On the linear stability of spiral flow between rotating cylinders

1982 ◽  
Vol 382 (1782) ◽  
pp. 83-102 ◽  
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Stability Boundary ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
Compound Matrix Method ◽  
Compound Matrix ◽  
High Reynolds ◽  
The Stability ◽  
Axisymmetric Disturbances

A numerical study is made of the effects of both axisymmetric and non-axisymmetric disturbances on the stability of spiral flow between rotating cylinders. If we let Ω 1 and Ω 2 be the angular speeds of the inner and outer cylinders, and R 1 and R 2 be their respective radii, then for fixed values of η = R 1 / R 2 and μ = Ω 2 / Ω 1 , the onset of instability depends on both the Taylor number T and the axial Reynolds number R . Here R is based on the gap width between the cylinders and the average axial velocity of the basic flow, while T is based on the average angular speeds of the cylinders. Using the compound matrix method, we have computed the complete stability boundary in the R , T -plane for axisymmetric disturbances with η = 0.95 and μ = 0. We find that, for sufficiently high Reynolds numbers, there are two distinct axisymmetric modes corresponding to the usual shear and rotational instabilities. We have also obtained the stability boundaries for non-axisymmetric disturbances for R ≼ 6000 for η = 0.95 and 0.77 with μ = 0. These last results are found to be in substantial agreement with the experimental observations of Snyder (1962, 1965), Nagib (1972) and Mavec (1973) in the low and moderate axial Reynolds number régimes.

Stability of spiral flow between concentric circular cylinders at low axial Reynolds number

1965 ◽  
Vol 21 (4) ◽  
pp. 635-640 ◽  
Author(s):  
Subhendu K. Datta
Keyword(s):  
Reynolds Number ◽  
Perturbation Theory ◽  
Viscous Liquid ◽  
Axial Flow ◽  
Circular Cylinders ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
The Stability

The stability of a viscous liquid between two concentric rotating cylinders with an axial flow has been investigated. Attention has been confined to the case when the cylinders are rotating in the same direction, the gap between the cylinders is small and the axial flow is small. A perturbation theory valid in the limit when the axial Reynolds number R → 0 has been developed and corrections have been obtained for Chandrasekhar's earlier results.

The stability of spiral flow between rotating cylinders

1968 ◽  
Vol 263 (1135) ◽  
pp. 57-91 ◽  
Keyword(s):  
Asymptotic Methods ◽  
Stability Boundary ◽  
Nonlinear Effects ◽  
Present Theory ◽  
Rotating Cylinders ◽  
Axial Pressure Gradient ◽  
Tollmien Schlichting ◽  
The Stability ◽  
Sommerfeld Equation ◽  
Axisymmetric Disturbances

The effect of an axial pressure gradient on the stability of viscous flow between rotating cylinders is discussed on the basis of the narrow gap approximation, the assumption of axisymmetric disturbances, and the assumption that the cylinders rotate in the same direction. The onset of instability then depends on both the Taylor number ( T ) and the axial Reynolds number (R). For large values of R, the dominant mechanism of instability is of the Tollmien-Schlichting type and the present theory is based therefore on a generalization of the asymptotic methods of analysis that have been developed for the Orr-Sommerfeld equation. The present results, when combined with previous results for small values of R, give the complete stability boundary in the -plane. Only limited agreement is found with existing experimental data and it is suggested therefore that it may be necessary to consider either non-axisymmetric disturbances or nonlinear effects.

scholarly journals The stability of developing pipe flow at high Reynolds number and the existence of nonlinear neutral centre modes

2011 ◽  
Vol 684 ◽  
pp. 284-315 ◽  
Author(s):  
Andrew G. Walton
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Pipe Wall ◽  
Fluid Velocity ◽  
Nonlinear Effects ◽  
Neutral Curve ◽  
High Reynolds ◽  
The Stability ◽  
Axisymmetric Disturbances

AbstractThe high-Reynolds-number stability of unsteady pipe flow to axisymmetric disturbances is studied using asymptotic analysis. It is shown that as the disturbance amplitude is increased, nonlinear effects first become significant within the critical layer, which moves away from the pipe wall as a result. It is found that the flow stabilizes once the basic profile has become sufficiently fully developed. By tracing the nonlinear neutral curve back to earlier times, it is found that in addition to the wall mode, which arises from a classical upper branch linear stability analysis, there also exists a nonlinear neutral centre mode, governed primarily by inviscid dynamics. The centre mode problem is solved numerically and the results show the existence of a concentrated region of vorticity centred on or close to the pipe axis and propagating downstream at almost the maximum fluid velocity. The connection between this structure and the puffs and slugs of vorticity observed in experiments is discussed.

scholarly journals Bifurcation Tracking for High Reynolds Number Flow Around an Airfoil

2017 ◽  
Vol 27 (04) ◽  
pp. 1750061 ◽  
Author(s):  
S. Huntley ◽  
D. Jones ◽  
A. Gaitonde
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Stability Boundary ◽  
Small Scale ◽  
Geometrical Parameters ◽  
Reynolds Number Flow ◽  
High Reynolds ◽  
The Stability ◽  
Two Parameters ◽  
Reynolds Number Flows

High Reynolds number flows are typical for many applications including those found in aerospace. In these conditions nonlinearities arise which can, under certain conditions, result in instabilities of the flow. The accurate prediction of these instabilities is vital to enhance understanding and aid in the design process. The stability boundary can be traced by following the path of a bifurcation as two parameters are varied using a direct bifurcation tracking method. Historically, these methods have been applied to small-scale systems and only more recently have been used for large systems as found in Computational Fluid Dynamics. However, these have all been concerned with flows that are inviscid. We show how direct bifurcation tracking methods can be applied efficiently to high Reynolds number flows around an airfoil. This has been demonstrated through the presentation of a number of test cases using both flow and geometrical parameters.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

A NUMERICAL STUDY OF FLUID INJECTION AND MIXING UNDER NEAR-CRITICAL CONDITIONS

2012 ◽  
Vol 19 ◽  
pp. 39-49 ◽  
Author(s):  
HUA-GUANG LI ◽  
XI-YUN LU ◽  
VIGOR YANG
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Numerical Study ◽  
Ideal Gas ◽  
Critical Conditions ◽  
Reference Case ◽  
Nitrogen Injection ◽  
Volume Dilatation ◽  
High Reynolds ◽  
The Ideal

Nitrogen injection under conditions in close vicinity of liquid-gas critical point is studied through numerical simulation. The thermodynamic and transport properties of fluid exhibit anomalies in the near-critical fluid regime. These anomalies can cause distinctive effects on heat transfer and hydrodynamics. To focus on the influence of the highly variable properties and avoid the difficulties encountered in modeling high Reynolds number flows, a relatively low injection Reynolds number is adopted. A reference case with the same configuration and Reynolds number is also simulated in the ideal gas regime. Full conservation laws, real-fluid thermodynamic and transport phenomena are accommodated in the model. The obtained results reveal that the flow features of the near-critical fluid jet are significantly different from the ideal gas case. The near-critical fluid jet spreads faster and mixes better with the ambient fluid compared to the ideal gas jet. It is also identified that vortex pairing process develops faster in the near-critical case than in the ideal gas case. Detailed analysis of data at different streamwise positions including both flat shear layer region and fully developed vortex region reveals the effect of volume dilatation and baroclinic torque plays an important role in the near-critical fluid case. The volume dilatation effect disturbs the shear layer and makes it more unstable. The volume dilatation and baroclinic effects strengthen the vorticity and stimulate the vortex rolling up and pairing process.

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Numerical Performance of Transition Models in Different Turbomachinery Flow Conditions: A Comparative Study

2000 ◽  
Author(s):  
Jiasen Hu ◽  
Torsten H. Fransson
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Numerical Study ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Flow Conditions ◽  
Transition Models ◽  
High Reynolds

A numerical study has been performed to compare the overall performance of three transition models when used with an industrial Navier-Stokes solver. The three models investigated include two experimental correlations and an integrated eN method. Twelve test cases in realistic turbomachinery flow conditions have been calculated. The study reveals that all the three models can work numerically well with an industrial Navier-Stokes code, but the prediction accuracy of the models depends on flow conditions. In general, all the three models perform comparably well to predict the transition in weak or moderate adverse pressure-gradient regions. The two correlations have the merit if the transition starts in strong favorable pressure-gradient region under high Reynolds number condition. But only the eN method works well to predict the transition controlled by strong adverse pressure gradients. The three models also demonstrate different capabilities to model the effects of turbulence intensity and Reynolds number.

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