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.

Since the 1960s, coalescence and breakup phenomena of droplets in gas-liquid mist flow have obtained extensive attention in many physical and chemical process applications [

Numerous semiempirical models that predict droplet size in gas-liquid mist flow have been developed. According to Woodmansee and Hanratty [

Shavit and Chigier [

In this paper, the distribution characteristics of mist flow droplet size are studied using a fractal mechanism. The fractal model of maximum droplet diameter is obtained by combining the analysis of the droplets total surface energy with that of gas flow total turbulent kinetic energy balance.

Many researchers study the distribution characteristics of liquid droplet size using statistical methods. Results show that cross-sectional distribution characteristics of liquid droplet size have fractal features [

Solving the differential of (

The negative variable in (

The cross-sectional area of gas-liquid mist flow,

In cross-section

Generally,

In cross-section

In gas-liquid mist flow, the relationship between liquid velocity,

Substituting (

It can be observed from (

Liquid droplet velocity can be synchronously measured by phase Doppler anemometry (Azzopardi and Teixeira [

According to the definition of velocity and superficial velocity of gas and liquid, the relationship between gas and liquid superficial velocity can be obtained from (

Substituting (

As the maximum droplet diameter,

The droplet breakup model is applied to describe the cause of mist flow formation. According to the balance relationship between the surface energy of the dispersed phase and the turbulent kinetic energy of the continuous phase, Hinze [

According to Adamson [

The total free surface energy of dispersed droplets in continuous gas flow is

It can be seen that the value of the droplet fractal dimension is

By substituting (

According to White [

Thus, the total turbulent kinetic energy of the continuous gas phase can be obtained:

According to Taitel et al. [

The friction factor

Substituting (

In high-speed gas flow, total droplet surface energy is equal to the total turbulent kinetic energy of the gas phase [

Substituting (

It can be seen from (

The droplet size distribution rule describes droplet distribution in gas-liquid mist flow. Droplet distribution is controlled by the balance relationship between total droplet surface energy and total gas turbulent kinetic energy. Therefore, the droplet fractal dimension under gas-liquid mist flow conditions can be calculated by substituting (

Equation (

By combining (

Equation (

Figure

Comparison between the proposed model predictions and experimental results (

Figure

Maximum droplet diameter and droplet fractal dimension versus

Figure

Maximum droplet diameter and droplet fractal dimension versus

Based on liquid droplet fractal size distribution properties in gas-liquid mist flow, we describe the characteristics of droplet distribution under mist flow conditions. The fractal expression of maximum droplet diameter is derived and the internal relationship between maximum droplet diameter and droplet fractal dimension is confirmed by analyzing the balance relationship between total droplet surface energy and total gas turbulent kinetic energy. Therefore, the fractal model of the maximum droplet diameter in gas-liquid mist flow is derived. Fractal expressions of cross-sectional area occupied by gas or liquid and the superficial velocity of gas and liquid are obtained. Every parameter proposed in this paper has clear physical meaning.

Agreement between predictions of the proposed fractal model and experimental measurements is obtained. Results verify the reliability of the proposed model.

The influence of gas and liquid superficial velocity on maximum liquid droplet diameter,

Cross-sectional area of a conduit,

Cross-sectional area occupied by gas,

Cross-sectional area occupied by liquid,

Conduit diameter, m

Droplet fractal dimensions

Total surface free energy, W

Total turbulent kinetic energy, W

Absolute pipe wall roughness, m

Surface free energy per unit volume, J/

Turbulent kinetic energy per unit area, J/

Friction factor at gas superficial velocity

Fractal accumulative droplet number

Reynolds number

Gas velocity, m/s

Liquid velocity, m/s

Gas superficial velocity, m/s

Liquid superficial velocity, m/s

Radial velocity, m/s

Droplet diameter, m

Maximum droplet diameter, m

Minimum droplet diameter, m

Gas density, kg/

Liquid density, kg/

Interfacial tension, N/m.

Gas phase

Liquid phase

Superficial

Turbulent.

The authors are grateful for financial support from the National Science Fund for Distinguished Young Scholars of China (Grant no. 51125019) and Science and Technology Innovation Fund of Southwest Petroleum University (Grant no. GIFSB0701).