Elsevier

Chemical Engineering Science

Volume 207, 2 November 2019, Pages 672-687
Chemical Engineering Science

Experimental and numerical study of cavitation flows in venturi tubes: From CFD to an empirical model

https://doi.org/10.1016/j.ces.2019.07.004Get rights and content

Highlights

  • Experimental and numerical studies of cavitating Venturi tubes.

  • The effect of scale-ratio was investigated numerically.

  • A semi-empirical model of cavitating Venturi tubes was derived.

Abstract

This work is devoted to experimental and numerical studies of cavitation phenomena in Venturi tubes with different geometries. A two-phase mixture model has been validated against experimental data. The numerical results showed good agreement with the experimental data. Experimental studies have been carried out for two different Venturi tubes with convergent angles of 19° and 45°, respectively. The effect of the convergent angle on the cavitation performance was investigated experimentally and numerically. Both the numerical and experimental studies reveal that the change in the convergent angle has significant effects on flow characteristics and the generation of cavitation. It was shown that a 45° convergent angle enhances cavitation in comparison with 19° angle. A scaled-up study of the Venturi geometry has been conducted using CFD-based numerical simulations. Finally, a semi-empirical model enabling the prediction of cavitation in Venturi tubes has been developed and validated.

Introduction

Cavitation, by definition, is the process by which vapor bubbles forming and growing in a liquid when the local static pressure falls below the vapor pressure at a constant ambient temperature (Knapp et al., 1970, Brennen, 2013).It is one of the most effective process that having been widely adopted in various industrial applications ranging from wastewater treatment (Gagola et al., 2018), chemical synthesis and food processing to mineral processing (Zhou et al., 1997a). In the specific case of applications in mineral processing, a Venturi tube is of great significance for improving fine particle flotation efficiency. Flotation is a primary used mineral extraction process in which bubbles of air attach on the intended minerals for separation from the solid particles with varied surface wettabilities (Yoon and Luttrell, 1986, Yoon et al., 1997). Due to the difference of densities, the intended minerals (hydrophobic) agglomerate on the top surface and then be collected for the next purification process, while the rest of particles (hydrophilic) settle down on the bottom and then be discharged. Flotation efficiency significantly depends on the particle size. A high flotation efficiency is limited to the minerals size in the range between 10 μm and 100 μm (Tao, 2005). The recovery rate decreases significantly for particles smaller than 20 μm (Zhou et al., 1997b). The low possibility of particle-bubble collisions contributed by the low mass and kinetic energy is responsible for the inefficient fine particles recovery (Zhou et al., 1997b). For this reason, hydrodynamic cavitation provides a practical method for efficient fine particle flotation as a result of increasing particle-bubble collision and attachment probability and decreasing detachment probability. The main advantages of using cavitation in flotation technologies are both the production of micron- and nano-sized vapor bubbles (Oliveira et al., 2018), which are advantageous for particle aggregation, and more effective collision of solid hydrophobic particles with air and vapor bubbles generated by cavitation. Fig. 1a shows a schematic drawing of a flotation column and the role of cavitational bubbles generated from a Venturi tube. It can be seen that a Venturi tube is composed of a convergent section, throat section, and divergent section, see Fig. 1b. When the pressure in the throat of the Venturi is lower than the vapor pressure as the fluid flows through the throat section, a quick phase transition from liquid to vapor occurs. Tiny bubbles generated by the cavitating Venturi tube coat the surface of hydrophobic particles and act as a bridge, producing an attractive force between the hydrophobic particle and the flotation size bubble (Ahmadi et al., 2014, Li, 2014). This attractive force enhances the fine particle aggregation, increasing their flotation efficiency (Zhou et al., 1997a). Thus, improving the efficiency of a cavitating Venturi tube, thereby enhancing the flotation performance of fine particles, has long been a goal in the minerals industry (Zhou et al., 2016).

The efficiency of the cavitating Venturi tube is mainly dependent on the cavitation phenomenon and its interaction with turbulent flow, which in turn depends on the geometry of the Venturi tube (Bashir et al., 2011, Ashrafizadeh and Ghassemi, 2015, Zhang, 2017). Some important geometrical parameters such as the throat length, the throat diameter or the convergent and divergent angles play a significant role in the design of a Venturi tube, since these parameters greatly affect the cavitational inception and yield in Venturi tubes.

With the continuous improvement of various cavitation models based on computational fluid dynamics (CFD) and their implementation in commercial CFD software, e.g. ANSYS Fluent (Jangir et al., 2017, Li et al., 2018) and open-source CFD software, e.g. OPEN Foam (Chen and Oevermann, 2018), noticeable numerical works have been published focusing on the influences of Venturi tube geometric parameters and operational conditions on cavitation flows in different Venturi tubes. For example, Ashrafizadeh and Ghassemi (2015) used a two-dimensional (2D) K-Epsilon (k-ε) turbulence model to investigate the influences of geometrical parameters such as the throat diameter, throat length and divergent angle on the critical pressure ratio and cavitation region. The numerical results indicate that the cavitating region and critical pressure ratio decrease as the throat diameter is reduced from 1.5 mm to 0.7 mm. The critical pressure ratio increases as the divergent angle decreases from 15 to 5°, and decreases as the throat length rises from 1 to 2.5 mm. Zhang (2017) carried out three-dimensional (3D) CFD simulations using a k-ε standard turbulence model to analyze the effects of the divergent angle, the contraction ratio (d/D), and the ratio of the throat section length to diameter (L/d) on the fluid flow and pressure distribution in the Venturi tube. The numerical results show that the vacuum pressure (the pressure difference between minimum pressure and atmosphere) and mass flux increase by 19 kPa and 0.03 kg/s respectively as the contraction ratio increases from 0.2 to 0.8. On the other hand, as the ratio of the throat section length to diameter increases from 1 to 7, the vacuum pressure and mass flux decrease by 2 kPa and 0.0002 kg/s, respectively. In addition, both the vacuum pressure and the mass flux drop 12 kPa and 12 kg/s as the divergent angle ascends from 15° to 60°. Zhao et al. (2019) performed 2D CFD simulations using a K-Omega (k-ω) turbulence model to study the effect of divergent angle on bubble breakup in Venturi tubes. The author showed that vortex region increases and bubble breakup positions are brought forward as the increase in the divergent angle from 5° to 12.5°. Bashir et al. (2011) conducted CFD analyses of different Venturi tubes such as circular, slit, and elliptical Venturis, at different ratios of throat diameter to throat length (1:0.5, 1:1, 1:2, and 1:3) and divergent angle (5.5°, 6.5°,7.5°, and 8.5°). k-ε was applied to model fluid turbulence in both 2D and 3D domains. The optimum divergent angle and ratio of throat diameter to throat length were found to be 5.5° and 1:1 for all the Venturi tubes considered.

Margot et al. (2012) used seven different 3D turbulence models (k-ε/low Re/hybrid, k-ε/high Re/standard, k-ε Re-Normalisation Group (RNG)/standard, k-ω shear stress transport (SST) and standard/high and low Re/hybrid and standard) to study the cavitation flow within a throttle channel at different operation conditions. The results show that the void volume fraction decreases as the liquid viscosity increases. The k-ε/low Re/hybrid model provides a better agreement against experiment data as compared to other models. It was shown that the total pressure distribution predicted numerically is lower than the experimental data due to the pressure loss at the entrance.

Srinivasan et al. (2010) developed a novel modeling approach (Volume-of-Fluid-Cavitation-Induced-Momentum-Defect) capable of simultaneously predicting the cavitation activities of liquid-vapor phases and the break-up dynamics of liquid-gas phases within the internal and exterior regions of the nozzle, in conjunction with the RNG k-ε turbulence model. The simulation results showed reasonable fit on the velocity profile against experimental data published in the literature. The cavitation cluster length is reduced as Reynolds number decreases from 70,000 to 58,000. In addition, the stretching or diffusion effects of the cluster in the downstream region decreased as the cavitation number increases from 0.65 to 0.94.

Kumar and Moholka (2007) proposed a conceptual design for a novel hydrodynamic cavitation reactor that uses a converging-diverging nozzle with a gas sparger to generate cavitational bubbles. Based on the simulation results, they found that increasing the upstream pressure (from 1 to 1.5 atm) and the nozzle length (from 3 to 6 in.) and decreasing the initial bubble size (from 200 to 100 μm) is a means of intensifying the sonochemical effects (bubble size, temperature and pressure peaks reached in the bubble at the first compression). They also found that an argon bubble can produce greater sonochemical effects in comparison with an air bubble.

The analysis of various works on the cavitating Venturi tube shows that the existing CFD models (Srinivasan et al., 2010, Li et al., 2018) and CFD studies (Jangir et al., 2017, Bashir et al., 2011, Ashrafizadeh and Ghassemi, 2015, Zhang, 2017) have largely been used to investigate the effect of some critical geometric parameters, including the divergent angle, the ratio of the throat section length to diameter, and the contraction ratio, on Venturi performances. However, little attention paid to the effect of the convergent angle in the cavitating Venturi tube. Additionally, the difference between lab-scale and large-scale Venturi tubes has not been investigated in details. Therefore, the main objective of this work is to study how the convergent angle affects the cavitation performance and to produce a numerical study of how scale-up affects cavitation phenomena. In this work the performance of lab-scale Venturi tube was investigated experimentally and numerically. Lab-scale experiments were carried out to validate the simulation results. The commercial CFD software ANSYS Fluent 16.2 (Inc Ansys, 2011) was employed in this study. The paper is organized as follows. Section 2 presents a description of the experiments. The details of the computational model are given in Section 3. Section 4 outlines the results of the present study. Finally, conclusions are drawn in Section 5.

Section snippets

Experimental setup

The experimental system is schematically illustrated in Fig. 2. The setup consists in a computer, an oscilloscope, a pressure transducer, a flow meter, a pump, a water tank and a cavitating Venturi tube. The whole system is a closed-loop system. The peristaltic pump (Masterflex I/P Easy-Load, Germany) can deliver the tap water flow from 0 to 10 LPM.

For the measurements, a pressure transducer (Transducers Direct TDH40, USA) with an accuracy of ±0.4% FS records information on the inlet pressure, P

Computational model

For the multiphase flow solutions, the single-fluid mixture model (available in the commercial CFD software ANSYS-Fluent (Inc Ansys, 2011)) is employed to simulate cavitating two-phase flows (water-vapor) in this study. The mixture model is capable to predict cavitation phenomena in water flows by solving a set of transport equations governing the mixture continuity, momentum, energy and the disperse phase for the volume fraction equation (Inc Ansys, 2011). The mixture model assumes that the

Results

To analyse the results, we use the so-called cavitation number, σ, which is one of the special dimensionless parameters in the Venturi tube used to evaluate the potential for the cavitation. It is defined as the ratio of the pressure drop between the throat and downstream section of the cavitating device to the kinetic head at the throat. The formula of the cavitation number is given as (Brennen, 2013):σ=P-PV(T)12ρlUth2where P is the fully recovered downstream pressure, PV is the vapor

Conclusions

In the present study, numerical simulations of cavitating Venturi tubes were performed using an axisymmetric 2D CFD-based model available in the commercial CFD software ANSYS FLUENT 16.2. A mixture model based on a water-vapor-phase mixture is used to reproduce the experiments. Comparison between the experimental measurements and numerical simulations showed good agreement. The influence of the convergent angle of cavitating Venturi tubes on flow characteristics and generation of cavitation was

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgments

Financial support from the Natural Science and Engineering Research Council of Canada (NSERC), the Canadian Centre for Clean Coal/Carbon and the Mineral Processing Technologies (C5MPT) and Canadian Mining Industry Research Organization (CAMIRO) is greatly appreciated.

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