A Method of Correlating Fully Developed Turbulent Friction in Triangular Ducts

2000 ◽  
Vol 122 (3) ◽  
pp. 634-636 ◽  
Author(s):  
S. F. Nan ◽  
M. Dou
Keyword(s):  
Reynolds Number ◽  
Circular Tube ◽  
Apex Angle ◽  
Hydraulic Diameter ◽  
Turbulent Friction ◽  
Friction Factors ◽  
Blasius Equation ◽  
Proper Length

Fanning factors in isosceles-triangular ducts are examined. Data obtained in the literature were examined for deviations from the smooth circular tube line. It was found that the constant C in a form of the Blasius equation 4f Re0.25=C decreases as the apex angle does within the extent of experiments, and has 20 percent low deviation at 4 degree. For the apex angles greater than 60 degree, it was found that the constant C decreases as the apex angle increases. It is thus concluded that the hydraulic diameter is not the proper length dimension to use in the Reynolds number to insure similarity between the circular and triangular ducts. Instead, if an area equivalent round diameter is used in the Reynolds number, the deviations from the smooth circular tube line is within ∼6 percent. By using this area equivalent round diameter, it is demonstrated that circular tube methods may be readily applied to triangular ducts eliminating large errors in estimation of friction factors. [S0098-2202(00)00503-4]

An Improvement in the Calculation of Turbulent Friction in Rectangular Ducts

1976 ◽  
Vol 98 (2) ◽  
pp. 173-180 ◽  
Author(s):  
O. C. Jones
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Circular Tube ◽  
Hydraulic Diameter ◽  
Published Data ◽  
Turbulent Friction ◽  
Frictional Pressure Drop ◽  
Aspect Ratios

Frictional pressure drop in rectangular ducts is examined. Using correspondence between theory and experiment in laminar flow as a means for acceptance of published data, turbulent flow data for smooth rectangular ducts were compared with smooth circular tube data. Data for ducts having aspect ratios between unity and 39:1 were obtained in the literature and, in conjunction with new experimental data, were examined for deviations from the smooth circular tube line (smooth Moody). It was found that at constant Reynolds number based on hydraulic diameter the friction factor increases monotonically with increasing aspect ratio. It was thus concluded that the hydraulic diameter is not the proper length dimension to use in the Reynolds number to insure similarity between the circular and rectangular ducts. Instead, it was determined that if a modified Reynolds number Re* was obtained so that geometric similarity was provided in laminar flow by the relation f = 64/Re* for all geometries, that this Reynolds number also provided good similarity in fully developed turbulent flow within a ∼ 5 percent scatter band about the smooth tube line. By using this “laminar equivalent” Reynolds number, Re*, it is demonstrated that circular tube methods may be readily applied to rectangular ducts eliminating large errors in estimation of friction factor.

Laminar, Transitional and Turbulent Friction Factors for Gas Flows in Smooth and Rough Microtubes

2008 ◽  
Author(s):  
Marco Lorenzini ◽  
Gian Luca Morini ◽  
Sandro Salvigni
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Turbulent Regime ◽  
Turbulent Friction ◽  
Compressibility Effect ◽  
Flow Acceleration ◽  
Friction Factors ◽  
Macro Scale ◽  
Fully Developed Turbulent Flow ◽  
Microscale Transport

Theoretical and experimental works on microscale transport phenomena have been carried out in the past decade in the attempt to analyse possible new effects and to assess the influence of scaling on the classical correlations which are used in macro-scale heat and fluid flow, following the need to supply engineers with reliable correlations to be used in the design of micro-scale devices. These results were sometimes in mutual contrast, as is the case for the determination of the friction factor, which has been found to be lower, higher or comparable to that for macroscopic channels, depending on the researchers. In this work the compressible flow of nitrogen inside circular microchannels from 26 μm to 508 μm in diameter and with different surface roughness (<1%) is investigated for the whole range of flow conditions: laminar, transitional and turbulence. Over 5000 experimental data have been collected and analysed. The data confirmed that in the laminar regime the agreement with the conventional theory is very good in terms of friction factors both for rough and smooth microtubes. For the smaller microchannels (<100 μm) when Re is greater than 1300 the friction factor tends to deviate from the Poiseuille law because the flow acceleration due to compressibility effect gains in importance. The transitional regime was found to start no earlier than at values of the Reynolds number around 1800–2000. Both smooth and sudden changes in the flow regime have been found, as reported for conventional tubes. Fully developed turbulent flow was attained with both smooth and rough tubes, and the results for smooth tubes seem to confirm Blasius’s relation, while for rough tubes the Colebrook’s correlation is found to be only partially in agreement with the experimental friction factors. In the turbulent regime the dependence of the friction factor on the Reynolds number is less pronounced for microtubes with respect to the prediction of the Colebrook’s correlation and the friction factor tends only to depend on the microtube relative roughness.

Investigation of laminar flow frictional losses in a large-hydraulic-diameter pipe and annulus

2005 ◽  
Vol 219 (1) ◽  
pp. 53-60
Author(s):  
P Suresh Kumar
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Hydraulic Diameter ◽  
Low Reynolds Numbers ◽  
Friction Factors ◽  
Diameter Pipe ◽  
High Reynolds ◽  
Different Diameters

In the present work an experimental study has been carried out to study the friction factor variation with Reynolds number for laminar flow in a large-hydraulic-diameter pipe and annulus. It is found that for low Reynolds numbers the friction factors are large than those reported in the literature for small-hydraulic-diameter pipe and annulus. Large hydrostatic pressure variation along the circumferential direction causes a different flow pattern in a large-hydraulic-diameter duct and may be why the present results do not match those reported in the literature. A correlation has been proposed in the present paper which is being developed using the present experimental results for both pipe and annulus to correlate the friction factor as a function of Reynolds number and a newly denned Jaga number Jg. An analysis has been carried out using the currently developed friction factor correlations to study how the friction factor will vary for different fluids and different diameters of the pipe and annulus. It is observed that, for high Reynolds numbers ( Re > 100), small-hydraulic-diameter duct and fluids with a large kinematic viscosity, the present correlations show good agreement with the results reported in the literature.

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.

Heat Transfer for High Aspect Ratio Rectangular Channels in a Stationary Serpentine Passage With Turbulated and Smooth Surfaces

2013 ◽  
Author(s):  
Matthew A. Smith ◽  
Randall M. Mathison ◽  
Michael G. Dunn
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Behavior ◽  
Reynolds Numbers ◽  
Hydraulic Diameter ◽  
Internal Cooling ◽  
Number Range ◽  
Aspect Ratios ◽  
Parallel Configuration

Heat transfer distributions are presented for a stationary three passage serpentine internal cooling channel for a range of engine representative Reynolds numbers. The spacing between the sidewalls of the serpentine passage is fixed and the aspect ratio (AR) is adjusted to 1:1, 1:2, and 1:6 by changing the distance between the top and bottom walls. Data are presented for aspect ratios of 1:1 and 1:6 for smooth passage walls and for aspect ratios of 1:1, 1:2, and 1:6 for passages with two surfaces turbulated. For the turbulated cases, turbulators skewed 45° to the flow are installed on the top and bottom walls. The square turbulators are arranged in an offset parallel configuration with a fixed rib pitch-to-height ratio (P/e) of 10 and a rib height-to-hydraulic diameter ratio (e/Dh) range of 0.100 to 0.058 for AR 1:1 to 1:6, respectively. The experiments span a Reynolds number range of 4,000 to 130,000 based on the passage hydraulic diameter. While this experiment utilizes a basic layout similar to previous research, it is the first to run an aspect ratio as large as 1:6, and it also pushes the Reynolds number to higher values than were previously available for the 1:2 aspect ratio. The results demonstrate that while the normalized Nusselt number for the AR 1:2 configuration changes linearly with Reynolds number up to 130,000, there is a significant change in flow behavior between Re = 25,000 and Re = 50,000 for the aspect ratio 1:6 case. This suggests that while it may be possible to interpolate between points for different flow conditions, each geometric configuration must be investigated independently. The results show the highest heat transfer and the greatest heat transfer enhancement are obtained with the AR 1:6 configuration due to greater secondary flow development for both the smooth and turbulated cases. This enhancement was particularly notable for the AR 1:6 case for Reynolds numbers at or above 50,000.

Non-Isothermal Peristaltic Flow of Newtonian Fluids in a Circular Tube

2009 ◽  
Author(s):  
M. S. Yun ◽  
B. P. Huynh
Keyword(s):  
Reynolds Number ◽  
Flow Pattern ◽  
Circular Tube ◽  
Pressure Change ◽  
Peristaltic Flow ◽  
Isothermal Flow ◽  
Newtonian Fluids ◽  
Fluid Viscosity ◽  
Fluid Properties ◽  
Isothermal Case

Non-isothermal peristaltic flow of Newtonian fluids in a circular tube is investigated numerically, using a commercial Computational Fluid Dynamics (CFD) software package. Simulation is performed over a range of Reynolds-number values, up to 1000. Temperature affects the flow field via fluid viscosity, which is assumed to decrease exponentially with temperature. Other fluid properties are assumed to be constant, and are similar to those of an oil. Allowing for temperature effects alters significantly the flow pattern and reduces pressure change. In the crest region, recirculation appears in non-isothermal flow at a much smaller Reynolds number Re than in isothermal flow. Influence of the Reynolds number itself is also reduced significantly, such that the flow pattern changes very little with increasing Re, in contrast to the isothermal case. Similarly, in non-isothermal flow, flow pattern is unchanged at different flow rate. This is also in contrast to the isothermal situation.

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.

scholarly journals Effect of the size of graded baffles on the performance of channel heat exchangers

2020 ◽  
Vol 24 (2 Part A) ◽  
pp. 767-775 ◽  
Author(s):  
Djamel Sahel ◽  
Houari Ameur ◽  
Touhami Baki
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Exchangers ◽  
Computer Code ◽  
Channel Length ◽  
Heat Transfer Characteristics ◽  
Enhancement Of Heat Transfer ◽  
Transfer Rates ◽  
Flow And Heat Transfer ◽  
Friction Factors

The baffling technique is well-known for its efficiency in terms of enhancement of heat transfer rates throught channels. However, the baffles insert is accompanied by an increase in the friction factor. This issue remains a great challenge for the designers of heat exchangers. To overcome this issue, we suggest in the present paper a new design of baffles which is here called graded baffle-design. The baffles have an up- or down-graded height along the channel length. This geometry is characterized by two ratios: up-graded baffle ratio and down-graded baffle ratio which are varied from 0-0.08. For a range of Reynolds number varying from 104 to 2 ? 104, the turbulent flow and heat transfer characteristics of a heat exchanger channel are numerically studied by the computer code FLUENT. The obtained results revealed an enhancement in the thermohydraulic performance offered by the new suggested design. For the channel with a down-graded baffle ratio equal to 0.08, the friction factors decreased by 4-8%

Spatially Resolved Heat Transfer and Friction Factors in a Rectangular Channel With 45-Deg Angled Crossed-Rib Turbulators

2003 ◽  
Vol 125 (3) ◽  
pp. 575-584 ◽  
Author(s):  
P. M. Ligrani ◽  
G. I. Mahmood
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Rectangular Channel ◽  
Test Surface ◽  
Spatially Resolved ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Smooth Channel ◽  
Rib Turbulators

Spatially resolved Nusselt numbers, spatially averaged Nusselt numbers, and friction factors are presented for a stationary channel with an aspect ratio of 4 and angled rib turbulators inclined at 45 deg with perpendicular orientations on two opposite surfaces. Results are given at different Reynolds numbers based on channel height from 10,000 to 83,700. The ratio of rib height to hydraulic diameter is .078, the rib pitch-to-height ratio is 10, and the blockage provided by the ribs is 25% of the channel cross-sectional area. Nusselt numbers are given both with and without three-dimensional conduction considered within the acrylic test surface. In both cases, spatially resolved local Nusselt numbers are highest on tops of the rib turbulators, with lower magnitudes on flat surfaces between the ribs, where regions of flow separation and shear layer reattachment have pronounced influences on local surface heat transfer behavior. The augmented local and spatially averaged Nusselt number ratios (rib turbulator Nusselt numbers normalized by values measured in a smooth channel) vary locally on the rib tops as Reynolds number increases. Nusselt number ratios decrease on the flat regions away from the ribs, especially at locations just downstream of the ribs, as Reynolds number increases. When adjusted to account for conduction along and within the test surface, Nusselt number ratios show different quantitative variations (with location along the test surface), compared to variations when no conduction is included. Changes include: (i) decreased local Nusselt number ratios along the central part of each rib top surface as heat transfer from the sides of each rib becomes larger, and (ii) Nusselt number ratio decreases near corners, where each rib joins the flat part of the test surface, especially on the downstream side of each rib. With no conduction along and within the test surface (and variable heat flux assumed into the air stream), globally-averaged Nusselt number ratios vary from 2.92 to 1.64 as Reynolds number increases from 10,000 to 83,700. Corresponding thermal performance parameters also decrease as Reynolds number increases over this range, with values in approximate agreement with data measured by other investigators in a square channel also with 45 deg oriented ribs.

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