Torque and flow patterns in supercritical circular Couette flow

Debler, Walter R.; Füner, E.; Schaaf, Bernard W.

doi:10.1007/978-3-642-85640-2_12

Cited by 7 publications

(2 citation statements)

References 9 publications

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“…To verify the accuracy of our experimental set-up, tests are carried out to determine the critical Reynolds number for the onset of Taylor vortices (Re c ) under quasi-steady condition, and our results for the three radius ratios are in very good agreement with the theoretical result of Taylor, 4 and the experimental results of DiPrima et al, 5 and Debler et al 6 The present results show that STVF regime is sensitive to changes in the radius ratio and aspect ratio. Among the three radius ratios investigated, STVF regime is found to exist in ϭ0.803 only, and not in ϭ0.660 and ϭ0.894.…”

supporting

confidence: 72%

Second Taylor vortex flow: Effects of radius ratio and aspect ratio

2002

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This paper is motivated by our earlier investigation on the stability of Taylor-Couette flow in which we discovered a previously unidentified flow regime, which we refer to as "Second Taylor vortex flow" (STVF) when an inner cylinder is subjected to some critical acceleration [Lim, Chew, and Xiao, Phys. Fluids 10, 3233 (1998)]. The aim here is to explore how the STVF regime is affected by changes in radius ratio and aspect ratio. Results show that the STVF regime is sensitive to the gap size between the two cylinders, and does not exist for some radius ratios, whereas it increases with decreasing aspect ratio

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confidence: 72%

Second Taylor vortex flow: Effects of radius ratio and aspect ratio

2002

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“…The wide-gap case is of significant potential interest in applications, since, with no mean axial flow, the stable range Ta 1 6 Ta 6 Ta 2 for steady axisymmetric Taylor vortex flow increases as η decreases (Debler, Füner & Schaaf 1969;Snyder 1970;DiPrima, Eagles & Ng 1984), with Ta 2 /Ta 1 seeming to be between 10 and 100 for η = 0.5, compared to much smaller values in the narrow-gap (η → 1) limit. Here, η ≡ R i /R o is the radius ratio, Ta ≡ Ω i (R o −R i ) 2 /ν is the Taylor number, R i and R o are the radii of the inner and outer cylinders, respectively, Ω i and ν are the angular speed of the inner cylinder and the kinematic viscosity, respectively, and Ta 1 and Ta 2 are the critical values at which steady Couette flow and steady Taylor vortex flow, respectively, lose their stability.…”

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confidence: 99%

Linear stability of spiral and annular Poiseuille flow for small radius ratio

Cotrell

Pearlstein

2006

J. Fluid Mech.

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For the radius ratio $\eta\,{\equiv}\,R_i/R_o\,{=}\,0.1$ and several rotation rate ratios $\mu\,{\equiv}\,\Omega_o/\Omega_i$, we consider the linear stability of spiral Poiseuille flow (SPF) up to ${\hbox {\it Re}}\,{=}\,10^5$, where $R_i$ and $R_o$ are the radii of the inner and outer cylinders, respectively, ${\hbox {\it Re}}\,{\equiv}\,\overline V_Z(R_o\,{-}R_i)/\nu$ is the Reynolds number, $\Omega_i$ and $\Omega_o$ are the (signed) angular speeds of the inner and outer cylinders, respectively, $\nu$ is the kinematic viscosity, and $\overline V_Z$ is the mean axial velocity. The Re range extends more than three orders of magnitude beyond that considered in the previous $\mu\,{=}\,0$ work of Recktenwald et al. (Phys. Rev. E, vol. 48, 1993, p. 444). We show that in the non-rotating limit of annular Poiseuille flow, linear instability does not occur below a critical radius ratio $\hat\eta\,{\approx}\,0.115$. We also establish the connection of the linear stability of annular Poiseuille flow for $0\,{<}\,\eta\,{\leq}\,\hat\eta$ at all Re to the linear stability of circular Poiseuille flow ($\eta\,{=}\,0$) at all Re. For the rotating case, with $\mu\,{=}\,{-}1$, ${-}\,0.5$, ${-}\,0.25$, 0 and 0.2, the stability boundaries, presented in terms of critical Taylor number ${\hbox {\it Ta}}\,{\equiv}\,\Omega_i(R_o\,{-}R_i)^2/\nu$ versus Re, show that the results are qualitatively different from those at larger $\eta$. For each $\mu$, the centrifugal instability at small Re does not connect to a high-Re Tollmien–Schlichting-like instability of annular Poiseuille flow, since the latter instability does not exist for $\eta\,{<}\,\hat\eta$. We find a range of Re for which disconnected neutral curves exist in the $k$–Ta plane, which for each non-zero $\mu$ considered, lead to a multi-valued stability boundary, corresponding to two disjoint ranges of stable Ta. For each counter-rotating ($\mu\,{<}\,0$) case, there is a finite range of Re for which there exist three critical values of Ta, with the upper branch emanating from the ${\hbox {\it Re}}\,{=}\,0$ instability of Couette flow. For the co-rotating ($\mu\,{=}\,0.2$) case, there are two critical values of Ta for each Re in an apparently semi-infinite range of Re, with neither branch of the stability boundary intersecting the Re = 0 axis, consistent with the classical result of Synge that Couette flow is stable with respect to all small disturbances if $\mu\,{>}\,\eta^2$, and our earlier results for $\mu\,{>}\,\eta^2$ at larger $\eta$.

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Taylor-Vortex Bioreactors for Enhanced Mass Transport

Curran

Black

2005

Bioreactors for Tissue Engineering

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Torque and flow patterns in supercritical circular Couette flow

Cited by 7 publications

References 9 publications

Second Taylor vortex flow: Effects of radius ratio and aspect ratio

Second Taylor vortex flow: Effects of radius ratio and aspect ratio

Linear stability of spiral and annular Poiseuille flow for small radius ratio

Taylor-Vortex Bioreactors for Enhanced Mass Transport

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