What Rayleigh-Bénard, Taylor-Couette and Pipe Flows have in Common

2007 ◽  
pp. 3-10
Author(s):  
Bruno Eckhardt ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Pipe Flows ◽  
Taylor Couette ◽  
Rayleigh Benard

scholarly journals Heat transport in Rayleigh–Bénard convection and angular momentum transport in Taylor–Couette flow: a comparative study

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160079 ◽  
Author(s):  
Hannes J. Brauckmann ◽  
Bruno Eckhardt ◽  
Jörg Schumacher
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Nusselt Numbers ◽  
Bénard Convection ◽  
Benard Convection ◽  
Taylor Couette ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Good Agreement ◽  
Taylor Couette Flow

Rayleigh–Bénard convection and Taylor–Couette flow are two canonical flows that have many properties in common. We here compare the two flows in detail for parameter values where the Nusselt numbers, i.e. the thermal transport and the angular momentum transport normalized by the corresponding laminar values, coincide. We study turbulent Rayleigh–Bénard convection in air at Rayleigh number Ra =10 7 and Taylor–Couette flow at shear Reynolds number Re S =2×10 4 for two different mean rotation rates but the same Nusselt numbers. For individual pairwise related fields and convective currents, we compare the probability density functions normalized by the corresponding root mean square values and taken at different distances from the wall. We find one rotation number for which there is very good agreement between the mean profiles of the two corresponding quantities temperature and angular momentum. Similarly, there is good agreement between the fluctuations in temperature and velocity components. For the heat and angular momentum currents, there are differences in the fluctuations outside the boundary layers that increase with overall rotation and can be related to differences in the flow structures in the boundary layer and in the bulk. The study extends the similarities between the two flows from global quantities to local quantities and reveals the effects of rotation on the transport. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders

2007 ◽  
Vol 581 ◽  
pp. 221-250 ◽  
Author(s):  
BRUNO ECKHARDT ◽  
SIEGFRIED GROSSMANN ◽  
DETLEF LOHSE
Keyword(s):  
Couette Flow ◽  
Power Law ◽  
Rotation Frequency ◽  
Strong Increase ◽  
Geometrical Factor ◽  
Driving Frequency ◽  
Taylor Couette ◽  
Rayleigh Benard ◽  
Gap Width ◽  
Taylor Couette Flow

Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) = uϕ(r,ϕ,z,t)/r across the cylinder gap and and the excess energy dissipation rate ϵw due to the turbulent, convective fluctuations (the ‘wind’) are derived and their dependence on the control parameters analysed. The very close correspondence of Taylor–Couette flow with thermal Rayleigh–Bénard convection is elaborated, using these basic quantities and the exact relations among them to calculate the torque as a function of the rotation frequencies and the radius ratio η = r1/r2 or the gap width d = r2 − r1 between the cylinders. A quantity σ corresponding to the Prandtl number in Rayleigh–Bénard flow can be introduced, $\sigma = ((1 + \eta)/2)/\sqrt{\etaacute;)^4$. In Taylor–Couette flow it characterizes the geometry, instead of material properties of the liquid as in Rayleigh–Bénard flow. The analogue of the Rayleigh number is the Taylor number, defined as Ta ∝ (ω1 − ω2)2 times a specific geometrical factor. The experimental data show no pure power law, but the exponent α of the torque versus the rotation frequency ω1 depends on the driving frequency ω1. An explanation for the physical origin of the ω1-dependence of the measured local power-law exponents α(ω1) is put forward. Also, the dependence of the torque on the gap width η is discussed and, in particular its strong increase for η → 1.

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