An experimental study of falling film evaporation on inclined plates using R-141b and R-134a.

INTRODUCTION

Falling film evaporation has been applied in many fields and showed high heat transfer efficiency. Falling film evaporation on vertical tubes has been utilized in many applications in the chemical industry. Horizontal plain tube falling film evaporators have been used in the desalination industry and tested in ocean thermal energy conversion pilot plants. Falling film (spray) evaporators have recently been used in vapor-compression refrigeration chillers. A falling film evaporator has a greater evaporative heat transfer coefficient under many operation conditions and requires much less refrigerant charge than a flooded evaporator for the same chiller capacity. Therefore, one expects that it has the advantages of increasing chiller efficiency, reducing capital and operating costs, and reducing global warming gases.

Earlier studies on falling evaporation were conducted on vertical tubes. Chun and Seban (1971) modified Nusselt's condensation theory to predict their experimental data on falling film evaporation outside a vertical tube. They also categorized the flow regimes of falling film evaporation as: laminar flow, wavy-laminar, and turbulent flow. Based on their experimental data, they developed the following correlations (Equations 1-3).

* Laminar flow (for [R.sub.ef] [less than or equal to] 2.44*[Ka.sup.-1/11]): The average Nusselt number (Nu) is correlated by Equation 1:

Nu = 1.1[[Re].sub.f.sup.-1/3]

where the Nusselt number is defined by Equation 2:

Nu = [h/k][([v.sup.2]/g).sup.1/3]

The Kapitza number, Ka, is defined as Ka = (g*[[mu].sup.4]) / ([rho]*[[sigma].sup.3]); [Re.sub.f] = (4.[GAMMA])/[mu] is the film Reynolds number; and [GAMMA] is the mass flow rate per unit length ([GAMMA] =m/L). For a vertical tube, L = [pi]D and [GAMMA] =m/[pi]D.

* Wavy laminar (for 2.44 [Ka.sup.-1/11] [less than or equal to] [Re.sub.f] [less than or equal to] 5800.[Pr.sup.-1.06], Pr = Prandtl number):

Nu = 0.822.[Re.sub.f.sup.-0.22]

* Turbulent (for [Re.sub.f] > 5800.[Pr.sup.-1.06]):

Nu = 3.8 x [10.sup.-3][Pr.sup.0.65][Re.sub.f.sup.0.4]

Shmerler and Mudawwar (1988) performed evaporation experiments of falling water film on a vertical tube and proposed a model for the turbulent regime. Their model well predicted their experimental data at Pr = 5.5 but failed to predict their data at Pr = 1.75 in the developing region. Alhusseini et al. (1998) proposed an asymptotic model, where the total heat transfer coefficient (h) is expressed in Equation 5 as the combination of the heat transfer coefficients in wavy laminar ([h.sub.lam]) and turbulent ([h.sub.t]) regions.

h = [([h.sub.lam.sup.5] + [h.sub.t.sup.5]).sup.1/5]

The wavy laminar coefficient ([h.sub.lam]) and turbulent coefficient ([h.sub.t]) were correlated from their experimental data, which were obtained over a wide range of Prandtl number (1.73 ~ 46.6).

Chien and Cheng (2006) developed a superposition model for falling film evaporation of refrigerant on smooth horizontal tubes. They accounted for the bubble nucleation effect and calculated the falling film evaporation with bubble nucleation by Equation 6. The predictive errors against data of R-22, R-123, R-134a, and R-141b on four different apparatuses are within ?20~+25%.

h = (0.185 + 56.21*[We.sub.F.sup.0.4531]]/[Bo.sub.F.sup.0.687]*[Re.sub.f.sup.1.3078]])*[h.sub.nb] + [h.sub.cv] (6)

In Equation 6, [Bo.sub.F] = ([q.sub*nb].[A.sub.e])/([h.sub.fg]*m) is the "modified boiling number" and [We.sub.F] = ([m.sup.2] * D)/([A.sub.e.sup.2]*[rho]*[sigma]) is the "modified Weber number." The [A.sub.e] in [Bo.sub.F] and [We.sub.F] is the evaporation surface area. The [h.sub.nb] is calculated by the Cooper (1984) nucleate boiling heat transfer correlation, and the [h.sub.cv] is adapted from the Alhusseini et al. (1998) falling film evaporation correlation given by Equation 4. According to the Nusselt analysis, the heat transfer of the falling liquid film on a horizontal tube surface can be treated as many small plates of various inclination angles. For inclined plates, the gravity acceleration term (g) in Equation 2 should be replaced by the effective gravity (g cos([theta])). The effect of the inclination angle of falling film evaporation on the plate should be investigated experimentally.

Nakayama et al. (1982) conducted falling film evaporation experiments on a vertical plate having enhanced surfaces using R-11 at atmospheric pressure. They tested a smooth surface, a vertically grooved surface, a laterally grooved surface, and a mechanically prepared porous surface. They found that the porous surface yields the highest heat transfer performance in either pool boiling or falling film evaporation modes. However, the effect of inclination was not investigated in Nakayama et al. (1982). Chien and Lin (2005) have conducted falling film evaporation experiments on a plain plate and a finned plate using refrigerant R-134a at 18[degrees]C (64.4[degrees]F) fluid temperature for the heat flux between 38.1 kW/[m.sup.2] (6709 Btu/h [ft.sup.2]) and 65.8 kW/[m.sup.2](11587 Btu/h [ft.sup.2]). The plate was inclined with angles between 10[degrees] and 40[degrees]. Chien and Lin (2005) found that the falling film evaporation performance increases as the inclination angle increases. However, some of their data showed nonuniform liquid flow coming from the guiding plate above the test surface at small inclination angles. This results in complexity in the investigation of the effect of inclination angle. In the present work, two layers of meshes were installed on the guiding plate to improve the uniformity on the guiding plate of the fluid distributor. A finned plate and a plain plate were tested with R-134a and R-141b at 10.5[degrees]C [+ or -] 0.5[degrees]C (50.9[degrees]F [+ or -] 0.9[degrees]F) and 15.5[degrees]C [+ or -] 0.5[degrees]C (59.9[degrees]F [+ or -] 0.9[degrees]F), respectively.

EXPERIMENTAL SETUP

In the present study, an apparatus was designed to test falling film evaporation experiments on a rectangular plate at various angles of inclination. The data scope of the present tests is shown in Table 1.

Table 1. Data Scope of the Present Experiments

Working                                R-134a
Fluid

Fluid                          10.5[degrees]C[+ or -]
Temperature                        0.5[degrees]C
                               (50.9[degrees]F [+ or
                                 -] 0.9[degrees]F)

Inclination                         10[degrees],
Angle                               20[degrees],
                                    30[degrees],
                                    40[degrees]

Heat Flux      kW/[m.sup.2]             17.9             25.7

             Btu/h [ft.sup.2]           5674             4526

Mass Flow          g/s                  0.64             0.78
Rate

                   lb/s               0.001411         0.00172

Surfaces       Plain, Fin-B

Working                              R-141b
Fluid

Fluid                            15.5[degrees]C
Temperature                          [+ or -]
                                  0.5[degrees]C
                                 (59.9[degrees]F
                                     [+ or -]
                                 0.9[degrees]F)

Inclination                        10[degrees],
Angle                              20[degrees],
                                   30[degrees],
                                   40[degrees]

Heat Flux      35.0      45.7      17.9, 25.7,
                                   35.0, 45.7

               6163      14486       5674, 4526,
                                   6163, 14486

Mass Flow      1.04      1.36        1.4~5.3
Rate

             0.002293  0.002998  0.003086~0.012

Surfaces                           Plain, Fin-B

Tests were conducted on a plain surface plate and a finned plate using refrigerant R-134a at 10.5[degrees]C [+ or -] 0.5[degrees]C (50.9[degrees]F [+ or -] 0.9[degrees]F) and R-141b at 15.5[degrees]C [+ or -] 0.5[degrees]C (59.9[degrees]F [+ or -] 0.9[degrees]F). R-134a is the actual working fluid in most spray-type chiller units. In the present work, R-141b was chosen for its low saturation pressure and some other properties that are quite different from R-134a. It would improve the fundamental understanding of this subject by testing another fluid that has significantly different thermal properties. The saturation temperature of the chiller evaporator is about 4[degrees]C~6[degrees]C (39.2[degrees]F~42.8[degrees]F) in practice. However, the fluid temperature was restricted by the condenser capacity in the present work. The test plate was inclined with angles between 10[degrees] and 40[degrees]. The heat flux varied between 17.9 kW/[m.sup.2] (5674 Btu/h*[ft.sup.2]) and 45.7 kW/[m.sup.2] (14486 Btu/ h*[ft.sup.2]). Two series of tests were conducted for R-141b. For a fixed mass flow rate of 1.6[+ or -]0.2 g/s (0.003527[+ or -]0.00044 lb/s), the heat flux was varied between 17.9 and 45.7 kW/[m.sup.2] (5674 and 14,486 Btu/h [ft.sup.2]). In another series, the mass flow rate was varied between 1.4 and 5.3 g/s (0.003086 and 0.012 lb/s) at a fixed heat flux of 45.7 kW/[m.sup.2] (14,486 Btu/h*[ft.sup.2]). For the tests of R-134a, the liquid level in the falling film test cell can only remain stable at a certain flow rate for each heat input. The mass flow rate corresponding to each heat flux in the present tests is given in Table 1. The Fin-B surface in the present test is similar to the finned surface (Fin-A) in the Chien and Lin (2005) study. The two finned surfaces have the same fin thickness (t) = 0.0003 m, and fin pitch ([P.sub.F]) = 0.0006 m, but the fin heights are different. The fin height of the Fin-B surface is 0.0003 m, but the fin height of the Fin-A surface is 0.0005 m.

Apparatus

The falling film evaporation test apparatus is shown in Figure 1. The working fluid evaporated in the test cell and entered a condenser, which was cooled by glycol-water mixture. The inlet temperature of the glycol-water mixture was maintained constant by a constant temperature bath. An accumulator collected condensed liquid from the condenser and excess liquid from the bottom of the test cell. The liquid in the accumulator passed through a dryer and was pumped into the test cell by a gear pump, driven by a variable-speed pump drive. Care was taken to ensure no vapor bubble entered the pump by inspecting the sight glass between the dryer and the pump. A flowmeter was connected between the pump and the test cell for flow rate measurement. Liquid entered the test cell through a liquid film distributor, located above the test surface. As shown in Figure 2, the liquid film distributor consists of a 0.00635 m (0.25 in.) outer diameter copper tube, having 0.001 m (0.0394 in.) diameter holes in 0.005 m (0.1968 in.) pitch along the tube length, and a rectangular guiding plate. The angle ([ALPHA] on Figure 2) between the normal line of the test surface and the guiding plate was fixed at 5[degrees] for the present test. Two layers of #50 mesh brass screens were installed on both sides of the guiding plate to improve the uniformity of the fluid in the distributor. The screens also prevent the influence of the liquid flow momentum falling on the guiding plate as the apparatus tilted.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The exploded diagram of the test cell is shown in Figure 3. A sight glass was installed in the front of the test cell for flow distribution observations. A high-speed camera system, whose maximum resolution is 1280 x 1024 and maximum frame rate is 2000 frames/sec, was used in the present visual observation study. A thermister probe (item i) and a thermocouple probe (item j) were inserted into the test vessel for system temperature measurement, and a pressure tap (item d) was connected on the opposite side of the vessel. The measured system temperature was compared with the saturation temperature at system pressure. The test surface was 0.05 m (1.968 in.) wide and 0.102 m (4.016 in.) long (item a), made on a copper block (Figure 4). The copper block had a test surface that was fixed to the back of the test vessel. For the purpose of preventing leakage, a 2.0 mm thick rubber gasket was inserted between the block and the vessel. Two pieces of film heater (item b) were attached on the back of the copper block. As shown on Figure 5, twenty-four 0.00051 m (0.02 in.) thick stainless-steel sheathed copperconstantan (T-type) thermocouples were inserted into the test block from both laterals for measurement of temperature variation at four different heights of the surface. For each height, the surface temperature is calculated by the temperature variation at three locations distributed from the film heater to the test surface. The distance between two thermocouples is 0.005 m (0.1968 in.), and the thermocouple closest to the test surface is 0.005 m (0.1968 in.) away from the surface. Thermal transfer compound was applied on the thermocouples and the film heater to ensure good thermal contact with the copper block.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Test Procedures

The experiments were conducted at fixed system temperatures (10.5[degrees]C [50.9[degrees]F [+ or -] 0.9[degrees]F] for R-134a or 15.5[degrees]C [59.9[degrees]F [+ or -] 0.9[degrees]F] for R-141b). The test surface and all parts of the test cell were cleaned with alcohol before installation. The tests of R-134a were performed according to the following steps:

1. Perform a leak-tight test before charging. The system was considered leak-tight if the system was able to sustain at its maximum pressure (about 6 bar absolute pressure) for at least 24 hours.

2. Evacuate the system for at least an hour by a vacuum pump.

3. Charge the working fluid into the system.

4. Turn on the gear pump and the heater and gradually increase their magnitudes. Then evacuate the system for some three seconds to remove the noncondensable gases in the fluid.

5. Turn the heater to the maximum output (about 350 W). Keep the pool temperature at the desired system temperature by adjusting the cooling water flow rate and the temperature of the constant temperature bath and maintain for at least an hour.

6. At a fixed heat input, adjust the flow rate by the pump drive consol to ensure stable flow condition and proper liquid level in the test cell.

7. Record the data after the system temperature is steady for at least five minutes.

8. Stepwise reduce the heat input and repeat steps 6 and 7.

The tests procedures for R-141b were similar to the above, except for steps 1, 3, and 6. Because the pressure of R-141b was less than the atmospheric pressure during the test, the leak-tight test (step 1) is performed under vacuum condition for 24 hours. After the system was charged (step 3), the measured saturation temperature was compared with the tabulated saturation temperature at the measured pressure. If they were different, the system would be evacuated for several seconds

and steps 4 and 5 would be repeated until they agreed within [+ or -]0.5[degrees]C (0.9[degrees]F). Step 6 was performed differently for the series of fixed mass flow rate--the heat flux was descended from 45.7 to 17.9 kW/[m.sup.2] (14486 to 5674 Btu/h*[ft.sup.2]) and the flow rate was kept at 1.6[+ or -]0.2 g/s. However, for the series of fixed heat flux, the mass flow rate was varied between 1.4 and 5.3 g/s and the heat flux was fixed at 45.7 kW/[m.sup.2] (14486 Btu/h*[ft.sup.2]).

Data Reduction and Uncertainty Analysis

The flowmeter was calibrated by measuring the liquid level rise in the test cell at 10[degrees], 20[degrees], 30[degrees], and 40[degrees] inclination angles. The test flow rate was calculated by the calibration curve for each inclination angle and fluid. The maximum uncertainty of the flow rate is [+ or -]0.1 g/s based on these calibrations.

The test surface wall temperature ([T.sub.w]) is extrapolated from the temperature variation as given by Equation 7.

[T.sub.w] = [SIGMA][T.sub.i] - [SIGMA][x.sub.i]*[[3.[SIGMA]([T.sub.i].[x.sub.i]) - [SIGMA][T.sub.i].[SIGMA][x.sub.i]]/[3.[SIGMA][x.sub.i.sup.2] - [([SIGMA][x.sub.i]).sup.2]]]

The system temperature ([T.sub.s]) is the average value of the two readings of the thermister (item i of Figure 4) and the thermocouple (item j) inserted in the vessel. The two readings are in good agreement with less than 0.2[degrees]C difference. The wall superheat ([DELTA]T) is defined as the difference between the wall temperature ([T.sub.w]) and the system temperature ([T.sub.s]).

The locations of the thermocouples were measured by a dial caliper having 0.02 mm minimum readings.

The heat input is calculated from the voltage (V) and total electric current (I) through the two film heaters. Assuming 100% transfer efficiency from electric energy to heat, the heat flux is calculated by Equation 8.

q = [Q/[A.sub.e]] = [[V * I]/[A.sub.e]]

where [A.sub.e] = 0.0051 [m.sup.2] (0.0549 [ft.sup.2]) is the test surface area. The heat transfer coefficient is calculated by Equation 9.

h = q/([T.sub.w] - [T.sub.s])

Experimental uncertainties of heat flux and heat transfer coefficient were evaluated accounting for the uncertainty of all measurement devices. Using the method described by Holman (1994), the uncertainty of the result R, w(R), is given by Equation 10:

[[w(R)]/R] = [[([[partial derivative]R]/[[partial derivative][x.sub.1]]*[w([x.sub.1])/R]).sup.2]] + ([[partial derivative]R]/[[partial derivative][x.sub.2]]*[w[([x.sub.2])/R).sup.2]] + ([[partial derivative]R]/[[partial derivative][x.sub.3]].[w[([x.sub.3]).sup.2]]/R) + ...].sup.[1/2]]

where R is a given function of the independent variables [x.sub.1], [x.sub.2], [x.sub.3], ... [x.sub.n], and w([x.sub.1]), w([x.sub.2])... are the uncertainty in the variables [x.sub.1], [x.sub.2], ... and [x.sub.n]. According to Equation 10, the uncertainty of heat transfer coefficient is given by Equation 11.

[[w(h)]/h] = [[(1*[w(q)/q].sup.2]]) + [(-1.[w([T.sub.w] - [T.sub.s])]/([T.sub.w] - [T.sub.s])).sup.2]].sup.[1/2]]

The uncertainties of the wall temperature ([T.sub.w]) and the heat flux (q) can also be calculated by Equation 10. We found the first term (w[q]/q) in Equation 11 is much smaller than the second term. Hence, Equation 11 can be reduced to Equation 12.

[[w(h)]/h][approximately equal to][[w([T.sub.w] - [T.sub.s])]/([T.sub.w] - [T.sub.s])] = 1.683[[w([T.sub.TC])]/[[T.sub.w] - [T.sub.s]]] (12)

The w([T.sub.TC]) in Equation 12 is the uncertainty of the thermocouple that is used to determine [T.sub.w] and [T.sub.s]. All thermocouples were connected to an Agilent 34970A data logging system. They were calibrated in a constant temperature bath before tests. The accuracy of the thermocouples was within [+ or -]0.2[degrees]C (0.36[degrees]F). The uncertainty of the pressure transducer is 0.4% of its reading. For R-134a, the measured saturation temperature agrees with the tabulated saturation temperature at the measured pressure within [+ or -]0.2[degrees]C. Therefore, w([T.sub.TC]) = w([T.sub.i]) = w([T.sub.s1]) = w([T.sub.s2]) = 0.2[degrees]C (0.36[degrees]F). Because the minimum wall superheat ([T.sub.w] - [T.sub.s]) in the present R-134a experiment is 2[degrees]C (3.6[degrees]F), the maximum experimental uncertainty of the heat transfer coefficient is 16.8%. For the R-141b tests, the maximum deviation between the measured saturation temperature and the saturation temperature at the measured pressure is 0.5[degrees]C (0.9[degrees]F). The minimum wall superheat of the present R-141b data is 5.3[degrees]C (9.54[degrees]F). Hence, the maximum uncertainty is 13.2% for R-141b if w([T.sub.s]) = 0.5[degrees]C (0.9[degrees]F).

EXPERIMENTAL RESULT

R-141b Data

The average heat transfer coefficients of falling film evaporation on the plain surface and the finned surface at a fixed flow rate of 1.6[+ or -]0.2 g/s (0.003527[+ or -]0.00044 lb/s) for R-141b at 15.5[degrees]C (59.9[degrees]F [+ or -] 0.9[degrees]F) are shown in Figure 5. The heat transfer coefficient increases as the heat flux increases for both the plain surface and the Fin-B surface at all inclination angles from 10[degrees] to 40[degrees]. For the Fin-B surface, the heat transfer coefficient increases as the inclination angle increases. However, the effect of inclination angle is negligible for the plain surface.

Figure 6 shows the effect of mass flow rate on the falling film evaporation of R-141b at a fixed heat flux (q = 45.7 kW/[m.sup.2] [14486 Btu/h*[ft.sup.2]]). For the plain surface at any inclination angle between 10[degrees] and 40[degrees], the heat transfer coefficient increases as the mass flow rate increases at a low flow rate (less than 2.2 g/s [0.00485 lb/s]). The influence of the mass flow rate is less pronounced on the Fin-B surface than on the plain surface. For a mass flow rate greater than 2.2 g/s (0.00485 lb/s), the flow rate has negligible effect on evaporation performance for both the plain surface and the Fin-B surface. The effect of inclination angle is negligible for the Fin-B surface at high flow rates, although the evaporation performance is influenced by the inclination angle at low flow rates (1.6[+ or -]0.2 g/s [0.003527[+ or -] 0.00044 lb/s])as shown in Figure 5. Similar to the results in Figure 5, the inclination angle has negligible effect on the plain surface at all mass flow rates between 1.6 g/s (0.003527 lb/s) and 5.3 g/s (0.012 lb/s).

[FIGURE 6 OMITTED]

R-134a Data

Figure 7 shows the falling film evaporation data of R-134a at various heat fluxes. Different from the tests of R-141b fluid, the liquid level in the falling film test cell was only stable within a small range of flow rate for each heat input. Therefore, the mass flow rate was dependent on the heat flux. The mass flow rate corresponding to each heat flux in the R-134a tests is given in Table 1. Similar to the results for R-141b, the falling film evaporative heat transfer coefficient of R-134a increased as the heat flux increased for all inclination angles on both surfaces as shown in Figure 7. For the plain surface, the 20[degrees], 30[degrees] and 40[degrees] inclination angles yielded similar evaporation performance, and the 10[degrees] inclination resulted in the lowest performance. The inclination angle has more significant influence on the Fin-B surface than on the plain surface. As the inclination angle increases, the evaporation performance of the Fin-B surface improves.

[FIGURE 7 OMITTED]

Observation of Boiling in the Falling Film

During the present tests, bubble nucleation phenomena were found under many test conditions on either the plain surface or the finned surface. More bubbles were observed on the finned surface than the plain surface. The boiling nucleation site density and frequency increased as the heat flux increased. The typical bubble size of R-141b was larger than that of R-134a at the same test conditions. This is probably because the vapor density of R-134a is larger than that of R-141b. Figures 8 and 9 are the photos taken by the high-speed camera during the falling film evaporation tests of R-141b at 25.7 kW/[m.sup.2] (4526 Btu/h [ft.sup.2]) heat flux and 1.6 g/s (0.003527 lb/s) flow rate on the plain surface and the Fin-B surface. Figures 8a and 8b show two consecutive photos, taken in 0.0025 second on the plain surface. Four big bubbles appear on Figure 8a, and several ripples and small bubbles are observed on this photo. The bubble under the "Ref." line vanishes on the second photo (Figure 8b). The other three bubbles move downward as compared with the "Ref." lines on both photos. In pool boiling, a bubble departs from the surface and floats in the liquid after it grows to a critical size. However, the bubble in a falling film breaks after it protrudes from the film and reaches a critical size. For the R-141b liquid film on the plain surface, the critical bubble diameter before being broken was about 2.2 mm (0.087 in.).

[FIGURE 8 OMITTED]

Figures 9a and 9b show two consecutive photos taken at 1/400 s frame rate on the Fin-B surface. For the finned surface, bubbles grew in the grooves between fins. A vapor embryo on the top and a bubble at the center are annotated in Figure 9a. After 0.0025 seconds, as shown in Figure 9b, the vapor embryo became a prolonged bubble, and the bubble at the center disappeared. Unlike the spherical bubbles on the plain surface, the bubbles prolonged as they grew between the fins. The bubble density and frequency of the finned surface were greater than those of the plain surface, but the bubble breaking size of the finned surface was smaller than that on the plain surface.

[FIGURE 9 OMITTED]

DISCUSSION

Comparison with Correlations

Three falling film evaporation correlations are compared with the present plain surface data of R-141b for 10[degrees] and 40[degrees] inclination angles in Figure 10. Both the Chun and Seban (1971) correlation and the Alhusseini et al. (1998) correlation underpredict the data. The curves of the Chien and Cheng (2006) correlation are in good agreement with the experimental data of 10[degrees] and 40[degrees] inclination angles. This is because the Chien and Cheng (2006) model has accounted for the bubble nucleation effect. Note that the Chien and Cheng (2006) correlation was developed based on horizontal tube data. In the predictions, the tube diameter (D) in the modified Weber number ([We.sub.F]) was replaced with the plate width (50 mm [1.97 in.]). All correlations predicted a slightly smaller heat transfer coefficient for a larger inclination angle as a result of a smaller effective gravity term (g*cos([theta])) in Equation 2. However, the present R-141 data showed negligible influence of the inclination angle. Possible reasons for this trend are discussed in the next section.

[FIGURE 10 OMITTED]

Heat Transfer Mechanisms

Note that the surface area ratio of the finned surface versus the smooth surface is 2.0, yet the heat transfer enhancement ratio varies from 1.5 to 4.8 according to the data in Figures 5-7. Although the heat transfer coefficient is calculated based on the nominal area, the experimental data reveal that the heat transfer enhancement of the finned surface is not only a result of the increase of surface area. Two mechanisms are involved in the falling film evaporation: (1) evaporation on the liquid-vapor interface and (2) bubble nucleation in the liquid. Therefore, the performances of the two surfaces are related to the following phenomena:

* A thinner liquid film thickness results in a smaller conduction resistance through the liquid film and better interface evaporation performance. Thin liquid film occurs at a medium heat flux where dryout did not occur.

* Dryout on the surface results in significant performance degradation.

* The boiling activities increase as the heat flux increases.

* A thicker liquid layer and proper nucleation sites result in a greater boiling effect.

Because the fin corners are good nucleation sites, bubble nucleation is more active on the finned surface than the smooth surface. The pronounced boiling effect on the finned surface explains the much higher heat transfer coefficient of the finned surface than the plain surface in Figures 5-7. For R-141b, the fin surface yields 1.5~1.8 times the heat transfer coefficients of the plain surface. For R-134a, the fins enhanced the heat transfer by 2.5~4.8-fold. The visual observation by the highspeed camera also showed that bubble nucleation was more active on the finned surface than the plain surface. The dryout phenomenon occurs at a high heat flux and a low flow rate in the Chien and Lin (2005) study. However, the dryout condition was not obvious in the present data because the largest heat flux in the present study was smaller than that in the Chien and Lin (2005) study.

As discussed in the previous section, the predictions by the correlations show that the convection term ([h.sub.cv]) decreases as the inclination angle increases. Contrarily, a larger inclination angle results in a thicker liquid film and, consequently, results in a greater nucleate boiling convection ([h.sub.nb]). For the finned surface, boiling is the dominant heat transfer mechanism. Therefore, the overall heat transfer increases as increasing inclination angle for the finned surface. This explains the trend that the heat transfer coefficient increases as the inclination angle increases for the Fin-B surface in both R-134a and R-141b. As observed in the present work, the bubble nucleation was less active on the plain surface than on the finned surface. Hence, the nucleate boiling convection ([h.sub.nb]) on the plain surface should be smaller than that on the finned surface. This explains that the heat transfer coefficient only increases slightly on R-134a as the inclination increases. As for the plain surface data of R-141b, no significant effect of inclination is found because the nucleate boiling ([h.sub.nb]) is even less than that for the plain surface in R-134a. The effects of decreasing film flow convection ([h.sub.cv]) and increasing nucleate boiling convection ([h.sub.nb]) by increasing inclination angle seem to offset it.

Three effects are expected as the mass flow rate increases:

1. Increasing forced convection as the flow velocity increases.

2. Increasing nucleate boiling effect as falling liquid film thickness increases with the increasing mass flow rate.

3. Reducing thin film evaporation rate as falling liquid film thickness increases.

According to the data in Figure 6, the first and second effects seem to dominate for a small mass flow rate (1.6 ~ 2.2 g/s) for the plain surface. Therefore, the heat transfer coefficient increases as the mass flow rate increases. However, the effect of mass flow rate is not significant for mass flow rate greater than 2.2 g/s (0.00485 lb/s) on the plain surface. This implies that the three effects are counterbalanced as the flow rate is greater than 2.2 g/s (0.00485 lb/s). The mass flow rate has less influence on the finned surface than on the plain surface because the flow in the channels between the fins is more stable than the flow on the plain surface.

CONCLUSION

From the present study, we conclude the following.

1. The finned surface yields better falling film evaporation heat transfer performance than the plain surface.

2. The falling film evaporative heat transfer coefficient increases as the heat flux increases for both the finned surface and the plain surface. This is mainly attributed to the bubble nucleation in the liquid film.

3. The heat transfer coefficient increases as the inclination angle increases for the Fin-B surface in both R-134a and R-141b. No significant effect of inclination is found on plain surface for R-141b.

4. Three falling film evaporation correlations are compared with the present plain surface data of R-141b for 10[degrees] and 40[degrees] inclination angles. The Chien and Cheng (2006) correlation yields the best agreement with the experimental data because the effect of bubble nucleation has been accounted for.

ACKNOWLEDGMENT 

This project was supported by National Science Council, Taiwan, grant number NSC92-2212-E-027-004. We thank Electric Power Science and Technology Center of National Taipei University of Technology for offering the high-speed camera system.

NOMENCLATURE 

[A.sub.e] = evaporation surface area, [mm.sup.2]

[Bo.sub.F] = modified Boiling number

D = tube diameter, mm

g = acceleration due to gravity, m/[s.sup.2]

h = heat transfer coefficient, kW/[m.sup.2]*K

[h.sub.cv] = convective heat transfer coefficient, kW/[m.sup.2]*K

[h.sub.fg] = latent heat of vaporization, kJ/kg

[h.sub.lam] = laminar heat transfer coefficient, kW/[m.sup.2]*K

[h.sub.nb] = nucleate boiling coefficient, kW/[m.sup.2]*K

[h.sub.t] = turbulent heat transfer coefficient, kW/[m.sup.2]*K

[H.sub.TC] = height of thermocouple, mm

k = thermal conductivity, W/m*K

Ka = Kapitza number

L = length of test surface, m

m= mass flow rate, kg/s

Nu = Nusselt number

[P.sub.F] = fin pitch, mm

[P.sub.r] = Prandtl number

q = heat flux, kW/[m.sup.2]

[Re.sub.f] = film Reynolds number

t = fin thickness, mm

[T.sub.s] = system temperature, [degrees]C

[T.sub.w] = test surface temperature, [degrees]C

[We.sub.F] = modified Weber number

Greek Symbols

[theta] = inclination angle, degree

[DELTA][T.sub.ws] = wall superheat, K

[alpha] = guiding plate angle (degree)

[GAMMA] = mass flow rate per unit length (kg/s m)

[mu] = dynamic viscosity (Pa*s)

[NU] = kinetic viscosity ([m.sup.2]/s)

[rho] = density (kg/[m.sup.3])

[sigma] = surface tension (N/m)

REFERENCES

Alhusseini, A.A., K. Tuzla, and J.C. Chen. 1998. Falling film evaporation of single component liquids. Int. J. of Heat and Mass Transfer 41(12):1623-32.

Chien, L.-H., and C.-H. Cheng. 2006. A predictive model of falling film evaporation with bubble nucleation on horizontal tubes. HVAC&R Research 12(1):69-87.

Chien, L.-H., and H.-T. Lin. 2005. Effect of inclination angle on falling film evaporation using R-134a. Proceedings of the 2005 ASME Summer Heat Transfer Conference, Paper No. HT2005-72149.

Chun, K.R., and R.A. Seban. 1971. Heat transfer to evaporating liquid films. Trans. ASME, J. Heat Transfer 93(3):391-96.

Cooper, M.G. 1984. Saturation nucleate pool boiling--A simple correlation. Int. Chem. Engng. Symp. Ser. 86:785-92.

Holman, J.P. 1994. Experimental Methods for Engineers, 6th ed. McGraw-Hill.

Nakayama, W., T. Dikoku, and Nakajima. 1982. Enhancement of boiling and evaporation on structured surfaces with gravity driven film flow of R-11. Proceedings of the 7th Heat Transfer Conference 6:409-14.

Shmerler, J.A., and I. Mudawwar. 1988. Local evaporative heat transfer coefficient in turbulent free-falling liquid films. Int. J. of Heat and Mass Transfer 31(4):734-42.

DISCUSSION

Mark Kedzierski, NIST, Gaithersburg, MD: Was the entire apparatus tilted or just the test section during the inclination tests?

Liang-Han Chien: The entire apparatus was inclined in the tests. That is why the flowmeter needs to be calibrated at various inclination angles.

Liang-Han Chien, PhD

Hung-Ta Lin

Liang-Han Chien is an associate professor in the Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei, Taiwan. Hung-Ta Lin is an engineer at Shih-Lin Electric Co., Hsin-Chu, Taiwan.