scholarly journals Modelling vertical concentration distributions of solids suspended in turbulent visco-plastic fluid

2021 ◽  
Vol 69 (3) ◽  
pp. 255-262
Author(s):  
Václav Matoušek ◽  
Andrew Chryss ◽  
Lionel Pullum
Keyword(s):  
Reynolds Number ◽  
Concentration Profile ◽  
Particle Motion ◽  
Turbulent Viscosity ◽  
Low Reynolds Number ◽  
Newtonian Fluids ◽  
Horizontal Pipe ◽  
Profile Model ◽  
Plastic Fluid ◽  
Tomographic Data

Abstract Vertical concentration distributions of solids conveyed in Newtonian fluids can be modelled using Rouse-Schmidt type distributions. Observations of solids conveyed in turbulent low Reynolds number visco-plastic carriers, suggest that solids are more readily suspended than their Newtonian counterparts, producing higher concentrations in the centre of the pipe. A Newtonian concentration profile model was adapted to include typical turbulent viscosity distributions within the pipe and particle motion calculated using non-Newtonian sheared settling. Predictions from this and the unmodified model, using the same wall viscosity, are compared with the chord averaged profile extracted from tomographic data obtained using a 50 mm horizontal pipe.

An experimental study of low-Reynolds-number exchange flow of two Newtonian fluids in a vertical pipe

2011 ◽  
Vol 682 ◽  
pp. 652-670 ◽  
Author(s):  
F. M. BECKETT ◽  
H. M. MADER ◽  
J. C. PHILLIPS ◽  
A. C. RUST ◽  
F. WITHAM
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Viscous Fluid ◽  
Flow Regime ◽  
Low Reynolds Number ◽  
Velocity Profiles ◽  
Newtonian Fluids ◽  
Exchange Flow ◽  
Volume Flux ◽  
Two Fluids

We present an experimental study of a buoyancy-driven, low-Reynolds-number (Re < 1) exchange flow of two Newtonian fluids in a vertical cylindrical pipe (length 1 m and diameter 38.4 mm) connecting two fluid reservoirs. The denser, more viscous fluid was golden syrup and the less dense, less viscous fluid was a golden syrup–water solution; the ratio of the viscosities of the two fluids (β) ranged from 2 to 1180. Flows were initiated by removing a bung in the base of the upper reservoir or sliding out a gate positioned at the top, middle or bottom of the pipe. We observe the flows over long time durations (up to 356 h), and define the development of the flow with reference to a non-dimensional time (τ). The initial transient development of the flow was dependent on which of the two fluids initially filled the pipe, but this did not systematically affect the flow regime observed at τ ≫ 1. Two distinct flow regimes were observed: axisymmetric core-annular flow (CAF), in which the less viscous fluid occupies a cylindrical core and the denser fluid flows downwards in an annulus, and side-by-side (SBS) flow where both fluids are in contact with the pipe and there is a single interface between them. CAF formed at β ≥ 75 and SBS flow at β ≤ 117. In several experiments, for 5 ≤ β ≤ 59, a slowly developing transitional SBS (TSBS) flow was observed where SBS flow and CAF occurred simultaneously with SBS in the lower portion of the pipe; SBS existed throughout most of the pipe and in one case grew with time to entirely fill the pipe. Velocity profiles determined by tracking tracer particles show that the observed CAFs are adequately described by the formulation of Huppert & Hallworth (J. Fluid Mech., vol. 578, 2007, pp. 95–112). Experimental SBS velocity profiles are not well produced by the formulation of Kerswell (J. Fluid Mech., 10.1017/jfm.2011.190), possibly because the latter is restricted to flows whose cross-section has an interface of constant curvature. Despite the variations in flow regime, volume fluxes can be described by a power-law function of β, Q1 = 0.059 β−0.74. A comparison of experimental data with the theoretical approaches of Huppert Hallworth (2007) and Kerswell (2011) indicates that fluids are not arranged in the regime that maximises volume flux (e.g. SBS or CAF), nor do they adopt the geometry that maximises volume flux within that particular regime.

scholarly journals Numerical Simulation of a Pseudo Plastic Fluid Through Sudden Enlargement

2019 ◽  
Vol 01 (01) ◽  
pp. 92-98 ◽  
Author(s):  
Djamel Belatrache ◽  
Abdelkader HARROUZ ◽  
Abdelwahed Abderrahmane ◽  
Saadeddine MANAA
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Velocity Profile ◽  
Physical Characteristic ◽  
Recirculation Zone ◽  
Newtonian Fluids ◽  
Stabilizing Effect ◽  
Plastic Fluid ◽  
Sudden Enlargement

This paper presents the flow of non-Newtonian fluids through sudden enlargements. The calculations are done by a code with the finished volumes. The stabilizing effect of the physical characteristic of the fluid is taken into consideration. In addition, we set as objective the influence of the main parameters like the index of structure of the fluid, the Reynolds number and the aspect ratio of the widening, on the evolution of the velocity profile, the length of establishment of the flow in front of the enlargement as well as on the recirculation zone. The results obtained were confronted whenever possible with results from other literature.

Proppant Settling Correlations for Non-Newtonian Fluids Under Static and Dynamic Conditions

1982 ◽  
Vol 22 (02) ◽  
pp. 164-170 ◽  
Author(s):  
Subhash N. Shah
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Particle Motion ◽  
Settling Velocity ◽  
Fluid Model ◽  
Reynolds Numbers ◽  
Newtonian Fluids ◽  
Velocity Data ◽  
Proppant Transport ◽  
Fracturing Fluids

Abstract This paper presents a new approach for analysis of proppant sealing data in non-Newtonian pseudoplastic fracturing fluids and develops drag coefficient correlations as a function of fluid model parameter n', Results of experiments with these fluids under static as well as dynamic conditions are discussed. A wide range of n' and particle Reynolds number is investigated. It is shown that at low-particle Reynolds numbers the fluid model parameter n' has a significant effect on proppant settling velocity. This effect diminishes at higher particle Reynolds numbers. The dynamic settling velocity data agree reasonably well with the correlations developed from static velocity data. Further, experimental results of earlier investigations agree well with the correlations of this study. Introduction Many examples of flow around submerged objects appear in engineering work. In the oilfield industry, one example is particle or proppant transport in a fracture during hydraulic fracturing. Hydraulic fracturing has been in use commercially for 30 years. The formations are fractured hydraulically by pumping a slurry of viscous fracturing fluid and proppant at high pressures. The purpose of the proppant is to hold the fracture open at the end of the treatment. The production increase resulting from the treatment depends on fracture conductivity and final proppant distribution. Knowledge of settling velocity of a single particle in the fracture and streamlines around the particle is of great value in understanding the complex transport process leading to a particular proppant distribution in the fracture. A thorough understanding of proppant transpose would help design better fracturing treatments. The purpose of this investigation is two fold:to gather experimental data of proppant settling velocity in several non-Newtonian fracturing fluids, andto develop correlations between drag coefficient and particle Reynolds number. These correlations later can be used to predict the settling velocity of a particular particle in a non-Newtonian fracturing fluid of known rheological properties. Experience has shown that most fracturing fluids exhibit highly non-Newtonian fluid characteristics. They may possess completely different properties under shear than when at rest. For simplicity, most of the studies reported in the literature are undertaken by dropping proppant in a stagnant fluid. In the actual fracturing process, however, the proppant is settling while fluid is moving in the fracture. Thus, to validate the correlations derived from the settling velocity data in a stagnant fluid, some dynamic experiments also are conducted. Literature Review The subject of particle motion in Newtonian fluids has been studied extensively by many investigators. In contrast, very little has been accomplished in the case of particle motion in non-Newtonian fluids, particularly on proppant transport in the fracture. Most recently, a preliminary work on dynamic proppant transport in fracturing gels has been reported by Hannah and Harrington. Experiments were conducted with a concentric cylinder tester to measure the fall rate of proppant in non-Newtonian fracturing gels. The test device used was similar to one reported previously by Novotny. Their experimental data did not agree with the theoretical predictions, and no explanation has been given for the discrepancy. Later, using a similar tester, Harrington et al. measured the settling rate of proppant in cross-linked fracturing gels. SPEJ P. 164^

An Improved Low-Reynolds-Number k – ϵ Model for Aerodynamic Flows

2016 ◽  
Vol 17 (2) ◽  
pp. 99-112
Author(s):  
Yang Zhang ◽  
Jun-Qiang Bai ◽  
Jing-Lei Xu ◽  
Xing-Si Han ◽  
Peng Wang
Keyword(s):  
Reynolds Number ◽  
Reynolds Shear Stress ◽  
Turbulent Viscosity ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Adverse Pressure Gradient ◽  
Turbulent Structure ◽  
Structure Parameter ◽  
New Model ◽  
Low Reynolds

AbstractA low-Reynolds-number k – ∈ model based on a new turbulent structure parameter ${a_{1\_{\rm{NC}}}}\left({= - \left| {{{\overline {u^' v^'}} \mathord{\left/ {\vphantom {{\overline {u^' v^'}} k}} \right.} k}} \right|} \right)$ and a recalibrated wall-damping function (WDF) ${f_\mu}$ is proposed and evaluated. In order to account for the effect of variation of Reynolds number on maximum value of the WDF, a ratio between two different turbulent Reynolds numbers is involved in the WDF. In addition, instead of using a constant ratio between Reynolds shear stress and turbulent kinetic energy, e. g. a1 = 0.31, the new turbulent structure parameter a1_NC is proposed based on several sets of direct numerical simulation (DNS) data. The deduction of near-wall asymptotic behavior is performed to prove that the new proposed model can yield a correct wall value for turbulent viscosity. The new model is validated with several well-documented flow cases, and the yielding results are in good agreement with experimental data. Moreover, three frequently used turbulence models are also involved into the comparisons and the results indicate that the new model offers remarkable improvement on the nonequilibrium flows, e. g. separated and adverse pressure gradient flows.

scholarly journals OSCILLATORY BOTTOM BOUNDARY LAYER BY LOW-REYNOLDS NUMBER TURBULENCE MODEL

1988 ◽  
Vol 1 (21) ◽  
pp. 55
Author(s):  
Toshiyuki Asano ◽  
Hitomi Goda ◽  
Yuichi Iwagaki
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Turbulence Model ◽  
Turbulent Viscosity ◽  
Low Reynolds Number ◽  
Viscous Sublayer ◽  
Mean Velocity ◽  
Bottom Boundary ◽  
Bottom Boundary Layers ◽  
Low Reynolds

Characteristics of mean velocity and turbulence properties in oscillatory bottom boundary layers are investigated with low- Reynolds number turbulence model. Since this model is capable to describe the flow field close to the bottom, special attentions are paid on the characteristics of the viscous sublayer. Several interesting results, which coincide with or differ from existing knowledge on steady bottom boundary layers, are presented in paticular on the mean velocity profile, turbulent viscosity coefficient and growth of the viscous sublayer.

Sign in / Sign up

Export Citation Format

Share Document