A study of critical heat flux for low flow of water in vertical round tubes under low pressure

Nuclear Engineering and Design 132 (1991) 225-237 North-Holland

225

A study of critical heat flux for low flow of water in vertical round tubes under low pressure Soon H e u n g Chang, W o n - P i l Baek a n d T a e M i n Bae Department of Nuclear Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, Korea Received 1 July 1991

The critical heat flux (CHF) phenomenon has been investigated for a stable flow of water in vertical tubes at low pressure and velocity conditions. Experiments have been performed with round tubes with diameters of 0.006 m and 0.0088 m for mass fluxes below 220 kg//17nEs under atmospheric pressure. Experimental results are discussed with special reference to the physical mechanism leading to the CHF at very low flow conditions. Finally a new design correlation is proposed based on the combination of the present data and other CHF data available in the literature. Assessments show reasonable agreement of predictions with experiments.

I. Introduction

The critical heat flux (CHF) condition is characterized by a sharp reduction of the local boiling heat transfer coefficient which results from the replacement of liquid by vapor adjacent to the heat transfer surface [1]. It constitutes a boundary between efficient and inefficient boiling heat transfer regimes, and therefore economic operation of heat transfer equipments can be achieved by designing them to operate near but not exceeding the CHF. It also constitutes the most important boundary in considering the two-phase flow regimes. Pressure drop as well as heat transfer generally decreases when the flow undergoes a transition from pre-CHF to post-CHF regimes. Extensive studies have been performed on the CHF over the past three decades especially with development of nuclear reactors. Now many aspects of the phenomenon are well understood and several reliable design correlations are available for most operating conditions. A number of excellent surveys of the CHF are available in books [1-5] and papers [6-8]. However we are confronted with two major problems. One is that there exist too many empirical correlations primarily due to insufficient understanding of the physical mechanisms leading to the CHF condition.

This problem can be partly solved through consistent classification of the CHF patterns and development of a correlation to each pattern [9]. The other is the unbalance of study, i.e., concentration of works on the high pressure and high velocity conditions which are the operating conditions of the commercial watercooled nuclear reactors. Therefore considerable efforts should be given to mitigate this unbalance. The CHF at low pressure and low velocity (LPLV) conditions is important in relation to the commercial nuclear reactors in accident conditions, the next-generation passive safety reactors, small-scale district heating reactors, and research reactors with typical characteristics of low pressure, low flow and low power density. However, the correlations developed mainly based on the high pressure data are usually used for the CHF at LPLV conditions in spite of the different CHF characteristics, because the experimental data are very limited and the phenomenon is not well understood. During the past decade, there has been an increasing effort in studying the CHF at this specific region [10-18]. This work continues this effort to improve understanding of the CHF phenomenon at LPLV conditions, to extend the experimental data base, and to provide an improved design correlation, by performing experiments with vertical round tubes.

0 0 2 9 - 5 4 9 3 / 9 1 / $ 0 3 . 5 0 © 1991 - Elsevier Science Publishers B.V. All rights reserved

226

S.H. Chang et aL / A study of critical heat flux

2. Background The CHF characteristics would be quite different at low pressure compared with high pressure conditions due to different water properties. Especially vapor-toliquid specific volume ratio at 0.1 MPa is about 1600, which is 260 times that at 15 MPa. This is the primary reason that flow becomes less stable at low pressure. The larger specific volume ratio also results in larger bubbles and therefore different boiling characteristics in channels of relatively small diameter. Significant changes in surface tension and viscosity would also affect the behavior of the liquid-vapor interface. In addition to these pressure effects, low velocity makes the buoyancy effect significant. So the LPLV CHF is a complex phenomenon and systematic interpretation is difficult. In this section, previous works on this subject are briefly reviewed. In late 1950s, Lowdermilk et al. [19] at NACA performed CHF experiments for water flowing in vertical round tubes of small diameter (D < 0.0048 m) near atmospheric pressure including low velocity conditions. They suggested the following empirical correlation for the low velocity region.

development of them. But we should note that only a few experimental data were available until the beginning of 1980s. Attention was also given to the CHF mechanism at zero flow condition (i.e., a vertical channel with complete bottom blockage) by several authors [22-24]. Their works revealed that the CHF mechanism at zero net flow in vertical channels is different from that in ordinary pool boiling and it is limited by the flooding condition except for very small L h / D . Considerable works have been reported for the present subject during the past decade. The most important and comprehensive works are those by Mishima et al. [10-13]. They performed a series of experiments for three different channel geometries: an internally heated annulus, two rectangular channels, and a round tube. Additional CHF experiments for LPLV conditions have been performed by other workers including Rogers et al. for water flow in annuli [14], Sudo et al. for rectangular channels [15,16], EI-Genk et al. for annuli [17], and recently Weber et al. for a short round tube [18]. Important findings can be summarized as follows: (a) The CHF at zero net flow occurs due to countercurrent flow limitation (CCFL) (flooding or flow reversal), which is represented by the following correlation [10,11,23]:

qc =183.9D-O.2(~_~) -°85 G°S5

A for G / ( L h / D ) 2 <_0.2034.

Note that effects of pressure and inlet subcooling are not included in the above correlation. Thereafter Macbeth [20] derived low velocity CHF correlations for water flow inside uniformly-heated round tubes and rectangular channels separately based on the data compiled from world-wide sources. Correlation for round tubes is given as follows:

qc = O . 1 5 0 h f g D - ° l G ° 5 ' ( 1 - X ).

(2)

Griffith et al. [21] suggested a correlation for low flow in the following form: qc = 0.131(1 - a)hfg p~g ~

C2hfg~'PggZlP D

(1)

(3)

Equation (3) is the Zuber's pool-boiling correlation multiplied by the liquid, fraction, (1 - a), and therefore called the modified Zuber correlation. It is used in several reactor safety codes such as RELAP5 and COBRA. Equations (1)-(3) were reported to have reasonable accuracy compared with the data base used for

It generally gives much lower CHF value than the pool-boiling CHF. And the CHF at LPLV conditions is lower than that predicted by conventional low-velocity CHF correlations. (b) The CHF as a function of mass flux shows different behavior between the round tube and the other channel geometries with unheated wall. The CHF is generally higher in round tubes. (c) The less stable the flow is, the lower CHF is observed at intermediate mass velocities. Downward flow is more susceptible to the instability and therefore has lower CHF value than upward flow. Downflow CHF is affected by the inlet subcooling, inlet throttling, and upstream compressibility more than the upflow CHF. (d) Flooding, churn-to-annular flow transition, dryout of liquid film surrounding the vapor plug in slug flow, and dryout of liquid film from annular flow are considered as the possible CHF mechanisms under LPLV conditions [25].

S.H. Chang et al. / A study of critical heat flux Frequently the CHF at LPLV conditions is analyzed using the following dimensionless parameters:

G* = G l {7 p gap ,

(5)

q*=q/(hfgV~),

(6)

D* = D / A ,

(7)

where

(8)

=

Several aspects are known today about the CHF at low pressure and low velocity conditions. However, we cannot find the design correlation which properly covers from the zero flow condition even for water flow in vertical round tubes.

3. Experiments 3.1. Experimental loop A low-pressure experimental loop was constructed to perform various boiling experiments under low pres-

227

sure. Its schematic diagram with normal flow path in upflow tests is shown in fig. 1. The loop consists of a test section, a condenser/cooler, a surge tank, a centrifugal pump, a rotameter assembly, a filter, a preheater, valves and connecting pipings with instrumentation. All parts are made up of Type-304 austenitic stainless steel as far as possible, to minimize the corrosion and to allow easy cleaning. And use of flanged joints is maximized for easy maintenance between experiments. The loop is filled with filtered and ion-exchanged water which was degassed through boiling prior to the experiment. Steam out of the test section is condensed in the condenser/cooler and enters into the surge tank. In atmospheric pressure experiments, the surge tank provides water inventory sufficient to maintain the pump inlet water temperature relatively constant during each series of experiments. An overhead tank installed above the surge tank is used to maintain pressure nearly constant at test section outlet. A centrifugal pump circulates water through the loop. Water flow rate at test section inlet is controlled by the bypass valve (V2) and valves before the rotameters (V3's). Four valves (V4, V6, VT, V8) are used to make possible

OVERHEAD~I~_ TANK VIO~' CONDENSER /COOLER TEST SECTION

City Water

Provision for Downflow Tests SURGE TANK

PREHEATER4---I' FILTER [ ROTAMETER ASSEMBLY,

11 V12 CENTRIFUGAL PUMP

Fig. 1. Schematic of the experimental loop.

228

S.H. Chang et aL / A study of critical heat flux

Thermocouples Copper Thermocouple ~ Electrode Support ,.~_ TC1 TC2 TC3 TC4 TC5 TC6 TC7 TC8

~"-~!

! !

~ _ J J J

!

if_ J

oooo,oo

!

!

l|

J _ff ~_

,oo ,oo ,oo S o

-,,o

,-

(type-K) thermocouples are spot-welded onto the outside of the stainless steel tube. The test section is fixed into the loop with flanged joints and thermally insulated by asbestos ribbon to minimize undesirable heat loss. 3.3. Instrumentation

6mm or 8.8ram-I.D.J Stainless Steel Tube

Fig. 2. Test sections and thermocouples.

both upward and downward flow experiments. Valves just before the test section inlet (V5 or V7) are used to provide inlet throttling. Water is filtered by a 5 ~m absorbent-type filter and preheated to a desired temperature in the preheater before entering the test section. Inlet temperature to the preheater is adjusted by the condenser/cooler and a heater in the surge tank. 3.2. Test sections

Two test sections were used as shown in fig. 2. They are made up of Type-304 stainless steel tube with heated length of 0.72 m. Test Section no. 1 (TS-1) is a 6 mm i.d. and 1 mm thick tube, while Test Section no. 2 (TS-2) is an 8.8 mm i.d. and 0.6 mm thick tube. A copper electrode is welded to each end of the stainless steel tube to transfer the electric power from a 100 V, 700 A dc power supply connected to it. The test section tube and copper electrodes are electrically insulated from the other parts of the loop by teflon rods. For detection of wall temperatures, eight Chromel-Alumel

Test section wall temperatures were detected by type-K thermocouples and analyzed by a data acquisition system consisting of an analog-to-digital converter (ADC), an IBM P C / A T , a strip chart recorder, and a scanning thermometer (Keithley System 740). The ADC and IBM P C / A T processed analog signals from all thermocouples into digital ones, while the scanning thermometer and the strip chart recorder traced the temperature of the location where occurrence of CHF was the most probable. Test section inlet and outlet temperatures were measured by type-T thermocouples with Omega Model 2176A digital indicator. Water temperature at the surge tank and preheater were measured by dial-type thermometers because only approximate values were required. The flow rate into the test section was measured by a rotameter assembly consisting of a 0.01-0.1 l/min, a 0.05-0.5 l / m i n and a 0.25-2.5 l/min, which is located upstream the filter. 3.4. Test conduct

Experiments have been performed for upward and downward flow of water with changing inlet conditions

Table 1 Summary of test conditions. The number in parenthesis indicates the number of data points. Test section

Flow direction

Inlet throttling

Inlet temperature 20 ° C

45°C

70°C

TS-1

Upflow

Large

6UTA1 (23) 0-222 kg/mm2s

6UTA2 (23) 0-222 kg/m2s

6UTA3 (19) 0-233 kg/m2s

TS-1

Upflow

No

6UOA1 (10) 0-210 kg/m2s

6UOA3 (8) 0-210 kg/m2s

TS-1

Downflow

Large

6DTA1 (14) 6-187 kg/m2s

6DTA3 (8) 29-187 kg/m2s

TS-2

Up/low .

Large

9UTA1 (18) 0-119 kg/m2s

9UTA3 (15) 0-108 kg/m2s

TS-2

Down/low

Large

9DTA1 (7) 3-27 kg/m2s

S.H. Chang et aL / A study of critical heat flux such as mass flux, inlet subcooling and inlet throttling. Three values of the inlet water temperature (20 °C, 45 ° C and 70 ° C) were selected to study the effect of inlet subcooling. However, the actual inlet temperature had some variation around the reference values. Ranges of parameters tested in the experiment are summarized in table 1. To reduce the possible non-condensable gas content, the water in the loop was circulated and boiled for about half an hour prior to the experiment. Then the water was cooled to a temperature that the desired inlet temperature could be easily obtained and the valves were set to obtain the desired flow orientation and flow rate. During the experiments, the pressure at the test section outlet was kept nearly constant at 110 kPa by maintaining a constant water level of the overhead tank. A bourdon-type pressure gauge (0.0-1.0 kgf/cm2-gauge) was used to confirm the actual pressure. After setting the water flow and inlet subcooling, the electric power was connected to the test section and increased step by step until the occurrence of the CH F condition. The increment of heat flux between power levels was kept sufficiently small and the measured parameters were stabilized before raising the power level again. The CHF condition was defined as the condition where the maximum wall temperature exceeded 2 5 0 ° C with a trend of rapid increase. This criteria was determined based on the observation that the wall temperature increased sharply to above 400 o C once it exceeded about 250 ° C while below the wall temperature could be maintained with oscillations. Practically use of a temperature greater than 250 ° C as the criteria gave no significant difference in the resuited C HF values. Figure 3 shows the typical change of test section wall temperatures near the CHF condition which were scanned by the IBM P C / A T with an time interval of 1.6 s. Here channel 1 indicates the thermocouple located at the top of the test section, i.e., the tube exit. The heat flux was calculated from the power to the test section and known heated area assuming a uniform heat flux. For each water inlet flow rate and temperature, at least two test runs were conducted and the average of the two CHFs was adopted. The CHF values were generally reproducible to within + 1.5%. The uncertainties of the final CHF data were estimated by considering the contribution of each independent variable affecting the parameter. The estimated uncertainties are as follows: outlet pressure + 1 kPa, inlet subcooling + 5 kJ/kg,

soo /

229

. . . . . . . . . . . . . .

"

t ,ost,o,o.,oo,3-,, 400~/ [

~ +

/

I-

Wall Temp. "P" l t°Cl /

, •-

+ ~

•

Ch. 1 (Top) Oh. 2 Oh. 3 Ch. 4

/ ~

/f

// ]]

ca. 6 Ch. 7

1O0 IJ 0 ~ 0

A--

/7 / \ //,/ \

Step Increaseof Test Section Power

T

5

/

t / 4

%1 I //| ~[

//1 //1 /I

~1

';0 1

10

15

Time Fig. 3. Change of test section wall temperatures near the CHF.

mass flux heat flux

_+ 5%, + 4%.

4. Results and discussion

4.1. Overall behavior o f CHF The overall behavior of CH F as a function of mass flux is shown in fig. 4 for the stable flow condition where flow excursion is avoided and flow oscillation is not large. Here the positive and negative mass flux denote upflow and downflow, respectively. Zero mass velocity means complete bottom blockage or zero net flow at test section inlet. Figure 4 shows almost symmetrical behavior of CHF about the line of zero mass flux, which indicates that the effect of buoyancy is not great for a stable flow. In both upflow and downflow, CHF monotonously increases with increasing mass flux from a minimum value at zero inlet mass flux. This minimum CHF agrees with the flooding-limited CH F correlation given by Eq. (4)with the constant C in the range of 0.97-1.41. The measured zero-flow CH F (30-40 k W / m 2) is much lower than that predicted by the ordinary pool boiling CHF correlation ( = 1000 kW/m2). This is further discussed in Section 4.4. Critical quality decreases as mass flux increases as shown in fig. 5. In fig. 5, the critical quality means the thermodynamic equilibrium quality at tube exit calculated based on the inlet flow condition and heat input which is frequently used in the plot and correlation of CHF data. It approaches to infinity as flow decreases

S.H. Chang et al. / A study of critical heat flux

230 1000

i

i

i

i

i

800

o

eo

1

600

qc [kW/m 2 ]

I

'~A8

400

0

i

-250

I

,

6UTA2

a

6UTA3

o

6UOA1

•

6UOA3

•

6DTA1

•

6DTA3

+

9UTA1

x

9UTA3

•

9DTA1

#6

olk

200

6UTA1

a

I

-200

-100

-150

-50

50

100

150

200

250

G [ k g / m 2 s]

Fig. 4. Overall behavior of CHF.

to zero while the actual flow quality cannot be greater than one even for the zero flow condition. At very low flow condition, the critical quality is very high with considerable scatter according to the test condition.

This indicates that the thermodynamic quality is not a useful measure of the flow condition at the C H F location and the correlation using it is not adequate for this region. However the critical quality merges to a

3.0-

o

6UTA1

+

2.0-

2

Xc[-] .! 1.0+

+

+0+

+

+

-

+

+

0.0

0

o

i

18!

+

i

i

i

i

5O

100

150

200

G [kg/m 2 s] Fig. 5. Trend of critical quality.

250

~,

6UTA2

a

6UTA3

o

6UOA1

•

6UOA3

•

6DTA1

•

6DTA3

+

9UTA1

x

9UTA3

•

9DTA1

S.H. Chang et al. / A study of critical heat flux line for a given test section as mass flux increases. This supports the critical quality concept in consideration of the CHF due to liquid film dryout from annular flow regime [26]. The critical quality is lower in the larger test section (TS-2) as the case of normal liquid film dryout [26].

1000"

OD

800 13

qc [kW/m

4.2. Parametric effects on the CHF data

231

600 2]

io~

400'

Now let us briefly examine the parametric effects found in our experimental data. Note that discussion is confined to the stable flow condition.

O

~o

t o

200

o

o q (6UTA1) t3 q (6UTA2)

o

•

q (6UOA1)

•

q (6UOA3)

O

0

Effect of mass flux The CHF monotonously increases as mass flux increases from zero regardless of the flow direction and inlet throttling for stable condition. The trend is almost linear in the lower flow region but the rate of increase decreases in the higher flow region. The behavior of CHF at near zero net flow is discussed in the subsequent section.

Effect of flow direction When large inlet throttling is provided, the downflow CHF is generally lower than the upflow CHF but the difference is not great (see fig. 6). On the other hand, it was almost impossible to maintain a stable downward flow condition without inlet throttling in our test loop. This indicates that downward flow is much more susceptible to the instabilities and premature CHF due to flow excursion can occur in downflow if such instabilities are not effectively suppressed.

o~

°°8888°

600

[3

qc

13

[kW/m 2 ] 400'

o•

200'

l 0

o|

•

"o| o• O q(6UTA1) o q (6UTA2)

~

•

q (6DTA1)

•

q (6DTA3)

•

i

. . . .

i

100

300

Fig. 7. Effect of inlet throttling.

Effect of inlet subcooling The effect of inlet subcooling is small and obscure in the stable low flow condition under low pressure (see figs. 4 and 5). There is some indication that the effect of inlet subcooling appears when mass flux exceeds about 190 kg/m2s for TS-1, but we could not proceed the experiment to a sufficiently high velocity region due to the limitation of the power supply system. Effect of inlet subcooling is considered to be a useful measure in defining the low flow region under low pressure.

Effect of inlet throttling

Effect of tube diameter

•

• a I~

50

200 G [kg/m 2 s]

D O •

~g~ . . . .

100

Throttling just before the inlet of a boiling channel under low pressure increases the stability of flow, and therefore generally increases the CHF. Its effect on the CHF is known to be small in the very low flow region [12]. It was almost negligible in our experimental range for upward flow condition as shown in fig. 7. It was significant for a down flow condition so that even a stable flow condition could not be established without inlet throttling.

1000

800

i

0

. . . .

j

. . . .

150

G [kg/m 2 sl

Fig. 6. Effect of flow direction.

j

200

. . . .

250

The larger diameter tube gives a higher CHF (see fig. 8) and a lower critical quality (see fig. 4 and 5) for a fixed inlet condition. Higher CHF in a larger tube is general when heated length, mass flux and inlet subcooling are fixed. As a summarizing comment, the behavior of CHF appears to be similar in LPLV conditions regardless of the flow direction, inlet subcooling and inlet throttling as long as a stable condition is maintained.

S.H. Chang et al. / A study of critical heat flux

232

800

1000"

oOD

800"

600

00[] 0

qe [kW/m2 ]

O0 °

ggo

600"

":•8 8

qe

• •

[kW/~ l

0

400

0

400" o [] • •

200"

q q q q

(6UTA1) (6UTA2) (9UTA1) (9UTA3)

S~o 20O

o

//-~o

c~-

Data (9UTA1)

•

Macbeth Lowdermilk et al. Katto

,

0

l

100

o ~

200

300

20

40

G [kg/m2s]

60

80

100

120

G [kg/m 2 s]

Fig. 8. Effect of tube diameter.

Fig. 10. Comparison of data with existing correlations (TS-2, T, = 20°C.

4.3. Comparison with existing correlation Figures 9 and 10 typically show the comparison of our test data with predictions by three existing CHF correlations for tubes: Lowdermilk et al. (eq. (1)), Macbeth (eq. (2)) and Katto [5]. Our data agree relatively well with eq. (1) but are considerably smaller than those predicted by other two correlations except the near-zero-flow region. The agreement with eq. (1) is natural because the test condition is very similar except the tube diameter. The larger discrepancy with TS-2 data indicates that eq. (1) cannot be used for

1000

oo

tubes of diameter much larger than those used in ref. [9] even at atmospheric pressure condition. The lower CHF at LPLV condition compared with the predictions by conventional low velocity correlations are also reported by other workers [10-14], which implies the need for special treatment of low pressure conditions. For boiling in a channel under low pressure, the vapor bubble-to-channel diameter ratio is large compared with the high pressure condition, which might be the primary reason for the lower CHF. In all the three illustrated and most other low velocity CHF correlations, CHF approaches to zero and critical quality approaches to 1 as mass flux decreases to zero. However the CHF increases from the heat flux predicted by the flooding criterion, so it is desirable to develop a correlation reflecting this situation. 4.4. Consideration o f the CHF mechanism at cery low

-

qc

o

eel•city

o

[kW/m2 ]

It is generally accepted that CHF occurs due to the flooding-like mechanism in a vertical channel with complete bottom blockage or extremely low upward flow unless the L h / D is very small. Pool boiling-like CHF could occur in cases of very small L h / D as follows:

4OO UTA1 ) /~'o /,~o o

200

0

~

Macbeth Lowdermdk et aL Katto

• •

,

0

50

100

150

200

250

qcP =

Khfg~rgAp

.

(9)

G [kg/m2 e] Fig. 9. C o m p a r i s o n of d a t a with existing c o r r e l a t i o n s ( T S - I ,

T~= 20 ° C).

The transition point can be estimated by finding the condition qcF = qcP, under the assumption that CHF at

S.H. Changet al. / A study of critical heat flux zero flow occurs by either of the two mechanisms which comes first: K[1 A~/-D

4

2

t

10)

C24~2~-/,~

A.

If we apply K = 0.118 (value for a vertical flat plate) and C = 1, the following threshold Lh/D is obtained as a function of diameter for a vertical round tube under atmospheric pressure:

( L / D ) = 31.6v~-.

(11)

The threshold length-to-diameter ratio is obtained as 2.45 and 2.96 for 0.006 and 0.0088 m tubes, respectively. Therefore flooding-limited CHF would occur at zero net flow condition for our test sections. Flooding-limited CHF can also occur at non-zero upward flow conditions, if the mass flux is sufficiently low so that counter-current flow can be established [24]. General expression for the flooding-limited CHF including non-zero flow conditions is derived in the Appendix, which also gives the maximum mass flux for flooding condition (GMax) and the corresponding CHF (qcF,Max)"

The measured CHF near zero flow condition is illustrated in fig. 11 for TS-2. The CHF at zero flow is predicted by eq. (4) with average C of 1.27 and 0.98 for TS-1 and TS-2, respectively. This variation of C is understandable considering that the Wallis correlation was developed mainly based on the air-water flow data in larger diameter tubes. Considering the trend and

140 120 .

100.

qc 80 [kW/~ 1 60. 40. • 9UTA3 --.o--9DTA 1

20, 0

i

5

10 G

15

[kg/m2s]

Fig. 11. CHF at very low flow rate (TS-2).

20

233

location of CHF occurrence (i.e., upstream CHF for flooding), G Max can be observed experimentally. It lies in the range of 5.8-11.7 kg/m2s for TS-1, and 5.4-8.1 kg/m2s or 8.1-10.8 kg/m2s for TS-2. The measurements generally agree with those predicted by eq. (All); 9.8 kg/m2s and 7.0 kg/m2s for TS-1 and TS-2, respectively. The change of upflow CHF behavior near GMax is clearly shown in fig. 11, whereas it is not clear in the qc-G plot for TS-1. The location of CHF occurrence is another interesting parameter. The CHF condition always occurred first at the tube exit except the cases of G < GMax and two data with TS-2. Upstream CHF with relatively high velocity occurred at only two mass fluxes of 76 and 87 kg/m2s for the inlet condition Ti = 70°C. In these cases, the quality at the CHF location is estimated to be about 0.45.

5. Correlation for LPLV condition

5.1. General considerations In this section, we examine the presently available steady-state LPLV CHF data and develop a correlation which can be applied to the stable flow in uniformlyheated vertical round tubes. The experimental data used are from: KAIST (in this experiment), Lowdermilk et al. [19], Firstenberg et al. [17], Becker et al. [28], Mishima [29] and Weber and Johannsen [18]. Examination of the data suggests us the following aspects of CHF at low pressure and low flow conditions: (a) CHF approaches qcF when G decreases to zero. (b) CHF is an increasing function of G. (c) CHF is a decreasing function of Lh/D. For given L h / D , CHF decreases as D increases. (d) Effect of inlet subcooling on the CHF is negligible. (e) Dimensionless quantities G* and q* reflect the effect of pressure relatively well. (f) The local condition-type correlation using the thermodynamic equilibrium quality is not adequate for the LPLV CHF. It is important but difficult to define the low pressure and low velocity condition. We cannot find any literature that adequately defines the boundary of the LPLV region. But the present authors' other work [9] suggests that it lies between 500-1000 kPa for the low flow and high quality condition. For definition of the low-flow region, the effect of inlet subcooling might be used as a measure though not fully grounded. It gives

S.H. Chang et al. / A study of criticalheat flux

234

a r o u n d 200 k g / m 2 s for several e x p e r i m e n t s [12,14,17 and p r e s e n t work]. In this work, we arbitrarily choose the data in the following range: P_< 1100 kPa, G _< 250 k g / m 2 s , a n d D >_ 0.003 m.

5.2. Correlation development

T h e r e are two p r o b l e m s in d e t e r m i n i n g the constants. O n e p r o b l e m is that the c o n s t a n t in the flooding equation, C, seems to considerably vary test section by test section a r o u n d 1. T h e o t h e r p r o b l e m is that the e x p o n e n t of I G * I, C4, is not a constant but a decreasing function of PG * I. In the p r e s e n t study, we take the average of all the available data for C and provide the following two correlations according to I G * I.

Based on the above discussions a n d preliminary assessment, the following dimensionless form of C H F correlation a p p e a r s to be most promising.

qc~-- qcF* +

q* = qc*F+ C,( D* )C2( Lh/D)C" IG* I C4.

q*H = qc~" + 0 . 0 5 6 6 4 ( D * )

(12)

This is the same form as eq. (1) except the use of dimensionless p a r a m e t e r s a n d the inclusion of the flooding-limited C H F for zero flow. A b s o l u t e value of G * is a d o p t e d to include the downflow data. For d e t e r m i n a t i o n of constants in eq. (12), we d e t e r m i n e the c o n s t a n t C in the flooding-limited C H F correlation at first based on the zero flow data from the p r e s e n t e x p e r i m e n t s and M i s h i m a et al. T h e n the constants CI-C 4 are d e t e r m i n e d t h r o u g h multiple regression of experimental data.

O.O1351(O*)-°a73(t/O) -°'5331G.1''45

for very low I G * I,

(13)

°247(L/D)-°5°l G * po.77,,

for higher I G * l,

(14)

where

qc*v= 1.61(A/Ah) DV/-~-/[1 + (Pg/Pf)'/4] 2

Practically we use the lower of C H F values predicted by eqs. (13) a n d (14) as follows: qc* = T h e lower of [qc*L, qc*H].

Table 2 Comparison of the proposed correlation with experimental data Reference

No. of data

Mean error (%)

RMS error (%)

Remarks

Becker et al.

98

-9.0

21.1

P > 316 kPa, D --- 0.00l m L h / D = 10-114, Up

Firstenberg et al.

67

+ 5.4

24.2

P = 103.690 kPa D = 0.003, 0.0239 m L / D = 10-92, Up

KAIST(TS-1)

105

+ 6.0

14.0

P = 110 kPa, D = 0.006 m L / d = 120, Up/Down

KAIST(TS-2)

40

+ 13.9

25.6

P = 110 kPa, D = 0.0088 m L / D = 82, Up/Down

Lowdermilk et al.

46

+ 3.1

26.3

P = 101 kPa, D = 0.0031-0.0048 m L / D = 25-250, Up

Mishima

84

-7.5

12.5

P = 101 kPa, D = 0.006 m L / D = 57, Up/Down

Weber & Johannsen

51

+ 7.2

21.5

P = 110-1000 kPa D = 0.0097 m L / D = 4.47, Up

491

+ 0.5

20.1

Total

(lS)

(16)

S.H. Chang et al. / A study of critical heat flux 0,6

~ - -

data and the results are shown in table 2 and figs. 12 and 13. The present correlation scheme agrees well to the data with reasonable RMS error of 20.1%. Table 2 indicates that the correlation does not predict well the data with TS-2 of the present work. However the resulted error is mainly due to the data at near zero flow and all the other data of [ G * I > 3.0 are predicted fairly well. This indicates the need for further improvement of the flooding correlation. It should be noted here that the present correlation is applicable only to the condition that the supply of cooling water from the top is not prevented in case of the very low upward flow.

m

0.5 0.4 +~

qc ICor) 0.3

- 30%

0.2 ÷ 4-

÷

.

0.1 0.0 0.0

,

+

i

,

i

0.1

0.2

I

I

0.3

I

0.4

0.5

0.6

qc ( E x p )

6. Conclusion

Fig. 12. CHF (prediction) versus CHF (experiments). The ranges of experimental data used in the correlation development are summarized as follows: pressure (P): 100-1098 kPa, diameter (D): 0.00305-0.0239 m ( D * = 1.218-9.545), length-to-diameter ratio ( L h / D ) : 4.47-250, mass flux (G): - 2 3 1 - + 250 kg/mEs (G* = - 66- + 68), critical heat flux (qc): 30-6600 k W / m 2 (q* = 0.0034-0.402).

5.3. Assessment o f the correlation The proposed correlation in the form of eq. (16) with eqs. (13)-(15) is assessed using the experimental

2.0 ,

+

+

1.5 + t

. ~

+

+

+

q~ m qc

+

+

+

+

. ~~ - +

*

¢

++.

+

:~+

+

+

+

~ :t ~

+30%

(Cor) 1.0

+

(Exp)

+

+

+~

++

+

+

- 30%

÷

0.5 0.0

I

20

I

40 G* [-]

235

I

60

Fig. 13. Accuracy of prediction versus G *.

80

In this work an experimental study has been performed for the stable CHF of water in vertical round tubes under low pressure and low velocity conditions. In addition, the CHF mechanism at very low region is discussed and a new CHF correlation is proposed. Important points are as follows: (a) The behavior of CHF in a vertical round tube appears to be similar in LPLV conditions regardless of the flow direction, inlet subcooling and inlet throttling as long as stable condition is maintained. (b) The measured CHF is generally lower than those predicted by existing low velocity correlations developed primarily based on the high pressure conditions. This indicates the need for special treatment of low pressure conditions. (c) The critical heat flux at near zero flow is predicted well by the Wallis correlation. The derived maximum mass flux for flooding agrees with the measurements. (d) The proposed correlation predicts the CHF for stable water flow in vertical tubes at LPLV conditions with reasonable accuracy. More experiments are required for extension of the data base, identification of mechanisms and clarification of the parametric effects including the pressure and geometrical effects. In addition, recommended are the efforts to determine the boundary of the LPLV condition and to improve the flooding correlation for the boiling channel.

Appendix. Derivation of the flooding-limited CHF and m a x i m u m m a s s flux for flooding

In this Appendix, we derive the expressions for the flooding-limited CHF and the maximum upward mass

S.H. Chang et aL / A study of critical heat flux

236

flux for which flooding can occur, based on the simple flooding correlation by Wallis. Wallis flooding correlation is given as

Equation (9) is the same as eq. (4) in section 2, which was derived for the zero flow condition. Maximum value of the flooding CHF is obtained as follows:

J~* + jVt~-f*= C ,

qcF.Ma× = ( A /Ah )CZhfg(PggAP D ,

(A1)

where

(A10)

at

j~ = jgf~g/gap D ,

(A2a)

GMax = qAh/hfgA = C 2 ~ g g A p D .

j~ = j f ~ f / g A p D .

(A2b)

Here GMax is equivalent to the maximum mass flux for counter-current flow as shown below. Counter-current flow can be established only when liquid flow is negative. This means the condition that total mass flux is less than the vapor mass flux generated by heat input. Using eq. (A7),

Squaring eq. (A1), we obtain

+ ~)2

j*(1

= C2.

(A3)

(A11)

Mass balance in counter-current flow condition:

G = pgjg - pfjf,

(A4)

where positive jf means downward liquid film flow. Therefore we obtain

jf/jg = pg/pf -- G / p f j g .

Ahq G
(A12)

Therefore eq. (A12) is equivalent to eq. ( A l l ) .

( A5) Nomenclature

Volumetric flux of vapor is calculated from heat balance as follows:

jg =

- ~ - q - GAh i .

(A6)

When G is very small, eq. (A6) is reduced to jg

Ahq Apghfg

.

(A7)

Substituting eqs. (A2), (A5) and (A6) into eq. (A3), we obtain the following implicit form of the flooding CHF:

qcF =

] 2"

(A8) For given P, G, and test section geometry, the flooding CHF can be calculated by iteration. Equation (A8) gives minimum value for the special case of G = 0,

A C2hfgf~ggAp D + ~ ) q c F ( G = O ) = ~ h × [1 4 2 "

Jf Jg Lh P q

( A/Ah)C2hfgffiggApD [1 + ~ / 1 - ( a / A h ) ( h f g G / q c F )

A Ah C D D* G G* g hfg Ahi

(A9)

qc qcv qcP q* X

flow area of a channel, m 2, heated surface area, m 2 constant in Wallis correlation for flooding, diameter, m, dimensionless diameter; D/A, mass flux, kg/mZs, dimensionless mass flux; G~ Afi-~ggAp, gravitational acceleration, m / s 2, latent heat of vaporization, kJ/kg, inlet subcooling, kJ/kg, superficial liquid velocity; G(1 - X ) / p f , m / s , superficial vapor velocity; GX/pg, m / s , channel heated length, m, pressure, kPa, heat flux, k W / m 2, critical heat flux, k W / m 2, flooding-limited CHF, k W / m 2, pool boiling CHF, k W / m 2, dimensionless heat flux; q / ( h f g ~ g z l p ), thermodynamic equilibrium quality calculated based on the inlet condition and heat input;

X = (Ahq/AGhfg) - (Ahi/hfg), Xc

critical quality.

Greek symbols a ?t

void fraction, Taylor wave length scale; vr~/gAp, m,

S.H. Chang et al. / A study of critical heat flux P Ap O"

density, density phases; surface

k g / m 3, difference b e t w e e n liquid a n d v a p o r p f - pg, k g / m 3, tension, N / m .

Subscripts f g fg

s a t u r a t e d liquid, s a t u r a t e d vapor, difference b e t w e e n s a t u r a t e d liquid a n d v a p o r phases.

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