A Study of Particle Settling in Non-Newtonian Fluids—Part I: A New Method for the Study of Particle Settling in Drilling and Fracturing Fluids

1994 ◽  
Vol 116 (1) ◽  
pp. 10-15 ◽  
Author(s):  
L. Jin ◽  
M. E. Chenevert
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Force Measurement ◽  
Newtonian Fluids ◽  
Particle Settling ◽  
Number Range ◽  
Fracturing Fluids ◽  
Wide Range ◽  
Good Set ◽  
Settling Of Particles

A drag force measurement method is presented which makes it possible to study the settling of particles in transparent and opaque fluids. A dimensionless treatment that takes into account the shear thinning effects of fluids was applied to normalize the measured drag force data. A wide range of particle Reynolds numbers can be covered by this method and a profile of friction factor versus Reynolds number can be established by the proposed dimensionless treatment. An algorithm for the prediction of settling of particles in non-Newtonian fluids was introduced. It can be executed by a computer program. With a good set of experimental data, the settling velocities predicted by the computer model are very close to the measured ones in the fluids tested. This method can be used to study the suspension properties of drilling and fracturing fluids, transparent or opaque. The wide coverage of Reynolds number range simplifies the experiment.

scholarly journals A Review of Passive Micromixers with a Comparative Analysis

Micromachines ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 455 ◽  
Author(s):  
Wasim Raza ◽  
Shakhawat Hossain ◽  
Kwang-Yong Kim
Keyword(s):  
Reynolds Number ◽  
Comparative Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Number Range ◽  
Pressure Drops ◽  
Convection Diffusion ◽  
Wide Range ◽  
Quantitative Analyses ◽  
Mixing Costs

A wide range of existing passive micromixers are reviewed, and quantitative analyses of ten typical passive micromixers were performed to compare their mixing indices, pressure drops, and mixing costs under the same axial length and flow conditions across a wide Reynolds number range of 0.01–120. The tested micromixers were selected from five types of micromixer designs. The analyses of flow and mixing were performed using continuity, Navier-Stokes and convection-diffusion equations. The results of the comparative analysis were presented for three different Reynolds number ranges: low-Re (Re ≤ 1), intermediate-Re (1 < Re ≤ 40), and high-Re (Re > 40) ranges, where the mixing mechanisms are different. The results show a two-dimensional micromixer of Tesla structure is recommended in the intermediate- and high-Re ranges, while two three-dimensional micromixers with two layers are recommended in the low-Re range due to their excellent mixing performance.

Forming Process of Taylor Vortex Flow of Polymer Solutions

2004 ◽  
Author(s):  
Shu Sumio ◽  
Keizo Watanabe ◽  
Satoshi Ogata
Keyword(s):  
Reynolds Number ◽  
Flow Visualization ◽  
Vortex Flow ◽  
Polymer Solutions ◽  
Newtonian Fluids ◽  
Experimental Result ◽  
Taylor Vortex ◽  
Number Range ◽  
Primary Mode ◽  
Taylor Vortex Flow

The laser-induced fluorescence (LIF) technique carried out the flow visualization for the formation of Taylor vortex, which occurred in the gap between the two coaxial cylinders. The test fluids were tap water and glycerin 60wt% solution as Newtonian fluids. Polyacrilamide (SeparanAP-30) solutions in the concentration range of 10 ppm to 1000 ppm and polyethylene-oxide (PEO15) solutions in the range of 20 ppm to 1000 ppm were tested as non-Newtonian fluids, respectively. The Reynolds number range was 80 &lt; Re &lt; 4.0 × 103 in the experiment. The rotating inner cylinder was accelerated under the slow condition (dRe*/ dt ≤ 1 min−1) in order to obtain a Taylor vortex flow of the stable primary mode. Flow visualization results showed that the Go¨rtler vortices of half the number of Taylor cells occurred in the gap when Taylor vortex flow of the primary mode was formed. In addition, the critical Reynolds number of the polymer solutions case, which Taylor vortices occur, because the generation of the Go¨rtler vortices was retarded. At the higher concentration of the polymer solutions, this effect became remarkable. Measurements of steady-state Taylor cells showed that the upper and the lower cells of polymer solutions became larger in wavelength than that of the Newtonian fluids. The Taylor vortex flow of non-Newtonian fluids was analyzed and the result of the Giesekus model agreed with the experimental result.

Shape optimization of a split-and-recombine micromixer by the local energy dissipation rate

2020 ◽  
Vol 234 (3) ◽  
pp. 243-251
Author(s):  
Eshaq Ebnereza ◽  
Kamran Hassani ◽  
Mahmoud Seraj ◽  
Katayoun Gohari Moghaddam
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Objective Function ◽  
Dissipation Rate ◽  
Computation Time ◽  
Energy Dissipation Rate ◽  
Local Energy ◽  
Number Range ◽  
Design Variables ◽  
Wide Range

A passive split-and-recombine micromixer was developed based on the concept of lamellar structure and advection mixing type for a serpentine structure. The flow patterns and mixing performance were analyzed using numerical simulation in Reynolds number range of 10≤ Reynolds ≤170. Two design variables, defining the shape of the split-and-recombine branch, were optimized by the local energy dissipation rate as the objective function. The reduction of computation time and the absence of numerical diffusion were the advantages of using the energy dissipation rate as the objective function. At each Reynolds number, 64 sample data was generated on the design space uniformly. Then a model was used based on the Radial basis neural network for the prediction of the objective function. The optimum values of the design variables within the constraint range were found on the response surface. The optimization study was performed at five Reynolds numbers of 10, 50, 90, 130, 170 and the mixing index was improved 0.156, 0.298, 0.417, 0.506, and 0.57, respectively. The effect of design variables on the objective function and the concentration pattern was presented and analyzed. Finally, the mixing characteristic of the split-and-recombine micromixer was studied in a wide range of Reynolds number and the flow was categorized to stratify and show the vortex regime based on the Reynolds number. The optimized split-and-recombine micromixer could be integrated by any system depending on the desired velocity and Reynolds number.

Flow of non-Newtonian fluids over a confined baffle

1991 ◽  
Vol 226 ◽  
pp. 475-496 ◽  
Author(s):  
F. T. Pinho ◽  
J. H. Whitelaw
Keyword(s):  
Reynolds Number ◽  
Polymer Concentration ◽  
Local Strain ◽  
Reynolds Numbers ◽  
Newtonian Fluids ◽  
Momentum Balance ◽  
Recirculation Region ◽  
Reynolds Stresses ◽  
Recirculation Bubble ◽  
Number Range

Measurements of wall pressure, and mean and r.m.s. velocities of the confined flow about a disk of 50 % area blockage have been carried out for two Newtonian fluids and four concentrations of a shear-thinning weakly elastic polymer in aqueous solution encompassing a Reynolds-number range from 220 to 138000. The flows of Newtonian and non-Newtonian fluids were found to be increasingly dependent on Reynolds numbers below 50000, with a decrease in the length of the recirculation region and dampening of the normal Reynolds stresses. At Reynolds numbers less than 25000, the recirculation bubble lengthened and all turbulence components were suppressed with increased polymer concentration so that, at a Reynolds number of 8000, the maximum values of turbulent kinetic energy were 35 and 45% lower than that for water, with 0.2% and 0.4% solutions of the polymer. Non-Newtonian effects were found to be important in regions of low local strain rates in low-Reynolds-number flows, especially inside the recirculation bubble and close to the shear layer, and are represented by both an increase in viscous diffusion and a decrease in turbulent diffusion to, respectively, 6% and 18% of the largest term of the momentum balance with a 0.4 % polymer solution at a Reynolds number of 7700. The asymmetry and unsteadiness of the flow at Reynolds numbers between 400 and 6000 is shown to be an aerodynamic effect which increases in range and amplitude with the more concentrated polymer solutions.

Thermal Stress Analysis and Determination of Stitching Pattern Effect on Aerodynamics of a Soccer Ball

2017 ◽  
Author(s):  
Mosfequr Rahman ◽  
Sirajus Salekeen ◽  
Asher Holland ◽  
Todd Nixon ◽  
Hunter Kight ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Thermal Stress ◽  
Turbulent Flow ◽  
Stress Analysis ◽  
Drag Force ◽  
Normal Condition ◽  
Soccer Ball ◽  
Thermal Stress Analysis ◽  
Maximum Deformation ◽  
Wide Range

Soccer is played all over the world in a wide range of temperature environments. One of the objectives of this numerical study is to determine whether temperature has an effect on the body and performance of a soccer ball. Another object is to aerodynamically determine the effect of stitching pattern of the ball on its flight. The soccer ball was modeled in ANSYS Workbench and tested with thermal-stress analysis tool at nominal temperatures of 0°C, 20°C, and 40°C. The maximum deformation of a soccer ball at normal condition occurred at 40°C which was 1.0503 cm as compared to the 0.9587 cm at 0°C. This normal condition means when the ball is subjected to an internal pressure of 80 kPa which is the standard inflation pressure. When an external 2700 Pa pressure was applied to the soccer ball which is the average force of a kick, the maximum deformation again occurred at 40°C which was 5.2289 cm as compared to the 4.7599 cm at 0°C. Therefore, the stiffness of the ball materials decreased as the temperature increased. This reveals that the ball delivers a greater force at the surface of contact when the temperature drops. The second part of this study as mentioned earlier was to study the aerodynamic effect on a soccer ball traveling through the air at a certain speed. Two types of soccer ball were analyzed for this reason to see which of the two flew better in the air. The two types were a regular FIFA soccer ball with stitching and a normal soccer ball without stitching. Two tests were performed on both types of the soccer ball. These tests were done using ANSYS FLUENT and the sought out output parameters were velocity, pressure, Reynolds Number and drag force. In the first test the soccer balls were rotating in the air and in the second test the soccer balls were not rotating in the air. For the first test, the ball without stitching had the higher velocity, Reynolds Number, and drag force, which were 126.2 m/s, 2.420 × 106, and 122.6 N respectively. This means the ball without stitching is experiencing a more random turbulent flow and is being pulled more into the direction of the drag force. This happens because the soccer ball without stitching will rotate faster and won’t have stitching patterns to create friction that will slow down the flow. For the second test, the ball with stitching had the higher velocity, Reynolds Number and drag force which were 42.22 m/s, 8.095 × 105, and 16.81 N respectively. This means the soccer ball with stitching is experiencing a random turbulent flow and is being pulled in the direction of the drag force because the stitching patterns are not in complete contact with the air to create friction.

scholarly journals Heat Transfer Results and Operational Characteristics of the NASA Lewis Research Center Hot Section Cascade Test Facility

1985 ◽  
Author(s):  
Herbert J. Gladden ◽  
Frederick C. Yeh ◽  
Dennis L. Fronek
Keyword(s):  
Reynolds Number ◽  
Gas Turbine ◽  
Operating Conditions ◽  
Research Center ◽  
Test Facility ◽  
Nasa Lewis Research ◽  
Number Range ◽  
Full Coverage ◽  
Operational Characteristics ◽  
Wide Range

The NASA Lewis Research Center gas turbine hot section test facility has been developed to provide a “real-engine” environment with well known boundary conditions for the aerothermal performance evaluation/verification of computer design codes. The initial aerothermal research data obtained at this facility are presented and the operational characteristics of the facility are discussed. This facility is capable of testing at temperatures and pressures up to 1600 K and 18 atm which corresponds to a vane exit Reynolds number range of 0.5×106 to 2.5×106 based on vane chord. The component cooling air temperature can be independently modulated between 330 and 700 K providing gas-to-coolant temperature ratios similar to current engine application. Research instrumentation of the test components provide conventional pressure and temperature measurements as well as metal temperatures measured by IR-photography. The primary data acquisition mode is steady state through a 704 channel multiplexer/digitizer. The test facility was configured as an annular cascade of full coverage film cooled vanes for the initial series of research tests. These vanes were tested over a wide range of gas Reynolds number, exit gas Mach number and heat flux levels. The range of test conditions was used to represent both actual operating conditions and similarity state conditions of a gas turbine engine. The results are presented for the aerothermal performance of the facility and the full coverage film cooled vanes.

Multiparticle Settling in Non-Newtonian Fluids

1999 ◽  
Author(s):  
Qinsheng Zhu ◽  
Peter E. Clark
Keyword(s):  
Experimental Work ◽  
Single Particle ◽  
Periodic Motion ◽  
Large Body ◽  
Particle Systems ◽  
Newtonian Fluids ◽  
Particle Settling ◽  
Mineral Extraction ◽  
Multiparticle Systems ◽  
Settling Of Particles

Abstract The settling of particles in non-Newtonian fluids is an important topic in industries from pharmaceuticals and foods to mineral extraction and construction. A large body of experimental work is available on single particle settling in both Newtonian and non-Newtonian fluids. Multi-particle systems are less well studied. Most reported work in multiparticle systems has been in Newtonian fluids. Recently, there has been increasing interest in multiparticle settling in non-Newtonian fluids. This paper will review some of the more important of these studies and present some new data on periodic motion observed in systems of three or more particles.

Conditional statistics of the turbulent/non-turbulent interface in a jet flow

2013 ◽  
Vol 731 ◽  
pp. 615-638 ◽  
Author(s):  
Markus Gampert ◽  
Venkat Narayanaswamy ◽  
Philip Schaefer ◽  
Norbert Peters
Keyword(s):  
Reynolds Number ◽  
High Speed ◽  
Mixture Fraction ◽  
Deep Understanding ◽  
Jet Flow ◽  
Scalar Dissipation ◽  
Number Range ◽  
Wide Range ◽  
Intermittency Factor ◽  
Conditional Statistics

AbstractUsing two-dimensional high-speed measurements of the mixture fraction $Z$ in a turbulent round jet with nozzle-based Reynolds numbers $R{e}_{0} $ between 3000 and 18 440, we investigate the scalar turbulent/non-turbulent (T/NT) interface of the flow. The mixture fraction steeply changes from $Z= 0$ to a final value which is typically larger than 0.1. Since combustion occurs in the vicinity of the stoichiometric mixture fraction, which is around $Z= 0. 06$ for typical fuel/air mixtures, it is expected to take place largely within the turbulent/non-turbulent interface. Therefore, deep understanding of this part of the flow is essential for an accurate modelling of turbulent non-premixed combustion. To this end, we use a composite model developed by Effelsberg & Peters (Combust. Flame, vol. 50, 1983, pp. 351–360) for the probability density function (p.d.f.) $P(Z)$ which takes into account the different contributions from the fully turbulent as well as the turbulent/non-turbulent interface part of the flow. A very good agreement between the measurements and the model is observed over a wide range of axial and radial locations as well as at varying intermittency factor $\gamma $ and shear. Furthermore, we observe a constant mean mixture fraction value in the fully turbulent region. The p.d.f. of this region is thus of non-marching character, which is attributed physically to the meandering nature of the fully turbulent core of the jet flow. Finally, the location and in particular the scaling of the thickness $\delta $ of the scalar turbulent/non-turbulent interface are investigated. We provide the first experimental results for the thickness of the interface over the above-mentioned Reynolds number range and observe $\delta / L\sim R{ e}_{\lambda }^{- 1} $, where $L$ is an integral length scale and $R{e}_{\lambda } $ the local Reynolds number based on the Taylor scale $\lambda $, meaning that $\delta \sim \lambda $. This result also supports the assumption often made in modelling of the stoichiometric scalar dissipation rate ${\chi }_{st} $ being a Reynolds-number-independent quantity.

Further Experiments and Investigations for Discharge Coefficient of PTC 6 Flow Nozzle in a Wide Range of Reynolds Number

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Noriyuki Furuichi ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
Kazuo Shibuya
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Power Plants ◽  
Discharge Coefficient ◽  
High Accuracy ◽  
Steam Turbines ◽  
Number Range ◽  
Accurate Evaluation ◽  
Discharge Coefficients ◽  
Wide Range

The discharge coefficients of the flow nozzles based on ASME PTC 6 are measured in a wide range of Reynolds number from Red = 5.8 × 104 to Red = 1.4 × 107, and the equations of the discharge coefficients are developed for the laminar, the transitional, and the turbulent flow ranges. The equation of the discharge coefficient consists of a nominal discharge coefficient and the tap effect. The nominal discharge coefficient is the discharge coefficient without tap, which is experimentally determined from the discharge coefficients measured for different tap diameters. The tap effects are correctly obtained by subtracting the nominal discharge coefficient from the discharge coefficient measured. The deviation of the present experimental results from the equations developed is from −0.06% to 0.04% for 3.0 × 106 < Red < 1.4 × 107 and from −0.11% to 0.16% for overall Reynolds number range examined. The developed equations are expected to be capable of estimating the discharge coefficient of the throat tap nozzle defined in PTC 6 with a high accuracy and contribute for the high accurate evaluation of steam turbines in power plants.

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^

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