As illustrated in Fig. 2, two-phase steam-water flow may occur in many regimes or structures. The transi- tion from one structure to another is continuous rather than abrupt, especially under heated conditions, and is strongly influenced by gravity, i.e., flow orientation. Because of the qualitative nature of flow pattern iden- tification, there are probably as many flow pattern descriptions as there are observers. However, for ver- tical, heated, upward, co-current steam-water flow in a tube, four general flow patterns are generally recognized (see Fig. 12):
1. Bubbly flow Relatively discrete steam bubbles are dispersed in a continuous liquid water phase. Bubble size, shape and distribution are dependent upon the flow rate, local enthalpy, heat input rate and pressure.
2. Intermediate flow This is a range of patterns be- tween bubbly and annular flows; the patterns are also referred to as slug or churn flow. They range from: a) large bubbles, approaching the tube size in diameter, separated from the tube wall by thin annular films and separated from each other by slugs of liquid which may also contain smaller bubbles, to b) chaotic mixtures of large nonsym- metric bubbles and small bubbles.
3. Annular flow A liquid layer is formed on the tube wall with a continuous steam core; most of the liq- Fig. 11 Thermophysical properties of water (English units).
Fig. 12 Flow pattern – upward, co-current steam-water flow in a
uid is flowing in the annular film. At lower steam qualities, the liquid film may have larger ampli- tude waves adding to the liquid droplet entrain- ment and transport in the continuous steam core. At high qualities, the annular film becomes very thin, bubble generation is suppressed and the large amplitude waves disappear.
4. Mist flow A continuous steam core transports en- trained water droplets which slowly evaporate until a single-phase steam flow occurs. This is also referred to as droplet or dispersed flow.
In the case of inclined and horizontal co-current steam-water flow in heated tubes, the flow patterns are further complicated by stratification effects. At high flow rates, the flow patterns approach those of verti- cal tubes. At lower rates, additional distinct flow pat- terns (wavy, stratified and modified plug) emerge as gravity stratifies the flow with steam concentrated in the upper portion of the tube. This can be a problem where inclined tubes are heated from the top. CHF or dryout conditions occur at much lower steam quali- ties and lower heat input rates in such inclined or horizontal tubes.
Additional complexity in patterns is observed when two-phase flow occurs in parallel or crossflow tube bundles. The tubes, baffles, support plates and mix- ing devices further disrupt the flow pattern formation. Flow maps The transitions from one flow regime to another are quite complex, with each transition rep- resenting a combination of factors. However, two di- mensional flow maps provide at least a general indi- cation of which flow pattern is likely under given op- erating conditions. The maps generally are functions of superficial gas and liquid velocities. An example for vertical, upward, steam-water co-current flow is pro- vided in Fig. 13.11 The axes in this figure represent
the superficial momentum fluxes of the steam (y-axis) and water (x-axis). A sample flow line is shown begin- ning at nearly saturated water conditions and end- ing with saturated steam conditions. The tube expe- riences bubbly flow only near its inlet. This is followed by a brief change to intermediate flow before annu- lar flow dominates the heated length.
Other flow maps are available for arrangements such as downflow tubes, inclined tubes and bundles. Flow maps, however, are only approximations provid- ing guidance in determining the relevant flow struc- ture for a given situation.
Pressure loss
The local pressure loss, ∆P [lb/ft2 (Pa)] or gradient δP/δl [lb/ft2/ft (Pa/m)] in a two-phase steam-water
system may be represented by:
∆P = ∆Pf +∆Pa +∆Pg +∆Pl (6a) or − = − − − + δ δ δ δ δ δ δ δ P l P l P l P l P f a g l ∆ (6b)
The ∆Pf and –(δ P/δ l)f terms account for local wall friction losses. The ∆Pa and –(δ P/δ l)a terms address
the momentum or acceleration loss incurred as the volume increases due to evaporation. The hydraulic or static head loss is accounted for by ∆Pg and –(δ P/ δ l)g. Finally, all of the local losses due to fittings, con- tractions, expansions, bends, or orifices are included in ∆Pl. The evaluation of these parameters is usually made using one of two models: homogeneous flow or separated flow.
A parameter of particular importance when evalu- ating the pressure loss in steam-water flows is void fraction. The void fraction can be defined by time-av- eraged flow area ratios or local-volume ratios of steam to the total flow. The area-based void fraction, α, can be defined as the ratio of the time-averaged steam flow cross-sectional area (Asteam) to the total flow area (Asteam + Awater):
α =
+
A
AsteamsteamAwater (7)
Using the simple continuity equation, the relation- ship between quality, x, and void fraction is:
α ρ ρ = +
(
−)
x x x g S f 1 (8) whereS = ratio of the average cross-sectional velocities of steam and water (referred to as slip) ρg = saturated steam density, lb/ft3 (kg/m3) ρf = saturated water density, lb/ft3 (kg/m3)
If the steam and water are moving at the same veloc- ity, S = 1 (no slip). Obviously, the relationship between void fraction and quality is also a strong function of system pressure. This relationship is illustrated in Fig. 14. The difference between the homogeneous and separated flow models is illustrated by the shaded band. The upper bound is established by the homo- geneous model and the lower bound by the separated flow model.
Homogeneous model The homogeneous model is the simpler approach and is based upon the premise that the two-phase flow behavior can be directly mod- eled after single-phase behavior (see Chapter 3) if appropriate average properties are determined. The temperature and velocities of steam and water are assumed equal. The mixed weight averaged specific volume (υ) or the inverse of the homogeneous density (1/ρhom) is used: υ =υf
(
1−x)
+υgx (9a) or 1 1 ρhom = ρ ρ −(
x)
+ x f g (9b) whereυf = saturated water specific volume, ft3/lb (m3/kg) υg = saturated steam specific volume, ft3/lb (m3/kg) ρf = saturated water density, lb/ft3 (kg/m3)
ρg = saturated steam density, lb/ft3 (kg/m3) x = steam quality
This model provides reasonable results when high or low steam qualities exist, when high flow rates are present, or at higher pressures. In these cases, the flow is reasonably well mixed.
The friction pressure drop (∆Pf) can be evaluated by the equations provided in Chapter 3 using the mix- ture thermophysical properties. The pressure differ- ence due to elevation (∆Pg) can be evaluated as:
∆P g g L g c = ± ρhom sinθ (10) where g = acceleration of gravity, ft/s2 (m/s2) gc = 32.17 lbm ft/lbf s2 (1 kg m/N s2) L = length, ft (m)
θ = angle from the horizontal
The constant gc is discussed in Chapter 2. A pressure gain occurs in downflow and a pressure loss occurs in upflow. The acceleration loss can be evaluated by:
∆P G g a c = − 2 1 1 ρout ρin (11) where G = mass flux, lb/s ft2 (kg/m2s)
ρout = outlet homogeneous density, lb/ft3 (kg/m3) ρin = inlet homogeneous density, lb/ft3 (kg/m3)
Separated flow model In the steady-state sepa- rated flow model, the steam and water are treated as separate streams under the same pressure gradient but different velocities and differing properties. When the actual flow velocities of steam and water are equal, the simplest separated flow models approach the ho- mogeneous case. Using one of several separated flow models1 with unequal velocities, the pressure drop
components (in differential form) are:
− = − δ δ δ δ φ P l P l f LO LO2 (friction) (12) − = δ δ υ P l f D G g LO i f c 2 2 (single-phase friction) (13) − = + −
(
)
−(
)
δ δ δ δ υ α υ α P l G g l x x a c g f 2 2 2 1 0 1 0 . . (accelerration)(14) − = + −(
)
δ δ θ α υ α υ P l g g g c g fsin 1 0. (static head)(15)
∆P ΦK G g l f c = 2 2 υ (local losses) (16) where Φ and
φ
LO2 = appropriate two-phase multipliers
G = mass flux, lb/s ft2 (kg/m2 s)
f = fanning friction factor (see Chapter 3)
Di = tube inside diameter, ft (m) g = acceleration of gravity, ft/s2 (m/s2) gc = 32.17 lbm ft/lbf s2 (1 kg m/N s2)
Fig. 14 Void fraction – quality relationship (homogeneous model,
υf = liquid specific volume, ft3/lb (m3/kg) υg = vapor specific volume, ft3/lb (m3/kg) x = steam quality
α = void fraction
θ = angle from the horizontal
K = loss coefficient
While ∆Pl usually represents just the irreversible pres- sure loss in single-phase flows, the complexity of two- phase flows results in the loss of ∆Pl typically represent- ing the reversible and irreversible losses for fittings.
To evaluate the individual pressure losses from Equations 12 through 16 and Equation 6b, it is nec- essary to calculate φLO2, α and Φ. Unfortunately, these
factors are not well defined.
Specific correlations and evaluations can only be used where experimental data under similar condi- tions provide confidence in the prediction. Proprietary correlations used by B&W are based upon experimen- tal data and practical experience.
For straight vertical tubes, generally available rep- resentative relationships include:
1. Acceleration loss The void fraction can frequently be evaluated with the homogeneous model (S = 1 in Equation 8).
2. Friction loss and void fraction Typical two-phase multiplier, φLO2 , and void fraction, α, relationships
are presented by Thom,12 Martinelli-Nelson,13
Zuber-Findlay14 and Chexal-Lellouche.15 For illus-
tration purposes the correlations of Thom are pre- sented in Figs. 15 and 16. These curves can be ap- proximated by: φ υ υ LO g f x x x x 2 0 5 0 97303 1 0 97303 1 =
(
−)
+ ×(
−)
+ . . . +(
−)
0 5 2 0 0 027 1 . . . x (17) and α γ γ = +(
−)
x x 1 1 (18) where γ = (υg/υf)n n = (0.8294 – 1.1672/P) P = pressure, psiυg = saturated steam specific volume, ft3/lb υf = saturated liquid specific volume, ft3/lb x = steam quality
Instabilities
Instability in two-phase flow refers to the set of operating conditions under which sudden changes in flow direction, reduction in flow rate and oscillating flow rates can occur in a single flow passage. Often in manifolded multi-channel systems, the overall mass flow rate can remain constant while oscillating flows in individual channels still may occur. Such unstable conditions in steam generating systems can result in:
1. unit control problems, including unacceptable variations in steam drum water level,
2. CHF/DNB/dryout,
3. tube metal temperature oscillation and thermal fatigue failure, and
4. accelerated corrosion attack.
Two of the most important types of instabilities in steam generator design are excursive instability, in- cluding Ledinegg and flow reversal, and density wave/pressure drop oscillations. The first is a static in- stability evaluated using steady-state equations while the last is dynamic in nature requiring the inclusion of time dependent factors.
Fig. 15 Thom two-phase friction multiplier.12
Excursive and flow reversal instability evaluation The excursive instability is characterized by conditions where small perturbations in operating parameters result in a large flow rate change to a separate steady- state level. This can occur in both single channel and multi-channel manifolded systems. Excursive insta- bilities can be predicted by using the Ledinegg crite- ria.16 Instability may occur if the slope of the pressure
drop versus flow characteristic curve (internal) for the tube becomes less than the slope of the supply (or applied) curve at any intersection point:
δ δ δ δ ∆P ∆ G P G ≤ internal applied (19)
The stable and unstable situations are illustrated in Fig. 17. As shown in the figure for unstable condi- tions, if the mass flow rate drops below point B then the flow rate continues to fall dramatically because the applied pumping head is less than that needed to move the fluid. For slightly higher mass flow rates (higher than point B), a dramatic positive flow excursion oc- curs because the pumping head exceeds the flow sys- tem requirement.
In most systems, the first term in Equation 19 is generally positive and the second is negative. There- fore, Equation 19 predicts stability. However, in two- phase systems, thermal-hydraulic conditions may com- bine to produce a local area where (δ∆P/δG)internal is
negative and the potential for satisfying Equation 19 and observing an instability exists. A heated tube flow characteristic showing a potential region of instabil- ity is illustrated in Fig. 18 where multiple flow rates can occur for a single applied pressure curve. Operat- ing at point B is unstable with small disturbances re- sulting in a shift to point A or point C. More intense dis- turbances could result in flow shifts between A and C.
For the relatively small subcooling found at the en- trance to tube panels in recirculating drum boilers and due to the relatively low exit steam qualities, negative slope regions in the pressure drop versus flow curves are typically not observed for positive flow cases. How- ever, for once-through fossil fuel boilers and nuclear steam generators with high subcooling at the inlet and evaporation to dryness, negative slope regions in the upflow portion of the pressure drop characteristic may occur. Steps can be taken to avoid operation in any re- gion where the circuit internal δ∆P/δG ≤ 0. General effects of operating and design parameters on the pres- sure drop versus mass flow curves include:
Parameter
Increased Effect on ∆P Comment
heat input decrease more stable
inlet ∆P increase more stable
pressure increase more stable
In situations where static instability may occur, the inlet pressure drop can be increased by adding an orifice or flow restriction to modify the overall flow characteristic as shown in Fig. 18.
Fig. 17 Stable and unstable flow-pressure drop characteristics.
Density wave/pressure drop instability Density wave instabilities involve kinematic wave propagation phe- nomena. Regenerative feedback between flow rate, vapor generation rate and pressure drop produce self sustaining alternating waves of higher and lower den- sity mixture that travel through the tube. This dy- namic instability can occur in single tubes that con- tain two-phase flows. In addition, when multiple tubes are connected by inlet and outlet headers, a more com- plex coupled channel instability, which is driven by density wave oscillations, may occur. Vertical heat flux distribution is a particularly sensitive parameter in dynamic instability evaluation.
Density wave oscillations can be predicted by the application of feedback control theory. A number of computer codes have been developed to provide these predictions. In addition, instability criteria, which use a series of dimensionless parameters to reduce the complexity of the evaluation, have been developed.
Effects of operating and design parameters on the density wave instability include:
Parameter
Increased Change in stability
mass flux improved
heat flux reduced
pressure improved
inlet ∆P improved
inlet subcooling improved (large subcooling)
reduced (small subcooling)
Steam-water separation
Subcritical pressure recirculating boilers and steam generators are equipped with large cylindrical vessels called steam drums. Their primary objective is to per- mit separation of the saturated steam from the steam- water mixture leaving the boiling heat transfer sur- faces. The steam-free water is recirculated with the feedwater to the heat absorbing surfaces for further steam generation. The saturated steam is discharged through a number of outlet nozzles for direct use or further heating. The steam drum also serves to: 1. mix the feedwater with the saturated water re-
maining after steam separation,
2. mix the corrosion control and water treatment chemicals (if used),
3. purify the steam to remove contaminants and re- sidual moisture,
4. remove part of the water (blowdown) to control the boiler water chemistry (solids content), and 5. provide limited water storage to accommodate
rapid changes in boiler load.
However, the primary function of the steam drum is to permit the effective separation of steam and wa- ter. This may be accomplished by providing a large steam-water surface for natural gravity-driven sepa- ration or by having sufficient space for mechanical separation equipment.
High efficiency separation is critical in most boiler applications in order to:
1. prevent water droplet carryover into the super- heater where thermal damage may occur,
2. minimize steam carryunder in the water leaving the drum where residual steam can reduce the effective hydraulic pumping head, and
3. prevent the carryover of solids dissolved in the steam- entrained water droplets into the superheater and turbine where damaging deposits may form. The last item is of particular importance. Boiler wa- ter may contain contaminants, principally in solution. These arise from impurities in the makeup water, treatment chemicals and condensate system leaks, as well as from the reaction of the water and contami- nants with the boiler and preboiler equipment mate- rials. Even low levels of these solids in the steam (less than 0.6 ppm) can damage the superheater and tur- bine. Because the solubility of these solids is typically several orders of magnitude less in steam than in wa- ter (see Chapter 42), small amounts of water droplet car- ryover (greater than 0.25% by weight) may result in dra- matically increased solids carryover and unacceptable deposition in the superheater and turbine. The deposits have caused turbine damage as well as superheater tube temperature increases, distortion and burnout.
A cross-section of a horizontal steam drum found on a modern high capacity fossil fuel boiler is shown in Fig. 19. This illustrates the general arrangement of the baffle plates, primary cyclone separators, sec- ondary separator elements (scrubbers), water dis- charger (downcomer) and feedwater inlets. The blow- down (water removal) connections are not shown. The steam-water separation typically takes place in two stages. The primary separation removes nearly all the steam from the water so that very little steam is recir- culated from the bottom of the drum through the out- let connection (downcomer) towards the heated tubes. The steam leaving the primary separators in high pressure boilers still typically contains too much liq- uid in the form of contaminant-containing droplets for satisfactory superheater and turbine performance. Therefore, the steam is passed through a secondary set of separators, or scrubber elements (usually closely spaced, corrugated parallel plates) for final water droplet removal. The steam is then exhausted through several connections. As this figure indicates, success- ful steam-water separation involves the integrated operation of primary separators, secondary scrubbers and general drum arrangement.
Factors affecting steam separation
Effective steam separation from the steam-water mixture relies on certain design and operating factors. The design factors include:
1. pressure,
2. drum length and diameter, 3. rate of steam generation, 4. average inlet steam quality,
5. type and arrangement of mechanical separators, 6. feedwater supply and steam discharge equipment
arrangement, and
7. arrangement of downcomer and riser connections to the steam drum.
The operating factors include: 1. pressure,
2. boiler load (steam flow), 3. type of steam load,
4. chemical analysis of boiler water, and 5. water level.
Primary separation equipment generally takes one of three forms:
1. natural gravity-driven separation, 2. baffle-assisted separation, and 3. high capacity mechanical separation. Natural gravity-driven separation
While simple in concept, natural steam-water sepa- ration is quite complex. It is strongly dependent upon inlet velocities and inlet locations, average inlet steam quality, water and steam outlet locations, and disen- gagement of liquid and steam above the nominal wa- ter surface. Some of these effects are illustrated in Figs. 20 and 21.
For a low rate of steam generation, up to about 3 ft/s (0.9 m/s) velocity of steam leaving the water sur- face, there is sufficient time for the steam bubbles to separate from the mixture by gravity without being drawn into the discharge connections and without
carrying entrained water droplets into the steam out- let (Fig. 20a). However, for the same arrangement at a higher rate of steam generation (Fig. 20b), there is insufficient time to attain either of these desirable results. Moreover, the dense upward traffic of steam bubbles in the mixture may also cause a false water level indication, as shown.
The effect of the riser or inlet connection locations in relation to the water level is illustrated in diagrams a and b of Fig. 21. Neither arrangement is likely to yield desirable results in a drum where gravity alone is used for separation.
From an economic standpoint, the diameter of a