Numerical study on wide gap Taylor Couette flow with flow transition

Abstract

This study aims to investigate the possible sources of non-axisymmetric disturbances and their propagation mechanism in Taylor Couette flow (TCF) for wide gap problems using direct numerical simulation with a radius ratio of 0.5 and Reynolds number (Re) ranging from 60 to 650. Here, attention is focused on the viscous layer (VL) thickness in near-wall regions and its spatial distribution along the axial direction to gain an insight into the origin and propagation of non-axisymmetric disturbances. The results show that an axisymmetric Taylor-vortex flow occurs when Re is between 68 and 425. Above Re = 425, transition from axisymmetric to non-axisymmetric flow is observed up to Re = 575 before the emergence of wavy-vortex flow. From the variation of VL thickness with Re, the VL does not experience any significant changes in the flow separation region of the inner wall, as well as jet impingement region of both the inner and outer walls. However, a sudden increase in VL thickness in the flow separation region of the outer wall reveals possible source of non-axisymmetric disturbances in the flow separation region of the outer wall. These disturbances develop into the periodic secondary flow as the axisymmetric flow transforms into non-axisymmetric flow and this leads to the emergence of azimuthal wave. The periodic secondary flow contributes to sudden increase in the natural wavelength and rapid reduction in the strength of two counter-rotating Taylor vortices. This in turn leads to a substantial reduction of torque in the transition flow vis-a-vis axisymmetric Taylor-vortex flow.

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

“…Furthermore, the wavy mode obtained by Razzak et al. (2019) was not predicted by the linear stability analysis done by Jones (1985). Therefore, we believe that additional experimental or numerical data are needed for a wide gap geometry.…”

“…of Snyder & Lambert (1966), Meincke & Egbers (1999) and King et al (1984). A recent direct numerical simulation by Razzak et al (2019) in a wide gap setup η = 0.5 yielded Re s ≈ 8.45Re c . In their study, a four wavelengths fluid column is considered (L = 4 Λ = 7.944) with periodic boundary conditions in the axial direction.…”

“…For this relatively small aspect ratio, Razzak et al. (2019) evidenced an intermediate step between TVF and WVF in the interval . They found that the flow becomes non-axisymmetric with a strong azimuthal wave in the inflow region (inward oriented flow of the TVF vortex array) as compared with the outflow region.…”

“…Additional numerical tests were made with . In the second situation, following several authors (Razzak et al. 2019; Ng, Jaiman & Lim 2018; Teng et al. 2015; Fasel & Booz 1984), we have assumed axial periodic boundary conditions at the upper and lower endwalls, i.e.…”

“…(1984). A recent direct numerical simulation by Razzak, Khoo & Lua (2019) in a wide gap setup yielded . In their study, a four wavelengths fluid column is considered () with periodic boundary conditions in the axial direction.…”