional Poiseuille flow rotating about the streamwise axis is sought by investigating the stability characteristics of the flow. Using linear modal analysis, we define the instability envelop and find that the rotation increases the exponential growth of the most unstable mode. For high levels of rotation, we observe a re-stabilisation of the flow. The influence of rotation on transient energy growth is investigated as the system of linear equations is non-normal. We show that the energetic growth can be of the order of O (10^3) in the subcritical region. It was found that there is a certain point where the maximal energy growth is caused by an oblique disturbance. At this point, the transient growth of the the rotational term dominates that of the non-rotating channel. This phenomenon is explained using scaling parameters. Getting novel insight from Lie-group theory, a general analysis was performed for the infinite hierarchy of multi-point velocity correlation equations involving not the fluctuating, but rather the full instantaneous flow fields. The advantage then of dealing with a formal linear system included new statistical symmetries which could be exploited to perform convincing fits to DNS data for the spanwise and wall-normal rotation cases of a turbulent channel flow. Unfortunately for the case of streamwise rotation no convincing fit could be constructed yet. A more refined analysis is needed to obtain reliable scaling laws for the case dealt herein. However, current investigations in this direction show already promising results.
Publications
- ”Stability characteristics of a rotating Poiseuille flow about the streamwise axis“ in American Physical Society, 61st Annual Meeting of the APS Division of Fluid Dynamics, November 23-25, 2008
J.-P. Hickey, G. Khujadze, M. Oberlack
- (2010). New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws. Discrete Contin. Dyn. Sys., 3, 451-471
Oberlack, M. & Rosteck, A.
- ”Streamwise rotating channel flow“ in proceedings SIG 35 workshop: Instabilities, turbulence and interactions in rotating shear flows, Marseille, CIRM, France, 2010
J.-P. Hickey, G. Khujadze, M. Oberlack
- (2011). Applications of the new symmetries of the multi-point correlation equations. J. Phys. Conf. Ser., 318, 042011
Oberlack, M. & Rosteck, A.
- (2011). Lie algebra of the symmetries of the multi-point equations in statistical turbulence theory. J. Nonlinear Math. Phys., 18, 251-264
Rosteck, A. & Oberlack, M.
- (2011). Turbulent scaling laws and what we can learn from the multi-point correlation equations, TSFP 7
Oberlack, M. & Rosteck, A.
