Modeling industrial multiphase flows using Computational Multiphase Fluid Dynamics

Simon Lo, CD-adapco, UK

Introduction

There are examples of multiphase flows everywhere. Naturally occurring multiphase flows might include air bubbles rising in a glass of sparkling water, sand particles carried by wind, rain drops in air. In industry, illustrations might be the injection of air bubbles in a bubble column, separation of particles in a cyclone separator or the spray drying of milk in a spray dryer.

Equations and Models

In order to study flow process using computer simulation, we first need to describe it using equations. These 'transport' equations are obtained by applying the conservation laws of mass, momentum and energy to each fluid phase in the flow domain. From these transport equations we ascertain volume fraction, velocity, and temperature for each phase. Since the phases are generally moving at different velocities and have different temperatures, there are exchanges of momentum and energy between the phases. Correct modeling of these inter-phase exchanges is one crucial factor in a successful simulation.

Taking inter-phase momentum exchanges as an example, the following forces can be identified: drag, turbulence drag, lift and virtual mass. These are exerted between the phases due to their relative motions. Empirical correlations for these forces are well established. As the particle concentration increases inter-particle effects become increasingly significant, so that modification to these forces must be considered. Fortunately, the required equations, models and their solution methods are readily available in STAR-CD from CD-adapco.

The art of formulating and solving the required system of transport equations together with the appropriate interaction terms is known as Computational Multiphase Fluid Dynamics or CMFD. The best way to illustrate the power of this computational technique in flow analyses is by way of examples, described below.

Multiphase Mixing Vessels

Mixing vessels operating in multiphase flow regimes are commonly found in the chemical and process industries. Examples include; catalyst particles that are introduced into vessels to promote specific reactions or gas bubbles that are injected in order to provide chemical species for reactions such as oxygen from air bubbles.

Figure 1 Gas-liquid mixing vessel

Figure 1 demonstrates the computed flow pattern and void distribution in a mixing vessel with a downward pumping, pitched blade impeller. We can clearly see the recirculating flow generated by the impeller in the lower region, and the bulk circulation over the whole tank. The void fraction plot shows that some bubbles are trapped by the recirculating flow resulting in increased gas volume fraction towards the center of the recirculation. Images like this provide valuable information to an engineer, promoting better understanding of the flow dynamics, the spatial distribution of the phases and what these mean in terms of reactions, heat and mass transfers.

Suspension of solid particles in liquids is common feature of many industry processes. To prevent settling of particles, impellers stir the mixture to maintain uniform distribution. Plant operators often ask “What is the optimum speed for the impeller to prevent settling?” Researchers at University of Palermo have carried out a series of experiments [1] using CFD to correctly compute the particle suspension level at different stirrer speeds.

Comparisons between the computed and the experimental results show that the particle suspension levels at three different stirrer speeds (300, 380 and 480 rpm) are in good agreement, see Figure 2.

Liquid-liquid extraction column

Liquid-liquid extraction is often used in the petrochemical industry to promote mass transfer between two fluids. To provide maximum contact between the two fluids a counter-current flow arrangement is used as in the example shown in Figure 3. The heavier fluid is introduced through a central inlet at the top of the column and a distributor screen is used to distribute the fluid. The lighter fluid enters the column through the central inlet at the bottom. Perforated trays are placed horizontally in the column to provide further contact between the two fluids in similar fashion to a distillation column. The two fluids can leave the column via the bottom or the top outer annuli. The flow inside this column is indeed complex. In the computed solution, Figure 3a, we can clearly see the expected collection of the heavier fluid on the trays, the rolling-off at the tips of the trays and the cascade down the column. The computed solution closely resembles the experimental results [2].

Fig2a Partical suspension level at 300rpm	Fig2a Partical suspension level at 380rpm	Fig2a Partical suspension level at 480rpm

Air-lift reactor

Air-lift reactors are also found in many applications, usually to provide the oxygen needed in an oxidation reaction in a liquid, to feed the biomaterials in a bioreactor, or to lift or to stir a liquid. In the example shown in Figure 4, the reactor is made of a straight cylindrical column with a central draft tube. Air is injected via a ring sparger placed in the outer annulus formed by the draft tube. The injection of air lifts the air-liquid mixture up the outer annulus (the riser) and the air disengages and escapes through the free surface. The liquid then circulates down the draft tube (the down-comer). Under some circumstances, the downward liquid flow can even be strong enough to pull some bubbles down the down-comer. The quantity of gas bubbles pulled into the down-comer and the depth they penetrate will depend on the speed of the liquid flow.

Figure 3 Computed solution and experimental results from Total Fina Elf

In this example, measured data is available for comparing the gas hold-up in the riser and down-comer against a wide range of gas injection rates [3]. The results show that gas hold-up in such a column can be predicted reasonably well.

Figure 4 Air-lift reactor and comparison of gas hold-up results

Settling tank

The settling of heavy particles from a liquid stream is an important step in separation, mineral processing and in the recovery of catalyst particles in chemical processes. One special feature about solid particles settling on top of each other is that it is not possible for the particles to fill up 100% of the available space. There are always small gaps between the particles. For solid spheres the maximum packing density is around 60 vol.%. The 'solid-pressure' force model is used to represent the inter-particle forces on particles settling on top of each other and ensure the correct maximum packing limit of the settled layer is obeyed.

Figure 5 Settling of heavy particles

Figure 5 shows the settling of solid particles in a simple tank. In this case the maximum packing limit is 45 vol.%. The building up of the settled layer and the corresponding clearing of particles in the liquid in time can be clearly seen.

Fluidized bed

Fluidized beds are often found in the petrochemical industry in form of a Fluidized Catalytic Cracker (FCC) and in drying of solid particles. The local concentration of solid particles is often near the maximum packing limit. Since particles are fluidized and densely packed, consideration of particle collision is critical. For fluidized bed applications the kinetic theory model for granular flows is commonly used in CFD simulations.

Figure 6 Rise of gas bubbles in a bubbling fluidised bed

Figure 6 shows some results from a simulation showing large gas bubbles rising through a fluidized bed of catalyst particles. First we note that the maximum packing limit of 63 vol.% set for this test case was observed. The particle distribution in the bed is in fact rather random. The rise of the gas bubble pushes up the level of the bed and distorts its profile. Many other interesting phenomena can be observed in a detailed investigation.

Conclusions

Multiphase flows are generally complex and prominent in many industrial processes. Modeling multiphase flows requires a good handle on the latest numerical techniques and having the appropriate and correct models to represent the different physics involved. Some of the difficult challenges in modeling multiphase flows have now been met with the use of CMFD and we have been able to demonstrate some successes in this article. The CMFD analysis technique is now readily available in STAR-CD by CD-adapco.

Engineering analysis tools such as CMFD and CFD will continue to go from strength to strength as engineers across all industries witness the growth in application of this technology and the complexity of the problems it can address.

References

1 G Micale, P Lettieri, F Grisafi, A Scuzzarella and A Brucato
“ CFD simulation of dense solid-liquid stirred suspensions”
CFD in CRE III, Davos, 25-30 May 2003.
2 Total Fina Elf
EU Brite/EuRam Project BE-4322.
3 EniChem
EU Brite/EuRam Project BE95-2039.

About the Author
Simon Lo

After completing his BSc in Mechanical Engineering at Queen Mary’s College, London, in 1980, Simon went on to study for his PhD at Imperial College, London, under Professor Brian Spalding between 1980 and 1984. The topic of his PhD was “CFD modeling of two-phase flows”.

After his PhD, Simon worked for the Central Technical Services of the UK Atomic Energy Authority (UKAEA) responsible for safety analyses of various systems in the UK's Fast Reactor Programme. In 1987, Simon became the Manager of a small consulting group at the Harwell Laboratory providing CFD modeling consultancy services to the Nuclear Industry. At the same time Simon also managed a large CFD model development programme developing a multiphase flow modeling capability using CFX software..

Simon then became the Business Development Manager responsible for expanding business opportunities from the nuclear industry to other industries and particularly to the Chemical and Process Industries in 1996. In 2002 Simon joined CD-adapco as Sector Manager for Chemical and Process Industry.