An Experimental Investigation for Bubble Rising in Non-Newtonian Fluids and Empirical Correlation of Drag Coefficient

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Fan Wenyuan ◽  
Ma Youguang ◽  
Jiang Shaokun ◽  
Yang Ke ◽  
Li Huaizhi
Keyword(s):  
Reynolds Number ◽  
Aqueous Solutions ◽  
Drag Coefficient ◽  
Bubble Diameter ◽  
Video Camera ◽  
Solution Concentration ◽  
Terminal Velocity ◽  
Newtonian Fluids ◽  
Rising Bubble ◽  
Moderate Reynolds Number

The velocity, shape, and trajectory of the rising bubble in polyacrylamide (PAM) and carboxymethylcellulose (CMC) aqueous solutions were experimentally investigated using a set of homemade velocimeters and a video camera. The effects of gas the flowrate and solution concentration on the bubble terminal velocity were examined respectively. Results show that the terminal velocity of the bubble increases with the increase in the gas flowrate and the decrease in the solution concentration. The shape of the bubble is gradually flattened horizontally to an ellipsoid with the increase in the Reynolds number (Re), Eötvös number (Eo), and Morton number (Mo). With the increase in the Re and Eo, the rising bubble in PAM aqueous solutions begin to oscillate, but there is no oscillation phenomena for CMC aqueous solutions. By dimensional analysis, the drag coefficient of a single bubble in non-Newtonian fluids in a moderate Reynolds number was correlated as a function of Re, Eo, and Archimedes number (Ar) based on the equivalent bubble diameter. The predicted results by the present correlation agree well with the experimental data.

Settling Behavior of Particles in Bubble Containing Newtonian Fluids: Experimental Study and Model Development

2021 ◽  
Author(s):  
Silin Jing ◽  
Xianzhi Song ◽  
Zhaopeng Zhu ◽  
Buwen Yu ◽  
Shiming Duan
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Volume Concentration ◽  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Newtonian Fluids ◽  
Spherical Particles ◽  
Bubble Volume ◽  
Particle Reynolds Number

Abstract Accurate description of cuttings slippage in the gas-liquid phase is of great significance for wellbore cleaning and the control accuracy of bottom hole pressure during MPD. In this study, the wellbore bubble flow environment was simulated by a constant pressure air pump and the transparent wellbore, and the settling characteristics of spherical particles under different gas volume concentrations were recorded and analyzed by highspeed photography. A total of 225 tests were conducted to analyze the influence of particle diameter (1–12mm), particle density (2700–7860kg/m^3), liquid viscosity and bubble volume concentration on particle settling velocity. Gas drag force is defined to quantitatively evaluate the bubble’s resistance to particle slippage. The relationship between bubble drag coefficient and particle Reynolds number is obtained by fitting the experimental results. An explicit settling velocity equation is established by introducing Archimedes number. This explicit equation with an average relative error of only 8.09% can directly predict the terminal settling velocity of the sphere in bubble containing Newtonian fluids. The models for predicting bubble drag coefficient and the terminal settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and bubble volume concentration ranging from 3.0% to 20.0%. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate bubble drag coefficient and settling velocity in bubble containing fluids. The results of this study will provide the theoretical basis for wellbore cleaning and accurate downhole pressure to further improve the performance of MPD in treating gas influx.

Drag Coefficient and Settling Velocity of Particles in Non-Newtonian Suspensions

1987 ◽  
Vol 109 (3) ◽  
pp. 319-323 ◽  
Author(s):  
M. Y. Dedegil
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Drag Coefficient ◽  
Yield Stress ◽  
Particle Velocity ◽  
Settling Velocity ◽  
Fluid Velocity ◽  
Newtonian Fluids ◽  
Drag Forces ◽  
Physical Composition

Drag forces on bodies in non-Newtonian fluids which are to be described by using the Reynolds number should only contain forces which are associated with the fluid velocity or particle velocity. Forces due to the yield stress τ0 must be considered separately. According to its physical composition, the Reynolds number must be calculated by means of the fully representative shear stress including the yield stress τ0. Then the drag coefficient cD as a function of the Reynolds number can be traced back to that of Newtonian fluids.

scholarly journals Aerodynamic properties of lentil seeds

2015 ◽  
Vol 29 (3) ◽  
pp. 391-396 ◽  
Author(s):  
Feizollah Shahbazi ◽  
Saman Valizadeh ◽  
Ali Dowlatshah ◽  
Ezatollah Hassanzadeh
Keyword(s):  
Reynolds Number ◽  
Moisture Content ◽  
Drag Coefficient ◽  
Terminal Velocity ◽  
Mean Value ◽  
Probability Level ◽  
Solid Materials ◽  
Aerodynamic Properties ◽  
Red Variety ◽  
Mathematical Relationships

Abstract Aerodynamic properties of solid materials have long been used to convey and separate seeds and grains during post-harvest operations. The objective of this study was evaluation of the aerodynamic properties of green and red lentil seeds as a function of moisture content from 10 to 25% (w.b.). The results showed that as the moisture content increased from 10 to 25%, the terminal velocity of seeds increased, following a linear relationship, from 6.90 to 9.14 and from 6.37 to 7.67 m s−1 for green and red lentil seeds, respectively. Seeds of the green variety had terminal velocities with a mean value of 7.89 m s−1, while the red variety had a mean value of 7.02 m s−1, for moisture content from 10 to 25%. The Reynolds number increased linearly from 2 310.90 to 3 269.23 and from 1 215.02 to 1 535.09 for green and red lentil seeds, respectively, with the increase of seeds moisture content from 10 to 25%. While, drag coefficient decreased from 0.69 to 0.40 and from 0.84 to 0.69 for green and red lentil seeds, respectively, with the increase of moisture content. Mathematical relationships were developed to relate the change in seeds moisture content with the values of aerodynamic properties obtained. The analysis of variance showed that the effect of moisture content on all aerodynamic properties of lentil beans was significant at the 1% probability level.

scholarly journals Evaluation and modeling of aerodynamic properties of mung bean seeds

2015 ◽  
Vol 29 (1) ◽  
pp. 121-126 ◽  
Author(s):  
Feizollah Shahbazi
Keyword(s):  
Reynolds Number ◽  
Moisture Content ◽  
Drag Coefficient ◽  
Mung Bean ◽  
Terminal Velocity ◽  
Mean Value ◽  
Probability Level ◽  
Solid Materials ◽  
Aerodynamic Properties ◽  
Mathematical Relationships

Abstract Aerodynamic properties of solid materials have long been used to convey and separate seeds and grains during post harvest operations. The objective of this study was the evaluation of the aerodynamic properties of mung bean seeds as a function of moisture content and two grades referred to above and below a cut point of 4.8 mm in length. The results showed that as the moisture content increased from 7.8 to 25% (w.b.), the terminal velocity of seeds increased following a polynomial relationship, from 7.28 to 8.79 and 6.02 to 7.12 m s-1, for grades A and B, respectively. Seeds at grade A had terminal velocities with a mean value of 8.05 m s-1, while at grade B had a mean value of 6.46 m s-1. The Reynolds number of both grades increased linearly with the increase of seeds moisture content, while the drag coefficient decreased with the increase of moisture content. Mathematical relationships were developed to relate the change in seeds moisture content with the obtained values of aerodynamic properties. The analysis of variance showed that moisture content had a significant effect, at 1% probability level, on all the aerodynamics properties of mung beans.

scholarly journals Graupel and Hail Terminal Velocities: Does a “Supercritical” Reynolds Number Apply?

2014 ◽  
Vol 71 (9) ◽  
pp. 3392-3403 ◽  
Author(s):  
Andrew Heymsfield ◽  
Robert Wright
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Terminal Velocity ◽  
Ice Crystals ◽  
Particle Sizes ◽  
Model Simulations ◽  
Ice Particles ◽  
Wide Range ◽  
Large Spherical

Abstract This study characterizes the terminal velocities of heavily rimed ice crystals and aggregates, graupel, and hail using a combination of recent drag coefficient and particle bulk density observations. Based on a nondimensional Reynolds number (Re)–Best number (X) approach that applies to atmospheric temperatures and pressures where these particles develop and fall, the authors develop a relationship that spans a wide range of particle sizes. The Re–X relationship can be used to derive the terminal velocities of rimed particles for many applications. Earlier observations suggest that a “supercritical” Reynolds number is reached where the drag coefficient for large spherical ice—hail—drops precipitously and the terminal velocities increase rapidly. The authors draw on observations and model simulations for slightly roughened large ice particles that suggest that the critical Reynolds number is dampened and that the rapid increase in the terminal velocity of smooth spherical ice particles rarely occurs for natural hailstones.

Flow of Newtonian and Non-Newtonian Fluids in a Concentric Annulus With Rotation of the Inner Cylinder

1994 ◽  
Vol 116 (4) ◽  
pp. 821-827 ◽  
Author(s):  
J. M. Nouri ◽  
J. H. Whitelaw
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Drag Coefficient ◽  
Cross Flow ◽  
Flow Region ◽  
Newtonian Fluids ◽  
Rossby Number ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Flow Components

Mean velocity and the corresponding Reynolds shear stresses of Newtonian and non-Newtonian fluids have been measured in a fully developed concentric flow with a diameter ratio of 0.5 and at a inner cylinder rotational speed of 300 rpm. With the Newtonian fluid in laminar flow the effects of the inner shaft rotation were a uniform increase in the drag coefficient by about 28 percent, a flatter and less skewed axial mean velocity and a swirl profile with a narrow boundary close to the inner wall with a thickness of about 22 percent of the gap between the pipes. These effects reduced gradually with bulk flow Reynolds number so that, in the turbulent flow region with a Rossby number of 10, the drag coefficient and profiles of axial mean velocity with and without rotation were similar. The intensity of the turbulence quantities was enhanced by rotation particularly close to the inner wall at a Reynolds number of 9,000 and was similar to that of the nonrotating flow at the higher Reynolds number. The effects of the rotation with the 0.2 percent CMC solution were similar to those of the Newtonian fluids but smaller in magnitude since the Rossby number with the CMC solution is considerably higher for a similar Reynolds number. Comparison between the results of the Newtonian and non-Newtonian fluids with rotation at a Reynolds number of 9000 showed similar features to those of nonrotating flows with an extension of non-turbulent flow, a drag reduction of up to 67 percent, and suppression of all fluctuation velocities compared with Newtonian values particularly the cross-flow components. The results also showed that the swirl velocity profiles of both fluids were the same at a similar Rossby number.

scholarly journals Simulation of Gas Flow Over a Micro Cylinder

2009 ◽  
Author(s):  
Yuan Hu ◽  
Quanhua Sun ◽  
Jing Fan
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Drag Coefficient ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Low Reynolds Number ◽  
Pressure Drag ◽  
Low Reynolds ◽  
Rarefied Gas Effect ◽  
Gas Effect

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum/particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

Vortex shedding from a circular cylinder in moderate-Reynolds-number shear flow

1980 ◽  
Vol 101 (4) ◽  
pp. 721-735 ◽  
Author(s):  
Masaru Kiya ◽  
Hisataka Tamura ◽  
Mikio Arie
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Shear Flow ◽  
Vortex Shedding ◽  
Transverse Velocity ◽  
Number Range ◽  
Uniform Shear ◽  
Reynolds Number Range ◽  
Moderate Reynolds Number ◽  
Shear Parameter

The frequency of vortex shedding from a circular cylinder in a uniform shear flow and the flow patterns around it were experimentally investigated. The Reynolds number Re, which was defined in terms of the cylinder diameter and the approaching velocity at its centre, ranged from 35 to 1500. The shear parameter, which is the transverse velocity gradient of the shear flow non-dimensionalized by the above two quantities, was varied from 0 to 0·25. The critical Reynolds number beyond which vortex shedding from the cylinder occurred was found to be higher than that for a uniform stream and increased approximately linearly with increasing shear parameter when it was larger than about 0·06. In the Reynolds-number range 43 < Re < 220, the vortex shedding disappeared for sufficiently large shear parameters. Moreover, in the Reynolds-number range 100 < Re < 1000, the Strouhal number increased as the shear parameter increased beyond about 0·1.

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