Entrance pressure losses for power-law fluid at small Reynolds number

1987 ◽  
Vol 26 (1) ◽  
pp. 92-95 ◽  
Author(s):  
C. A. Hieber
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Small Reynolds Number ◽  
Power Law Fluid ◽  
Pressure Losses ◽  
Entrance Pressure

scholarly journals Deformation of a Capsule in a Power-Law Shear Flow

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Fang-Bao Tian
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Lattice Boltzmann Method ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Immersed Boundary ◽  
Power Law Fluid ◽  
Boltzmann Method ◽  
Power Law Index

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

scholarly journals On Taylor dispersion in oscillatory channel flows

2006 ◽  
Vol 462 (2076) ◽  
pp. 3501-3509 ◽  
Author(s):  
Kalvis M Jansons
Keyword(s):  
Reynolds Number ◽  
Phase Difference ◽  
Computer Algebra ◽  
Power Law ◽  
Poiseuille Flow ◽  
Fluid Flows ◽  
Taylor Dispersion ◽  
Power Law Fluid ◽  
Oscillatory Flows ◽  
Oscillatory Power

We revisit Taylor dispersion in oscillatory flows at zero Reynolds number, giving an alternative method of calculating the Taylor dispersivity that is easier to use with computer algebra packages to obtain exact expressions. We consider the effect of out-of-phase oscillatory shear and Poiseuille flow, and show that the resulting Taylor dispersivity is independent of the phase difference. We also determine exact expressions for several examples of oscillatory power-law fluid flows.

Turbulent Flow Simulation of Power-Law Fluid in Annular Channel

2020 ◽  
Author(s):  
Andrey Gavrilov ◽  
Yaroslav Ignatenko ◽  
Oleg Bocharov ◽  
Roger Aragall
Keyword(s):  
Steady State ◽  
Power Law ◽  
Drill Pipe ◽  
Three Dimensional ◽  
Annular Channel ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Power Law Fluid ◽  
Pressure Losses ◽  
Viscous Shear

Abstract Transient three-dimensional flow simulations of power–law fluid in a long axisymmetric annular channel considering 0.5 diameter ratio were performed. An in–house CFD code considering URANS (Unsteady Reynolds Averaged Navier–Stokes), 2D RANS (steady-state axially uniform 2D RANS) and LES (Large Eddy Simulation) approaches were compared to perform the simulations. Flow structure was analyzed. Numerical experiments showed that rotation of the inner cylinder (drill pipe) leads to two effects: decrease of apparent viscosity in the region close to the rotating cylinder, thus decreasing viscous shear stresses; development of secondary vorticity structures increasing energy loss. First mechanism decreases pressure losses and dominates when Re < 300. At Re ∼ 300 the mechanisms compete with each other and pressure losses depends on power–law index n. At Re > 300 mechanism of second vortex structured dominates and increases pressure loss with rotation. Pressure losses for two-dimensional steady-state and three-dimensional transient problems were compared. Pressure losses using a two-dimensional approach can be underestimated by up to 30%.

Power-Law Fluid Flow Passing Two Square Cylinders in Tandem Arrangement

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Izadpanah Ehsan ◽  
Sefid Mohammad ◽  
Nazari Mohammad Reza ◽  
Jafarizade Ali ◽  
Ebrahim Sharifi Tashnizi
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Newtonian Fluids ◽  
Power Law Fluid ◽  
Tandem Arrangement ◽  
Square Cylinders ◽  
Shear Thickening Fluids ◽  
Power Law Index

Two-dimensional laminar flow of a power-law fluid passing two square cylinders in a tandem arrangement is numerically investigated in the ranges of 1< Re< 200 and 1 ≤ G ≤ 9. The fluid viscosity power-law index lies in the range 0.5 ≤ n ≤ 1.8, which covers shear-thinning, Newtonian and shear-thickening fluids. A finite volume code based on the SIMPLEC algorithm with nonstaggered grid is used. In order to discretize the convective and diffusive terms, the third order QUICK and the second-order central difference scheme are used, respectively. The influence of the power-law index, Reynolds number and gap ratio on the drag coefficient, Strouhal number and streamlines are investigated, and the results are compared with other studies in the literature to validate the methodology. The effect of the time integration scheme on accuracy and computational time is also analyzed. In the ranges of Reynolds number and power-law index studied here, vortex shedding is known to occur for square cylinders in tandem. This study represents the first systematic investigation of this phenomenon for non-Newtonian fluids in the open literature. In comparison to Newtonian fluids, it is found that the onset of leading edge separation occurs at lower Reynolds number for shear-thinning fluids and is delayed to larger values for shear-thickening fluids.

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 Numerical simulation of a non-isothermal power-law fluid flow in a channel with abrupt contraction

2019 ◽  
Author(s):  
К.Е. Рыльцева ◽  
Г.Р. Шрагер
Keyword(s):  
Fluid Flow ◽  
Viscous Dissipation ◽  
Power Law ◽  
Two Dimensional ◽  
Power Law Fluid ◽  
Local Pressure ◽  
Pressure Losses ◽  
Flow Through ◽  
Abrupt Contraction ◽  
Power Law Index

Проводится исследование ламинарного стационарного неизотермического течения степенной жидкости в цилиндрическом канале с внезапным сужением. Формулируется математическая модель течения, которая включает уравнения гидродинамики, записанные в переменных функция токавихрь, и уравнение энергии. Реологические свойства жидкости описываются степенным законом Оствальда де Ваале, в модифицированной форме которого учитывается зависимость эффективной вязкости от температуры. Для решения задачи используется метод установления с последующей реализацией конечноразностного метода на основе схемы переменных направлений. Выполняется оценка влияния вязкой диссипации на структуру потока псевдопластичной, ньютоновской и дилатантной жидкостей. Демонстрируются поля температуры и эффективной вязкости. Приводятся результаты параметрического исследования коэффициента местного гидравлического сопротивления. Viscous fluid flow through a sudden contraction is frequently encountered in a number of industrial equipment dealing with processing and transporting of liquid materials. Generally, the fluid exhibits non-Newtonian behavior and flows under non-isothermal conditions. Such flow is characterized by specific structure, viscous dissipation, and local pressure losses. In this work, a numerical solution to the problem of a non-isothermal power-law fluid flow through a two-to-one axisymmetric abrupt contraction is presented. Mathematical model includes the momentum, continuity and energy equations written in terms of stream function, vorticity and temperature variables. The rheological behavior of the fluid is specified by the Ostwald-de Waele power law. The proposed flow model accounts for viscous dissipation and temperature-dependent rheological properties. To solve the problem, the relaxation method is used, followed by the implementation of the finitedifference method based on the scheme of alternative directions. The equations in a discrete form are solved using the tridiagonal matrix algorithm. It is found that the flow includes both one-dimensional and two-dimensional flow regions. The lengths of these regions are studied versus the Reynolds number, the Peclet numder, and power-law index. Comparing isothermal and non-isothermal cases, it is revealed that an increase in the power-law index leads to a decrease in the downstream two-dimensional zone in the first case, and, in contrast, it provides a significant increase in the second case. The viscosity and temperature distributions are presented to show the effect of the Peclet number for pseudoplastic, Newtonian, and dilatant fluids. The parametric investigation of the local pressure losses is implemented in a wide range of the main parameters.

Pressure Losses of Power-Law Fluid Flow through an Axisymmetric Sudden Contraction

2016 ◽  
Vol 685 ◽  
pp. 47-50 ◽  
Author(s):  
Evgeny Borzenko ◽  
Kira Boyarkina ◽  
Gennady R. Shrager
Keyword(s):  
Fluid Flow ◽  
Power Law ◽  
Relaxation Method ◽  
Local Resistance ◽  
Power Law Fluid ◽  
Mathematical Statement ◽  
Pressure Losses ◽  
Contraction Ratio ◽  
Flow Through ◽  
Resistance Coefficients

In this paper the laminar stationary power-law fluid flow through an axisymmetric pipe contraction is investigated. The mathematical statement of the problem is formulated using stream function and vorticity variables. For obtaining a stationary solution the relaxation method with following realization of numerical algorithm based on finite difference alternative directions scheme is utilized. Implemented parametrical investigations allow obtaining the dependence of local resistance coefficients on Reynolds number, nonlinearity degree and piping contraction ratio.

Pressure Losses in Power-Law Fluid Flow through a Tube of Variable Cross-Section

2021 ◽  
Vol 56 (1) ◽  
pp. 1-9
Author(s):  
E. I. Borzenko ◽  
I. A. Ryl’tsev ◽  
G. R. Schrager
Keyword(s):  
Fluid Flow ◽  
Cross Section ◽  
Power Law ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Power Law Fluid ◽  
Pressure Losses ◽  
Flow Through
Sign in / Sign up

Export Citation Format

Share Document