New power-law scaling for friction factor of extreme Reynolds number pipe flows

2020 ◽  
Vol 32 (9) ◽  
pp. 095121
Author(s):  
H. R. Anbarlooei ◽  
D. O. A. Cruz ◽  
F. Ramos
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Power Law ◽  
Pipe Flows

Analytical Solution for Newtonian Laminar Flow Through the Concave and Convex Ducts

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
M. Firouzi ◽  
S. H. Hashemabadi
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Friction Factor ◽  
Cross Section ◽  
Cross Sections ◽  
Fully Developed Flow ◽  
Pipe Flows ◽  
Dimensionless Velocity ◽  
Flow Through ◽  
Fanning Friction Factor

In this paper, the motion equation for steady state, laminar, fully developed flow of Newtonian fluid through the concave and convex ducts has been solved both numerically and analytically. These cross sections can be formed due to the sedimentation of heavy components such as sand, wax, debris, and corrosion products in pipe flows. The influence of duct cross section on dimensionless velocity profile, dimensionless pressure drop, and friction factor has been reported. Finally based on the analytical solutions three new correlations have been proposed for the product of Reynolds number and Fanning friction factor (Cf Re) for these geometries.

A Rational Friction Factor Correlation for Laminar Fully-Developed Pipe Flows of Shear-Thinning Non-Newtonian Fluids

2021 ◽  
Author(s):  
Robert Brewster
Keyword(s):  
Shear Rate ◽  
Friction Factor ◽  
Power Law ◽  
Fluid Model ◽  
Shear Thinning ◽  
Newtonian Fluids ◽  
Cross Model ◽  
Pipe Flows ◽  
Design Calculations ◽  
Friction Factor Correlation

Abstract A friction factor correlation for laminar, hydrodynamically fully-developed pipe flows of shear-thinning non-Newtonian fluids is derived through analysis and asymptotic considerations. The specific non-Newtonian fluid model used is the Extended Modified Power Law (EMPL) model, which is functionally equivalent to the Cross model. The EMPL model spans the entire shear rate range from the low to the high shear rate Newtonian regions, and includes the intermediate shear rate power law region. The friction factor correlation has an explicit form and is a function of three dimensionless parameters, making it well-suited to design calculations. The overall accuracy of the correlation is 6.6%, though it is much better in most cases. Graphical results for the correlation, and deviations with respect to high-accuracy numerical calculations are presented and discussed.

Transition Criteria for Laminar to Turbulent Flow for Yield Power Law (YPL) Fluids Based on Stability Analysis

2013 ◽  
Author(s):  
Goktug Kalayci ◽  
Evren M. Ozbayoglu ◽  
Stefan Z. Miska ◽  
Mengjiao Yu ◽  
Nicholas Takach ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Yield Stress ◽  
Flow Regime ◽  
Power Law ◽  
Laminar Flow Regime

It is well known that a Newtonian fluid with the presence of solid particles in suspension behaves non-Newtonian. Higher the solid content, more significant the yield stress of the fluid. Determination of the hydraulic behavior of fluids having a significant yield stress is a challenging task. For engineering purposes, pressure drop within the system, during pipeline transportation, has to be estimated carefully and accurately. Flow regime plays a vital role during hydraulic calculations. The inaccurate determination of flow regime can lead us to large errors in frictional pressure drop calculations and ultimately leads to error in designing and flow assurance point of view, since hydraulic calculations are including a friction factor term, which is a direct function of flow regime. In general, Reynolds number is the main parameter used by the industry for determining the flow regime, and the friction factor. This approach works reasonably accurate for Newtonian fluids. However, as the yield stress of the fluid increases, this conventional technique for determining the flow regime is not as accurate. Although many approaches have been introduced for estimating the flow regime for non-Newtonian fluids, there exists a lack of information and confidence of such predictions for fluids having high yield stress, such as Yield Power Law (YPL) fluids (i.e., Herchel-Bulkley). (1)τ=τy+Kγm This study presents an analytical solution for predicting the transition from laminar to non-laminar flow regime based on Ryan & Johnson’s approach using the stability analysis and equation of motion for YPL fluids. Comparing with the experimental results for YPL fluids under different flow conditions, including laminar and non-laminar flow regimes, show that presented approach gives a better estimation of the transition from laminar to non-laminar flow regime than conventional Reynolds number approach. In some cases, it is observed that although the Reynolds number is high, flow is still laminar, which is predicted accurately using the presented model. This study provides a higher accuracy in estimating the flow regime, which leads to a higher confidence in hydraulic designs and determining limitations of the system in concern.

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.

Numerical Study of Convective Heat Transfer From Expanding Annular Pipe Flows

2016 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Diameter Ratio ◽  
Wall Heat Transfer ◽  
Reattachment Point ◽  
Transfer Rates ◽  
Pipe Flows ◽  
Annular Pipe

Convective heat transfer from suddenly expanding annular pipe flows are numerically investigated within the steady laminar flow regime. A parametric study is performed to reveal the influence of the annular diameter ratio, k, the Prandtl number, Pr, and the Reynolds number, Re, over the following range of parameters: k = {0, 0.5, 0.7}, Pr = {0.7, 1, 7, 100}, and Re = {25, 50, 100}. Heat transfer enhancement downstream of the expansion plane is only observed for Pr > 1. Peak wall-heat-transfer-rates always appear downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e. k = 0. However, for suddenly expanding annular pipe flows, i.e., k = 0.5 and 0.7, peak wall-heat-transfer-rates always appear upstream of the flow reattachment point. The observed heat transfer augmentation is more dramatic for suddenly expanding annular flows, in comparison with the one observed for suddenly expanding pipe flows. For a given annular diameter ratio and Reynolds number, increasing the Prandtl number, always results in higher wall-heat-transfer-rates downstream the expansion plane.

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

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.

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