Couette Flow Profiles for Two Nonclassical Taylor-Couette Cells

2000 ◽  
Vol 122 (2) ◽  
pp. 435-438
Author(s):  
Michael C. Wendl ◽  
Ramesh K. Agarwal
Keyword(s):  
High Resolution ◽  
Exact Solutions ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Convergence Rates ◽  
Initial Conditions ◽  
Convergence Acceleration ◽  
Flow Profiles ◽  
Convergence Acceleration Algorithm ◽  
Taylor Couette

Exact solutions for the Couette profile in two nonclassical Taylor-Couette cells are reported. The profiles take the form of eigenfunction expansions, whose convergence rates can be significantly accelerated using a representative convergence acceleration algorithm. Results are thus suitable as initial conditions for high resolution numerical simulations of transition phenomena in these configurations. [S0098-2202(00)02602-X]

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Due to a Time-Dependent Couple

2011 ◽  
Vol 66 (1-2) ◽  
pp. 40-46 ◽  
Author(s):  
Corina Fetecau ◽  
Muhammad Imran ◽  
Constantin Fetecau
Keyword(s):  
Exact Solutions ◽  
Couette Flow ◽  
Bessel Functions ◽  
Time Dependent ◽  
Second Grade ◽  
Governing Equations ◽  
Material Parameters ◽  
Taylor Couette ◽  
Similar Solutions ◽  
Taylor Couette Flow

Taylor-Couette flow in an annulus due to a time-dependent torque suddenly applied to one of the cylinders is studied by means of finite Hankel transforms. The exact solutions, presented under series form in terms of usual Bessel functions, satisfy both the governing equations and all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for Maxwell, second grade, and Newtonian fluids performing the same motion. Finally, some characteristics of the motion, as well as the influence of the material parameters on the behaviour of the fluid, are emphasized by graphical illustrations.

Bursting dynamics due to a homoclinic cascade in Taylor–Couette flow

2008 ◽  
Vol 613 ◽  
pp. 357-384 ◽  
Author(s):  
J. ABSHAGEN ◽  
J. M. LOPEZ ◽  
F. MARQUES ◽  
G. PFISTER
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Low Frequency ◽  
Accumulation Point ◽  
Infinite Length ◽  
Phase Dynamics ◽  
Taylor Couette ◽  
Taylor Couette Flow

Transitions between regular oscillations and bursting oscillations that involve a bifurcational process which culminates in the creation of a relative periodic orbit of infinite period and infinite length are investigated both experimentally and numerically in a short-aspect-ratio Taylor–Couette flow. This bifurcational process is novel in that it is the accumulation point of a period-adding cascade at which the mid-height reflection symmetry is broken. It is very rich and complex, involving very-low-frequency states arising via homoclinic and heteroclinic dynamics, providing the required patching between states with very different dynamics in neighbouring regions of parameter space. The use of nonlinear dynamical systems theory together with symmetry considerations has been crucial in interpreting the laboratory experimental data as well as the results from the direct numerical simulations. The phenomenon corresponds to dynamics well beyond the first few bifurcations from the basic state and so is beyond the reach of traditional hydrodynamic stability analysis, but it is not fully developed turbulence where a statistical or asymptotic approach could be employed. It is a transitional phenomenon, where the phase dynamics of the large-scale structures (jets of angular momentum emanating from the boundary layer on the rotating inner cylinder) becomes complicated. Yet the complicated phase dynamics remains accessible to an analysis of its space–time characteristics and a comprehensive mechanical characterization emerges. The excellent agreement between the experiments and the numerical simulations demonstrates the robustness of this complex bifurcation phenomenon in a physically realized system with its inherent imperfections and noise. Movies are available with the online version of the paper.

Numerical Simulations of Heat Transfer in Taylor-Couette Flow

1998 ◽  
Vol 120 (1) ◽  
pp. 65-71 ◽  
Author(s):  
R. Kedia ◽  
M. L. Hunt ◽  
T. Colonius
Keyword(s):  
Heat Transfer ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Stokes Equations ◽  
Taylor Vortex ◽  
Cylinder Surface ◽  
Stable States ◽  
Grashof Number ◽  
Taylor Couette ◽  
Taylor Couette Flow

Numerical simulations have been performed to study the effects of the gravitational and the centrifugal potentials on the stability of heated, incompressible Taylor-Couette flow. The flow is confined between two differentially heated, concentric cylinders, and the inner cylinder is allowed to rotate. The Navier-Stokes equations and the coupled energy equation are solved using a spectral method. To validate the code, comparisons are made with existing linear stability analysis and with experiments. The code is used to calculate the local and average heat transfer coefficients for a fixed Reynolds number (Re = 100) and a range of Grashof numbers. The investigation is primarily restricted to radius ratios 0.5 and 0.7 for fluids with Prandtl number of about 0.7. The variation of the local coefficients of heat transfer on the cylinder surface is investigated, and maps showing different stable states of the flow are presented. Results are also presented in terms of the equivalent conductivity, and show that heat transfer decreases with Grashof number in axisymmetric Taylor vortex flow regime, and increases with Grashof number after the flow becomes nonaxisymmetric.

scholarly journals Secondary instabilities in Taylor–Couette flow of shear-thinning fluids

2021 ◽  
Vol 933 ◽  
Author(s):  
S. Topayev ◽  
C. Nouar ◽  
J. Dusek
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
Vortex Flow ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Thinning Fluids ◽  
Taylor Vortex Flow ◽  
Viscous Shear ◽  
Taylor Couette ◽  
Shear Thinning Fluid

The stability of the Taylor vortex flow in Newtonian and shear-thinning fluids is investigated in the case of a wide gap Taylor–Couette system. The considered radius ratio is $\eta = R_1/R_2=0.4$ . The aspect ratio (length over the gap width) of experimental configuration is 32. Flow visualization and measurements of two-dimensional flow fields with particle image velocimetry are performed in a glycerol aqueous solution (Newtonian fluid) and in xanthan gum aqueous solutions (shear-thinning fluids). The experiments are accompanied by axisymmetric numerical simulations of Taylor–Couette flow in the same gap of a Newtonian and a purely viscous shear-thinning fluid described by the Carreau model. The experimentally observed critical Reynolds and wavenumbers at the onset of Taylor vortices are in very good agreement with that obtained from a linear theory assuming a purely viscous shear-thinning fluid and infinitely long cylinders. They are not affected by the viscoelasticity of the used fluids. For the Newtonian fluid, the Taylor vortex flow (TVF) regime is found to bifurcate into a wavy vortex flow with a high frequency and low amplitude of axial oscillations of the vortices at ${Re} = 5.28 \, {Re}_c$ . At ${Re} = 6.9 \, {Re}_c$ , the frequency of oscillations decreases and the amplitude increases abruptly. For the shear-thinning fluids the secondary instability conserves axisymmetry. The latter is characterized by an instability of the array of vortices leading to a continuous sequence of creation and merging of vortex pairs. Axisymmetric numerical simulations reproduce qualitatively very well the experimentally observed flow behaviour.

scholarly journals Physical mechanisms governing drag reduction in turbulent Taylor–Couette flow with finite-size deformable bubbles

2018 ◽  
Vol 849 ◽  
Author(s):  
Vamsi Spandan ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Drag Reduction ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Finite Size ◽  
Carrier Fluid ◽  
Long Time ◽  
Taylor Couette ◽  
Taylor Couette Flow

The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is, however, not well understood. In this paper, we use three-dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor–Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_{i}=5\times 10^{3}$ and $Re_{i}=2\times 10^{4}$; the deformability of the bubbles is controlled through the Weber number, which is varied in the range $We=0.01{-}2.0$. Our numerical simulations show that increasing the deformability of bubbles (that is, $We$) leads to an increase in drag reduction. We look at the different physical effects contributing to drag reduction and analyse their individual contributions with increasing bubble deformability. Profiles of local angular velocity flux show that, in the presence of bubbles, turbulence is enhanced near the inner cylinder while attenuated in the bulk and near the outer cylinder. We connect the increase in drag reduction to the decrease in dissipation in the wake of highly deformed bubbles near the inner cylinder.

scholarly journals nsCouette – A high-performance code for direct numerical simulations of turbulent Taylor–Couette flow

SoftwareX ◽  
2020 ◽  
Vol 11 ◽  
pp. 100395 ◽  
Author(s):  
Jose Manuel López ◽  
Daniel Feldmann ◽  
Markus Rampp ◽  
Alberto Vela-Martín ◽  
Liang Shi ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
High Performance ◽  
Direct Numerical Simulations ◽  
Taylor Couette ◽  
Taylor Couette Flow
Sign in / Sign up

Export Citation Format

Share Document