- Email: [email protected]
Critical heat flux in transient flow boiling during simultaneous variations in flow rate and thermal power
Critical Heat Flux in Transient Flow Boiling During Simultaneous Variations in Flow Rate and Thermal Power I
G. P. Celata M. Cumo F. D'Annibale G. E. Fareilo ENEA C.R.E. Casaccia-- TERM/ISP Heat Transfer Laboratory, Rome, Italy
1 T h e results of an experimental investigation on critical heat flux in forced convective flow during transients caused by simultaneous variations of flow rate and thermal power are reported. The two parameters were varied according to an exponential law for the flow rate decrease and according to a ramp and a step law for the input power increase. Experiments were carried out with a tubular test section that was electrically and uniformly heated. Test parameters included the flow rate, half-flow decay time, several values of the initial power (before the transient) and final power (at the end of the transient) in the case of step transients, and the slope of the ramp in the case of ramp transients. The pressure was kept constant during the transients. An analysis of the experimental data was conducted on the basis of the local conditions approach and applying the quasi-steady-state method. The effect of the simultaneous variation of mass flow rate and power on the time to crisis was also analyzed with respect to transients in which only one of the two parameters was varied.
Keywords: critical heat flux, flow boiling, transient boiling, experimental investigation
INTRODUCTION The thermal crisis or critical heat flux (CHF) condition is known to be an important limiting operational mode for nuclear reactors and a limiting phenomenon in the nuclear reactor core thermohydraulic design. As such, the CHF phenomenon has been extensively investigated in the past for steady-state reactor operating conditions [1-5]. However, when the CHF occurs in a nuclear reactor, it is most likely to occur during transient accident conditions. In the unlikely event of a loss of coolant accident (LOCA) in a pressurized water reactor (PWR), severe transients in pressure, mass flow rate, and heat flux may occur and cause the coolant to behave in a complicated manner. It is therefore important not only to determine the range of applicability of steady-state correlations in predicting the CHF during transients, but also to analyze the CHF behavior in transient conditions as a function of the various system parameters [6-13]. Our previous CHF investigations have dealt with separate effects of mass flow rate [14], pressure [15], and power [16] transient experiments (ie, conditions where only the flow rate, pressure, and power, respectively, change). The present paper presents the results of an experimental investigation devoted to the study of the critical heat flux using the refrigerant R-12 flowing through a vertical tube. The CHF condition is induced by a step or a ramp increase in the thermal power delivered to the test section, together with a simultaneons exponential decrease in the mass flow rate. Parameters
such as pressure and inlet fluid subcooling are kept constant during the transient tests. Experimental results are presented together with quasisteady-state predictions obtained using the ANATRA code [ 17] for evaluations of local conditions. EXPERIMENTAL APPARATUS The experimental R-12 loop is schematically illustrated in Fig. 1. It consists of a piston pump, a fluid-to-fluid preheater, an electric heater to control the inlet fluid temperature, a watercooled condenser, and an R-12 tank. The use of R-12 as a test fluid allows the simulation of water flow at higher pressures and over a wider range of system parameters. The maximum operating pressure of the loop is 3.5 MPa, whereas the maximum mass flux is 1800 kg/(m 2 s). The available electric power is 5 kW for the electric preheater and 10 kW for the test section. The test section is a stainless steel tube 7.7 nun in diameter and electrically heated uniformly over a length of 2.30 or 1.18 m. Its thermal diffusivity is around 4.1 x 10 -6 m2/s. The test section instrumentation consists of 0.5 nun K-type thermocoupies inserted into the tube wall and distributed as shown in Fig. 1. There are 12 wall temperature and 6 fluid temperature measuring stations available on the test section. The onset of the CHF condition is indicated by the thermocouple placed at the test section end, where the fluid exits from the tube. R-12 flow is upwards with subcooled inlet conditions. The data
Address correspondence to Dr. Ing. Gian Piero Celata, ENEA--Casaccia TERM/ISP Heat Transfer Laboratory, Via Anguillarese, 301-00060 Roma, Italia. Experimental Thermal and Fluid Science 1989; 2:134-145 © 1989 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
134
0894-1777/89/$3.50
CHF in Transient Flow Boiling
135
9.5
TF: FLUIDTHERNOCUUPLE REGULATING VALVES
TW: WALL THERN~OUPLE PRE-HEATER VVX/V
+
~ I~WATER CONDENSER
•
.I TEST SECTION
t
INLET
WATER OUTLE1
WATERINLE1 ,&',
TI
AIR SUPPLY- ~ x ~
~
~ FILTER
--
ou,PER( i
__,w
LOW.ETERS T ELECTRICHEATER
t Figure 1. Schematic of the experimental apparatus and the test section. acquisition is accomplished by a Digital Micro PDP 11 computer, coupled with a Watanabe eight-channel graphic multirecorder system. E X P E R I M E N T A L RESULTS
data and predictions obtained using the above-reported correlation is illustrated in Fig. 2 for mass flux ranging from 350 to 1500 kg/(m 2 s). As shown in the figure, this agreement is good and within a + 10% band for 96% of the experimental data points.
Steady-State Critical Heat Flux Experiments
Test Matrix and Transients Characteristics
To establish the reference conditions for transients analysis, we first carried out a set of steady-state critical heat flux tests [18]. In this investigation the pressure ranged from 1.25 MPa (corresponding to 8 MPa for water) to 2.75 MPa (corresponding to 16.2 MPa for water), whereas the mass flux ranged from 400 to 1600 kg/(m 2 s). The inlet subcooling varied from 23"C to 0*C. As far as CHF predictions with R-12 are concerned, very few correlations are available in the literature [18]. A correlation proposed by Bertoletti et al [19] for both water and R-12 was adopted for the present situation. It was slightly modified to behave better with the experimental data as a function of pressure. The correlation has the following form (SI units):
Transients with simultaneous variation of mass flow rate and thermal power involved three independent parameters: the initial pressure P0, the mass flux before the transient Go, and the thermal power input before the transient W0. The transient is characterized by several parameters. The mass flux decrease is characterized by the half-flow decay time th, ie, the time necessary to halve the initial value Go. The step thermal power increase is characterized by the thermal power input at the end of the transient, W**. The ramp thermal power increase is characterized by the slope of the straight line to which the power ramp tends, ct (kW/s). The test matrix can be represent~xl as follows:
it
go [kg/( m2 s)]
rhfg a-Xin
qCHF= x D L 1 + b / L
th (s) ot (kW/s)
a = 10(1.18 - 2.07Pr + 1.55p2)/G °'33 b = 0.3786(1/Pr- l)°'4Dl'4G
p0 (MPa)
(1)
where P~ is the reduced pressure, ie, the ratio of the operating pressure p to the critical value Peat (P~t = 4.2 MPa). The comparison between the steady-state CHF experimental
1.2;
1.5;
2.0;
2.75
1030; 1250; 1500 0.4;
1.0;
3.0;
7.0
0.66; 1.43; 1.81
The values of the thermal powers Wo and W® are linked to WCHF.,/70, and G, WCHFbeing the steady-state critical thermal power calculated before the beginning of the transient. These latter values are reported in Table 1. As for the step power variations, the values of /410 were
136 G . P . Celata et al.
.\.
12
Jy /
It
/
/
E 3: e"
/o~ ~
LL "e"
f
PoIHPol ATsubi°cl: L [ m ] o
L2
= 23
'2.3
• n • X zx • •
12 1.5 .1.5 1.75 2.0 2.0 2.0
2.3 2.3 2..1 2.3 23 2.3
o
2.2 2./,
0 •
2.7 2.7
o 1
3o
": Z 3 : 23 < 23 =23 -'23 • 23 :23 -'-23 "-23 = 23 < Z3 -" 23
i
I 8
130 2.3 2.3 Z.3 2.3 2.3
12
q" I:HF, exp [W/ mz] ,,10 Figure 2. Steady-state reference CHF tests: predictions obtained using correlation given by Eq. (1).
fixed such that the difference between W e l l F and W0 (margin to crisis, M ) was constantly equal to 0.5, 1.0, and 1.7 kW. Similarly, the value of W,, was chosen such that the difference between W~. and WCHF(excess to crisis, E ) was always equal to 2.0 kW. In the case of ramp power transients, the value of /4"o was foled such that M was always equal to 1.0 kW. Mass flow rate decays were obtained by means of a hydraulic integrator consisting of a regulating valve and a
bleed controlled with pressurized air: higher pressures correspond to longer half-flow decay times h . Decay curves of inlet mass flux are approximated by the mathematical expression G ( t ) / Go = t/~t/22[(a~ + ta2) exp(t/i t) + ( bl + tb2) exp(/~2t)]
(2)
with a l ---- -- {2/[/~1 ( ~ l --/~2) 3 ] q- l / [ / ~ f ( / ~ l --/~2)21}
a2 = 1/[~1(/32- ~1) 2]
bl = - {2/[fl2 (f12-/~l) 3] + 1/[~22(fl2 - ~/i)2] }
Table 1. Experimental Critical Heat Flux Data Po (MPa)
G [kg/(s me)]
WCHF (IV)
1.2 1.2 1.5 1.5 2.0 2.0 2.0 2.75 2.75
1000 1470 1000 1470 1000 1250 1470 1000 1470
4170 5020 3740 4570 3320 3770 4160 2800 3680
b2 = 1/[~2(~2 - BI) 2] where/~l and ~2 are values linked to the hydraulic integrator, obtained with best-fit procedures on experimental data of G (see Tables 2 and 3). The step thermal power input to the test section during a transient is not, however, of a step nature, owing to the f'mite time constants of the electric power system. The timedependent expression of the step input power to the test section wall, W ( t ) , is approximated by the following expression: W(t) = W + X~X~( W= - Wo) • [(Cl+tCz) e x p ( h l t ) + ( d ~ + t d z ) exp(kzt)]
(3)
CHF in Transient Flow Boiling Table 2. Power-Flow Transients (step) L = 2.3 Name
Po
[MPa] 240420 240440 240460 280420 280440 280460 280620 280640 280660 280820 280840 280860 340620 340640 340660 340820 340840 340860 640420 640440 640460 640620 640640 640660 640820 640840 640860 660420 660440 660460 660620 660640 660660
660820 660840 680420 680440 680460 680620 680640 680660 680820 680840 680860 840440 840460 840640 840660 840840 840860 880440 880460 880620 880640 880660 880820 880840 880860
1.245 1.243 1.238 2.369 1.238 1.240 1.232 1.240 1.242 1.252 1.239 1.239 1.354 1.370 1.356 1.364 1.356 1.357 1.991 1.994 2.002 2.000 1.997 2.004 2.005 1.993 1.998 2.000 1.997 1.999 2.000 1.991 1.991 2.001 2.004 2.006 2.004 1.994 1.999 1.991 1.983 2.004 1.995 2.017 2.737 2.738 2.748 2.742 2.731 2.753 2.745 2.747 2.736 2.745 2.739 2.709 2.731 2.742
Tin
Go 2
[~cl [kg/m s) 27.56 27.44 27.64 27.09 27.24 28.11 28.74 28.58 29.01 27.52 27.87 27.87 27.60 27.87 27.68 28.11 27.71 27.75 49.37 49.61 49.45 49.25 49.61 49.41 48.54 48.82 48.94 48.54 49.06 50.16 49.72 49.17 49.53 49.29 49.29 49.76 49.68 49.76 49.61 49.72 49.96 49.21 49.41 49.41 64.97 65.84 68.01 67.30 67.81 65.37 66.12 66.08 66.04 65.72 65.57 65.57 66.51 67.30
ATsub = 23 AC
m
1011.5 1015.6 1015.9 1456.4 1468.9 1470.3 1473.4 1482.1 1474.7 1512.6 1495.7 1495.0 1047.1 1029.6 1044.1 1065.1 1055.1 1059.5 1016.6 1017.5 1018.5 1007.0 1027.7 1023.9 1052.6 1060.9 1062.2 1249.7 1259.8 1241.5 1263.6 1261.1 1258.8 1249.7 1290.2 1469.4 1483.2 1480.7 1465.6 1468.1 1477.6 1491.9 1519.7 1521.5 986.8 1013.4 1027.7 990.1 1065.4 1054.1 1430.3 1459.6 1463.9 1480.7 1461.2 1501.4 1491.4 1497.6
Wo
Wss
Wreg
X1
X2
~1
~2
th
(kW]
[kW]
|kw]
[l/s)
[l/s]
[l/s]
[-]
Is]
(s]
2.421 3.154 3.636 3.325 4.107 4.534 3.276 4.015 4.540 3.324 4.015 4.515 2.462 3.183 3.672 2.463 3.159 3.684 1.547 2.243 2.732 1.553 2.219 2.750 1.510 2.219 2.707 1.981 2.640 3.183 1.993 2.646 3.165 1.962 2.689 2.378 3.049 3.562 2.316 3.055 3.580 2.304 3.013 3.568 1.810 2.482 1.853 2.366 1.908 2.433 2.714 3.245 2.073 2.775 3.306 2.084 2.714 3.233
4.085 4.098 4.093 5.544 4.944 4.904 4.877 4.900 4.867 5.002 4.955 4.954 4.148 4.098 4.138 4.166 4.160 4.168 3.262 3.255 3.266 3.251 3.276 3.278 3.372 3.373 3.372 3.737 3.728 3.642 3.702 3.722 3.700 3.700 3.771 4.039 4.063 4.049 4.038 4.030 4.027 4.104 4.130 4.147 2.858 2.870 2.800 2.759 2.866 2.982 3.600 3.652 3.649 3.707 3.680 3.712 3.656 3.626
5.881 5.999 5.998 6.956 7.009 6.988 6.792 6.909 6.972 6.845 6.788 7.017 5.796 6.017 6.019 5.916 6.009 5.943 5.085 5.138 5.161 5.236 5.073 5.166 5.070 5.108 5.111 5.537 5.590 3.200 5,605 5.672 6,857 5,570 5.718 5.975 5.945 5.976 6.021 5.917 6.193 5.974 5.891 6.060 4.728 4.822 4.841 4.846 4.770 4.816 5.668 5.801 5.842 5.768 5.945 5.742 5.755 7.700
-4.98 -4.96 -5.18 -7.99 -4.36 -5.17 -11.06 -4.83 -4.93 -5.21 -5.86 -11.70 -7.55 -5.39 -8.81 -5.52 -5.28 -5.25 -5.25 -4.90 -8.97 -14.39 -5.20 -6.39 -5.02 -5.22 -6.73 -5.29 -5.19 -5.06 -9.34 -8.67 -13.03 -5.00 -4.71 -4.97 -5.12 -4.83 -9.25 -6.47 -11.04 -4.76 -5.24 -4.64 -6.68 -5.59 -7.18 -8.30 -6.54 -5.01 -6.95 -8.66 -4.83 -5.10 -5.86 -4.72 -5.02 -21.23
1.61 1.82 2.01 1.85 1.99 1.72 1.08 1.12 1.17 0.49 0.48 0.49 2.84 2.13 2.52 0.51 0.53 0.56 2.81 2.87 2.49 0.91 1.41 1.40 0.67 0.62 0.67 2.37 2.49 2.40 1.07 1.04 1.02 0.74 0.59 2.78 2.22 2.29 0.88 0.81 0.83 0.57 0.53 0.61 3.93 3.89 1.21 1.18 0.56 0.63 2.61 2.42 1.71 1.75 1.43 0.54 0.54 0.49
0.85 0.71 0.56 0.97 0.68 0.49 0.70 0.01 0.47 0.47 0.36 0.03 0.88 0.69 0.56 0.50 0.41 0.32 0.97 0.03 0.62 0.71 0.75 0.56 0.67 0.52 0.43 0.96 0.81 1.28 0.78 0.65 0.52 0.67 0,47 0,94 0.77 0.60 0.70 0.55 0.43 0.57 0.42 0.35 0.87 0.61 0.70 0.52 0.46 0.38 0.74 0.55 0.93 0.71 0.49 0.52 0.40 0.25
tCHF, ss
L = 2.3 m Nam
PO
[MPa| 670622 670662 670862
2.002 2.001 1.982
Tin
GO 2
['C] [kg/m s | 63.20 63.12 63.32
1443.6 1442.4 1466.3
-4.67 -3.772 -4.64 -7.943 -4.62 -16.553 -3.33 -28.112 -4.48 -124.520 -4.48 -15.711 -3.07 -3.386 -4.52 -3.388 -4.26 -4.092 -4.68 -7.673 -4.49 -13.164 -3.14 -7.586 -4.01 -5.282 -4.76 -16.432 -3.37 -45.270 -4.70 -11.406 -5.01 -12.425 -4.87 -9.452 -4.72 -6.346 -4.94 -6.501 -3.78 -9.347 -2.97 -8.417 -5.04 -4.185 -4.31 -10.i15 -4.61 -5.674 -4.96 -11.761 -4.31 -11.875 -4.77 -4.354 -4.96 -9.713 -5.06 -7.854 -3.33 -4.143 -3.45 -5.721 -2.13 -3.827 -4.79 -7.536 -4.86 -12.551 -4.73 -13.288 -4.84 -19.864 -5.04 -50.084 -3.20 -5.827 -4.23 -7.433 -2.94 -4.556 -4.87 -12.761 -4.99 -34.261 -4.57 -9.696 -4.26 -9.264 -4.98 -16.973 -3.95 -4.518 -3.75 -3.024 -4.54 -14.435 -5.27 -15.147 -4.15 -2101.400 -3.54 -61.852 -4.62 -2.203 -4.85 -26.827 -4.21 -15.986 -4.65 -37.019 -4.66 -26.369 -1.70 -14.115
-1.592 -1.081 -0.889 -0.949 -0.851 -1.057 -3.436 -3.185 -2.529 -7.333 -5.269 -7.521 -0.685 -0.837 -0.678 -5.141 -4.692 -4.999 -0.676 -0.658 -0.737 -2.545 -1.831 -1.403 -5.441 -3.801 -3.410 -0.888 -0.737 -0.786 -2.927 -2.473 -3.389 -3.624 -3.977 -0.639 -0.794 -0.746 -3.235 -3.195 -4.294 -4.153 -3.575 -4.332 -0.452 -0.445 -2.254 -3.227 -4.023 -3.419 -0.644 -0.702 -2.098 -1.006 -1.287 -3.468 -3.644 -4.971
tCHF,ss
texp
Is] 1.461 1.212 0.984 1.269 1.062 0,858 1.168 0.996 0,895 1.062 0.842 0.670 1.542 1.159 0.943 1.233 0.956 0.805 1.571 1.273 1.045 1.412 1.208 0.996 1.412 1.041 0.915 1.412 1.131 0.886 1.302 1.086 0.907 1.212 1.000 1.257 1.074 0.870 1.188 0.960 0.833 1.094 0.927 0.846 1.290 0.854 1.135 0.846 0.939 0.768 1.135 0.939 1.343 1.017 0.797 1.033 0.658 0.491
&Tsub = 10 *C WO
WSS
[kW]
[kW]
2.732 2.762 2.775
3.219 3.222 3.228
Wreg
[kW] 5.165 5.145 5.559
81
82
th
[l/s]
kl
[1/s]
X2
[l/s]
|-]
|s]
is]
-9.10 -6.71 -4.90
-3.81 -4.43 -4.49
-140.800 -39.198 -15.729
3.79 3.70 0.56
0.60 0.61 0.34
-0.445 -0.460 -3.892
t®xP
is] 0.813 0.837 0.736
137
138
G.P. Celata et al. Table 3. Power-Flow Transients (ramp) L = 2.3 11, Name
246640 262620 262660 262820 262840 262860 266620 266660 286640 442620 442660 442820 642220 642460 642860 644260 644420 644860 682820 682860 684260 684420 684820 684860 882840 882860 884220 884820 884840 884860 882220 882240 882460 882820 882840
O
T. In
[MPa]
P
[^Cl
1.238 1.241 1.243 1.238 1.234 1.232 1.237 1.244 1.235 1.528 1.533 1.540 2.000 1.998 1.990 1.987 1.998 1.984 1.998 1.985 1.997 2.002 2.002 1.984 2.740 2.739 2.735 2.756 2.737 2.750 2.739 2.729 2.737 2.708 2.740
28.15 28.34 28.22 28.38 27.99 28.22 27.95 28.54 28.42 37.75 37.83 37.26 50.35 49.37 50.24 49.72 49.92 50.35 50.39 49.96 50.51 50.35 50.75 49.72 66.51 65.64 65.68 66.51 65.80 65.84 65.60 66.20 65.53 65.64 66.51
G
O
[kg/m2s ] 1007.9 1235.4 1250.3 1273.5 1265.7 1291.0 1232.9 1246.5 1478.9 1027.7 1022.3 1077.9 1024.8 1012.5 1069.5 1024.8 1016.9 1051.1 1492.0 1513.4 1464.6 1477.7 1525.3 1512.1 1498.9 1513.1 1478.2 1519.5 1505.7 1507.5 1471.5 1449.8 1459.7 1495.9 1498.9
L = 2.3 m Name
Po [MPa]
Tin ['C]
602422 602462 602822 602862
2.007 1.996 1.993 2.008
63.47 63.20 63.12 62.76
Go [kg/m2sI 1440.9 1439.5 1460.8 1466.4
6Tsub = 23 ^C W
W
o
[kWl 3.142 2.904 4.149 2.916 3.661 4.125 2.922 4.167 3.990 2.021 3.224 2.070 1.559 2.744 2.756 2.738 1.541 2.793 2.408 3.592 3.635 2.439 2.426 3.580 2.738 3.251 2.024 2.109 2.738 3.245 2.042 2.763 3.251 1.999 2.738
~,
=
SS
[kW|
[ kw/s ]
4.057 1.886 4.497 0.613 4.529 0.237 4.564 0.607 4.567 0.663 4.601 0.331 4.509 1.901 4.509 1.934 4.901 1.598 3.705 0.669 3.691 0.599 3.825 0.737 3.239 0.802 3.256 0.549 3.326 0.510 3.263 1.226 3.242 1.598 3.285 1.438 4.033 0.773 4.082 0.895 3.984 1.483 4.016 1.513 4.064 71.096 4.094 1.270 3.679 0.694 3.758 0.562 3.694 1.572 3.729 1.390 3.733 1.455 3.748 1.260 3.694 0.716 3.609 0.613 3.677 0.526 3.697 59.717 3.679 0.694
~2
th
[l/s]
[-1
Is]
Is]
-1.580 -2.358 -2.878 -1.846 -7.448 -8.198 -1.919 -8.665 -5.527 -1.627 -5.211 -10.752 -1.460 -3.481 -1.487 -6.255 -2.008 -12.916 -2.130 -2.597 -2.110 -4.269 -1.516 -5.590 -1.736 -0.387 -2.304 -35.314 -2.832 -15.609 -1.829 -6.714 -1.785 0.523 -1.494 -8.099 -1.556 -12.737 -1.224 -55.834 -1.316 -1470.800 -1.641 -19.095 0.i01 -14.253 -1.850 -19.999 -1.669 -15.851 -2.122 -25.561 -1.467 -2.753 -1.950 -18.996 -1.570 -23.657 -1.883 -22.524 -1.968 -5.973 -1.671-10163.000 -2.286-18303.000 0.074 -19.354 -1.669 -15.849
-2.372 -2.839 -1.579 -4.105 -5.360 -3.999 -2.109 -1.655 -1.391 -2.464 -1.805 -5.420 -1.392 -0.462 -3.859 -0.326 -0.643 -4.028 -4.111 -3.429 -0.394 -0.467 -3.964 -3.922 -3.803 -4.015 -0.353 -3.897 -3.763 -3.954 -0.271 -0.291 -0.594 -4.124 -3.804
0.00 1.28 1.35 0.65 0.68 0.62 1.39 1.35 1.37 1.46 1.42 0.67 5.84 3.69 0.57 5.45 3.16 0.68 0.57 0.53 4.26 3.70 0.57 0.54 0.57 0.50 5.50 0.54 0.54 0.52 6.53 5.78 2.83 0.51 0.57
0.01 1.28 0.64 0.69 0.54 0.36 1.26 0.63 0.88 1.51 0.82 0.78 3.11 1.41 0.38 1.42 2.23 0.44 0.63 0.28 1.13 2.01 0.63 0.31 0.46 0.28 2.42 0.58 0.43 0.28 3.07 2.23 1.04 0.59 0.46
~1
[l/s]
tCHF,ss
texp
Is] 1.852 2.463 1.489 2.003 1.436 1.115 2.088 1.367 1.530 2.920 1.681 2.590 4.170 2.370 1.082 2.235 3.066 1.155 2.019 1.005 1.811 2.716 1.962 0.911 1.339 0.679 3.099 1.644 1.302 0.719 3.995 3.062 1.982 1.799 1.339
6Tsub = 10 ^C
W° [kW] 1.608 2.817 1.578 2.793
Wss [kw] 3.202 3.212 3.239 3.275
~ [kW/s] 0.834 0.842 0.843 0.702
where
X [l/s]
~1 I1/s]
-1.512 -4.971 -1.159 -3290.500 -1.532 -15.812 -1.517 -22.399
82 [-]
t h tCHF,ss [s] Is]
-0.949 -0.669 -3.910 -3.711
2.18 2.51 0.56 0.55
2.13 1.12 0.75 0.35
texp Is] 3.091 1.934 2.231 1.009
where cl = - {2/[)~1 0~l - X2)3] d- 1/[h~()q - ~2)2]}
-2
~= x-r,
1
~2=~,
2
"n=~,
1
"y2=~
c2 ~-- 1/[ht (h2 - ~1) 2] dl -- - {2/[X2(X2 - Xl) 3] + I/[X22(X2 - Xl)2]} d2 = 1/[~,2(~ 2 - )~1)2]
where Al and ~2 were determined through the best-fit procedure on the experimental data points (see Table 2). In the ease of the ramp input power variation, the timedependent expression 14:(t) is approximated by the expression W(t)= Wo+ctA2[(el+~2t)eXt+(W+72t)]
(4)
Analogously to other mathematical laws, we got the value of h from the best-fit procedure of the experimental data points (for the values of each test, see Tables 2 and 3). The parameter a is defined as the slope of W(t) for t >i 3 [ h [; after this time the curve can be considered a straight line. In mathematical terms,
dt
t~
CHF in Transient Flow Boiling The electrical power is read by instnnnents directly at the terminals placed on the test channel ends; therefore it is exactly equal to the thermal power delivered to the wall. Computerized data acquisition accounts for the heat loss from the test section, which (although very small) was experimentally determined as a function of the wall temperature. Consequently W ( t ) represents the actual net thermal power delivered to the test channel wall. The actual thermal power delivered to the fluid, Wy, depends not only on the response of the electrical power system as discussed above, but also on the thermal capacity of the test section wall. Assuming that the test channel can be characterized by an average temperature Tw, we may write
aTw
W/(t) = W(t) -(pcp V)m dt
(6)
the heat balance equation (5) becomes dTw W(t) = hS[Tw(t)- Tb] + (ocp V)m dt
Wo w~ W®
tCHF,ss tCHF,tr O~
~l, ~2
(5)
where p is the density, ca is the specific heat, and V is the volume of the test section tube wall. Since the heat flux to the fluid can also be expressed in terms of the heat transfer coefficient from the wall to the fluid, h, heat transfer area S, and bulk fluid temperature Tb, ie, Wf(t) = hS[ T,(t) - Tb]
Tin Go
(7)
This equation can now be solved for the wall temperature distribution T, by using the stainless steel test section material properties and Eq. (3), or Eq. (4), for the test section input power distribution. It was solved numerically by means of the A N A T R A code [17]. Parameters hi and 3,2 in Eq. (3) (step power variations) have the physical meaning of the inverse of the time constants of the eleOxical feeding system, which can be represented by two inseries delay blocks (each with a transfer function characterized by a pole of multiplicity 2). Concerning ramp power variations, Eq. (4), the electrical feeding system can be represented by only a delay block of the same kind, characterized by )~. The time-dependent expression of mass flux, G(t), was derived by analogy from power timedependent laws. Parameters B1 and B2 in Eq. (2) have no direct physical meaning in the present analysis. As for the derivation of the numerical values of/~1,/~2, hi, )~2, and ~, they were obtained by fu'st equating Eqs. (2)-(4) to the measured values of G(t) and W ( t ) and then applying a best-fit procedure.
tt= Lpfo/ Go
•
Transient Critical Heat Flux Experiments Results and Data Reduction
initial inlet pressure
(8)
as the time necessary for a fluidparticleto pass through the test section channel with no power input to the system, the experimental results are plotted versus the ratio of the halfflow decay time th and tt. More precisely, in Fig. 3 the transient to steady-state criticalmass flux ratio is reported versus th/itfor both step and ramp power variations.The ratio of the transientto steady-statecriticalthermal power is plotted in Fig. 4 against tJtt, and similarly the transientto steadystate time to crisisratio is shown in Fig. 5. Speaking of steady-statecriticalvalues of mass flux,thermal power, and time to crisis,we mean values calculated at the time in which, considering the transient as a sequence of steady-statetime steps,CISE-modified correlationforeseesthe onset of CHF. In mathematical terms, such values are obtained by solving the system made up by Eqs. (I), (2), and (3) or (4). Experimental results are grouped by the pressure p and the margin to crisisM in the case of step power variations,and by the mass flux G and ramp slope ~ in the case of ramp power transients. Looking at Figs. 3-5 it is possible to argue that the transient does not seem to be affected by either the pressure or the mass flux. Regarding the step power variations, the following observations can be made:
An evaluation of the experimental uncertainty was achieved by carrying out 20 runs of the same test (step power variations). Experimental results of time to crisis lie around the mean value (1.5 s) with a standard deviation of 0.05 s and a maximum deviation of + 0.1 s.
Po
inlet temperature initial inlet mass flux initial thermal power steady-state critical thermal power before the transient thermal power at the end of transient (step input thermal power) half-flow decay time time to crisis calculated using correlation (1) at inlet conditions experimental time to crisis ramp input power slope parameters in Eq. (2) parameter in Eq. (4) parameters in Eq. (3)
A graphic representation of experimental data is reported in Figs. 3-5. Defining the time transit parameter tt
Experimental Uncertainty
Experimental results are summarized in Tables 2 and 3, where the following parameters are listed:
139
•
For a fixed value of th/tt, the lower M is, the higher both the GCHF,tr/GcHF,ssand WcnF,~/WCHV,~ ratios are. That means that experimental results are closer to calculated steady-state values for small values of M. From a general analysis of data points, it appears that CHF behavior under transient conditions can be predicted with the steady-state approach at inlet conditions for values of th/tt greater than 3. Beyond this threshold it is evident from Figs. 3-5 that the ratios between the transient and steady-state values of mass flux, thermal power, and time to crisis tend to unity. The threshold is greatly reduced in comparison with that observed in single flow rate transients (th/tt > 8) (ie, conditions where only the flow rate changes) [14]. Of course, this is a negative aspect from the safety viewpoint, as the onset of CHF is anticipated. As far as time to crisis values are concerned, the comparison between thermal power transients [16],
140
G . P . Celata et al,
1.2
{/1
u."
I
'
I
Doe
0.8
'
I
'
I
•
"I" (.3 .,o
~
[]
O.4
ID•
•
0o
0.5
H [kW] 1.0 1.7
A
A
1.2 1.5
A
p
2.0 [HPa]
AS
E]
0.0
I 0.5
0.0
]
[]
•
2.7
I 1.5
I
1.0
I 2.0
2.5
th/ttr (a)
1.2
I
'
I
'
I
oe Ul
eA
A
O~
[]
~0.8
i
A@
=2
5 E
O A
G [kg/e2s] 1030 1250 1500
=-" o.4
5
A
~
0.5 0.7
A
(x
1.5 [kW/s] 2.0 0.0
I
O.
I 1.
i
I 2.
,
I 3.
i
I 4.
i 5.
th/ttr (b) Figure 3. Transient to steady-state critical mass flux ratio versus half-flow decay time to transit time parameter ratio. (a) Step power variations; (b) ramp power variations.
where only the power changes, and present double parameter transients, shows a reduction of the time to crisis up to a factor of 2. Comparing present results with mass flux transients [14], where only the mass flux changes, time to crisis is reduced by up to a factor of 4. That means that power variations affect the transient more than mass flux variations.
Because of the small values of time to crisis (less than unity), the ratio between the transient and the steadystate time to crisis, tCHF,~/tcHF,,,, is inversely affected by M with respect to the results reported in Figs. 3 and 4. In the case of ramp variations we have behavior similar to that observed for step variations, even though with less
CHF in Transient Flow Boiling
2.5
'
I
'
'
I
141
!
I
~I [kW] 1.0 1.7
0.5
1.2
2.0 A
@
A
-1¢lJ
p [MPa]
1.5 2.0 2.7
A @
3
1.5
=." -r
Oo []
1.0
0.0
I
O
I 0.5
l
1 1.0
t
I 1.5
i
I 2.0
2.5
th/ttr (a)
I
'
I
'
|
'
1
2.0 G [kg/12s] 1030 1250 1500
0
5
A
A
*
@
0.5 0.7 1.5 2.0
@ A
1.2
a [kW/s]
A
1
0.8
-I
O.
[
1.
I
1
I
I
2.
3.
I
I
4.
I
5.
th/ttr (b)
Figure 4. Transient to steady-state critical thermal power ratio versus half-flow decay time to transit time parameter ratio. (a) Step power variations; (b) ramp power variations.
intensity, comparing present results to simple flow rate transients [14]. Ramp/flow rate transient behavior lies between that of the step/flow rate and that of simple flow rate. Consequently, time to crisis values are greater than those observed in step/flow rate transients. From the observations reported above, it can be stated that
the simultaneous occurrence of flow rate and thermal power variations generally gives rise to a synergistic effect in the sense of drastically reducing the difference between the experimental occurrence of CHF and the prediction obtained with the steady-state approach at inlet conditions, as achieved in simple transients analysis [14, 16]. For a fLxed half-flow
G . P . Celata et al.
142
'
I
'
l
'
I
.
I~
[kW]
0.5
1.0
1.7
&
t,
A
1.2 G~
d- r
.
1.5 2.0 2.7
~J
p [NPa]
.
-r
r
~a .
I 0.5
0"0.0
,
I 1.0
J
I 1.5
I 2.0
2.5
th/ttr (a) .
'
I
'
I
'
A
I
'
1030
1250
1500 0.5 0.7 1.5 2.0
t~ t~
¢.J .
<"
[]
0
.# %
.#
'
G [kg/m2s]
.
.#
I
Q
,.~
~
•
[]
[]
•
a [kW/s]
•
kk. "t" ¢.J
.
0.0.
I
I 1.
i
I 2.
,
I 3.
i
I 4.
i
I 5.
th/ttr (b) Figure 5. Transient to steady-state time-to-crisis ratio versus half-flow decay time parameter ratio. (a) Step power variations; (b) ramp power variations. decay time th, the described behavior is more and more evident when the input thermal power rate is increased. For what concerns the data reduction, the simplest approach in predicting the time to crisis tCHF Consists in equating the timedependent expression of the input thermal power delivered to the fluid, Wl(t), to a reliable steady-state CHF correlation, calculated at inlet conditions, including the instantaneous value of the inlet mass flux.
As shown in Fig. 6, this approach tends to underestimate the
experimental data, which is not acceptable even for screening calculations. A more suitable approach consists in using correlation (1) with the local instantaneous values of the parameters of interest; this method is sometimes called the quasi-steady-state approach. To calculate the local conditions, an original computer code, ANATRA [17], based on reassessed heat transfer correlations [18], was employed. For the
CHF in Transient Flow Boiling '
I
'
L
I
~
4.
'
I
[
STEP
~
,0f
3.
143
i Po
RANP
[MPa)
£>
1.5
o A o
1.25 1.35 2.02
n
2.77
•
u2 1.
c3
1.0
D n ~ E3
t
I
0'0.
1.
2.
3.
.
o. ~'.
4.
'
:,1.
.
"
,
4 I.
Figure 6. Time-to-crisis predictions using the steady-state approach at inlet conditions. prediction of CHF conditions the quasi-steady-state method consists in calculating at every time step the value of the local heat flux (or steam quality) and comparing the computed value with the value predicted using correlation (1) (or other equivalent reliable correlation). The CHF condition is indicated when the local value of heat flux (or steam quality) is greater than or equal to the value given by correlation (1). An overall representation of local conditions analysis is reported in Fig. 7, where the calculated time to crisis is plotted versus the experimental value. The agreement is quite satisfactory, most of the data being within a + 20% band. Predicted ramp power variations seem to be a little less scattered than predicted step power variations, because of the minor quickness of the power transient. This latter observation is more evident in Fig. 8, in which the ratio between the calculated and experimental times to crisis is plotted against the half-flow decay time for both types of thermal power variations. In Fig. 9, the ratio between the calculated and experimental times to crisis is reported versus the margin to crisis M for step transients (Fig. 9a), and versus the ramp slope o~ for ramp transients (Fig. 9b). No systematic influence of either pressure or mass flux is shown. Finally, in Fig. 10, six examples of ANATRA code wall and fluid temperature predictions at the outlet section of the test channel are shown together with the experimental measure-
I
2.5
'
[
I
2.0
0 A
.ou
©
1.5
)
0. So'
0'0
1.
2.
t
exp
3.
&
I
I
,
0.5
I
,
Figure 7. Time-to-crisis predictions using the steady-state appreach at local conditions (quasi-steady-state method).
L
I
1.5
1.0
l
2.0
2.5
(a) I
/
I
I
RAMP-VARIATION
[]
o
Go
I~T~alb
[kg/m2-s] 1030 1250 1500 1450
[K] 23 23 23 10
A A
0
4.
is]
[K] 23 23 23 10
M [kW]
1.0
I
~Tsub
1.0
.....
~
Go [kg/m2'-s) 1030 1250 1500 1450
& []
U
I
I
STEP-VARIATION
1.5 --4 e: U
,
8.
The main objective of this research was to obtain CHF experimental data during transients caused by the simultaneous variation of power and flow rate and to verify the quasi-steadystate method for their prediction. Such a method is also adopted in RELAP 5/MOd 2 code. The results of this study
-£
I
'
Practical Significance
O A
,
I.
ments. The steady-state condition before the transient is also calculated by the steady-state section of the code.
2.0
~ ' r a
,
Figure 8. Calculated to experimental time-to-crisis ratio versus half-flow decay time.
2.5
~'~'#
.
t h Is]
tCHF. exp [ s ]
i.
.
' "50.0
.
. . 0 0
'
.
.
.
.
.
.
<>
I 0.5
,
.
[]
. . "" &
I , I 1.0 1.5 a [kWls]
.
.
,
. O
I 2.0
.
,
2.5
(b)
Figure 9. Calculated to experimental time-to-crisis ratio (a) versus the margin to the thermal crisis and (b) versus the ramp slope.
144
G. P. Celata et al. 90. ~
,
1
'
• OIF,exp O Tw, exp
t[ | [
r
'
I--
I
r - -q |STEP-WISE)
~
100.
CHF,exp Tw,exp
.....
- .......
7~
STEP-WISE TRANSIENT
Tw, cal E3 E]
......
Tf, cal
/'(~]
.U_~.J'
96.
_
<
<
7¢:
II~E]
75.
i.-1
U
92.
~. ............ . ........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
...............................
"""-,
70.
8B. ,
O. 0
O.S
1.0 t [s]
I
,
8.4
).0
1.5
'
85.
,(
I
t [s]
[
Tw,exp Tw, cal Tf,cal
--
'
I
STEP-WISE TRANSIENT
100. ///
Tw, exp [ Tw,cal | ...... Tf,cal |
RAHP~ISE TRANSIENT
t[! '
_ ~ _ ~ . _.
es. -
80
w
90.
75.
70.
..,...... ...............
85. ,
O.
I 0.4
,
I 0.8
,
1
0.
1.2
...............................................
. . . . . , . ......................
,
L
l
1.
,
l
2.
75.
70.
[
,
J
4.
(d)
'
CHF, exp Tw,exp Tw, c a l ...... T f , c a l
I
3.
t Is]
t [s] (c)
<
1 1.2
,
(b)
(a)
90.
t
O.B
90.
I
I
I RCg,IP'4aISE BS. / (
65. i
f
~..
CHF, exp Tw,exp Tw, c a l " Tf, cal
I
[
[
~tP'~ISE TRANSIENT
80,
k-,
75.
60.
55 '0.0
L
0.5
,
[ 1.0
~
I
1.5
L
70 "0 .'0
'
I
~
0.4
t Is] (e)
1 0.8
,
1.
t [s] (f)
Figure 10. Typical predictions of experimental outlet wall temperatures versus time using the ANATRA code.
SUMMARY AND CONCLUSIONS
experimental data revealed the general inadequacy of using the steady-state critical heat flux correlations at inlet conditions in predicting transient situations. An analysis of the local conditions (quasi-steady-state approach) is shown to reproduce the test data reasonably well, with an uncertainty of + 20%.
An experimental investigation of the critical heat flux with flow rate and step or ramp input thermal power simultaneous variations was performed using R-12 in a vertical channel. The
We are deeply grateful to G. Farina, M. Morlacca, and A. Lattanzi, who performed the experimental runs and gave useful suggestions. Thank~ ale due also to Mrs. B. Perra for her helpful assistance in editing the paper.
allow one to establish with experiments the performance and the confidence level of the method where the investigated range is very wide and is therefore related to practical situations.
CHF in Transient Flow Boiling NOMENCLATURE a l , a2 a b l , b2 b el, c2 cp d l , dz D E G h h/s L M p q~ S
t T V x W
constants in Eq. (2), s 4, s 3 parameter in Eq. (1), dimensionless constants in Eq. (2), s 4, s 3 parameter in Eq. (1), m constants in Eq. (3), s 4, s 3 specific heat, J/(kg K) constants in Eq. (3), s 4, s 3 diameter of test section, m excess power to crisis, W mass flux, kg/(m 2 s) heat transfer coefficient, W / ( m z K) latent heat, J/kg length of heated test section, m margin power to crisis, W pressure, Pa heat flux, W / m 2 wall/fluid heat transfer surface, m 2
time, s temperature, °C volume of the test section wall, m 3 steam quality, dimensionless thermal power, W
Greek Symbols ot ~1,/~2 71, 72 ~1, ~2
1" X ),1, ),2 p
ramp slope, W/s parameters in Eq. (2), s-1 parameters in Eq. (4), S 3, S2 parameters in Eq. (4), s 3, s 2 mass flow rate, kg/s parameter in Eq. (4), s-1 parameters in Eq. (3), s - i density, kg/m 3
Subcripts b CHF crit f h in m r ss t tr w 0 oo
bulk fluid critical heat flux, thermal crisis critical condition fluid half-flow inlet metal reduced steady-state transit transient test section wall referred to the situation before the transit referred to the situation at the end of the transient
2. Bergles, A. E., Collier, J. G., Delhaye, J. M., Hewitt, G. F., and Mayinger, F., Two-Phase Flow and Heat Transfer in the Power and Process Industries, pp. 256-280, Hemisphere, Washington, D.C., 1981. 3. Hewitt, G. F., Burnout, in Handbook of Multiphase Systems, G. Hetsroni, Ed., Hemisphere, Washington, D.C., 1982. 4. Katto, Y., Forced-Convection Boiling in Uniformly Heated Channels, in Handbook of Heat and Mass Transfer, N. P. Cheremisinoff, Ed., pp. 303-325, Gulf, Houston, Texas, 1986. 5. Katto, Y., Critical Heat Flux in Boiling, Proc. 8th International Heat Transfer Conference, Vol. 1, pp. 171-180, Hemisphere, Washington, D.C., 1986. 6. Lahey, R. T., The Analysis of Transient Critical Heat Flux, General Electric Report, GEAP 13249, 1972. 7. Hein, D., and Mayinger, F., Burnout Power in Transient Conditions, Proceedings of the Seminar on Two-Phase Flow Thermohydraulics, ENEA Report Rome, 1972. 8. Shiralkar, B. S., Polomik, E. E., Lahey, R. T., Gonzales, J. M., Radcliffe, D. W., and Schnebly, L. E., Transient Critical Heat Flux--Experimental Results, General Electric Report, GEAP 13295, 1972. 9. Leung, J. C. M., Transient CHF and Blowdown Heat Transfer Studies, Argonne National Laboratory Report, ANL/RAS/LWR-802, April 1980. 10. Moxon, D., and Edwards, P. A., Dryout during Flow and Power Transient, Proc. European Two-Phase Flow Group Meeting, Winfrith, UK, June 1967. 11. Cumo, M., Fabrizi, F., and Palazzi, G., Transient Critical Heat Flux in Loss of Flow Transients, Int. J. Multiphase Flow, 4, 497-509, 1978. 12. Kataoka, I., Serizawa, A., and Sakural, A., Transient Boiling Heat Transfer under Forced Convection, Int. J. Heat Mass Transfer, 26, 583-595, 1983. 13. Kataoka, I., Serizawa, A., Transient Boiling Heat Transfer under Forced Convection, in Handbook of Heat and Mass Transfer, N. P. Cheremisinoff, Ed., pp. 327-383, Gulf, Houston, Texas, 1986. 14. Celata, G. P., Cumo, M., D'Annibale, F., Farello, G. E., and Setaro, T., Critical Heat Flux in Flow Transients, Proceedings of 8th International Heat Transfer Conference, Vol. 5, pp. 24292436, Hemisphere, Washington, D.C., 1986." 15. Celata, G. P., Cumo, M., D'Annibale, F., and Fareilo, G. E., CHF in Flow Boiling during Pressure Transients, Proc. 4th Miami International Symposium on Multi-Phase Transport and Particulate Phenomena, Miami Beach, December 1986. 16. Celata, G. P., Cumo, M., D'Annibale, F., Farello, G. E., and Abou Said, S., Critical Heat Flux in Flow Boiling during Power Transients, Proceedings of ASME-AIChE-ANS National Heat Transfer Conference, Pittsburgh, Pa., August 1987. 17. Celata, G. P., Cumo, M., D'Annibale, F., Farello, G. E., and Abou Said, S., ANATRA--A Computer Code for Transit Critical Heat Flux Analysis with Refrigerant-12, in print as ENEA Report. 18. Celata, G. P., Cumo, M., D'Annibale, F., Farello, G. E., and Setaro, T., Reassessment of Forced Convection Heat Transfer Correlations for Refrigerant-12, Energia Nucleate, 3(1), 19-32, 1986. 19. Bertoletti, S., Gaspari, G. P., Lombardi, C., Peterlongo, G., and Silvestri, M., Heat Transfer Crisis with SWam-Water Mixtures, Energia Nucleate, 12(13), 121-172, 1965.
REFERENCES 1. Collier, J. G., Convective Boiling and Condensation, 2nd ed., pp. 248-313, McGraw-Hill, New York, 1972.
145
Received May 17, 1988; revised December 8, 1988
G. P. Celata M. Cumo F. D'Annibale G. E. Fareilo ENEA C.R.E. Casaccia-- TERM/ISP Heat Transfer Laboratory, Rome, Italy
1 T h e results of an experimental investigation on critical heat flux in forced convective flow during transients caused by simultaneous variations of flow rate and thermal power are reported. The two parameters were varied according to an exponential law for the flow rate decrease and according to a ramp and a step law for the input power increase. Experiments were carried out with a tubular test section that was electrically and uniformly heated. Test parameters included the flow rate, half-flow decay time, several values of the initial power (before the transient) and final power (at the end of the transient) in the case of step transients, and the slope of the ramp in the case of ramp transients. The pressure was kept constant during the transients. An analysis of the experimental data was conducted on the basis of the local conditions approach and applying the quasi-steady-state method. The effect of the simultaneous variation of mass flow rate and power on the time to crisis was also analyzed with respect to transients in which only one of the two parameters was varied.
Keywords: critical heat flux, flow boiling, transient boiling, experimental investigation
INTRODUCTION The thermal crisis or critical heat flux (CHF) condition is known to be an important limiting operational mode for nuclear reactors and a limiting phenomenon in the nuclear reactor core thermohydraulic design. As such, the CHF phenomenon has been extensively investigated in the past for steady-state reactor operating conditions [1-5]. However, when the CHF occurs in a nuclear reactor, it is most likely to occur during transient accident conditions. In the unlikely event of a loss of coolant accident (LOCA) in a pressurized water reactor (PWR), severe transients in pressure, mass flow rate, and heat flux may occur and cause the coolant to behave in a complicated manner. It is therefore important not only to determine the range of applicability of steady-state correlations in predicting the CHF during transients, but also to analyze the CHF behavior in transient conditions as a function of the various system parameters [6-13]. Our previous CHF investigations have dealt with separate effects of mass flow rate [14], pressure [15], and power [16] transient experiments (ie, conditions where only the flow rate, pressure, and power, respectively, change). The present paper presents the results of an experimental investigation devoted to the study of the critical heat flux using the refrigerant R-12 flowing through a vertical tube. The CHF condition is induced by a step or a ramp increase in the thermal power delivered to the test section, together with a simultaneons exponential decrease in the mass flow rate. Parameters
such as pressure and inlet fluid subcooling are kept constant during the transient tests. Experimental results are presented together with quasisteady-state predictions obtained using the ANATRA code [ 17] for evaluations of local conditions. EXPERIMENTAL APPARATUS The experimental R-12 loop is schematically illustrated in Fig. 1. It consists of a piston pump, a fluid-to-fluid preheater, an electric heater to control the inlet fluid temperature, a watercooled condenser, and an R-12 tank. The use of R-12 as a test fluid allows the simulation of water flow at higher pressures and over a wider range of system parameters. The maximum operating pressure of the loop is 3.5 MPa, whereas the maximum mass flux is 1800 kg/(m 2 s). The available electric power is 5 kW for the electric preheater and 10 kW for the test section. The test section is a stainless steel tube 7.7 nun in diameter and electrically heated uniformly over a length of 2.30 or 1.18 m. Its thermal diffusivity is around 4.1 x 10 -6 m2/s. The test section instrumentation consists of 0.5 nun K-type thermocoupies inserted into the tube wall and distributed as shown in Fig. 1. There are 12 wall temperature and 6 fluid temperature measuring stations available on the test section. The onset of the CHF condition is indicated by the thermocouple placed at the test section end, where the fluid exits from the tube. R-12 flow is upwards with subcooled inlet conditions. The data
Address correspondence to Dr. Ing. Gian Piero Celata, ENEA--Casaccia TERM/ISP Heat Transfer Laboratory, Via Anguillarese, 301-00060 Roma, Italia. Experimental Thermal and Fluid Science 1989; 2:134-145 © 1989 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
134
0894-1777/89/$3.50
CHF in Transient Flow Boiling
135
9.5
TF: FLUIDTHERNOCUUPLE REGULATING VALVES
TW: WALL THERN~OUPLE PRE-HEATER VVX/V
+
~ I~WATER CONDENSER
•
.I TEST SECTION
t
INLET
WATER OUTLE1
WATERINLE1 ,&',
TI
AIR SUPPLY- ~ x ~
~
~ FILTER
--
ou,PER( i
__,w
LOW.ETERS T ELECTRICHEATER
t Figure 1. Schematic of the experimental apparatus and the test section. acquisition is accomplished by a Digital Micro PDP 11 computer, coupled with a Watanabe eight-channel graphic multirecorder system. E X P E R I M E N T A L RESULTS
data and predictions obtained using the above-reported correlation is illustrated in Fig. 2 for mass flux ranging from 350 to 1500 kg/(m 2 s). As shown in the figure, this agreement is good and within a + 10% band for 96% of the experimental data points.
Steady-State Critical Heat Flux Experiments
Test Matrix and Transients Characteristics
To establish the reference conditions for transients analysis, we first carried out a set of steady-state critical heat flux tests [18]. In this investigation the pressure ranged from 1.25 MPa (corresponding to 8 MPa for water) to 2.75 MPa (corresponding to 16.2 MPa for water), whereas the mass flux ranged from 400 to 1600 kg/(m 2 s). The inlet subcooling varied from 23"C to 0*C. As far as CHF predictions with R-12 are concerned, very few correlations are available in the literature [18]. A correlation proposed by Bertoletti et al [19] for both water and R-12 was adopted for the present situation. It was slightly modified to behave better with the experimental data as a function of pressure. The correlation has the following form (SI units):
Transients with simultaneous variation of mass flow rate and thermal power involved three independent parameters: the initial pressure P0, the mass flux before the transient Go, and the thermal power input before the transient W0. The transient is characterized by several parameters. The mass flux decrease is characterized by the half-flow decay time th, ie, the time necessary to halve the initial value Go. The step thermal power increase is characterized by the thermal power input at the end of the transient, W**. The ramp thermal power increase is characterized by the slope of the straight line to which the power ramp tends, ct (kW/s). The test matrix can be represent~xl as follows:
it
go [kg/( m2 s)]
rhfg a-Xin
qCHF= x D L 1 + b / L
th (s) ot (kW/s)
a = 10(1.18 - 2.07Pr + 1.55p2)/G °'33 b = 0.3786(1/Pr- l)°'4Dl'4G
p0 (MPa)
(1)
where P~ is the reduced pressure, ie, the ratio of the operating pressure p to the critical value Peat (P~t = 4.2 MPa). The comparison between the steady-state CHF experimental
1.2;
1.5;
2.0;
2.75
1030; 1250; 1500 0.4;
1.0;
3.0;
7.0
0.66; 1.43; 1.81
The values of the thermal powers Wo and W® are linked to WCHF.,/70, and G, WCHFbeing the steady-state critical thermal power calculated before the beginning of the transient. These latter values are reported in Table 1. As for the step power variations, the values of /410 were
136 G . P . Celata et al.
.\.
12
Jy /
It
/
/
E 3: e"
/o~ ~
LL "e"
f
PoIHPol ATsubi°cl: L [ m ] o
L2
= 23
'2.3
• n • X zx • •
12 1.5 .1.5 1.75 2.0 2.0 2.0
2.3 2.3 2..1 2.3 23 2.3
o
2.2 2./,
0 •
2.7 2.7
o 1
3o
": Z 3 : 23 < 23 =23 -'23 • 23 :23 -'-23 "-23 = 23 < Z3 -" 23
i
I 8
130 2.3 2.3 Z.3 2.3 2.3
12
q" I:HF, exp [W/ mz] ,,10 Figure 2. Steady-state reference CHF tests: predictions obtained using correlation given by Eq. (1).
fixed such that the difference between W e l l F and W0 (margin to crisis, M ) was constantly equal to 0.5, 1.0, and 1.7 kW. Similarly, the value of W,, was chosen such that the difference between W~. and WCHF(excess to crisis, E ) was always equal to 2.0 kW. In the case of ramp power transients, the value of /4"o was foled such that M was always equal to 1.0 kW. Mass flow rate decays were obtained by means of a hydraulic integrator consisting of a regulating valve and a
bleed controlled with pressurized air: higher pressures correspond to longer half-flow decay times h . Decay curves of inlet mass flux are approximated by the mathematical expression G ( t ) / Go = t/~t/22[(a~ + ta2) exp(t/i t) + ( bl + tb2) exp(/~2t)]
(2)
with a l ---- -- {2/[/~1 ( ~ l --/~2) 3 ] q- l / [ / ~ f ( / ~ l --/~2)21}
a2 = 1/[~1(/32- ~1) 2]
bl = - {2/[fl2 (f12-/~l) 3] + 1/[~22(fl2 - ~/i)2] }
Table 1. Experimental Critical Heat Flux Data Po (MPa)
G [kg/(s me)]
WCHF (IV)
1.2 1.2 1.5 1.5 2.0 2.0 2.0 2.75 2.75
1000 1470 1000 1470 1000 1250 1470 1000 1470
4170 5020 3740 4570 3320 3770 4160 2800 3680
b2 = 1/[~2(~2 - BI) 2] where/~l and ~2 are values linked to the hydraulic integrator, obtained with best-fit procedures on experimental data of G (see Tables 2 and 3). The step thermal power input to the test section during a transient is not, however, of a step nature, owing to the f'mite time constants of the electric power system. The timedependent expression of the step input power to the test section wall, W ( t ) , is approximated by the following expression: W(t) = W + X~X~( W= - Wo) • [(Cl+tCz) e x p ( h l t ) + ( d ~ + t d z ) exp(kzt)]
(3)
CHF in Transient Flow Boiling Table 2. Power-Flow Transients (step) L = 2.3 Name
Po
[MPa] 240420 240440 240460 280420 280440 280460 280620 280640 280660 280820 280840 280860 340620 340640 340660 340820 340840 340860 640420 640440 640460 640620 640640 640660 640820 640840 640860 660420 660440 660460 660620 660640 660660
660820 660840 680420 680440 680460 680620 680640 680660 680820 680840 680860 840440 840460 840640 840660 840840 840860 880440 880460 880620 880640 880660 880820 880840 880860
1.245 1.243 1.238 2.369 1.238 1.240 1.232 1.240 1.242 1.252 1.239 1.239 1.354 1.370 1.356 1.364 1.356 1.357 1.991 1.994 2.002 2.000 1.997 2.004 2.005 1.993 1.998 2.000 1.997 1.999 2.000 1.991 1.991 2.001 2.004 2.006 2.004 1.994 1.999 1.991 1.983 2.004 1.995 2.017 2.737 2.738 2.748 2.742 2.731 2.753 2.745 2.747 2.736 2.745 2.739 2.709 2.731 2.742
Tin
Go 2
[~cl [kg/m s) 27.56 27.44 27.64 27.09 27.24 28.11 28.74 28.58 29.01 27.52 27.87 27.87 27.60 27.87 27.68 28.11 27.71 27.75 49.37 49.61 49.45 49.25 49.61 49.41 48.54 48.82 48.94 48.54 49.06 50.16 49.72 49.17 49.53 49.29 49.29 49.76 49.68 49.76 49.61 49.72 49.96 49.21 49.41 49.41 64.97 65.84 68.01 67.30 67.81 65.37 66.12 66.08 66.04 65.72 65.57 65.57 66.51 67.30
ATsub = 23 AC
m
1011.5 1015.6 1015.9 1456.4 1468.9 1470.3 1473.4 1482.1 1474.7 1512.6 1495.7 1495.0 1047.1 1029.6 1044.1 1065.1 1055.1 1059.5 1016.6 1017.5 1018.5 1007.0 1027.7 1023.9 1052.6 1060.9 1062.2 1249.7 1259.8 1241.5 1263.6 1261.1 1258.8 1249.7 1290.2 1469.4 1483.2 1480.7 1465.6 1468.1 1477.6 1491.9 1519.7 1521.5 986.8 1013.4 1027.7 990.1 1065.4 1054.1 1430.3 1459.6 1463.9 1480.7 1461.2 1501.4 1491.4 1497.6
Wo
Wss
Wreg
X1
X2
~1
~2
th
(kW]
[kW]
|kw]
[l/s)
[l/s]
[l/s]
[-]
Is]
(s]
2.421 3.154 3.636 3.325 4.107 4.534 3.276 4.015 4.540 3.324 4.015 4.515 2.462 3.183 3.672 2.463 3.159 3.684 1.547 2.243 2.732 1.553 2.219 2.750 1.510 2.219 2.707 1.981 2.640 3.183 1.993 2.646 3.165 1.962 2.689 2.378 3.049 3.562 2.316 3.055 3.580 2.304 3.013 3.568 1.810 2.482 1.853 2.366 1.908 2.433 2.714 3.245 2.073 2.775 3.306 2.084 2.714 3.233
4.085 4.098 4.093 5.544 4.944 4.904 4.877 4.900 4.867 5.002 4.955 4.954 4.148 4.098 4.138 4.166 4.160 4.168 3.262 3.255 3.266 3.251 3.276 3.278 3.372 3.373 3.372 3.737 3.728 3.642 3.702 3.722 3.700 3.700 3.771 4.039 4.063 4.049 4.038 4.030 4.027 4.104 4.130 4.147 2.858 2.870 2.800 2.759 2.866 2.982 3.600 3.652 3.649 3.707 3.680 3.712 3.656 3.626
5.881 5.999 5.998 6.956 7.009 6.988 6.792 6.909 6.972 6.845 6.788 7.017 5.796 6.017 6.019 5.916 6.009 5.943 5.085 5.138 5.161 5.236 5.073 5.166 5.070 5.108 5.111 5.537 5.590 3.200 5,605 5.672 6,857 5,570 5.718 5.975 5.945 5.976 6.021 5.917 6.193 5.974 5.891 6.060 4.728 4.822 4.841 4.846 4.770 4.816 5.668 5.801 5.842 5.768 5.945 5.742 5.755 7.700
-4.98 -4.96 -5.18 -7.99 -4.36 -5.17 -11.06 -4.83 -4.93 -5.21 -5.86 -11.70 -7.55 -5.39 -8.81 -5.52 -5.28 -5.25 -5.25 -4.90 -8.97 -14.39 -5.20 -6.39 -5.02 -5.22 -6.73 -5.29 -5.19 -5.06 -9.34 -8.67 -13.03 -5.00 -4.71 -4.97 -5.12 -4.83 -9.25 -6.47 -11.04 -4.76 -5.24 -4.64 -6.68 -5.59 -7.18 -8.30 -6.54 -5.01 -6.95 -8.66 -4.83 -5.10 -5.86 -4.72 -5.02 -21.23
1.61 1.82 2.01 1.85 1.99 1.72 1.08 1.12 1.17 0.49 0.48 0.49 2.84 2.13 2.52 0.51 0.53 0.56 2.81 2.87 2.49 0.91 1.41 1.40 0.67 0.62 0.67 2.37 2.49 2.40 1.07 1.04 1.02 0.74 0.59 2.78 2.22 2.29 0.88 0.81 0.83 0.57 0.53 0.61 3.93 3.89 1.21 1.18 0.56 0.63 2.61 2.42 1.71 1.75 1.43 0.54 0.54 0.49
0.85 0.71 0.56 0.97 0.68 0.49 0.70 0.01 0.47 0.47 0.36 0.03 0.88 0.69 0.56 0.50 0.41 0.32 0.97 0.03 0.62 0.71 0.75 0.56 0.67 0.52 0.43 0.96 0.81 1.28 0.78 0.65 0.52 0.67 0,47 0,94 0.77 0.60 0.70 0.55 0.43 0.57 0.42 0.35 0.87 0.61 0.70 0.52 0.46 0.38 0.74 0.55 0.93 0.71 0.49 0.52 0.40 0.25
tCHF, ss
L = 2.3 m Nam
PO
[MPa| 670622 670662 670862
2.002 2.001 1.982
Tin
GO 2
['C] [kg/m s | 63.20 63.12 63.32
1443.6 1442.4 1466.3
-4.67 -3.772 -4.64 -7.943 -4.62 -16.553 -3.33 -28.112 -4.48 -124.520 -4.48 -15.711 -3.07 -3.386 -4.52 -3.388 -4.26 -4.092 -4.68 -7.673 -4.49 -13.164 -3.14 -7.586 -4.01 -5.282 -4.76 -16.432 -3.37 -45.270 -4.70 -11.406 -5.01 -12.425 -4.87 -9.452 -4.72 -6.346 -4.94 -6.501 -3.78 -9.347 -2.97 -8.417 -5.04 -4.185 -4.31 -10.i15 -4.61 -5.674 -4.96 -11.761 -4.31 -11.875 -4.77 -4.354 -4.96 -9.713 -5.06 -7.854 -3.33 -4.143 -3.45 -5.721 -2.13 -3.827 -4.79 -7.536 -4.86 -12.551 -4.73 -13.288 -4.84 -19.864 -5.04 -50.084 -3.20 -5.827 -4.23 -7.433 -2.94 -4.556 -4.87 -12.761 -4.99 -34.261 -4.57 -9.696 -4.26 -9.264 -4.98 -16.973 -3.95 -4.518 -3.75 -3.024 -4.54 -14.435 -5.27 -15.147 -4.15 -2101.400 -3.54 -61.852 -4.62 -2.203 -4.85 -26.827 -4.21 -15.986 -4.65 -37.019 -4.66 -26.369 -1.70 -14.115
-1.592 -1.081 -0.889 -0.949 -0.851 -1.057 -3.436 -3.185 -2.529 -7.333 -5.269 -7.521 -0.685 -0.837 -0.678 -5.141 -4.692 -4.999 -0.676 -0.658 -0.737 -2.545 -1.831 -1.403 -5.441 -3.801 -3.410 -0.888 -0.737 -0.786 -2.927 -2.473 -3.389 -3.624 -3.977 -0.639 -0.794 -0.746 -3.235 -3.195 -4.294 -4.153 -3.575 -4.332 -0.452 -0.445 -2.254 -3.227 -4.023 -3.419 -0.644 -0.702 -2.098 -1.006 -1.287 -3.468 -3.644 -4.971
tCHF,ss
texp
Is] 1.461 1.212 0.984 1.269 1.062 0,858 1.168 0.996 0,895 1.062 0.842 0.670 1.542 1.159 0.943 1.233 0.956 0.805 1.571 1.273 1.045 1.412 1.208 0.996 1.412 1.041 0.915 1.412 1.131 0.886 1.302 1.086 0.907 1.212 1.000 1.257 1.074 0.870 1.188 0.960 0.833 1.094 0.927 0.846 1.290 0.854 1.135 0.846 0.939 0.768 1.135 0.939 1.343 1.017 0.797 1.033 0.658 0.491
&Tsub = 10 *C WO
WSS
[kW]
[kW]
2.732 2.762 2.775
3.219 3.222 3.228
Wreg
[kW] 5.165 5.145 5.559
81
82
th
[l/s]
kl
[1/s]
X2
[l/s]
|-]
|s]
is]
-9.10 -6.71 -4.90
-3.81 -4.43 -4.49
-140.800 -39.198 -15.729
3.79 3.70 0.56
0.60 0.61 0.34
-0.445 -0.460 -3.892
t®xP
is] 0.813 0.837 0.736
137
138
G.P. Celata et al. Table 3. Power-Flow Transients (ramp) L = 2.3 11, Name
246640 262620 262660 262820 262840 262860 266620 266660 286640 442620 442660 442820 642220 642460 642860 644260 644420 644860 682820 682860 684260 684420 684820 684860 882840 882860 884220 884820 884840 884860 882220 882240 882460 882820 882840
O
T. In
[MPa]
P
[^Cl
1.238 1.241 1.243 1.238 1.234 1.232 1.237 1.244 1.235 1.528 1.533 1.540 2.000 1.998 1.990 1.987 1.998 1.984 1.998 1.985 1.997 2.002 2.002 1.984 2.740 2.739 2.735 2.756 2.737 2.750 2.739 2.729 2.737 2.708 2.740
28.15 28.34 28.22 28.38 27.99 28.22 27.95 28.54 28.42 37.75 37.83 37.26 50.35 49.37 50.24 49.72 49.92 50.35 50.39 49.96 50.51 50.35 50.75 49.72 66.51 65.64 65.68 66.51 65.80 65.84 65.60 66.20 65.53 65.64 66.51
G
O
[kg/m2s ] 1007.9 1235.4 1250.3 1273.5 1265.7 1291.0 1232.9 1246.5 1478.9 1027.7 1022.3 1077.9 1024.8 1012.5 1069.5 1024.8 1016.9 1051.1 1492.0 1513.4 1464.6 1477.7 1525.3 1512.1 1498.9 1513.1 1478.2 1519.5 1505.7 1507.5 1471.5 1449.8 1459.7 1495.9 1498.9
L = 2.3 m Name
Po [MPa]
Tin ['C]
602422 602462 602822 602862
2.007 1.996 1.993 2.008
63.47 63.20 63.12 62.76
Go [kg/m2sI 1440.9 1439.5 1460.8 1466.4
6Tsub = 23 ^C W
W
o
[kWl 3.142 2.904 4.149 2.916 3.661 4.125 2.922 4.167 3.990 2.021 3.224 2.070 1.559 2.744 2.756 2.738 1.541 2.793 2.408 3.592 3.635 2.439 2.426 3.580 2.738 3.251 2.024 2.109 2.738 3.245 2.042 2.763 3.251 1.999 2.738
~,
=
SS
[kW|
[ kw/s ]
4.057 1.886 4.497 0.613 4.529 0.237 4.564 0.607 4.567 0.663 4.601 0.331 4.509 1.901 4.509 1.934 4.901 1.598 3.705 0.669 3.691 0.599 3.825 0.737 3.239 0.802 3.256 0.549 3.326 0.510 3.263 1.226 3.242 1.598 3.285 1.438 4.033 0.773 4.082 0.895 3.984 1.483 4.016 1.513 4.064 71.096 4.094 1.270 3.679 0.694 3.758 0.562 3.694 1.572 3.729 1.390 3.733 1.455 3.748 1.260 3.694 0.716 3.609 0.613 3.677 0.526 3.697 59.717 3.679 0.694
~2
th
[l/s]
[-1
Is]
Is]
-1.580 -2.358 -2.878 -1.846 -7.448 -8.198 -1.919 -8.665 -5.527 -1.627 -5.211 -10.752 -1.460 -3.481 -1.487 -6.255 -2.008 -12.916 -2.130 -2.597 -2.110 -4.269 -1.516 -5.590 -1.736 -0.387 -2.304 -35.314 -2.832 -15.609 -1.829 -6.714 -1.785 0.523 -1.494 -8.099 -1.556 -12.737 -1.224 -55.834 -1.316 -1470.800 -1.641 -19.095 0.i01 -14.253 -1.850 -19.999 -1.669 -15.851 -2.122 -25.561 -1.467 -2.753 -1.950 -18.996 -1.570 -23.657 -1.883 -22.524 -1.968 -5.973 -1.671-10163.000 -2.286-18303.000 0.074 -19.354 -1.669 -15.849
-2.372 -2.839 -1.579 -4.105 -5.360 -3.999 -2.109 -1.655 -1.391 -2.464 -1.805 -5.420 -1.392 -0.462 -3.859 -0.326 -0.643 -4.028 -4.111 -3.429 -0.394 -0.467 -3.964 -3.922 -3.803 -4.015 -0.353 -3.897 -3.763 -3.954 -0.271 -0.291 -0.594 -4.124 -3.804
0.00 1.28 1.35 0.65 0.68 0.62 1.39 1.35 1.37 1.46 1.42 0.67 5.84 3.69 0.57 5.45 3.16 0.68 0.57 0.53 4.26 3.70 0.57 0.54 0.57 0.50 5.50 0.54 0.54 0.52 6.53 5.78 2.83 0.51 0.57
0.01 1.28 0.64 0.69 0.54 0.36 1.26 0.63 0.88 1.51 0.82 0.78 3.11 1.41 0.38 1.42 2.23 0.44 0.63 0.28 1.13 2.01 0.63 0.31 0.46 0.28 2.42 0.58 0.43 0.28 3.07 2.23 1.04 0.59 0.46
~1
[l/s]
tCHF,ss
texp
Is] 1.852 2.463 1.489 2.003 1.436 1.115 2.088 1.367 1.530 2.920 1.681 2.590 4.170 2.370 1.082 2.235 3.066 1.155 2.019 1.005 1.811 2.716 1.962 0.911 1.339 0.679 3.099 1.644 1.302 0.719 3.995 3.062 1.982 1.799 1.339
6Tsub = 10 ^C
W° [kW] 1.608 2.817 1.578 2.793
Wss [kw] 3.202 3.212 3.239 3.275
~ [kW/s] 0.834 0.842 0.843 0.702
where
X [l/s]
~1 I1/s]
-1.512 -4.971 -1.159 -3290.500 -1.532 -15.812 -1.517 -22.399
82 [-]
t h tCHF,ss [s] Is]
-0.949 -0.669 -3.910 -3.711
2.18 2.51 0.56 0.55
2.13 1.12 0.75 0.35
texp Is] 3.091 1.934 2.231 1.009
where cl = - {2/[)~1 0~l - X2)3] d- 1/[h~()q - ~2)2]}
-2
~= x-r,
1
~2=~,
2
"n=~,
1
"y2=~
c2 ~-- 1/[ht (h2 - ~1) 2] dl -- - {2/[X2(X2 - Xl) 3] + I/[X22(X2 - Xl)2]} d2 = 1/[~,2(~ 2 - )~1)2]
where Al and ~2 were determined through the best-fit procedure on the experimental data points (see Table 2). In the ease of the ramp input power variation, the timedependent expression 14:(t) is approximated by the expression W(t)= Wo+ctA2[(el+~2t)eXt+(W+72t)]
(4)
Analogously to other mathematical laws, we got the value of h from the best-fit procedure of the experimental data points (for the values of each test, see Tables 2 and 3). The parameter a is defined as the slope of W(t) for t >i 3 [ h [; after this time the curve can be considered a straight line. In mathematical terms,
dt
t~
CHF in Transient Flow Boiling The electrical power is read by instnnnents directly at the terminals placed on the test channel ends; therefore it is exactly equal to the thermal power delivered to the wall. Computerized data acquisition accounts for the heat loss from the test section, which (although very small) was experimentally determined as a function of the wall temperature. Consequently W ( t ) represents the actual net thermal power delivered to the test channel wall. The actual thermal power delivered to the fluid, Wy, depends not only on the response of the electrical power system as discussed above, but also on the thermal capacity of the test section wall. Assuming that the test channel can be characterized by an average temperature Tw, we may write
aTw
W/(t) = W(t) -(pcp V)m dt
(6)
the heat balance equation (5) becomes dTw W(t) = hS[Tw(t)- Tb] + (ocp V)m dt
Wo w~ W®
tCHF,ss tCHF,tr O~
~l, ~2
(5)
where p is the density, ca is the specific heat, and V is the volume of the test section tube wall. Since the heat flux to the fluid can also be expressed in terms of the heat transfer coefficient from the wall to the fluid, h, heat transfer area S, and bulk fluid temperature Tb, ie, Wf(t) = hS[ T,(t) - Tb]
Tin Go
(7)
This equation can now be solved for the wall temperature distribution T, by using the stainless steel test section material properties and Eq. (3), or Eq. (4), for the test section input power distribution. It was solved numerically by means of the A N A T R A code [17]. Parameters hi and 3,2 in Eq. (3) (step power variations) have the physical meaning of the inverse of the time constants of the eleOxical feeding system, which can be represented by two inseries delay blocks (each with a transfer function characterized by a pole of multiplicity 2). Concerning ramp power variations, Eq. (4), the electrical feeding system can be represented by only a delay block of the same kind, characterized by )~. The time-dependent expression of mass flux, G(t), was derived by analogy from power timedependent laws. Parameters B1 and B2 in Eq. (2) have no direct physical meaning in the present analysis. As for the derivation of the numerical values of/~1,/~2, hi, )~2, and ~, they were obtained by fu'st equating Eqs. (2)-(4) to the measured values of G(t) and W ( t ) and then applying a best-fit procedure.
tt= Lpfo/ Go
•
Transient Critical Heat Flux Experiments Results and Data Reduction
initial inlet pressure
(8)
as the time necessary for a fluidparticleto pass through the test section channel with no power input to the system, the experimental results are plotted versus the ratio of the halfflow decay time th and tt. More precisely, in Fig. 3 the transient to steady-state criticalmass flux ratio is reported versus th/itfor both step and ramp power variations.The ratio of the transientto steady-statecriticalthermal power is plotted in Fig. 4 against tJtt, and similarly the transientto steadystate time to crisisratio is shown in Fig. 5. Speaking of steady-statecriticalvalues of mass flux,thermal power, and time to crisis,we mean values calculated at the time in which, considering the transient as a sequence of steady-statetime steps,CISE-modified correlationforeseesthe onset of CHF. In mathematical terms, such values are obtained by solving the system made up by Eqs. (I), (2), and (3) or (4). Experimental results are grouped by the pressure p and the margin to crisisM in the case of step power variations,and by the mass flux G and ramp slope ~ in the case of ramp power transients. Looking at Figs. 3-5 it is possible to argue that the transient does not seem to be affected by either the pressure or the mass flux. Regarding the step power variations, the following observations can be made:
An evaluation of the experimental uncertainty was achieved by carrying out 20 runs of the same test (step power variations). Experimental results of time to crisis lie around the mean value (1.5 s) with a standard deviation of 0.05 s and a maximum deviation of + 0.1 s.
Po
inlet temperature initial inlet mass flux initial thermal power steady-state critical thermal power before the transient thermal power at the end of transient (step input thermal power) half-flow decay time time to crisis calculated using correlation (1) at inlet conditions experimental time to crisis ramp input power slope parameters in Eq. (2) parameter in Eq. (4) parameters in Eq. (3)
A graphic representation of experimental data is reported in Figs. 3-5. Defining the time transit parameter tt
Experimental Uncertainty
Experimental results are summarized in Tables 2 and 3, where the following parameters are listed:
139
•
For a fixed value of th/tt, the lower M is, the higher both the GCHF,tr/GcHF,ssand WcnF,~/WCHV,~ ratios are. That means that experimental results are closer to calculated steady-state values for small values of M. From a general analysis of data points, it appears that CHF behavior under transient conditions can be predicted with the steady-state approach at inlet conditions for values of th/tt greater than 3. Beyond this threshold it is evident from Figs. 3-5 that the ratios between the transient and steady-state values of mass flux, thermal power, and time to crisis tend to unity. The threshold is greatly reduced in comparison with that observed in single flow rate transients (th/tt > 8) (ie, conditions where only the flow rate changes) [14]. Of course, this is a negative aspect from the safety viewpoint, as the onset of CHF is anticipated. As far as time to crisis values are concerned, the comparison between thermal power transients [16],
140
G . P . Celata et al,
1.2
{/1
u."
I
'
I
Doe
0.8
'
I
'
I
•
"I" (.3 .,o
~
[]
O.4
ID•
•
0o
0.5
H [kW] 1.0 1.7
A
A
1.2 1.5
A
p
2.0 [HPa]
AS
E]
0.0
I 0.5
0.0
]
[]
•
2.7
I 1.5
I
1.0
I 2.0
2.5
th/ttr (a)
1.2
I
'
I
'
I
oe Ul
eA
A
O~
[]
~0.8
i
A@
=2
5 E
O A
G [kg/e2s] 1030 1250 1500
=-" o.4
5
A
~
0.5 0.7
A
(x
1.5 [kW/s] 2.0 0.0
I
O.
I 1.
i
I 2.
,
I 3.
i
I 4.
i 5.
th/ttr (b) Figure 3. Transient to steady-state critical mass flux ratio versus half-flow decay time to transit time parameter ratio. (a) Step power variations; (b) ramp power variations.
where only the power changes, and present double parameter transients, shows a reduction of the time to crisis up to a factor of 2. Comparing present results with mass flux transients [14], where only the mass flux changes, time to crisis is reduced by up to a factor of 4. That means that power variations affect the transient more than mass flux variations.
Because of the small values of time to crisis (less than unity), the ratio between the transient and the steadystate time to crisis, tCHF,~/tcHF,,,, is inversely affected by M with respect to the results reported in Figs. 3 and 4. In the case of ramp variations we have behavior similar to that observed for step variations, even though with less
CHF in Transient Flow Boiling
2.5
'
I
'
'
I
141
!
I
~I [kW] 1.0 1.7
0.5
1.2
2.0 A
@
A
-1¢lJ
p [MPa]
1.5 2.0 2.7
A @
3
1.5
=." -r
Oo []
1.0
0.0
I
O
I 0.5
l
1 1.0
t
I 1.5
i
I 2.0
2.5
th/ttr (a)
I
'
I
'
|
'
1
2.0 G [kg/12s] 1030 1250 1500
0
5
A
A
*
@
0.5 0.7 1.5 2.0
@ A
1.2
a [kW/s]
A
1
0.8
-I
O.
[
1.
I
1
I
I
2.
3.
I
I
4.
I
5.
th/ttr (b)
Figure 4. Transient to steady-state critical thermal power ratio versus half-flow decay time to transit time parameter ratio. (a) Step power variations; (b) ramp power variations.
intensity, comparing present results to simple flow rate transients [14]. Ramp/flow rate transient behavior lies between that of the step/flow rate and that of simple flow rate. Consequently, time to crisis values are greater than those observed in step/flow rate transients. From the observations reported above, it can be stated that
the simultaneous occurrence of flow rate and thermal power variations generally gives rise to a synergistic effect in the sense of drastically reducing the difference between the experimental occurrence of CHF and the prediction obtained with the steady-state approach at inlet conditions, as achieved in simple transients analysis [14, 16]. For a fLxed half-flow
G . P . Celata et al.
142
'
I
'
l
'
I
.
I~
[kW]
0.5
1.0
1.7
&
t,
A
1.2 G~
d- r
.
1.5 2.0 2.7
~J
p [NPa]
.
-r
r
~a .
I 0.5
0"0.0
,
I 1.0
J
I 1.5
I 2.0
2.5
th/ttr (a) .
'
I
'
I
'
A
I
'
1030
1250
1500 0.5 0.7 1.5 2.0
t~ t~
¢.J .
<"
[]
0
.# %
.#
'
G [kg/m2s]
.
.#
I
Q
,.~
~
•
[]
[]
•
a [kW/s]
•
kk. "t" ¢.J
.
0.0.
I
I 1.
i
I 2.
,
I 3.
i
I 4.
i
I 5.
th/ttr (b) Figure 5. Transient to steady-state time-to-crisis ratio versus half-flow decay time parameter ratio. (a) Step power variations; (b) ramp power variations. decay time th, the described behavior is more and more evident when the input thermal power rate is increased. For what concerns the data reduction, the simplest approach in predicting the time to crisis tCHF Consists in equating the timedependent expression of the input thermal power delivered to the fluid, Wl(t), to a reliable steady-state CHF correlation, calculated at inlet conditions, including the instantaneous value of the inlet mass flux.
As shown in Fig. 6, this approach tends to underestimate the
experimental data, which is not acceptable even for screening calculations. A more suitable approach consists in using correlation (1) with the local instantaneous values of the parameters of interest; this method is sometimes called the quasi-steady-state approach. To calculate the local conditions, an original computer code, ANATRA [17], based on reassessed heat transfer correlations [18], was employed. For the
CHF in Transient Flow Boiling '
I
'
L
I
~
4.
'
I
[
STEP
~
,0f
3.
143
i Po
RANP
[MPa)
£>
1.5
o A o
1.25 1.35 2.02
n
2.77
•
u2 1.
c3
1.0
D n ~ E3
t
I
0'0.
1.
2.
3.
.
o. ~'.
4.
'
:,1.
.
"
,
4 I.
Figure 6. Time-to-crisis predictions using the steady-state approach at inlet conditions. prediction of CHF conditions the quasi-steady-state method consists in calculating at every time step the value of the local heat flux (or steam quality) and comparing the computed value with the value predicted using correlation (1) (or other equivalent reliable correlation). The CHF condition is indicated when the local value of heat flux (or steam quality) is greater than or equal to the value given by correlation (1). An overall representation of local conditions analysis is reported in Fig. 7, where the calculated time to crisis is plotted versus the experimental value. The agreement is quite satisfactory, most of the data being within a + 20% band. Predicted ramp power variations seem to be a little less scattered than predicted step power variations, because of the minor quickness of the power transient. This latter observation is more evident in Fig. 8, in which the ratio between the calculated and experimental times to crisis is plotted against the half-flow decay time for both types of thermal power variations. In Fig. 9, the ratio between the calculated and experimental times to crisis is reported versus the margin to crisis M for step transients (Fig. 9a), and versus the ramp slope o~ for ramp transients (Fig. 9b). No systematic influence of either pressure or mass flux is shown. Finally, in Fig. 10, six examples of ANATRA code wall and fluid temperature predictions at the outlet section of the test channel are shown together with the experimental measure-
I
2.5
'
[
I
2.0
0 A
.ou
©
1.5
)
0. So'
0'0
1.
2.
t
exp
3.
&
I
I
,
0.5
I
,
Figure 7. Time-to-crisis predictions using the steady-state appreach at local conditions (quasi-steady-state method).
L
I
1.5
1.0
l
2.0
2.5
(a) I
/
I
I
RAMP-VARIATION
[]
o
Go
I~T~alb
[kg/m2-s] 1030 1250 1500 1450
[K] 23 23 23 10
A A
0
4.
is]
[K] 23 23 23 10
M [kW]
1.0
I
~Tsub
1.0
.....
~
Go [kg/m2'-s) 1030 1250 1500 1450
& []
U
I
I
STEP-VARIATION
1.5 --4 e: U
,
8.
The main objective of this research was to obtain CHF experimental data during transients caused by the simultaneous variation of power and flow rate and to verify the quasi-steadystate method for their prediction. Such a method is also adopted in RELAP 5/MOd 2 code. The results of this study
-£
I
'
Practical Significance
O A
,
I.
ments. The steady-state condition before the transient is also calculated by the steady-state section of the code.
2.0
~ ' r a
,
Figure 8. Calculated to experimental time-to-crisis ratio versus half-flow decay time.
2.5
~'~'#
.
t h Is]
tCHF. exp [ s ]
i.
.
' "50.0
.
. . 0 0
'
.
.
.
.
.
.
<>
I 0.5
,
.
[]
. . "" &
I , I 1.0 1.5 a [kWls]
.
.
,
. O
I 2.0
.
,
2.5
(b)
Figure 9. Calculated to experimental time-to-crisis ratio (a) versus the margin to the thermal crisis and (b) versus the ramp slope.
144
G. P. Celata et al. 90. ~
,
1
'
• OIF,exp O Tw, exp
t[ | [
r
'
I--
I
r - -q |STEP-WISE)
~
100.
CHF,exp Tw,exp
.....
- .......
7~
STEP-WISE TRANSIENT
Tw, cal E3 E]
......
Tf, cal
/'(~]
.U_~.J'
96.
_
<
<
7¢:
II~E]
75.
i.-1
U
92.
~. ............ . ........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
...............................
"""-,
70.
8B. ,
O. 0
O.S
1.0 t [s]
I
,
8.4
).0
1.5
'
85.
,(
I
t [s]
[
Tw,exp Tw, cal Tf,cal
--
'
I
STEP-WISE TRANSIENT
100. ///
Tw, exp [ Tw,cal | ...... Tf,cal |
RAHP~ISE TRANSIENT
t[! '
_ ~ _ ~ . _.
es. -
80
w
90.
75.
70.
..,...... ...............
85. ,
O.
I 0.4
,
I 0.8
,
1
0.
1.2
...............................................
. . . . . , . ......................
,
L
l
1.
,
l
2.
75.
70.
[
,
J
4.
(d)
'
CHF, exp Tw,exp Tw, c a l ...... T f , c a l
I
3.
t Is]
t [s] (c)
<
1 1.2
,
(b)
(a)
90.
t
O.B
90.
I
I
I RCg,IP'4aISE BS. / (
65. i
f
~..
CHF, exp Tw,exp Tw, c a l " Tf, cal
I
[
[
~tP'~ISE TRANSIENT
80,
k-,
75.
60.
55 '0.0
L
0.5
,
[ 1.0
~
I
1.5
L
70 "0 .'0
'
I
~
0.4
t Is] (e)
1 0.8
,
1.
t [s] (f)
Figure 10. Typical predictions of experimental outlet wall temperatures versus time using the ANATRA code.
SUMMARY AND CONCLUSIONS
experimental data revealed the general inadequacy of using the steady-state critical heat flux correlations at inlet conditions in predicting transient situations. An analysis of the local conditions (quasi-steady-state approach) is shown to reproduce the test data reasonably well, with an uncertainty of + 20%.
An experimental investigation of the critical heat flux with flow rate and step or ramp input thermal power simultaneous variations was performed using R-12 in a vertical channel. The
We are deeply grateful to G. Farina, M. Morlacca, and A. Lattanzi, who performed the experimental runs and gave useful suggestions. Thank~ ale due also to Mrs. B. Perra for her helpful assistance in editing the paper.
allow one to establish with experiments the performance and the confidence level of the method where the investigated range is very wide and is therefore related to practical situations.
CHF in Transient Flow Boiling NOMENCLATURE a l , a2 a b l , b2 b el, c2 cp d l , dz D E G h h/s L M p q~ S
t T V x W
constants in Eq. (2), s 4, s 3 parameter in Eq. (1), dimensionless constants in Eq. (2), s 4, s 3 parameter in Eq. (1), m constants in Eq. (3), s 4, s 3 specific heat, J/(kg K) constants in Eq. (3), s 4, s 3 diameter of test section, m excess power to crisis, W mass flux, kg/(m 2 s) heat transfer coefficient, W / ( m z K) latent heat, J/kg length of heated test section, m margin power to crisis, W pressure, Pa heat flux, W / m 2 wall/fluid heat transfer surface, m 2
time, s temperature, °C volume of the test section wall, m 3 steam quality, dimensionless thermal power, W
Greek Symbols ot ~1,/~2 71, 72 ~1, ~2
1" X ),1, ),2 p
ramp slope, W/s parameters in Eq. (2), s-1 parameters in Eq. (4), S 3, S2 parameters in Eq. (4), s 3, s 2 mass flow rate, kg/s parameter in Eq. (4), s-1 parameters in Eq. (3), s - i density, kg/m 3
Subcripts b CHF crit f h in m r ss t tr w 0 oo
bulk fluid critical heat flux, thermal crisis critical condition fluid half-flow inlet metal reduced steady-state transit transient test section wall referred to the situation before the transit referred to the situation at the end of the transient
2. Bergles, A. E., Collier, J. G., Delhaye, J. M., Hewitt, G. F., and Mayinger, F., Two-Phase Flow and Heat Transfer in the Power and Process Industries, pp. 256-280, Hemisphere, Washington, D.C., 1981. 3. Hewitt, G. F., Burnout, in Handbook of Multiphase Systems, G. Hetsroni, Ed., Hemisphere, Washington, D.C., 1982. 4. Katto, Y., Forced-Convection Boiling in Uniformly Heated Channels, in Handbook of Heat and Mass Transfer, N. P. Cheremisinoff, Ed., pp. 303-325, Gulf, Houston, Texas, 1986. 5. Katto, Y., Critical Heat Flux in Boiling, Proc. 8th International Heat Transfer Conference, Vol. 1, pp. 171-180, Hemisphere, Washington, D.C., 1986. 6. Lahey, R. T., The Analysis of Transient Critical Heat Flux, General Electric Report, GEAP 13249, 1972. 7. Hein, D., and Mayinger, F., Burnout Power in Transient Conditions, Proceedings of the Seminar on Two-Phase Flow Thermohydraulics, ENEA Report Rome, 1972. 8. Shiralkar, B. S., Polomik, E. E., Lahey, R. T., Gonzales, J. M., Radcliffe, D. W., and Schnebly, L. E., Transient Critical Heat Flux--Experimental Results, General Electric Report, GEAP 13295, 1972. 9. Leung, J. C. M., Transient CHF and Blowdown Heat Transfer Studies, Argonne National Laboratory Report, ANL/RAS/LWR-802, April 1980. 10. Moxon, D., and Edwards, P. A., Dryout during Flow and Power Transient, Proc. European Two-Phase Flow Group Meeting, Winfrith, UK, June 1967. 11. Cumo, M., Fabrizi, F., and Palazzi, G., Transient Critical Heat Flux in Loss of Flow Transients, Int. J. Multiphase Flow, 4, 497-509, 1978. 12. Kataoka, I., Serizawa, A., and Sakural, A., Transient Boiling Heat Transfer under Forced Convection, Int. J. Heat Mass Transfer, 26, 583-595, 1983. 13. Kataoka, I., Serizawa, A., Transient Boiling Heat Transfer under Forced Convection, in Handbook of Heat and Mass Transfer, N. P. Cheremisinoff, Ed., pp. 327-383, Gulf, Houston, Texas, 1986. 14. Celata, G. P., Cumo, M., D'Annibale, F., Farello, G. E., and Setaro, T., Critical Heat Flux in Flow Transients, Proceedings of 8th International Heat Transfer Conference, Vol. 5, pp. 24292436, Hemisphere, Washington, D.C., 1986." 15. Celata, G. P., Cumo, M., D'Annibale, F., and Fareilo, G. E., CHF in Flow Boiling during Pressure Transients, Proc. 4th Miami International Symposium on Multi-Phase Transport and Particulate Phenomena, Miami Beach, December 1986. 16. Celata, G. P., Cumo, M., D'Annibale, F., Farello, G. E., and Abou Said, S., Critical Heat Flux in Flow Boiling during Power Transients, Proceedings of ASME-AIChE-ANS National Heat Transfer Conference, Pittsburgh, Pa., August 1987. 17. Celata, G. P., Cumo, M., D'Annibale, F., Farello, G. E., and Abou Said, S., ANATRA--A Computer Code for Transit Critical Heat Flux Analysis with Refrigerant-12, in print as ENEA Report. 18. Celata, G. P., Cumo, M., D'Annibale, F., Farello, G. E., and Setaro, T., Reassessment of Forced Convection Heat Transfer Correlations for Refrigerant-12, Energia Nucleate, 3(1), 19-32, 1986. 19. Bertoletti, S., Gaspari, G. P., Lombardi, C., Peterlongo, G., and Silvestri, M., Heat Transfer Crisis with SWam-Water Mixtures, Energia Nucleate, 12(13), 121-172, 1965.
REFERENCES 1. Collier, J. G., Convective Boiling and Condensation, 2nd ed., pp. 248-313, McGraw-Hill, New York, 1972.
145
Received May 17, 1988; revised December 8, 1988