Development-Length Requirements for Fully Developed Laminar Pipe Flow of Inelastic Non-Newtonian Liquids

2007 ◽  
Vol 129 (10) ◽  
pp. 1281-1287 ◽  
Author(s):  
R. J. Poole ◽  
B. S. Ridley
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Pipe Flow ◽  
Fluid Flows ◽  
Development Length ◽  
Simple Modification ◽  
Judicious Choice ◽  
High Reynolds ◽  
Newtonian Liquids ◽  
Power Law Index

In the current study, we report the results of a detailed and systematic numerical investigation of developing pipe flow of inelastic non-Newtonian fluids obeying the power-law model. We are able to demonstrate that a judicious choice of the Reynolds number allows the development length at high Reynolds number to collapse onto a single curve (i.e., independent of the power-law index n). Moreover, at low Reynolds numbers, we show that the development length is, in contrast to existing results in the literature, a function of power-law index. Using a simple modification to the recently proposed correlation for Newtonian fluid flows (Durst, F. et al., 2005, “The Development Lengths of Laminar Pipe and Channel Flows,” J. Fluids Eng., 127, pp. 1154–1160) to account for this low Re behavior, we propose a unified correlation for XD∕D, which is valid in the range 0.4<n<1.5 and 0<Re<1000.

Development Length Requirements for Fully Developed Laminar Pipe Flow of Yield Stress Fluids

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
R. J. Poole ◽  
R. P. Chhabra
Keyword(s):  
Reynolds Number ◽  
Yield Stress ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Development Length ◽  
Bingham Number ◽  
Nonmonotonic Function ◽  
Yield Stress Fluids ◽  
High Reynolds ◽  
Laminar Pipe Flow

In this technical brief, we report the results of a systematic numerical investigation of developing laminar pipe flow of yield stress fluids, obeying models of the Bingham-type. We are able to show that using a suitable choice of the Reynolds number allows, for high Reynolds number values at least, the development length to collapse to the Newtonian correlation. On the other hand, the development length remains a weak, nonmonotonic, function of the Bingham number at small values of the Reynolds number (Re≤40).

Simulation of Power-Law Fluid Flows in Two-Dimensional Square Cavity Using Multi-Relaxation-Time Lattice Boltzmann Method

2014 ◽  
Vol 15 (1) ◽  
pp. 265-284 ◽  
Author(s):  
Qiuxiang Li ◽  
Ning Hong ◽  
Baochang Shi ◽  
Zhenhua Chai
Keyword(s):  
Reynolds Number ◽  
Relaxation Time ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Fluid Flows ◽  
Two Dimensional ◽  
Square Cavity ◽  
Power Law Fluid ◽  
Boltzmann Method ◽  
Power Law Index

AbstractIn this paper, the power-law fluid flows in a two-dimensional square cavity are investigated in detail with multi-relaxation-time lattice Boltzmann method (MRT-LBM). The influence of the Reynolds number (Re) and the power-law index (n) on the vortex strength, vortex position and velocity distribution are extensively studied. In our numerical simulations, Re is varied from 100 to 10000, and n is ranged from 0.25 to 1.75, covering both cases of shear-thinning and shear-thickening. Compared with the Newtonian fluid, numerical results show that the flow structure and number of vortex of power-law fluid are not only dependent on the Reynolds number, but also related to power-law index.

scholarly journals INVESTIGATION OF A HYDRODYNAMIC ENTRANCE REGION FOR A POWER-LAW FLUID FLOW IN A ROUND PIPE

2020 ◽  
pp. 78-88
Author(s):  
Evgeniy I. BORZENKO ◽  
◽  
Dmitriy N. GARBUZOV ◽  
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Power Law ◽  
Simple Procedure ◽  
Mathematical Formulation ◽  
Flow Region ◽  
Inlet Section ◽  
Development Length ◽  
Flow Zone ◽  
Power Law Index

The paper presents a study of the Ostwald – de Waele fluid flow in a round pipe with a uniform velocity profile specified at the inlet section. Mathematical formulation of the problem is presented using dimensionless variables. A numerical algorithm is developed on the basis of the finite volume method and SIMPLE procedure. Parametric studies of the flow are carried out for the Reynolds number varying from 0.1 to 80 and the power-law index varying from 0.2 to 1.5. It is shown that the flow can be distinguished into a developing flow zone in the inlet boundary vicinity and a fully developed flow zone in the rest part of the flow region. Dependency diagrams are plotted for the development length depending on the power-law index and Reynolds number. The first diagram is found to be non-monotonic. The development length is shown to be almost linearly dependent on the Reynolds number in the range from 1 to 80. In the region of low Reynolds numbers, the length remains almost uniform. The agreement of the obtained numerical results with data from other studies is shown.

Flow of Power-Law Fluids Past a Rotating Cylinder At High Reynolds Numbers

2021 ◽  
Author(s):  
Pooja Thakur ◽  
Naveen Tiwari ◽  
Raj P. Chhabra
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Rotational Velocity ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Rotating Cylinder ◽  
Critical Values ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Power Law Index

Abstract In this study, a rotating cylinder is placed in a stream of shear-thinning fluids, flowing with an uniform velocity. Detailed investigations are performed for the following range of conditions: Reynolds number 100 ? Re ? 500, power-law index 0.2 ? n ? 1 and rotational velocity 0 ? ? ? 5. Flow transitions are observed from steady to unsteady at critical values of the Reynolds number, the rotational velocity, and the power-law index. Critical values of the Reynolds number Re^c have been obtained for varying levels of the rotational velocity, and the power-law index. Re^c varies non-monotonically with the rotational velocity. At a particular Reynolds number, an increase of the rotational velocity acts as a vortex suppression technique. For shear-thinning ?uids considered here, the vortex suppression occurs at a larger value of the critical rotational velocity ?^c, relative to Newtonian ?uids. For the unsteady ?ow, lift coef?cient versus time curve exhibits oscillatory behavior, and this has been used to delineate the ?ow regime as steady or unsteady ?ow. For unsteady ?ow regimes, both the amplitude of the lift coef?cient and the Strouhal number increase with increasing Reynolds numbers. The results presented in this work for such high Reynolds numbers elucidate the possible complex interplay between the kinematic and rheological parameters of non-Newtonian ?uids. This investigation also complements the currently available low Reynolds number results up to ? Re = 140.

scholarly journals Video: DNS of turbulent pipe flow at high Reynolds number

2021 ◽  
Author(s):  
Alessandro Ceci ◽  
Sergio Pirozzoli ◽  
Joshua Romero ◽  
Massimiliano Fatica ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Turbulent Pipe Flow ◽  
High Reynolds

Dynamics of Marangoni convection in radiative flow of power-law fluid with entropy optimization

2021 ◽  
pp. 2150280
Author(s):  
Hunida Malaikah ◽  
M. Ijaz Khan
Keyword(s):  
Power Law ◽  
Marangoni Convection ◽  
Mhd Flow ◽  
Transfer Characteristic ◽  
Radiation Parameter ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Newtonian Liquids ◽  
Power Law Index

The flow of non-Newtonian liquids and their heat transfer characteristic gained more importance due to their technological, industrial and in many engineering applications. Inspired by these applications, the magnetohydrodynamic (MHD) flow of non-Newtonian liquid characterized by a power-law model is scrutinized. Further, viscous dissipation, Marangoni convection and thermal radiation are taken into the account. In addition, the production of entropy is investigated as a function of temperature, velocity and concentration. For different flow parameters, the total entropy production (EP) rate is examined. The appropriate similarity transformations are used to reduce the modeled equations reduced into ordinary differential equations (ODEs). The Runge–Kutta–Fehlberg 45-order procedure is then used to solve these reduced equations numerically using the shooting technique. Results reveal that the escalating values of radiation parameter escalate the heat transference, but the contrary trend is portrayed for escalating values of power-law index. The augmented values of thermal Marangoni number decline the heat transference. The gain in values of radiation parameter progresses the entropy generation.

The effect of rigid rotation on the finite-amplitude stability of pipe flow at high Reynolds number

1984 ◽  
Vol 148 ◽  
pp. 193-205 ◽  
Author(s):  
T. R. Akylas ◽  
J.-P. Demurger
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Neutral Stability ◽  
Axisymmetric Mode ◽  
High Reynolds

A theoretical study is made of the stability of pipe flow with superimposed rigid rotation to finite-amplitude disturbances at high Reynolds number. The non-axisymmetric mode that requires the least amount of rotation for linear instability is considered. An amplitude expansion is developed close to the corresponding neutral stability curve; the appropriate Landau constant is calculated. It is demonstrated that the flow exhibits nonlinear subcritical instability, the nonlinear effects being particularly strong owing to the large magnitude of the Landau constant. These findings support the view that a small amount of extraneous rotation could play a significant role in the transition to turbulence of pipe flow.

Experimental study on high Reynolds number pipe flow

2019 ◽  
Vol 2019.68 (0) ◽  
pp. 217
Author(s):  
Kusano Eisuke ◽  
Noriyuki Furuichi ◽  
Wada Yuki ◽  
Yoshiyuki Tsuji
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
High Reynolds
Sign in / Sign up

Export Citation Format

Share Document