Uncertainty Analysis

An uncertainty analysis is carried out here to estimate the uncertainty levels in the experiment. Kline and McClintock [41] proposed a formula for evaluating the uncertainty in the result F as a function of independent variables, X₁, X_2, X₃∙∙∙∙∙∙∙∙∙∙∙∙Xn,

F=F (X1 ,X2, X3∙∙∙∙∙∙∙∙∙∙∙∙Xn) (3.7) The absolute uncertainty of F is expressed as

2

and the relative uncertainty of F is

2

2

level associated with the variableX . The values of the uncertainty intervals_i X_i are obtained by a root-mean-square combination of the precision uncertainty of the instruments and the unsteadiness uncertainty, as recommended by Moffat [42]. The choice of the variableX to be included in the calculation of the total uncertainty _i level of the result F depends on the purpose of the analysis.

The uncertainties of the parameters in the present study are calculated as follows:

(1) Uncertainty of temperature difference, Tw=Tw-Tb

 

(2) Uncertainty of total power input, Q_t

V

Cu (4) Uncertainty of space-average heat transfer coefficient, h

w

A summary of the results from the present uncertaintly analysis is given in Table 3.1.

Table 3.1 Summary of the results from the uncertainty analysis.

Parameter Uncertainty

Geometry Length & thickness (%)

Area (%) Particle diameter (%)

Particle density(%)

0.167%

0.334%

10.0%

13.4%

Parameter measurement Temperature, T (C)

Temperature difference, ∆𝑇_𝑤 (C) System pressure, P (kPa)

0.05

0.36

0.5 Boiling heat transfer on the copper flat plate Total power input, Qt (%)

Imposed net heat flux, 𝑞_𝑛(%) Heat transfer coefficient, h(%)

5.9%

8.3%

11.0%

Fig. 3.1 Schematic diagram of six main directions of the heat loss.

2

3

4 5

6

1

Copper block

Fig. 3.2 Schematic diagram of T'5 and T'6

Film heater

Copper block

T′₅ T′₆

T₆

CHAPTER 4

POSSIBLE SUBCOOLED POOL BOILING HEAT TRANSFER ENHANCEMENT OF FC-72 OVER HEATED COPPER SURFACE

The experimental results to illustrate possible enhancement of subcooled pool boiling heat transfer of FC-72 by placing movable particles on the heating surface obtained in the present study are examined in this chapter. The present experiments are carried out for the liquid subcooled temperature set at ∆𝑇_𝑠𝑢𝑏=5℃, 10℃, 15℃ and 20℃. The diameter of the particles d_𝑝 is fixed at 1.0 and 1.5 mm, and the total number of particles 𝑁_𝑝 varied from 100 to 1800 for the particles with the diameter 1.0 mm or from 100 to 800 for the particles with the diameter 1.5 mm. The FC-72 liquid in the test chamber is maintained at subcooled liquid state corresponding to the atmospheric pressure. Note that the maximum numbers of particles forming a single closely packed particle layer over the boiling surface 𝑁_𝑝𝑓 are 900 and 400 respectively for the particles with the diameter of 1.0 mm and 1.5 mm when each particle contact directly with neighboring particles. In the experiment tests are also conducted for the particle number well exceeds 𝑁_𝑝𝑓 and many particles are on top of the other particles. The measured data are presented in terms of the boiling curves and boiling heat transfer coefficients for various diameters and numbers of the copper particles. Effects of the experimental parameters on the possible subcooled boiling heat transfer enhancement will be examined in detail. Selected data are presented in the following to illustrate the possible pool boiling heat transfer enhancement by the boiling flow driven metallic particles.

4.1 Single-phase Natural Convection Heat Transfer

Before conducting the pool boiling experiment, we first measure steady natural convection heat transfer of FC-72 liquid over the heated copper surface without the presence of any particles which prevails at low imposed heat flux, intending to verify the present experimental setup. The measured data for the natural convection heat transfer coefficient are compared with the empirical correlation of Radziemska and Lewandowski [43] in Fig. 4.1. Their correlation is

NuL=(2.1e^-48W+1.2)RaL0.2

(4.1) where w is the width of the heating plate (m). The correlation given in Eq.(4.1) is based on the data for a small horizontal plate heated from below for 10⁵<RaL<10⁸. Note that the characteristic length L used in defining the dimensionless groups in the above equation is chosen to be the ratio of the heated surface area and its perimeter, and the Nusselt and Rayleigh numbers are respectively defined as

(4.2) and

(4.3) The results in Fig. 4.1 indicate that our natural convection data are in good agreement with that calculated from Eq. (4.1). Thus the experimental system established here is considered to be suitable for the present study.

4.2 Saturated Pool Boiling on Bare Copper Surface

To further verify the suitability of the present experimental system, we first measured boiling curve for saturated pool boiling of liquid FC-72 on the bare heated copper plate (𝑁_𝑝 = 0). These data are compared with that from Rainey and You [22]

in Fig. 4.2 for pool boiling of FC-72 on a square copper plate of 5 × 5 cm² in surface k

Nu_L  hL



 ³

L

)L Ra g (T^sat



area. Note that the present saturated pool boiling data are in good agreement with theirs.

4.3 Effect of Surface Aging on Boiling over Bare Copper Plate

It is well known that the change of the boiling surface properties with time, the so called “aging effect”, can be significant in affecting the boiling heat transfer from a surface after the surface has been used over certain period of time. Obviously, the measured boiling heat transfer data for the cases with and without the presence of the particles on the surface can be meaningfully compared only when the surface aging effect is small. Thus tests are carried out here to investigate the aging effect of subcooled FC-72 liquid boiling on the present heated surface. The results show that the boiling curves and heat transfer coefficients measured over a time interval of 6 hours do not differ to a noticeable degree, as seen from Fig. 4.3. But a significant aging effect is found for an interval of 24 hours. Thus in the present experiment the boiling heat transfer data for the corresponding cases with and without the presence of particles on the surface are obtained within 6 hours.

4.4 Effects of Moving Copper Particles on Boiling Heat Transfer

Possible FC-72 boiling heat transfer enhancement by the copper particles moving on the heated surface is then examined. Results are presented first for the small liquid subcooling with ∆𝑇_𝑠𝑢𝑏=5℃ by showing the boiling heat transfer data for the bare surface and for the surface with copper particles on it for d_𝑝=1 mm and various 𝑁_𝑝 in Figs. 4.4-4.18. The results in Figs. 4.4-4.6 for d_𝑝=1.0 mm and 𝑁_𝑝=100 to 300 indicate that at a small particle number the boiling heat transfer can be slightly enhanced by the copper particles only at low wall superheat near the onset of

nucleate boiling. The enhancement gets smaller at increasing wall superheat. Besides, the moving copper particles does not affect the boiling heat transfer to a significant degree in the single-phase flow at very low wall superheat and in the fully developed nucleate boiling region at high wall superheat. Moreover, a slight reduction in the boiling heat transfer by the copper particles is noted at an even higher wall superheat.

As the total number of the copper particles is increased to 400, 500 and 600, noticeable augmentation in the boiling heat transfer by the motion of the copper particles appears at low wall superheat (Figs. 4.7-4.9). On the other hand, the degradation in the boiling heat transfer at high wall superheat is not noticeably increased. For a further increase in the number of the copper particles to 700-900, the particles on the copper plate are rather crowded. However, enhancement in the boiling heat transfer by the copper particles is even more significant at low ∆𝑇_𝑠𝑎𝑡 (Figs.

4.10-4.12), implying strong interactions between the particles and boiling flow at this large 𝑁_𝑝. Note that when 𝑁_𝑝>700, the boiling heat transfer at high wall superheat starts to degenerate to a significant degree. In fact, substantial retardation in the boiling heat transfer by the copper particles exists at high ∆𝑇_𝑤. It is of interest to note from the data given in Figs. 4.13-4.18 that even when the total number of the copper particles well exceeds 𝑁_𝑝𝑓 for 𝑁_𝑝 ≥ 1,000 the boiling heat transfer enhancement by the copper particles is still significant at low ∆𝑇_𝑤. This suggests that the presence of a large number of the copper particles on top of the other particles does not lower the boiling heat transfer performance at low wall superheat.

To be more quantitative on the boiling heat transfer affected by the copper particles presented above for ^∆𝑇_𝑠𝑢𝑏=5℃ and d_𝑝=1.0 mm, the ratios of the boiling heat transfer coefficients for the cases with to that without the presence of the particles ℎ_𝑝⁄ are shown in Fig. 4.19 for various ∆𝑇ℎ _𝑤 and 𝑁_𝑝. Note that the

enhancement in the boiling heat transfer can exceed 200% for 𝑁_𝑝 ≥800. The best enhancement for these cases is 300% for 𝑁_𝑝=1800 at ∆𝑇_𝑤 ≈16.3K. Note that the best enhancement usually occurs at very low ∆T_𝑤 near the onset of nucleate boiling.

Beyond this low ∆T_𝑤 the case with 𝑁_𝑝=1600 has the best average heat transfer over the whole boiling process. Besides, for 𝑁_𝑝 ≥ 1200 the onset of nucleate boiling takes place much earlier than the bare surface. For instance, at 𝑁_𝑝=1400 a 28%

reduction in the incipient boiling wall superheat can be obtained by the moving particles. On the contrary the reduction in the boiling heat transfer at high ∆𝑇_𝑤 can be as high as 20%. Note that for the FC-72 saturated pool boiling examined by Wei [2], the reduction can be even higher at 25%. Moreover, in the single-phase natural convection flow the change in the heat transfer coefficient by the particles is within

±13% of that for the bare surface.

Aside from the boiling heat transfer, the above results also show that the presence of the copper particles can substantially lower the wall superheat needed for the onset of nucleate boiling for most cases (Table 4.1). This will cause lower operating temperature and is also beneficial in electronics cooling by employing moving metallic particles on the boiling surface.

Next, the measured heat transfer data for the higher degree of the liquid subcooling with ^∆𝑇_𝑠𝑢𝑏=10℃ are given in Figs. 4.20-4.28 for 𝑁_𝑝 ranging from 200 to 1800. By and large, these results are similar to those for ∆𝑇_𝑠𝑢𝑏=5℃ presented above. However, some noted differences do exist. Due to the bulk temperature in the chamber is lower, the onset of nucleate boiling occurs at a higher wall superheat. In Fig. 4.29 we find that the best enhancement can reach 200% for 𝑁_𝑝= 1600, which is much lower than that for ∆𝑇_𝑠𝑢𝑏=5℃. On the other hand, the reduction in boiling heat transfer at high wall superheat is slightly lower.

But for the cases with even higher degree of liquid subcooling, results are quite different. The data in Figs. 4.30-4.32 indicate that there are nearly no heat transfer enhancement for ∆𝑇_𝑠𝑢𝑏=15℃ for 𝑁_𝑝 ranging from 200 to 600. Only when 𝑁_𝑝 ≥ 800, heat transfer can be enhanced slightly (Fig.4.33 & 4.34). For an even higher liquid subcooling at ∆𝑇_𝑠𝑢𝑏=20℃ the boiling heat transfer is reduced by the copper particles, as evident from Figs. 3.35 & 3.36. No heat transfer augmentation by the particles is found. Besides, the incipience boiling wall superheat can be even higher with the presence of the particles.

Attention is then turned to the data shown in Figs. 4.37-4.57 for the larger copper particles with 𝑑_𝑝= 1.5 mm. The results clearly indicate that the effects of the larger copper particles on the boiling heat transfer exhibit similar trend to the smaller particles presented above. At ∆𝑇_𝑠𝑢𝑏=5℃, the boiling heat transfer enhancement can be up to 292% for 𝑁_𝑝=800 at low wall superheat.

4.5 Effects of Subcooling Degree in the Bulk Liquid

To illustrate the effects of the copper particles on the boiling heat transfer enhancement for various degrees of the bulk liquid subcooling, we compare the measured heat transfer data ℎ & ℎ_𝑝

⁄ for ℎ ^∆𝑇_𝑠𝑢𝑏 ranging from 0℃ to 20℃ in Fig.

4.58-4.65 at selected 𝑁_𝑝. The data in Fig.4.58-4.61 manifest that for a given 𝑁_𝑝 the wall superheat for the boiling onset is noticeably higher for a higher liquid subcooling and the boiling heat transfer enhancement is smaller. In fact, at ∆𝑇_𝑠𝑢𝑏=15℃ the enhancement is nearly negligible. According to our flow observation, the bubbles departing from the heated surface is fewer and smaller at a higher ∆𝑇_𝑠𝑢𝑏. The resulting thrust acting on the particles by the bubbles are weaker, leading to a smaller boiling heat transfer augmentation. Note that at the high liquid subcooling with

∆𝑇_𝑠𝑢𝑏=20℃, the boiling heat transfer is retarded by the copper particles for all 𝑁_𝑝 tested here (Fig. 4.62-4.65). The boiling heat transfer retardation is more pronounced for a larger larger 𝑁_𝑝.

During the course of this study we also test copper particles of much smaller size with 𝑑_𝑝=0.5 mm to find whether there is any enhancement in such high liquid subcooling situation. Results from such test shown in Figs. 4.66-4.69 indicate that for

∆𝑇_𝑠𝑢𝑏=15℃ and 𝑁_𝑝=1800 & 3600 there is a slight enhancement after the onset of boiling but no positive effect for ∆𝑇_𝑠𝑢𝑏=20℃. We can conclude that when there is high liquid subcooling, the departing bubbles will become very fewer and smaller and the particle motion is relatively weak. The boiling heat transfer enhancement by the particles is not significant.

4.6 Interactions between Particles and Boiling Flow

To delineate the complicate effects of the moving copper particles on the boiling heat transfer, motions of the particles and bubbles in the boiling flow are visualized. The results from this visualization for selected cases are presented in Figs.

4.70-4.76. More specifically, photos taken from the side view of the subcooled boiling flow in a small region above the heating plate are shown in Fig. 4.70 for the small copper particles with 𝑁_𝑝=600 at low imposed heat flux of 0.78 𝑤 𝑚⁄ ² and

∆𝑇_𝑠𝑢𝑏=5℃. In these figures, the symbol “t=0” denotes an arbitrary time instant in the statistical state. At high heat flux the vigorous motions of the particles and bubbles and their strong interactions are prone to overshadow each other, causing the top view photos to be rather ambiguous. Thus only the side view photos are shown here.

Our flow visualization reveals that when a given heat flux slightly higher than that needed for ONB is imposed to the boiling surface the fast growth of bubbles after

their incipience on the heated surface can push the surrounding particles to move away from their original sites horizontally over a certain distance. As the particles move on the heated surface, they in turn can push the bubbles along their path to depart from the heating surface, resulting in earlier bubble departure. Besides, the moving particles can collide with other particles. At higher imposed heat flux more bubbles nucleate from the heated plate and force resulting from the growth of bubbles can be very strong. Consequently, the particles can be lifted directly up by the growing bubbles too. Later, the heavy metallic particles may drop back to the plate due to gravity and the surrounding bubbles and liquid can be pushed away. Besides, collision between the particles is frequent. These mutual particle-bubble interactions in the boiling flow schematically shown in Fig. 4.77 get more intense at increasing heat flux, causing the three-phase liquid-vapor-particle flow over the heated surface to become highly turbulent and tending to enhance boiling heat transfer from the plate. It is also noted that at a higher liquid subcooling the bubble growth is slower and the bubbles departing from the heated surface are smaller and at a lower rate. Thus the bubble- particle interactions are weaker and their effects on the boiling heat transfer diminish.

However, at an even higher heat flux a very large number of bubbles nucleate at the heated surface and the copper particles can impede the bubbles of certain size to grow further and depart from the heated surface. The bubbles are then trapped beneath the particles, as schematically illustrated in Fig. 4.78. Meanwhile, the particles can reduce the inrush of the bulk liquid to the heated surface especially at large particle number. Therefore the boiling heat transfer is retarded by the particles. These heat transfer retarding effects are more severe at higher heat flux when more particles are placed on the heated plate.

4.7 Proposed Correlations

The mean absolute error (MAE) for the above correlation for ℎ_𝑝⁄ when compared ℎ with the present data is 20.7%.

Finally, we illustrate the ranges of the experimental parameters in which the boiling heat transfer can be enhanced by placing the copper particles on the heated surface in Fig. 4.79-4.82. The results manifest that the lower bounds of the imposed heat flux for enhancing boiling heat transfer do not significantly vary with the ratio of the particle number placed on the plate to the maximum particle number forming a single particle layer on the plate 𝑁_𝑝⁄𝑁_𝑝𝑓 and with the particle size. But the lower bounds for the wall superheat decrease noticeably with 𝑁_𝑝⁄𝑁_𝑝𝑓 (Fig. 4.79 (b) and Fig. 4.80 (b)). The upper bounds of q and ∆𝑇_𝑤 for enhancing boiling heat transfer, however, show nonmonotonic variations with 𝑁_𝑝⁄𝑁_𝑝𝑓, particle size and subcooling.

Note that in Fig. 7.82 for ∆𝑇_𝑠𝑢𝑏=20℃ the boiling heat transfer can not be enhanced by the moving copper particles in the present attempt.

Table 4.1 Wall superheats at onset of nuclear boiling for 1.0 mm copper particles

Table 4.2 Wall superheats at onset of nuclear boiling for 1.5 mm copper particles

Particle Diameter

Subcooling Degree

𝑁_𝑝 (∆𝑇_𝑤)_𝑂𝑁𝐵(℃) (∆𝑇_𝑤)_𝑂𝑁𝐵(℃) for bare surface

𝑑_𝑝=1.5 (mm)

5℃

100 15.4 16.2

200 14.7 16.2

400 14.1 16.3

600 13.5 16.1

800 13.3 16.1

10℃

200 19.3 20.9

400 16.1 21.2

600 18.1 20.5

800 16.6 20.6

15℃

200 24.5 25.5

400 23.4 24.6

600 23.5 24.8

800 24.0 24.9

20℃

200 28.2 28.0

400 30.0 27.9

600 29.1 28.8

800 29.0 28.1

8.0x10⁶ 1.0x10⁷ 1.2x10⁷ 1.4x10⁷ 1.6x10⁷ Ra_L

20 40 60 80 100

NuL

Single-phase liquid Natural Convection Heat Transfer at T_w=56^C

Radzimeska and Lewandowski (2005) : Nu_L=(2.1e^-48W+1.2)Ra_L^0.2



Present data at 1 atm

Fig. 4.1 Comparison of the present single-phase natural convection data with the empirical correlation of Radziemska and Lewandowski (2005).

0 10 20 30

Tw (K)

0 2 4 6

q (W/cm2)

 Rainy and You (2000)(5x5-cm²) for polished plate

 Present data for bare surface

Fig. 4.2 Comparison of the present apparatus of saturated nucleate boiling heat transfer data for bare surface with Rainy and You (2000).

Fig. 4.3 Effects of surface aging on subcooled pool boiling curves (a) and boiling heat transfer coefficients (b) for ∆𝑇_𝑠𝑢𝑏= 5℃ for the bare surface.

0 10 20 30

Tw (K) 0

2 4 6 8

q(W/cm2)

(a)

 bare surface-1(measured at time t)

 bare surface-2(measured at time t+6 hours)

0 10 20 30

Tw (K) 0

1000 2000 3000 4000

h(W/m2

K)

(b)

 bare surface-1(measured at time t)

 bare surface-2(measured at time t+6 hours)

0 5 10 15 20 25

T_w (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=100

0 5 10 15 20 25

T_w(K) 0

1000 2000 3000 4000 5000

h(W/m2

K

)

(b) Heat transfer Coefficients for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=100

Fig. 4.4 Effects of copper particle diameter and number on subcooled pool boiling curves (a) and boiling heat transfer coefficients (b) for ^∆𝑇_𝑠𝑢𝑏= 5℃ at d_𝑝=1.0 mm and 𝑁_𝑝 = 100.

ONB ONB

ONB

ONB

0 5 10 15 20 25

T_w (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=200

0 5 10 15 20 25

T_w (K) 0

1000 2000 3000 4000 5000

h(W/m2

K

)

(b) Heat transfer Coefficients for Tsub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=200

Fig. 4.5 Effects of copper particle diameter and number on subcooled pool boiling curves (a) and boiling heat transfer coefficients (b) for ^∆𝑇_𝑠𝑢𝑏= 5℃ at d_𝑝=1.0 mm and 𝑁_𝑝 = 200.

ONB ONB

ONB ONB

0 5 10 15 20 25

T_w (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=300

0 5 10 15 20 25

T_w (K) 0

1000 2000 3000 4000 5000

h(W/m2

K)

(b) Heat transfer Coefficients for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=300

Fig. 4.6 Effects of copper particle diameter and number on subcooled pool boiling curves (a) and boiling heat transfer coefficients (b) for ^∆𝑇_𝑠𝑢𝑏= 5℃ at d_𝑝=1.0 mm and 𝑁_𝑝 = 300.

ONB

ONB

ONB ONB

0 5 10 15 20 25

T_w (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=400

0 5 10 15 20 25

T_w (K) 0

1000 2000 3000 4000 5000

h(W/m2

K)

(b) Heat transfer Coefficients for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=400

Fig. 4.7 Effects of copper particle diameter and number on subcooled pool boiling curves (a) and boiling heat transfer coefficients (b) for ^∆𝑇_𝑠𝑢𝑏= 5℃ at d_𝑝=1.0 mm and 𝑁_𝑝 = 400.

Subcooling 5℃ with 200 copper particles

ONB

ONB

0 5 10 15 20 25

T_w (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=500

0 5 10 15 20 25

T_w (K) 0

1000 2000 3000 4000 5000

h(W/m2

K)

(b) Heat transfer Coefficients for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=500

Fig. 4.8 Effects of copper particle diameter and number on subcooled pool boiling curves (a) and boiling heat transfer coefficients (b) for ^∆𝑇_𝑠𝑢𝑏= 5℃ at d_𝑝=1.0 mm and 𝑁_𝑝 = 500.

ONB ONB

ONB ONB

0 5 10 15 20 25

T_w (K) 0

2 4 6 8

q (W/cm2)

(a) Boiling Curves for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=600

0 5 10 15 20 25

T_w (K) 0

1000 2000 3000 4000 5000

h(W/m2

K)

(b) Heat transfer Coefficients for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=600

Fig. 4.9 Effects of copper particle diameter and number on subcooled pool boiling curves (a) and boiling heat transfer coefficients (b) for ^∆𝑇_𝑠𝑢𝑏= 5℃ at d_𝑝=1.0 mm and 𝑁_𝑝 = 600.

ONB ONB

ONB ONB

0 5 10 15 20 25

(b) Heat transfer Coefficients for T_sub=5^oC

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=700

Fig. 4.10 Effects of copper particle diameter and number on subcooled pool boiling

Fig. 4.10 Effects of copper particle diameter and number on subcooled pool boiling

在文檔中 放置可移動擾動銅粒子在一水平加熱銅板上對FC-72池沸騰熱傳增強研究 (頁 45-0)