The random packing of fibres in three dimensions

1995 ◽  
Vol 451 (1943) ◽  
pp. 737-746 ◽  
Keyword(s):  
Packing Density ◽  
Volume Fraction ◽  
Random Packing ◽  
Experimental Results ◽  
Three Dimensions ◽  
Approximate Relationship

An investigation has been carried out of the limiting packing density of an array of long straight rigid fibres distributed randomly in space as a function of the length of the fibre. We derive an approximate relationship between the limiting volume fraction V f and the slenderness λ of the fibres defined as length divided by diameter. The formula agrees well with our experimental results and those found in the literature.

Random sequential packing simulations in three dimensions for aligned cubes

1989 ◽  
Vol 26 (3) ◽  
pp. 664-670 ◽  
Author(s):  
Douglas W. Cooper
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Random Packing ◽  
Limit Problem ◽  
Three Dimensions ◽  
Standard Errors ◽  
Cube Root ◽  
Random Errors ◽  
Infinite Region ◽  
The Mean

This particular three-dimensional random packing limit problem is to determine the mean fraction of a cubic space that would be occupied by aligned, fixed, equalsize cubes, placed at random locations sequentially until no more can be added. No analytical solution has yet been found for this problem. Simulation results for a finite region and finite number of attempts were extrapolated to an infinite number of attempts (N →∞) in an infinite region by multiple linear regression, using volume fraction occupied (F) as a linear combination of the ratio of the length of the small cube sides (S) to the length of the cubic region side (L) and the cube root of the ratio of the region volume to the total volume of cubes tried, (L3/NS3)⅓. These results for random packing in a volume with penetrable walls can be adjusted with a multiplicative correction factor to give the results for impenetrable walls. A total of N = 107 attempts at placement were made for L/S = 20/1 and N = 14 × 106 attempts were made for L/S = 10/1. The results for volume fraction packed are correlated by F = 0.430(±0.008) + 0.966(±0.072)(S/L) – 0.236(±0.029)(L3/NS)⅓. The numbers in parentheses are twice the standard errors of estimate of the coefficients, indicating the 95% confidence intervals due to random errors. This value for the packing density limit, 0.430 ± 0.008, is slightly larger than that given by a conjecture by Palásti [10], 0.4178. Our value is consistent with that obtained by rather different simulation methods by Jodrey and Tory [8], 0.4227 ± 0.0006, and by Blaisdell and Solomon [2], 0.4262.

Random sequential packing simulations in three dimensions for aligned cubes

1989 ◽  
Vol 26 (03) ◽  
pp. 664-670 ◽  
Author(s):  
Douglas W. Cooper
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Random Packing ◽  
Limit Problem ◽  
Three Dimensions ◽  
Standard Errors ◽  
Cube Root ◽  
Random Errors ◽  
Infinite Region ◽  
The Mean

This particular three-dimensional random packing limit problem is to determine the mean fraction of a cubic space that would be occupied by aligned, fixed, equalsize cubes, placed at random locations sequentially until no more can be added. No analytical solution has yet been found for this problem. Simulation results for a finite region and finite number of attempts were extrapolated to an infinite number of attempts (N →∞) in an infinite region by multiple linear regression, using volume fraction occupied (F) as a linear combination of the ratio of the length of the small cube sides (S) to the length of the cubic region side (L) and the cube root of the ratio of the region volume to the total volume of cubes tried, (L 3/NS 3)⅓. These results for random packing in a volume with penetrable walls can be adjusted with a multiplicative correction factor to give the results for impenetrable walls. A total of N = 107 attempts at placement were made for L/S = 20/1 and N = 14 × 106 attempts were made for L/S = 10/1. The results for volume fraction packed are correlated by F = 0.430(±0.008) + 0.966(±0.072)(S/L) – 0.236(±0.029)(L 3/NS)⅓ . The numbers in parentheses are twice the standard errors of estimate of the coefficients, indicating the 95% confidence intervals due to random errors. This value for the packing density limit, 0.430 ± 0.008, is slightly larger than that given by a conjecture by Palásti [10], 0.4178. Our value is consistent with that obtained by rather different simulation methods by Jodrey and Tory [8], 0.4227 ± 0.0006, and by Blaisdell and Solomon [2], 0.4262.

scholarly journals The Investigation of Effects of Temperature and Nanoparticles Volume Fraction on the Viscosity of Copper Oxide-ethylene Glycol Nanofluids

2017 ◽  
Author(s):  
Mohammad Hemmat Esfe
Keyword(s):  
Ethylene Glycol ◽  
Copper Oxide ◽  
Volume Fraction ◽  
Relative Viscosity ◽  
Experimental Results ◽  
Different Temperatures ◽  
Nanoparticles Volume Fraction ◽  
Effects Of Temperature ◽  
Nanofluid Viscosity ◽  
Experimental Values

In the present article, the effects of temperature and nanoparticles volume fraction on the viscosity of copper oxide-ethylene glycol nanofluid have been investigated experimentally. The experiments have been conducted in volume fractions of 0 to 1.5 % and temperatures from 27.5 to 50 °C. The shear stress computed by experimental values of viscosity and shear rate for volume fraction of 1% and in different temperatures show that this nanofluid has Newtonian behaviour. The experimental results reveal that in a given volume fraction when temperature increases, viscosity decreases, but relative viscosity varies. Also, in a specific temperature, nanofluid viscosity and relative viscosity increase when volume fraction increases. The maximum amount of increase in relative viscosity is 82.46% that occurs in volume fraction of 1.5% and temperature of 50 °C. Some models of computing nanofluid viscosity have been suggested. The greatest difference between the results obtained from these models and experimental results was down of 4 percent that shows that there is a very good agreement between experimental results and the results obtained from these models.

scholarly journals Comparison of Analytical Approaches Predicting the Compressive Strength of Fibre Reinforced Polymers

Materials ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 2517 ◽  
Author(s):  
Christian Leopold ◽  
Sergej Harder ◽  
Timo Philipkowski ◽  
Wilfried Liebig ◽  
Bodo Fiedler
Keyword(s):  
Compressive Strength ◽  
Prediction Accuracy ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Experimental Results ◽  
Analytical Models ◽  
Reinforced Polymers ◽  
Reinforced Polymer ◽  
Fibre Reinforced Polymer ◽  
Analytical Approaches

Common analytical models to predict the unidirectional compressive strength of fibre reinforced polymers are analysed in terms of their accuracy. Several tests were performed to determine parameters for the models and the compressive strength of carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP). The analytical models are validated for composites with glass and carbon fibres by using the same epoxy matrix system in order to examine whether different fibre types are taken into account. The variation in fibre diameter is smaller for CFRP. The experimental results show that CFRP has about 50% higher compressive strength than GFRP. The models exhibit significantly different results. In general, the analytical models are more precise for CFRP. Only one fibre kinking model’s prediction is in good agreement with the experimental results. This is in contrast to previous findings, where a combined modes model achieves the best prediction accuracy. However, in the original form, the combined modes model is not able to predict the compressive strength for GFRP and was adapted to address this issue. The fibre volume fraction is found to determine the dominating failure mechanisms under compression and thus has a high influence on the prediction accuracy of the various models.

scholarly journals The Mechanical Properties of Steel-Polypropylene Fibre Composites Concrete (HyFRCC)

2015 ◽  
Vol 773-774 ◽  
pp. 949-953 ◽  
Author(s):  
Izni Syahrizal Ibrahim ◽  
Wan Amizah Wan Jusoh ◽  
Abdul Rahman Mohd Sam ◽  
Nur Ain Mustapa ◽  
Sk Muiz Sk Abdul Razak
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Compressive Strength ◽  
Flexural Strength ◽  
Volume Fraction ◽  
Concrete Strength ◽  
Fibre Volume Fraction ◽  
Fibre Volume ◽  
Polypropylene Fibre ◽  
Experimental Results

This paper discusses the experimental results on the mechanical properties of hybrid fibre reinforced composite concrete (HyFRCC) containing different proportions of steel fibre (SF) and polypropylene fibre (PPF). The mechanical properties include compressive strength, tensile strength, and flexural strength. SF is known to enhance the flexural and tensile strengths, and at the same time is able to resist the formation of macro cracking. Meanwhile, PPF contributes to the tensile strain capacity and compressive strength, and also delay the formation of micro cracks. Hooked-end deformed type SF fibre with 60 mm length and fibrillated virgin type PPF fibre with 19 mm length are used in this study. Meanwhile, the concrete strength is maintained for grade C30. The percentage proportion of SF-PPF fibres are varied in the range of 100-0%, 75-25%, 50-50%, 25-75% and 0-100% of which the total fibre volume fraction (Vf) is fixed at 0.5%. The experimental results reveal that the percentage proportion of SF-PPF fibres with 75-25% produced the maximum performance of flexural strength, tensile strength and flexural toughness. Meanwhile, the percentage proportion of SF-PPF fibres with 100-0% contributes to the improvement of the compressive strength compared to that of plain concrete.

A Percolation Equation for Modeling Experimental Results for Continuum Percolation Systems

2001 ◽  
Vol 699 ◽  
Author(s):  
D.S. McLachlan ◽  
C. Chiteme ◽  
W.D. Heiss ◽  
Junjie Wu
Keyword(s):  
Experimental Data ◽  
Ac Conductivity ◽  
Volume Fraction ◽  
Power Laws ◽  
Second Order ◽  
Experimental Results ◽  
Analytical Equation ◽  
Scaling Properties ◽  
First Order ◽  
Dc And Ac Conductivity

AbstractThe standard percolation equations or power laws, for dc and ac conductivity (dielectric constant) are based on scaling ansatz, and predict the behaviour of the first and second order terms, above and below the percolation or critical volume fraction (øc), and in the crossoverregion. Recent experimental results on ac conductivity are presented, which show that these equations, with the exception of real σm above øc and the first order terms in the crossover region, are only valid in the limit σi/σc = 0, where for an ideal dielectric σi=ωε0εr.A single analytical equation, which has the same parameters as the standard percolation equations, and which, for ac conductivity, reduces to the standard percolation power laws in the limit σi(ωε0εr)/σc = 0 for all but one case, is presented. The exception is the expression for real σm below øc, where the standard power law is always incorrect. The equation is then shown to quantitatively fit both first and second order dc and ac experimental data over the entire frequency and composition range. This phenomenological equation is also continuous, has the scaling properties required at a second order metal-insulator and fits scaled first order dc and ac experimental data. Unfortunately, the s and t exponents that are necessary to fit the data to the above analytical equation are usually not the simple dimensionally determined universal ones and depend on a number of factors.

scholarly journals Postheated Model of Confined High Strength Fibrous Concrete

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Kaleem A. Zaidi ◽  
Umesh K. Sharma ◽  
N. M. Bhandari ◽  
P. Bhargava
Keyword(s):  
High Temperature ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
High Strength ◽  
Fibre Volume ◽  
Experimental Results ◽  
Confined Concrete ◽  
Structural Safety ◽  
Stress Strain ◽  
Fibrous Concrete

HSC normally suffers from low stiffness and poor strain capacity after exposure to high temperature. High strength confined fibrous concrete (HSCFC) is being used in industrial structures and other high rise buildings that may be subjected to high temperature during operation or in case of an accidental fire. The proper understanding of the effect of elevated temperature on the stress-strain relationship of HSCFC is necessary for the assessment of structural safety. Further stress-strain model of HSCFC after exposure to high temperature is scarce in literature. Experimental results are used to generate the complete stress-strain curves of HSCFC after exposure to high temperature in compression. The variation in concrete mixes was achieved by varying the types of fibre, volume fraction of fibres, and temperature of exposure from ambient to 800°C. The degree of confinement was kept constant in all the specimens. A comparative assessment of different models on the high strength confined concrete was also conducted at different temperature for the accuracy of proposed model. The proposed empirical stress-strain equations are suitable for both high strength confined concrete and HSCFC after exposure to high temperature in compression. The predictions were found to be in good agreement and well fit with experimental results.

Investigation of Heterogeneous Mixtures With Dual-Modality Transducers Fabricated Using Thick-Film Technology

Volume 1 ◽  
2004 ◽  
Author(s):  
Guangtian Meng ◽  
Artur J. Jaworski ◽  
T. Dyakowski ◽  
J. M. Hale ◽  
N. M. White
Keyword(s):  
Thick Film ◽  
Speed Of Sound ◽  
Volume Fraction ◽  
Measurement Techniques ◽  
Electrical Measurement ◽  
Experimental Results ◽  
Process Conditions ◽  
Dual Modality ◽  
Theoretical Predictions ◽  
Thick Film Technology

The work presented in this paper focuses on development of a dual modality sensor, for deployment within an oil and gas extraction plant to measure the composition of oil-water mixtures. The sensors combine ultrasonic and electrical measurement techniques. These are of course non-destructive, rapid, and can potentially provide an on-line industrial measurement. In addition, the combination of two techniques could potentially be reliable in a wider range of process conditions and could contain self-calibration features. The sensors used in the current study were manufactured using thick-film technology, which enables construction of multilayered structures of both conductive and non-conductive layers, some of which may exhibit piezoelectric properties for ultrasonic measurement purposes. These are later fired on a ceramic substrate to provide rugged sensors, capable of working in aggressive industrial environments. Experiments were conducted for mixtures of vegetable oil and saline water to investigate the feasibility of such dual dual-modality sensors. The time of flight of ultrasonic wave in pure liquids and heterogeneous mixtures was measured. It has been shown that the signal obtained from the transducers is sufficiently strong to warrant the measurement of the speed of sound in heterogeneous mixtures of oil and water. A study of the effects of oil concentration and temperature on the speed of sound has been conducted. A mathematical model has been tested, which relates the speed of sound to the volume fraction taking into account the reflection and refraction on the droplet interfaces. The experimental results subjected to linear regression agree very well with the theoretical predictions. The electrical measurement was conducted at three different frequencies. In general, the values of capacitance and conductance decrease with increasing oil percentage. In the middle oil percentages a discontinuity occurs in the decreasing trend. In the high oil percentages, the experimental results agree very well with theoretical predictions.

The Investigation of the Kinetic Energy of Slug in a Horizontal Channel Using VOF Method

2018 ◽  
Author(s):  
Nariman Ashrafi ◽  
Mohammad Reza Ansari ◽  
Armin Chegini ◽  
Ali Sadeghi
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Cross Section ◽  
Volume Fraction ◽  
Rectangular Cross Section ◽  
Vof Method ◽  
Experimental Results ◽  
Two Phase ◽  
Trapped Air ◽  
Helmholtz Condition

In this article, two-phase slug regime in a duct with rectangular cross-section is investigated numerically, using the volume of fluid (VOF) method. Equations of mass, momentum and advection of volume fraction are solved accompanying k-∈ realizable turbulence equations. To ensure the creditability, numerical results have been compared with experimental results using same geometry. With occurrence of instability in the entrance of duct, Kelvin-Helmholtz condition satisfies and with increasing instability, slug phenomenon occurs. With closing the cross-section of duct, slug causes pressure gradient in it. Trapped air behind a slug transfers the momentum and increases the kinetic energy of slug. In this research the kinetic energy of a slug is investigated.

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