The effect of radius ratio on the stability of Couette flow and Taylor vortex flow

DiPrima, R. C.; Eagles, P. M.; Ng, B. S.

doi:10.1063/1.864544

Cited by 57 publications

(43 citation statements)

References 13 publications

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“…In figure 2 we show the Reynolds number at the instability onset as a function of k for different Ma; we define the critical Reynolds number, Re 1c , and corresponding wavenumber, k c , as the minimum of Re 1 at instability onset when optimised over k. In the incompressible limit, Ma ≈ 0, we obtain the well-known results of Rogers & Beard (1969) (see also DiPrima, Eagles & Ng 1984). By increasing gradually Ma from 0 to 5, we find that the effect of compressibility is to stabilise the system and increase the critical wavenumber k c slightly (see table 1 below); a similar behaviour for Re 1c and k c has also been observed when Ma > 5.…”

Section: Axisymmetric Instabilitiesmentioning

confidence: 55%

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

Welsh¹,

Kersalé²,

Jones³

2014

J. Fluid Mech.

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Taylor-Couette flow in a compressible perfect gas is studied. The onset of instability is examined as a function of the Reynolds numbers of the inner and outer cylinder, the Mach number of the flow and the Prandtl number of the gas. We focus on the case of a wide gap, with radius ratio 0.5. We find new modes of instability at high Prandtl number, which can allow oscillatory axisymmetric modes to onset first. We also find that onset can occur even when the angular momentum increases outwards, so that the classical Rayleigh criterion can be violated in the compressible case. We have also considered the case of counter-rotating cylinders, where the m = 0 and m = 1 modes can onset simultaneously to give a codimension 2 bifurcation, leading to the formation of complex flow patterns. In compressible flow we also find codimension 3 points. The Mach number and the critical inner and outer Reynolds numbers can be adjusted so that the two neutral curves for the m = 0 and m = 1 modes touch rather than cross. Complex codimension 3 points occur more readily in the compressible case than in the Boussinesq case, and they are expected to lead to a rich nonlinear behaviour.

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Section: Axisymmetric Instabilitiesmentioning

confidence: 55%

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

Welsh¹,

Kersalé²,

Jones³

2014

J. Fluid Mech.

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“…From DiPrima et al (1984), the corresponding critical Reynolds number and wavenumber are 317 and 0.46 respectively, in units of D and U C . These values are comparable to the square cavity flow data in table 1, highlighting once more the centrifugal character of the three-dimensional instabilities.…”

Section: Couette Flowsmentioning

confidence: 99%

“…The stability of such a flow has been widely studied and is often mentioned as a classical example of centrifugal instabilities. DiPrima, Eagles & Ng (1984) computed the critical values of the Reynolds number and corresponding axial wavenumber in Couette flow as a function of the radius ratio R 1 /R 2 for axisymmetric stationary modes. Note that their results were made dimensionless by scaling length with the gap width d = R 2 − R 1 and velocity with the inner cylinder velocity Ω 1 R 1 .…”

Section: Couette Flowsmentioning

confidence: 99%

Three-dimensional instabilities in compressible flow over open cavities

2008

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Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.

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“…The timescales for onset of such transient dynamic instabilities (<0.2 s) may be nearly instantaneous while investigating dynamic shear stress patterns within in vitro experiments. Highly complex flow behavior has been reported for annular Couette flows depending on radius and aspect (ratio of gap width to cylindrical height) ratios [37,38], Reynolds number and dynamics of rotation, such as transitions from circular Couette to Taylor Couette to wavy vortex to turbulent vortex flow [39]. Dynamics of such flow effects can be predicted numerically and explain the enhanced platelet activation in regions of complex flow with relatively smaller Reynolds numbers, but with presumably higher exposure times and collision frequencies.…”

Section: Taylor Number and Annular Flowmentioning

confidence: 97%

“…Such effects may therefore be substantially enhanced due to recirculation within Taylor vortices, where the duration of shear exposure and platelet-platelet collisions may be significantly increased relative to bulk flow. The shear stresses due to such flow effects can be effectively reproduced in Couette viscometers by appropriate choice of geometrical (e.g., radius ratio of the inner rotating and outer stationary cylinders, and aspect ratio, of the Couette viscometer) and experimental (e.g., rotational velocity and acceleration of the inner cylinder, viscosity of the fluid and overall shear stress) parameters [31,37]. Shear stress waveforms from numerical simulations may thus be reproduced in vitro with a dynamically controlled viscometer and thrombin generation from shear-stress activated platelets can be measured to determine thrombogenicity associated with PHV or recirculation devices.…”

Section: Plateletsmentioning

confidence: 99%

Biological effects of dynamic shear stress in cardiovascular pathologies and devices

Girdhar

Bluestein

2008

Expert Review of Medical Devices

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Altered and highly dynamic shear stress conditions have been implicated in endothelial dysfunction leading to cardiovascular disease, and in thromboembolic complications in prosthetic cardiovascular devices. In addition to vascular damage, the pathological flow patterns characterizing cardiovascular pathologies and blood flow in prosthetic devices induce shear activation and damage to blood constituents. Investigation of the specific and accentuated effects of such flow-induced perturbations on individual cell-types in vitro is critical for the optimization of device design, whereby specific design modifications can be made to minimize such perturbations. Such effects are also critical in understanding the development of cardiovascular disease. This review addresses limitations to replicate such dynamic flow conditions in vitro and also introduces the idea of modified in vitro devices, one of which is developed in the authors' laboratory, with dynamic capabilities to investigate the aforementioned effects in greater detail.Keywords cardiovascular disease; cone-plate viscometers; dynamic shear stress; platelet activation; prosthetic heart valves; turbulence Implantable blood recirculation devices, artificial hearts and heart valves, have long been used as life-saving alternatives for people with severe cardiovascular diseases. However, such devices require complex anticoagulation therapy and, as a consequence, are linked to postimplant complications, such as hemorrhage. Despite the anticoagulation therapy, the risk for cardioembolic stroke is not eliminated. Although biocompatibility of these recirculation devices is of utmost importance, optimizing the geometric design of these devices is also critical to avoid flow-induced trauma to blood. Over the years, a definite link between fluid shearstress-induced damage and activation of blood constituents such as platelets and red blood cells, has been established. Irregular flow patterns arising around complex geometries (e.g., the hinge regions of mechanical heart valves [MHV]) have been recently characterized by numerical calculations and noninvasive flow measurements, and are implicated in causing flow-induced thromboembolism (TE). For instance, the Medtronic Parallel™ valve exhibited regions of elevated turbulent stress around the hinges due to its specific geometry, which, in †Author for correspondence: Department of Biomedical Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794-8181, USA, Tel.: +1 631 444 1259, Fax: +1 631 444 6646, danny.bluestein@sunysb.edu. Financial & competing interests disclosure:The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties. No writing assistance was utilized in the production of this manu...

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The effect of radius ratio on the stability of Couette flow and Taylor vortex flow

Cited by 57 publications

References 13 publications

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

Three-dimensional instabilities in compressible flow over open cavities

Biological effects of dynamic shear stress in cardiovascular pathologies and devices

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