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.

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.

Predicting fiber drag coefficient and settling velocity of sphere in fiber containing Newtonian fluids

2017 ◽  
Vol 159 ◽  
pp. 409-418 ◽  
Author(s):  
Zhengming Xu ◽  
Xianzhi Song ◽  
Gensheng Li ◽  
Qingling Liu ◽  
Zhaoyu Pang ◽  
...  
Keyword(s):  
Drag Coefficient ◽  
Settling Velocity ◽  
Newtonian Fluids

scholarly journals Numerical Investigation of the Flow around a Feather Shuttlecock with Rotation

Proceedings ◽  
2020 ◽  
Vol 49 (1) ◽  
pp. 28
Author(s):  
John Hart ◽  
Jonathan Potts
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Drag Coefficient ◽  
Numerical Investigation ◽  
Computational Fluid Dynamic ◽  
High Reynolds Number ◽  
Fluid Dynamic ◽  
Flow Structures ◽  
Drag Forces ◽  
High Reynolds

This paper presents the first scale resolving computational fluid dynamic (CFD) investigation of a geometrically realistic feather shuttlecock with rotation at a high Reynolds number. Rotation was found to reduce the drag coefficient of the shuttlecock. However, the drag coefficient is shown to be independent of the Reynolds number for both rotating and statically fixed shuttlecocks. Particular attention is given to the influence of rotation on the development of flow structures. Rotation is shown to have a clear influence on the formation of flow structures particularly from the feather vanes, and aft of the shuttlecock base. This further raises concerns regarding wind tunnel studies that use traditional experimental sting mounts; typically inserted into this aft region, they have potential to compromise both flow structure and resultant drag forces. As CFD does not necessitate use of a sting with proper application, it has great potential for a detailed study and analysis of shuttlecocks.

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.

Friction Coefficients for Bingham and Power-Law Fluids in Abrupt Contractions and Expansions

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Sergio L. D. Kfuri ◽  
Edson J. Soares ◽  
Roney L. Thompson ◽  
Renato N. Siqueira
Keyword(s):  
Reynolds Number ◽  
Yield Stress ◽  
Power Law ◽  
Reynolds Numbers ◽  
Newtonian Fluids ◽  
Rheological Parameters ◽  
Friction Coefficients ◽  
K Value ◽  
Power Law Fluids ◽  
Pipeline Systems

Industrial processes with non-Newtonian fluids are common in many segments such as petroleum, cosmetic, and food industries. Slurries, emulsions, and gas–liquid dispersions are some examples with industrial relevance. When a fluid flows in a pipe system, pressure losses are always present. For Newtonian fluids, a quite reasonable understanding of this phenomenon was already achieved and is available in the literature. The same cannot be stated for non-Newtonian fluids owing to their complex characteristics, such as pseudoplasticity, viscoplasticity, elasticity, and thixotropy. The understanding of the influence of these characteristics on flow behavior is very important in order to design efficient pipeline systems. The design of such systems requires the estimation of the pressure drop due to friction effects. However, there are few works regarding friction losses for non-Newtonian fluids in pipeline systems, making this task a difficult one. In this study, two classes of fluids are investigated and compared with the Newtonian results. The first category of fluids are the ones that exhibits pseudoplastic behavior and can be modeled as a power-law fluid, and the second category are the ones that possesses a yield stress and can be modeled as a Bingham fluid. Polyflow was used to compute the friction losses in both abrupt contractions and expansions laminar flow conditions. It shows that for the expansion cases, the aspect ratio affects more the local friction coefficients than for the contraction cases. The influence of the power index n on local friction losses is similar for both cases, abrupt contractions and abrupt expansions. At low Reynolds numbers, dilatant fluids present the lowest values of the friction coefficient, K, independent of geometry. At high Reynolds numbers, a reversal of the curves occurs, and the dilatant fluid presents larger values of K coefficient. For the cases investigated, there is also a Reynolds number in which all the curves exhibit the same value of K for any value of the power-law index. The effect of τy′ shows a different behavior between contractions and expansions. In the case of contractions, the material with the highest dimensionless yield stress has the highest K value. In the case of the expansions, the behavior is the opposite, i.e., the higher the yield stress, the lower is the values of the K coefficient. Equations for each accessory as a function of the rheological parameters of the fluid and the Reynolds number of the flow are also proposed. The data were adjusted according to two main equations: the two Ks method proposed by Hooper (1981, “The Two-K Method Predicts Head Losses in Pipe Fittings,” Chem. Eng., 81, pp. 96–100.) is used for all the contractions cases, and the equation proposed by Oliveira et al. (1997, “A General Correlation for the Local Coefficient in Newtonian Axisymmetric Sudden Expansions,” Int. J. Heat Fluid Flow, 19(6), pp. 655–660.) is used for all the expansions cases. The equations found were compared with the numerical results and showed satisfactory precision and thus can be used for engineering applications.

scholarly journals Featuresof velocity distribution in a turbulent flow

Vestnik MGSU ◽  
2015 ◽  
pp. 103-109
Author(s):  
Valeriy Stepanovich Borovkov ◽  
Valeriy Valentinovich Volshanik ◽  
Irina Aleksandrovna Rylova
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Velocity Distribution ◽  
Drag Coefficient ◽  
Viscous Flow ◽  
Measured Velocity ◽  
Displacement Thickness ◽  
Logarithmic Velocity Profile

In this article the questions of kinematic structure of steady turbulent flow near a solid boundary are considered. It has been established that due to friction the value of the local Reynolds number decreases and always becomes smaller than the critical value of the Reynolds number, which leads to formation of viscous flow near a wall. Velocity profiles for the area of viscous flow with constant and variable shear stress are obtained. The experimental investigations of different authors showed that in this area the flow is of unsteady character, where viscous flow occurs intermittently with turbulent flow. With increasing distance from the wall the flow becomes fully turbulent. In the area where generation and dissipation of turbulence are very intensive, there is a developed turbulent flow with increasing distance from the wall. Dissipation of turbulence is an action of viscous force. The logarithmic velocity profile was obtained by L. Prandtl disregarding the viscous component and the linear variation of the shear stress in the depth flow. The profile parameters C and k were determined from Nikuradze’s experiments. The detailed investigations of Nikuradze’s experiments established the part of the flow where the logarithmic velocity profile is correctly confirmed.This part of the flow was called “Prandtl layer”. The measured velocity distribution above this layer deviates in the direction of greater values. Processing of experimental data revealed that the thickness of the “Prandtl layer”, normalized to the radius of a pipe, depend on a drag coefficient. The formula for determining the thickness of the “Prandtl layer” with the known value of the drag coefficient is obtained. It is shown that the thickness of “Prandtl layer” almost coincides with the boundary layer displacement thickness formed on the wall of the pipe.

Influence of Particle Shape on the Drag Coefficient for Isometric Particles

1994 ◽  
Vol 59 (12) ◽  
pp. 2583-2594 ◽  
Author(s):  
Miloslav Hartman ◽  
Otakar Trnka ◽  
Karel Svoboda ◽  
Václav Veselý
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Fluidized Beds ◽  
Fluid Velocity ◽  
Particle Diameter ◽  
Free Fall ◽  
Fall Velocity ◽  
Gas Cleaning ◽  
Explicit Formulae

A comprehensive correlation has been developed of the drag coefficient for nonspherical isometric particles as a function the Reynolds number and the particle sphericity on the basis of data reported in the literature. The proposed formula covers the Stokes, the transitional and the Newton region. The predictions of the reported correlation have been compared to experimental data measured in this work with the dolomitic materials in respect to their use in calcination and gas cleaning processes with fluidized beds. Approximative explicit formulae have also been reported that make it possible to estimate the terminal free-fall velocity of a given particle or to predict the particle diameter corresponding to a fluid velocity of interest.

Low Reynolds Number Flow Computations of a Sphere With Slip

2005 ◽  
Author(s):  
O. Pulat ◽  
R. N. Parthasarathy
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Reynolds Numbers ◽  
Water Medium ◽  
Reynolds Number Flow ◽  
Drag Forces ◽  
Falling Sphere ◽  
Number Flow ◽  
High Reynolds ◽  
Flow Past A Sphere

A computational fluid dynamics package (FLUENT) was used to simulate the conditions of a falling sphere through a water medium with a zero shear stress condition (full slip) for Reynolds numbers in the range. Comparisons of the results were made with simulations of the flow past a sphere with no slip. Specific differences were observed in the drag coefficient, drag forces, axial velocity, radial velocity, and wake characteristics. A significant reduction in the drag coefficient was observed with the presence of slip on the surface. With a decrease in the Reynolds number the decreases in the wake structure became negligible, however, the differences in drag coefficient became significant. At high Reynolds numbers, the wake was skewed towards the rear of the sphere, under the full slip condition.

Model Construction and Finite Element Simulate Based on Experiment Study of Magneto Rheological Finished Machine

2014 ◽  
Vol 620 ◽  
pp. 288-296
Author(s):  
Hang Song Yang ◽  
Peng Li ◽  
Li Zhi Gu ◽  
Hui Juan Guo
Keyword(s):  
Reynolds Number ◽  
Finite Element ◽  
Shear Stress ◽  
Magnetic Fluid ◽  
Critical Reynolds Number ◽  
Fluid Velocity ◽  
Mathematics Model ◽  
Magnetic Liquid ◽  
Fluid State ◽  
Magneto Rheological

In this paper, turn the medium of magneto rheological liquid into continuation, and using of the critical Reynolds number determine method of liquid move state and compound with non-Newton fluid, get the conclusion of finished machine abrasive magnetic liquid fluid as laminar fluid, for having no mathematics’ model practical or be fit with the experiment, especially the distribution of shear and velocity stress, In this paper, using of the critical Reynolds number to determine the liquid state of magnetic fluid state, and in determined the fluid state, using non-Newton fluid dynamics and tensor analysis theory and also compound with the double dynamic viscosity model, analysis the abrasive magnetic fluid quality of kinematics shear stress, according to the quality, contracture the dynamic model of abrasive magnetic liquid finished machine, during the interfere, using the double viscosity fluid model, we may get the conclusion, liquid magnetic abrasive, when the shear stress more or less the bend stress, and mark with plasticity viscosity ηp0, ηpγ which round the work piece center, the velocity distribution as laminar, and also, analysis the flow field mathematics’ model by the finite element, and also going on the numerical simulate for the magnetic fluid velocity field of finished machine.

Drag on a Group of Cylinders

1977 ◽  
Vol 99 (1) ◽  
pp. 152-157 ◽  
Author(s):  
C. Dalton ◽  
J. M. Szabo
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Stream Flow ◽  
Free Stream ◽  
Orientation Angle ◽  
Mutual Interaction ◽  
Strain Gages ◽  
Drag Forces ◽  
A Value

An experimental investigation of the effects of spacing, orientation and Reynolds number on the drag of each cylinder in a group of two and three cylinders was carried out. The drag forces were measured by means of strain gages. The results indicate that the drag is strongly affected by mutual interaction with neighboring cylinders over a range of separation distances and angles of orientation with respect to the free-stream flow. The interaction decreases with increasing orientation angle, becoming very weak at θ = 90 deg when the cylinders are separated by at least two diameters. For spacings of approximately four diameters, the drag coefficients for the three-cylinder geometry reach a value which will remain almost constant for larger spacings. This is true for all three cylinders and for all orientations. The orientation of the cylinders influences only slightly the drag on the upstream cylinder for groups of both two and three cylinders. For downstream cylinders, the drag coefficient decreases with increasing Reynolds number due to the increased amount of unsteadiness contained in the flow behind the upstream cylinder.

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