Heat Transfer in Flow Boiling Over a Bundle of Horizontal Tubes

0263–8762/05/$30.00+0.00 # 2005 Institution of Chemical Engineers Trans IChemE, Part A, May 2005 Chemical Engineering Research and Design, 83(A5): 527–538

www.icheme.org/journals doi: 10.1205/cherd.04313

HEAT TRANSFER IN FLOW BOILING OVER A BUNDLE OF HORIZONTAL TUBES B. M. BURNSIDE
and N. F. SHIRE† School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK

T

he paper describes tests boiling R113 at atmospheric pressure in upward flow over a 17 row column of square pitched electrically heated tubes. Uniform heat fluxes of 10 – 65 kW m2 and maximum Reynolds numbers, Remax , between 7800 and 27 000 were used. The data at the lower heat fluxes of 10 and 20 kW m2 consistently exhibited a linear increase of heat transfer coefficient, h, with quality, the slope lower at 20 kW m2 , so that h at 10 kW m2 exceeded that at 20 kW m2 and both reached h at 40 kW m2 for the maximum quality tested. At the higher heat fluxes a nucleate boiling controlled region was observed at low quality, with h equal to the value at the same heat flux as observed with an isolated tube in a pool, followed by a rise in h at higher quality. The results were compared with the work of other researchers. Heat transfer coefficients for q  40 kW m2 were predicted to an average r.m.s. deviation of 7%, using the asymptotic flow boiling model. However, the sensitivity of h to change of quality and flowrate predicted was much lower than measured and in some cases exhibited opposite trends. Keywords: cross-flow heat transfer; 2-phase flow; boiling models.

INTRODUCTION

flowing alone, hl . These boiling and convective components are combined additively in equation (1). Equation (2) is used usually with S ¼ 1. A variable degree of smooth transition, from the near pool boiling conditions at low velocity and void fraction to dominant convection at high velocities and void fraction, is afforded by varying the index n^ . The void fraction and 2-phase friction multiplier are linked to the flow velocity, quality and properties by experimentally based correlations (Schrage et al., 1988; Hsu and Jensen, 1988; Dowlati et al., 1992). The object of this work is to provide heat transfer coefficient data over a range of quality, heat flux and flow velocity to help to validate current methods of prediction used in heat exchanger design.

Design of cross-flow boiling heat exchangers (Brisbane et al., 1980; Palen and Yang, 1981; Burnside, 1999) depends on the availability of reliable flow boiling correlations. Supporting these, 2-phase flow void fraction and friction multiplier correlations are required. The accuracy of these correlations must be checked by experiment. Two types of correlations for flow boiling heat transfer coefficient, h, (Webb and Gupte, 1992) are used in design. They are the superimposition type, equation (1), h ¼ Shnpb þ Fhl

(1)

and the asymptotic type, equation (2), ^ h ¼ {Shnnpb þ (Fhl )n^ }1=^n

APPARATUS

(2)

A full description of the apparatus can be found in Shire (1995) and Shire and Burnside (1999). The boiler is shown in Figure 1. It was adapted from a 732 mm internal diameter thin slice kettle reboiler by introducing two brass walls. These sealed off a passage of rectangular crosssection, 102 mm wide and 52 mm deep, between the reboiler backplate and its toughened glass viewing window. The original shell space outside the brass walls was packed with polypropylene insulation. Mounted in the backplate of the reboiler shell, the 17 row 25.4 mm square pitched bundle of 19 mm diameter, 51 mm long 90 Cu:10 Ni tubes comprised five columns of five tubes with boiling surfaces in

S(,1) is a suppression factor allowing for the effect of 2-phase flow in reducing the isolated tube boiling heat transfer coefficient, hnpb , and F is a flow factor accounting for the enhancement effect of 2-phase flow on the heat transfer coefficient in convection of the liquid phase


Correspondence to: Dr B. M. Burnside, School of Engineering and Physical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK. E-mail: [email protected]

†

Currently at British Energy.

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Figure 1. Experimental boiler.

the ‘as machined’ condition. The outside tubes of each row were fitted into horizontal semi-cylindrical grooves in the two brass side walls. Thus the rising test fluid washed three columns of tubes in the centre and two columns of half tubes at the outside. The tubes were separated from the window at the front by a 1.5 mm viton washer and from the tubeplate at the back by a 3 mm gasket. A locknut and washer secured the assembly. The wall thickness of the tube section (Figure 2), was 1.3 mm along the length located in the tubeplate. This, together with the insulating effect of the seals and a thick layer of cotton covered fibreglass insulation over the back of the shell, ensured minimal heat loss from the tube section to the backplate and the surroundings. A 9.5 mm diameter, 250 W cartridge heater fitted closely into a pocket machined in each tube section. The leads protruded through the back of the boiler. Wall thermocouples were mounted on a 15 mm pitch circle diameter in a 2 mm diameter hole drilled all the way from the window end to emerge in the interior as shown in the figure. The Ni/Cr, Ni/Al thermocouple was soldered into a hole drilled in the end of a 2 mm diameter copper slug. These, in turn were soldered into the holes in the tube section forming a seal at the window end. The

thermocouple leads were fed through the open end of the tube section and connected to compensating cable in an isothermal zone behind the boiler. The three full tubes in each row were fitted with wall thermocouples in this way. In the bottom 12 rows and the 14th row, one thermocouple was fitted at the top of the tube, halfway along the heated section, as shown in Figure 2. In the other rows, the central three tubes were fitted with four thermocouples spaced at 908 around the circumference. In seven of these tubes the thermocouples were in the centre of the heated length. In four others the top and bottom thermocouples were positioned one-quarter and three-quarters of the heated length from the window end, respectively. Eight mineral insulated metal clad (mimc) thermocouples, mounted on the tubeplate, were located in the centre of the space between the four adjacent tubes in the positions shown in Figure 1. A further mimc thermocouple (not shown) was positioned at the feed entry. R113 was pumped from a reservoir through a metric series rotameter. It flowed through an electrically heated preheater before entering the boiler through three 28 mm copper pipes and a wire mesh flow distributor (Figure 1). The two phase mixture left the shell through a 102 mm diameter opening in the backplate (Burnside et al., 2001). It passed into a 150 mm  150 mm  100 mm pyrex tee where disengagement occurred. The liquid fraction flowed by gravity back to the reservoir. The vapour flowed up a 100 mm riser into a vented, water cooled condenser whence it returned to the reservoir. The boiler, preheater and feed lines and the vapour riser were covered with a thick layer of insulation. The 85 tube heaters were connected to seven voltage regulators. Power to these banks was measured by electronic wattmeter. In addition the voltage drop was measured across standard 0:47 V resistances in series with each heater. This enabled individual power to each heater to be determined. All the thermocouple emfs were monitored by a computer controlled data logging system sensitive to +3 mV. The thermocouples were calibrated using the identical measuring system to +0:15 K. A further uncertainty in surface temperature arises due to the effect of uncertainty in the radial position of the thermocouple on the correction for conduction in the tube wall. This is estimated to be 0.5 mm on either side of the nominal 15 mm diameter. The accuracy of measurements of heat flux varies from +1% at q ¼ 65 kW m2 to +16% at 2 kW m2 . Based on these figures, the overall estimated uncertainty in the heat transfer coefficient h is +0:1 kW m2 K at q ¼ 65 kW m2 K rising to +0:25 kW m2 K at q ¼ 2 kW m2 K, where no evaporation occurs. In some cases these uncertainties may be higher due to doubt about the precise position of some of the thermocouples in the tube wall due to ‘wander’ of the drill in the tough tube material when drilling the thermocouple pocket (Shire 1995; Burnside et al., 2001). This will be referred to again below. EXPERIMENTAL PROCEDURE AND DATA REDUCTION

Figure 2. Heater tube section assembly.

Initially, 10 runs were carried out with a uniform q of 2.5 kW m2 K. No vapour formation was observed. The inlet liquid temperature was kept to within 1 K of the normal boiling point. Mass fluxes, Gmax , between 200 and 710 kg m2 s 1 , referred to the minimum flow area, were used. In these tests the guard heater tubes at the outsides of

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the guard heaters, plus half the heat flux in the current row. The error in x at the first row level was estimated (Shire, 1995) to vary from 14% at 5 kW m2 to 8% at 65 kW m2 . At row 17, the corresponding figures are 4% at all heat fluxes. Average tubewall temperatures of each row, Twm , were taken to be the arithmetic mean of the measured values for each of the three central tubes, corrected for heat conduction. Tw was taken to be the single value available for the tubes with one thermocouple and the arithmetic mean of the four available on the other tubes. The local liquid temperatures were calculated as the mean values of the two nearest measurements, Tlm (Figure 1). Mean heat transfer coefficients for each row were calculated using equation (4). qm is the average heat flux and Twm the arithmetic mean wall temperature for the three central tubes in the row. Figure 3. Comparison of liquid only convection test data and prediction.

each row were set to 0.5q. The results are shown in Figure 3 in the form h versus Remax , defined by equation (3). D is the tube diameter and ml is the liquid phase viscosity. Remax ¼

Gmax D ml

hm ¼

qm (Twm  Tlm )

It was noticeable that the resulting values of hm , for the rows including tubes with four thermocouples, were not altered significantly by different methods of averaging Tw . RESULTS

(3)

The values presented are the arithmetic means for the 17 rows measured. For comparison the predictions of ESDU 73031 (1973) are shown. Although the data are somewhat above the prediction at the lower Reynolds numbers, the agreement is within the predicted experimental error indicating the validity of the estimate of error. Fifty-two boiling tests were conducted at mass fluxes from 200 to 710 kg m2 s1 over the heat flux range 10 to 65 kW m2 . In the majority of the tests the guard heaters were set at the same heat flux, q, as the central tubes in the bundle. In the remainder it was set at 0.5q with no effect on the variation of h with x, provided the correct row average heat flux was used in calculating the local quality x. To avoid hysteresis, before commencing the tests the heat flux was set high before being reduced to the nominal value. The rig was allowed to settle to steady conditions for about two hours before data were taken. Then tubewall and liquid temperatures, heater power and the mass flowrate of R113 entering the column and R113 condensate leaving the condenser were monitored. It was not possible to carry out a meaningful heat balance for the column. The high mass flowrates used resulted in entrainment of an unknown amount of liquid with the vapour rising to the condenser. This led to an overestimate of the enthalpy flux to the fluid based on the assumption that the flow into the condenser was all vapour. As a result the calculated difference between power input and the enthalpy flux to the fluid was consistently negative. However, due to the design of the tube section fixing, any heat flux direct from the heaters to the backplate or to the surroundings was very small. This was confirmed by tests on the full boiler (Shire, 1995) where the overall heat loss from the shell and vapour riser fell from about 7% at q ¼ 5 kW m2 K to much lower values at higher q. The quality, x, at each row level was calculated from the mass flux and the heat flux in the rows below, including

(4)

Figure 4(a) shows the variation of measured heat transfer coefficient with quality for the lowest Reynolds number used in the tests, Remax ¼ 7800. In this and subsequent figures, data from the bottom three rows of the column have been omitted to avoid the distorting effect of subcooling at entry. The values shown in the figure are calculated from the data for all combinations of row position in the bundle and for all heat fluxes used. On the right hand ordinate the isolated tube pool boiling heat transfer coefficients, hnpb , predicted by the Mostinski (1963) correlation, are marked for comparison.1 These have been verified by Tarrad (1991) in tests on the tube sections used in this investigation. Also plotted is hl , the convective heat transfer coefficient for the liquid phase flowing alone based on the ESDU (1973) correlations. The data have been fitted by least squares and the fitted lines are plotted in the figure. Root mean square deviations, 1h , of h from the fits, defined by equation (5), are shown in Table 1. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S(h  hfit )2 1h ¼ N 1

(5)

They vary from +0:09 kW m2 K at q ¼ 10 kW m2 to +0:13 kW m2 K at q ¼ 40 kW m2 . This compares well with the estimated error of the experiment. However, the data for rows 13 and 14 exhibit more scatter at all heat fluxes than is observed for the other rows, reaching +0:25 kW m2 K at 40 kW m2 . Moreover, values of h at row 13 are consistently much higher than at row 14 which itself is lower than the trend of the other rows. This points to a systematic error and is attributed to greater than assumed uncertainty in the radial positioning of the thermocouples in these rows. Raising this to between +1 and +1:5 mm results in estimated errors of the magnitude of the scatter in 1 The scale of h on this ordinate is the same as on the left hand ordinate in this and subsequent figures.

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Figure 4. Data h versus x, with hnpb and hl , (a) Remax ¼ 7800, all rows 4–17; (b) Remax ¼ 7800, rows 4–12, 15 –17; (c) Remax ¼ 14 000; (d) Remax ¼ 19 500; (e) Remax ¼ 23 000; (f) Remax ¼ 27 000 (A, q ¼ 10 kW m22; 4, q ¼ 20; , q ¼ 40; W, q ¼ 50; O, q ¼ 65).

Table 1. Standard deviation of data from least square fits, kW m22 K (
all rows 4–17). q (kW m22) Remax

10

20

40

50

65

7 800
7 800 14 000 15 400 19 500 23 000 24 000 27 000

0.09 0.06 0.06 – 0.09 0.07 – 0.08

0.10 0.05 0.07 – 0.08 – 0.08 0.09

0.13 0.08 0.09 – 0.09 0.09 – 0.09

– – 0.11 – 0.10 0.10 – 0.11

– – – 0.12 0.12 0.12 – 0.12

h observed around these rows at all tested values of q and Remax . No marked difference in flow boiling conditions could be seen around these rows. It was decided to ignore the data taken at rows 13 and 14 rather than attempt to correct it to account for notional uncertainty in Dt=c . Figure 4(b) shows the remaining data for Remax ¼ 7800. As expected, 1h is reduced (Table 1). Data for Remax ¼ 14 000, 19 500, 23 000, 24 000 and 27 000 are shown in Figures 4(c) –(f) respectively, and 1h , omitting rows 13 and 14, in Table 1. Below 50 kW m2 1h is less than +0:10 kW m2 K and rises to a maximum of +0:12 kW m2 K at 65 kW m2 . Using the fits h ; h(x,q) at constant Remax , shown in Figures 4(b) – (f), cross-plots in the form h versus Remax and h versus q, both at constant quality, were obtained over the whole range of qualities tested. The latter is

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Figure 5. Cross-plot h versus q at constant quality with hnpb and hl , (a) x ¼ 0.022; (b) x ¼ 0.12. (Remax values: A, 7800; 4, 14 000; , 19 500; W, 23 000; †, 23 800; þ, 27 000).

shown in Figure 5. The range of the plots was limited, at low qualities because high heat flux data were not available at the lower values of Remax and, at the higher qualities, because low heat flux data were not available at the higher Remax . To show the sensitivity of heat transfer coefficient to quality and flowrate, the slopes of the h versus x measured data, (@h=@x)q,Re , and h versus Remax cross plots, (@h=@Re)q,x , were calculated over the range of data available. Figures 6 and 7(a) show (@h=@x)q,Re for q ¼ 10 and 20 kW m2 and the higher heat fluxes, respectively. (@h=@Re)q,x is shown in Figure 7(b). DISCUSSION Limit of Zero Quality Using the curvefits, the h versus quality data in Figure 4 were extrapolated to the value hx¼0 at each flowrate and heat flux, Table 2. At the higher heat fluxes, q 5 20 kW m2 , hx¼0 ¼ hnpb within experimental error, at all flowrates. This agrees with a summary of early work by Collier (1990). Cornwell and Scoones (1988) investigated the boiling of R113 at atmospheric pressure in a tube bundle of slightly different geometry. Their data at Remax ¼ 5700, as revealed by

Figure 6. Data, plot of (@h=@x)q,Re versus Reynolds number, q ¼ 10 and 20 kW m22.

Webb and Gupte (1992), are plotted together with the Remax ¼ 7800 data of the present work (Figure 4(b)), the closest possible match, in Figure 8. Their test bundle was more tightly packed, s=D ¼ 1.25, and the tube diameter larger, 25.4 mm, than the values s=D ¼ 1.33 and D ¼ 19.1 mm used here. Extrapolating to zero quality, this data revealed hx¼0 ranging from 18% to 10% greater than hnpb as q rose from 12 to 36 kW m2 . Hsu and Jensen (1988) plotted h versus quality for 1500 , Remax , 6000 at q ¼ 12.6 kW m2 in a square pitched bundle of 7.94 mm diameter tubes, s=D ¼ 1.3 and 1.7 in vertical upflow of R113 at 2.06 b. For these conditions hnpb ¼ 1.1 kW m2 (Mostinski, 1963). Although the scatter was high near x ¼ 0, hx¼0 varied from 40 to 60% higher than hnpb between the lowest and highest flowrates, respectively (Hsu and Jensen, 1988). However, Fujita et al. (1984) and other studies of boiling on tubes in a column located in a pool of saturated liquid, have shown that h on the bottom tube is the same as hnpb measured with the tube on its own in the pool (Fujita et al., 1988). The crossflow induced by recirculation had no effect on nucleate boiling. In the present tube bundle study, at q ¼ 10 kW m2 , hx¼0 is greater than both hnpb and hl up to Remax ¼ 19 500 (Table 2). Thus, the explanation cannot be simply that each mode occurs on an area of tube surface separate from the other. In some way the two must be complementary. At higher flowrates hnpb , hx¼0 , hl . Sufficient nucleate boiling sites are active to stop convection occurring over the whole surface. Hwang and Yao (1986), also in R113 at 1 atm, measured hx¼0 direct for upward flow of 6 K subcooled liquid over a single 19 mm diameter horizontal tube in a channel 87 mm wide for 220 , Remax , 17 300. At q ¼ 10 kW m2 , hx¼0 at Remax ¼ 17 300 was 30% greater than at Remax ¼ 220. At q ¼ 20 kW m2 , it was 20% greater. At higher heat fluxes hx¼0 did not vary with flowrate, all the data merging into a ‘fully developed’ boiling curve, hx¼0 ¼ 0.224 q0:67 which they assumed to merge with hnpb (q). Notably, this ‘fully developed’ boiling curve data is higher than the Mostinski (1963) pool boiling values. Thus the measured hx¼0 (Hwang and Yao, 1986) was 30% higher than the Mostinski hnpb at Remax ¼ 220, rising to 85% higher at Remax ¼ 17 300. The corresponding figures were 35% and 60% higher respectively, at q ¼ 20 kW m2 . At higher q,

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Figure 7. Sensitivity of h to quality and flowrate. (a) Data, plot of (@h=@x)q,Re versus Reynolds number; (b) Data, plot of (@h=@Re)q,x versus quality; (c) Equation (2) n^ ¼ 4, (@h=@x)q,Re versus Reynolds number; (d) Equation (2), n^ ¼ 4, (@h=@Re)q,x versus quality.

where hx¼0 did not depend on flowrate, the directly measured hx¼0 was 30% higher than the Mostinski hnpb at both q ¼ 40 and 65 kW m2 . Contrary to the present data, these results show a large dependence of hx¼0 on flowrate at low q and fully developed nucleate boiling levels of hx¼0 very much higher than hnpb predicted by the Mostinski correlation.

Two Phase Flow Before discussing the results for 2-phase crossflow it is important to identify the flow regimes obtaining. For a given flow geometry and tube surface character, flowrate, quality and heat flux have an influence on flow regime. Void fraction for the conditions of the tests was calculated using the Schrage et al. correlation (Schrage et al., 1988),

equation (6), which has been shown to fit R113 1 atm data (Schrage et al., 1988).

a ¼ 1 þ 0:123 Fr 0:191 ln x ah

(6)

If a=ah , 0:1 then a=ah ¼ 0:1. Based on this, the co-ordinates of the Grant and Chisholm (1979) flow pattern map, Ugs (rg =rl )0:5 , and Uls (rl ml )1=3 =s were evaluated over a range of values of Gmax and x covering the data. Extrapolating where necessary, the flowmap placed all the tests in the bubbly flow regime. This was surprising since, at

Table 2. Limiting values hx¼0 of h(kW m22 K) as x ! 0.

hx¼0,q¼10 hx¼0,q¼20 hx¼0,q¼40 hx¼0,q¼50 hx¼0,q¼65 hl

Remax

hnpb (Mostinski, 1963)

7 800

14 000

19 500

23 000

27 000

0.76 1.23 2.00 2.33 2.80 –

0.9 1.1 2.0 – – 0.60

1.0 1.1 2.0 2.3 – 0.81

1.1 1.2 2.0 2.3 2.6 0.96

0.9 – 2.1 2.3 2.7 1.05

0.9 1.2 2.1 2.3 2.7 1.14

Figure 8. Comparison of present data with Cornwell and Scoones (1988).

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HEAT TRANSFER IN FLOW BOILING OVER HORIZONTAL TUBES the higher qualities and lower flowrates, intermittent or annular flow was observed in the column of fluid flowing in the passage formed by the gaps between the in-line configuration tubes. Xu et al. (1998) have produced a modified version of this flowmap taking into account their air/water experiments, which used a square pitch configuration, s=D ¼ 1:25. The data of this investigation are shown on the map in Figure 9. All the tests at q ¼ 10 and 20 kW m2 were predicted to be in the bubbly flow regime. At q ¼ 40 kW m2 and Remax ¼ 7800, the data were in the intermittent region at low quality, extending into annular flow at the higher qualities tested. At higher flowrates bubbly flow was predicted in all the tests. At 50 and 65 kW m2 , at the highest qualities annular flow was predicted at all flowrates, with bubbly flow at the lower qualities. Bearing in mind that the flow pattern maps were based on adiabatic experiments with tubes of lower diameter, this was in reasonable agreement with observation. From a design point of view, the dependence of h on x at constant Remax and q in the experiments (Figure 4), is directly related to the development of the flow up the columns of a kettle reboiler bundle, including any change of flow regime. Each point on the loci of h versus Remax at constant x and q is derived from data at constant x obtained from tube rows successively lower down the bundle. Each point represents data from different tests at the same q. Thus the relation hx,q ; h(Re) does not refer to a development of flow in a reboiler but purely the effect of changing the flowrate on h in the general design correlation, equation (7). h ; h(x, Re, q, Freg, Geom, Scond)

(7)

and applied as such in design. In equation (7), Freg is the flow regime, Geom is the flow geometry and Scond is the tubewall surface condition. In the tests, all the tubes were manufactured in the same batch. The entry effects were eliminated by ignoring the data from the first four rows. Thus, the effects of surface condition and geometry, in this case the position of the row in the column, were minimized. In addition to the evidence of the cross-plots hq ; hq (Remax ,x ¼ c), it would be useful to get physical evidence of the form which this relationship should take. A hypothetical experiment may be devised to do this

Figure 9. Data plotted on flow pattern map of Xu et al. (1998). Locus of maximum ordinate at each q shown.

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directly for a specific tube row. Consider a uniformly heated channel, heat flux q. At entrance to the channel the flowrate and quality (or subcooling), xinch (DTsub ) can be varied. Conditions are kept within the range of the data. Heat transfer measurements are made on an instrumented tube row at a series of increasing flowrates, simultaneously increasing xinch (decreasing DTsub ) so that the approach quality to the instrumented row remains the same. It was shown above that most of the data were in the bubbly flow regime. In fact, all of the points covered by the h ; h(Re, x ¼ c) cross-plots, referred to at the end of the Results section, represent data in bubbly flow, as in our hypothetical experiment. In these cross-plots, points at successively higher values of Remax represent rows increasingly higher up the bundle, whereas the data from the hypothetical experiment is all for the same row. The approximation involved in this assumption lies in ignoring any effect of row level on the correlation, equation (7). This might result, for example, from a difference in the distribution of bubbles at the same void fraction, or even a change in the relationship between void fraction, x and Remax , due to different development of the flow up to the levels from which data points were obtained. The approximation involved in ignoring these effects is assumed to be of the same order as that involved in the use of design equations such as equation (6), which is used to predict void fraction at any level in the bundle and at any values of x, G and q. Similarly, Figure 5 and the dependence h ; hx,Re may be given physical significance as the data from experiments on the same experimental set up. This time the flowrate is held constant and xinch increased (DTsub decreased) to maintain quality as the uniform q of the bundle is decreased. These arguments will be developed in the later section on correlation. Results: q 5 10 and 20 kW m22 At q ¼ 10 kW m2 , hl , hnpb at Remax ¼ 7800 and, rising with flowrate, hl . hnpb above Remax ¼ 14 000, Figures 4(b) – (f). To within experimental error h increased linearly with x, rising from 2.4 to 2:7  hnpb and from 3.4 to 1:8  hl between Remax ¼ 7800 and 27 000, for the values of x used in the tests. (@h=@x)q,Re (Figure 6), rises linearly with flowrate to Remax ¼ 19 500 and even more rapidly thereafter. At Remax ¼ 27 000 the effect of increase in quality on h is over four times that at Remax ¼ 7800. Extrapolating to zero flowrate, (@h=@x)q,Re ! 0, inferring that quality ceases to affect the heat transfer coefficient in ‘pool’ conditions, at the low values used in this study (x  0:06). This seems reasonable since forced convection is absent and nucleate boiling should be dominant. At this heat flux, the sensitivity, (@h=@Re)q,x , of h to flowrate is independent of flowrate (Figure 7(b)), and is twice as great at x ¼ 0.04 as at x ¼ 0.02. Similar results were obtained at q ¼ 20 kW m2  hl , hnpb at all flowrates (Figures 4(b) –(f)). At the maximum qualities tested, as Remax was increased from 7800 to 27 000, h rose to between 1.5 and 1:7  hnpb and 1.5 and 1:8  hl . The effect of increase in quality on h was about half that at q ¼ 10 kW m2 but again quadrupled over the range 7800  Remax  27 000 (Figure 6). (@h=@Re)q,x was again independent of flowrate, and increased by more than 70% over the range 0:02  x  0:04 (Figure 7(b)).

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These data at the lower heat fluxes of 10 and 20 kW m2 consistently exhibit unusual behaviour, with h increasing almost linearly with x at low x. The values of h increase more rapidly at 10 kW m2 so that, surprisingly, they exceed the value of h at 20 kW m2 . Also h10 and h20 reached h40 at the maximum quality tested. Because all the data were obtained after decreasing heat flux, they could not be influenced by hysteresis in the initial activation of nucleation sites. This unusual behaviour at low heat fluxes, with heat transfer coefficients increasing with quality and decreasing with heat flux, has not been reported in other studies of boiling in tube bundles or on single tubes. However, the study of Cornwell and Scoones (1988) (Webb and Gupte, 1992) referred to above, showed a similar steep rise in h with quality at Remax ¼ 5700 and low heat fluxes of 6, 12 and 18 kW m2 (Webb and Gupte, 1992), (Figure 8).

q  40 kW m22 The effect of change in quality and flowrate on heat transfer coefficient was much less than at q ¼ 10 and 20 kW m22 (Figures 4(c) – (f), 7(a) and (b)). At all qualities tested, increase in heat flux decreased the tendency of h to rise as quality increased, (@h=@x)q,Re , while increase in quality and flowrate increased it (Figure 7(a)). At low qualities, to the accuracy involved in its estimation, (@h=@Re)q,x differed insignificantly from zero at all values of Remax (Figure 7(b)). This behaviour indicated the tendency of h to remain constant at hnpb up to a threshold flowrate, above which it rose steadily at higher flowrates. Increase in heat flux also decreased the tendency of h to rise with flowrate, (@h=@Re)q,x , while increase in quality and flowrate increased it (Figure 7(b)). Figure 5(a) and (b) show the dependence of h on q at constant quality and flowrate. As q increased at constant low quality, x ¼ 0.022, firstly h remained constant at Remax ¼ 7800 and then fell at higher flowrates (Figure 5(a)). As q increased further h ! hnpb at all flowrates. This behaviour was repeated at first as quality was raised, but with further increase h remained greater than hnpb at the higher flowrates (Figure 5(b)). Within the test range of q the divergence of h from hnpb increased with flowrate. The following explanation is offered for the fundamental difference between the effect of 2-phase flow on heat transfer coefficient at high and low heat fluxes. When the heat flux was low, boiling was of low intensity and the density of active sites low. Convection of heat into the 2-phase fluid flowing past the tubes reduced the temperature gradient in the superheated liquid layer at the wall, which controls bubble growth (Chen, 1966; Bennett et al., 1980). Thus nucleate boiling was further suppressed. At low q the flow regime predicted was bubbly flow (Figure 9). Evaporation from superheated liquid at the tube wall across the surface of bubbles ‘sliding’ along the tube surface (Cornwell, 1990) or very close to the surface offered less heat transfer resistance than that to much smaller bubbles growing in nucleate boiling. The advantage increased as the flowing bubble size rose. Evidence of these phenomena is that h was very much higher than both hnpb and hl and that the rise in h with quality was so great. Referring now to our hypothetical experiment, earlier in this section, where quality is constant and flowrate varied at a given row

level, the greater sensitivity of h to rise in quality, (@h=@x)q,Re , as Remax was increased (Figure 7(a)), may be due to greater suppression of nucleation by increased convection. This freed more of the wall for direct evaporation across the surface of vapour bubbles of relatively low curvature very close to it. Further, narrowing of the wake behind the tubes (ESDU, 1974) as Remax increased may have enhanced this effect. (dhl =dRe), based on the curvefit to the data (Figure 3), ranged from 2.2 –3.7  1025 kW m22 K over the range of the tests. At x ¼ 0:02, q ¼ 10 kW m22 K it can be seen that the enhancement of h due to increase in Remax , (@h=@Re)q,x was nearly twice this (Figure 7(b)). Presumably, the enhancement was caused by the normal convective increase of heat transfer rate through the boundary layer which is a necessary precursor to evaporation. At the same quality with q ¼ 20 kW m22, the enhancement was lower, close to hl . In this case, more of the surface was controlled by nucleation, reducing the overall effect of the 2-phase flow on evaporation. At both q ¼ 10 and 20 kW m22, increase in quality increased the sensitivity of h to flowrate, (@h=@Re)q,x . As expected nucleate boiling played an increasingly important role as heat flux increased. In the conventional view it is suppressed by convection, due to alteration of the temperature gradient in the liquid layer at the wall (Chen, 1966; Bennett et al., 1980). The fact that all the present data for q  40 kW m22 at zero, low and moderate qualities showed h ¼ hnpb suggests that nucleate boiling dominated under these conditions. It is true that the value of h ¼ hnpb measured may comprise a suppressed nucleate boiling and an enhanced convective component, as displayed in equations (1) or (2), over this whole range of heat fluxes and qualities. This seems very unlikely and the authors conclude that at low qualities and flowrates nucleate boiling prevails to such an extent that no convection occurred other than that associated with the nucleation and growth of bubbles. However, at high enough flowrates and qualities, nucleation and growth were affected by the 2-phase flow. Although nucleate boiling may not be much influenced on areas of the tube sheltered from the 2-phase flow, elsewhere evaporation at the interface between the superheated liquid layer near the wall and the flowing vapour became increasingly important, whether in bubbly, intermittent or annular flow. The temperature gradient in the layer was reduced, suppressing nucleate boiling, but heat transfer enhancement occurred due to lower curvature at the interfaces than exists in the growth stage of bubbles growing after nucleation. As quality and flowrate increased, h increased due to this behaviour. To support such an explanation, observations of in-tube boiling showed that at high enough Reynolds number, nucleate boiling was completely suppressed by forced convection (Jung et al., 1989), all vaporization being due to evaporation. Comparison with Other Work The investigations of Cornwell and Scoones (1988) and Hwang and Yao (1986) and the present one all used R113 at 1 atm but bundles of different geometry (Table 3). It is possible to compare the heat transfer coefficient data measured at q ¼ 10 and 20 kW m22 at the same quality x ¼ 0:05.

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HEAT TRANSFER IN FLOW BOILING OVER HORIZONTAL TUBES

535

Table 3. Tube bundle geometries and h. Remax ¼ 5700 (Cornwell and Scoones, 1988), 5030 (Hwang and Yao, 1986), 5700 this work (extrapolated). s/D 1.25 (Cornwell and Scoones, 1988)

1.33 (this work)

1.5 (Hwang and Yao, 1986)

brass 25.4 6.35 159 0.60 96 1.12 1.45

90 Cu:10 Ni 19.1 6.3 167 0.31 52 1.53 1.27

s.s 19.1 9.55 112 0.31 35 2.15 2.25

Material D mm Gap mm Asv m22 (m3) tR s21 Asc m22 (m3 s21) hx¼0.05 q ¼ 10 hx¼0.05 q ¼ 20

Figure 10. Effect of parameter Asc on h at low q, x ¼ 0:05.

To aid comparison, h from Cornwell and Scoones shown in Table 3 at q ¼ 10 and 20 kW m22 was interpolated from the data (Webb and Gupte, 1992). Also, the values of h of this work were extrapolated from Remax ¼ 7800 to 5700 using the slope (@h=@Re)q,x¼0:05 from the data. Table 3 shows the large discrepancy between the data obtained. In the light of the discussion of the heat transfer mechanism at low heat fluxes, given earlier, can these differences be related to the differences in bundle configuration other than simply D and s=D? Three other parameters were used in this investigation in an attempt to predict the observed differences in h between the bundle used here and those of Cornwell and Scoones (1988) and Hwang and Yao (1986) at low heat fluxes: . Asv , equation (8), the ratio of the tube heating surface area to the volume of fluid surrounding them. This is a measure of likelihood of contact of fluid with the tubes. Asv ¼

4 D{(4=p)(s=D)2  1}

(8)

. tR, equation (9), the time taken for a mass of fluid, equal to that occupying the void space between four adjacent tubes, to flow into and out of the space, for the current value of Gmax . tR ¼ (1  a)

pDrl (4=p)(s=D)2  1 (s=D)  1 4Gmax

(9)

where (rl =rg  1. a was calculated using equation (6). tR is a measure of the residence time of fluid in the vicinity of the tubes. . Since increase in both the heating surface area/unit volume, Asv , and the residence time, tR , seem likely to increase the conditions promoting evaporation of bubbles near the wall it seems logical to combine them, equation (10). Asc ¼ Asv tR

ð10Þ

The values of these parameters are shown in Table 3 and h at x ¼ 0:05 is shown plotted versus Asc in Figure 10. Of the three investigations, Hwang and Yao (1986) consistently showed the highest h by some margin. The trend is for

h to fall with decrease in s=D, tube gap and increase in Asc . All of these trends suggests that heat transfer is aided by less access of flowing fluid to the tubes. If the distribution of vapour in the fluid were uniform, this would imply that heat transfer is improved by reduced access of vapour to the wall. The reason for this is not clear to the authors but must arise from the effect of tube geometry on the development of the superheated liquid layer round the tubes. The arguments above are far from conclusive. The material and number of active sites on the tube surfaces at the lower heat fluxes must be a major factor in determining the proportion of the tube surface where nucleate boiling occurs. Notably, the tube materials, surface preparation and probably ageing of the surfaces were different. Because of the higher resistance of nucleate boiling to heat transfer than evaporation, or even convection at low enough heat fluxes, widely differing h can be expected from different surfaces. It is not clear why h . hnpb at the higher heat fluxes in the nucleate boiling controlled region in the Cornwell and Scoones (1988) tests (Figure 8), whereas h ¼ hnpb in this region in the present tests at all flowrates and heat fluxes q . 20 kW m22. When q . 20 kW m22, observation suggested that local nucleate boiling was well developed leaving little scope for direct contact between flowing bubbles and the tube walls. However, the greater residence time of bubbles near the rows may have allowed some evaporation in the Cornwell and Scoones (1988) tests but not in the present tests.

Correlation The 10 and 20 kW m22 data trends and assumed heat transfer mechanism were far from those presupposed in the use of equations (1) and (2). Therefore, in evaluating the utility of heat transfer coefficient predictions using these equations, the low heat flux data were not included. From a practical point of view this is no loss since heat exchanger designs normally operate at higher heat fluxes. The data points based on the imposed values, Gmax , x and q were compared to the values obtained using equation (2). For the reasons set out earlier use of equation (1) was not considered.

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The quality used was calculated from the flowrate and the heat input to the rows below the current one. So that the limiting values of h as x ! 0, hx¼0 ¼ hnpb , the suppression factor was set to zero, as is common in design. The 2-phase multiplier, f2l , was calculated using the correlation of Ishihara et al. (1980),

f2l ¼ 1 þ

8 1 þ Xtt Xtt2

(11)

where Xtt is the Martinelli parameter      1  x 0:9 rv 0:5 ml 0:1 Xtt ¼ x rl mv 

(12)

The flow factor, F, was calculated using equation (13), F ¼ {f2l }m=(2n)

(13)

where m and n are the Reynolds number exponents for turbulent heat transfer and friction. Over the test range of flowrates m was calculated using ESDU 73031 (1973), as 0.65 together with the related value of hl . As is common in design, n was set at 0.2. This led to an index of f2l , m=(2  n) ¼ 0:36, in equation (13). It is recognized that the use of the 2-phase multiplier in the form of equation (11) is valid only for pipe flow, and does not account for the form drag or the effect of wakes on heat transfer in cross-flow. hnpb was calculated using the Mostinski (1963) equation. Since it was not known ab initio what proportions of the uniform heat flux q goes to nucleate boiling and convection, it was necessary to solve equations (2) and (13) iteratively to determine wall superheat, DT. The predictions of h were carried out using equation (2) with n^ set at 2, 4 and 10. Root mean square deviations of the accuracy of the predictions, as a percentage of hdata , were calculated using equation (14). sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S(hpred =hdata  1)2 1h ¼ 100 N1

(14)

The deviations, 1h , were 13.3, 7.1 and 6.4% with n^ of 2, 4 and 10, respectively. Clearly, there is benefit in raising n^ from 2 to 4 but not much in any further increase. Figure 11 shows hpred plotted versus hdata using n^ ¼ 4. The agreement is satisfactory in view of the assumptions made in the correlations. It should be noted that use of the more common ‘pipe flow’ value for m, 0.8, leading to index m=(2  n) ¼ 0:44, leads to overprediction of the influence of the 2-phase flow on the heat transfer coefficient, greatest at the highest flowrates. Figures 7(c) and (d) show (@h=@x)q,Re and (@h=@Re)q,x , the sensitivities of h to change of quality and flowrate, predicted by equation (2) with index n^ ¼ 4. These were calculated numerically from equation (2). Generally, the sensitivity of h to quality is seen to fall with increase in quality and to rise with increase in heat flux and flowrate, except at the highest flowrates and lowest qualities. The data values (Figure 7(a)), also rise with flowrate but contrary to the model values, rise with quality and fall with rise in heat flux. Also very noticeable is the disparity in relative

Figure 11. Comparison of prediction of h with measured data, equation (2), n^ ¼ 4.

magnitude of the coefficients (@h=@x)q,Re , the data values are much higher than the model predicts. The sensitivity of h to flowrate, (@h=@Re)q,x , shows the same qualitive dependency on the 2-phase flow parameters as the data (Figure 7(b)), namely rise with increase in quality and flowrate and fall with increase in heat flux. Again the magnitude of the data values is greater than predicted. The greater magnitude of both data coefficients compared to the model values seems strange in view of the good agreement between predicted and measure values of the heat transfer coefficient itself (Figure 11). However, it is only the increase of h above the value hnpb occurring at the lower values of x and Remax which is affected by the sensitivity coefficients, equation (15).  ð  ð  @h @h dx þ dRe x @x q,Re Re @Re q,x

(15)

This is a small part of the total, decreasing as heat flux increases, as the deviation of h from hnpb falls. Thus, as might be expected the most important factor from the design point of view is to know the pool boiling heat transfer coefficient accurately. Summing up, although equation (2) predicts heat transfer coefficients well, it does not predict the effects of quality and flowrate on the values measured in this work numerically well and in some cases exhibited opposite trends to the measurements. Flow boiling models such as equations (1) and (2) were developed for in-tube flow boiling where the fluid dynamic conditions are entirely different from flow around tube bundles. This affects fundamentally conditions for both nucleate boiling suppression in the flow and enhancement of convection in the presence of flowing vapour. For example, the analogy between flow and heat transfer, which is implied in equation (13), patently does not apply to the bundle configuration. These facts, together with the evidence presented here, that evaporation into the flowing vapour must play a major role in heat transfer at low heat fluxes, suggests that more experimental research into flow boiling in tube bundles is required. This is appropriate, particularly at a time when sophisticated optical techniques have become available (Raffel et al., 1998).

Trans IChemE, Part A, Chemical Engineering Research and Design, 2005, 83(A5): 527–538

HEAT TRANSFER IN FLOW BOILING OVER HORIZONTAL TUBES CONCLUSIONS Heat transfer coefficient data were obtained for upward cross-flow of R113 at 1 atm over a square in-line bundle of 19 mm diameter tubes, s=D ¼ 1:33. The bundle was uniformly heated with 10  q  65 kW m22 and the flowrate 7800  Remax  27 000. Notably: . Least square fits of h to quality, extrapolated to hx¼0 , equalled hnpb for q  20 kW m22 and all flowrates, within experimental error. However, at q ¼ 10 kW m22, hx¼0 was greater than hnpb at all flowrates and greater than hl , the value for the liquid flowing alone, for Remax  14 000. . At q ¼ 10 and 20 kW m22, h rose linearly and very rapidly with quality, to the limits tested, at all flowrates. The rate of rise decreased with increase in q so that hq¼10 . hq¼20 . hq¼40 over a range of qualities and flowrates. This phenomenon was attributed to suppression of nucleate boiling by the 2-phase flow at low heat fluxes, accompanied by evaporation into flowing vapour of relatively low curvature coming in contact with the superheated layer of liquid on the tube surface. . With q  40 kW m22 in the so-called ‘nucleate boiling controlled’ region h ¼ hnpb within experimental error at all flowrates. This finding contradicts the work of Cornwell and Scoones (1988) who found h . hnpb in this region. This was attributed to geometric factors affecting the accessibility of fluid to the heated wall and to differences in tube material and surface preparation. The same reasons are advanced to explain the heat transfer coefficients measured by Hwang and Yao (1986) which were much higher than the values of Cornwell and Scoones (1988) and the present work. . Although equation (2) predicted the 40 –65 kW m22 data to within 7%, the predicted dependence of heat transfer coefficient on quality and flowrate was numerically much less and even in some cases exhibited opposite trends to the measurements. . Experimental work is required to determine the flow patterns and quality distribution in the boiling flow around tube bundles to facilitate development of more realistic flow boiling equations.

NOMENCLATURE Asv Asc D F Fr Gmax g h m,n n^ N q Remax S s T tR Ugs Uls x Xtt

surface/volume coefficient, equation (8), m2 m3 coefficient, equation (10), m1 s diameter, m flow factor pffiffiffiffiffiffi Froude number, G=(rl gD) mass flux based on minimum area, kg m2 s1 gravitational acceleration, m s22 heat transfer coefficient, kW m2 K exponents in equation (13) index in equation (2) number of data points heat flux density, tube outside wall, kW m2 Re based on minimum flow area suppression factor tube pitch, m temperature, 8C residence time, equation (9), s superficial vapour phase velocity, Figure 9, m s21 superficial liquid phase velocity, Figure 9, m s21 mass quality Martinelli parameter, equation (12)

537

Greek letters a void fraction 1 rms error m liquid viscosity, kg m1 s1 r density, kg m3 s surface tension, N m21 f2l 2-phase friction multiplier, DPfTP =DPl Subscripts dat f fit h inch l lm m npb pred sub TP w x¼0

data value frictional based on least squares fit homogeneous flow inlet to channel liquid flowing alone mean value for the liquid mean value nucleate pool boiling value for operating q prediction subcooled 2-phase flow value outside wall value value extrapolated to zero quality

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ACKNOWLEDGEMENTS The authors are grateful to the Heat Transfer and Fluid Flow Service (AECL) and the Canadian Ministry of Energy, Mines and Resources (PERD) for financial support. They are grateful also to David Walker for his invaluable technical assistance. The manuscript was received 21 October 2003 and accepted for publication after revision 28 February 2005.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2005, 83(A5): 527–538