Boiling point and thermophysical properties The boiling point, or saturation temperature, of a liquid can be defined as the temperature at which its vapor pressure is equal to the total local pressure. The saturation temperature for water at atmospheric pres- sure is 212F (100C). This is the point at which net vapor generation occurs and free steam bubbles are formed from a liquid undergoing continuous heating. As discussed in Chapter 2, this saturation tempera-
ture (Tsat) is a unique function of pressure. The Ameri- can Society of Mechanical Engineers (ASME) and the International Association for the Properties of Steam (IAPS) have compiled extensive correlations of thermo- physical characteristics of water. These characteristics include the enthalpy (or heat content) of water, the enthalpy of evaporation (also referred to as the latent heat of vaporization), and the enthalpy of steam. As the pressure is increased to the critical pressure [3200 psi (22.1 MPa)], the latent heat of vaporization declines to zero and the bubble formation associated with boil- ing no longer occurs. Instead, a smooth transition from liquid to gaseous behavior occurs with a continuous in- crease in temperature as energy is applied.
Two other definitions are also helpful in discussing boiling heat transfer:
1. Subcooling For water below the local saturation temperature, this is the difference between the saturation temperature and the local water tem- perature (Tsat – T ).
2. Quality This is the flowing mass fraction of steam (frequently stated as percent steam by weight or %SBW after multiplying by 100%): x m m m = +
watersteamsteam (1)
where
msteam = steam flow rate, lb/h (kg/s)
mwater = water flow rate, lb/h (kg/s)
Thermodynamically, this can also be defined as:
x H H H or H H H H f fg f g f = − − − (2) where
H = local average fluid enthalpy, Btu/lb (J/kg)
Hf = enthalpy of water at saturation, Btu/lb (J/kg) Hg = enthalpy of steam at saturation, Btu/lb (J/kg) Hfg = latent heat of vaporization, Btu/lb (J/kg) When boiling is occurring at saturated, thermal equilibrium conditions, Equation 2 provides the frac- tional steam flow rate by mass. For subcooled condi-
tions where H < Hf, quality (x) can be negative and is an indication of liquid subcooling. For conditions where
H > Hg, this value can be greater than 100% and repre- sents the amount of average superheat of the steam. Boiling curve
Fig. 1 illustrates a boiling curve which summarizes the results of many investigators. This curve provides the results of a heated wire in a pool, although the characteristics are similar for most situations. The heat transfer rate per unit area, or heat flux, is plotted versus the temperature differential between the metal surface and the bulk fluid. From points A to B, con- vection heat transfer cools the wire and boiling on the surface is suppressed. Moving beyond point B, which is also referred to as the incipient boiling point, the temperature of the fluid immediately adjacent to the heated surface slightly exceeds the local saturation temperature of the fluid while the bulk fluid remains subcooled. Bubbles, initially very small, begin to form adjacent to the wire. The bubbles then periodically collapse as they come into contact with the cooler bulk fluid. This phenomenon, referred to as subcooled boil-
ing, occurs between points B and S on the curve. The
heat transfer rate is quite high, but no net steam gen- eration occurs. From points S to C, the temperature of the bulk fluid has reached the local saturation tem- perature. Bubbles are no longer confined to the area immediately adjacent to the surface, but move into the bulk fluid. This region is usually referred to as the
nucleate boiling region, and as with subcooled boil-
ing, the heat transfer rates are quite high and the metal surface is only slightly above the saturation temperature.
As point C is approached, increasingly large sur- face evaporation rates occur. Eventually, the vapor generation rate becomes so large that it restricts the liquid return flow to the surface. The surface eventu- ally becomes covered (blanketed) with an insulating layer of steam and the ability of the surface to trans- fer heat drops. This transition is referred to as the
critical heat flux (CHF), departure from nucleate boil- ing (DNB), burnout, dryout, peak heat flux, or boil- ing crisis. The temperature response of the surface un-
der this condition depends upon how the surface is being heated. In fossil fuel boiler furnaces and nuclear reactor cores, the heat input is effectively independent of surface temperature. Therefore, a reduction in the heat transfer rate results in a corresponding increase in surface temperature from point D to D′ in Fig. 1. In some cases, the elevated surface temperature is so high that the metal surface may melt. If, on the other hand, the heat input or heat transfer rate is depen- dent upon the surface temperature, typical of a nuclear steam generator, the average local tempera- ture of the surface increases as the local heat trans- fer rate declines. This region, illustrated in Fig. 1 from points D to E, is typically referred to as unstable film
boiling or transition boiling. Because a large surface
temperature increase does not occur, the main conse- quences are a decline in heat transfer performance per unit surface area and less overall energy transfer. The actual local phenomenon in this region is quite com- plex and unstable as discrete areas of surface fluctu- ate between a wetted boiling condition and a steam blanketed, or dry patch, condition. From position E through D′ to F, the surface is effectively blanketed by an insulating layer of steam or vapor. Energy is transferred from the solid surface through this layer by radiation, conduction and microconvection to the liquid-vapor interface. From this interface, evapora- tion occurs and bubbles depart. This heat transfer region is frequently referred to as stable film boiling. In designing steam generating systems, care must be exercised to control which of these phenomena oc- cur. In high heat input locations, such as the furnace area of fossil fuel boilers or nuclear reactor cores, it is important to maintain nucleate or subcooled boiling to adequately cool the surface and prevent material failures. However, in low heat flux areas or in areas where the heat transfer rate is controlled by the boil- ing side heat transfer coefficient, stable or unstable film boiling may be acceptable. In these areas, the resultant heat transfer rate must be evaluated, any temperature limitations maintained and only allow- able temperature fluctuations accepted.
Flow boiling
Flow or forced convective boiling, which is found in
virtually all steam generating systems, is a more com- plex phenomenon involving the intimate interaction of two-phase fluid flow, gravity, material phenomena and boiling heat transfer mechanisms. Fig. 2 is a clas- sic picture of boiling water in a long, uniformly heated, circular tube. The water enters the tube as a subcooled liquid and convection heat transfer cools the tube. The point of incipient boiling is reached (point 1 in Fig. 2). This results in the beginning of subcooled boiling and bubbly flow. The fluid temperature continues to rise until the entire bulk fluid reaches the saturation tem- perature and nucleate boiling occurs, point 2. At this location, flow boiling departs somewhat from the simple pool boiling model previously discussed. The steam-water mixture progresses through a series of Fig. 1 Boiling curve – heat flux versus applied temperature difference.
flow structures or patterns: bubbly, intermediate and annular. This is a result of the complex interaction of surface tension forces, interfacial phenomena, pres- sure drop, steam-water densities and momentum ef- fects coupled with the surface boiling behavior. While boiling heat transfer continues throughout, a point is reached in the annular flow regime where the liquid film on the wall becomes so thin that nucleation in the film is suppressed, point 3. Heat transfer then occurs through conduction and convection across the thin annular film with surface evaporation at the steam- water interface. This heat transfer mechanism, called
convective boiling, also results in high heat transfer
rates. It should also be noted that not all of the liquid is on the tube wall. A portion is entrained in the steam core as dispersed droplets.
Eventually, an axial location, point 4, is reached where the tube surface is no longer wetted and CHF or dryout occurs. This is typically associated with a temperature rise. The exact tube location and magni- tude of this temperature, however, depend upon a variety of parameters, such as the heat flux, mass flux, geometry and steam quality. Fig. 3 illustrates the effect of heat input rate, or heat flux, on CHF loca- tion and the associated temperature increase. From points 4 to 5 in Fig. 2, post-CHF heat transfer, which is quite complex, occurs. Beyond point 5, all of the liq- uid is evaporated and simple convection to steam occurs.
Boiling heat transfer evaluation
Engineering design of steam generators requires the evaluation of water and steam heat transfer rates un- der boiling and nonboiling conditions. In addition, the
identification of the location of critical heat flux (CHF) is important where a dramatic reduction in the heat transfer rate could lead to: 1) excessive metal tempera- tures potentially resulting in tube failures, 2) an un- acceptable loss of thermal performance, or 3) unaccept- able temperature fluctuations leading to thermal fa-
Fig. 3 Tube wall temperatures under different heat input conditions.
tigue failures. Data must also be available to predict the rate of heat transfer downstream of the dryout point. CHF phenomena are less important than the heat transfer rates for performance evaluation, but are more important in defining acceptable operating conditions. As discussed in Chapter 4, the heat transfer rate per unit area or heat flux is equal to the product of tem- perature difference and a heat transfer coefficient. Heat transfer coefficients
Heat transfer correlations are application (surface and geometry) specific and The Babcock & Wilcox Company (B&W) has developed extensive data for its applications through experimental testing and field experience. These detailed correlations remain propri- etary to B&W. However, the following generally avail- able correlations are provided here as representative of the heat transfer relationships.
Single-phase convection Several correlations for forced convection heat transfer are presented in Chap- ter 4. Forced convection is assumed to occur as long as the calculated forced convection heat flux is greater than the calculated boiling heat flux (point 1 in Fig. 2):
′′ > ′′
qForced Convection qBoiling (3)
While not critical in most steam generator applica- tions, correlations are available which explicitly de- fine this onset of subcooled boiling and more accurately define the transition region.1
Subcooled boiling In areas where subcooled boil- ing occurs, several correlations are available to char- acterize the heat transfer process. Typical of these is the Jens and Lottes2 correlation for water. For inputs
with English units:
∆Tsat = 60
(
q′′/106)
1 4/ e−P/900 (4a)and for inputs with SI units:
∆Tsat = 25
( )
q′′ 1 4/ e−P/ .6 2 (4b)where
∆Tsat = Tw – Tsat, F (C)
Tw = wall temperature, F (C)
Tsat = saturated water temperature, F (C)
′′
q = heat flux, Btu/h ft2 (MW t/m2) P =pressure, psi (MPa)
Another relationship frequently used is that developed by Thom.3
Nucleate and convective boiling Heat transfer in the saturated boiling region occurs by a complex combi- nation of bubble nucleation at the tube surface (nucle- ate boiling) and direct evaporation at the steam-wa- ter interface in annular flow (convective boiling). At low steam qualities, nucleate boiling dominates while at higher qualities convective boiling dominates. While separate correlations are available for each range, the most useful relationships cover the entire saturated boiling regime. They typically involve the summation of appropriately weighted nucleate and convective
boiling components as exemplified by the correlation developed by J.C. Chen and his colleagues.4 While
such correlations are frequently recommended for use in saturated boiling systems, their additional precision is not usually required in many boiler or reactor ap- plications. For general evaluation purposes, the subcooled boiling relationship provided in Equation 4 is usually sufficient.
Post-CHF heat transfer As shown in Fig. 3, substan- tial increases in tube wall metal temperatures are possible if boiling is interrupted by the CHF phenom- enon. The maximum temperature rise is of particular importance in establishing whether tube wall over- heating may occur. In addition, the reliable estima- tion of the heat transfer rate may be important for an accurate assessment of thermal performance. Once the metal surface is no longer wetted and water droplets are carried along in the steam flow, the heat transfer process becomes more complex and includes: 1) con- vective heat transfer to the steam which becomes su- perheated, 2) heat transfer to droplets impinging on the surface from the core of the flow, 3) radiation di- rectly from the surface to the droplets in the core flow, and 4) heat transfer from the steam to the droplets. This process results in a nonequilibrium flow featur- ing superheated steam mixed with water droplets. Current correlations do not provide a good estimate of the heat transfer in this region, but computer models show promise. Accurate prediction requires the use of experimental data for similar flow conditions.
Reflooding A key concept in evaluating emergency core coolant systems for nuclear power applications is
reflooding. In a loss of coolant event, the reactor core
can pass through critical heat flux conditions and can become completely dry. Reflooding is the term for the complex thermal-hydraulic phenomena involved in rewetting the fuel bundle surfaces as flow is returned to the reactor core. The fuel elements may be at very elevated temperatures so that the post-CHF, or steam blanketed, condition may continue even in the presence of returned water flow. Eventually, the surface tem- perature drops enough to permit a rewetting front to wash over the fuel element surface. Analysis includes transient conduction of the fuel elements and the in- teraction with the steam-water heat transfer processes. Critical heat flux phenomena
Critical heat flux is one of the most important pa- rameters in steam generator design. CHF denotes the set of operating conditions (mass flux, pressure, heat flux and steam quality) covering the transition from the relatively high heat transfer rates associated with nucleate or forced convective boiling to the lower rates resulting from transition or film boiling (Figs. 1 and 2). These operating conditions have been found to be geometry specific. CHF encompasses the phenomena of departure from nucleate boiling (DNB), burnout, dryout and boiling crisis. One objective in recirculat- ing boiler and nuclear reactor designs is to avoid CHF conditions. In once-through steam generators, the objective is to design to accommodate the temperature increase at the CHF locations. In this process, the heat flux profile, flow passage geometry, operating pressure
and inlet enthalpy are usually fixed, leaving mass flux, local quality, diameter and some surface effects as the more easily adjusted variables.
Factors affecting CHF Critical heat flux phenomena under flowing conditions found in fossil fuel and nuclear steam generators are affected by a variety of parameters.5 The primary parameters are the operat-
ing conditions and the design geometries. The oper- ating conditions affecting CHF are pressure, mass flux and steam quality. Numerous design geometry factors include flow passage dimensions and shape, flow path obstructions, heat flux profile, inclination and wall surface configuration. Several of these effects are il- lustrated in Figs. 3 through 7.
Fig. 3 illustrates the effect of increasing the heat input on the location of the temperature excursion in a uniformly heated vertical tube cooled by upward flow- ing water. At low heat fluxes, the water flow can be al- most completely evaporated to steam before any tem- perature rise is observed. At moderate and high heat fluxes, the CHF location moves progressively towards the tube inlet and the maximum temperature excur- sion increases. At very high heat fluxes, CHF occurs at a low steam quality and the metal temperature excur- sion can be high enough to melt the tube. At extremely high heat input rates, CHF can occur in subcooled water. Avoiding this type of CHF is an important de- sign criterion for pressurized water nuclear reactors.
Many large fossil fuel boilers are designed to oper- ate between 2000 and 3000 psi (13.8 and 20.7 MPa). In this range, pressure has a very important effect, shown in Fig. 4, with the steam quality limit for CHF
falling rapidly near the critical pressure; i.e., at con- stant heat flux, CHF occurs at lower steam qualities as pressure rises.
Many CHF correlations have been proposed and are satisfactory within certain limits of pressure, mass velocity and heat flux. Fig. 5 is an example of a corre- lation which is useful in the design of fossil fuel natu- ral circulation boilers. This correlation defines safe and unsafe regimes for two heat flux levels at a given pres- sure in terms of steam quality and mass velocity. Ad- ditional factors must be introduced when tubes are used in membrane or tangent wall construction, are inclined from the vertical, or have different inside di- ameter or surface configuration. The inclination of the flow passage can have a particularly dramatic effect on the CHF conditions as illustrated in Fig. 6.6
Ribbed tubes Since the 1930s, B&W has investi- gated a large number of devices, including internal twisters, springs and grooved, ribbed and corrugated tubes to delay the onset of CHF. The most satisfactory overall performance was obtained with tubes having helical ribs on the inside surface.
Two general types of rib configurations have been developed:
1. single-lead ribbed (SLR) tubes (Fig. 8a) for small internal diameters used in once-through subcriti- cal pressure boilers, and
2. multi-lead ribbed (MLR) tubes (Fig. 8b) for larger in- ternal diameters used in natural circulation boilers. Both of these ribbed tubes have shown a remark- able ability to delay the breakdown of boiling. Fig. 7
Fig. 5 Steam quality limit for CHF as a function of mass flux. Fig. 4 Steam quality limit for CHF as a function of pressure.
compares the effectiveness of a ribbed tube to that of a smooth tube in a membrane wall configuration. This plot is different from Fig. 5 in that heat flux is given as an average over the flat projected surface. This is more meaningful in discussing membrane wall heat absorption.
The ribbed bore tubes provide a balance of improved CHF performance at an acceptable increase in pres- sure drop without other detrimental effects. The ribs generate a swirl flow resulting in a centrifugal action which forces the water to the tube wall and retards entrainment of the liquid. The steam blanketing and film dryout are therefore prevented until substantially higher steam qualities or heat fluxes are reached.
Because the ribbed bore tube is more expensive than a smooth bore tube, its use involves an economic bal- ance of several design factors. In most instances, there is less incentive to use ribbed tubes below 2200 psi (15.2 MPa).
Evaluation CHF is a complex combination of ther- mal-hydraulic phenomena for which a comprehensive theoretical basis is not yet available. As a result, ex- perimental data are likely to continue to be the basis for CHF evaluations. Many data and correlations de- fine CHF well over limited ranges of conditions and