# Experimental study of effects of solution subcooling and wall superheat on heat transfer of a horizontal-tube, falling-film heat exchanger.

INTRODUCTION

A horizontal-tube, falling-film heat exchanger is typically constructed of an array of horizontal tubes over which a solution fluid is dripped or sprayed and through which a heating fluid flows. This type of heat exchanger or evaporator is widely used due to its high solution side heat transfer coefficient and its relatively small liquid inventory compared to flooded evaporators. Preferably, the solution fluid is distributed uniformly over the entire surface area of the tube array, creating a thin liquid film ideal for evaporative heat transfer. However, in an attempt to facilitate this thin film, an unwetted area on the evaporator tube is unavoidable and it is known that this unwetted area increases as the solution flow rate decreases, the heat flux is increased, and the number of tube rows is increased [1-3]. The coupled nature of this phenomenon makes it very difficult to optimize this system strictly for evaporation. It is therefore beneficial to introduce some amount of solution subcooling so as to maximize sensible heat transfer from the earlier tube rows while still maintaining fully-wetted thin-film evaporation conditions on the bottommost rows. Furthermore, an understanding of the effects that varying wall superheat values have on the ratio of sensible to evaporative heat transfer is critical to optimizing the falling film heat exchanger.

The goal of this work is to investigate the duality of these two temperature differentials and how they work together to affect the portions of sensible and evaporative heat transfer in a two-phase system, specifically a horizontal tube, falling-film heat exchanger. With a better understanding of the overall effects of the inlet temperatures of both the heating and solution fluid, this system can be tuned to maximize both sensible and evaporative heat transfer for a given tube array.

EXPERIMENTAL SETUP

A detailed description of the experimental setup as well as the instrumentation used is given in the group's earlier work [4], as a very similar setup was used to conduct the current investigation. For this experiment however, a stainless steel evaporator was constructed, housing two solution dispensers and eight horizontal evaporator tubes. Also, plumbing lines for the heating and solution fluids, a stainless steel solution reservoir, a thermal bath heating fluid reservoir, and all necessary instrumentation were utilized, as shown in Figure 1. The solution dispenser and horizontal tubes were vertically aligned in an inline arrangement so that the solution fluid could drip over each tube in the column. Two 1" thick transparent acrylic windows were used as the front and back of the steel housing to facilitate visualization of the chamber.

[FIGURE 1 OMITTED]

A side view of the tube array depicting the dispensers and the two columns of four evaporator tubes is shown in Figure 1(b). Each solution dispenser tube has 44 holes drilled in a row, each with a diameter of 1 mm (0.039 in.) and a spacing of 6.35 mm (2 in.). A cross-sectional view of one of the horizontal tubes showing the tube diameters is provided in Figure 1(d). A concentric-tube design is used for the evaporator tubes to increase the heat transfer coefficient of the heating fluid flowing in the annulus side of the tubes, between D1 and D2. All dimensions of the tube setup shown in Figure 1 are listed in Table 1.

RESULTS AND DISCUSSION

A detailed analysis of the heat transfer equations used to calculate the total, sensible, and evaporative heat transfers for this experiment can be found in the group's earlier works [4, 5]. Suffice it to say that the total heat lost from the heating fluid is defined as

[Q.sub.h] = [[[[??].sub.cp] ([T.sub.i] - [T.sub.o])].sub.h] (1)

The sensible heat portion of the heat transfer rate used to raise the temperature of the solution fluid is calculated by

[Q.sub.s] = [[[[??].sub.cp] ([T.sub.o] - [T.sub.i])].sub.s] (2)

The evaporative portion of the heat transfer rate used for phase change of the solution fluid is calculated by

[Q.sub.eva] = [Q.sub.h] = [Q.sub.s] (3)

Since the subcooling will vary from tube to tube in the array and the temperatures between the tubes are not known, solution subcooling is defined as the difference between the saturation temperature of the system and the inlet temperature of the solution fluid. Also, this investigation defines tube wall superheat as the difference between the inlet heating fluid temperature and saturation temperature of the system. By introducing different subcooling and superheat conditions, the ratio of evaporative-to-sensible heat transfer can be controlled.

As the subcooling approaches zero (i.e. the solution fluid is dispensed at approximately saturation temperature), evaporation can begin immediately at the first tube. However, the problem of over-wetting of the upstream tubes versus partial-dryout of the downstream tubes becomes important. In order to maintain a fully wetted bottom row, the first row must be flooded with a surplus of solution fluid, thus thickening the liquid layer and stifling evaporative heat transfer. Conversely, by supplying just enough solution to optimize evaporation on the first row, dry patches occur on the downstream row(s) due to lack of solution fluid and/or flow merging [4]. By introducing subcooling, sensible heat transfer is promoted for the upstream rows and evaporation heat transfer is dominant at the downstream rows. This is ideal because, due to the counter-flow design of the heating and solution fluid lines, the bottommost row always has the highest wall superheat and therefore produces the greatest evaporative heat transfer.

The tube wall superheat also contributes to the overall ratio of evaporative-to-sensible heat transfer in the falling-film heat exchanger. By raising the superheat, the solution fluid is warmed faster and evaporation happens earlier. Thus, higher wall superheat produces greater heat duty until the point at which the fluid is being evaporated faster than it's being supplied. This condition is known as partial (or total) dryout. Another factor leading to partial-drayout of the tube surface is the thermocapillary effect caused by the higher temperature of the solution fluid in contact with the wall compared to that of the fluid further from the wall. Due to the surface tension gradient induced by this temperature differential, the warm fluid tends to be drawn to the cooler fluid, thus creating a coalescing effect and lessening the liquid spreading over the tube surface. This phenomenon is more pronounced at higher wall superheats. If the superheat is raised high enough, the onset of nucleate boiling (ONB) can occur before the liquid has a chance to leave the tube surface. In order to understand the combined effects of solution subcooling and evaporator wall superheat on the heat duty of a falling-film heat exchanger, subcooling values of 5, 10, and 15[degrees]C were analyzed under wall superheat conditions of 5, 10, and 15[degrees]C.

Effect of Subcooling

Figure 2 shows the comparison of evaporative, sensible, and overall heat duty for each individual subcooling condition at the three superheat values investigated. It can be seen that an increase in the solution subcooling increases the overall sensible heat transfer of the tube array for each superheat case. This is evident from the increasing slope of the overall heat duty plot with solution Reynolds number. Sensible heat flux is a function of the convective heat transfer coefficient and the temperature differential between the solution fluid and the heating fluid. Once in the turbulent flow regime (Res > 80), the heat transfer coefficient increases with solution flow rate, thus increasing heat transfer [1, 4].

It can be seen from the figure that the 5[degrees]C subcooled solution [Figure 2(a)] shows the smallest heat duty values for the tube array, while the 15[degrees]C [Figure 2(c)] subcooled solution shows the highest heat duty. The majority of this difference comes from the upstream tubes, where sensible heat transfer is dominant. This is because the temperature differential that drives the convective heat transfer at these tube rows is relatively small for the 5[degrees]C subcooled solution fluid. So, even with the same solution flow rate over the same tube area, the sensible heat transfer is going to suffer as the temperature differential between the solution fluid and the evaporator tube wall decreases. As the fluid progresses through the array, it warms up until evaporation becomes the dominant method of heat dissipation.

Since evaporation is enhanced as wall superheat is increased and as the thickness of the solution film decreases (due to less thermal resistance), it would seem that rather than constant heat duty for the whole solution flow regime, the heat duty would decrease with increased solution Reynolds number due to the thicker liquid film on the evaporator tubes. But, as solution Reynolds number is increased, the wetted area for heat transfer is also increased. So the increase in film thickness (decreasing evaporative heat transfer) and the increase in wetted area (increasing heat transfer) seem to cancel each other out, thus causing the heat duty to remain relatively constant over the entire solution flow regime [Figure 2(c)]. As the solution subcooling is decreased, the slope of the overall heat duty plot should also decrease because the low subcooling allows for evaporation to begin earlier in the tube array, removing the solution flow rate dependence. A decreasing slope of the total heat duty plot with decreasing subcooling can be seen in all three cases shown in Figure 2.

Figure 3 shows the comparison of evaporative, sensible, and overall heat duty for each individual superheat condition at the three subcooling values investigated. It can easily be seen that the lowest subcooling value of 5[degrees]C [Figure 3(a)] shows only a minor dependence on solution Reynolds number. When the subcooling is increased to 10[degrees]C [Figure 3(b)], a distinct positive slope is seen at the lowest superheat value, where the overall heat duty increases significantly with solution flow rate. This is because the sensible heat transfer portion is increased and in fact the dominant method of heat dissipation at high solution flow rates, since the solution fluid enters much cooler than the saturation temperature. The majority of the heat from the evaporator tubes is used to warm the fluid rather than evaporate it. This same trend is enhanced when the subcooling is raised to 15[degrees]C, since the fluid is colder still. The slope of the total heat duty graph with solution flow rate is steeper and evaporation heat transfer is again stifled by the cool fluid. This slope directly correlates to the ratio of evaporative-to-sensible heat transfer, as is also shown by the individual [Q.sub.s] and [Q.sub.e] plots in Figures 2 and 3. The higher heat transfer rate for the 15[degrees]C subcooled fluid is due to the high sensible heat transfer caused by the larger temperature differential between the evaporator tubes and the solution fluid.

An interesting phenomenon was seen when increasing the subcooling from 5 to 10[degrees]C. Although the overall heat duty remained relatively the same for the highest wall superheat, the portion that came from evaporation was less for the 10[degrees]C subcooled fluid. Figure 3(b) depicts that the 10oC subcooled cases show a significant portion of the overall heat duty being used for sensible heat transfer rather than evaporation. When looking at Figure 3(c), the 15[degrees]C subcooled fluid shows a high overall heat duty, but as a function of solution Reynolds number for the 5 and 10[degrees]C superheats. This implies that the highly subcooled condition is a sensible dominated regime, but the initial temperature differential is high enough to offset the evaporative losses and still produce high energy transfer. At the highest superheat value of 15[degrees]C, however, it is evident from Figure 3(c) that evaporation is dominant at the lower half of the solution flow regime. This is because thin liquid films facilitated at these low flow rates combined with the high wall superheat prove to be ideal for evaporation heat transfer.

[FIGURE 2 OMITTED]

It is clear from the data presented that the solution subcooling directly correlates to the ratio of evaporative-tosensible heat transfer in a falling-film heat exchanger. By increasing the subcooling, the sensible heat transfer needed to warm the fluid is also increased. This knowledge allows for the tuning of an array based on inlet flow rate, temperature, and number of tube rows to maximize the heat transfer (sensible upstream in the array and evaporation downstream) of a given system.

Effect of Wall Superheat

The overall heat duty of the falling-film heat exchanger is highly affected by wall superheat, whether it is sensible or evaporative heat transfer. Since evaporation is a function of film thickness and wall superheat, the evaporation heat transfer becomes more pronounced as the wall gets hotter. At the low subcooling value of 5[degrees]C, Figure 3(a) shows a dramatic increase in heat duty with increasing superheat, but the sensible portion remains relatively the same. This implies that at low subcooling values, additional wall superheat works to significantly enhance evaporation.

The data also show a larger increase in heat duty between 10 and 15oC wall superheat than there is between 5 and 10[degrees]C. It can be said that this boost in heat transfer is due to the onset of nucleate boiling (ONB). It was noted during the experiment that the solution fluid was more volatile at the highest superheat value, showing bubble growth in the droplets as they left the tube surface, especially at the lower tube rows. Typical superheat for ONB in plain surface pool boiling applications is around 5[degrees]C, but the falling-film application is very different from pool boiling. Forced rather than free convection causes a reduction in the thermal boundary layer thickness (St). This decrease in thermal boundary layer thickness combined with the lower thermal resistance associated with the thin liquid film works to suppress ONB until a higher wall superheat is attained. ONB was seen to occur between 10 and 15[degrees]C wall superheat, showing good agreement with the predicted value of 12[degrees]C, which was found using the following equation for ONB under saturated conditions [6]

[T.sub.sh,ONB] = [12.8[sigma][T.sub.sat]/[[rho].sub.v][h.sub.lv][[delta].sub.t]] (4)

Figure 4(a) and (b) show how the normalized ratio [Q.sub.e]/[Q.sub.s] varies with solution Reynolds number at the lowest and highest heating fluid Reynolds numbers, respectively. As the solution flow rate is increased, evaporation heat transfer is decreased due to the increase in solution film thickness. Contrastingly, sensible heat transfer increases with solution Reynolds number due to the increase in heat transfer coefficient associated with the higher solution flow rates. The ratio [Q.sub.e]/[Q.sub.s] therefore shows a decreasing trend with solution flow rate as sensible heat transfer is enhanced and evaporative heat transfer is stifled by the thick film. It is also evident that the increased wall superheat works to enhance evaporation significantly, especially at the lowest flow rates, where evaporation is as much as eight times greater than the sensible heat transfer [Figure 4 (b)].

[FIGURE 3 OMITTED]

The insight gained from this investigation can help tune a given array for a specific heat transfer requirement. For example, if evaporation heat transfer is to be maximized in a falling-film application, Figure 4 shows that a high heating fluid Reynolds number, high wall superheat, low solution subcooling, and a low solution Reynolds number will produce the highest [Q.sub.e]. If on the other hand, all that is required is a maximum total heat duty, then high heating fluid Reynolds number, high wall superheat, high solution subcooling, and high solution Reynolds number will produce significant sensible and

[FIGURE 4 OMITTED]

CONCLUSIONS

An experiment was conducted to investigate the combined effects of solution subcooling and evaporator wall superheat on the ratio of evaporative-to-sensible heat transfer in a falling-film heat exchanger. Three different subcooling values were each tested at three different superheat conditions. In all cases, the total heat transfer from the evaporator tubes was found to be a combination of both sensible and evaporation, but the ratios proved highly dependent on the subcooling of the solution fluid, the evaporator wall superheat, and the solution fluid flow rate. By using the upstream tubes in the array for sensible heat transfer and the downstream tubes for evaporative heat transfer, the problem of flooding versus partial-dryout can be solved. The flooded condition created by the high solution flow rates is beneficial to sensible heat transfer due to the increased heat transfer coefficient. Also, by warming the solution with the upstream rows, the downstream rows can be used for evaporation, where the film thickness is thinnest and the wall superheat is greatest.

ACKNOWLEDGEMENTS

The authors extend their thanks for the financial support from the U.S. Department of Energy (Contract No.DOE EE0003231).

NOMENCLATURE

D diameter [mm]

d solution dispenser nozzle hole diameter [mm]

h latent heat of vaporization [J/kg]

L length [mm]

Q heat transfer rate [kW]

[Re.sub.h] Reynolds number for heating fluid, [Re.sub.h] = [rho][V.sub.h][D.sub.d]/[[mu].sub.h]

[Re.sub.s] Reynolds number for solution fluid, [Re.sub.s] = 4[GAMMA]/[[mu].sub.s]

S tube spacing [mm]

s solution dispenser nozzle hole spacing [mm]

T temperature [[degrees]C]

V velocity [m-[s.sup.-1]]

Subscripts

c column

d hydraulic diameter

ds solution dispenser

eva evaporation

h heating fluid

i inlet

lv liquid-vapor

nz solution dispenser nozzle hole

o outlet or outer

s solution or sensible

sat saturation

sc subcooling

sh wall superheat

t tube or thermal

tot total

v vapor

Greek symbols

[delta] boundary layer thickness [m]

[GAMMA] solution mass flow rate per unit length and per side [kg-[s.sup.-1] [m.sup.-1]], [GAMMA] = [??]/2L

[mu] dynamic viscosity [kg [m.sup.-1] [s.sup.-1]]

[??] density [kg [m.sup.-3]]

REFERENCES

[1] Fujita, Y., and Tsutsui, M., 1998, "Experimental investigation of falling film evaporation on horizontal tubes," Heat Transfer Japanese Research, 27(8), pp. 609-618.

[2] Thome, J. R., 1999, "Falling film evaporation: State-of-the-art review of recent work," Journal of Enhanced Heat Transfer, 6(2), pp. 263-277.

[3] Ribatski, G., and Jacobi, A. M., 2005, "Falling-film evaporation on horizontal tubes - A critical review," International Journal of Refrigeration, 28(5), pp. 635-653.

[4] Koroglu, B., Bogan, N., and Park, C., 2012, "Experimental Study of Tube Row effects and Evaporation Heat Transfer Enhancement Using a Micro-Scale, Porous-Layer Coating on a Horizontal-Tube, Falling-Film Heat Exchanger," ASME 2012 3rd Micro/Nanoscale Heat & Mass Transfer International ConferenceAtlanta, Georgia, MNHMT2012-75333.

[5] Lee, S., Koroglu, B., and Park, C., 2010, "Experimental investigation of capillary-assisted solution wetting and heat transfer using a micro-scale, porous-layer coating on horizontal-tube, falling-film heat exchanger," International Journal of Refrigeration, 35, pp. 1176-1187.

[6] Carey, V. P., 2008, Liquid-vapor phase-change phenomena : an introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment, Taylor and Francis, New York.

Nick Bogan

Chanwoo Park, Ph.D.

Nick Bogan is a graduate research assistant in the mechanical engineering department, University of Nevada, Reno. Chanwoo Park is assistant professor in the mechanical engineering department, University of Nevada, Reno.

A horizontal-tube, falling-film heat exchanger is typically constructed of an array of horizontal tubes over which a solution fluid is dripped or sprayed and through which a heating fluid flows. This type of heat exchanger or evaporator is widely used due to its high solution side heat transfer coefficient and its relatively small liquid inventory compared to flooded evaporators. Preferably, the solution fluid is distributed uniformly over the entire surface area of the tube array, creating a thin liquid film ideal for evaporative heat transfer. However, in an attempt to facilitate this thin film, an unwetted area on the evaporator tube is unavoidable and it is known that this unwetted area increases as the solution flow rate decreases, the heat flux is increased, and the number of tube rows is increased [1-3]. The coupled nature of this phenomenon makes it very difficult to optimize this system strictly for evaporation. It is therefore beneficial to introduce some amount of solution subcooling so as to maximize sensible heat transfer from the earlier tube rows while still maintaining fully-wetted thin-film evaporation conditions on the bottommost rows. Furthermore, an understanding of the effects that varying wall superheat values have on the ratio of sensible to evaporative heat transfer is critical to optimizing the falling film heat exchanger.

The goal of this work is to investigate the duality of these two temperature differentials and how they work together to affect the portions of sensible and evaporative heat transfer in a two-phase system, specifically a horizontal tube, falling-film heat exchanger. With a better understanding of the overall effects of the inlet temperatures of both the heating and solution fluid, this system can be tuned to maximize both sensible and evaporative heat transfer for a given tube array.

EXPERIMENTAL SETUP

A detailed description of the experimental setup as well as the instrumentation used is given in the group's earlier work [4], as a very similar setup was used to conduct the current investigation. For this experiment however, a stainless steel evaporator was constructed, housing two solution dispensers and eight horizontal evaporator tubes. Also, plumbing lines for the heating and solution fluids, a stainless steel solution reservoir, a thermal bath heating fluid reservoir, and all necessary instrumentation were utilized, as shown in Figure 1. The solution dispenser and horizontal tubes were vertically aligned in an inline arrangement so that the solution fluid could drip over each tube in the column. Two 1" thick transparent acrylic windows were used as the front and back of the steel housing to facilitate visualization of the chamber.

[FIGURE 1 OMITTED]

A side view of the tube array depicting the dispensers and the two columns of four evaporator tubes is shown in Figure 1(b). Each solution dispenser tube has 44 holes drilled in a row, each with a diameter of 1 mm (0.039 in.) and a spacing of 6.35 mm (2 in.). A cross-sectional view of one of the horizontal tubes showing the tube diameters is provided in Figure 1(d). A concentric-tube design is used for the evaporator tubes to increase the heat transfer coefficient of the heating fluid flowing in the annulus side of the tubes, between D1 and D2. All dimensions of the tube setup shown in Figure 1 are listed in Table 1.

RESULTS AND DISCUSSION

A detailed analysis of the heat transfer equations used to calculate the total, sensible, and evaporative heat transfers for this experiment can be found in the group's earlier works [4, 5]. Suffice it to say that the total heat lost from the heating fluid is defined as

[Q.sub.h] = [[[[??].sub.cp] ([T.sub.i] - [T.sub.o])].sub.h] (1)

The sensible heat portion of the heat transfer rate used to raise the temperature of the solution fluid is calculated by

[Q.sub.s] = [[[[??].sub.cp] ([T.sub.o] - [T.sub.i])].sub.s] (2)

The evaporative portion of the heat transfer rate used for phase change of the solution fluid is calculated by

[Q.sub.eva] = [Q.sub.h] = [Q.sub.s] (3)

Since the subcooling will vary from tube to tube in the array and the temperatures between the tubes are not known, solution subcooling is defined as the difference between the saturation temperature of the system and the inlet temperature of the solution fluid. Also, this investigation defines tube wall superheat as the difference between the inlet heating fluid temperature and saturation temperature of the system. By introducing different subcooling and superheat conditions, the ratio of evaporative-to-sensible heat transfer can be controlled.

As the subcooling approaches zero (i.e. the solution fluid is dispensed at approximately saturation temperature), evaporation can begin immediately at the first tube. However, the problem of over-wetting of the upstream tubes versus partial-dryout of the downstream tubes becomes important. In order to maintain a fully wetted bottom row, the first row must be flooded with a surplus of solution fluid, thus thickening the liquid layer and stifling evaporative heat transfer. Conversely, by supplying just enough solution to optimize evaporation on the first row, dry patches occur on the downstream row(s) due to lack of solution fluid and/or flow merging [4]. By introducing subcooling, sensible heat transfer is promoted for the upstream rows and evaporation heat transfer is dominant at the downstream rows. This is ideal because, due to the counter-flow design of the heating and solution fluid lines, the bottommost row always has the highest wall superheat and therefore produces the greatest evaporative heat transfer.

The tube wall superheat also contributes to the overall ratio of evaporative-to-sensible heat transfer in the falling-film heat exchanger. By raising the superheat, the solution fluid is warmed faster and evaporation happens earlier. Thus, higher wall superheat produces greater heat duty until the point at which the fluid is being evaporated faster than it's being supplied. This condition is known as partial (or total) dryout. Another factor leading to partial-drayout of the tube surface is the thermocapillary effect caused by the higher temperature of the solution fluid in contact with the wall compared to that of the fluid further from the wall. Due to the surface tension gradient induced by this temperature differential, the warm fluid tends to be drawn to the cooler fluid, thus creating a coalescing effect and lessening the liquid spreading over the tube surface. This phenomenon is more pronounced at higher wall superheats. If the superheat is raised high enough, the onset of nucleate boiling (ONB) can occur before the liquid has a chance to leave the tube surface. In order to understand the combined effects of solution subcooling and evaporator wall superheat on the heat duty of a falling-film heat exchanger, subcooling values of 5, 10, and 15[degrees]C were analyzed under wall superheat conditions of 5, 10, and 15[degrees]C.

Effect of Subcooling

Figure 2 shows the comparison of evaporative, sensible, and overall heat duty for each individual subcooling condition at the three superheat values investigated. It can be seen that an increase in the solution subcooling increases the overall sensible heat transfer of the tube array for each superheat case. This is evident from the increasing slope of the overall heat duty plot with solution Reynolds number. Sensible heat flux is a function of the convective heat transfer coefficient and the temperature differential between the solution fluid and the heating fluid. Once in the turbulent flow regime (Res > 80), the heat transfer coefficient increases with solution flow rate, thus increasing heat transfer [1, 4].

It can be seen from the figure that the 5[degrees]C subcooled solution [Figure 2(a)] shows the smallest heat duty values for the tube array, while the 15[degrees]C [Figure 2(c)] subcooled solution shows the highest heat duty. The majority of this difference comes from the upstream tubes, where sensible heat transfer is dominant. This is because the temperature differential that drives the convective heat transfer at these tube rows is relatively small for the 5[degrees]C subcooled solution fluid. So, even with the same solution flow rate over the same tube area, the sensible heat transfer is going to suffer as the temperature differential between the solution fluid and the evaporator tube wall decreases. As the fluid progresses through the array, it warms up until evaporation becomes the dominant method of heat dissipation.

Since evaporation is enhanced as wall superheat is increased and as the thickness of the solution film decreases (due to less thermal resistance), it would seem that rather than constant heat duty for the whole solution flow regime, the heat duty would decrease with increased solution Reynolds number due to the thicker liquid film on the evaporator tubes. But, as solution Reynolds number is increased, the wetted area for heat transfer is also increased. So the increase in film thickness (decreasing evaporative heat transfer) and the increase in wetted area (increasing heat transfer) seem to cancel each other out, thus causing the heat duty to remain relatively constant over the entire solution flow regime [Figure 2(c)]. As the solution subcooling is decreased, the slope of the overall heat duty plot should also decrease because the low subcooling allows for evaporation to begin earlier in the tube array, removing the solution flow rate dependence. A decreasing slope of the total heat duty plot with decreasing subcooling can be seen in all three cases shown in Figure 2.

Figure 3 shows the comparison of evaporative, sensible, and overall heat duty for each individual superheat condition at the three subcooling values investigated. It can easily be seen that the lowest subcooling value of 5[degrees]C [Figure 3(a)] shows only a minor dependence on solution Reynolds number. When the subcooling is increased to 10[degrees]C [Figure 3(b)], a distinct positive slope is seen at the lowest superheat value, where the overall heat duty increases significantly with solution flow rate. This is because the sensible heat transfer portion is increased and in fact the dominant method of heat dissipation at high solution flow rates, since the solution fluid enters much cooler than the saturation temperature. The majority of the heat from the evaporator tubes is used to warm the fluid rather than evaporate it. This same trend is enhanced when the subcooling is raised to 15[degrees]C, since the fluid is colder still. The slope of the total heat duty graph with solution flow rate is steeper and evaporation heat transfer is again stifled by the cool fluid. This slope directly correlates to the ratio of evaporative-to-sensible heat transfer, as is also shown by the individual [Q.sub.s] and [Q.sub.e] plots in Figures 2 and 3. The higher heat transfer rate for the 15[degrees]C subcooled fluid is due to the high sensible heat transfer caused by the larger temperature differential between the evaporator tubes and the solution fluid.

An interesting phenomenon was seen when increasing the subcooling from 5 to 10[degrees]C. Although the overall heat duty remained relatively the same for the highest wall superheat, the portion that came from evaporation was less for the 10[degrees]C subcooled fluid. Figure 3(b) depicts that the 10oC subcooled cases show a significant portion of the overall heat duty being used for sensible heat transfer rather than evaporation. When looking at Figure 3(c), the 15[degrees]C subcooled fluid shows a high overall heat duty, but as a function of solution Reynolds number for the 5 and 10[degrees]C superheats. This implies that the highly subcooled condition is a sensible dominated regime, but the initial temperature differential is high enough to offset the evaporative losses and still produce high energy transfer. At the highest superheat value of 15[degrees]C, however, it is evident from Figure 3(c) that evaporation is dominant at the lower half of the solution flow regime. This is because thin liquid films facilitated at these low flow rates combined with the high wall superheat prove to be ideal for evaporation heat transfer.

[FIGURE 2 OMITTED]

It is clear from the data presented that the solution subcooling directly correlates to the ratio of evaporative-tosensible heat transfer in a falling-film heat exchanger. By increasing the subcooling, the sensible heat transfer needed to warm the fluid is also increased. This knowledge allows for the tuning of an array based on inlet flow rate, temperature, and number of tube rows to maximize the heat transfer (sensible upstream in the array and evaporation downstream) of a given system.

Effect of Wall Superheat

The overall heat duty of the falling-film heat exchanger is highly affected by wall superheat, whether it is sensible or evaporative heat transfer. Since evaporation is a function of film thickness and wall superheat, the evaporation heat transfer becomes more pronounced as the wall gets hotter. At the low subcooling value of 5[degrees]C, Figure 3(a) shows a dramatic increase in heat duty with increasing superheat, but the sensible portion remains relatively the same. This implies that at low subcooling values, additional wall superheat works to significantly enhance evaporation.

The data also show a larger increase in heat duty between 10 and 15oC wall superheat than there is between 5 and 10[degrees]C. It can be said that this boost in heat transfer is due to the onset of nucleate boiling (ONB). It was noted during the experiment that the solution fluid was more volatile at the highest superheat value, showing bubble growth in the droplets as they left the tube surface, especially at the lower tube rows. Typical superheat for ONB in plain surface pool boiling applications is around 5[degrees]C, but the falling-film application is very different from pool boiling. Forced rather than free convection causes a reduction in the thermal boundary layer thickness (St). This decrease in thermal boundary layer thickness combined with the lower thermal resistance associated with the thin liquid film works to suppress ONB until a higher wall superheat is attained. ONB was seen to occur between 10 and 15[degrees]C wall superheat, showing good agreement with the predicted value of 12[degrees]C, which was found using the following equation for ONB under saturated conditions [6]

[T.sub.sh,ONB] = [12.8[sigma][T.sub.sat]/[[rho].sub.v][h.sub.lv][[delta].sub.t]] (4)

Figure 4(a) and (b) show how the normalized ratio [Q.sub.e]/[Q.sub.s] varies with solution Reynolds number at the lowest and highest heating fluid Reynolds numbers, respectively. As the solution flow rate is increased, evaporation heat transfer is decreased due to the increase in solution film thickness. Contrastingly, sensible heat transfer increases with solution Reynolds number due to the increase in heat transfer coefficient associated with the higher solution flow rates. The ratio [Q.sub.e]/[Q.sub.s] therefore shows a decreasing trend with solution flow rate as sensible heat transfer is enhanced and evaporative heat transfer is stifled by the thick film. It is also evident that the increased wall superheat works to enhance evaporation significantly, especially at the lowest flow rates, where evaporation is as much as eight times greater than the sensible heat transfer [Figure 4 (b)].

[FIGURE 3 OMITTED]

The insight gained from this investigation can help tune a given array for a specific heat transfer requirement. For example, if evaporation heat transfer is to be maximized in a falling-film application, Figure 4 shows that a high heating fluid Reynolds number, high wall superheat, low solution subcooling, and a low solution Reynolds number will produce the highest [Q.sub.e]. If on the other hand, all that is required is a maximum total heat duty, then high heating fluid Reynolds number, high wall superheat, high solution subcooling, and high solution Reynolds number will produce significant sensible and

[FIGURE 4 OMITTED]

CONCLUSIONS

An experiment was conducted to investigate the combined effects of solution subcooling and evaporator wall superheat on the ratio of evaporative-to-sensible heat transfer in a falling-film heat exchanger. Three different subcooling values were each tested at three different superheat conditions. In all cases, the total heat transfer from the evaporator tubes was found to be a combination of both sensible and evaporation, but the ratios proved highly dependent on the subcooling of the solution fluid, the evaporator wall superheat, and the solution fluid flow rate. By using the upstream tubes in the array for sensible heat transfer and the downstream tubes for evaporative heat transfer, the problem of flooding versus partial-dryout can be solved. The flooded condition created by the high solution flow rates is beneficial to sensible heat transfer due to the increased heat transfer coefficient. Also, by warming the solution with the upstream rows, the downstream rows can be used for evaporation, where the film thickness is thinnest and the wall superheat is greatest.

ACKNOWLEDGEMENTS

The authors extend their thanks for the financial support from the U.S. Department of Energy (Contract No.DOE EE0003231).

NOMENCLATURE

D diameter [mm]

d solution dispenser nozzle hole diameter [mm]

h latent heat of vaporization [J/kg]

L length [mm]

Q heat transfer rate [kW]

[Re.sub.h] Reynolds number for heating fluid, [Re.sub.h] = [rho][V.sub.h][D.sub.d]/[[mu].sub.h]

[Re.sub.s] Reynolds number for solution fluid, [Re.sub.s] = 4[GAMMA]/[[mu].sub.s]

S tube spacing [mm]

s solution dispenser nozzle hole spacing [mm]

T temperature [[degrees]C]

V velocity [m-[s.sup.-1]]

Subscripts

c column

d hydraulic diameter

ds solution dispenser

eva evaporation

h heating fluid

i inlet

lv liquid-vapor

nz solution dispenser nozzle hole

o outlet or outer

s solution or sensible

sat saturation

sc subcooling

sh wall superheat

t tube or thermal

tot total

v vapor

Greek symbols

[delta] boundary layer thickness [m]

[GAMMA] solution mass flow rate per unit length and per side [kg-[s.sup.-1] [m.sup.-1]], [GAMMA] = [??]/2L

[mu] dynamic viscosity [kg [m.sup.-1] [s.sup.-1]]

[??] density [kg [m.sup.-3]]

REFERENCES

[1] Fujita, Y., and Tsutsui, M., 1998, "Experimental investigation of falling film evaporation on horizontal tubes," Heat Transfer Japanese Research, 27(8), pp. 609-618.

[2] Thome, J. R., 1999, "Falling film evaporation: State-of-the-art review of recent work," Journal of Enhanced Heat Transfer, 6(2), pp. 263-277.

[3] Ribatski, G., and Jacobi, A. M., 2005, "Falling-film evaporation on horizontal tubes - A critical review," International Journal of Refrigeration, 28(5), pp. 635-653.

[4] Koroglu, B., Bogan, N., and Park, C., 2012, "Experimental Study of Tube Row effects and Evaporation Heat Transfer Enhancement Using a Micro-Scale, Porous-Layer Coating on a Horizontal-Tube, Falling-Film Heat Exchanger," ASME 2012 3rd Micro/Nanoscale Heat & Mass Transfer International ConferenceAtlanta, Georgia, MNHMT2012-75333.

[5] Lee, S., Koroglu, B., and Park, C., 2010, "Experimental investigation of capillary-assisted solution wetting and heat transfer using a micro-scale, porous-layer coating on horizontal-tube, falling-film heat exchanger," International Journal of Refrigeration, 35, pp. 1176-1187.

[6] Carey, V. P., 2008, Liquid-vapor phase-change phenomena : an introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment, Taylor and Francis, New York.

Nick Bogan

Chanwoo Park, Ph.D.

Nick Bogan is a graduate research assistant in the mechanical engineering department, University of Nevada, Reno. Chanwoo Park is assistant professor in the mechanical engineering department, University of Nevada, Reno.

Table 1. Dimensions of Experimental Setup Unit Dimension Inner Rod [D.sub.1] mm (in) 11.11(0.4375) [L.sub.r] mm (in) 279.4 (11.00) Outer Tube [D.sub.2] mm (in) 13.39 (0.527) [D.sub.3] mm (in) 15.88 (0.625) [L.sub.t] mm (in) 279.4 (11.00) Solution [d.sub.ds,nz] mm (in) 1.000 (0.039) Dispenser [L.sub.ds] mm (in) 279.4 (11.00) [s.sub.ds,nz] mm (in) 6.35 (0.250) Evaporator [S.sub.t] mm (in) 50.80 (2.000) Chamber [S.sub.c] mm (in) 50.80 (2.000) L mm (in) 279.4 (11.00)

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Author: | Bogan, Nick; Park, Chanwoo |
---|---|

Publication: | ASHRAE Transactions |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jul 1, 2013 |

Words: | 3323 |

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