LECTURE 2

During the simultaneous flow of two phases through any conduit, the two fluids can distribute themselves

in a wide variety of ways, which is not under the control of the experimenter or the designer. There could be a large number of possible distributions, depending on the geometry and orientation of the tube as well as physical properties and velocity of the two phases.Nevertheless, a few factors restrict the variety of interfacial distribution. These include (a) the surface tension effects which tend to create curved interfaces and keeps the channel wall always wet with liquid during gas-liquid flows (unless the wall temperature is above the saturation temperature) and (b) gravity which tends to pull the heavier phase at the bottom in a non-vertical channel. A close observation of the different interfacial distributions reveals that they can be broadly delineated into different flow regimes or flow patterns which are characterised by typical topographical distribution of the two phases. An accurate estimation of the different patterns is essential for the understanding and analysis of two phase flow since all the transport processes like momentum, heat as well as mass transfer are strongly

influenced by the phase distribution. Therefore, a large number of studies, both experimental and theoretical, have been reported on the characterization of flow patterns for different combinations of the two phases. From a survey of the past studies, it is observed that many of the two phase systems have a common geometrical structure. Accordingly, two phase flow can be classified into several major groups such as separated flow, transitional or mixed flow and dispersed flow. The different flow patterns which confirm to the aforementioned descriptions for different fluid types are listed in Table2.1.

Table 1: Generalised flow patterns for different fluid types

Flow pattern

Classification of flow pattern

Schematic Description Application

Separated flow

• Film flow • Gas‐liquid stratified

flow • Liquid‐liquid

stratified flow • Gas‐liquidliquid

three layer flow

Liquid film in

gas/Gas film in liquid. Lighter fluid flowing over the heavier one

• Film condensation • Film boiling

• Annular flow • Core annular flow (for liquid‐liquid

cases)

Gas core Liquid film

Viscous liquid core and water film

Annular Flow, Rewetting, Film boiling, Transportation of crude oil

• Jet flow

Liquid jet in gas/

Gas jet in liquid

Jet condenser

Dispersed flow Bubbly

Gas bubbles in liquid

Chemical reactors

Droplet flow namely

Oil droplet in water Water droplet in oil

Liquid droplets in an immiscible liquid/ gas

Spray cooling

Particulate flow

Solid particles in gas/liquid

Transportation of powder

Mixed/transitional flow

Cap, slug, churn

Sodium boiling in forced convection

Bubbly annular flow

Gas bubbles in liquid film Gas core

Evaporators with wall nucleation

Droplet

annular flow/ Wispy annular flow

Gas core with droplets and annular liquid film Irregular liquid chunks

in continuous gas core which is separated from pipe wall by an annular liquid film

Steam generator

Bubbly droplet

Annular flow

Gas core with droplets

Liquid film with gas bubbles

Boiling nuclear reactor channel

Three layer flow

Oil at top Water at bottom

Oil-water droplets at middle.

Oil transportation

Depending on the type of interface, the class of separated flow can be divided into plane flow which

includes film and stratified flow and quasi-axisymmetric flow consisting of the annular and jet flow regimes. The class of dispersed flow is usually subdivided by considering the phase of dispersion. Accordingly, three regimes are distinguished: bubbly, droplet or mist and particulate flow. In each regime, the geometry of dispersion can be spherical, spheroidal, distorted, etc. Since the change of interfacial structures occur gradually, we have a third class which is characterised by the presence of both separated and dispersed flow. In this case too, it is more convenient to subdivide the class of mixed flow according to the phase of dispersion. The flow patterns thus obtained are depicted in Table 2.1.

In the following section, the typical flow patterns for different fluid combinations (gas-liquid, liquid-liquid, gas-solid and gas-liquid-liquid), pipe orientations (vertical/horizontal) and flow conditions (heated or unheated) have been discussed in order to understand the influence of operating variables on phase

distribution. A short discussion on the influence of pipe fittings has been provided to compliment the chapter. In conclusion, a discussion on the different ways of representing the range of existence of various flow patterns viz the flow pattern maps have been presented.

1.Vertical co-current gas-liquid upflow:

A schematic of the different air-water flow regimes observed in a vertical tube are shown in Fig.2.1 and described below:

a. Bubbly flow- Liquid flows as a continuous phase in which gas bubbles of approximately uniform size are observed. The bubble diameter is not comparable to the diameter of the tube.

b. Slug flow- As the gas flow rate is increased, number of bubbles increase and they coalesce to form elongated bubbles having spherical nose and cylindrical tail. These bullet shaped axisymmetric bubbles are termed as Taylor bubbles in two phase terminology. Such bubbles are also observed during the draining of water from bottles with a narrow neck and when a volume of air rises through a stationary column of liquid. In slug flow, the Taylor bubbles are separated by liquid slugs which may or may not be aerated. The periodic passage of Taylor bubbles and liquid slugs across any cross-section (Fig.2.1) characterises slug flow. In the Taylor bubble regions, the liquid flows downward as a thin annular film from the preceding to the succeeding liquid slug. This forms a wake region when it meets the liquid slug. The vorticity induced in the wake shears bubbles from the tail of the Taylor bubble and aerates the liquid slugs.

c. Churn flow-With a further increase in airflow, the Taylor bubbles become longer till they break and cause a random and chaotic mixture propagating through the tube. This pattern is known

as churn flow. It is highly unstable and oscillatory in nature and can be differentiated from slug flow by the absence of the periodic character.

d. Annular Flow- With further increase in gas flow, the gas bubbles coalesce to form a continuous gas core and the liquid is forced to flow as an annular film between the gas core and the pipe wall. Some liquid gets sheared from the film and forms a bridge in the gas phase. Several researchers have identified this as a different flow pattern and named it as wispy annular flow.

Fig.2.1. Gas-liquid Flow patterns in vertical upflow

2. Horizontal co-current gas-liquid flow

In a horizontal pipe, the effect of gravity causes stratification of the two phases and accounts for the differences in flow regimes. The different patterns are presented in Fig.2.2 and described as follows:

(a) Bubbly flow - In case of horizontal flow, the bubbles accumulate on the top for moderate liquid velocity.

(b) Plug/Slug flow - As the air flow rate increases, the bubbles coalesce and form long plugs which are also confined to the upper region of the tube. The intermittent liquid slugs may or may not be aerated.

(c) Stratified flow - With further increase of air flow rate, plugs coalesce to form stratified flow. At relatively lower flow rates the interface is smooth while at higher flow rates, the interface becomes wavy and the wave amplitude increases with phase velocities.

(d) Annular Flow - This has the same appearance as mentioned in vertical flow and is characterised by

a continuous gas core and an annular liquid film between the gas core and the pipe wall. However, the film thickness is not uniform and the liquid film is substantially thicker at the bottom of the pipe.

Fig.2.2 Flow pattern in horizontal flow

LECTURE 3

3. Flow Patterns in vertical heated tubes:

The flow patterns observed in a vertical heated tube are different from those observed in an unheated

tube under the same flow conditions due to the presence of heat flux at the channel wall. As a result of heat transfer through the wall, thermodynamic non- equilibrium exists at a particular cross section. This is evident from the simultaneous presence of sub-cooled liquid and superheated vapour. Further, as the quality changes along the direction of flow, different flow regimes appear along the flow direction. For a long tube there could be transition from sub-cooled liquid regime to super heated vapour regime through a number of flow patterns. A schematic representation of vertical tubular channel heated by a uniform low heat flux and fed at its base with liquid below its saturation temperature is shown in Fig.2.3. It shows

the absence of the chaotic churn flow pattern and the appearance of mist/ droplet flow at high vapour velocities. Such a distribution is not formed in an unheated tube.

Fig. 2.3 Flow regimes in vertical evaporator tubes

4. The corresponding situation in horizontal heated tubes –

The influence of gravity makes the situation more complex in a horizontal heated channel. There is

departure from hydrodynamic and thermal equilibrium as in vertical flows through heated channels as well as asymmetric phase distribution and stratification due to horizontal orientation. Therefore several important features can be observed namely:

1. Possibility of intermittent drying and rewetting of upper surface of tube in wavy flow.

2. Progressive drying out over long tube length of upper circumference of tube wall in annular flow.

3. Less obvious effect of gravity at higher inlet liquid velocities give more symmetrical flow patterns and closer similarities to vertical flows.

Unique flow patterns can also be observed during condensationas shown in Fig. 2.4.

Fig. 2.4

5. Flow patterns for liquid-liquid systems:

Certain interesting features are noted when the gas phase is replaced by a second immiscible liquid (say oil). For horizontal pipes, the stratified flow pattern gives way to three layer flow with increase in

phase flow rate. This pattern is characterised by an oil layer at the top and a water layer at the bottom with a dense dispersion of droplets separating the two as shown in Fig. 2.5 (a). Such a distribution has not been observed for gas-liquid cases under any flow conditions. Moreover, liquid-liquid dispersed flow can comprise of either oil in water dispersion or water in oil dispersion depending on the flow conditions unlike the presence of only gas-in liquid dispersions for the previous case. This is evident from Fig. 2.5 (c) which presents flow patterns for a vertical pipe of the same dimension. The transition between the

two types of dispersed flow is termed as phase inversion and is unique to liquid-liquid flows. It has received much academic interest and industrial concern due to its uniqueness and complexity. For vertical tubes, the flow is either dispersed or core-annular with the tendency of formation of the core-annular pattern increasing with the viscosity of the oil. This is an extremely fortunate situation since it results in a drastic reduction of the power required to pump the liquid. A comparison of Figs 2.5 (a) and

(b) highlights the tendency of slugging at reduced tube dimensions.

Fig. 2.5 Typical flow patterns during oil-water flow through (a) horizontal pipe of 25.4 mm (b) horizontal pipe of 12.7 mm (c) vertical pipe of 25.4mm

6. Flow patterns for gas-liquid-liquid three phase flows: Simultaneous flow of two immiscible liquids and a gas is not uncommon in industry. A large variety of flow patterns can be observed during such three phase flow. A brief description of the typical flow pattern in three phase flow is provided here. In horizontal pipes, a three layer flow pattern is observed at low flow rates (Fig.2.6). At higher phase

velocities, the air usually exists as plugs which alternate with liquid slugs. The distribution of the two liquids in the slug can be either stratified or dispersed depending on the flow rates. The slug flow pattern is also the most predominant flow pattern for vertical pipes where they are characterised by axisymmetric bullet shaped air Taylor bubbles intercepted by liquid slugs. The distribution in the liquid slug can be either oil in water dispersed flow, water in oil dispersed flow or an emulsified flow at high phase velocities as shown inFig. 2.7.

Fig.2.6 Flow patterns in horizontal co-current upward air-water-kerosene flow

LECTURE 4

7. The commonly encountered patterns in gas-solid flows (pneumatic conveying and fluidisation):

Traditionally, flow regimes have been divided into two main groups: dilute and dense. The transition between these two regimes for vertical conveying systems is defined by the choking velocity. The dense

flow regime is usually divided into specific flow regimes such as slugging, bubbling, fluidizing and plugging (Fig.2.8). The accumulated and classical choking presents two possible transitions from dilute flow regime. When the gas velocity is reduced at a fixed solid flow rate, the dilute flow turns into slugging flow or a non-slugging dense phase flow. The condition when the dilute flow becomes non-slugging is called accumulated choking and is related to the accumulation of solid at the bottom of the pipe line. The condition when the dilute flow becomes a slugging flow is called classical choking and is related to the formation of slugs. Although pneumatic conveying and fluidized bed systems are designated for different tasks, they nonetheless have many similarities. For example, for both systems dilute flow, fast fluidization, turbulent fluidization, slugging fluidization, bubbling flow and fluidized flow regimes occur. The dilute flow regime is characterized by suspension flow at high gas velocity and low solid mass flow rate. For pneumatic systems, the dilute flow regime is most commonly used, while for fluidized bed systems this regime might occur as a bypass process for emptying the column or when the inserted sample has a wide size

distribution. For a wide particle size distribution, the large particles are fluidized at the lower part of the column while the fine powders might be carried over by a dilute flow regimes. By reducing the gas velocity, suspension flow is halted and particle clusters might appear. The flow regime occurring after the appearances of particle clusters is termed as fluidization. The turbulent fluidization regime is characterized by extreme particle turbulence without large discrete bubbles or voids. The slugging flow regime is characterized by a particle dense phase transport that is facilitated by bubbles whose size is comparable to the pipe diameter. The bubbling flow regime, on the other hand, is characterized by smaller bubbles.

Two more possible flow regimes occur in a pneumatic conveying system, but are not common in fluidized system. The first is the plug flow regime which is characterized by particles that are transported as plugs separated by air gaps. Sometimes these particles fall from the bottom of one plug and collect at the front of consequent plug. This phenomenon is known as “particle rain” and occurs when the cohesion force between the particles is smaller than the particle weight. The worst case scenario for designers of pneumatic conveying systems is blockage. The flow conditions which causes blockage can be defined as a kind of flow regime.

Fig. 2.8 Typical flow patterns during gas-solid flow

8. Gas-liquid flow patterns in other applications:

a. Vertical downward flow: Downward flow of a gas-liquid mixture is unstable as the gas phase

tends to move up. However, in certain range of the operating condition such flow can be established. Annular flow regime occurs at low liquid flow rates while a falling liquid film occurs with no gas flow. Slug and bubbly flow occur only at liquid velocities greater than bubble rise velocity.

b. Inclined Channels: Usually stratification occurs only for very low superficial velocities and inclinations close to the horizontal. Smooth stratified flow disappears on slight deviation from the horizontal orientation and stratification disappears completely for inclinations beyond 300. In addition, the shape of the Taylor bubbles changes as the inclination is increased from horizontal to vertical. The nose becomes more pointed and the bubble more asymmetric as the inclination increases from 0 to 450 (approximately) from the horizontal as shown in the fig.2.9.

Subsequently, the nose of the bubble assumes the nice rounded shape observed for Taylor bubbles in vertical tubes. This results in higher rise velocity of the bubble with increase in inclination from 0 to 450 and a subsequent decrease with a further increase in inclination.

Fig.2.9 Taylor bubble in (a) Vertical tube (b) Inclined tube

c. Rectangular Channels: In these channels flow is similar to circular channels when the aspect ratio is not very different from unity. Nevertheless, unique flow regimes may be observed for extreme values of the aspect ratio. Presence of corners in the flow geometry influences the flow

regime as the corner regions tend to retain the liquid film. However, such effects are pronounced in flow channels of smaller cross-sections.

d. Annular channels: A very interesting phenomena occurs when a rod is inserted in the flow passage of circular tubes. The rod induces gross asymmetry in the slug flow pattern. This asymmetry arises due to the asymmetric shape of the Taylor bubbles. They partially enclose the inner tube and form open annular rings as shown in Fig 2.10.

Fig 2.10 Taylor bubble in (a) circular tube (b) concentric annulus

LECTURE 5

Bends and Coils: A bend or a coil acts to separate the phases due to the presence of centrifugal

force. For example, a bend will induce coalescence of bubbles to form slug flow and will separate entrained droplets in annular flow. At low superficial velocity, the action of gravitational forces and the fact that vapour phase tends to flow faster than the liquid phase greatly complicates the picture. In a vertical pipe joined to a horizontal pipe via a 90 degree bend the momentum of the upflowing liquid tries to carry it to the outside of the bend and gravitational forces tend to make it fall to the inside of the bend. Fig 2.11 presents a few photographs to highlight the effect of pipe

fittings on oil-water flow. The phenomena of film inversion as oil-water stratified flow turns round a return bend is evident from Fig. 2.11 (a). The change of interfacial distribution as liquid-liquid

flow encounters an abrupt contraction or expansion is evident from the following two figures. They emphasis upon the onset of dispersion as the flow encounters an expansion and the reverse phenomena as the cross-section reduces abruptly.

Effect of Pipe fittings

Fig.2.11 Effect of pipe fittings on oil-water two phase flow

(a) Film Inversion at a hairpin bend (b) Onset of dispersion at an expansion (c) Coalescing effect at a contraction

9. Flow Pattern Maps:

It is very important to predict the pattern which is likely to occur for a given set of flow parameters. One method of representing the various transitions is in the form of a flow pattern map which is a two dimensional graph segregated into areas representing the range of existence of the different patterns.

Different dimensional as well as dimensionless parameters have been frequently used as the co-ordinate axes of the maps. Some of the frequently used non-dimensional parameters include two phase Froude number, Eotvos number and Weber number, Reynolds number of the individual phases/mixture for gas-liquid and liquid-liquid systems and Reynolds number and Archimedes number for fluid-particle systems. However the most commonly used axes for gas-liquid and liquid-liquid flow maps are the actual or superficial phase velocities of the two phases defined as the volumetric flow rate per unit cross-sectional area of the pipe. The flow pattern maps commonly used for horizontal and vertical gas-liquid flow are shown in Figs 2.12 (a) and (b). It may be noted that although the use of superficial velocity restricts the

application of the maps to fluids with a limited variation of properties, it is preferred due to its simplicity. In addition, one dimensionless parameter which may be adequate to represent one particular transition may not be suitable for a different transition governed by a different balance of forces.

Fig 2.12 (a) Flow Regime map for horizontal gas-liquid flow

Fig 2.12 (b) Flow Regime map for vertical gas-liquid flow

An alternative and more flexible method to overcome this difficulty is to examine each transition

individually and derive a criterion for that particular transition based on the principle underlying the

mechanism. For example bubble to slug flow transition is generally modelled on the basis of bubble

coalescence which depends on a critical void fraction whereas flooding and flow reversal are responsible

for slug-churn and churn-annular transition.

Recently, soft computing that includes Artificial Neural Network, Fuzzy logic or Genetic Algorithm is

being increasingly used to produce generalised flow pattern maps from known input parameters..