One-Dimensional Simulation of Transient Flows in Non-Newtonian Fluids

An unstable flow of non-Newtonian fluid, with friction in a pipe is studied, describing the water hammer phenomenon. The equations of the problem are given, then solved by a numerical approach. The non-Newtonian behavior of the fluid, as well as the effect of the coefficient of friction which represents an additional mechanism of energy dissipation are investigated. The 1D and 2D problem is used simultaneously, based on the Runge-kutta method for the descritization in time, Finite differences, Characteristics for the descritization in space. The results of this article show by verifying with experience that these methods used, in addition to being simple, are also effective and give reasonable results.

show abstract

“…In the transient pipeline flow (Figure 1), the continuity and momentum global equations are given by the following system (Eq. ( 1)) [27]:…”

Section: Methodology 21 Governing Equations 211 Global Systemmentioning

confidence: 99%

Investigation of Non-Newtonian Fluid Behavior and Coefficient of Friction in Water Hammer Phenomena

Achak

Rkibi

Bahrar³

et al. 2021

ARFMTS

View full text Add to dashboard Cite

show abstract

“…Assuming negligible fluid and particle inertia, the fluid dynamics of the investigated system is governed by the following mass and momentum balance equations [10,[14][15][16], as given in equations 7-10, where u -velocity; τ -shear stress tensor; p -pressure; I -unit tensor (3x3); η -viscosity; σ -strain rate tensor, and T means that velocity vector is transposed.…”

Section: Shear-thinning Model and Friction Factor In Extrusion-based 3d Bioprintingmentioning

confidence: 99%

Experimental Study and Analytical model of Shear Thinning in 3D Bioprinting of Gelatin

Busarac¹,

Jovanović²,

Njezić³

et al. 2020

Tribol. Ind.

View full text Add to dashboard Cite

This paper presented extrusion-based 3D bioprinting of gelatin hydrogel and optimisation of material properties and process parameters, in order to improve printability of hydrogel. Gelatin hydrogel was prepared by mixing it with water in concentration of 13.04 wt%. Dimensional accuracy of the bioprinting was studied and significant changes in comparison with designed geometry were noted. Gelatin hydrogel made only with water showed inadequate thixotropy for extrusion based bioprinting and poor mechanical properties of the printed sample, and needs additional constituents to enable good printability with satisfying dimensional accuracy. We presented parameter optimisation index (POI), shear thinning model and friction factor of gelatin hydrogel by using analytical approach. Friction factor of the gelatin hydrogel during bioprinting was 0.268 10 -5 . Analytical models of shear thinning and friction factor were in consistence with experimental data, and indicated that such approach can be used in optimisation of bioprinting parameters and material properties.

show abstract

“…Hossam [14] first used the wave characteristic line method to numerically simulate the transient flow in a viscoelastic pipe, re-derived the Joukowsky equation of the elastic pipe, and derived the quadratic equation of energy conservation in the viscoelastic pipe. Khamoushi [15] proposed a one-dimensional model of transient flow in non-Newtonian fluids, using Zielke's unsteady friction solution for power law fluids and cross fluids. The time increment updated the weight function of the Zielke model.…”

Section: Introductionmentioning

confidence: 99%

Establishment and Solution of Four Variable Water Hammer Mathematical Model for Conveying Pipe

Duan

Jin³

2022

Energies

View full text Add to dashboard Cite

Transient flow in pipe is a much debated topic in the field of hydrodynamics. The water hammer effect caused by instantaneous valve closing is an important branch of transient flow. At present, the fluid density is regarded as a constant in the study of the water hammer effect in pipe. When there is gas in the pipe, the variation range of density is large, and the pressure-wave velocity should also change continuously along the pipe. This study considers the interaction between pipeline fluid motion and water hammer wave propagation based on the essence of water hammer, with the pressure, velocity, density and overflow area set as variables. A new set of water hammer calculation equations was deduced and solved numerically. The effects of different valve closing time, flow rate and gas content on pressure distribution and the water hammer effect were studied. It was found that with the increase in valve closing time, the maximum fluctuating pressure at the pipe end decreased, and the time of peak value also lagged behind. When the valve closing time increased from 5 s to 25 s, the difference in water hammer pressure was 0.72 MPa, and the difference in velocity fluctuation amplitude was 0.076 m/s. The findings confirm: the greater the flow, the greater the pressure change at the pipe end; the faster the speed change, the more obvious the water hammer effect. High-volume flows were greatly disturbed by instantaneous obstacles such as valve closing. With the increase of time, the pressure fluctuation gradually attenuated along the pipe length. The place with the greatest water hammer effect was near the valve. Under the coupling effect of time and tube length, the shorter the time and the shorter the tube length, the more obvious the pressure fluctuation. Findings also confirm: the larger the gas content, the smaller the fluctuation peak of pipe end pressure; the longer the water hammer cycle, the smaller the pressure-wave velocity. The actual pressure fluctuation value was obviously lower than that without gas, and the size of the pressure wave mainly depended on the gas content. When the gas content increased from 1% to 9%, the difference of water hammer pressure was 0.41 MPa.

show abstract

One-Dimensional Simulation of Transient Flows in Non-Newtonian Fluids

Cited by 10 publications

References 32 publications

Investigation of Non-Newtonian Fluid Behavior and Coefficient of Friction in Water Hammer Phenomena

Investigation of Non-Newtonian Fluid Behavior and Coefficient of Friction in Water Hammer Phenomena

Experimental Study and Analytical model of Shear Thinning in 3D Bioprinting of Gelatin

Establishment and Solution of Four Variable Water Hammer Mathematical Model for Conveying Pipe

Contact Info

Product

Resources

About