Influence of forced oscillation, orbital motion, axial flow and free motion of the inner pipe on Taylor–Couette flow

Abstract

The present study focuses on tridimensional and incompressible Taylor–Couette flow of Newtonian fluid by using the immersed boundary method in order to investigate the influence of forcing oscillation, orbital motion, axial flow and free motion of the inner pipe on the fluid flow. For this purpose, the Taylor–Couette flow, eccentric Taylor–Couette flow and spiral Taylor–Couette flow are used as basis. Four forcing oscillating frequencies are considerate, where the amplitude was held fixed at \(1\%\) of the imposed velocity on the inner pipe surface. Results show that the oscillating amplitude increases with forcing frequency reduction for radial and azimuthal velocity components; however, when orbital motion of the inner pipe is present, the forcing frequency of \(f_{c} = 0.463Hz\) varies its amplitude oscillation through time, which is characterized as amplitude modulation. During the orbital motion the counter-rotating vortices adapt to the variable gap, which modify its local dynamic characteristic. When axial flow is present, there are two types of structures, toroidal and helical. As Re increases, there is a predominance of helical structure compared to toroidal ones. The vortices shrink due to the axial flow and the vortices located toward the outer pipe are larger than those toward the inner pipe. The fluid–structure interaction problem, which is considered for the free motion, shows that the displacement amplitude decreases with time, dampened by the viscous fluid force, reaching the equilibrium position with time, for all four Taylor numbers studied.

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Abbreviations

\(A\) :

Oscillating amplitude m

\(f\) :

Eulerian force N

\(F\) :

resultant force N

\(F_{Lag}^{{}}\) :

Lagrangian force N

\(F_{{{\text{springs}}}}^{{}}\) :

spring force N

\(f_{c}\) :

frequency Hz

\(p\) :

pressure Pa

\({\text{Re}}\) :

Reynolds number

\(R_{i}\) :

inner radius m

\(R_{o}\) :

outer radius m

\(Ta\) :

Taylor number

\(u\) :

velocity in radial direction m/s

\(v\) :

velocity in azimuthal direction m/s

\(w\) :

velocity in axial direction m/s

\(W_{i}\) :

axial velocity of the inner pipe m/s

\(W\) :

inner pipe axial velocity m/s

\(x,y,z\) :

Cartesian coordinates m

\(r,\theta ,z\) :

cylindrical coordinates m

\(\varepsilon\) :

eccentricity

\(\rho\) :

mass specific kg/m3

\(\nu\) :

kinematic viscosity kg/m3

ω:

angular velocity 1/s

Ω:

orbital velocity m/s

\(\Gamma\) :

aspect ratio

η:

radius ratio

\(t + 1\) :

current time

\(*\) :

estimated variable

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Acknowledgement

The authors wish to thank to the FAPEMIG, CNPq and the CENPES/Petrobras for the financial support.

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Correspondence to Jonatas Emmanuel Borges.

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Borges, J.E., Padilla, E.L.M. Influence of forced oscillation, orbital motion, axial flow and free motion of the inner pipe on Taylor–Couette flow. J Braz. Soc. Mech. Sci. Eng. 43, 85 (2021). https://doi.org/10.1007/s40430-020-02764-x

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Keywords

  • Taylor–Couette flow
  • Eccentric Taylor–Couette flow
  • Spiral Taylor–Couette flow
  • Fluid–structure interaction
  • Immersed boundary method