A NOVEL FRACTAL SOLUTION FOR LAMINAR FLOW RESISTANCE IN ROUGHENED CYLINDRICAL MICROCHANNELS

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050097
Author(s):  
BOQI XIAO ◽  
YONGHUI LIU ◽  
HANXIN CHEN ◽  
XUBING CHEN ◽  
GONGBO LONG
Keyword(s):  
Laminar Flow ◽  
Friction Factor ◽  
Present Model ◽  
Fractal Theory ◽  
Fractal Model ◽  
Average Height ◽  
Relative Roughness ◽  
Darcy Friction Factor ◽  
Poiseuille Number ◽  
Cylindrical Microchannel

In this work, a novel fractal model for the laminar flow in roughened cylindrical microchannels is proposed. The average height of rough elements is derived using the fractal theory. The effects of relative roughness on the friction factor and the Poiseuille number are discussed. It is found that the Darcy friction factor and the Poiseuille number increase with the increase in the relative roughness in the cylindrical microchannel. Besides, it is observed that the Darcy friction factor decreases with the increase in the Reynolds number. Each parameter of the proposed model has a clear physical meaning. The present model can properly reveal some mechanisms that affect the laminar flow in roughened cylindrical microchannels. The present model improves the understanding of the physical mechanisms of fluid flows through roughened cylindrical microchannels. Our model predictions are compared with the existing experimental data, and good agreement can be found.

scholarly journals Prediction on Droplet Sauter Mean Diameter in Gas-Liquid Mist Flow Based on Droplet Fractal Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Jian-Yi Liu ◽  
Xiao-Hua Tan ◽  
Zhou Fan ◽  
Xu-Tao You ◽  
Zhou Li ◽  
...  
Keyword(s):  
Present Model ◽  
Fractal Theory ◽  
Fractal Model ◽  
Droplet Surface ◽  
Superficial Velocity ◽  
Sauter Mean Diameter ◽  
Model Predictions ◽  
Mist Flow ◽  
Mean Diameter ◽  
Fluid Characteristics

We present a fractal model for droplet Sauter mean diameter in gas-liquid mist flow, based on the droplet fractal theory and the balance relationship between total droplet surface energy and total gas turbulent kinetic energy. The present model is expressed as functions of the droplet fractal dimension, gas superficial velocity, liquid superficial velocity, and other fluid characteristics. Agreement between the present model predictions and experimental measurements is obtained. Results verify the reliability of the present model.

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.

Simulation Calculation of Friction Factor of the End Face for Mechanical Seals Based on Fractal Theory

2014 ◽  
Vol 687-691 ◽  
pp. 142-147 ◽  
Author(s):  
Long Wei ◽  
Peng Gao Zhang ◽  
Gui Fang Fang
Keyword(s):  
Liquid Film ◽  
Surface Topography ◽  
Friction Factor ◽  
Fractal Theory ◽  
Fluid Pressure ◽  
Fractal Model ◽  
Contact Friction ◽  
Mechanical Seals ◽  
Viscous Shear Stress ◽  
Viscous Shear

In order to study the effects of operating parameters and surface topography on friction factors between the end faces for mechanical seals, a friction factor fractal model between end faces for contact mechanical seals was established based on the contact fractal model and the average film thickness fractal model, adopting fractal parameters to represent surface topography, separating friction into viscous shear friction of liquid film and contact friction of asperities, and representing the effect of actual rough surface on viscous shear stress of liquid film by introducing the contact factor. The influencing factors of friction factor for B104a-70 mechanical seal were analyzed by simulating. Results showed that the friction factor between the surfaces increases with the increases of spring pressure when the end faces are coarser, while the friction factor decreases slightly with the increases of spring pressure when the end faces are smoother. The friction factor between the faces decreases with the increases of the sealed fluid pressure, which increases approximate linearly with the increases of rotating speed, and it increases with the increases of fractal dimension of end faces and the decreases of the characteristic scale factor.

Visual Experimental Study of Flow Field in Rectangular Microchannels With Different Surface Roughness

2007 ◽  
Author(s):  
Chunping Zhang ◽  
Dawei Tang ◽  
Peng Han ◽  
Xuegong Hu
Keyword(s):  
Experimental Study ◽  
Surface Roughness ◽  
Reynolds Number ◽  
Flow Field ◽  
Friction Factor ◽  
Transitional Flow ◽  
Traditional Values ◽  
Relative Roughness ◽  
Laminar To Turbulent Transition ◽  
Poiseuille Number

A new visual experimental study is performed on flow field for laminar to turbulent transition in three different roughness microchannels with almost the same aspect ratio. The red trace is a thin straight line in microchannels at the low Reynolds number. The exit, middle and entrance region become diffuse and transitional flow occurs successively with increasing Reynolds number. The transition Reynolds number is about 1700 for relative roughness smaller than 3%, but the transition Reynolds number is about 1500 with relative roughness is 3.15%, which show that transition occurs earlier than the traditional values. The friction factor and Poiseuille number were also measured in microchannels. It is found that the friction factor and Hagen-Poiseuille number increased with surface roughness, and were significantly greater than the classical values.

A Novel Explicit Equation for Friction Factor in Smooth and Rough Pipes

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Atakan Avci ◽  
Irfan Karagoz
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Entire Range ◽  
Present Model ◽  
Good Prediction ◽  
Explicit Equation ◽  
Relative Roughness ◽  
Logarithmic Velocity Profile

In this paper, we propose a novel explicit equation for friction factor, which is valid for both smooth and rough wall turbulent flows in pipes and channels. The form of the proposed equation is based on a new logarithmic velocity profile and the model constants are obtained by using the experimental data available in the literature. The proposed equation gives the friction factor explicitly as a function of Reynolds number and relative roughness. The results indicate that the present model gives a very good prediction of the friction factor and can reproduce the Colebrook equation and its Moody plot. Therefore, the new approximation for the friction factor provides a rational, accurate, and practically useful method over the entire range of the Moody chart in terms of Reynolds number and relative roughness.

A FRACTAL MODEL FOR PREDICTING OXYGEN EFFECTIVE DIFFUSIVITY OF POROUS MEDIA WITH ROUGH SURFACES UNDER DRY AND WET CONDITIONS

Fractals ◽  
2021 ◽  
pp. 2150076
Author(s):  
BOQI XIAO ◽  
QIWEN HUANG ◽  
BOMING YU ◽  
GONGBO LONG ◽  
HANXIN CHEN
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Oxygen Diffusion ◽  
Water Saturation ◽  
Rough Surfaces ◽  
Effective Diffusivity ◽  
Fractal Model ◽  
Relative Roughness ◽  
Oxygen Diffusivity ◽  
Dry And Wet Conditions

Oxygen diffusion in porous media (ODPM) with rough surfaces (RS) under dry and wet conditions is of great interest. In this work, a novel fractal model for the oxygen effective diffusivity of porous media with RS under dry and wet conditions is proposed. The proposed fractal model is expressed in terms of relative roughness, the water saturation, fractal dimension for tortuosity of tortuous capillaries, fractal dimension for pores, and porosity. It is observed that the normalized oxygen diffusivity decreases with increasing relative roughness and fractal dimension for capillary tortuosity. It is found that the normalized oxygen diffusivity increases with porosity and fractal dimension for pore area. Besides, it is seen that that the normalized oxygen diffusivity under wet condition decreases with increasing water saturation. The determined normalized oxygen diffusivity is in good agreement with experimental data and existing models reported in the literature. With the proposed analytical fractal model, the physical mechanisms of oxygen diffusion through porous media with RS under dry and wet conditions are better elucidated. Every parameter in the proposed fractal model has clear physical meaning, with no empirical constant.

Prediction of Heat Transfer in Turbulent Decaying Swirling Flow

1999 ◽  
Author(s):  
Yusuf A. Uskaner
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Experimental Study ◽  
Friction Factor ◽  
Loss Factor ◽  
Swirling Flow ◽  
Swirling Flows ◽  
Heat Transfer Augmentation ◽  
Relative Roughness ◽  
Inlet Swirl

Abstract This paper presents an aproach for the prediction of heat transfer augmentation in decaying swirling flow in a pipe by making an analogy between the increase in friction factor due to swirl and increase in heat transfer due to swirl. The proposed method can be used to predict heat transfer for decaying swirling flow in smooth and rough pipes which can be applied to different swirl generators based on the known inlet swirl conditions. An experimental study is performed regarding the swirling flow of air in smooth and rough pipes. The experimental study covered only the fluid dynamics of swirling flow. No heat transfer experiments were done. It is determined experimentally that in swirling flows degree of swirl decays continuously along the smooth and rough pipes and the total loss factor is the sum of friction factor for non-swirling flow and the swirl loss factor. Swirl loss factor is found to be a function of the degree of swirl and pipe relative roughness. Using the relations obtained experimentally for the variation of swirl strength and loss factor along the pipe, an equation is proposed to be used for the prediction of heat transfer in turbulent decaying swirling flows.

Experimental Study on Roughness Effect for Laminar Micro-Channel Gas Flow

2001 ◽  
Author(s):  
Jih-Hsing Tu ◽  
Fangang Tseng ◽  
Ching-Chang Chieng
Keyword(s):  
Experimental Study ◽  
Surface Roughness ◽  
Friction Factor ◽  
Gas Flow ◽  
Micro Channel ◽  
Micro Machining ◽  
Roughness Effect ◽  
Relative Roughness ◽  
Smooth Channel ◽  
Micro Channels

Abstract Present study investigates the roughness effect on laminar gas flow for microchannels ranging from 40 to 600 μm with various roughness heights (40–82 nm) by systematical experiments. The micro-channels are manufactured by micro-machining technology and KOH anisotropic etching is employed to achieve various roughness patterns. Experimental results shows that higher product levels of Reynolds number (Reh) and friction factor (f) are obtained for microchannels of larger size and smaller relative roughness and friction factor f approaches to laminar flow theory value f0 for very smooth channel but the ratio of (f/f0) decreases as the surface roughness increases.

Normal Contact Stiffness Fractal Geometric Model Based on the Gamma Distribution of Rough Joint Surface

2013 ◽  
Vol 760-762 ◽  
pp. 2064-2067 ◽  
Author(s):  
Jing Fang Shen ◽  
Ke Xiang Wu ◽  
Fei Yang
Keyword(s):  
Convex Body ◽  
Gamma Distribution ◽  
Contact Stiffness ◽  
Geometric Model ◽  
Fractal Theory ◽  
Fractal Model ◽  
Joint Surface ◽  
Engineering Practice ◽  
Normal Contact ◽  
Normal Contact Stiffness

In this article, according to WenShuHua and Zhangxueniang fractal model, we point out the deficiency. Based on the fractal theory and Zhang, Wens contact stiffness fractal model, this paper puts forward Gamma distribution of rough joint surface normal contact stiffness. This paper considers micro convex body for ellipsoid, contact area for elliptic. This is slightly convex body for sphere hypothesis is more close to the actual situation. At the same time by using statistics theory, considering the contact ellipse long, short axis a and b are greater than zero, the assumption of a and b to two-dimensional Gamma distribution, it is more suitable for engineering practice.

COMPRESSIVE STRENGTH OF FRACTAL-TEXTURED FOAMED CONCRETE

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940003 ◽  
Author(s):  
Y. CHEN ◽  
Y. F. XU
Keyword(s):  
Compressive Strength ◽  
Fractal Dimension ◽  
Porous Structure ◽  
Fractal Theory ◽  
Scaling Law ◽  
Weight Ratio ◽  
High Strength ◽  
Labor Cost ◽  
Fractal Model ◽  
Foamed Concrete

Foamed concrete possesses characteristics such as high strength-to-weight ratio and low density, and widely used to reduce dead loads on the structure and foundation, contributes to energy conservation, and lowers the labor cost during construction. In this paper, the objective is to propose prediction relation for the compressive strength of foamed concrete by fractal theory. A theoretical relation was derived for the compressive strength relating to porosity based on the fractal model for foamed concrete. The proposed relation stands out compared to empirical model since it employs easily measurable parameter, the fractal dimension of porous structure in foamed concrete. The fractal dimension of porous structure can be calculated from the scaling law of the compressive strength of foamed concrete. The fractal model for porous structure serves as a simple and effective tool for predicting the compressive strength of foamed concrete because of its ease in application. The prediction relation of the compressive strength developed in this paper is found to match well with the measured strength.

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