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...of the tubes may be plain or enhanced. This paper is concerned only with upward flow across plain tubes.
An evaporator/boiler involves one or more of the following modes of heat transfer:
* subcooled boiling
* saturated boiling prior to dryout
* post-dryout heat transfer
The author has previously presented a general correlation for subcooled boiling heat transfer (Shah 1984, 2005). This paper is concerned exclusively with saturated boiling at vapor qualities from zero upwards, prior to dryout.
Because of the practical importance of such heat exchangers, many experimental studies have been conducted to observe and measure heat transfer on tube bundles and single tubes with cross flow. Further, many correlations for predicting heat transfer have been published. Many of these experimental studies and prediction methods have been reviewed fairly recently by Browne and Bansal (1999) and Cascario and Thome (2001). Study of this literature shows that no well-validated general method for predicting heat transfer in saturated boiling is available in the open literature. The study reported here was undertaken to fill this gap.
It is agreed by most researchers that correlations for bundle mean heat transfer cannot be generally applicable. For reliable design, one has to use models such as that of Brisbane et al. (1980) that perform calculations of heat transfer coefficients of each tube from bottom to top in terms of the local flow, quality, and heat flux. Hence, the author's efforts were directed toward developing a correlation applicable to individual tubes in bundles.
Presented here is a dimensionless correlation that shows good agreement with data for single tubes and tube bundles from many sources covering a wide range of parameters, including seven fluids (water, n-pentane, R-11, R-12, R-113, R-123, and R-134a), reduced pressures from 0.005 to 0.189, mass velocities from 1.3 to 1391 kg/[m.sup.2]s, heat flux from 1 to 1000 kW/[m.sup.2], tube diameters from 3 to 25.4 mm, and pitch to diameter ratios from 1.17 to 1.5. A total of 690 data points are correlated with a mean deviation of 15.2%. The results of comparisons of the new correlation with test data are presented and discussed.
TRENDS SHOWN BY EXPERIMENTAL DATA
The reports on the effect of quality on heat transfer are apparently conflicting. A number of researchers have reported large increases in heat transfer coefficients on a slight increase of quality above zero. Examples are Bitter (1973), Polley et al. (1980), and Burnside and Shire (2005). On the other hand, many researchers report that quality had no effect on heat transfer. Examples are Cotchin and Boyd (1992), Grant et al. (1983), Abbot and Comley (1938), and Webb and Chien (1994). Jensen et al. (1992) found no effect of quality except at very low qualities. Burnside and Shire (2005) reported a modest increase of heat transfer coefficient with quality. Chien and Wu (2004) found a significant increase in heat transfer with increasing quality at higher heat fluxes. Hwang and Yao (1986) found the heat transfer coefficient to increase with quality at low heat flux.
Most of the studies show that at high heat fluxes, the heat transfer coefficient depends on heat flux only and is about the same as that during pool boiling on a single tube; mass flow rate and quality have no effect. Examples are Cotchin and Boyd (1992), Grant et al. (1983), Abbot and Comley (1938), and Webb and Chien (1994). However, methods for determining the heat flux beyond which this occurs are not available. Further, there is the question about which pool boiling correlation to use. The present research proposes answers to these questions.
Many researchers report an increase in the heat transfer coefficient with increasing mass flow rates, for example Hwang and Yao (1986). On the other hand, no effect of mass flow rate is reported by many authors, as noted in the previous paragraph.
From the above, it appears that the different trends reported by various researchers occur under different combinations of parameters. What is needed is to find under what combinations of parameters the various trends occur, i.e., to define the regimes in which particular trends occur. The next requirement is to find methods to predict heat transfer coefficients in the various regimes. This is what the research reported here attempts to do.
THE NEW CORRELATION
This author studied and analyzed test data from many sources. As a result, three regimes of heat transfer were identified and separate equations were developed for heat transfer in each regime, as is given in the following.
Heat Transfer Regimes
Three regimes of heat transfer were identified:
1. Regime I (Intense Boiling Regime). In this regime, heat transfer depends only on heat flux; mass velocity and vapor quality have a negligible effect. This regime occurs when
[Y.sub.IB]>0.0008. (1)
2. Regime II (Convective Boiling Regime). In this regime, both heat flux and mass velocity have an effect on heat transfer; vapor quality has a negligible effect. Thus, both nucleate boiling and convection contribute to heat transfer. This regime occurs when
0.00021<[Y.sub.IB][less than or equal to]0.0008. (2)
3. Regime III (Convection Regime). In this regime, heat transfer is affected by mass velocity and vapor quality; heat flux has a negligible effect. This suggests that bubble nucleation is completely suppressed. This regime occurs when
[Y.sub.IB][less than or equal to]0.00021. (3)
The boiling intensity parameter [Y.sub.IB] is defined as
[Y.sub.IB] = [F.sub.pb]Bo[Fr.sup.0.3] (4)
where
[F.sub.pb] = [h.sub.pb,actual]/[h.sub.cooper]. (5)
The variable [h.sub.cooper] is the pool boiling heat transfer coefficient calculated by the simplified Cooper correlation, Equation 6:
[h.sub.cooper] = 55.1[q.sup.0.67][p.sub.r.sup.0.12][( - log[p.sub.r]).sup.[ - 0.55]][M.sup.[ - 0.55]] (6)
The variable [h.sub.pb,actual] is the same as [h.sub.cooper] unless pool boiling test data is available for the tubes to be used in the heat exchanger; in that case, [h.sub.pb,actual] is calculated from the test data. Thus, [F.sub.pb] = 1 unless test data for the actual tubes used or to be used are available.
Figures 1-4 illustrate the data in the three regimes.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Heat Transfer Equations
In regime I, [h.sub.TP] = [F.sub.pb][h.sub.cooper]. (7)
In regime II, [phi] = [[phi].sub.0]. (8)
In regime III, [phi] = [2.3/[[Z.sup.0.08][Fr.sup.0.22]]]. (9)
The parameter Z was introduced by this author to correlate heat transfer during film condensation in tubes (Shah 1979). As heat transfer during film condensation in tubes is due to convective effects only, it was felt that it may be applicable in this regime. It is defined as
Z = [([1 - x]/x).sup.0.8][p.sub.r.sup.0.4]. (10)
In the heat transfer equations above,
[phi] = [h.sub.TP]/[h.sub.LT], (11)
where [[phi].sub.0] is the value of [phi] when x = 0. It is the highest of that calculated by the following relations:
[phi] = 443[Bo.sup.0.65][F.sub.pb] (12)
[[phi].sub.0] = 31[Bo.sup.0.33][F.sub.pb] (13)
[[phi].sub.0] = 1 (14)
With [F.sub.pb] = 1, Equations 12 and 13 are the same as that developed by this author through analysis of varied data from many sources for flow across single tubes at zero vapor quality (Shah 2005).
The...
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