Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

2009 ◽  
Vol 621 ◽  
pp. 69-102 ◽  
Author(s):  
MURALI R. CHOLEMARI ◽  
JAYWANT H. ARAKERI
Keyword(s):  
Reynolds Number ◽  
Rayleigh Number ◽  
Turbulent Flow ◽  
Density Gradient ◽  
Schmidt Number ◽  
Shear Stresses ◽  
Mean Flow ◽  
Vertical Pipe ◽  
Velocity Correlation ◽  
Number Range

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

The Numerical Simulation of Turbulent Flow in Semi-Closed Rotor-Stator Cavity

2016 ◽  
Author(s):  
Guohu Luo ◽  
Shengde Wang ◽  
Hong Shen ◽  
Zhenqiang Yao
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Pressure Difference ◽  
Tangential Velocity ◽  
Reynolds Stress Model ◽  
Mean Flow ◽  
Closed Cavity ◽  
Turbulent Field ◽  
Effects Of Rotation

The present work numerically considered the turbulent flow in a semi-closed rotor-stator cavity with a superimposed throughflow based on Reynolds Stress Model (RSM). The mean flow structure and turbulent field in the semi-closed cavity (SC) were identified by comparison with the flow in open cavity (OC) and closed cavity (CC). Then the effects of rotation Reynolds number, ranging from 1 × 106 to 4 × 106, on the flow in SC were investigated. The superimposed flow noticeably decreases the tangential velocity, resulting that the pressure difference between central hub and periphery in SC is greater than the OC but less than the CC. The flow in SC belongs to Stewartson type in the region between inlet and outlet, but to Bachelor type between outlet and periphery. Around the outlets, the flow is greatly affected, especially for turbulent field, where the turbulence intensities maintain at higher levels outside the two boundary layers. With the increase of Reynolds number, the tangential velocity goes up, resulted the attenuation of jet impinging effects, the shrinking of affected zones by outlets and the enlargement of pressure difference. Moreover, with the Bödewadt layer moving toward the central hub, the turbulence intensities increase inside two boundary layers but decrease outside them. Consequently, the flow is transited to Stewartson and then Batchelor type.

Application of Non-Linear k–ω Model to the Turbulent Flow Inside a Sharp U-Bend

2000 ◽  
Author(s):  
B. Song ◽  
R. S. Amano
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Higher Order ◽  
Shear Stresses ◽  
Complex Flow ◽  
Streamline Curvature ◽  
Non Linear ◽  
Low Reynolds

Simulation of the complex flow inside a sharp U-bend needs both refined turbulence models and higher order numerical discretization schemes. In the present study, a nonlinear low-Reynolds number (low-Re) k–ω model including the cubic terms was employed to predict the turbulent flow through a square cross-sectioned U-bend with a sharp curvature, Rc/D = 0.65. In the turbulence model employed for the present study, the cubic terms are incorporated to represent the effect of extra strain-rates such as streamline curvature and three-dimensionality on both turbulence normal and shear stresses. In order to accurately predict such complex flowfields, a higher-order bounded interpolation scheme (Song, et al., 1999) has been used to discretize all the transport equations. The calculated results by using both the non-linear k–ω model and the linear low-Reynolds number k–ε model (Launder and Sharma, 1974) have been compared with experimental data. It is shown that the present model produces satisfactory predictions of the flow development inside the sharp U-bend and well captures the characteristics of the turbulence anisotropy within the duct core region and wall sub-layer.

Further Investigation of Discharge Coefficient for PTC 6 Flow Nozzle in High Reynolds Number

2015 ◽  
Author(s):  
Noriyuki Furuichi ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
Kazuo Shibuya
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
High Reynolds Number ◽  
Discharge Coefficient ◽  
Flow Region ◽  
Number Range ◽  
Discharge Coefficients ◽  
Reynolds Number Range ◽  
High Reynolds

The discharge coefficients of the throat tap flow nozzle based on ASME PTC 6 are measured in wide Reynolds number range from Red=5.8×104 to Red=1.4×107. The nominal discharge coefficient (the discharge coefficient without tap) is determined from the discharge coefficients measured for different tap diameters. The tap effects are correctly obtained by subtracting the nominal discharge coefficient from the discharge coefficient measured. Finally, by combing the nominal discharge coefficient and the tap effect determined in three flow regions, that is, laminar, transitional and turbulent flow region, the new equations of the discharge coefficient are proposed in three flow regions.

Heat Transfer to Mercury Flowing In-Line Through a Bundle of Circular Rods

1964 ◽  
Vol 86 (2) ◽  
pp. 180-186 ◽  
Author(s):  
M. W. Maresca ◽  
O. E. Dwyer
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Number Range ◽  
Heat Transfer Coefficients ◽  
Turbulent Flow Regime ◽  
Measuring Surface ◽  
Theoretical Predictions

Experimental results were obtained for the case of in-line flow of mercury through an unbaffled bundle of circular rods, and they were compared with theoretical predictions. The bundle consisted of 13 one-half-in-dia rods arranged in an equilateral triangular pattern, the pitch:diameter ratio being 1.750. Measurements were taken only on the central rod. Six different rods were tested. All rods in the bundle were electrically heated to provide equal and uniform heat fluxes throughout the bundle. The rods were of the Calrod type. The test rods had copper sheaths with fine thermocouples imbedded below the surface for measuring surface temperatures. Some rods were plated with a layer of nickel, followed by a very thin layer of copper, to provide “wetting” conditions, while others were chromeplated to provide “nonwetting” conditions. Heat-transfer coefficients were obtained under the following conditions: (a) Prandtl number, 0.02; (b) Reynolds number range, 7500 to 200,000; (c) Peclet number range, 150 to 4000; (d) “Wetting” versus “nonwetting”; (e) Both transition and fully established flow; (f) Variation of Lf/De ratio from 4 to 46. The precision of the results is estimated to be within 2 to 3 percent. An interesting finding, consistent with earlier predictions, was that the Nusselt number, under fully established turbulent-flow conditions, remained essentially constant, at the lower end of the turbulent flow regime, until a Reynolds number of about 40,000 was reached.

Mixing Enhancement in a Chaotic Micromixer Using Pulsating Flow

2014 ◽  
Author(s):  
Mohammad Karami ◽  
Mojtaba Jarrahi ◽  
Ebrahim Shirani ◽  
Hassan Peerhossaini
Keyword(s):  
Reynolds Number ◽  
Lyapunov Exponent ◽  
Steady Flow ◽  
Concentration Distribution ◽  
Pulsating Flow ◽  
Chaotic Advection ◽  
Mixing Enhancement ◽  
Mean Flow ◽  
Number Range ◽  
Velocity Amplitude

This study determines the simultaneous effects of spatial disturbance and flow pulsation on micromixing by using three different metrics: concentration distribution, Lyapunov exponent and axial vorticity. Numerical simulations are performed for both steady and pulsating flows through a microchannel made up of C-curved repeating units. Moreover, a straight microchannel is analyzed to compare the effects of chaotic advection and molecular diffusion, the main mechanisms of transverse mixing in the chaotic and straight mixer respectively. Simulations are carried out in the steady flow for the Reynolds number range 1≤Re≤50 and in the pulsating flow for velocity amplitude ratios 1≤β≤2.5, and the ratio of the peak oscillatory velocity component to the mean flow velocity, Strouhal numbers 0.1≤St≤0.5. It was found that chaotic advection improves mixing without significant increase in pressure drop. The analysis of concentration distribution implied that full mixing occurs after Reynolds number 50 in the steady flow. When the flow is pulsatile, small and moderate values of the Strouhal number (0.1≤St≤0.3) and high values of velocity amplitude ratio (β ≥ 2) are favorable conditions for mixing enhancement. Moreover, mixing has an oscillating trend along the microchannel due to the coexistence of regular and chaotic zones in the fluid. These results correlate closely with those obtained using two other metrics, analysis of the Lyapunov exponent and axial vorticity.

scholarly journals STUDY OF THE BEHAVIOURS OF SINGLE-PHASE TURBULENT FLOW AT LOW TO MODERATE REYNOLDS NUMBERS THROUGH A VERTICAL PIPE. PART I: 2D COUNTERS ANALYSIS

2020 ◽  
pp. 108-122
Author(s):  
Akeel M. Ali Morad ◽  
Rafi M. Qasim ◽  
Amjed Ahmed Ali
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Single Phase ◽  
Static Pressure ◽  
Fluid Velocity ◽  
Mixing Length ◽  
Shearing Force ◽  
Vertical Pipe ◽  
Moderate Reynolds Number

This study presents a model to investigate the behavior of the single-phase turbulent flow at low to moderate Reynolds number of water through the vertical pipe through (2D) contour analysis. The model constructed based on governing equations of an incompressible Reynolds Average Navier-Stokes (RANS) model with (k-ε) method to observe the parametric determinations such as velocity profile, static pressure profile, turbulent kinetic energy consumption, and turbulence shear wall flows. The water is used with three velocities values obtained of (0.087, 0.105, and 0.123 m/s) to represent turbulent flow under low to moderate Reynolds number of the pipe geometry of (1 m) length with a (50.8 mm) inner diameter. The water motion behavior inside the pipe shows by using [COMSOL Multiphysics 5.4 and FLUENT 16.1] Software. It is concluded that the single-phase laminar flow of a low velocity, but obtained a higher shearing force; while the turbulent flow of higher fluid velocity but obtained the rate of dissipation of shearing force is lower than that for laminar flow. The entrance mixing length is affected directly with pattern of fluid flow. At any increasing in fluid velocity, the entrance mixing length is increase too, due to of fluid kinetic viscosity changes. The results presented the trends of parametric determinations variation through the (2D) counters analysis of the numerical model. When fluid velocity increased, the shearing force affected directly on the layer near-wall pipe. This leads to static pressure decreases with an increase in fluid velocities. While the momentum changed could be played interaction rules between the fluid layers near the wall pipe with inner pipe wall. Finally, the agreement between present results with the previous study of [1] is satisfied with the trend

Investigation of Mean and Turbulent Flow Behaviour Over an Escarpment

2016 ◽  
Author(s):  
R. Kilpatrick ◽  
K. Siddiqui ◽  
H. Hangan ◽  
D. Parvu
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Behaviour ◽  
Scale Model ◽  
Mean Flow ◽  
Scaled Model ◽  
Energy And Environment ◽  
Flow Parameters ◽  
Image Velocimetry ◽  
Bolund Hill

Mean and turbulent flow behaviour over a 1:25 scale model of Bolund hill was investigated at Western University’s Wind Engineering, Energy, and Environment Research Institute (WindEEE) using Particle Image Velocimetry (PIV). A range of upstream flow and surface conditions were considered. Results showed almost no Reynolds dependency on the mean flow and weak dependency of Reynolds number on the upstream surface roughness conditions. However, a strong Reynolds number and upstream surface rough dependency is observed on the turbulent flow particularly in the shear layer formed in the immediate downstream region of the escarpment. It is concluded that the consideration of Reynolds number independency must be cautiously used when extrapolating the flow parameters from scaled model testing to full scale in the field.

Turbulent flow in smooth concentric annuli with small radius ratios

1974 ◽  
Vol 64 (2) ◽  
pp. 263-288 ◽  
Author(s):  
K. Rehme
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Turbulent Flow ◽  
Strong Influence ◽  
Maximum Velocity ◽  
Small Radius ◽  
Stress Distributions ◽  
Number Range ◽  
Fully Developed Turbulent Flow ◽  
Flow Through

Fully developed turbulent flow through three concentric annuli was investigated experimentally for a Reynolds-number rangeRe= 2 × 104−2 × 105. Measurements were made of the pressure drop, the positions of zero shear stress and maximum velocity, and the velocity distribution in annuli of radius ratios α = 0.02, 0.04 and 0.1, respectively. The results for the key problem in the flow through annuli, the position of zero shear stress, showed that this position is not coincident with the position of maximum velocity. Furthermore, the investigation showed the strong influence of spacers on the velocity and shear-stress distributions. The numerous theoretical and experimental results in the literature which are based on the coincidence of the positions of zero shear stress and maximum velocity are not in agreement with reality.

Pulsatile Blood Flow and Oxygen Transport Past a Circular Cylinder

2007 ◽  
Vol 129 (2) ◽  
pp. 202-215 ◽  
Author(s):  
Jennifer R. Zierenberg ◽  
Hideki Fujioka ◽  
Ronald B. Hirschl ◽  
Robert H. Bartlett ◽  
James B. Grotberg
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Circular Cylinder ◽  
Oxygen Transport ◽  
Schmidt Number ◽  
Gas Mixtures ◽  
Cylinder Surface ◽  
Shear Stresses ◽  
Saturation Curve ◽  
Pulsatile Blood Flow

The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the x direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter (α), pulsation amplitude (A), and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure O2 and air. The flow and concentration fields were computed for Re=5, 10, and 40, 0≤A≤0.75, α=0.25, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as A and α are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure O2 feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small A) for both feed-gas mixtures. The time averaged Sherwood number, Sh̿, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with A. Little change is observed with varying α for the ranges investigated. The effect of pulsatility on Sh̿ is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.

Analysis of Aerothermal Characteristics of Surface Micro-Structures

2017 ◽  
Author(s):  
M. Kapsis ◽  
L. He
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Regime ◽  
Computational Study ◽  
Number Range ◽  
High Loss ◽  
Turbulent Flow Regime ◽  
Roughness Elements ◽  
Element Pattern ◽  
Micro Structures

Recent advances in manufacturing technologies, such as additive manufacturing, have raised the potential of choosing surface finish pattern as a design parameter. Hence, understanding and prediction of aerothermal effects of machined micro-structures (‘machined roughness’) would be of great interest. So far, however, roughness has been largely considered as a stochastic attribute and empirically modelled. A relevant question is: if and how would shape of the machined roughness elements matter at such fine scales? In this paper, a systematic computational study has been carried out on the aerothermal behaviour and impact of some discrete micro-structures. Two shapes of micro-structure configurations are considered: hemispherical and rectangular elements for a Reynolds number range typical for those roughness elements (Re<5000). Several validation cases are studied as well as the turbulence modelling and grid sensitivities are examined to ensure the consistence of the numerical results. Furthermore, LES analyses are performed to contrast the behaviour in a well-established turbulent flow regime to a transitional one. The present results reveal a distinctive common flow pattern change (from an ‘open separation’ to a ‘reattached separation’) associated with a drastic change of drag/loss correlation from a low to a high loss regime. The results also indicate a clear dependence of drag and heat transfer characteristics on the element pattern and orientation relative to the flow. The distinctive performance correlations with Reynolds number can be affected considerably by the element shape, for both a transitional and a turbulent flow regime. The results also consistently illustrate that conventional empirical stochastic roughness parameters would be unable to predict these trends.

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