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Pressure drop with highly subcooled flow boiling in small-diameter tubes
ELSEVIER
Pressure Drop with Highly Subcooled Flow Boiling in Small-Diameter Tubes Wei Tong* Arthur E. Bergles Michael K. Jensen Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
• Pressure drop may be the most important consideration in designing heat-removal systems utilizing high-heat-flux subcooled boiling. In this study, an experimental investigation was performed to identify the important parameters affecting pressure drop across small-diameter tubes in highly subcooled flow boiling. The effects of five parameters--mass flux, inlet temperature, exit pressure, tube internal diameter, and length-to-diameter ratio--on both single- and two-phase pressure drop were studied and evaluated. Experiments were carried out with tubes having inside diameters ranging from 1.05 to 2.44 mm. Mass fluxes ranged from 25,000 to 45,000 k g / ( m 2 s), exit pressures from 4 to 16 bar, and inlet temperatures from 22 to 66°C. Two length-to-diameter ratios were tested. These conditions resulted in critical heat flux levels of 50-80 M W / m 2. The experimental results indicate that mass flux, tube diameter, and length-to-diameter ratio are the major parameters that alter the pressuredrop curves. Both single- and two-phase pressure drops increase with increasing mass flux and length-to-diameter ratio but decrease with increasing internal diameter. Inlet temperature and exit pressure have been shown to have significant effects on two-phase pressure drop but very small effects on single-phase pressure drop. These results agree well with those from other investigations under similar conditions. As a result of this study, pressure-drop correlations are presented for predicting both single-phase and subcooled boiling pressure drop in small-diameter tubes under different heat-flux conditions. © Elsevier Science Inc., 1997
Keywords: pressure drop, subcooled flow boiling, water, small-diameter tubes, critical heat flux
INTRODUCTION Subcooled flow boiling has been recognized for several decades as one of the most effective heat-transfer modes. In studies of subcooled boiling, much effort has been devoted to the critical heat flux (CHF) condition owing to its importance in a wide variety of industrial applications, including supercomputers, high power laser optics, engine turbines, heat exchangers, plasma-facing components in fusion reactors, and so forth. However, pressure drop, which is strongly coupled to the C H F conditions; is somewhat overlooked by many investigators. In practice, the pressure-drop increase is usually a crucial factor that limits attempts to increase the C H F by increasing fluid velocity. A fundamental study of pressure drop not only enriches our knowledge of subcooled boiling heat transfer, but also helps our understanding of the C H F mechanism.
Experiments have shown that C H F of subcooled flow boiling through uniformly heated tubes is mainly affected by five variables: mass flux, inlet subcooling, exit pressure, tube diameter, and length-to-diameter ratio. Furthermore, it has been reported that, under certain circumstances, a test section can burn out at very low heat-flux levels [1-5]. This phenomenon, known as premature failure (or premature burnout), has constrained the use of subcooled boiling as a cooling technique. Several investigations have suggested that premature failure could result from system-induced instabilities and is closely associated with the pressure drop of the test section. Styrikovich et al. [1] were the first to point out that the presence of oscillations of pressure and flow rate can have a marked effect on the values of CHF. Bergles [2] carried out an experimental investigation of flow boil-
*Currently with Babcock & Wilcox, Naval Nuclear Fuel Division, Lynchburg, VA 24505. Address correspondence to Professor A. E. Bergles, Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590.
Experimental Thermal and Fluid Science 1997; 15:202-212 © Elsevier Science Inc., 1997 655 Avenue of the Americas, New York, NY 10010
0894-1777/97/$17.00 PII S0894-1777(97)00018-6
Pressure Drop with Highly Subcooled Flow 203 ing with water in small-diameter tubes. It was found that an upstream compressible volume can cause flow oscillations, which result in premature failure. Other studies have suggested that the parallel channel excursive instability and upstream compressible volume oscillatory instability are associated with a minimum in the pressure drop-flow rate curve; that is, a(AP)/aG = 0. System-induced instability of either the excursive or the oscillatory type may limit the maximum heat flux to a value well below the stable critical heat flux [3-5]. An analytical prediction of the initiation of system-induced instabilities was performed by Maulbetsch and Griffith [6]. In their study, the stability criteria were found to be dependent on the critical slope of the overall pressure-drop-versusmass-flow-rate curve. The comparison between the analytical model and the available experimental data, including those of Styrikovich [1], demonstrated good agreement. More recently, Vandervort et al. [7] reported premature burnout data of small-diameter stainless steel tubes. In their experiments, more than two-thirds of all tests with the diameters of 1.8 and 2.44 mm resulted in premature failure, with no discernible dependence on the five primary parameters. The general behavior of pressure drop for low pressure, straight pipe flow under a varying, uniform heat flux is shown in Fig. 1. At low heat-flux conditions, the flow is single-phase over the whole tube length. Pressure drop decreases with an increase in heat flux owing to a decrease in the near-wall fluid viscosity. Increasing heat flux leads to an increase in the wall temperature. As the wall superheat, Tw - Tsat, reaches some critical value, boiling occurs near the tube exit, and, consequently, a thin bubbly layer builds up on the heated surface. As a result, pressure drop starts to increase. Continuously raising the heat flux causes the movement of the incipient boiling point toward the flow inlet and boiling generation near the exit. Therefore, two-phase pressure drop (including both single-phase and subcooled boiling pressure drop) increases owing to the increase of void fraction, until the te*st section burns out at the CHF point. It has been' found that premature failures often accompany the transition from boiling incipience into nucleate boiling near
i
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CHF --~
&P
ONB
BD
Sh~l©-Pha~ [ _
Two-Phase
'-1
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q" Figure 1. General behavior of single- and two-phase pressure drop. ONB, onset of nucleate boiling; BD, bubble departure.
a(AP)/aq" = 0 [7]. This transition is thus defined as the "danger zone." Hence, the pressure drop can serve as an indicator to determine stable CHF or premature failure. Studies of pressure drop in subcooled flow boiling can be generally classified into two categories. The first category deals with the pressure gradient along the tube length direction. Various empirical correlations have been proposed to predict the ratio of the two-phase pressure gradient to single-phase pressure gradient (or shear stress ratio) for water flow [8-11]. However, because these correlations were mainly based on the operating conditions of light water reactors, they may not be applicable to small flow area channels. Hoffman and Wong [12] developed a semiempirical model for the prediction of the pressure distribution along the tube in subcooled flow boiling. This model, covering the single-phase and fully developed boiling regime, includes the effects of nonequilibrium quality and property variations. The pressure drop predicted by this model was compared with more than 100 experimental runs and was found to agree within approximately 20%. A pressure-gradient correlation for refrigerants was reported recently by Hahne et al. [13]. The second category is to investigate the effects of the test-section geometry and thermal-hydraulic parameters on pressure drop across the test section. Dormer and Bergles [5] were among the first to present results of pressure drop in subcooled flow boiling through stainless steel tubes of diameter less than 5 mm at low pressure. A "chart" correlation was proposed for small-tube diameters (1.57-4.57 mm) with different thermal-hydraulic conditions. Recently, this problem was investigated experimentally by Inasaka et al. [14] for tube diameters of 1 and 3 mm. The experiments were conducted at nearly ambient pressure, whereas mass flux varied from 7000 to 20,000 kg/(m 2 s). The pressure-drop ratio of subcooled flow boiling to nonheating water flow was examined. The results for 3-mm diameter tubes were found to agree with the Dormer-Bergles correlation [3]. However, experimental data and correlations for the pressure-drop dependence on various parameters are still rather limited in the literature so far. For regular subcooled boiling flow through a uniformly heated tube, three flow regimes can be generally identified: single-phase 'flow, subcooled boiling, and saturated boiling [12, 13]. However, under high mass flux and high exit-pressure conditions, subcooling at the flow downstream is so high that the flow may never reach the saturated boiling regime. Owing to strong condensation, the void fraction is rather small, even at the tube exit. This heat-transfer mode, which is the focus of the present study, is defined as highly subcooled flow boiling to distinguish it from regular subcooled flow boiling. The objective of this study is to investigate the effects of five parameters--mass flux, inlet temperature, exit pressure, tube internal diameter, and length-to-diameter ratio - - o n both single- and two-phase pressure drop in highly subcooled flow boiling. The tube internal diameters used in this investigation were: 1.05, 1.38, 1.80, and 2.44 ram. Two length-to-diameter ratios (25 and 50) were tested. Wide range of mass fluxes [25,000-45,000 kg/(m 2 s)], inlet temperatures (22-66°C), and exit pressures (4-16 bar) were considered and examined. These conditions resulted in high CHF levels of 50-80 M W / m 2.
204 W. Tong et al.
I
Vent
Heat Exchanger
2kW
Bypass
] Dernineralizer
Test Dissolved Gas Measurement
[]Filter Bypass
Prehcater Pump
Filter Flowtr~ter
I
t"
.7kWx3 l llOkW
_1Each
Relief Valve
t t
(~) Control valve Ball valve
t~ Pressurerelief valve (~ Thcrmocouple (~) Pressure transducer Figure 2. Diagram of experimental apparatus. EXPERIMENTAL SETUP
Experimental Apparatus and Test Section The experimental apparatus used in this investigation consisted of a water loop, a temperature-controlling and deionizing system, and a dc power supply, as shown in Fig. 2. Water flowed upward through the test section and was transported by a diaphragm pump with a digital speedcontrolling regulator. The inlet bulk temperature was regulated by using both electric heaters and a heat exchanger. The deionizing system, including an ion exchanger and a filter arranged in series, was used to purify the distilled water. A series of bypasses and valves was designed to control the flow rate and exit pressure of the test section. The test section was uniformly heated (Joule effect) by means of a 100-kW thyristor-controlled transformer-rectifier, with a smoothly controlled current of 0-2500 A and a dc voltage of 0 - 4 0 V. To minimize electrical measurement uncertainties, current was measured though a 0-600-A, 50-mV shunt, and voltage was directly measured across the test section. The resulting uncertainty for current was _+2.5% and for voltage was ± 0.02% of reading. The test section was made 304 stainless steel tubing, with two brass bushings as the power connectors (Fig. 3). All exterior surfaces were covered with glass fiber insulation to minimize convective heat loss. Pressure taps were situated at the inlet and exit of the test section. In an effort to prevent premature burnout, a flexible structure was designed to connect the test section to the loop piping. The inlet and exit fittings were threaded directly to heat-resistant Teflon couplings to secure electrical insula-
tion. In an effort to eliminate or minimize system-induced flow instabilities, a large pressure drop (10-30 bar) was set across a throttle valve directly upstream of the test section. Experimental Procedure Noncondensible gases dissolved in water have been reported to affect the boiling process [15]. To eliminate any dissolved-gas effect on pressure drop, the distilled water was degassed before each experiment. The degassing was accomplished by vigorous boiling and venting in the water tank for a 1-2-h period. In the process, water was circulated periodically through the water loop. When degassing was completed, the system was adjusted to the desired operating mass flux, inlet temperature, and exit pressure. As steady-state was attained, power was added to the test section. The power input was initially set at a very low value ( < 0.2 kW) and increased by small increments. Several sets of data were taken at each equilibrium condition to detect any possible transient effect on pressure drop. The reading at each heat-flux level was chosen when all controlled variables were within the allowed uncertainties. In this investigation, the experimental uncertainties were controlled to the selected operating values as mass flux, + 1%; inlet temperature, _+5%; and exit pressure, _+3%.
Parameter Measurement A modular computerized data acquisition system was used to collect data in all runs. The main instruments of the system include an HP-3497A data acquisition controller,
Pressure Drop with Highly Subcooled Flow 205
Brass now
Bushing
Silver /Solder
Lh
-
Inlet Pressure Tap
L.,2~
Exit Pressure Tap Lt
=
Figure 3. Test-section geometry.
an HP-3457 digital multimeter, and an HP 9000/300 computer. This system has the capability of measuring 60 thermocouples and 25 general instrumentation readings. The data acquisition and reduction programs were written in HP Basic 5.1 and were developed specifically for the control and collection of data in the present experiments. Pressure drop across a test section was measured by a Validyne DP15 differential pressure transducer, operating along with a CD15 carrier demodulator for signal amplification. The instrument diaphragms could be changed to cover a wide range of pressure-drop measurements. In an effort to make precise pressure measurements, pressures at the inlet and exit were monitored individually by both an Omega pressure transducer and a pressure gage. All transducers were calibrated by using a dead-weight tester. The uncertainty of pressure-drop measurement was less than _+1.0% of reading. One of the three turbine flowmeters, with measuring capacities of 0.0631 to 1.00, 0.95 and 87.5, and 25 to 1562 cm3/s, was used to measure the volumetric flow rate through the test section. These flowmeters were carefully calibrated to ensure that the experimental uncertainty was within +_0.5% of reading. The mass flux was calculated by the measured volumetric flow rate, water density, and flow area. Temperature measurements were made by applying copper-constantan thermocouples, which were inserted through plastic couplings at approximately the midpoint of the water flow. The measurement errors associated with these thermocouples were within +0.1°C. The conversion of the thermocouple output to temperature was made by using calibration correlations. A Kaye ice-point reference, with a repeatability of + 0.02°C, was used. The heat flux was calculated on the basis of the total power input and the tube inner heated surface. The uncertainty of the heat flux was estimated to be + 6.0% for D i n = 1.05 mm and +-4.0% for D i n = 2.44 mm. The power input was computed by evaluating the product of the measured current and voltage applied to the test section: /~
(1)
= V/.
The electrical power dissipation was checked by comparison against the enthalpy gain rate for a single-phase flow with the equation
= GAcp(T,
-
Ti) ,
(2)
where A is the flow cross-sectional area. The relative difference between the values obtained with Eqs. (1) and (2) was generally less than +_5% and, in most experiments, less than _+3%. This method is unreliable for two-phase flow, because thermocouple readings are affected by the bubbles. Data
Reduction
As shown in Fig. 3, the total length between the two pressure taps is the sum of the heated and the adiabatic lengths. Thus, the measured total pressure drop can be considered the sum of the pressure drop of the heated section and the pressure drop of the adiabatic section; that is, APt = Ap h + A p a. (3) When boiling occurs near the exit at high heat fluxes, Ap~ becomes a sum of two components: the single-phase adiabatic pressure drop at the inlet, A Pa, 1~, and the two-phase adiabatic pressure drop at the exit, APa,2~, where =
G2
fl~
A Pa, 14'
2p i
(Din/La,I¢~)'
G2
f2,
A Pa' 2¢~
2p e (Din/La,2¢~)'
(4)
(S)
where fl~ and f2~ are the single-phase adiabatic friction factors, respectively. Because the void fraction is very small for highly subcooled boiling, quality is not taken into account in Eq. (5). Note that both A P a , ld, and A P a , 2 4 , affect the thermal field (temperature profile) but not the flow field (velocity profile). The hydrodynamic entrance and exit effects are determined by the entrance length (from the tube inlet to the inlet pressure tap) and the exit length (from the exit pressure tap to the tube exit), respectively. The single-phase friction factor, fl~, can be easily obtained experimentally, and the two-phase friction factor, f2~, can be calculated approximately by using the Blasius equation [16]: f2~ =
0.316 Re -°25,
(6)
where Re = G D i n / / ~ l . Thus, the pressure drop across the heated tube length is obtained by subtracting the two adiabatic pressure drops from the measured total pressure drop.
206
W. Tong et al.
Although the direct uncertainty of Eq. (6) is unknown, Bowers and Mudawar [17] reported that, on the basis of calculated values by Eq. (6), the predicted total pressure drop, which is the sum of the pressure drop in single-phase, boiling, and outlet sections of the channel, is characterized by a + 30% error band (including uncertainties from all parts) with experimental data. The equation should be quite adequate for the small correction in the outlet pressure reading. RESULTS AND DISCUSSION Adiabatic
Single-Phase Friction Factor
Performing single-phase tests has a twofold objective: (1) to validate the experimental apparatus and data acquisition system and (2) to obtain adiabatic single-phase friction factors for the data reduction and the single-phase pressure drop correlation. The single-phase adiabatic friction factor is calculated from the measured total pressure drop and mass flux as
Ap, fa,l~,
=
(G2/2~)(Lt/Din)
(7)
The variations of fa, 1~ with Reynolds number for tubes of different diameters are given in Fig. 4. The comparison between the present experimental data and those calculated from well-known correlations (for smooth circular tubes) shows reasonable agreement. Because of surface roughness, the measured data are higher than the predicted values at high Reynolds numbers. It can be seen from Fig. 4 that, at low Reynolds numbers, the transitions from laminar to turbulent flow occur randomly as the tube diameter varies. With the use of a standard least-square curve-fitting technique, adiabatic friction factor data can be correlated in the form of (excluding the transition parts from the database) fa = a Re b (8)
Table
Coefficients in Eq.
1.
(8)
Din (ram)
a
b
1.05 1.38 1.80 2.44
0.218 0.218 0.148 0.106
- 0.201 - 0.201 -0.170 - 0.103
where a and b are constant (Table 1). Bhatti and Shah [24] and Olsson and Sund6n [25] pointed out that the performance of small-sized tubes (usually for Din < 2 mm) in single-phase turbulent flow is not similar to that of large-sized tubes. The turbulent eddy mechanism for fluid flow and heat transfer is suppressed by the tube internal diameter, resulting in lower friction factors and heattransfer coefficients. The present experimental results have confirmed such a trend. Analysis of the experimental data leads to five fundamental effects on single- and two-phase pressure drop. These effects are presented and discussed in the next sections.
Mass-Flux Effect As mass flux increases, pressure drop increases, owing to the shear-stress enhancement on the wall. In Fig. 5, pressure drop is plotted against heat flux under different mass fluxes. To eliminate the uncertainties, including fabricating uncertainty, tube geometry uncertainty, and material uncertainty, introduced by the use of different test sections, all experiments for the mass-flux effect were performed by using the same test section. Because each test section was used only three times at most, there is no fouling problem. In addition, the water-purity subsystem was used in all experiments. Each experiment stopped when heat flux was very close to CHF (identified by the "boiling sound"), and the test
lO-I . . . . . .
I
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o []
' Di~ '= 1. 0 5 ' m m ' D~ = 1.38 mm
'
Dia = 1 . 8 0 m m Din = 2 . 4 4 m m
• v
- -
McAdams [ 18 ]
~-.~.-:-£~o
- - -- --
Blasius, [19] Filonenko [ 20 ]
-n=-..._~o,~_o
------ Colebrook, [211
~ ~ - - ~ . ° ° O o o ^
o
~
~
o
oo
0 rtVVV"
[]
[22]
". . . . . . . . .
Tcchoetai.
....
Whiteq[23]
-'"
•0
O
v v
[]
Figure 4. Comparison of experimental singlephase adiabatic friction factor with correlations.
I 1 0 -2 3 x 10 3
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lOs
l O4
Re
Pressure Drop with Highly Subcooled Flow 207 is normalized by the saturated heat flux at the tube exit, tt qsat, GcpDm q's't 4L-""'~(Tsat'e - Ti)' (9)
6.0 o
z
G = 25,000 kg/m2-s G = 35,000 kg/m2-s G = 45,000 kg/m2-s
v
z
z
5.0
~A
A~ A
where T~t,~ is determined by the exit pressure, and Cp is evaluated at the average temperature of T~at,~ and T i. From Fig. 6, it can be seen that, though the Dormer-Bergles correlation was based on somewhat different conditions (listed in the caption), the measured data at all mass fluxes agree well with the correlation. The test section burned out at A P / A P a -~ 1.
~ A
AP
zx
1~ A
4.0
CHF
\
(bar)
v V
vv
3.0 ~VVV
Exit-Pressure Effect
V VVVVVV
The effect of exit pressure on pressure drop is given in Fig. 7, which shows that the single-phase pressure drop is completely independent of exit pressure (as expected), but the two-phase pressure drop is significantly affected by exit pressure. The reason is that, for a single-phase flow, the exit pressure has nothing to do with flow patterns and temperature field. However, as the flow turns into twophase, a higher exit pressure always gives a higher subcooling, which causes a higher condensation of the bubbles. At very high pressure conditions, most bubbles condense and disappear in the core of the fluid flow, thus leading to a lower pressure drop.
Dm = 1.05 mm
2.0
Ti = 26.5*(2 P~ = 6.2 bar L,/D~ = 24
OO ° O ~
1.0
0
i
0
0 O0
,
,
0
I
o°
i
i
O0 0
t
20
I
,
i
i
40 q"
I
,
i
,
60
I
,
,
,
80
100
( M W / m 2)
Figure 5. Effect of mass flux on pressure drop.
section burned out at the last run. The results show that a higher mass flux results in a higher pressure drop for both single- and two-phase flows. For instance, as mass flux increases from 25,000 to 45,000 k g / ( m 2 s), the pressure drop increases by a factor of 3. The present experimental data were compared with the Dormer-Bergles "chart" correlation [3] terms of dimensionless quantities (Fig. 6). The measured pressure drop is normalized by the measured adiabatic single-phase pressure drop attained at q" = 0, A P v and the actual heat flux
1.4
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1.2
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I n l e t - T e m p e r a t u r e Effect Changes in the inlet temperature affect the inlet subcooling to the test section and the subcooling along the test section. For single-phase flow, decreasing the inlet temperature results in a higher fluid viscosity, which is associated with a higher pressure drop. For boiling two-phase flow, reducing the inlet temperature results in stronger condensation in the core region and, thus, makes a lower pressure drop for a given heat flux (Fig. 8).
'
'
'
G = 25,000 kg/mLs
v o --
'
/
G = 35,000 kg/m2-s G = 45,000 kg/m2-s Donner and Bergles [3 ]
/ / / o
//o AP
1.0
0.8 Din = 1.05 mm
T i = 26.5°C
0.6
Pe = 6.2 bar
Lh/Dm = 24 0.4
0.0
0.1
0.2 g
0.3 w
q /. q~t
0.4
Figure 6. Comparison of experimental pressure-drop data with Dormer and Bergles correlation. Dormer and Bergles: Din = 1.57 mm, Ti = 23.9°C, G = 3000-15,000 kg//(m 2 s), Pe = 2.0-5.52 bar, Lh//Oin = 25.
208
W. Tong et al. 2.5
have a thinner boundary layer (or the bubbly layer for boiling two-phase flow), they have higher velocity gradients and, in turn, higher pressure drops. The effect of tube internal diameter on pressure drop is shown in Fig. 9.
I
P~ = 4.3 bar P, = 15.4 bar
Length-to-Diameter-Ratio Effect 2.0 -
9 CI-IF
AP
\ V
(bar)
0
v
0
0
v
0 v
0
1.5
OV
VV
Din= 1.18 nun G = 30,000 kg/m2-s Ti = 23oc L h / D i . = 24 1.0
I
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I
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I
I
20
0
I
I
I
40
60
(MW/m2)
q"
Figure 7. Effect of exit pressure on pressure drop. T u b e - D i a m e t e r Effect According to the boundary-layer theory, the total apparent shear stress (a sum of the turbulent and viscous shear stress) is directly proportional to the velocity gradient perpendicular to the flow direction within the turbulent boundary layer [26]. Under constant mass-flux conditions, changes in the tube diameter result in variation of the boundary-layer thickness. Because small-diameter tubes
At a fixed mass flux and tube diameter, an increasing Lh/Oin ratio is a result of an increase in the test-section length. Thus, it results in the pressure drop increasing. The increase in pressure drop to increased length-to-diameter ratio is shown in Fig. 10 for a tube diameter of 1.03 ram, mass flux of 30,000 k g / ( m 2 s), and exit pressure of 10.4 bar. Figure 11 shows a comparison of reduced pressure drop between the experimental data and the Dormer-Bergles correlation under different conditions (listed in the caption). It shows that, for Lh/Di, = 25, the measured single-phase pressure drop data agree rather well with the correlation, and the measured two-phase pressure drop data are a little lower than the correlation. For Lh/Din = 50, the experimental data deviate from the correlation, which may be caused by the tube-diameter and inlet-temperature effects. It also can be seen from Fig. 11 that, unlike the Dormer-Bergles correlation [3] with C H F occurring at A P / A P a = 3 ~ 5, the experimental pressure drop curves stop at the C H F points where A P / A P a < 1. This is mainly a consequence of the high exit pressures used in the present experiments, which resulted in high saturation temperatures and, in turn, relatively low subcoolings and CHF. P r e s s u r e - D r o p Correlation In this study, single-phase and two-phase pressure drop data were correlated separately. For this purpose, the
4.0
3.5
I
I
v
Ti = 22.2oC Ti = 4 ! .5~C
°
T i = 66.5°(2
o
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3.0
o v
Di. ffi 1.04 m m Dm = 1 3 8 m m
a o
Di. = 1.80 m m D~. = 2 . 4 4 m m
3.0'
AP
(bar)
oo
7o ~0 0 2.5 . ~ @ o
O
o 00000
0
v
o
v~6~
(bar)
o v
~v~O
AP
00
VV 0 o o
o%vo v v v o 0 0 0 O0
2.0
°Ooo o o ° = : ; o,¢,
2.0
G = 30,000 kg/m2-s T~= 23*(2 Pe = 10.4 bar Lh/Di. = 24
Di, = 1.05 m m
G = 30,000 kg/m2-s Pc = 10.4 bar
l~/Di, = 24 1.0
1.5
i
0
i
i
I
20
L
,
L
I
i
40
i
i
I
i
60
q" (MW/m2) Figure 8. Effect of inlet temperature on pressure drop.
,
0
s
,
I
20
,
t
L
l
,
,
40
,
[
60
,
t
,
80
q" (MW/m2) Figure 9. Effect of tube internal diameter on pressure drop. Test section burned out at the last point of each curve.
Pressure Drop with Highly Subcooled Flow 209 6.0
'
'
I
I
The single-phase friction factor, f, was calculated from the measured mass flux and the pressure drop across the heated tube length as
I
v
vvvv 5.0
AP
L,/Di, = 50.3
V v ~V
V V VV
V
f =
V ~' V
AP h (G 2/2 p )( L h/Din )"
(10)
From the energy-balance equation, the average fluid temperature along the tube length is given as
4.0
Dia = 1.03
G
2q"L h
mm
30,000 kg/m2-s Ti = 23*(2 P = 10.4 bar
(bar) 3.0
T, = T i + - G~pDin "
=
(11)
Thus, the average wall temperature becomes q"
°°°° L~/Dm = 23.9 0 0 0 0 0 0 0 0 000 0 0 0 0
Tw = Tl + -if,
o °° °~pt9
where h is the average heat-transfer coefficient and can be obtained from the correlation [5]
2.0
Nu = 0.0157 Pr°4Re °'85. 1.0
0
,
i
20
40
,
,
,
I
,
,
,
60
80
q" (MW/m~) Figure 10. Effect of length-to-diameter ratio on pressure drop. Test section burned out at the last point of each curve.
pressure-drop-heat-flux curves were single-phase and two-phase data.
(12)
used
to
isolate
Single-phase (nonboiling) pressure drop has been successfully correlated by many investigators [5, 27, 28]. In this study, single-phase pressure drop data have been correlated by presenting the friction factor ratio, f/fa, versus the wall-to-bulk viscosity ratio, ~w/~l. Single-Phase Flow
(13)
The results of single-phase flow friction factor are presented in Fig. 12 (see also Table 2). It shows that the friction factor ratio decreases with the decreasing wall-tobulk viscosity ratio; that is, with the decreasing temperature difference, Tw - T,. According to Eq. (12), the higher temperature difference represents the higher heat flux applied to the tube, resulting in a lower pressure drop. The friction factor correlation for fully developed turbulent single-phase flow can be expressed as
f/fa = ( ~ w / ~ l )0"163'
(14)
where ~w and ~l were taken at the average wall and fluid temperature, respectively. The proposed correlation provides a good evaluation of the experimental values, with all the predictions within _+15% error band. From Fig. 12, it can also be seen that this correlation is in reasonable agreement with that of Bergles and Dormer [5].
1.2
°v ,o l~/Dm = 50.3 -1.0,
AP
/jo
]l Arn~erandBergles [ 3 ] / I
/'"='"'"7
%°.
0.8
0.6 0.0
\\ ,
G~ 30,000 kg/m2-s T'=23°C. I .
I
0.1
Lo" --y ,
I
0.2
,
I
,
0.3 le
I
0.4 l0
q [qsat
,
I
0.5
,
0.6
Figure 11. Experimental data compared with Dormer-Bergles correlation. Dormer and Bergles: D i n = 3.0480 mm, G = 3000-15,000 kg/(m e s), T i = 23.9 C (Lh/Din = 2 5 ) , T i = 18.3-62.8°C ( L h / D i n = 5 0 ) , P e = 2.0-5.5 bar.
210
W. Tong et al. 1.5
I
I
I
I
f /fo = (-:,, /~,)o.,,, .......
1.0
+15%
.
....
--,:~/~ ,I
"I
f/f~ 0.5
This study . . . . . Bergles and Donner [5] l
0.0
0.0
0.2
i
i
,
I
0.4
,
0.6
l
0.8
,
1.0
Figure 12. Single-phase friction factor correlation. Subeooled Boiling The correlation of subcooled boiling pressure drop data for small-diameter tubes can be achieved by presenting a correlation in graphical form. In such a way, the ratio of the subcooled boiling pressure drop, APsb, to the adiabatic pressure drop, APa, is plotted versus the ratio of the subcooled boiling length, L~b, to the length necessary to produce saturated conditions at the tube exit, Lsar Owing to the high heat fluxes considered, the pressure-drop data were taken for conditions where boiling occurred essentially over the whole tube length. The saturated length, Lsat, containing both single-phase and boiling two-phase regions is given as
Lsat
GcpDin
4 q , ~ (/'sat, e -- Ti)
(15)
Symbol [] • • @ O [] • • • + [] ×
G
25,000 35,000 45,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000
GCpDin
Lsat = Lh +
4q"
ATsub e"
(16)
Thus, for ATsub, e = 0, Lsat = Lh; for ATsub,e > 0, Lsat > L h•
Figure 13 presents the correlation of test data for pressure drop in subcooled boiling flow. These data can be primarily grouped according to the length-to-diameter ratio. For small Lh//Oin cases, a dimensionless pressure drop can be generally correlated as
APsb l a =A (gsb)l'3exp[(gsb) xgsa---~/ P L\~sat
+ 1.35 .
(17)
The scatter in the data is shown in Fig. 13. Of all experimental results, 94.4% fall within the range _+15% derivation. Both inlet-temperature and diameter effects were obtained with the general trends to increase pressure drop with larger parameter values under low heat-flux conditions. At high heat fluxes, the effect of inlet temperature becomes insignificant. For = 50, the data are correlated as
Lh/Din
Table 2. Symbols in Figs. 12 and 13
Din
and can be related to L h as
(ram) [kg / (m2 s)]
Ti
Pe
(°C) (bar) L h / Di~
1.05 1.05 1.05 1.18 1.18 1.05 1.05 1.05 1.03 1.03 1.38 1.80 2.44
26.5 26.5 26.5 23.0 23.0 22.2 41.5 66.5 23.0 23.0 23.0 23.0 23.0
6.5 6.5 6.5 4.3 15.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4
24 24 24 24 24 24 24 24 24 50 24 24 24
1
+ 0 4]
Equations (17) and (18) show that APsb always approaches zero as Lsb does. It can be observed from Fig. 13 that, for Lh/Din = 50, the pressure-drop curve shifts rightward from the main data. This is mainly a consequence of the large adiabatic pressure drop reference APa. The comparison of the present results of two-phase flow with Bergles-Dormer [5] correlation curves presented in Fig. 13 shows a relatively large discrepancy. As indicated in Fig. 13, Bergles-Dormer curves give much lower values than do the present experimental data. This is essentially a consequence of the saturation length reference, LsatFrom Eq. (15), it can be seen that Lsa t is directly propor-
Pressure Drop with Highly Subcooled Flow 211 1.4
jl I f~
1.2
I (" /
1.0
~,
,exam
0.8
aP.
0.6
I
[I
| mm+X~ / .'-
-
oa,I
" 7,.'
Th"%'o>...,.'"
J
.,"
..'"
0.4
. " " Bergles & Dormer [ 5 ] 0.2
0.0 0.0
0.2
0.4
tional to mass flux G and exit saturation temperature T~at,e (i.e., exit pressure Pc). Because the present exPeriments used high mass fluxes (2 ~ 10 times as high those in Bergles-Dormer) and exit pressures (2 ~ 5 times as high), the saturation lengths are much longer than those in Bergles-Dormer. This may cause the separation of the present two-phase pressure-drop data from the BerglesDormer correlation. P R A C T I C A L S I G N I F I C A N C E / USEFULNESS With parallel-channel systems, as would be encountered in the cooling of large surfaces, the ability of subcooled boiling to accommodate high heat fluxes may be severely limited by the pressure drop across the channels. In particular, the C H F may occur at the minimum in the pressure drop-flow rate (mass flux) curve (unstable CHF). For this reason and because of the need to lower the pressure drop, especially at high mass fluxes where the stable CHF is high, pressure-drop data are needed for highly subcooled flow boiling. Pressure-drop data are presented, and correlations are developed for the low-heat-flux (nonboiling) region and the high-heat-flux (developed boiling) regions. These correlations may be combined to yield a total correlation that can be used to design cooling systems to accommodate high heat fluxes. Because the pressure-drop tests terminate at CHF, stable C H F data also are obtained. F U T U R E R E S E A R C H NEEDS For comprehensive design of high flux cooling systems, more pressure drop data are needed over a wider range of conditions. Methods should be developed to transform the data into the AP-G plane so that the minimum can be defined and the associated unstable CHF estimated. Designers of high-heat-flux cooling system must be made aware of the possibility of the occurrence of relatively low unstable CHF's.
0.8
0.6
Figure 13. Two-phase pressure drop correlation. Bergles and Dormer [5] data are as follows: ....... : Din (mm), 2.39; G (kg/m 2 s), 3000-15,2000; Ti (°C), 23.9-29.4; Pe (bar), 2.1-5.5; Lh/Din , 24.5. - . . . . : 3.07, 3000-9100, 26.1-30.0, 2.1-5.5, 49.0. CONCLUSIONS
Experiments were performed to obtain pressure drop in highly subcooled flow boiling from vertical small-diameter tubes. The results of both single- and two-phase pressure drops are mainly dependent on three parameters: mass flux, tube diameter, and length-to-diameter ratio. It has been found that pressure drop is directly proportional to mass flux and length-to-diameter ratio, but inversely proportional to tube diameter. The experimental data are in good agreement with those from other investigations. For predicting single- and two-phase flow friction pressure drop in small diameter tubes, single-phase and subcooled boiling pressure-drop data were correlated separately. These correlations can particularly benefit the design of cooling systems to accommodate high heat fluxes. The authors would like to acknowledge the financial support of the U.S. Department of Energy under Grant No. DE-FC07-88ID12772. They are also indebted to R. A. Pabisz, Jr., for correlating the data in Fig. 13.
A cv Din /~ f G h k I L Nu P Pr
NOMENCLATURE flow area, m 2 specific heat at constant pressure, J / ( k g K) tube internal diameter, m power, W friction factor mass flux, k g / ( m 2 s) heat-transfer coefficient, W / ( m e k ) thermal conductivity W / ( m K) electric current, A length, m Nusselt number, hDin/l¢l pressure, N / m 2 Prandtl number, ~l~'p/~:l
212
W. T o n g et al.
Ap q" Re T V
pressure drop N/m 2 h e a t flux, W / m 2 R e y n o l d s n u m b e r , GDin/~X 1 temperature, K voltage, V
Greek Symbols /x p
d y n a m i c viscosity, N / ( s m 2) density, k g / m 3
Subscripts a e h i 1 sat sub sb t w 105 2~b
adiabatic at t h e test section exit heated at t h e test section inlet liquid saturation subcooling s u b c o o l i n g boiling total wall single-phase two-phase REFERENCES
1. Styrikovich, M. A., Miropolsky, Z. L., Shitsrnan, M. Ye., Mostinski, I. L., Stavrovski, A. A., and Factorovich, L. E., The Effect of Prefixed Units on the Occurrence of Critical Boiling in Steam Generating Tubes. Teploenergetika 6(5), 81-88, 1960. 2. Bergles, A. E., Subcooled Burnout in Tubes of Small Diameter. ASME Paper No. 63-WA-182, 1963. 3. Dormer, T., Jr., and Bergles, A. E., Pressure Drop with Surface Boiling in Small Diameter Tubes. MIT Heat Transfer Laboratory Report No. 8767-31, 1964, 4. Daleas, R. S, and Bergles, A. E., Effects of Upstream Compressibility on Subcooled Critical Heat Flux. ASME Paper No. 65-HT67, 1965. 5. Bergles, A. E., and Dormer, T., Jr., Subcooled Boiling Pressure Drop with Water at Low Pressure. Int. J. Heat Mass Transfer 12, 459-470, 1969. 6. Maulbetsch, J. S., and Griffith, P., A Study of System-Induced Instabilities in Forced-Convective Flows with Subcooled Boiling. Proc. 3rd Int. Heat Transfer Conf. 4, 247-257, 1966. 7. Vandervort, C. L., Bergles, A. E., and Jensen, M. K., An Experimental Study of Critical Heat Flux in Very High Heat Flux Subcooled Boiling. Int. J. Heat Mass Transfer 37(Suppl. 1), 161-173, 1994. 8. Reynolds, J. B., Local Boiling Pressure Drop. ANL-5178, 1954. 9. Owens, W. L., and Schrock, V. E., Local Pressure Gradients for Subcooled Boiling of Water in Vertical Tubes. ASME Paper No. 60-WA-249, 1960. 10. Tarasova, N. V., and Orlov, V. M., An Investigation into Hydraulic Resistance with Surface Boiling of Water in a Tube. Teploenergetika 9(6), 48-52, 1962.
11. Tarasova, N. V., Leontiev, A. I, Hlopushin, V. I., and Orlov, V. M., Pressure Drop of Boiling Subcooled Water and StreamWater Mixture Flowing in Heated Channels. Proc. 3rd Int. Heat Transfer Conf. 4, 178-183, 1963. 12. Hoffman, M. A., and Wong, C. F., Prediction of Pressure Drops in Forced Convection Subcooled Boiling Water Flows. Int. J. Heat Mass Transfer 35, 3291-3299, 1992. 13. Hahne, E., Spindler, K., and Skok, H , A New Pressure Drop Correlation for Subeooled Flow Boiling of Refrigerants. Int. J. Heat Mass Transfer 36, 4267-4274, 1993. 14. Inasaka, F., Nariai, H., and Shimura, T., Pressure Drops in Subcooled Flow Boiling in Narrow Tubes. Heat TransferJpn. Res. 18(1), 70-82, 1989. 15. McAdams, W. H., Kennel, W. E., Minden, C. S., Carl, R., Picornell, P. M., and Dew, J. E., Heat Transfer at High Rates to Water with Surface Boiling. Ind. Eng. Chem. 41, 1945-1953, 1949. 16. Collier, J. G., Convective Boiling and Condensation. 2nd ed., McGraw-Hill, London, 1981. 17. Bowers, M. B., and Mudawar, I., High Flux Boiling in Low Flux Rate, Low Pressure Drop Mini-channel and Micro-channel Heat Sinks. Int. J. Heat Mass Transfer 37, 321-332, 1994. 18. McAdams, W. H., Heat Transmission. 3rd ed., McGraw-Hill, New York, 1954. 19. Blasius, H., cited by W. M. White in Fluid Mechanics. 2nd ed., p. 329, McGraw-Hill, New York, 1911. 20. Filonenko, G. K., Hydraulic Resistance in Pipes, Teploenergetika 1(4), 40-44, 1954. 21. Colebrook, C. F., Turbulent Flow in Pipes with Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws. J. Inst. Civil Eng. 11, 133-156, 1938-1939. 22. Techo, R., Tickner, R. R., and James, R. E., An Accurate Equation for the Computation of the Friction Factor for Smooth Pipes from the Reynolds Number. J. Appl. Mech. 87, 443-454, 1965. 23. White, F. M., Viscous Fluid Flow. McGraw-Hill, New York, 1974. 24. Bhatti, M. S., and Shah, R. K., Turbulent and Transition Flow Convective Heat Transfer in Ducts. In Handbook of Single-Phase Convective Heat Transfer, S. Kaka~, R. K. Shah, and W. Aung, Eds., pp. 4.1-4.166, Wiley, New York, 1987. 25. Olsson, C. O., and Sund6n, B., Pressure Drop Characteristics of Small-Sized Tubes. ASME Paper No. 94-WA/HT-1, 1994. 26. Kays, W. M., and Crawford, M. E., Convective Heat and Mass Transfer. 2nd ed., McGraw-Hill, New York, 1980. 27. Ricque, R., and Siboul, R., Ebullition locale de l'eau en convection forc6. Centre D'Etudes Nucl6aires de Grenoble, Service Des Transferts Thermiques, Report TT No. 76, 1967. 28. LaFay, J., Mesure du coefficient de frottement avec transfert de chaleur en convection forc6e duns un canal circulaire. Centre D'Etudes Nuclgaires de Grenoble, Service Des Transferts Thermiques, Note TT No. 275, 1967.
Received January 15, 1996; revised July 1, 1996
Pressure Drop with Highly Subcooled Flow Boiling in Small-Diameter Tubes Wei Tong* Arthur E. Bergles Michael K. Jensen Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
• Pressure drop may be the most important consideration in designing heat-removal systems utilizing high-heat-flux subcooled boiling. In this study, an experimental investigation was performed to identify the important parameters affecting pressure drop across small-diameter tubes in highly subcooled flow boiling. The effects of five parameters--mass flux, inlet temperature, exit pressure, tube internal diameter, and length-to-diameter ratio--on both single- and two-phase pressure drop were studied and evaluated. Experiments were carried out with tubes having inside diameters ranging from 1.05 to 2.44 mm. Mass fluxes ranged from 25,000 to 45,000 k g / ( m 2 s), exit pressures from 4 to 16 bar, and inlet temperatures from 22 to 66°C. Two length-to-diameter ratios were tested. These conditions resulted in critical heat flux levels of 50-80 M W / m 2. The experimental results indicate that mass flux, tube diameter, and length-to-diameter ratio are the major parameters that alter the pressuredrop curves. Both single- and two-phase pressure drops increase with increasing mass flux and length-to-diameter ratio but decrease with increasing internal diameter. Inlet temperature and exit pressure have been shown to have significant effects on two-phase pressure drop but very small effects on single-phase pressure drop. These results agree well with those from other investigations under similar conditions. As a result of this study, pressure-drop correlations are presented for predicting both single-phase and subcooled boiling pressure drop in small-diameter tubes under different heat-flux conditions. © Elsevier Science Inc., 1997
Keywords: pressure drop, subcooled flow boiling, water, small-diameter tubes, critical heat flux
INTRODUCTION Subcooled flow boiling has been recognized for several decades as one of the most effective heat-transfer modes. In studies of subcooled boiling, much effort has been devoted to the critical heat flux (CHF) condition owing to its importance in a wide variety of industrial applications, including supercomputers, high power laser optics, engine turbines, heat exchangers, plasma-facing components in fusion reactors, and so forth. However, pressure drop, which is strongly coupled to the C H F conditions; is somewhat overlooked by many investigators. In practice, the pressure-drop increase is usually a crucial factor that limits attempts to increase the C H F by increasing fluid velocity. A fundamental study of pressure drop not only enriches our knowledge of subcooled boiling heat transfer, but also helps our understanding of the C H F mechanism.
Experiments have shown that C H F of subcooled flow boiling through uniformly heated tubes is mainly affected by five variables: mass flux, inlet subcooling, exit pressure, tube diameter, and length-to-diameter ratio. Furthermore, it has been reported that, under certain circumstances, a test section can burn out at very low heat-flux levels [1-5]. This phenomenon, known as premature failure (or premature burnout), has constrained the use of subcooled boiling as a cooling technique. Several investigations have suggested that premature failure could result from system-induced instabilities and is closely associated with the pressure drop of the test section. Styrikovich et al. [1] were the first to point out that the presence of oscillations of pressure and flow rate can have a marked effect on the values of CHF. Bergles [2] carried out an experimental investigation of flow boil-
*Currently with Babcock & Wilcox, Naval Nuclear Fuel Division, Lynchburg, VA 24505. Address correspondence to Professor A. E. Bergles, Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590.
Experimental Thermal and Fluid Science 1997; 15:202-212 © Elsevier Science Inc., 1997 655 Avenue of the Americas, New York, NY 10010
0894-1777/97/$17.00 PII S0894-1777(97)00018-6
Pressure Drop with Highly Subcooled Flow 203 ing with water in small-diameter tubes. It was found that an upstream compressible volume can cause flow oscillations, which result in premature failure. Other studies have suggested that the parallel channel excursive instability and upstream compressible volume oscillatory instability are associated with a minimum in the pressure drop-flow rate curve; that is, a(AP)/aG = 0. System-induced instability of either the excursive or the oscillatory type may limit the maximum heat flux to a value well below the stable critical heat flux [3-5]. An analytical prediction of the initiation of system-induced instabilities was performed by Maulbetsch and Griffith [6]. In their study, the stability criteria were found to be dependent on the critical slope of the overall pressure-drop-versusmass-flow-rate curve. The comparison between the analytical model and the available experimental data, including those of Styrikovich [1], demonstrated good agreement. More recently, Vandervort et al. [7] reported premature burnout data of small-diameter stainless steel tubes. In their experiments, more than two-thirds of all tests with the diameters of 1.8 and 2.44 mm resulted in premature failure, with no discernible dependence on the five primary parameters. The general behavior of pressure drop for low pressure, straight pipe flow under a varying, uniform heat flux is shown in Fig. 1. At low heat-flux conditions, the flow is single-phase over the whole tube length. Pressure drop decreases with an increase in heat flux owing to a decrease in the near-wall fluid viscosity. Increasing heat flux leads to an increase in the wall temperature. As the wall superheat, Tw - Tsat, reaches some critical value, boiling occurs near the tube exit, and, consequently, a thin bubbly layer builds up on the heated surface. As a result, pressure drop starts to increase. Continuously raising the heat flux causes the movement of the incipient boiling point toward the flow inlet and boiling generation near the exit. Therefore, two-phase pressure drop (including both single-phase and subcooled boiling pressure drop) increases owing to the increase of void fraction, until the te*st section burns out at the CHF point. It has been' found that premature failures often accompany the transition from boiling incipience into nucleate boiling near
i
i
~
i
i
i
i
CHF --~
&P
ONB
BD
Sh~l©-Pha~ [ _
Two-Phase
'-1
II
I
I
I
I
I
I
I
q" Figure 1. General behavior of single- and two-phase pressure drop. ONB, onset of nucleate boiling; BD, bubble departure.
a(AP)/aq" = 0 [7]. This transition is thus defined as the "danger zone." Hence, the pressure drop can serve as an indicator to determine stable CHF or premature failure. Studies of pressure drop in subcooled flow boiling can be generally classified into two categories. The first category deals with the pressure gradient along the tube length direction. Various empirical correlations have been proposed to predict the ratio of the two-phase pressure gradient to single-phase pressure gradient (or shear stress ratio) for water flow [8-11]. However, because these correlations were mainly based on the operating conditions of light water reactors, they may not be applicable to small flow area channels. Hoffman and Wong [12] developed a semiempirical model for the prediction of the pressure distribution along the tube in subcooled flow boiling. This model, covering the single-phase and fully developed boiling regime, includes the effects of nonequilibrium quality and property variations. The pressure drop predicted by this model was compared with more than 100 experimental runs and was found to agree within approximately 20%. A pressure-gradient correlation for refrigerants was reported recently by Hahne et al. [13]. The second category is to investigate the effects of the test-section geometry and thermal-hydraulic parameters on pressure drop across the test section. Dormer and Bergles [5] were among the first to present results of pressure drop in subcooled flow boiling through stainless steel tubes of diameter less than 5 mm at low pressure. A "chart" correlation was proposed for small-tube diameters (1.57-4.57 mm) with different thermal-hydraulic conditions. Recently, this problem was investigated experimentally by Inasaka et al. [14] for tube diameters of 1 and 3 mm. The experiments were conducted at nearly ambient pressure, whereas mass flux varied from 7000 to 20,000 kg/(m 2 s). The pressure-drop ratio of subcooled flow boiling to nonheating water flow was examined. The results for 3-mm diameter tubes were found to agree with the Dormer-Bergles correlation [3]. However, experimental data and correlations for the pressure-drop dependence on various parameters are still rather limited in the literature so far. For regular subcooled boiling flow through a uniformly heated tube, three flow regimes can be generally identified: single-phase 'flow, subcooled boiling, and saturated boiling [12, 13]. However, under high mass flux and high exit-pressure conditions, subcooling at the flow downstream is so high that the flow may never reach the saturated boiling regime. Owing to strong condensation, the void fraction is rather small, even at the tube exit. This heat-transfer mode, which is the focus of the present study, is defined as highly subcooled flow boiling to distinguish it from regular subcooled flow boiling. The objective of this study is to investigate the effects of five parameters--mass flux, inlet temperature, exit pressure, tube internal diameter, and length-to-diameter ratio - - o n both single- and two-phase pressure drop in highly subcooled flow boiling. The tube internal diameters used in this investigation were: 1.05, 1.38, 1.80, and 2.44 ram. Two length-to-diameter ratios (25 and 50) were tested. Wide range of mass fluxes [25,000-45,000 kg/(m 2 s)], inlet temperatures (22-66°C), and exit pressures (4-16 bar) were considered and examined. These conditions resulted in high CHF levels of 50-80 M W / m 2.
204 W. Tong et al.
I
Vent
Heat Exchanger
2kW
Bypass
] Dernineralizer
Test Dissolved Gas Measurement
[]Filter Bypass
Prehcater Pump
Filter Flowtr~ter
I
t"
.7kWx3 l llOkW
_1Each
Relief Valve
t t
(~) Control valve Ball valve
t~ Pressurerelief valve (~ Thcrmocouple (~) Pressure transducer Figure 2. Diagram of experimental apparatus. EXPERIMENTAL SETUP
Experimental Apparatus and Test Section The experimental apparatus used in this investigation consisted of a water loop, a temperature-controlling and deionizing system, and a dc power supply, as shown in Fig. 2. Water flowed upward through the test section and was transported by a diaphragm pump with a digital speedcontrolling regulator. The inlet bulk temperature was regulated by using both electric heaters and a heat exchanger. The deionizing system, including an ion exchanger and a filter arranged in series, was used to purify the distilled water. A series of bypasses and valves was designed to control the flow rate and exit pressure of the test section. The test section was uniformly heated (Joule effect) by means of a 100-kW thyristor-controlled transformer-rectifier, with a smoothly controlled current of 0-2500 A and a dc voltage of 0 - 4 0 V. To minimize electrical measurement uncertainties, current was measured though a 0-600-A, 50-mV shunt, and voltage was directly measured across the test section. The resulting uncertainty for current was _+2.5% and for voltage was ± 0.02% of reading. The test section was made 304 stainless steel tubing, with two brass bushings as the power connectors (Fig. 3). All exterior surfaces were covered with glass fiber insulation to minimize convective heat loss. Pressure taps were situated at the inlet and exit of the test section. In an effort to prevent premature burnout, a flexible structure was designed to connect the test section to the loop piping. The inlet and exit fittings were threaded directly to heat-resistant Teflon couplings to secure electrical insula-
tion. In an effort to eliminate or minimize system-induced flow instabilities, a large pressure drop (10-30 bar) was set across a throttle valve directly upstream of the test section. Experimental Procedure Noncondensible gases dissolved in water have been reported to affect the boiling process [15]. To eliminate any dissolved-gas effect on pressure drop, the distilled water was degassed before each experiment. The degassing was accomplished by vigorous boiling and venting in the water tank for a 1-2-h period. In the process, water was circulated periodically through the water loop. When degassing was completed, the system was adjusted to the desired operating mass flux, inlet temperature, and exit pressure. As steady-state was attained, power was added to the test section. The power input was initially set at a very low value ( < 0.2 kW) and increased by small increments. Several sets of data were taken at each equilibrium condition to detect any possible transient effect on pressure drop. The reading at each heat-flux level was chosen when all controlled variables were within the allowed uncertainties. In this investigation, the experimental uncertainties were controlled to the selected operating values as mass flux, + 1%; inlet temperature, _+5%; and exit pressure, _+3%.
Parameter Measurement A modular computerized data acquisition system was used to collect data in all runs. The main instruments of the system include an HP-3497A data acquisition controller,
Pressure Drop with Highly Subcooled Flow 205
Brass now
Bushing
Silver /Solder
Lh
-
Inlet Pressure Tap
L.,2~
Exit Pressure Tap Lt
=
Figure 3. Test-section geometry.
an HP-3457 digital multimeter, and an HP 9000/300 computer. This system has the capability of measuring 60 thermocouples and 25 general instrumentation readings. The data acquisition and reduction programs were written in HP Basic 5.1 and were developed specifically for the control and collection of data in the present experiments. Pressure drop across a test section was measured by a Validyne DP15 differential pressure transducer, operating along with a CD15 carrier demodulator for signal amplification. The instrument diaphragms could be changed to cover a wide range of pressure-drop measurements. In an effort to make precise pressure measurements, pressures at the inlet and exit were monitored individually by both an Omega pressure transducer and a pressure gage. All transducers were calibrated by using a dead-weight tester. The uncertainty of pressure-drop measurement was less than _+1.0% of reading. One of the three turbine flowmeters, with measuring capacities of 0.0631 to 1.00, 0.95 and 87.5, and 25 to 1562 cm3/s, was used to measure the volumetric flow rate through the test section. These flowmeters were carefully calibrated to ensure that the experimental uncertainty was within +_0.5% of reading. The mass flux was calculated by the measured volumetric flow rate, water density, and flow area. Temperature measurements were made by applying copper-constantan thermocouples, which were inserted through plastic couplings at approximately the midpoint of the water flow. The measurement errors associated with these thermocouples were within +0.1°C. The conversion of the thermocouple output to temperature was made by using calibration correlations. A Kaye ice-point reference, with a repeatability of + 0.02°C, was used. The heat flux was calculated on the basis of the total power input and the tube inner heated surface. The uncertainty of the heat flux was estimated to be + 6.0% for D i n = 1.05 mm and +-4.0% for D i n = 2.44 mm. The power input was computed by evaluating the product of the measured current and voltage applied to the test section: /~
(1)
= V/.
The electrical power dissipation was checked by comparison against the enthalpy gain rate for a single-phase flow with the equation
= GAcp(T,
-
Ti) ,
(2)
where A is the flow cross-sectional area. The relative difference between the values obtained with Eqs. (1) and (2) was generally less than +_5% and, in most experiments, less than _+3%. This method is unreliable for two-phase flow, because thermocouple readings are affected by the bubbles. Data
Reduction
As shown in Fig. 3, the total length between the two pressure taps is the sum of the heated and the adiabatic lengths. Thus, the measured total pressure drop can be considered the sum of the pressure drop of the heated section and the pressure drop of the adiabatic section; that is, APt = Ap h + A p a. (3) When boiling occurs near the exit at high heat fluxes, Ap~ becomes a sum of two components: the single-phase adiabatic pressure drop at the inlet, A Pa, 1~, and the two-phase adiabatic pressure drop at the exit, APa,2~, where =
G2
fl~
A Pa, 14'
2p i
(Din/La,I¢~)'
G2
f2,
A Pa' 2¢~
2p e (Din/La,2¢~)'
(4)
(S)
where fl~ and f2~ are the single-phase adiabatic friction factors, respectively. Because the void fraction is very small for highly subcooled boiling, quality is not taken into account in Eq. (5). Note that both A P a , ld, and A P a , 2 4 , affect the thermal field (temperature profile) but not the flow field (velocity profile). The hydrodynamic entrance and exit effects are determined by the entrance length (from the tube inlet to the inlet pressure tap) and the exit length (from the exit pressure tap to the tube exit), respectively. The single-phase friction factor, fl~, can be easily obtained experimentally, and the two-phase friction factor, f2~, can be calculated approximately by using the Blasius equation [16]: f2~ =
0.316 Re -°25,
(6)
where Re = G D i n / / ~ l . Thus, the pressure drop across the heated tube length is obtained by subtracting the two adiabatic pressure drops from the measured total pressure drop.
206
W. Tong et al.
Although the direct uncertainty of Eq. (6) is unknown, Bowers and Mudawar [17] reported that, on the basis of calculated values by Eq. (6), the predicted total pressure drop, which is the sum of the pressure drop in single-phase, boiling, and outlet sections of the channel, is characterized by a + 30% error band (including uncertainties from all parts) with experimental data. The equation should be quite adequate for the small correction in the outlet pressure reading. RESULTS AND DISCUSSION Adiabatic
Single-Phase Friction Factor
Performing single-phase tests has a twofold objective: (1) to validate the experimental apparatus and data acquisition system and (2) to obtain adiabatic single-phase friction factors for the data reduction and the single-phase pressure drop correlation. The single-phase adiabatic friction factor is calculated from the measured total pressure drop and mass flux as
Ap, fa,l~,
=
(G2/2~)(Lt/Din)
(7)
The variations of fa, 1~ with Reynolds number for tubes of different diameters are given in Fig. 4. The comparison between the present experimental data and those calculated from well-known correlations (for smooth circular tubes) shows reasonable agreement. Because of surface roughness, the measured data are higher than the predicted values at high Reynolds numbers. It can be seen from Fig. 4 that, at low Reynolds numbers, the transitions from laminar to turbulent flow occur randomly as the tube diameter varies. With the use of a standard least-square curve-fitting technique, adiabatic friction factor data can be correlated in the form of (excluding the transition parts from the database) fa = a Re b (8)
Table
Coefficients in Eq.
1.
(8)
Din (ram)
a
b
1.05 1.38 1.80 2.44
0.218 0.218 0.148 0.106
- 0.201 - 0.201 -0.170 - 0.103
where a and b are constant (Table 1). Bhatti and Shah [24] and Olsson and Sund6n [25] pointed out that the performance of small-sized tubes (usually for Din < 2 mm) in single-phase turbulent flow is not similar to that of large-sized tubes. The turbulent eddy mechanism for fluid flow and heat transfer is suppressed by the tube internal diameter, resulting in lower friction factors and heattransfer coefficients. The present experimental results have confirmed such a trend. Analysis of the experimental data leads to five fundamental effects on single- and two-phase pressure drop. These effects are presented and discussed in the next sections.
Mass-Flux Effect As mass flux increases, pressure drop increases, owing to the shear-stress enhancement on the wall. In Fig. 5, pressure drop is plotted against heat flux under different mass fluxes. To eliminate the uncertainties, including fabricating uncertainty, tube geometry uncertainty, and material uncertainty, introduced by the use of different test sections, all experiments for the mass-flux effect were performed by using the same test section. Because each test section was used only three times at most, there is no fouling problem. In addition, the water-purity subsystem was used in all experiments. Each experiment stopped when heat flux was very close to CHF (identified by the "boiling sound"), and the test
lO-I . . . . . .
I
'
o []
' Di~ '= 1. 0 5 ' m m ' D~ = 1.38 mm
'
Dia = 1 . 8 0 m m Din = 2 . 4 4 m m
• v
- -
McAdams [ 18 ]
~-.~.-:-£~o
- - -- --
Blasius, [19] Filonenko [ 20 ]
-n=-..._~o,~_o
------ Colebrook, [211
~ ~ - - ~ . ° ° O o o ^
o
~
~
o
oo
0 rtVVV"
[]
[22]
". . . . . . . . .
Tcchoetai.
....
Whiteq[23]
-'"
•0
O
v v
[]
Figure 4. Comparison of experimental singlephase adiabatic friction factor with correlations.
I 1 0 -2 3 x 10 3
I
I
I
I
I ~7]
I
I
I
1
I
I
I
I
lOs
l O4
Re
Pressure Drop with Highly Subcooled Flow 207 is normalized by the saturated heat flux at the tube exit, tt qsat, GcpDm q's't 4L-""'~(Tsat'e - Ti)' (9)
6.0 o
z
G = 25,000 kg/m2-s G = 35,000 kg/m2-s G = 45,000 kg/m2-s
v
z
z
5.0
~A
A~ A
where T~t,~ is determined by the exit pressure, and Cp is evaluated at the average temperature of T~at,~ and T i. From Fig. 6, it can be seen that, though the Dormer-Bergles correlation was based on somewhat different conditions (listed in the caption), the measured data at all mass fluxes agree well with the correlation. The test section burned out at A P / A P a -~ 1.
~ A
AP
zx
1~ A
4.0
CHF
\
(bar)
v V
vv
3.0 ~VVV
Exit-Pressure Effect
V VVVVVV
The effect of exit pressure on pressure drop is given in Fig. 7, which shows that the single-phase pressure drop is completely independent of exit pressure (as expected), but the two-phase pressure drop is significantly affected by exit pressure. The reason is that, for a single-phase flow, the exit pressure has nothing to do with flow patterns and temperature field. However, as the flow turns into twophase, a higher exit pressure always gives a higher subcooling, which causes a higher condensation of the bubbles. At very high pressure conditions, most bubbles condense and disappear in the core of the fluid flow, thus leading to a lower pressure drop.
Dm = 1.05 mm
2.0
Ti = 26.5*(2 P~ = 6.2 bar L,/D~ = 24
OO ° O ~
1.0
0
i
0
0 O0
,
,
0
I
o°
i
i
O0 0
t
20
I
,
i
i
40 q"
I
,
i
,
60
I
,
,
,
80
100
( M W / m 2)
Figure 5. Effect of mass flux on pressure drop.
section burned out at the last run. The results show that a higher mass flux results in a higher pressure drop for both single- and two-phase flows. For instance, as mass flux increases from 25,000 to 45,000 k g / ( m 2 s), the pressure drop increases by a factor of 3. The present experimental data were compared with the Dormer-Bergles "chart" correlation [3] terms of dimensionless quantities (Fig. 6). The measured pressure drop is normalized by the measured adiabatic single-phase pressure drop attained at q" = 0, A P v and the actual heat flux
1.4
'
'
'
'
I
o
1.2
'
'
'
'
I
'
'
'
'
I
I n l e t - T e m p e r a t u r e Effect Changes in the inlet temperature affect the inlet subcooling to the test section and the subcooling along the test section. For single-phase flow, decreasing the inlet temperature results in a higher fluid viscosity, which is associated with a higher pressure drop. For boiling two-phase flow, reducing the inlet temperature results in stronger condensation in the core region and, thus, makes a lower pressure drop for a given heat flux (Fig. 8).
'
'
'
G = 25,000 kg/mLs
v o --
'
/
G = 35,000 kg/m2-s G = 45,000 kg/m2-s Donner and Bergles [3 ]
/ / / o
//o AP
1.0
0.8 Din = 1.05 mm
T i = 26.5°C
0.6
Pe = 6.2 bar
Lh/Dm = 24 0.4
0.0
0.1
0.2 g
0.3 w
q /. q~t
0.4
Figure 6. Comparison of experimental pressure-drop data with Dormer and Bergles correlation. Dormer and Bergles: Din = 1.57 mm, Ti = 23.9°C, G = 3000-15,000 kg//(m 2 s), Pe = 2.0-5.52 bar, Lh//Oin = 25.
208
W. Tong et al. 2.5
have a thinner boundary layer (or the bubbly layer for boiling two-phase flow), they have higher velocity gradients and, in turn, higher pressure drops. The effect of tube internal diameter on pressure drop is shown in Fig. 9.
I
P~ = 4.3 bar P, = 15.4 bar
Length-to-Diameter-Ratio Effect 2.0 -
9 CI-IF
AP
\ V
(bar)
0
v
0
0
v
0 v
0
1.5
OV
VV
Din= 1.18 nun G = 30,000 kg/m2-s Ti = 23oc L h / D i . = 24 1.0
I
I
[
I
I
I
I
I
20
0
I
I
I
40
60
(MW/m2)
q"
Figure 7. Effect of exit pressure on pressure drop. T u b e - D i a m e t e r Effect According to the boundary-layer theory, the total apparent shear stress (a sum of the turbulent and viscous shear stress) is directly proportional to the velocity gradient perpendicular to the flow direction within the turbulent boundary layer [26]. Under constant mass-flux conditions, changes in the tube diameter result in variation of the boundary-layer thickness. Because small-diameter tubes
At a fixed mass flux and tube diameter, an increasing Lh/Oin ratio is a result of an increase in the test-section length. Thus, it results in the pressure drop increasing. The increase in pressure drop to increased length-to-diameter ratio is shown in Fig. 10 for a tube diameter of 1.03 ram, mass flux of 30,000 k g / ( m 2 s), and exit pressure of 10.4 bar. Figure 11 shows a comparison of reduced pressure drop between the experimental data and the Dormer-Bergles correlation under different conditions (listed in the caption). It shows that, for Lh/Di, = 25, the measured single-phase pressure drop data agree rather well with the correlation, and the measured two-phase pressure drop data are a little lower than the correlation. For Lh/Din = 50, the experimental data deviate from the correlation, which may be caused by the tube-diameter and inlet-temperature effects. It also can be seen from Fig. 11 that, unlike the Dormer-Bergles correlation [3] with C H F occurring at A P / A P a = 3 ~ 5, the experimental pressure drop curves stop at the C H F points where A P / A P a < 1. This is mainly a consequence of the high exit pressures used in the present experiments, which resulted in high saturation temperatures and, in turn, relatively low subcoolings and CHF. P r e s s u r e - D r o p Correlation In this study, single-phase and two-phase pressure drop data were correlated separately. For this purpose, the
4.0
3.5
I
I
v
Ti = 22.2oC Ti = 4 ! .5~C
°
T i = 66.5°(2
o
I
I
I
I
3.0
o v
Di. ffi 1.04 m m Dm = 1 3 8 m m
a o
Di. = 1.80 m m D~. = 2 . 4 4 m m
3.0'
AP
(bar)
oo
7o ~0 0 2.5 . ~ @ o
O
o 00000
0
v
o
v~6~
(bar)
o v
~v~O
AP
00
VV 0 o o
o%vo v v v o 0 0 0 O0
2.0
°Ooo o o ° = : ; o,¢,
2.0
G = 30,000 kg/m2-s T~= 23*(2 Pe = 10.4 bar Lh/Di. = 24
Di, = 1.05 m m
G = 30,000 kg/m2-s Pc = 10.4 bar
l~/Di, = 24 1.0
1.5
i
0
i
i
I
20
L
,
L
I
i
40
i
i
I
i
60
q" (MW/m2) Figure 8. Effect of inlet temperature on pressure drop.
,
0
s
,
I
20
,
t
L
l
,
,
40
,
[
60
,
t
,
80
q" (MW/m2) Figure 9. Effect of tube internal diameter on pressure drop. Test section burned out at the last point of each curve.
Pressure Drop with Highly Subcooled Flow 209 6.0
'
'
I
I
The single-phase friction factor, f, was calculated from the measured mass flux and the pressure drop across the heated tube length as
I
v
vvvv 5.0
AP
L,/Di, = 50.3
V v ~V
V V VV
V
f =
V ~' V
AP h (G 2/2 p )( L h/Din )"
(10)
From the energy-balance equation, the average fluid temperature along the tube length is given as
4.0
Dia = 1.03
G
2q"L h
mm
30,000 kg/m2-s Ti = 23*(2 P = 10.4 bar
(bar) 3.0
T, = T i + - G~pDin "
=
(11)
Thus, the average wall temperature becomes q"
°°°° L~/Dm = 23.9 0 0 0 0 0 0 0 0 000 0 0 0 0
Tw = Tl + -if,
o °° °~pt9
where h is the average heat-transfer coefficient and can be obtained from the correlation [5]
2.0
Nu = 0.0157 Pr°4Re °'85. 1.0
0
,
i
20
40
,
,
,
I
,
,
,
60
80
q" (MW/m~) Figure 10. Effect of length-to-diameter ratio on pressure drop. Test section burned out at the last point of each curve.
pressure-drop-heat-flux curves were single-phase and two-phase data.
(12)
used
to
isolate
Single-phase (nonboiling) pressure drop has been successfully correlated by many investigators [5, 27, 28]. In this study, single-phase pressure drop data have been correlated by presenting the friction factor ratio, f/fa, versus the wall-to-bulk viscosity ratio, ~w/~l. Single-Phase Flow
(13)
The results of single-phase flow friction factor are presented in Fig. 12 (see also Table 2). It shows that the friction factor ratio decreases with the decreasing wall-tobulk viscosity ratio; that is, with the decreasing temperature difference, Tw - T,. According to Eq. (12), the higher temperature difference represents the higher heat flux applied to the tube, resulting in a lower pressure drop. The friction factor correlation for fully developed turbulent single-phase flow can be expressed as
f/fa = ( ~ w / ~ l )0"163'
(14)
where ~w and ~l were taken at the average wall and fluid temperature, respectively. The proposed correlation provides a good evaluation of the experimental values, with all the predictions within _+15% error band. From Fig. 12, it can also be seen that this correlation is in reasonable agreement with that of Bergles and Dormer [5].
1.2
°v ,o l~/Dm = 50.3 -1.0,
AP
/jo
]l Arn~erandBergles [ 3 ] / I
/'"='"'"7
%°.
0.8
0.6 0.0
\\ ,
G~ 30,000 kg/m2-s T'=23°C. I .
I
0.1
Lo" --y ,
I
0.2
,
I
,
0.3 le
I
0.4 l0
q [qsat
,
I
0.5
,
0.6
Figure 11. Experimental data compared with Dormer-Bergles correlation. Dormer and Bergles: D i n = 3.0480 mm, G = 3000-15,000 kg/(m e s), T i = 23.9 C (Lh/Din = 2 5 ) , T i = 18.3-62.8°C ( L h / D i n = 5 0 ) , P e = 2.0-5.5 bar.
210
W. Tong et al. 1.5
I
I
I
I
f /fo = (-:,, /~,)o.,,, .......
1.0
+15%
.
....
--,:~/~ ,I
"I
f/f~ 0.5
This study . . . . . Bergles and Donner [5] l
0.0
0.0
0.2
i
i
,
I
0.4
,
0.6
l
0.8
,
1.0
Figure 12. Single-phase friction factor correlation. Subeooled Boiling The correlation of subcooled boiling pressure drop data for small-diameter tubes can be achieved by presenting a correlation in graphical form. In such a way, the ratio of the subcooled boiling pressure drop, APsb, to the adiabatic pressure drop, APa, is plotted versus the ratio of the subcooled boiling length, L~b, to the length necessary to produce saturated conditions at the tube exit, Lsar Owing to the high heat fluxes considered, the pressure-drop data were taken for conditions where boiling occurred essentially over the whole tube length. The saturated length, Lsat, containing both single-phase and boiling two-phase regions is given as
Lsat
GcpDin
4 q , ~ (/'sat, e -- Ti)
(15)
Symbol [] • • @ O [] • • • + [] ×
G
25,000 35,000 45,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000
GCpDin
Lsat = Lh +
4q"
ATsub e"
(16)
Thus, for ATsub, e = 0, Lsat = Lh; for ATsub,e > 0, Lsat > L h•
Figure 13 presents the correlation of test data for pressure drop in subcooled boiling flow. These data can be primarily grouped according to the length-to-diameter ratio. For small Lh//Oin cases, a dimensionless pressure drop can be generally correlated as
APsb l a =A (gsb)l'3exp[(gsb) xgsa---~/ P L\~sat
+ 1.35 .
(17)
The scatter in the data is shown in Fig. 13. Of all experimental results, 94.4% fall within the range _+15% derivation. Both inlet-temperature and diameter effects were obtained with the general trends to increase pressure drop with larger parameter values under low heat-flux conditions. At high heat fluxes, the effect of inlet temperature becomes insignificant. For = 50, the data are correlated as
Lh/Din
Table 2. Symbols in Figs. 12 and 13
Din
and can be related to L h as
(ram) [kg / (m2 s)]
Ti
Pe
(°C) (bar) L h / Di~
1.05 1.05 1.05 1.18 1.18 1.05 1.05 1.05 1.03 1.03 1.38 1.80 2.44
26.5 26.5 26.5 23.0 23.0 22.2 41.5 66.5 23.0 23.0 23.0 23.0 23.0
6.5 6.5 6.5 4.3 15.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4
24 24 24 24 24 24 24 24 24 50 24 24 24
1
+ 0 4]
Equations (17) and (18) show that APsb always approaches zero as Lsb does. It can be observed from Fig. 13 that, for Lh/Din = 50, the pressure-drop curve shifts rightward from the main data. This is mainly a consequence of the large adiabatic pressure drop reference APa. The comparison of the present results of two-phase flow with Bergles-Dormer [5] correlation curves presented in Fig. 13 shows a relatively large discrepancy. As indicated in Fig. 13, Bergles-Dormer curves give much lower values than do the present experimental data. This is essentially a consequence of the saturation length reference, LsatFrom Eq. (15), it can be seen that Lsa t is directly propor-
Pressure Drop with Highly Subcooled Flow 211 1.4
jl I f~
1.2
I (" /
1.0
~,
,exam
0.8
aP.
0.6
I
[I
| mm+X~ / .'-
-
oa,I
" 7,.'
Th"%'o>...,.'"
J
.,"
..'"
0.4
. " " Bergles & Dormer [ 5 ] 0.2
0.0 0.0
0.2
0.4
tional to mass flux G and exit saturation temperature T~at,e (i.e., exit pressure Pc). Because the present exPeriments used high mass fluxes (2 ~ 10 times as high those in Bergles-Dormer) and exit pressures (2 ~ 5 times as high), the saturation lengths are much longer than those in Bergles-Dormer. This may cause the separation of the present two-phase pressure-drop data from the BerglesDormer correlation. P R A C T I C A L S I G N I F I C A N C E / USEFULNESS With parallel-channel systems, as would be encountered in the cooling of large surfaces, the ability of subcooled boiling to accommodate high heat fluxes may be severely limited by the pressure drop across the channels. In particular, the C H F may occur at the minimum in the pressure drop-flow rate (mass flux) curve (unstable CHF). For this reason and because of the need to lower the pressure drop, especially at high mass fluxes where the stable CHF is high, pressure-drop data are needed for highly subcooled flow boiling. Pressure-drop data are presented, and correlations are developed for the low-heat-flux (nonboiling) region and the high-heat-flux (developed boiling) regions. These correlations may be combined to yield a total correlation that can be used to design cooling systems to accommodate high heat fluxes. Because the pressure-drop tests terminate at CHF, stable C H F data also are obtained. F U T U R E R E S E A R C H NEEDS For comprehensive design of high flux cooling systems, more pressure drop data are needed over a wider range of conditions. Methods should be developed to transform the data into the AP-G plane so that the minimum can be defined and the associated unstable CHF estimated. Designers of high-heat-flux cooling system must be made aware of the possibility of the occurrence of relatively low unstable CHF's.
0.8
0.6
Figure 13. Two-phase pressure drop correlation. Bergles and Dormer [5] data are as follows: ....... : Din (mm), 2.39; G (kg/m 2 s), 3000-15,2000; Ti (°C), 23.9-29.4; Pe (bar), 2.1-5.5; Lh/Din , 24.5. - . . . . : 3.07, 3000-9100, 26.1-30.0, 2.1-5.5, 49.0. CONCLUSIONS
Experiments were performed to obtain pressure drop in highly subcooled flow boiling from vertical small-diameter tubes. The results of both single- and two-phase pressure drops are mainly dependent on three parameters: mass flux, tube diameter, and length-to-diameter ratio. It has been found that pressure drop is directly proportional to mass flux and length-to-diameter ratio, but inversely proportional to tube diameter. The experimental data are in good agreement with those from other investigations. For predicting single- and two-phase flow friction pressure drop in small diameter tubes, single-phase and subcooled boiling pressure-drop data were correlated separately. These correlations can particularly benefit the design of cooling systems to accommodate high heat fluxes. The authors would like to acknowledge the financial support of the U.S. Department of Energy under Grant No. DE-FC07-88ID12772. They are also indebted to R. A. Pabisz, Jr., for correlating the data in Fig. 13.
A cv Din /~ f G h k I L Nu P Pr
NOMENCLATURE flow area, m 2 specific heat at constant pressure, J / ( k g K) tube internal diameter, m power, W friction factor mass flux, k g / ( m 2 s) heat-transfer coefficient, W / ( m e k ) thermal conductivity W / ( m K) electric current, A length, m Nusselt number, hDin/l¢l pressure, N / m 2 Prandtl number, ~l~'p/~:l
212
W. T o n g et al.
Ap q" Re T V
pressure drop N/m 2 h e a t flux, W / m 2 R e y n o l d s n u m b e r , GDin/~X 1 temperature, K voltage, V
Greek Symbols /x p
d y n a m i c viscosity, N / ( s m 2) density, k g / m 3
Subscripts a e h i 1 sat sub sb t w 105 2~b
adiabatic at t h e test section exit heated at t h e test section inlet liquid saturation subcooling s u b c o o l i n g boiling total wall single-phase two-phase REFERENCES
1. Styrikovich, M. A., Miropolsky, Z. L., Shitsrnan, M. Ye., Mostinski, I. L., Stavrovski, A. A., and Factorovich, L. E., The Effect of Prefixed Units on the Occurrence of Critical Boiling in Steam Generating Tubes. Teploenergetika 6(5), 81-88, 1960. 2. Bergles, A. E., Subcooled Burnout in Tubes of Small Diameter. ASME Paper No. 63-WA-182, 1963. 3. Dormer, T., Jr., and Bergles, A. E., Pressure Drop with Surface Boiling in Small Diameter Tubes. MIT Heat Transfer Laboratory Report No. 8767-31, 1964, 4. Daleas, R. S, and Bergles, A. E., Effects of Upstream Compressibility on Subcooled Critical Heat Flux. ASME Paper No. 65-HT67, 1965. 5. Bergles, A. E., and Dormer, T., Jr., Subcooled Boiling Pressure Drop with Water at Low Pressure. Int. J. Heat Mass Transfer 12, 459-470, 1969. 6. Maulbetsch, J. S., and Griffith, P., A Study of System-Induced Instabilities in Forced-Convective Flows with Subcooled Boiling. Proc. 3rd Int. Heat Transfer Conf. 4, 247-257, 1966. 7. Vandervort, C. L., Bergles, A. E., and Jensen, M. K., An Experimental Study of Critical Heat Flux in Very High Heat Flux Subcooled Boiling. Int. J. Heat Mass Transfer 37(Suppl. 1), 161-173, 1994. 8. Reynolds, J. B., Local Boiling Pressure Drop. ANL-5178, 1954. 9. Owens, W. L., and Schrock, V. E., Local Pressure Gradients for Subcooled Boiling of Water in Vertical Tubes. ASME Paper No. 60-WA-249, 1960. 10. Tarasova, N. V., and Orlov, V. M., An Investigation into Hydraulic Resistance with Surface Boiling of Water in a Tube. Teploenergetika 9(6), 48-52, 1962.
11. Tarasova, N. V., Leontiev, A. I, Hlopushin, V. I., and Orlov, V. M., Pressure Drop of Boiling Subcooled Water and StreamWater Mixture Flowing in Heated Channels. Proc. 3rd Int. Heat Transfer Conf. 4, 178-183, 1963. 12. Hoffman, M. A., and Wong, C. F., Prediction of Pressure Drops in Forced Convection Subcooled Boiling Water Flows. Int. J. Heat Mass Transfer 35, 3291-3299, 1992. 13. Hahne, E., Spindler, K., and Skok, H , A New Pressure Drop Correlation for Subeooled Flow Boiling of Refrigerants. Int. J. Heat Mass Transfer 36, 4267-4274, 1993. 14. Inasaka, F., Nariai, H., and Shimura, T., Pressure Drops in Subcooled Flow Boiling in Narrow Tubes. Heat TransferJpn. Res. 18(1), 70-82, 1989. 15. McAdams, W. H., Kennel, W. E., Minden, C. S., Carl, R., Picornell, P. M., and Dew, J. E., Heat Transfer at High Rates to Water with Surface Boiling. Ind. Eng. Chem. 41, 1945-1953, 1949. 16. Collier, J. G., Convective Boiling and Condensation. 2nd ed., McGraw-Hill, London, 1981. 17. Bowers, M. B., and Mudawar, I., High Flux Boiling in Low Flux Rate, Low Pressure Drop Mini-channel and Micro-channel Heat Sinks. Int. J. Heat Mass Transfer 37, 321-332, 1994. 18. McAdams, W. H., Heat Transmission. 3rd ed., McGraw-Hill, New York, 1954. 19. Blasius, H., cited by W. M. White in Fluid Mechanics. 2nd ed., p. 329, McGraw-Hill, New York, 1911. 20. Filonenko, G. K., Hydraulic Resistance in Pipes, Teploenergetika 1(4), 40-44, 1954. 21. Colebrook, C. F., Turbulent Flow in Pipes with Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws. J. Inst. Civil Eng. 11, 133-156, 1938-1939. 22. Techo, R., Tickner, R. R., and James, R. E., An Accurate Equation for the Computation of the Friction Factor for Smooth Pipes from the Reynolds Number. J. Appl. Mech. 87, 443-454, 1965. 23. White, F. M., Viscous Fluid Flow. McGraw-Hill, New York, 1974. 24. Bhatti, M. S., and Shah, R. K., Turbulent and Transition Flow Convective Heat Transfer in Ducts. In Handbook of Single-Phase Convective Heat Transfer, S. Kaka~, R. K. Shah, and W. Aung, Eds., pp. 4.1-4.166, Wiley, New York, 1987. 25. Olsson, C. O., and Sund6n, B., Pressure Drop Characteristics of Small-Sized Tubes. ASME Paper No. 94-WA/HT-1, 1994. 26. Kays, W. M., and Crawford, M. E., Convective Heat and Mass Transfer. 2nd ed., McGraw-Hill, New York, 1980. 27. Ricque, R., and Siboul, R., Ebullition locale de l'eau en convection forc6. Centre D'Etudes Nucl6aires de Grenoble, Service Des Transferts Thermiques, Report TT No. 76, 1967. 28. LaFay, J., Mesure du coefficient de frottement avec transfert de chaleur en convection forc6e duns un canal circulaire. Centre D'Etudes Nuclgaires de Grenoble, Service Des Transferts Thermiques, Note TT No. 275, 1967.
Received January 15, 1996; revised July 1, 1996