scholarly journals A Leakage Model of Contact Mechanical Seals Based on the Fractal Theory of Porous Medium

Coatings ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Xingya Ni ◽  
Chenbo Ma ◽  
Jianjun Sun ◽  
Yuyan Zhang ◽  
Qiuping Yu
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Pore Diameter ◽  
Fractal Theory ◽  
Leakage Rate ◽  
Contact Interface ◽  
Mechanical Seals ◽  
The Real ◽  
Leakage Model ◽  
Contact Mechanical

A theoretical model for calculating the leakage rate of contact mechanical seals based on the fractal theory of the porous media, which can consider the real seal contact interface and objectively reflect the flow of the interfacial fluid from a microscopic perspective, is established. In order to obtain the microstructural parameters of the porous media included in the leakage model, such as the fractal dimension and the maximum pore diameter, the real seal contact interface obtained from experiments is reconstructed, a contact model between the dynamic and static rings is proposed, and then the calculation methods for the interface characteristic parameters are provided. Numerical simulation results show that as the contact pressure increases from 0.05 to 0.5 MPa, the interface porosity and the maximum pore diameter decreases gradually. Furthermore, the fractal dimension of the pore area increases and the leakage rate of the interface decreases from 0.48 to 0.33 mL/h. The proposed method provides a novel way of calculating the leakage rate of contact mechanical seals.

scholarly journals A Porous Media Leakage Model of Contact Mechanical Seals Considering Surface Wettability

Coatings ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1338
Author(s):  
Guangyao Bei ◽  
Chenbo Ma ◽  
Jianjun Sun ◽  
Xingya Ni ◽  
Yafei Ma
Keyword(s):  
Contact Angle ◽  
Porous Media ◽  
Slip Length ◽  
Apparent Contact Angle ◽  
Leakage Rate ◽  
Surface Wettability ◽  
Mechanical Seals ◽  
Leakage Model ◽  
Proposed Model ◽  
Contact Mechanical

The fluid leakage channel found in contact mechanical seals belongs to the microchannel category. Thus, upon further inspection, the influence of surface wettability and other factors neglected in previous studies becomes obvious. The porous leakage model of contact mechanical seals considering the surface wettability presented in this paper was based on the Cassie model and slip theory. The variations of the microchannel slip length and the velocity under various wettability conditions were studied and the relationship between the slip length and the apparent contact angle was established. Moreover, using porous media theory, the theoretical model of the leakage rate in contact mechanical seals considers the surface wettability depending on various parameters. The observed parameters included the surface contact angle, sealing medium pressure, viscosity coefficient, fractal dimension, and maximum pore diameter. The simulation results obtained using the proposed model have shown that the leakage rate increases with the increase of the apparent contact angle. Particularly when the contact pressure is small, the influence of the surface wettability is more significant. Furthermore, the leakage rate results obtained via the proposed model were compared to those of existing models. The comparison confirmed that the proposed model is applicable and that the necessity of considering wettability significantly affects the leakage rate calculation accuracy. The proposed model lays a foundation for further improving the calculation accuracy, making it easier for both the researchers and practitioners to suppress the leakage in contact mechanical seals.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

2018 ◽  
Vol 29 (02) ◽  
pp. 1850019 ◽  
Author(s):  
X.-H. Tan ◽  
C.-Y. Liu ◽  
X.-P. Li ◽  
H.-Q. Wang ◽  
H. Deng
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Stress Sensitivity ◽  
Maximum Diameter ◽  
Proposed Model ◽  
Fractal Parameters ◽  
Stress Changes ◽  
Capillary Bundle ◽  
Definition Of

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster [Formula: see text] become bigger with an increase of stress. However, the pore fractal dimension of solid cluster [Formula: see text] and capillary bundle [Formula: see text] remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

INVESTIGATION OF DYNAMIC TEXTURE AND FLOW CHARACTERISTICS OF FOAM TRANSPORT IN POROUS MEDIA BASED ON FRACTAL THEORY

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940013 ◽  
Author(s):  
FEI WANG ◽  
HAIFENG LI ◽  
DONGXING DU ◽  
XU DONG
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Quantitative Description ◽  
Flow Characteristics ◽  
Transport In Porous Media ◽  
Steady Stage ◽  
Profile Control ◽  
Fractal Characteristics

Foam fluid has found wide applications in oilfield development, such as profile control, water plugging, gas channeling control, fracturing, and so on. As a non-Newtonian fluid, the successful application of foam is significantly influenced by its structure. The foam texture, however, is complex and irregular, and becomes even more complicated in porous media by the boundary effects. Therefore, the description of dynamic foam structure is crucial and a quantitative description method for foam fluid is worth exploring. In this paper, the fractal characteristics of foam in porous media are verified and combined with foam microdisplacement experiment, and the fractal rule of foam is found. The relationship between fractal dimension and pressure is also discussed. The results show that foam has dynamic fractal characteristics during transport in porous media and the box-counting fractal dimension ranges from 1 to 2. Furthermore, the dynamic change of foam fractal dimension during transport in porous media could be divided into three stages. In the first stage when no foam forms, the fractal dimension is about 2; in the second unsteady foam stage, the fractal dimension is reduced from 1.9 to 1.6; the last one is the steady stage and the fractal dimension is almost constant (about 1.6). Besides, the fractal dimension of foam fluid is closely related to displacement pressure. Low pressure corresponds to higher fractal dimension, and high pressure corresponds to lower fractal dimension. Pressure is negatively linearly correlated with fractal dimension. These results are expected to enrich the understanding of the foam dynamic characteristics in their advanced applications.

A DIFFUSIVITY MODEL FOR GAS DIFFUSION IN DRY POROUS MEDIA COMPOSED OF CONVERGING–DIVERGING CAPILLARIES

Fractals ◽  
2016 ◽  
Vol 24 (03) ◽  
pp. 1650034 ◽  
Author(s):  
SHIFANG WANG ◽  
TAO WU ◽  
YONGJU DENG ◽  
QIUSHA ZHENG ◽  
QIAN ZHENG
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Fractal Model ◽  
Gas Diffusion ◽  
Pore Area ◽  
Relative Diffusivity ◽  
Fluctuation Amplitude

Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging–diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging–diverging effect included is in good agreement with reported experimental data.

A model for allometric permeation in fractal branching channel net driven by capillary pressure

2015 ◽  
Vol 25 (8) ◽  
pp. 1886-1895 ◽  
Author(s):  
Jie Fan ◽  
Na Zhu ◽  
Zhi Liu ◽  
Qian Cheng ◽  
Yong Liu
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Capillary Pressure ◽  
Design Methodology ◽  
Fractal Theory ◽  
Geometrical Parameters ◽  
Content Type ◽  
Artificial Materials ◽  
Net Affect

Purpose – The purpose of this paper is to investigate the allometric permeation performance in fractal branching channel net driven by capillary pressure and analyze how the geometrical parameters of the branching channel net affect the permeability of the fluid transportation. Design/methodology/approach – An allometric permeation model is proposed based on the fractal theory by considering capillary pressure as the main driven force of fluid permeation. Findings – It is found that the permeability efficiency is a function of fractal dimension, bifurcation number, and number of branching level. Different fluid permeation efficiencies of the channel net can be obtained by changing the three parameters. Originality/value – The allometric permeation model established provides a better understanding of the permeation mechanism in fractal porous media which could further help with the design of bio-mimetic artificial materials.

A FRACTAL MODEL FOR KOZENY–CARMAN CONSTANT AND DIMENSIONLESS PERMEABILITY OF FIBROUS POROUS MEDIA WITH ROUGHENED SURFACES

Fractals ◽  
2019 ◽  
Vol 27 (07) ◽  
pp. 1950116 ◽  
Author(s):  
BOQI XIAO ◽  
YIDAN ZHANG ◽  
YAN WANG ◽  
GUOPING JIANG ◽  
MINGCHAO LIANG ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fluid Transport ◽  
Fractal Theory ◽  
Fractal Model ◽  
Physical Mechanisms ◽  
Relative Roughness ◽  
Fibrous Porous Media ◽  
Effect Of Surface ◽  
Good Agreement

In this paper, fluid transport through fibrous porous media is studied by the fractal theory with a focus on the effect of surface roughness of capillaries. A fractal model for Kozeny–Carman (KC) constant and dimensionless permeability of fibrous porous media with roughened surfaces is derived. The determined KC constant and dimensionless permeability of fibrous porous media with roughened surfaces are in good agreement with available experimental data and existing models reported in the literature. It is found that the KC constant of fibrous porous media with roughened surfaces increases with the increase of relative roughness, porosity, area fractal dimension of pore and tortuosity fractal dimension, respectively. Besides, it is seen that the dimensionless permeability of fibrous porous media with roughened surfaces decreases with increasing relative roughness and tortuosity fractal dimension. However, it is observed that the dimensionless permeability of fibrous porous media with roughened surfaces increases with porosity. With the proposed fractal model, the physical mechanisms of fluids transport through fibrous porous media are better elucidated.

scholarly journals A Novel Porous Media Permeability Model Based on Fractal Theory and Ideal Particle Pore-Space Geometry Assumption

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 510 ◽  
Author(s):  
Yongquan Hu ◽  
Qiang Wang ◽  
Jinzhou Zhao ◽  
Shouchang Xie ◽  
Hong Jiang
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Great Influence ◽  
Particle Radius ◽  
Particle Model ◽  
Permeability Model ◽  
Minimum Value ◽  
Pore Area ◽  
The Impact

In this paper, a novel porous media permeability model is established by using particle model, capillary bundle model and fractal theory. The three-dimensional irregular spatial characteristics composed of two ideal particles are considered in the model. Compared with previous models, the results of our model are closer to the experimental data. The results show that the tortuosity fractal dimension is negatively correlated with porosity, while the pore area fractal dimension is positively correlated with porosity; The permeability is negatively correlated with the tortuosity fractal dimension and positively correlated with the integral fractal dimension of pore surface and particle radius. When the tortuosity fractal dimension is close to 1 and the pore area fractal dimension is close to 2, the faster the permeability changes, the greater the impact. Different particle arrangement has great influence on porous media permeability. When the porosity is close to 0 and close to 1, the greater the difference coefficient is, the more the permeability of different arrangement is affected. In addition, the larger the particle radius is, the greater the permeability difference coefficient will be, and the greater the permeability difference will be for different particle arrangements. With the increase of fractal dimension, the permeability difference coefficient first decreases and then increases. When the pore area fractal dimension approaches 2, the permeability difference coefficient changes faster and reaches the minimum value, and when the tortuosity fractal dimension approaches 1, the permeability difference coefficient changes faster and reaches the minimum value. Our research is helpful to further understand the connotation of medium transmission in porous media.

scholarly journals Mathematical Model for Effective Gas Diffusion Coefficient in Multi-scale Fractal Porous Media

2021 ◽  
Vol 248 ◽  
pp. 01026
Author(s):  
Du Zhehua
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Diffusion Coefficient ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Effective Diffusion ◽  
Gas Diffusion ◽  
Pore Connectivity ◽  
Multi Scale ◽  
Pore Area

Based on the capillary hypothesis and fractal theory, a mathematical model for calculating the effective gas diffusion coefficient in porous media is established. By using fractal geometry theory, pore area fractal dimension, tortuosity fractal dimension and pore connectivity are introduced to quantitatively characterize the real internal structure in the porous media. An effective gas diffusion coefficient model for the fractal porous media is derived, and the influence of multi-scale porous media microstructure parameters on the effective gas diffusion coefficient is discussed. The results show that effective gas diffusion coefficient approximates to linearly increase with the increase of porosity, the pore area fractal dimension and the effective gas diffusion coefficient is positive correlation, but the tortuosity fractal dimension is negatively related to it. In the case of different porosities, the gas effective diffusion coefficient varies with the change of the pore diameter ratio, the effective gas diffusion coefficient increases with the increase of pore connectivity.

scholarly journals Modeling water movement in horizontal columns using fractal theory

2010 ◽  
Vol 34 (4) ◽  
pp. 1463-1468 ◽  
Author(s):  
Tairone Paiva Leão ◽  
Edmund Perfect
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Nonlinear Regression ◽  
Hurst Exponent ◽  
Water Movement ◽  
Fractal Theory ◽  
Heterogeneous Porous Media ◽  
Water Infiltration ◽  
Soil Infiltration ◽  
Time Exponent

Fractal mathematics has been used to characterize water and solute transport in porous media and also to characterize and simulate porous media properties. The objective of this study was to evaluate the correlation between the soil infiltration parameters sorptivity (S) and time exponent (n) and the parameters dimension (D) and the Hurst exponent (H). For this purpose, ten horizontal columns with pure (either clay or loam) and heterogeneous porous media (clay and loam distributed in layers in the column) were simulated following the distribution of a deterministic Cantor Bar with fractal dimension H" 0.63. Horizontal water infiltration experiments were then simulated using Hydrus 2D software. The sorptivity (S) and time exponent (n) parameters of the Philip equation were estimated for each simulation, using the nonlinear regression procedure of the statistical software package SAS®. Sorptivity increased in the columns with the loam content, which was attributed to the relation of S with the capillary radius. The time exponent estimated by nonlinear regression was found to be less than the traditional value of 0.5. The fractal dimension estimated from the Hurst exponent was 17.5 % lower than the fractal dimension of the Cantor Bar used to generate the columns.

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