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.

Numerical simulation of pressure drop for three-dimensional rectangular microchannels

2018 ◽  
Vol 35 (6) ◽  
pp. 2234-2254 ◽  
Author(s):  
Zhipeng Duan ◽  
Peng Liang ◽  
Hao Ma ◽  
Niya Ma ◽  
Boshu He
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Three Dimensional ◽  
Numerical Data ◽  
Rectangular Microchannels ◽  
Content Type ◽  
Aspect Ratios ◽  
Rectangular Channels

Purpose The purpose of this paper is to numerically investigate the flow characteristics and extend the data of friction factor and Reynolds number product of hydrodynamically developing laminar flow in three-dimensional rectangular microchannels with different aspect ratios. Design/methodology/approach Using a finite-volume approach, the friction factor characteristics of Newtonian fluid in three-dimensional rectangular ducts with aspect ratios from 0.1 to 1 are conducted numerically under no-slip boundary conditions. A simple model that approximately predicts the apparent friction factor and Reynolds number product fappRe is referenced as a semi-theoretical fundamental analysis for numerical simulations. Findings The accurate and reliable results of fappRe are obtained, which are compared with classic numerical data and experimental data, and the simple semi-theoretical model used and all comparisons show good agreement. Among them, the maximum relative error with the classic numerical data is less than 3.9 per cent. The data of fappRe are significantly extended to other different aspect ratios and the novel values of fappRe are presented in the tables. The characteristics of fappRe are analyzed as a function of a non-dimensional axial distance and the aspect ratios. A more effective and accurate fourth-order fitting equation for the Hagenbach's factor of rectangular channels is proposed. Originality/value From the reliable data, it is shown that the values of fappRe and the model can be references of pressure drop and friction factor for developing laminar flow in rectangular channels for researchers and engineering applications.

Turbulent Flow in D-Type Corrugated Pipes: Flow Pattern and Friction Factor

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
H. Stel ◽  
A. T. Franco ◽  
S. L. M. Junqueira ◽  
R. H. Erthal ◽  
R. Mendes ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Pattern ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Important Change ◽  
Groove Width ◽  
Simple Method ◽  
Pressure Drag ◽  
Aspect Ratios

Turbulent flow in d-type corrugated pipes of various aspect ratios has been numerically investigated in terms of flow pattern and friction factor, for Reynolds numbers ranging from 5000 to 100,000. The present numerical model was verified by comparing the friction factor with experimental and numerical results from the literature. The numerical analysis suggested that d-type behavior exists for groove aspect ratios up to w/k = (groove width/rib height) = 2 independent of the pitch. However, for a ratio of w/k = 3 an important change in the flow pattern occurs so that the pressure drag exerted by the groove walls becomes important. It is shown that the friction factor is independent of the groove height as long as the flow is similar to a flow in a d-type corrugated pipe. Moreover, the friction factor curve for d-type pipes shows a logarithmic behavior as function of the Reynolds number, so that a simple method can be used to derive an expression for the friction factor as a function of the Reynolds number and the relative groove width only. The results may be useful to engineering projects that require a better prediction of the friction factor in d-type corrugated pipes.

Turbulent Flow in a Microchannel With Surface Patterned Microribs Oriented Parallel to the Flow Direction

2007 ◽  
Author(s):  
K. Jeffs ◽  
D. Maynes ◽  
B. W. Webb
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Solid Wall ◽  
Flow Direction ◽  
Flowing Liquid ◽  
Free Region ◽  
Flow Through ◽  
Oriented Parallel

Due to the increase of application in a number of emerging technologies, a growing amount of research has focused on the reduction of drag in microfluidic transport. A novel approach reported in the recent literature is to fabricate micro-ribs and cavities in the channel wall that are then treated with a hydrophobic coating. Such surfaces have been termed super- or ultrahydrophobic and the contact area between the flowing liquid and the solid wall is greatly reduced. Previous numerical studies have focused primarily on the laminar flow through such channels with reductions in the flow resistance as large as 87% being predicted and observed. There has been little work however, that has explored the physics and the potential drag reduction associated with turbulent flow through microchannels with ultrahydrophobic walls. This paper reports the results of a numerical investigation of the turbulent flow in a parallel plate microchannel with ultrahydrophobic walls. In this study microribs and cavities are oriented parallel to the flow direction. The channel walls are modeled in an idealized fashion, with the shape of the liquid-vapor meniscus approximated as flat. A k-ω turbulence modeling scheme is implemented for closure to the turbulent RANS equations. Results are presented for the friction factor Reynolds number product as a function of relevant governing dimensionless parameters. The Reynolds number was varied from 2,000 to 10,000. Results show, as with the laminar flow case, that as the shear-free region increases the friction factor-Reynolds number product decreases. The observed reduction, however, was found to be significantly greater under turbulent flow conditions than for the laminar flow scenarios.

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.

Laminar Flow Heat Transfer and Pressure Drop in a Circular Tube Having Wire-Coil and Helical Screw-Tape Inserts

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Pratap Kumar Rout ◽  
Sujoy Kumar Saha
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Friction Factor ◽  
Circular Tube ◽  
Inertia Force ◽  
Large Reynolds Number ◽  
Nusselt Numbers ◽  
Wire Coil ◽  
Flow Through

The experimental friction factor and Nusselt number data for laminar flow through a circular duct having wire-coil and helical screw-tape inserts have been presented. Peripherally and axially local temperatures on the duct outside wall have been measured. The temperature drop across the duct wall has been calculated to obtain the duct inside wall temperatures. Peripherally averaged and axially local temperatures have been used to get axially local Nusselt numbers. These axially local Nusselt numbers have been averaged over the whole length of the duct to get the mean Nusselt number. Predictive friction factor and Nusselt number correlations developed by log-regression analysis have also been presented. Nusselt number correlation takes care of the thermal development length represented by the Graetz number, swirl and inertia force due to forced convection at large Reynolds number, buoyancy force due to natural convection at low Reynolds number represented by Rayleigh number and the geometrical parameters of wire-coil and helical screw-tape inserts. The thermohydraulic performance has been evaluated. The helical screw-tape inserts in combination with wire-coil inserts perform better than the individual enhancement technique acting alone for laminar flow through a circular tube up to a certain value of fin parameter.

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]

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.

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.

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