scholarly journals A Fractal Model for the Maximum Droplet Diameter in Gas-Liquid Mist Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-Hua Tan ◽  
Jian-Yi Liu ◽  
Xiao-Ping Li ◽  
Guang-Dong Zhang ◽  
Chuan Tang
Keyword(s):  
Fractal Dimension ◽  
Droplet Size ◽  
Liquid Droplet ◽  
Fractal Theory ◽  
Droplet Diameter ◽  
Droplet Size Distribution ◽  
Fractal Model ◽  
Droplet Surface ◽  
Superficial Velocity ◽  
Mist Flow

Distribution characteristics of liquid droplet size are described using the fractal theory for liquid droplet size distribution in gas-liquid mist flow. Thereby, the fractal expression of the maximum droplet diameter is derived. The fractal model for maximum droplet diameter is obtained based on the internal relationship between maximum droplet diameter and the droplet fractal dimension, which is obtained by analyzing the balance between total droplet surface energy and total gas turbulent kinetic energy. Fractal model predictions of maximum droplet diameter agree with the experimental data. Maximum droplet diameter and droplet fractal dimension are both found to be related to the superficial velocity of gas and liquid. Maximum droplet diameter decreases with an increase in gas superficial velocity but increases with an increase in liquid superficial velocity. Droplet fractal dimension increases with an increase in gas superficial velocity but decreases with an increase in liquid superficial velocity. These are all consistent with the physical facts.

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.

Numerical Simulation of Droplet Size Distribution in Vertical Upward Annular Flow

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Y. Liu ◽  
W. Z. Li
Keyword(s):  
Size Distribution ◽  
Droplet Size ◽  
Annular Flow ◽  
Liquid Droplet ◽  
Large Diameter ◽  
Droplet Size Distribution ◽  
Population Balance ◽  
Balance Model ◽  
Diameter Distribution ◽  
Two Fluid

The liquid droplet size distribution in gas-liquid vertical upward annular flow is investigated through a CFD (computational fluid dynamics)-PBM (population balance model) coupled model in this paper. Two-fluid Eulerian scheme is employed as the framework of this model and a population balance equation is used to obtain the dispersed liquid droplet diameter distribution, where three different coalescence and breakup kernels are investigated. The Sauter mean diameter d32 is used as a bridge between a two-fluid model and a PBM. The simulation results suggest that the original Luo–Luo kernel and the mixed kernel A (Luo’s coalescence kernel incorporated with Prince and Blanch’s breakup kernel) can only give reasonable predictions for large diameter droplets. Mixed kernel B (Saffman and Turner’s coalescence kernel incorporated with Lehr’s breakup kernel) can accurately capture the particle size distribution (PSD) of liquid droplets covering all droplet sizes, and is appropriate for the description of liquid droplet size distribution in gas-liquid annular flow.

Evaluation of Models for Droplet Shear Effect of Centrifugal Pump

2018 ◽  
Author(s):  
Ramin Dabirian ◽  
Shihao Cui ◽  
Ilias Gavrielatos ◽  
Ram Mohan ◽  
Ovadia Shoham
Keyword(s):  
Experimental Data ◽  
Size Distribution ◽  
Centrifugal Pump ◽  
Droplet Size ◽  
Separation Efficiency ◽  
Droplet Diameter ◽  
Droplet Size Distribution ◽  
Production Equipment ◽  
Transportation Equipment ◽  
Log Normal

During the process of petroleum production and transportation, equipment such as pumps and chokes will cause shear effects which break the dispersed droplets into smaller size. The smaller droplets will influence the separator process significantly and the droplet size distribution has become a critical criterion for separator design. In order to have a better understanding of the separation efficiency, estimation of the dispersed-phase droplet size distribution is very important. The objective of this paper is to qualitatively and quantitatively investigate the effect of shear imparted on oil-water flow by centrifugal pump. This paper presents available published models for the calculation of droplet size distribution caused by different production equipment. Also detailed experimental data for droplet size distribution downstream of a centrifugal pump are presented. Rosin-Rammler and Log-Normal Distributions utilizing dmax Pereyra (2011) model as well as dmin Kouba (2003) model are used in order to evaluate the best fit distribution function to simulate the cumulative droplet size distribution. The results confirm that applying dmax Pereyra (2011) model leads to Rosin-Rammler distribution is much closer to the experimental data for low shear conditions, while the Log-Normal distribution shows better performance for higher shear rates. Furthermore, the predictions of Modified Kouba (2003) dmin model show good results for predicting the droplet distribution in centrifugal pump, and even better predictions under various ranges of experiments are achieved with manipulating cumulative percentage at minimum droplet diameter F(Dmin).

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.

Study about Characteristics of Cement Paste on Fractal Theory

2013 ◽  
Vol 423-426 ◽  
pp. 1051-1054
Author(s):  
Tian Yang Zhai
Keyword(s):  
Compressive Strength ◽  
Fractal Dimension ◽  
Cement Paste ◽  
Permeability Coefficient ◽  
Fractal Theory ◽  
Fractal Model ◽  
Concrete Compressive Strength ◽  
Internal Pore Structure ◽  
The Relationship ◽  
Internal Pore

A fractal model to simulate cement paste internal pore structure, and on this basis deduce that fractal dimension is D and the corresponding pore is r, the relationship between porosity is P. MIP was measured test. Then calculated the different ages of the fractal dimension of cement and concrete compressive strength, tensile strength and permeability coefficient. The results showed that: compressive strength, permeability and fractal dimension has a good correlation. Whey in cement in the process of hydration of cement products continue to fill the pores, making the compressive strength increased 70%, permeability is declining.

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.

scholarly journals Research On the Fractal Dimensions of the Organic-Rich Shale Pores Via Different Models

2022 ◽  
Vol 2152 (1) ◽  
pp. 012020
Author(s):  
Fangyao Dai
Keyword(s):  
Fractal Dimension ◽  
Gas Adsorption ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Relative Pressure ◽  
Longmaxi Formation ◽  
High Relative Pressure ◽  
Adsorption Data ◽  
Different Dimensions

Abstract Fractal dimension can be used to the pore surface characterize. For pore structures in different sizes, the calculation models of fractal theory should be distinguished due to the different principles of the gas adsorption experiments. To further study the adaptability of the fractal model for gas adsorption experimental data, the author collected shale samples of Longmaxi formation from Well JY1, then CO2 and N2 adsorption provided the PSD curves. In addition, the fractal dimensions of micropore and mesopore were calculated by the Jaroniec fractal model and Frenkel–Halsey–Hill (FHH) fractal model respectively. The research shows that the Jaroniec model may be suitable to calculate CO2 adsorption data and could characterize the fractal dimension of micropore, while the FHH model may be suitable to calculate N2 adsorption data in the high relative pressure region. It suggests that the micropore and mesopore could have different dimensions and the evaluation of the structure in shale pores should consider both of them.

scholarly journals Dinamika tetes dalam kolom isian

2018 ◽  
Vol 7 (1) ◽  
pp. 710
Author(s):  
Danu Ariono ◽  
Dwiwahju Sasongko ◽  
Priyono Kusumo
Keyword(s):  
Mass Transfer ◽  
Transfer Coefficient ◽  
Mass Transfer Coefficient ◽  
Size Distribution ◽  
Droplet Size ◽  
Droplet Diameter ◽  
Mass Transfer Rate ◽  
Packed Column ◽  
Droplet Size Distribution ◽  
Droplet Dynamics

To date, evaluation of the performance of liquid-liquid extraction in packed columns has not been able to produce satisfactory results, because the correlations used in this evaluation are empirical in nature, with a very limited range of validity. One of the causes of this limitation is the use of the assumption that the dynamics of liquid dispersed in droplets is constant (in terms of shape, dimensions, and numbers), so that the mass transfer interfacial area and mass transfer coefficient in the column are assumed to be constant. In reality, dynamics of droplets in a column is not constant, due to the imbalance between droplet coalescence and disintegration. For a given droplet diameter, there is an increase in numbers of droplets due to coalescence of smaller droplets, and a  decrease in numbers of droplets due to disintegration into smaller droplets. These coalescence and disintegration phenomena may be caused by various factors, including the existence of packings which impede the flow of droplets. These phenomena impact the mass transfer rate from continuous to dispersed phase, and vice versa, due to a variation in the interfacial contact area and mass transfer coefficient. The observation of droplet dynamics from droplet formation until its motion through void spaces between packings is a critical factor in developing a model that can describe the performance of the packed column. The dynamics of droplets is influenced by various operational and physical variables.  A droplet dynamics experiment has been undertaken, aimed at obtaining the droplet size distribution at specific heights along the column. This distribution is to be used to develop mass transfer coefficient correlations in the continuous and dispersed phases.Keywords: droplet size distribution, packed column Abstrak Evaluasi unjuk kerja ekstraksi cair-cair dalam kolom isian (packed column) hingga saat ini belum dapat memberikan hasil yang memuaskan karena korelasi-korelasi yang  digunakan  masih  bersifat  empiris serta daerah keberlakuannya sangat terbatas. Salah satu penyebab keterbatasan berlakunya korelasi tersebut ialah penggunaan anggapan bahwa dinamika cairan yang terdispersi dalam bentuk tetesan bersifat konstan (bentuk, ukuran serta jumlahnya), sehingga harga luas perpindahan massa dan harga koefisien perpindahan massa dalam kolom dianggap tetap. Kenyataannya dinamika tetesan dalam kolom tidak konstan akibat adanya tetesan yang bergabung dan pecah dalam jumlah yang  tidak sama. Pada suatu harga diameter tetesan tertentu, ada penambahan jumlah tetesan akibat penggabungan tetesan­ tetesan yang ukurannya lebih kecil serta adanya pengurangan jumlah tetesan akibat pecahnya tetesan menjadi tetesan-tetesan yang lebih kecil. Peristiwa penggabungan dan pemecahan tetesan dapat disebabkan berbagai faktor temasuk adanya isian yang menghalangi gerakan tetesan. Kejadian tersebut akan mempengaruhi laju proses perpindahan massa dari fasa kontinyu ke fasa  terdispersi  atau sebaliknya, karena adanya variasi luas permukaan kontak serta koefisien perpindahan massanya. Pengamatan dinamika tetesan mulai saat pembentukan tetes hingga pergerakannya saat melewati sela-sela isian merupakan faktor penting dalam  membangun model  yang  dapat menggambarkan unjuk kerja kolom isian. Dinamika tetesan tersebut dipengaruhi oleh berbagai variabel operasi dan variabel fisik. Eksperimen dinamika fetes yang dilakukan diarahkan untuk memperoleh distribusi ukuran tetes pada posisi ketinggian tertentu dan distribusi tersebut akan digunakan untuk pengembangan  korelasi koefisien perpindahan massa difasa  dispersi danfasa kontinyu.Kata kunci: distribusi ukuran tetes, kolom isian.

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.

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