A Combined Packed-Bed Friction Factor Equation: Extension to Higher Reynolds Number with Wall Effects

AIChE Journal ◽  
2013 ◽  
Vol 59 (3) ◽  
pp. 703-706 ◽  
Author(s):  
Luke D. Harrison ◽  
Kyle M. Brunner ◽  
William C. Hecker
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Packed Bed ◽  
Wall Effects ◽  
Bed Friction ◽  
Factor Equation

Friction factor calculation for turbulent flow in annulus with temperature effects

2019 ◽  
Vol 30 (7) ◽  
pp. 3755-3763
Author(s):  
Mehmet Sorgun ◽  
Erman Ulker
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Pressure Loss ◽  
Diameter Ratio ◽  
Pipe Diameter ◽  
Fluid Temperature ◽  
Flow Loop ◽  
Content Type ◽  
Pipe Rotation ◽  
Factor Equation

Purpose The purpose of this paper is to present a new friction factor equation for practical use, including fluid temperature, pipe diameter ratio and inner pipe rotation effects. Design/methodology/approach A friction factor relationship is developed by applying Buckingham’s Theorem of dimensional analysis. Then, the formula is calibrated using experimental data conducted at Izmir Katip Celebi University flow loop. Moreover, the effects of fluid temperature, inner pipe rotation and pipe diameter ratio on friction factor are investigated experimentally. Findings Satisfactory agreements are obtained between proposed formula and experiments. The experimental results indicate that major variable parameters affecting friction factor is Reynolds number. Pipe rotation has negligible effect on friction factor at high Reynolds number. Prandtl number is one of the important parameters affecting the friction factor. Moreover, as the pipe diameter ratio is decreased, friction factor increases. Originality/value Determining fluid behavior of fluids under high temperature is especially important for deep wells during drilling. Temperature drastically changes fluid properties and flow characteristics in wells. These changes have a remarkable effect on pressure losses. However, since the temperature is considered constant in the calculation of the pressure loss, problems can be encountered in most systems. Friction factor is one of the important parameters for determining pressure loss in closed conduits. The originality of this work is to propose a new friction factor equation for practical use, including fluid temperature, pipe diameter ratio and inner pipe rotation effects.

Numerical and Experimental Analysis of Turbulent Flow in Corrugated Pipes

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Henrique Stel ◽  
Rigoberto E. M. Morales ◽  
Admilson T. Franco ◽  
Silvio L. M. Junqueira ◽  
Raul H. Erthal ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Velocity Magnitude ◽  
Geometric Configurations ◽  
Corrugated Surfaces ◽  
Friction Factors

This article describes a numerical and experimental investigation of turbulent flow in pipes with periodic “d-type” corrugations. Four geometric configurations of d-type corrugated surfaces with different groove heights and lengths are evaluated, and calculations for Reynolds numbers ranging from 5000 to 100,000 are performed. The numerical analysis is carried out using computational fluid dynamics, and two turbulence models are considered: the two-equation, low-Reynolds-number Chen–Kim k-ε turbulence model, for which several flow properties such as friction factor, Reynolds stress, and turbulence kinetic energy are computed, and the algebraic LVEL model, used only to compute the friction factors and a velocity magnitude profile for comparison. An experimental loop is designed to perform pressure-drop measurements of turbulent water flow in corrugated pipes for the different geometric configurations. Pressure-drop values are correlated with the friction factor to validate the numerical results. These show that, in general, the magnitudes of all the flow quantities analyzed increase near the corrugated wall and that this increase tends to be more significant for higher Reynolds numbers as well as for larger grooves. According to previous studies, these results may be related to enhanced momentum transfer between the groove and core flow as the Reynolds number and groove length increase. Numerical friction factors for both the Chen–Kim k-ε and LVEL turbulence models show good agreement with the experimental measurements.

Thermal Performance Assessment of Turbulent Flow Through Dimpled Tubes

2010 ◽  
Author(s):  
Pornchai Nivesrangsan ◽  
Somsak Pethkool ◽  
Kwanchai Nanan ◽  
Monsak Pimsarn ◽  
Smith Eiamsa-ard
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Friction Factor ◽  
Heat Transfer Rate ◽  
Thermal Performance ◽  
Transfer Rate ◽  
Staggered Arrangement ◽  
Plain Tube ◽  
Pitch Ratio ◽  
Surface Patterns

This paper presents the heat transfer augmentation and friction factor characteristics by means of dimpled tubes. The experiments were conducted using the dimpled tubes with two different dimpled-surface patterns including aligned arrangement (A-A) and staggered arrangement (S-A), each with two pitch ratios (PR = p/Di = 0.6 and 1.0), for Reynolds number ranging from 9800 to 67,000. The experimental results achieved from the dimpled tubes are compared with those obtained from the plain tube. Evidently, the dimpled tubes with both arrangements offer higher heat transfer rates compared to the plain tube and the dimpled tube with staggered arrangement shows an advantage on the basis of heat transfer enhancement over the dimpled tube with aligned arrangement. The increase in heat transfer rate with reducing pitch ratio is due to the higher turbulent intensity imparted to the flow between the dimple surfaces. The mean heat transfer rate offered by the dimpled tube with staggered arrangement (S-A) at the lowest pitch ratio (PR = 0.6), is higher than those provided by the plain tube and the dimpled tube with aligned arrangement (A-A) at the same PR by around 127% and 8%, respectively. The empirical correlations developed in terms of pitch ratio (PR), Prandtl number (Pr) and Reynolds number, are fitted the experimental data within ±8% and ±2% for Nusselt number (Nu) and friction factor (f), respectively. In addition, the thermal performance factors under an equal pumping power constraint of the dimple tubes for both dimpled-surface arrangements are also determined.

Heat Transfer And Pressure Drop Of An Angled Discrete Turbulator At Elevated Reynolds Numbers Up To 900,000

2021 ◽  
pp. 1-29
Author(s):  
Sam Ghazi-Hesami ◽  
Dylan Wise ◽  
Keith Taylor ◽  
Peter Ireland ◽  
Étienne Robert
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Friction Factor ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Enhance Heat Transfer ◽  
Near Surface ◽  
Number Range ◽  
Smooth Channel

Abstract Turbulators are a promising avenue to enhance heat transfer in a wide variety of applications. An experimental and numerical investigation of heat transfer and pressure drop of a broken V (chevron) turbulator is presented at Reynolds numbers ranging from approximately 300,000 to 900,000 in a rectangular channel with an aspect ratio (width/height) of 1.29. The rib height is 3% of the channel hydraulic diameter while the rib spacing to rib height ratio is fixed at 10. Heat transfer measurements are performed on the flat surface between ribs using transient liquid crystal thermography. The experimental results reveal a significant increase of the heat transfer and friction factor of the ribbed surface compared to a smooth channel. Both parameters increase with Reynolds number, with a heat transfer enhancement ratio of up to 2.15 (relative to a smooth channel) and a friction factor ratio of up to 6.32 over the investigated Reynolds number range. Complementary CFD RANS (Reynolds-Averaged Navier-Stokes) simulations are performed with the κ-ω SST turbulence model in ANSYS Fluent® 17.1, and the numerical estimates are compared against the experimental data. The results reveal that the discrepancy between the experimentally measured area averaged Nusselt number and the numerical estimates increases from approximately 3% to 13% with increasing Reynolds number from 339,000 to 917,000. The numerical estimates indicate turbulators enhance heat transfer by interrupting the boundary layer as well as increasing near surface turbulent kinetic energy and mixing.

Determination of Incompressible Flow Friction in Smooth Circular and Noncircular Passages: A Generalized Approach Including Validation of the Nearly Century Old Hydraulic Diameter Concept

1988 ◽  
Vol 110 (4) ◽  
pp. 431-440 ◽  
Author(s):  
N. T. Obot
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Critical Reynolds Number ◽  
Pressure Coefficient ◽  
Hydraulic Diameter ◽  
Length Scale ◽  
The Difference ◽  
Friction Method ◽  
Reduced Data

It has been demonstrated conclusively that the widely observed differences in data for frictional pressure coefficient between circular and noncircular passages derive from the inseparably connected effects of transition and the choice of a length scale. A relatively simple approach, the critical friction method (CFM), has been developed and when applied to triangular, rectangular, and concentric annular passages, the reduced data lie with remarkable consistency on the circular tube relations. In accordance with the theory of dynamical similarity, it has also been shown that noncircular duct data can be reduced using the hydraulic diameter or any arbitrarily defined length scale. The proposed method is what is needed to reconcile such data with those for circular tubes. With the hydraulic diameter, the critical friction factor almost converges to a universal value for all passages and the correction is simply that required to account for the difference in critical Reynolds number. By contrast, with any other linear parameter, two corrections are needed to compensate for variations in critical friction factor and Reynolds number. Application of the method to roughened passages is discussed.

Effect of Surface Roughness on Gaseous Flow Through Microchannels

2000 ◽  
Author(s):  
Stephen E. Turner ◽  
Hongwei Sun ◽  
Mohammad Faghri ◽  
Otto J. Gregory
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Helium Flow ◽  
Local Pressure ◽  
Aspect Ratios ◽  
Corrugated Surfaces ◽  
Flow Through ◽  
Effect Of Surface

Abstract This paper presents an experimental investigation on nitrogen and helium flow through microchannels etched in silicon with hydraulic diameters between 10 and 40 microns, and Reynolds numbers ranging from 0.3 to 600. The objectives of this research are (1) to fabricate microchannels with uniform surface roughness and local pressure measurement; (2) to determine the friction factor within the locally fully developed region of the microchannel; and (3) to evaluate the effect of surface roughness on momentum transfer by comparison with smooth microchannels. The friction factor results are presented as the product of friction factor and Reynolds number plotted against Reynolds number. The following conclusions have been reached in the present investigation: (1) microchannels with uniform corrugated surfaces can be fabricated using standard photolithographic processes; and (2) surface features with low aspect ratios of height to width have little effect on the friction factor for laminar flow in microchannels.

Friction Factor Comparison Between Mixing Length Theory and Empirical Correlation

2022 ◽  
Author(s):  
M Prasad
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Friction Factor ◽  
High Reynolds Number ◽  
Mathematical Representation ◽  
Mixing Length ◽  
Series Form ◽  
High Reynolds ◽  
Mixing Length Theory ◽  
Grain Roughness

Abstract Equivalent sand grain roughness is required for estimating friction factor for engineering applications from empirical relation via Haalands equation. The real surfaces are different from the sand grain profile. The correlations for friction factor were derived from use of discrete roughness elements with regular shapes such as cones, bars etc. The purpose of the paper is to derive analytical expression of friction factor for a 2 dimensional semi-cylindrical roughness (not exactly a 3 dimensional sand grain but for the circular profile of cross- section) using Navier Stoke equation and mixing length theory. This is compared with the modified series mathematical representation of Haalands equation for friction factor in terms of equivalent sand grain roughness. The comparison is valid for high Reynolds number where the velocity profile is almost flat beyond boundary layer and approximately linear all throughout the boundary layer. The high Reynolds number approximation for Haalands equation is derived and the series form of the friction factor compares approximately with the series form derived from first principles, where in the exponents of the series expansion are close.

Experimental and Numerical Studies of Fluid Flow Confined in Microchannel

2016 ◽  
Author(s):  
Yan Wang ◽  
Xiang Ling
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Friction Factor ◽  
Heat Transfer Performance ◽  
Pure Water ◽  
High Heat Flux ◽  
Transfer Performance ◽  
Parallel Microchannels

The heat transfer performance of fluid flowing in a microchannel was experimentally studied, to meet the requirement of extremely high heat flux removal of microelectronic devices. There were 10 parallel microchannels with rectangular cross-section in the stainless steel plate, which was covered by a glass plate to observe the fluid flowing behavior, and another heating plate made of aluminum alloy was positioned behind the microchannel. Single phase heat transfer and fluid flow downstream the microchannel experiments were conducted with both deionized water and ethanol. Besides experiments, numerical models were also set up to make a comparison with experimental results. It is found that the pressure drop increases rapidly with enlarging Reynolds number (200), especially for ethanol. With comparison, the flow resistance of pure water is smaller than ethanol. Results also show that the friction factor decreases with Reynolds number smaller than the critical value, while increases the velocity, the friction factor would like to keep little changed. We also find that the water friction factors obtained by CFD simulations in parallel microchannels are much larger than experiment results. With heat flux added to the fluid, the heat transfer performance can be enhanced with larger Re number and the temperature rise could be weaken. Compared against ethanol, water performed much better for heat removal. However, with intensive heat flux, both water and ethanol couldn’t meet the requirement and the temperature at outlet would increase remarkably, extremely for ethanol. These findings would be helpful for thermal management design and optimization.

scholarly journals The Effect of Nanofluid Volume Concentration on Heat Transfer and Friction Factor inside a Horizontal Tube

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Adnan M. Hussein ◽  
K. V. Sharma ◽  
R. A. Bakar ◽  
K. Kadirgama
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Thermal Properties ◽  
Friction Factor ◽  
Volume Concentration ◽  
Convection Heat Transfer ◽  
Horizontal Tube ◽  
Maximum Deviation ◽  
Flat Tube

The additives of solid nanoparticles to liquids are significant enhancement of heat transfer and hydrodynamic flow. In this study, the thermal properties of three types of nanoparticles (Al2O3, TiO2, and SiO2) dispersed in water as a base fluid were measured experimentally. Forced convection heat transfer turbulent flow inside heated flat tube was numerically simulated. The heat flux around flat tube is 5000 W/m2and Reynolds number is in the range of5×103to50×103. CFD model by finite volume method used commercial software to find hydrodynamic and heat transfer coefficient. Simulation study concluded that the thermal properties measured and Reynolds number as input and friction factor and Nusselt number as output parameters. Data measured showed that thermal conductivity and viscosity increase with increasing the volume concentration of nanofluids with maximum deviation 19% and 6%, respectively. Simulation results concluded that the friction factor and Nusselt number increase with increasing the volume concentration. On the other hand, the flat tube enhances heat transfer and decreases pressure drop by 6% and −4%, respectively, as compared with circular tube. Comparison of numerical analysis with experimental data available showed good agreement with deviation not more than 2%.

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