A Modified Cubic Law for single-phase saturated laminar flow in rough rock fractures

2018 ◽  
Vol 103 ◽  
pp. 107-115 ◽  
Author(s):  
Zhihe Wang ◽  
Chaoshui Xu ◽  
Peter Dowd
Keyword(s):  
Laminar Flow ◽  
Single Phase ◽  
Rock Fractures ◽  
Cubic Law

scholarly journals A Corrected Cubic Law for Single-phase Laminar Flow through Rough-walled Fractures

2021 ◽  
pp. 103984
Author(s):  
Xupeng He ◽  
Marwa Sinan ◽  
Hyung Kwak ◽  
Hussein Hoteit
Keyword(s):  
Laminar Flow ◽  
Single Phase ◽  
Cubic Law ◽  
Flow Through

Improved Correlations for Counting the Effect of Natural Convection on Laminar Flow of Nanofluids

2013 ◽  
Author(s):  
Si-pu Guo ◽  
Zhao-zan Feng ◽  
Ze-cong Fang ◽  
Wei Li ◽  
Jin-liang Xu ◽  
...  
Keyword(s):  
Experimental Data ◽  
Natural Convection ◽  
Laminar Flow ◽  
Prandtl Number ◽  
Single Phase ◽  
Colloidal Suspensions ◽  
Horizontal Tube ◽  
Laminar Mixed Convection ◽  
Wide Range ◽  
Phase Fluid

Nanofluids are colloidal suspensions of nano-scale particles in water, or other base fluids. In this paper, the effect of natural convection on laminar flow of nanofluids in a horizontal tube has been addressed. The obtained experimental data could not be reconciled with existing correlations over a wide range of Prandtl number under laminar mixed convection. Three improved correlations have been derived by using single-phase fluid approach. These correlations fit our data to within ± 10 % and also agree with the data in literature quite well. Such results verify that nanofluids can be treated as a homogeneous mixture with effective thermophysical properties. Utimately, the new correlations have grasped the essence of natural convection and can reduce to both normal forced convection and pure natural convection equations at limiting cases.

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

Transport of reactive tracers in rock fractures

1999 ◽  
Vol 378 ◽  
pp. 335-356 ◽  
Author(s):  
V. CVETKOVIC ◽  
J. O. SELROOS ◽  
H. CHENG
Keyword(s):  
Mass Transfer ◽  
Flow Equation ◽  
Transfer Reactions ◽  
Fracture Plane ◽  
Fracture Aperture ◽  
Rock Fractures ◽  
Advective Transport ◽  
Rock Matrix ◽  
Cubic Law ◽  
Diffusive Mass Transfer

Transport of tracers subject to mass transfer reactions in single rock fractures is investigated. A Lagrangian probabilistic model is developed where the mass transfer reactions are diffusion into the rock matrix and subsequent sorption in the matrix, and sorption on the fracture surface as well as on gauge (infill) material in the fracture. Sorption reactions are assumed to be linear, and in the general case kinetically controlled. The two main simplifying assumptions are that diffusion in the rock matrix is one-dimensional, perpendicular to the fracture plane, and the tracer is displaced within the fracture plane by advection only. The key feature of the proposed model is that advective transport and diffusive mass transfer are related in a dynamic manner through the flow equation. We have identified two Lagrangian random variables τ and β as key parameters which control advection and diffusive mass transfer, and are determined by the flow field. The probabilistic solution of the transport problem is based on the statistics of (τ, β), which we evaluated analytically using first-order expansions, and numerically using Monte Carlo simulations. To study (τ, β)-statistics, we assumed the ‘cubic law’ to be applicable locally, whereby the pressure field is described with the Reynolds lubrication equation. We found a strong correlation between τ and β which suggests a deterministic relationship β∼τ3/2; the exponent 3/2 is an artifact of the ‘cubic law’. It is shown that flow dynamics in fractures has a strong influence on the variability of τ and β, but a comparatively small impact on the relationship between τ and β. The probability distribution for the (decaying) tracer mass recovery is dispersed in the parameter space due to fracture aperture variability.

Experimental Study on Thermal-Hydraulic Performance of Single-Phase Water Flow in Narrow Rectangular Channel

2009 ◽  
Author(s):  
Mei Wang ◽  
Yan Wen ◽  
Suizheng Qiu ◽  
Guanghui Su ◽  
Weifeng Ni
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Friction Factor ◽  
Water Flow ◽  
Single Phase ◽  
Rectangular Channel ◽  
Flow Region ◽  
Phase Water

The purpose of this study is to discover the differences of pressure drop and heat transfer of single-phase water flow between conventional channels and narrow rectangular channels. Furthermore, the differences between the level and the vertical channel have been studied. The gap of the test channel is 1.8mm. Compared with conventional channels, the narrow rectangular channel showed differences in both flow and heat transfer characteristics. The critical Reynolds number of transition from laminar flow to turbulent flow is 900∼1300, which is smaller compared with conventional channels. The friction factor is larger than that of the conventional channels and the correlation of friction factor with Reynolds number was given by experimental results. From the relation graph of Nusselt number and Reynolds number, the demarcation of the laminar flow region and turbulence flow region is obvious. In laminar region, Nusselt number almost remained constant and approximately consistent with numerical simulation results. While in turbulent region, Nusselt number increased significantly with increasing Reynolds number. A new Nusselt number correlation was obtained based on Dittus-Boelter equation, and the coefficients were less about 13% than that of Dittus-Boelter equation.

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