Cylindrical Couette Flow of a Rarefied Gas From Macro- to Micro-Scales

2009 ◽  
Author(s):  
Sheng Wang ◽  
Kangbin Lei ◽  
Xilian Luo ◽  
Kiwamu Kase ◽  
Elia Merzari ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Velocity Profile ◽  
Couette Flow ◽  
Knudsen Number ◽  
Rarefied Gas ◽  
Outer Cylinder ◽  
Tangential Velocity ◽  
Flow Field Characteristics ◽  
Dimensional Parameters

The cylindrical Couette flow of a rarefied gas from macro- to micro-scales, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest, is extensively investigated by direct simulation Monte Carlo (DSMC) code incorporated with a Volume-CAD software. The generalized soft sphere (GSS) model is applied to an intermolecular collision calculation. The diffuse reflection model and Cercignani-Lampis-Lord (CLL) model are used to model the molecule-surface interaction by considering the accommodation coefficients on inner cylinder (ACI hereafter) and outer cylinder (ACO hereafter) separately. The contents in this paper include following three aspects: I the flow field characteristics and force and torque on inner cylinder for eccentric Couette flow between different scales with same non-dimensional parameters (accommodation coefficients, eccentricity-clearance ratio, Knudsen number and Reynolds number) are compared; the flow field characteristics for different scales are same; with the increase of the scale, the total force on the inner cylinder increases slightly, while the torque is proportional to the scale; II the velocity profiles in concentric Couette flow under different non-dimensional parameters are studied; the result shows that the phenomenon of inverted velocity profile in the concentric Couette flow is only induced by a smooth outer cylinder; the non-dimensional tangential velocity, as well as its gradient is high at low Reynolds number; the Knudsen number has great impact on the tangential velocity profile, and the velocity profile may not be inverted in the case of low Knudsen number; III the flow field characteristics in eccentric Couette flow under different non-dimensional parameters are obtained; the recirculation zone may not appear when Knudsen number is high; the position of its center may be different depending on Reynolds number; with the increase of Reynolds number, the compressibility effect becomes important; stratified distribution of the density becomes obvious at low Knudsen number.

scholarly journals Exploring the phase diagram of fully turbulent Taylor–Couette flow

2014 ◽  
Vol 761 ◽  
pp. 1-26 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Phase Diagram ◽  
Reynolds Number ◽  
Couette Flow ◽  
Parameter Space ◽  
Coriolis Force ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Aspect Ratios ◽  
Cylinder Rotation

AbstractDirect numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to $3\times 10^{5}$, corresponding to Taylor numbers of $\mathit{Ta}=4.6\times 10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15 % of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner versus outer Reynolds number parameter space and in the Taylor versus inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech., vol. 164, 1986, pp. 155–183) phase diagram towards the ultimate regime.

Velocity profiles, flow structures and scalings in a wide-gap turbulent Taylor–Couette flow

2017 ◽  
Vol 831 ◽  
pp. 330-357 ◽  
Author(s):  
A. Froitzheim ◽  
S. Merbold ◽  
C. Egbers
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Cylinder Wall ◽  
Taylor Vortices ◽  
Wide Gap ◽  
Taylor Couette ◽  
Taylor Couette Flow

Fully turbulent Taylor–Couette flow between independently rotating cylinders is investigated experimentally in a wide-gap configuration ($\unicode[STIX]{x1D702}=0.5$) around the maximum transport of angular momentum. In that regime turbulent Taylor vortices are present inside the gap, leading to a pronounced axial dependence of the flow. To account for this dependence, we measure the radial and azimuthal velocity components in horizontal planes at different cylinder heights using particle image velocimetry. The ratio of angular velocities of the cylinder walls $\unicode[STIX]{x1D707}$, where the torque maximum appears, is located in the low counter-rotating regime ($\unicode[STIX]{x1D707}_{max}(\unicode[STIX]{x1D702}=0.5)=-0.2$). This point coincides with the smallest radial gradient of angular velocity in the bulk and the detachment of the neutral surface from the outer cylinder wall, where the azimuthal velocity component vanishes. The structure of the flow is further revealed by decomposing the flow field into its large-scale and turbulent contributions. Applying this decomposition to the kinetic energy, we can analyse the formation process of the turbulent Taylor vortices in more detail. Starting at pure inner cylinder rotation, the vortices are formed and strengthened until $\unicode[STIX]{x1D707}=-0.2$ quite continuously, while they break down rapidly for higher counter-rotation. The same picture is shown by the decomposed Nusselt number, and the range of rotation ratios, where turbulent Taylor vortices can exist, shrinks strongly in comparison to investigations at much lower shear Reynolds numbers. Moreover, we analyse the scaling of the Nusselt number and the wind Reynolds number with the shear Reynolds number, finding a communal transition at approximately $Re_{S}\approx 10^{5}$ from classical to ultimate turbulence with a transitional regime lasting at least up to $Re_{S}\geqslant 2\times 10^{5}$. Including the axial dispersion of the flow into the calculation of the wind amplitude, we can also investigate the wind Reynolds number as a function of the rotation ratio $\unicode[STIX]{x1D707}$, finding a maximum in the low counter-rotating regime slightly larger than $\unicode[STIX]{x1D707}_{max}$. Based on our study it becomes clear that the investigation of counter-rotating Taylor–Couette flows strongly requires an axial exploration of the flow.

Flow of Yield Power Law Fluids in Horizontal Pipes-Flow Field Characterization Using Particle Image Velocimetry Technique

2021 ◽  
Author(s):  
Yanxin (Sussi) Sun ◽  
Abdulla Abou-Kassem ◽  
Majid Bizhani ◽  
Ergun Kuru
Keyword(s):  
Experimental Study ◽  
Flow Field ◽  
Velocity Profile ◽  
Yield Stress ◽  
Power Law ◽  
Pipe Flow ◽  
Hydrodynamic Behaviour ◽  
Yield Stress Fluids ◽  
Power Law Fluids ◽  
Flow Field Characteristics

Abstract Yield Power Law (YPL) rheological model is commonly used to describe the pipe and annular flow of drilling fluids. However, the hydrodynamic behaviour of fluids with yield stress are difficult to predict because they exhibit an inherent plug (solid like) region where the velocity gradient is zero. Moreover, it is not easy to identify the transition between this solid like and liquid regions. Theoretical studies have been conducted in the past to describe YPL fluid flow in pipes and annuli. As a result, several models have been proposed for determining flow field characteristics (e.g. velocity profile, plug width, etc.) and frictional pressure losses. However, most of these models have been validated by limited experimental and/or field data. Similar future modeling studies may benefit from more data collected under controlled experimental conditions. Therefore, we have conducted an experimental study to investigate the hydrodynamic behaviour of yield stress fluids under laminar pipe flow conditions and the results are presented in this paper. Water-based Yield Power Law fluids were prepared by using Carbopol® 940, a synthetic high-molecular-weight polyacrylic acid-based cross-linked polymer. Fluids with yield stresses varying from 0.75 Pa (1.56 lb/100 ft2) to 4.37 Pa (9.13 lb/100 ft2) were obtained by using Carbopol concentrations changing from 0.060% w/w to 0.073% w/w. A 9m long horizontal pipeline with, 95 mm diameter (ID) was used for the experiments. Reynolds number range varying from 97 to 1268 confirmed that all flow field characteristics measurements of YPL fluids were conducted under laminar flow regimes. Experimental study provided detailed information about pipe flow characteristics of yield stress fluids, including full annular velocity profile, near wall velocity profile, wall slip velocity and the plug region thickness. The study was concluded by comparing experimental results (i.e. full velocity profile, frictional pressure loss, and plug width) to predictions of models presented in the literature. Practical implications of the results have also been discussed by considering the hydraulic design of some practical field operations such as hole cleaning.

scholarly journals Self-sustaining critical layer/shear layer interaction in annular Poiseuille–Couette flow at high Reynolds number

2020 ◽  
Vol 476 (2235) ◽  
pp. 20190600 ◽  
Author(s):  
Rishi Kumar ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Axial Direction ◽  
Critical Layer ◽  
Large Reynolds Number ◽  
Cylindrical Annulus ◽  
Axial Pressure Gradient ◽  
High Reynolds

The nonlinear stability of annular Poiseuille–Couette flow through a cylindrical annulus subjected to axisymmetric and helical disturbances is analysed theoretically at asymptotically large Reynolds number R based on the radius of the outer cylinder and the constant axial pressure gradient applied. The inner cylinder moves with a prescribed positive or negative velocity in the axial direction. A distinguished scaling for the disturbance size Δ =  O ( R −4/9 ) is identified at which the jump in vorticity across the fully nonlinear critical layer is in tune with that induced across a near-wall shear layer. The disturbance propagates at close to the velocity of the inner cylinder and possesses a wavelength comparable to the radius of the outer cylinder. The dynamics of the critical layer, shear layer and the Stokes layer adjacent to the stationary wall are discussed in detail. In the majority of the pipe, the disturbance is governed predominantly by inviscid dynamics with the pressure perturbation satisfying a form of Rayleigh’s equation. For a radius ratio δ in the range 0 <  δ  < 1 and a positive sliding velocity V , a numerical solution of the Rayleigh equation exists for sliding velocities in the range 0 <  V  < 1 −  δ 2  + 2 δ 2 ln δ , whereas if V  < 0, solutions exist for 1 −  δ 2  + 2ln δ  <  V  < 0. The amplitude equations for both these situations are derived analytically, and we further find that the corresponding asymptotic structures break down when the maximum value of the basic flow becomes located at the inner and outer walls, respectively.

Fluid Flow and Heat Transfer Over a Micro-Sphere

2007 ◽  
Author(s):  
M. A. Antar
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Flow Field ◽  
Knudsen Number ◽  
External Flow ◽  
Basic Flow ◽  
Numerical Code ◽  
Flow And Heat Transfer ◽  
Micro Sphere

Due to the increased power dissipation for the new generation of microprocessors, cooling technologies represent a challenge to the manufacturers of such components. This is especially true as the component size is getting smaller and hence the heat generated per unit area is increasing significantly. Moreover, the importance of the microscale fluid flow rises from the new applications of micro-scale electromechanical systems that encounter fluid flow, such as micro-pumps, micro-turbines and micro-robotics. An understanding of the basic flow field and heat transfer in the case of external flow around miniature components is an essential tool to find proper means for cooling these small electronic/electromechanical devices. This work introduces a fundamental investigation of the external flow field and heat transfer characteristic around a micro sphere. In this study, the fluid flow and forced convection heat transfer characteristics over a micro-sphere at moderate to high values of Reynolds number are numerically investigated. The classical boundary condition of uniform wall temperature is considered in this work. In spite of the significance of this topic in understanding the basic flow and heat transfer features about a miniature sphere, it received little attention in the open literature. In this model, the effect of the engineering parameters such as Reynolds number and Knudsen number on the velocity and temperature profiles are investigated. The numerical code has the capability of accurate determination of the angle of external flow separation. The Knudsen number values used are limited by the continuity range where the Navier-Stokes Equations are used. Therefore, The Knudsen number is assumed small enough to apply a continuum model for the flow field with a temperature jump and frictional slip at the sphere’s surface.

scholarly journals Large Eddy Simulation and Flow Field Analysis of Car on the Bridge under Turbulent Crosswind

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Juyue Ding ◽  
Weitan Yin ◽  
Yongqi Ma
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Large Eddy Simulation ◽  
Wind Tunnel Test ◽  
Simulation Method ◽  
Field Analysis ◽  
Long Span Bridges ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Flow Field Characteristics

As more long-span bridges continue to be completed and opened to traffic, the safety of cars driving across the bridge has attracted more and more attention, especially when the car is suddenly affected by the crosswind, the car is likely to have direction deviation or even a rollover accident. In this paper, the large eddy simulation method is used to study the flow field characteristics and safety of the car on the bridge under the turbulent crosswind. The numerical simulation model is established by referring to the Donghai Bridge, and the correctness of the car model is validated by combining with the data of wind tunnel test. The influence of factors such as the porosity and height of the bridge guardrail and the Reynolds number of airflow on the flow field characteristics is analyzed. The study shows that, in order to ensure the safety of cars on the bridge, the bridge guardrail porosity should be small, 35.8% is more suitable, the guardrail height should be more suitable within the range of 1.5–1.625 meters, and the Reynolds number should not be 3.51e + 5. The research results of this paper will provide reference for the optimal design of bridge guardrail.

Density ratio effects on reacting bluff-body flow field characteristics

2012 ◽  
Vol 706 ◽  
pp. 219-250 ◽  
Author(s):  
Benjamin Emerson ◽  
Jacqueline O’Connor ◽  
Matthew Juniper ◽  
Tim Lieuwen
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Shear Layer ◽  
Parametric Excitation ◽  
Bluff Body ◽  
Density Ratio ◽  
Global Mode ◽  
Measured Velocity ◽  
Number Range ◽  
Flow Field Characteristics

AbstractThe wake characteristics of bluff-body-stabilized flames are a strong function of the density ratio across the flame and the relative offset between the flame and shear layer. This paper describes systematic experimental measurements and stability calculations of the dependence of the flow field characteristics and flame sheet dynamics upon flame density ratio,${\rho }_{u} / {\rho }_{b} $, over the Reynolds number range of 1000–3300. We show that two fundamentally different flame/flow behaviours are observed at high and low${\rho }_{u} / {\rho }_{b} $values: a stable, noise-driven fixed point and limit-cycle oscillations, respectively. These results are interpreted as a transition from convective to global instability and are captured well by stability calculations that used the measured velocity and density profiles as inputs. However, in this high-Reynolds-number flow, the measurements show that no abrupt bifurcation in flow/flame behaviour occurs at a given${\rho }_{u} / {\rho }_{b} $value. Rather, the flow field is highly intermittent in a transitional${\rho }_{u} / {\rho }_{b} $range, with the relative fraction of the two different flow/flame behaviours monotonically varying with${\rho }_{u} / {\rho }_{b} $. This intermittent behaviour is a result of parametric excitation of the global mode growth rate in the vicinity of a supercritical Hopf bifurcation. It is shown that this parametric excitation is due to random fluctuations in relative locations of the flame and shear layer.

Experimental Study of Axial Slit Wall Effect on Taylor-Couette Flow

2007 ◽  
Author(s):  
Sang-Hyuk Lee ◽  
Hyoung-Bum Kim
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Vortex Flow ◽  
Outer Cylinder ◽  
Velocity Fields ◽  
Taylor Vortex ◽  
Stable Mode ◽  
Taylor Vortex Flow ◽  
Taylor Couette ◽  
Taylor Couette Flow

Taylor-Couette flow has been studied extensively and lots of variables which affect the flow instability are being reported. The wall geometry effect of Taylor-Couette flow, however, has been less studied. In this study, we investigated the effect of axial slit of outer cylinder. This kind of configuration can be easily seen in rotating machinery. Particle image velocimetry method was used to measure the velocity fields in longitudinal and latitudinal planes. The index matching method was used to avoid light refraction. The velocity fields between the slit and plain model which has the smooth wall were compared. From the experiments, both models have the same flow mode below Re = 143. The transition from circular Couette flow to plain Taylor vortex flow began at Re = 103, and the next transition to wavy vortex flow occurred at 124. The effect of slit wall appeared when the Reynolds number is larger than Re = 143. Above this Reynolds number, there was no stable mode and plain and wavy Taylor vortex flow randomly appeared.

scholarly journals Transition in circular Couette flow

1965 ◽  
Vol 21 (3) ◽  
pp. 385-425 ◽  
Author(s):  
Donald Coles
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Discrete Spectrum ◽  
Couette Flow ◽  
Travelling Waves ◽  
Outer Cylinder ◽  
Spectral Lines ◽  
Wave Number ◽  
Cascade Process ◽  
Spectral Evolution

Two distinct kinds of transition have been identified in Couette flow between concentric rotating cylinders. The first, which will be called transition by spectral evolution, is characteristic of the motion when the inner cylinder has a larger angular velocity than the outer one. As the speed increases, a succession of secondary modes is excited; the first is the Taylor motion (periodic in the axial direction), and the second is a pattern of travelling waves (periodic in the circumferential direction). Higher modes correspond to harmonics of the two fundamental frequencies of the doubly-periodic flow. This kind of transition may be viewed as a cascade process in which energy is transferred by non-linear interactions through a discrete spectrum to progressively higher frequencies in a two-dimensional wave-number space. At sufficiently large Reynolds numbers the discrete spectrum changes gradually and reversibly to a continuous one by broadening of the initially sharp spectral lines.These periodic flows are not uniquely determined by the Reynolds number. For the case of the inner cylinder rotating and the outer cylinder at rest, as many as 20 or 25 different states (each state being defined by the number of Taylor cells and the number of tangential waves) have been observed at a given speed. As the speed changes, theso states replace each other in a repeatable but irreversible pattern of transitions; vortices appear or disappear in pairs, and waves are added or subtracted. More than 70 such transitions have been found in the speed range up to about 10 times the first critical speed. Regardless of the state, however, the angular velocity of the tangential waves is nearly constant at 0.34 times the angular velocity of the inner cylinder.The second kind of transition, which will be called catastrophic transition, is characteristic of the motion when the outer cylinder has a larger angular velocity than the inner one. At a fixed Reynolds number, the fluid is divided into distinct regions of laminar and turbulent flow, and these regions are separated by interfacial surfaces which may be propagating in either direction. Under some conditions the turbulent regions may appear and disappear in a random way; under other conditions they may form quite regular patterns. One common pattern of particular interest is a spiral band of turbulence which rotates at very nearly the mean angular velocity of the two walls without any change in shape except possibly an occasional shift from a right-hand to a left-hand pattern. One example of this spiral turbulence is being studied in some detail in an attempt to clarify the role played in transition by interfaces and intermittency.

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