Flow Through a Finite Packed Bed of Spheres: A Note on the Limit of Applicability of the Forchheimer-Type Equation

2004 ◽  
Vol 126 (1) ◽  
pp. 139-143 ◽  
Author(s):  
Agne`s Montillet
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Flow Regime ◽  
Fluid Velocity ◽  
Type Equation ◽  
Packed Bed ◽  
Turbulent Flow Regime ◽  
Fully Developed Turbulent Flow ◽  
Flow Through

The variation of the pressure drop measured as a function of the fluid velocity through a packed bed of spheres is presented and discussed in the range of particle Reynolds number 30–1500. Based on previous studies, the observed limit of validity of the so-called Forchheimer law may be attributed to the concomitant effects of the finite character of the tested bed and of the transition of flow regime which is marking the beginning of the fully developed turbulent flow regime. The limit of validity of the Forchheimer-type law was formerly noticed by several authors.

Loss Characteristics of Orifices and Nozzles

1978 ◽  
Vol 100 (3) ◽  
pp. 299-307 ◽  
Author(s):  
S. H. Alvi ◽  
K. Sridharan ◽  
N. S. Lakshmana Rao
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Regime ◽  
Discharge Coefficient ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Center Line ◽  
Laminar Regime ◽  
Variation Of Parameters ◽  
Turbulent Flow Regime

Loss characteristics of sharp-edged orifices, quadrant-edged orifices for varying edge radii, and nozzles are studied for Reynolds numbers less than 10,000 for β ratios from 0.2 to 0.8. The results may be reliably extrapolated to higher Reynolds numbers. Presentation of losses as a percentage of meter pressure differential shows that the flow can be identified into fully laminar regime, critical Reynolds number regime, relaminarization regime, and turbulent flow regime. An integrated picture of variation of parameters such as discharge coefficient, loss coefficient, settling length, pressure recovery length, and center line velocity confirms this classification.

Effects of the Divergence Angle on the Onset of Asymmetric Flow Through a Planar Diffuser

2009 ◽  
Author(s):  
Majid Nabavi ◽  
Luc Mongeau
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Asymmetric Flow ◽  
Symmetric Flow ◽  
Turbulent Flow Regime ◽  
Flow Through ◽  
Gradual Expansion

In this study, two-dimensional laminar incompressible and turbulent compressible flow through the planar diffuser (gradual expansion) for different divergence half angles of the diffuser (θ), and different Reynolds numbers (Re) was numerically studied. The effects of θ on the critical Reynolds number at which the onset of asymmetric flow is observed, were investigated. In the laminar flow regime, it was observed that for every values of θ, there is a critical Re beyond which the flow is asymmetric. However, in the turbulent flow regime, for θ ≥ 20°, even at low Reynolds number the flow is asymmetric. Only for θ ≤ 10°, symmetric flow was observed below a critical Re.

Frictional Pressure Drop in Micro-Channel

2004 ◽  
Author(s):  
Yasuo Koizumi ◽  
Hiroyasu Ohtake ◽  
Hiroki Takahashi ◽  
Yoshiaki Ohno
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Friction Factor ◽  
Frictional Pressure Drop ◽  
Turbulent Transition ◽  
Friction Factors ◽  
Turbulent Flow Regime ◽  
Form Pressure ◽  
Laminar And Turbulent Flow ◽  
Flow Through

The friction characteristics of water in a sub-millimeter scale channel were investigated experimentally. The friction factors and the critical Reynolds number were measured using water flow through circular tubes with diameters of 0.5, 0.25 and 0.17 mm. The experimental results show that the measured friction factor for water agreed well with the conventional Poiseuille (λ = 64/Re) and Blasius (λ = 0.316 Re−0.25) equations in laminar and turbulent flow regime; the laminar-turbulent transition Reynolds number was approximately 2300 for diameter 0.5 mm. For diameter 0.25 mm, the friction factor evaluated by the form pressure drop also agreed well with the Poiseuille equation. For diameter 0.17 mm, the measured total friction factor was close to the Poiseuille prediction.

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.

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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