In gas-liquid or vapor-liquid flow, the two phases can adopt various geometric configurations known as flow patterns or flow regimes. Many flow patterns are present during flow in tubes, including those observed by both Collier and Hewitt, and a few of the more important ones will be described.
The total mass flow rate through a tube is equal to the sum of the mass flow rates of gas, mg, and liquid, m.
m = mg+ m (2.7.1)
The ratio of the mass flow rate of gas to the total mass flow rate is known as the dryness factor or quality, i.e.,
(2.7.2)
where G is the mass flux based on the total cross-sectional area of the tube—also referred to as the superficial mass velocity. The subscript grefers to the gas.
The void fraction, α is defined as the ratio of the gas flow cross-section-al area, Ag, to the total cross-sectional area, Ats.
(2.7.3) A
/ A
= g ts
α
/G G
= /m m
=
x g g
When both phases are flowing upwards in a tube, cocurrent flow, possible flow patterns obtained are shown in Figure 2.7.1 for increasing gas flow or quality.
Fig. 2.7.1 Flow Patterns in Vertical Upflow in Tube
• Bubble flow. At low gas or vapor flow rate and low to moderate liquid flow rates, the gas phase tends to become distributed throughout the liquid continuum as bubbles.
• Slug flow (also called plug flow). If the gas flow rate of a dispersed bubble flow is increased, the bubbles coalesce to form large bullet shaped bubbles, which approach the tube diameter in size. The bubbles are separated by slugs of liquid containing small entrained gas bubbles.
• Churn flow. With a further increase in gas flow rate, the liquid slugs break down and give rise to this unstable flow of an oscillatory nature according to Jayanti, Mao, and Hewitt.
• Annular flow. At high gas velocities and low liquid flow rates, the liquid travels partly as wavy annular film on the wall of the tube and partly as small drops distributed in the gas, which flows in the center of the tube.
• Mist flow. At a gas velocity much higher than that of annular flow, there is an increase in the number of liquid droplets being sheared away from the film flow until nearly all liquid is entrained in the gas core flow.
More details of vertical cocurrent upward flow are given in the literature from sources such as Oschinowo, Taitel, Hewitt, McQuillan, and Cindric.
Vertical cocurrent downward flow patterns have been described by Oschinowo and Charles, Barnea et al., Crawford et al., and Mukherjee and Brill. A few of these patterns are shown in Figure 2.7.2 for increasing gas flow rate.
Fig. 2.7.2 Flow Patterns in Vertical Downflow in Tube
• Bubble flow. At very low gas flow rates and high liquid flow rates, the gas phase flows as discrete bubbles in a downward flowing continu-um. Shear stresses decrease from the tube wall to a minimum at the tube center, therefore the resultant imbalance in shear force acting on each bubble causes it to migrate towards the center of the tube.
• Slug flow. At higher gas flow rates, the dispersed bubbles coalesce to form larger bubbles separated by liquid slugs.
• Falling film flow. At low liquid and gas flow rates, the liquid flows in the form of a thin film. The gas core flow entrains very few or no liq-uid droplets. There is a tendency for dry spots to develop on the tube wall. This flow pattern is sometimes classified as an annular flow although its nature is different.
• Churn flow. If the gas flow rate in a slug flow pattern is increased, a point is reached where the high gas concentration in the liquid slug causes the slug to collapse. As this happens, the liquid slug falls then regroups with other liquid drops until it is able to bridge the tube again. The mixture is turbulent but much less agitated than for ver-tical upward churn flow.
• Annular flow. At high gas flow rates and moderate liquid flow rates, the liquid flows as an annular film while the gas forms a continuous core flow at the center of the tube. The high velocity gas core flow may entrain a portion of the wavy liquid film.
• Mist flow. At very high gas flow rates, all or most of the liquid film is entrained into the gas core flow in the form of small droplets.
The results of many studies of countercurrent two-phase flows in vertical tubes have been reported by sources such as Wallis and Taitel. Flow patterns include bubble, slug, and annular flow or falling film.
Horizontal two-phase flows in tubes generate patterns which are more complex than vertical flow patterns because the gravitational influence is no longer in the axial direction of flow. The horizontal flow pattern description shown in Figure 2.7.3 are combinations of the categorization of a number of researchers such as Taitel, Hewitt, Mukherjee, and Cindric.
• Stratified flow. This flow pattern occurs at low gas and liquid volume flow rates. The liquid phase flows along the bottom of the tube, and its surface is relatively smooth—also referred to as stratified smooth flow. Increasing gas flow causes the liquid surface to become wavy—
also referred to as stratified wavy flow.
• Bubble flow. Bubble flow occurs at low gas flow rates and moderate liquid flow rates. Bubbles tend to concentrate near the top of the tube due to buoyancy forces.
• Slug flow. At higher gas flow rates than for dispersed bubble flow, coa-lescence of bubbles occurs forming large bubbles separated by slugs of liquid.
• Annular flow. At high gas flow rates, shear forces at the vapor-liquid interface may be large compared to gravitational forces. The interaction between these forces and the waves on the liquid surface causes the liquid to flow up the tube wall until the liquid film flows as an eccentric annulus according to James and Lin. The effect of gravity causes the liquid film to be thicker at the bottom than at the top of the tube.
• Mist flow. At very high gas flow rates, all the liquid film tends to be entrained into the gas core as small droplets or mist.
Fig. 2.7.3 Flow Patterns in Horizontal Flow in Tube
Flow patterns for inclined tubes are a superposition of the flow patterns for horizontal and vertical flows. However, a quantitative prediction of flow pattern transition for inclined tubes is more difficult according to Hewitt.
More detailed studies of two-phase flows in inclined tubes have appeared in the literature from authors such as Spedding, Crawford, Mukherjee, Stanislav, and Barnea.
Numerous attempts have been made to present different flow patterns on a two-dimensional graph having different areas that correspond to the different flow patterns. Such flow pattern maps may use the same axes for all flow patterns and transitions, or they may employ different axes for different transitions.
Baker was the first to develop a horizontal tube-side flow pattern map that could be used for any fluid. His map was subsequently modified by Scott (Fig. 2.7.4) and further evaluated by Bell et al. The map is plotted in terms of Gg/λ and Gψ where Gg = mg/Ats and G = m/Ats are the superficial mass velocities of the gas and liquid, and the factors λ and ψ are given by
(2.7.4)
(2.7.5)
where
σ = surface tension
a = physical properties of air w = physical properties of water
= properties of the liquid flowing in the tube g = properties of the gas flowing in the tube ρw= 1000 kg/m3
ρa = 1.23 kg/m3
(
/) [
(
/)(
/) ]
= w
2 w
0.333
w σ µ µ ρ ρ
ψ σ
( ) ( )
[
/ /]
= ρg ρa ρ ρw 0.5
λ
Fig. 2.7.4 Modified Baker Flow Pattern Map for Horizontal Flow in a Tube
The dynamic viscosity of water is taken as µw= 10-3 kg/ms, and the surface tension is σw= 0.072 N/m. The Baker map works reasonably well for water/air and oil/gas mixtures in small diameter (< 0.05 m) tubes.
One of the disadvantages of the Baker map is the parameters are dimensional and empirical, so it is not possible to relate the map boundaries theoretically to any known physical characteristics of the flow. Taitel and Dukler approach the flow regime transitions theoretically and present a more complex type of flow pattern map. Other graphical presentations have been proposed by Breber, with some based on studies conducted during condensation of vapors in horizontal tubes.
The Hewitt and Roberts map shown in Figure 2.7.5 is a widely used chart for vertical upflow in a tube, while a map proposed by Oschinowo and Charles is applicable to downflow in a vertical tube. The Hewitt and Roberts map works reasonably well for water/air and water/steam systems, again in
small diameter tubes. Note that wispy annular flow is a subcategory of annular flow, which occurs at high mass flux when the entrained drops are said to appear as wisps or elongated droplets.
Fig. 2.7.5 Hewitt and Roberts Map for Vertical Upflow in a Tube
Maps for patterns in inclined tubes have been presented by various authors such as Spedding, Crawford, Mukherjee, Stanislav, and Barnea.
A systematic and practical approach for determining changes in pressure in two-phase flows is presented by Carey.
Flooding
The flooding process is illustrated in Figure 2.7.6, and a description found in Hewitt and Bankoff is summarized in the following.
Fig. 2.7.6 Flow Regime Transitions during the Flooding Process inside a Vertical Tube (a-h)
Liquid enters the top of the tube through a porous section and is removed through a porous section at the bottom of the tube. At low gas flow rates, a stable counterflow exists (Fig. 2.7.6a). As the gas flow rate is increased, the interface becomes wavy, liquid is entrained, and the film starts creeping up past the liquid inlet (Fig. 2.7.6b). This flow transition is defined as flooding and is also sometimes referred to as the onset of flooding or limiting condition for countercurrent flow. Eventually, liquid flows up past the liquid inlet (Fig. 2.7.6c), and a state of partial liquid delivery exists. With a further increase in gas flow, the liquid flow below the inlet porous section changes to a climbing film flow (Fig. 2.7.6d), and a state of cocurrent annular or churn upward flow above the liquid inlet porous section is reached (Fig. 2.7.6e).
When the gas flow rate is reduced, the liquid begins to creep below the liquid feed (Fig. 2.7.6f). This point is known as flow reversal. A further decrease in gas flow rate results in a state of simultaneous climbing and falling film flow (Fig. 2.7.6g). Finally, the initial state of countercurrent flow is obtained (Fig. 2.7.6h). The last transition has been termed the deflooding point by Clift et al.
There are various mechanisms by which flooding is said to occur. They fall into two fundamental categories, namely: film flow theory assuming a smooth gas-liquid interface and flow instability/wave growth theory.
McQuillan and Whalley studied air-water flow experiments in vertical tubes with porous wall liquid injection and removal. They concluded the following concerning flooding:
• The gas-liquid interface is wavy when the flooding point is approached.
• These waves grow in amplitude as they travel downwards.
• The velocity of the falling waves decreases as they fall. At the flooding gas flow rate, the wave reaching the lower porous wall becomes stationary and grows rapidly in size. The result is a large disturbance wave, which moves upwards and causes flooding.
• Prior to the formation of the large disturbance wave, there is very little entrainment of liquid droplets into the gas stream.
• For an airflow rate just below the flooding rate, an artificially injected wave grows to form a disturbance wave, which is indistinguishable from the flooding disturbance.
It is known that the geometry of liquid and gas entry can affect the gas velocity at which flooding occurs. According to Hewitt, a square edged gas inlet introduces more turbulence than a rounded inlet, promotes wave growth on the liquid film, and reduces the gas velocity where flooding occurs. If the turbulence level is low, the tube length has an effect on the gas velocity necessary to initiate flooding. In longer tubes, Whalley found the liquid waves have more time to build up, so the flooding occurs at lower values of the gas velocity.
Reviews of the flooding literature are presented by numerous researchers such as Tien, McQuillan, Bankoff, and Stephan. There tends to be a consid-erable amount of scatter in the available data. In part this can be ascribed to the fact that different definitions for flooding exist.
Many correlations have been proposed for predicting the onset of flooding.
The method based on the semiempirical correlation of Wallis is widely used to predict flooding, i.e.,
(2.7.6)
=a Fr +a
Fr 0.25 2
D 1 0.25
Dg
where the superficial densimetric Froude numbers for the gas and the liquid are defined as
(2.7.7)
(2.7.8)
The superficial velocities are defined as follows:
(2.7.9)
(2.7.10) where
Ats = total cross-sectional area of the tube
The constants a1and a2depend upon the liquid inlet and outlet flow condition and geometric characteristics. For turbulent air-water flow, the constant a1is close to unity while the approximate value chosen for the other constant generally is as follows:
• a2≈ 1.00 for very smooth liquid inlet and outlet, e.g., porous, with minimal flow disturbance
• a2≈ 0.88 for very smooth liquid inlet and outlet, e.g., porous, with high flow disturbance
• a2≈ 0.88 for rounded or tapered inlet and outlet flanges
• a2≈ 0.725 for sharp or square-edged inlet and outlet flanges
A significant increase in pressure drop is measured when flooding occurs.
Zapke and Kröger conducted adiabatic counterflow experiments to investigate the effect of the duct geometry, duct inclination, and the liquid and gas physical properties on flooding. Typical flooding data generated during the course of the experiment for air-water flow in a flattened tube having a square-edged (90°) inlet is shown in Figure 2.7.7 as a function of the duct inclination.
(
A)
m /
= G /
vs= ρ ρ ts
(
A)
m/
= G /
vgs= g ρg g ρg ts
FrD = ρ vs2 /
[(
ρ - ρg)gd]
FrDg = ρg vgs2 /
[(
ρ - ρg)gd]
Fig. 2.7.7 Flooding Data for Air-Water Flow in an Inclined Duct
As a result of the different flow patterns encountered during counterflow in inclined ducts as opposed to vertical ducts, a significant decrease in the flooding gas velocity was observed as the duct inclination changed from just off the vertical to the vertical. Separate correlations were developed by Zapke for flooding in inclined and vertical ducts.
For inclined round and flattened tubes with a square-edged gas inlet, where a3and a4are functions of the duct inclination ϕ, i.e.,
(2.7.11)
where ϕ is in degrees and
ϕ
ϕ -2ϕ2 -4 3
4=18.149 -1.9471 +6.7058 x 10 -5.3227 x 10 a
ϕ ϕ
ϕ -4 2 -6 3
-3
3=7.9143 x 10-2+4.9705 x 10 +1.5183 x 10 -1.9852 x 10 a
(
-a Fr Oh)
exp a
FrDg= 3 4 D0.6 0.2
The Ohnesorge number is a dimensionless parameter that accounts for the effect of the liquid properties on flooding and in this case is defined as:
where
de= the hydraulic diameter of the duct
In the case of flattened or elliptical tubes, FrDgis based on the inside height, while FrDis based on the hydraulic or equivalent diameter.
Equation 2.7.11 is based on tests conducted within these ranges:
10 mm ≤ W (inside duct width) ≤ 20 mm (flattened tubes) 50 mm ≤ H (inside duct height) ≤ 150 mm (flattened tubes) d = 30 mm (tubes)
2°≤ ϕ ≤ 80° (duct inclination to the horizontal)
For vertical round and flattened tubes with a square-edged gas inlet,
(2.7.12)
within the ranges:
10 mm ≤ W (inside duct width) ≤ 20 mm (flattened tubes) 50 mm ≤ H (inside duct height) ≤ 100 mm (flattened tubes) di= 30 mm (tubes)
ϕ = 90°
(
Fr Oh)
0.0055
=
Fr 0.2D 0.3
-1
Dg
Oh 0.04 Fr0.6D 0.2≤
(
ρ σ)
l / d
Oh = e
0.5
Limited extrapolation outside the geometric ranges specified is possible.