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Simulation and analysis of thermal-hydraulic phenomena in a PWR hot leg related to SBLOCA
Nuclear ELSEVIER
Nuclear Engineering and Design 155 (1995) 643 652
Simulation and analysis of thermal-hydraulic phenomena in a PWR hot leg related to SBLOCA M.J. Wang, F. Mayinger * Lehrstuhl A J~ir Thermodynamik, Technische Universitdt Miinchen, 80290 Miinchen, Germany
Received 29 August 1994; revised 2 December 1994
Abstract Thermal-hydraulic phenomena in the hot leg of a pressurized water reactor during the small break loss-of-coolant accident (SBLOCA) are simulated and studied in this paper. They include the single-phase flow dynamics, the cocurrent stratified flow during the natural circulation conditions, and the countercurrent stratified flow during the reflux condensation conditions. Satisfactory results were obtained from the computations in comparison with the data from the German Upper Plenum Test Facility. It is revealed that the fluid flow exhibits strong multi-dimensional effects, i.e. an appreciable acceleration and deceleration along different regions of the hot leg, and a four-vortex secondary flow structure in the cross-section of the bend region. Cocurrent stratified flow under the natural circulation conditions is successfully simulated, presenting two different water transport mechanisms. Under the reflux condensation conditions, different countercurrent flow structures are found under the conditions away from and with the countercurrent flow limit.
I. Introduction Safety analysis and accident management of nuclear reactor systems during a loss-of-coolant accident (LOCA) require a better understanding of the thermal-hydraulic phenomena related to the reactor transients. To this end, sponsored by the German Ministry of Research and Technology (BMFT), extensive separate and integral multi-dimensional studies of the pressurized water reactor (PWR) transients have been performed at the full scale Upper Plenum Test Facility (UPTF) in recent years (Mayinger, 1993; Sonnenberg, 1993; Weiss, 1988). This paper further provides a
numerical study of the thermal-hydraulic phenomena specific in the hot leg during the small break loss-of-coolant accident (SBLOCA) under the U P T F experimental conditions. A-A steam generator
"Hutze" I
A ,
*"~o ,_ / " ":
7/,'/;~
ete.m, ,
~
3/Zo/"
T
L
upper ptenum
* Corresponding author. 0029-5493/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved S S D I 0029-5493(95)00977-9
A
~ ' ~ ~~ ' ECC n -ie jc o itn pipe
Fig. 1. Configuration of the UPTF broken hot leg.
644
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643 652
During different stages of an SBLOCA transient in a PWR, several flow phenomena appear in the hot leg which influence the core cooling conditions. A t the early stage when a break appears, steam is formed in the reactor core due to depressurization. The mixture level is at first above the hot legs and steam entry into the hot legs is almost impossible. Single-phase natural circulation is established in the primary loop. With a further loss of coolant, the mixture level drops down in the upper plenum and a transition from single-phase to two-phase natural circulation takes place. As the leakage of coolant continues, void fraction increases in the hot legs and in the U-tubes of the steam generators correspondingly. As long as no water is transported into the hot leg, reflux condensation mode begins. In this case steam condenses in the steam generators, producing a downward condensate flow in countercurrent to the stream of steam along the hot leg back into the reactor vessel. These three flow phenomena are numerically investigated in the present paper. Computations were based upon the layout of the UPTF broken hot leg (Siemens, 1992), shown in Fig. 1. The Harwell PLOW3D code (AEA, 1992) was used to study the single- and two-phase flow behavior in the hot leg. In the following, theoretical principle and methodology of the numerical study are introduced firstly. Computational results are then discussed on the aforementioned thermal-hydraulic phenomena. Several concluding remarks are then presented.
2. Methodology The single-phase flow in the hot leg is simulated by solving the Navier-Stokes equations. A detailed description of the methodology is available in Wang (1993) and will not be discussed here. The two-phase flow in the hot leg, the central issue of this paper, is numerically studied using the two-fluid model that treats mass and momentum balance for each phase separately and determines the interphase transfer terms through the constitutive relations. The equations are numerically solved using the finite-difference code FLOW3D.
2.1. Conservation equations for two-phase flow Several important assumptions are made in this paper, namely, the flow is steady and adiabatic; both steam and water are incompressible and in saturation state. Using the two-fluid model, the conservation equations of the two-phase flow are given for mass V(~kp~ Vk) = 0
(1)
for momentum
V(akpk Vk Vk ) = -- O~kVpk + ~kP~g + Vo~k(~ + rt~ ) + Mik
(2)
where k denotes phase k, i denotes value at the interface, V is the velocity vector, ~ is the volume fraction, r is the shear stress (~ is the average viscous stress, r~, is the turbulent shear stress), and Mik is the total interracial shear stress.
2.2. Constitutive equation for interphase momentum transfer According to Ishii and Mishima (1984), Mik has two sources, namely, the generalized drag Dik and the contribution due to the interfacial shear r, and the void gradient VTk Mik = Dik -- V~k ~'i
(3)
M~k is the weakest term of two-fluid model formulation and is dependent upon experiment. There are two models provided in FLOW3D for interphase momentum transfer in non-dispersed flows, i.e. the mixture model and the stratified model. They are based upon the concept of dispersed flow treatment, accounting for the total drag exerted by phase j on phase k per unit volume with the form
M k / : CDPkjAk/Iv/-- Vk I(Vj -- Vk )
(4)
where CD is the drag coefficient, Pkj is the mixture density ~kPk + ~jPj, Akj is the interfacial area per unit volume ~k ~j/dk/and dkj is the interface length scale. A physically sounder model for interphase momentum transfer is the interfacial friction model.
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643-652
Considering a separated two-phase flow, the dominant contribution to the total drag comes from the interfacial shear stress (Ishii, 1984), namely Mi/,. -- - V~k Z'ik
(5)
Following the treatment of V~kz~ from Ishii and Mishima for the annular flow, Eq. (5) can be derived as Mkj = 2~/ipg IVj - V~ [(V/- v , )
(6)
where di is the interfacial length scale, i.e. the mixture volume divided by the interface area, f is the interracial friction coefficient. There are several correlations for f derived from one-dimensional stratified flow experiments, among which the following two are frequently quoted in literature. Ohnuki et al. (1987) arrived at an empirical correlation from the hot leg model tests, which was claimed to be valid for the countercurrent stratified flow in the full-scale hot leg. f = i.84Jwg
(7)
where the wall friction factor of the gas phase fwg is a function of the gas Reynolds number fwg
=
[16/Reg laminar flows ~0.079/Re°25 Reg < 105 (8) [0.0008 q- 0.05525/Re °'237 Reg ~ 105
Here the gas Reynolds number is defined as
Reg- pg VgDg Itg
(9)
where the equivalent diameter Dg is defined as 4Ag/Zg. Here Ag is the area occupied by gas phase, and Lg is the wetted circumference of the gas phase. Lee and Bankoff (1983) presented another correlation based upon experiments of the countercurrent steam water flow in a nearly horizontal channel
645
where Re* is given by 1.837 x 105Re~. fi in Eq. (10) varies from 0.005 to 0.05 in the given Reynolds number region. For the full scale PWR hot leg under reflux condensation, the Reynolds number is beyond the scope of Eq. (10), and f is over-predicted by the Lee and Bankoff correlation. Therefore, a simplified treatment is used here, assuming a constant f of 0.015 for cocurrent flow and 0.02 for countercurrent flow. The above two empirical correlations of the interfacial friction model were used with VLOW3D and were extended for multi-dimensional stratified flow simulation.
2.3. Numerical methodology In the present calculations, the following options of methodology were employed. The Upwind differencing scheme was used for all transport equations. The algebraic multi-grid method was used as the equation solver for each phase. The coupled equations of two phases (through interphase transfer) were solved using the inter-phase slip algorithm (IPSA) of Spalding, with the simultaneous solution of non-linearly coupled equations (SINCE) method of Lo for accelerating convergence (AEA, 1992). Turbulence was modeled as an extension of single-phase flow standard k - - E model. The homogeneous assumption was used for the interphase transfer terms in the transport equations for k and E. Inlet flow parameters were set to be constant and the fully developed assumption was applied to the outlet. For cocurrent flow and single-phase flow computations, inlet was set at the hot leg end near the reactor vessel. For countercurrent flow computations, inlet was assumed at the hot leg end near the steam generator. In the present study, no coolant injection from the deflector nozzle ("Hutze") was considered. Computations were carried out on a three-dimensional grid for the single-phase flow and a fine two-dimensional grid for two-phase flow, illustrated in Fig. 2. A HP750/PVRX workstation was used for simulation.
'0.012 + 5.179 × 10 4(Reg - Re*)/lO00 f = ~0.012 + 2.694 x lO-4(Re,/lOOO)"534(Reg-- Re*)/lO00
23 000 < Reg < Re* Re* <~Reg <<,51 000
(lO)
646
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643-652
SC UP
(a) "/ ,,n I 3663E+00
region
i
1386E+00 oI 9109E+00 06831E+00 0 4554E+00
(b) Fig. 2. Grid layout in the hot leg: (a) two-dimensional grid; (b) three-dimensional grid.
0 2277E+00 o O000E+0O
(a)
3. Results and discussion
3.1. Single-phase flow Single-phase flow is studied briefly in this section to gain an insight into the basic fluid-dynamic behavior in the hot leg. Computations were performed in a three-dimensional grid (Fig. 2(b)) of the hot leg under the boundary conditions listed in Table 1. Figs. 3 and 4 show the computed flow structures in laminar and turbulent regimes. As seen from Figs. 3(a) and 4(a), the fluid experiences acceleration in the horizontal part due to the layout o f the emergency core cooling (ECC)-injection pipe. In the bend and the riser part, a nonsymmetric pattern of velocity distribution is observed. The fluid velocity near the inner elbow is almost twice the value near the outer elbow. This behavior is qualitatively in accordance with other numerical and experimental studies in the bends of large tube-to-bend radius ratios (Ito, 1986). In addition, a small flow reversal region is found downstream of the ECC-injection pipe up to the middle of the bend in the laminar regime (Fig. 3(a)). As the mean velocity increases, the reversal region is remarkably reduced (Fig. 4(a)). Table 1 Boundary conditions of single-phase flow computations Flow pattern
p (bar)
Re
D (m)
Laminar Turbulent
15 15
1088 108 800
0.75 0.75
'~ J " 15 °
l. . . . . " " j 30 °
outer
45 °
(b) Fig. 3. Single-phase laminar flow in the 3-d hot
leg,
Re = 1088: (a) velocity field on the symmetric plane; (b) secondary flow in the bend region. In the bend region of the hot leg, a development of the four-vortex secondary flow structure is observed. Figs. 3(b) and 4(b) show such flow pattern at different cross-section planes, i.e. 15° , 30 ° and 45 ° bend angles from bend entrance towards the steam generator. Two small vortexes (one vortex in the half cross-section) develop near the outer side of the curvature, whereas the other two are larger and appear near the side region. The vortex centers move slightly towards the outside of the bend when the flow changes from laminar to turbulent.
3.2. Cocurrent stratified flow during natural circulation A second part of the numerical research is the development of the cocurrent stratified two-phase flow and the water transport mechanisms in the hot leg during natural circulation. According to the U P T F Test A2 (Sonnenburg, 1993), stratified
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643 652
depth unchanged, leads to the formation of a critical flow, when the velocity of the disturbance traveling upstream becomes zero. Further increasing the fluid velocity gives supercritical flow when all small disturbances travel downstream. Gardner (1989) gave a criterion for this critical condition, which corresponds to a water mass flow rate of 300 kg s 1 in the U P T F Test A2 (Sonnenburg, 1993). Based on this knowledge, computational conditions covering the two flow patterns were chosen from the transient runs of U P T F - A 2 Run 03C. Table 2 lists the specific boundary conditions used. Here HI,in represents the water level at the entrance of the hot leg from the upper plenum, determined from the U P T F measurements near that region. The velocities of two phases were calculated based on this water level and the mass flow rates. They were then used as the inlet velocities for computations. The simplified interfacial friction model was used as the standard interphase m o m e n t u m transfer model.
SC
UP
HOW
i1
f t~V~r~dl
regqon
2 7 0 5 E+OO
1.0587E+00 0 8470E+00 0.6325E+00 0 4235E+00 0.2118E+00 0.O000E+00
(a)
/
/
iy / outer 15 °
30 °
647
45 °
(b) Fig. 4. Single-phase turbulent flow in the 3-d hot leg, Re = 108 800: (a) velocity field on the symmetric plane; (b)
3.2. I. Behavior of subcritical stratified flow
secondary flow in the bend region.
Fig. 5 shows a typical two-dimensional simulation of the subcritical stratified flow in the hot leg under the condition of U P T F - A 2 Run 03C, time interval 380-473 s. As the flow in this time interval is unstable, the boundary condition was taken specifically around the time 450s. The U P T F measurements of water level and vapor velocity along the hot leg are also presented in the figure for comparison. The water level was measured at two locations using the 7-densitometer and five other locations using the differential pressure transducers. It is seen from Fig. 5 that both the water level and the vapor velocity agree with the U P T F measurements quite satisfactorily. Fig. 5(a) shows a predicted void fraction field, in which a wavy
flow is a typical flow pattern during the natural circulation m o d e within the water mass flow rates up to 400 kg s - ' and a constant steam mass flow rate of about 10 kg s - l . Depending on the water flow rate, two different patterns m a y exist, i.e. the subcritical stratified flow and the supercritical stratified flow. Here the terminologies subcritical and supercritical flow originate from the hydraulic engineer's analysis of small surface disturbances in one-dimensional channel flow, where two disturbances are found traveling at different velocities (Gardner, 1989). In subcritical flow, one disturbance travels upstream and another downstream. Increasing the fluid velocity, with the Table 2 Boundary conditions for cocurrent flow computations UPTF Test
Time (s)
p (bar)
/f/g (kgs i)
/I)/I (kgs 1)
Vg.in (ms -I)
Vi.i,, (ms -I)
Ht,i, (m)
A2 Run 03C A2 Run 03C
380 473 585-672
15 15
9.5 10.0
125 390
7.41 8.75
0.528 1.54
0.445 0.47
648
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643-652
SG
UP
cx Measurement of water level:
~ +: from Ap-signals
X: from ~-signals
1.0000E+00 8.3333E-01 6.6667E-01 5.0000~: o l 3.3333E Ol 1.6667E Ol 4 7441E 09
(a) SG
UP
steam generator. This is again qualitatively in agreement with the U P T F observation that a strong entrainment exists in the bend and in the riser part. Fig. 5(b) shows the predicted vapor velocity field along the hot leg. Owing to the existence of the ECC-injection pipe, steam is accelerated in that region. The same phenomenon is also observed in the riser part because of the reduction of the vapor passage. Fig. 5(c) shows an amplified flow structure in the bend and the riser part. It is interesting to find a clear, though not large, water circulation: water near the interface flows upward in the same direction as the vapor, whereas it flows downward near the outer wall of the bend and the riser. This phenomenon has been revealed by the U P T F experiment as another peculiar feature of the subcritial stratified flow.
v, [m/s] U: Position of velocity measurement
.... ~
I
Vl, M : 8.7 m/s V2, M = 6.9 m/s V3, M = 14.1 m/$
(b)
2,3847E+01 1.9872E+0[ 1.5898E+01 1.1923E+01 7.9489E+00 3.9744E÷00 o ooo0E+OO
SG
horizontal
part
iiiiii
(c) Fig. 5. Cocurrent stratified flow in the hot leg during the natural circulation condition, UPTF-A2 Run 03C, time interval 380-473 s: (a) void fraction field; (b) vapor velocity field; (c) flow structure in the bend and the riser part. interface is revealed in the horizontal part of the hot leg. Downstream of the ECC-injection pipe water level increases. This behavior is consistent with the experiment (Sonnenburg, 1993), and can be regarded as a characteristic of the subcritical flow pattern. At the end of the hot leg, void fraction is found somewhat less stratified, implying probably a higher phase interaction near the
3.2.2. Behavior o f supercritical stratified flow Increasing the water mass flow rate, the flow becomes supercritical. Fig. 6 shows a simulation of this flow pattern in the hot leg under the condition of UPTF-A2 Run 03C, time interval 585-672 s. Since the flow in this region was shown to be rather stable in the measurement, the assumption of steady state is reasonably adopted in the simulation. Again, the computation agrees well with the U P T F experiment both on the water level and on the vapor velocity. Compared with the subcritical flow, the supercritical stratified flow exhibits different behavior. The most important behavior is a decrease in water level downstream from the ECC-injection pipe, correctly predicted in the present study. This feature may cause a change in the water transport mechanism towards the steam generator. In addition, Fig. 6(c) indicates that the flow structure in the elbow and the riser part differs completely from that in the subcritical flow. Both liquid and vapor flow in the same direction, and no water circulation is found under this condition. Similar velocity effects on the flow structure have already been revealed in the single-phase simulation. 3.2.3. Effect of different &terphase transfer models Different interphase momentum transfer models were studied regarding their reliability for stratified flow simulation. Compared with the
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643 652
U P T F experiments, FLOW3D interphase momentum models did not provide reasonable results. In most cases they led to quick divergence, obviously due to their unrealistic physics. On the contrary, the interfacial friction model incorporated into FLOW3D code gave rather satisfactory results. It was found that the Ohnuki interfacial friction correlation provided very similar flow patterns to
j,~/2 0.8 j,gl/2 + j,~/2 = 0.7 0.6
?
+: from Ap-signals x: from
~-signals
(a)
~
1
al. 1978)
; 39
0.4: 37 0.2
Measurement o f water level:
(Richteret
./
L = 0.639 m A = 0.3974 m 2
SG
up
649
0
0.05
0.1
0.15
0.2
0.25 j.~/2
Fig. 7. Numerical and UPTF experimental runs on the Wallis diagram.
~r t O000E+OO 8 . 3 3 3 3 E Ol 6 6667E-01
those presented above from the simplified Lee and Bankoff correlation. Therefore the interfacial friction model can be satisfactorily used in two-dimensional stratified flow simulation.
5 ooooz-ol 3 3333E-01 I 6667E-01 2.9716E 09
SG
uP
v, {m/s] 2.257 IE+01 [3: P o s i t i o n o f v e l o c i t y m e a s u r e m e n t
Vt, M = 13.7 m/s V2, M :
8 9 m/s
V3, M = 2 5 . 1 m / s
(b)
i
I
1.8809E+01 1.5047E+01 1.1285E+01
7 5235E+00 3 7618E+00 o O000E+O0
5G
horizontal
part
(c) Fig. 6. Cocurrent stratified flow in the hot leg during the natural circulation condition, UPTF-A2 Run 03C, time interval 585-672 s: (a) void fraction field; (b) vapor velocity field; (c) flow structure in the bend and the riser part.
3.3. Countercurrent stratified flow during reflux condensation The last part of the numerical study is the countercurrent flow during reflux condensation mode, corresponding to the conditions of the U P T F Test 11 (Weiss, 1988). Numerous experiments indicated that the countercurrent flow has its l i m i t - - a t each particular gas flow rate there is a maximum liquid flow rate, and vice versa. Such phenomenon, called countercurrent flow limit (CCFL) or flooding, can be best described by the Richter correlation in PWR hot legs (Richter, 1978). In the Wallis diagram of Fig. 7, three computational points of different flow status relative to the Richter line were chosen from the U P T F Test 11, and they are listed in Table 3. Here the Wallis parameter in Fig. 7 is defined as Jk--Jk[pk/gL(pl--pg)] 1'2, where the length scale L is taken as the hydraulic diameter in the ECC pipe region. In Table 3, h)/j is the measured water mass flow rate from the hot leg to the reactor vessel, whereas h;/Li,j is the total water mass flow rate injected from the steam generator during the experiment.
650
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643-652
Table 3 Boundary condition for countercurrent flow computations UPTF Test 11
p (bar)
Mg (kg s - 1 )
/~/I (kg s -I)
~/i,i.j (kg s -~)
Status
Run 37 Run 38 Run 39
15 15 15
8.3 18.1 24.0
9.8 29.4 25.2
9.8 29.4 29.6
Without CCFL Without CCFL With CCFL
3.3.1. Behavior o f countercurrent flow without CCFL Fig. 8 shows the predicted flow structure of U P T F Test 11 Run 37 under the typical reflux condensation condition using the simplified interfacial friction model. As illustrated in Fig. 7, Run 37 is far away from the C C F L in the hot leg, and was shown to be a stable point (Sonnenburg, 1993). Owing to lack of information on the water level near the steam generator, three steady runs SG
UP
a) HLin = 0.1875 In SG
UP
b) HLi. = 0.375 m
of different inlet void fractions were performed. It can be seen that the three computations reveal some c o m m o n features. There is a gradual increase in water level in the direction from the upper plenum towards the steam generator, obviously due to the retardation effect of the interfacial shear force. Such hydraulic phenomenon has also been observed in the hot leg model experiments of Ohnuki (1986). It is also found in this study that the ECC-injection pipe brings about an appreciable disturbance on the flow structure in the horizontal part, although the two-dimensional assumption may amplify such an effect. The greatest water level under this condition is found in the bend region, where flooding might eventually be initiated under favorable hydraulic conditions. Application of other interphase m o m e n t u m models to simulate the countercurrent flow was also tried. Again, it was found that the interphase models provided by FLOW3D code failed to give the right flow pattern, or even convergent results. On the contrary, the interfacial friction model with the Ohnuki correlation provided similar convergent results to the simplified Lee and Bankoff correlation.
5G
UP
c) HLio = 0.5625 nl ce 10000E+00 Mg = 8.3 kg/s
i
8.3333E-01 6.6667E-01 5.0OOOE-Ol
M I = 9.8 kg/s
3.3333E OI 1.6667E-01 1.0000E-08
Fig. 8. Void fraction field of the countercurrent stratified flow in the hot leg during typical reflux condensation condition, UPTF Test 11 Run 37 with different inlet water levels.
3.3.2. Behavior o f countercurrent flow near and with CCFL Fig. 9 illustrates the numerical simulation of U P T F Test 11 Run 38, at which the countercurrent stratified flow is still maintained, but is already near the flooding line. Fig. 10 presents the numerical result of U P T F Test 11 Run 39, at which flooding takes place and there is only partial delivery of liquid to the upper plenum of the reactor vessel. In the j~l/2_j,l/2 diagram of Fig. 7, Runs 38 and 39 are very close to each other. It can be found from Figs. 9 and 10 that the flow structures of these two runs exhibit a very similar
M.J. Wang, F. Mayinger /Nuclear Engineering and Design 155 (1995) 643-652 SG
uP
~ooooE+oo 8.3333E-01
Hlin = 0.5625 m
1
6.6667E OI
bag =
I
5.OO00Eol
18.1
kg/s
3.3333E-01
bAI : 29,4 kg/s
1.6667E OI I OOOOE-O8
Fig. 9. Void fraction field of the countercurrent flow in the hot leg during the reflux condensation condition, U P T F Test 11 R u n 38 near C C F L .
behavior. Downstream of the liquid inlet, water level decreases rapidly. Only a very thin liquid film was found in the bend region and the horizontal region. This implies a strong interphase momentum exchange. Between the pure liquid layer at the bottom and the pure vapor layer at the top of the hot leg, there is a relatively large region where void fraction lies between one and zero. This could be explained by the fact that under these conditions part of the liquid may be entrained in the vapor stream, forming a chaotic pattern in the core region.
4. Conclusions Thermal-hydraulic phenomena in the hot leg of a PWR during SBLOCA are simulated and analyzed in this paper. The main conclusions are
651
given as follows. The present study has shown, in principle, the applicability of the computational fluid dynamics method to the analysis of the thermal-hydraulic processes related to the SBLOCA as long as the relevant constitutive equations are well formulated. Thus, the numerical simulation provides an alternative to the reactor safety study. The hot leg configuration of the PWR presents a strong multi-dimensional effect which has not been properly considered in some one-dimensional thermal-hydraulic codes (Cappiello, 1988; Dillistone, 1992). Fundamental study of the single-phase laminar and turbulent flows reveals a remarkable flow distortion along the hot leg in the ECC pipe region, the elbow and the riser regions, and a four-vortex flow structure in the cross-section of the elbow. Steady state co- and counter-current flows in the hot leg are successfully simulated under the boundary conditions of UPTF Test A2 and Test 11 for natural circulation mode and reflux condensation mode. Interfacial friction models based on the Lee-Bankoff correlation and the Ohnuki correlation were implemented into the code FLOW3D for the interfacial momentum transfer. Satisfactory results were obtained in the subcritical and supercritical regions of the cocurrent stratified flow under the natural circulation conditions, where the same water transport mechanisms as shown in the UPTF experiment were predicted. Under the reflux condensation conditions, numerical computations reveal that different flow structures appeared in the region away from the CCFL line and in the region near the CCFL line.
SG
up
1.0000E+OO
Hlln = 0.5625 m bag = 24.0 kg/s
i
The authors acknowledge with great gratitude the financial support of the German Ministry of Research and Technology (BMFT) for this study.
6.6667E8"3333EO ' Io[ ~0oooE-ol 3 3333E~01
M~= 25.2 kg/s
Acknowledgment
1.6667E-01
Appendix A: Nomenclature
1 O000E-O8
Fig. 10. Void fraction field of the countercurrent flow in the hot leg during the reflux condensation condition, U P T F Test l l R u n 39 with C C F L .
A CD di
area drag coefficient interfacial length scale
M.J. Wang, F. May&ger / Nuclear Engineering and Design 155 (1995) 643-652
652 D
D
f g H
J J* L
M
if/ P
Ap Re
V(V)
tube diameter generalized drag i n t e r f a c i a l f r i c t i o n coefficient gravitational acceleration w a t e r level superfacial velocity Wallis parameter l e n g t h scale t o t a l i n t e r f a c i a l s h e a r stress mass rate pressure pressure drop Reynolds number velocity (vector)
Greek letters volume fraction dynamic viscosity density s h e a r stress
Subscripts g i in inj k 1 M t w
vapor interface inlet injection phase k liquid measurement turbulent wall
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M. Cappiello, Posttest analysis of the Upper Plenum Test Facility small-break loss-of-coolant accident test with TRAC-PF1/MODI and MOD2, Los Alamos National Laboratory, Rep. LA-CP-88-154, 1988. M.J. Dillistone, Analysis of the UPTF separate effects test 11 (steam-water countercurrent flow in the broken loop hot leg) using RELAP5/MOD2, Winfrith Technology Centre, Rep. NUREG/IA-0071, 1992. G.C. Gardner, Air-water model studies of cocurrent flow into and along a PWR hot leg to the steam generator, Nucl. Eng. Des. 117 (1989) 251 261. M. Ishii and K. Mishima, Two-fluid model and hydrodynamic constitutive relations, Nucl. Eng. Des. 82 (1984) 107-126. H. Ito, Flow in curved pipes, JSME Int. J. 30 (1986) 543 552. S.C. Lee and S.G. Bankoff, Stability of steam water countercurrent flow in an inclined channel: Flooding, J. Heat Transfer 105 (1983) 713-718. F. Mayinger, P.A. Weiss and K. Wolfert, Two-phase flow phenomena in full-scale reactor geometry, Nucl. Eng. Des. 145 (1993) 47-61. A. Ohnuki, Experimental study of counter-current two-phase flow in horizontal tube connected to inclined riser, J. Nucl. Sci. Technol. 23 (1986) 219-232. A. Ohnuki, H. Adachi and Y. Murao, Scale effects on countercurrent gas-liquid flow in horizontal tube connected to inclined riser, ANS Proc. 1987 National Heat Transfer Conf., American Nuclear Society, La Grange Park, pp. 40-49. H.J. Richter, G.B. Wallis, K.H. Carter and S.L. Murphy, De-entrainment and countercurrent air-water flow in a model PWR-hot leg, Thayer School of Engineering, US Nuclear Regulatory Commission Rep. NRC-0193-9, September 1978. Siemens/KWU, UPTF test instrumentations: Measurement system identification, engineering units and computed parameters, Siemens AG, Energieerzeugung, $554/92/13, November 1992. H.G. Sonnenburg and V.V. Palazov, Two-phase flow behavior in the UPTF hot leg under natural circulation conditions, GRS Proc. of the TRAM Working Group of Experts Meet., Mannheim, December 6-8, 1993. M.J. Wang, Phase distribution, secondary flow and heat transfer of dispersed flow in circular bends, Verlag Shaker, Aachen, 1993. P.A. Weiss and R.J. Hertlein, UPTF Test results: First three separate effect tests, Nucl. Eng. Des. 108 (1988) 249-263.
Nuclear Engineering and Design 155 (1995) 643 652
Simulation and analysis of thermal-hydraulic phenomena in a PWR hot leg related to SBLOCA M.J. Wang, F. Mayinger * Lehrstuhl A J~ir Thermodynamik, Technische Universitdt Miinchen, 80290 Miinchen, Germany
Received 29 August 1994; revised 2 December 1994
Abstract Thermal-hydraulic phenomena in the hot leg of a pressurized water reactor during the small break loss-of-coolant accident (SBLOCA) are simulated and studied in this paper. They include the single-phase flow dynamics, the cocurrent stratified flow during the natural circulation conditions, and the countercurrent stratified flow during the reflux condensation conditions. Satisfactory results were obtained from the computations in comparison with the data from the German Upper Plenum Test Facility. It is revealed that the fluid flow exhibits strong multi-dimensional effects, i.e. an appreciable acceleration and deceleration along different regions of the hot leg, and a four-vortex secondary flow structure in the cross-section of the bend region. Cocurrent stratified flow under the natural circulation conditions is successfully simulated, presenting two different water transport mechanisms. Under the reflux condensation conditions, different countercurrent flow structures are found under the conditions away from and with the countercurrent flow limit.
I. Introduction Safety analysis and accident management of nuclear reactor systems during a loss-of-coolant accident (LOCA) require a better understanding of the thermal-hydraulic phenomena related to the reactor transients. To this end, sponsored by the German Ministry of Research and Technology (BMFT), extensive separate and integral multi-dimensional studies of the pressurized water reactor (PWR) transients have been performed at the full scale Upper Plenum Test Facility (UPTF) in recent years (Mayinger, 1993; Sonnenberg, 1993; Weiss, 1988). This paper further provides a
numerical study of the thermal-hydraulic phenomena specific in the hot leg during the small break loss-of-coolant accident (SBLOCA) under the U P T F experimental conditions. A-A steam generator
"Hutze" I
A ,
*"~o ,_ / " ":
7/,'/;~
ete.m, ,
~
3/Zo/"
T
L
upper ptenum
* Corresponding author. 0029-5493/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved S S D I 0029-5493(95)00977-9
A
~ ' ~ ~~ ' ECC n -ie jc o itn pipe
Fig. 1. Configuration of the UPTF broken hot leg.
644
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643 652
During different stages of an SBLOCA transient in a PWR, several flow phenomena appear in the hot leg which influence the core cooling conditions. A t the early stage when a break appears, steam is formed in the reactor core due to depressurization. The mixture level is at first above the hot legs and steam entry into the hot legs is almost impossible. Single-phase natural circulation is established in the primary loop. With a further loss of coolant, the mixture level drops down in the upper plenum and a transition from single-phase to two-phase natural circulation takes place. As the leakage of coolant continues, void fraction increases in the hot legs and in the U-tubes of the steam generators correspondingly. As long as no water is transported into the hot leg, reflux condensation mode begins. In this case steam condenses in the steam generators, producing a downward condensate flow in countercurrent to the stream of steam along the hot leg back into the reactor vessel. These three flow phenomena are numerically investigated in the present paper. Computations were based upon the layout of the UPTF broken hot leg (Siemens, 1992), shown in Fig. 1. The Harwell PLOW3D code (AEA, 1992) was used to study the single- and two-phase flow behavior in the hot leg. In the following, theoretical principle and methodology of the numerical study are introduced firstly. Computational results are then discussed on the aforementioned thermal-hydraulic phenomena. Several concluding remarks are then presented.
2. Methodology The single-phase flow in the hot leg is simulated by solving the Navier-Stokes equations. A detailed description of the methodology is available in Wang (1993) and will not be discussed here. The two-phase flow in the hot leg, the central issue of this paper, is numerically studied using the two-fluid model that treats mass and momentum balance for each phase separately and determines the interphase transfer terms through the constitutive relations. The equations are numerically solved using the finite-difference code FLOW3D.
2.1. Conservation equations for two-phase flow Several important assumptions are made in this paper, namely, the flow is steady and adiabatic; both steam and water are incompressible and in saturation state. Using the two-fluid model, the conservation equations of the two-phase flow are given for mass V(~kp~ Vk) = 0
(1)
for momentum
V(akpk Vk Vk ) = -- O~kVpk + ~kP~g + Vo~k(~ + rt~ ) + Mik
(2)
where k denotes phase k, i denotes value at the interface, V is the velocity vector, ~ is the volume fraction, r is the shear stress (~ is the average viscous stress, r~, is the turbulent shear stress), and Mik is the total interracial shear stress.
2.2. Constitutive equation for interphase momentum transfer According to Ishii and Mishima (1984), Mik has two sources, namely, the generalized drag Dik and the contribution due to the interfacial shear r, and the void gradient VTk Mik = Dik -- V~k ~'i
(3)
M~k is the weakest term of two-fluid model formulation and is dependent upon experiment. There are two models provided in FLOW3D for interphase momentum transfer in non-dispersed flows, i.e. the mixture model and the stratified model. They are based upon the concept of dispersed flow treatment, accounting for the total drag exerted by phase j on phase k per unit volume with the form
M k / : CDPkjAk/Iv/-- Vk I(Vj -- Vk )
(4)
where CD is the drag coefficient, Pkj is the mixture density ~kPk + ~jPj, Akj is the interfacial area per unit volume ~k ~j/dk/and dkj is the interface length scale. A physically sounder model for interphase momentum transfer is the interfacial friction model.
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643-652
Considering a separated two-phase flow, the dominant contribution to the total drag comes from the interfacial shear stress (Ishii, 1984), namely Mi/,. -- - V~k Z'ik
(5)
Following the treatment of V~kz~ from Ishii and Mishima for the annular flow, Eq. (5) can be derived as Mkj = 2~/ipg IVj - V~ [(V/- v , )
(6)
where di is the interfacial length scale, i.e. the mixture volume divided by the interface area, f is the interracial friction coefficient. There are several correlations for f derived from one-dimensional stratified flow experiments, among which the following two are frequently quoted in literature. Ohnuki et al. (1987) arrived at an empirical correlation from the hot leg model tests, which was claimed to be valid for the countercurrent stratified flow in the full-scale hot leg. f = i.84Jwg
(7)
where the wall friction factor of the gas phase fwg is a function of the gas Reynolds number fwg
=
[16/Reg laminar flows ~0.079/Re°25 Reg < 105 (8) [0.0008 q- 0.05525/Re °'237 Reg ~ 105
Here the gas Reynolds number is defined as
Reg- pg VgDg Itg
(9)
where the equivalent diameter Dg is defined as 4Ag/Zg. Here Ag is the area occupied by gas phase, and Lg is the wetted circumference of the gas phase. Lee and Bankoff (1983) presented another correlation based upon experiments of the countercurrent steam water flow in a nearly horizontal channel
645
where Re* is given by 1.837 x 105Re~. fi in Eq. (10) varies from 0.005 to 0.05 in the given Reynolds number region. For the full scale PWR hot leg under reflux condensation, the Reynolds number is beyond the scope of Eq. (10), and f is over-predicted by the Lee and Bankoff correlation. Therefore, a simplified treatment is used here, assuming a constant f of 0.015 for cocurrent flow and 0.02 for countercurrent flow. The above two empirical correlations of the interfacial friction model were used with VLOW3D and were extended for multi-dimensional stratified flow simulation.
2.3. Numerical methodology In the present calculations, the following options of methodology were employed. The Upwind differencing scheme was used for all transport equations. The algebraic multi-grid method was used as the equation solver for each phase. The coupled equations of two phases (through interphase transfer) were solved using the inter-phase slip algorithm (IPSA) of Spalding, with the simultaneous solution of non-linearly coupled equations (SINCE) method of Lo for accelerating convergence (AEA, 1992). Turbulence was modeled as an extension of single-phase flow standard k - - E model. The homogeneous assumption was used for the interphase transfer terms in the transport equations for k and E. Inlet flow parameters were set to be constant and the fully developed assumption was applied to the outlet. For cocurrent flow and single-phase flow computations, inlet was set at the hot leg end near the reactor vessel. For countercurrent flow computations, inlet was assumed at the hot leg end near the steam generator. In the present study, no coolant injection from the deflector nozzle ("Hutze") was considered. Computations were carried out on a three-dimensional grid for the single-phase flow and a fine two-dimensional grid for two-phase flow, illustrated in Fig. 2. A HP750/PVRX workstation was used for simulation.
'0.012 + 5.179 × 10 4(Reg - Re*)/lO00 f = ~0.012 + 2.694 x lO-4(Re,/lOOO)"534(Reg-- Re*)/lO00
23 000 < Reg < Re* Re* <~Reg <<,51 000
(lO)
646
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643-652
SC UP
(a) "/ ,,n I 3663E+00
region
i
1386E+00 oI 9109E+00 06831E+00 0 4554E+00
(b) Fig. 2. Grid layout in the hot leg: (a) two-dimensional grid; (b) three-dimensional grid.
0 2277E+00 o O000E+0O
(a)
3. Results and discussion
3.1. Single-phase flow Single-phase flow is studied briefly in this section to gain an insight into the basic fluid-dynamic behavior in the hot leg. Computations were performed in a three-dimensional grid (Fig. 2(b)) of the hot leg under the boundary conditions listed in Table 1. Figs. 3 and 4 show the computed flow structures in laminar and turbulent regimes. As seen from Figs. 3(a) and 4(a), the fluid experiences acceleration in the horizontal part due to the layout o f the emergency core cooling (ECC)-injection pipe. In the bend and the riser part, a nonsymmetric pattern of velocity distribution is observed. The fluid velocity near the inner elbow is almost twice the value near the outer elbow. This behavior is qualitatively in accordance with other numerical and experimental studies in the bends of large tube-to-bend radius ratios (Ito, 1986). In addition, a small flow reversal region is found downstream of the ECC-injection pipe up to the middle of the bend in the laminar regime (Fig. 3(a)). As the mean velocity increases, the reversal region is remarkably reduced (Fig. 4(a)). Table 1 Boundary conditions of single-phase flow computations Flow pattern
p (bar)
Re
D (m)
Laminar Turbulent
15 15
1088 108 800
0.75 0.75
'~ J " 15 °
l. . . . . " " j 30 °
outer
45 °
(b) Fig. 3. Single-phase laminar flow in the 3-d hot
leg,
Re = 1088: (a) velocity field on the symmetric plane; (b) secondary flow in the bend region. In the bend region of the hot leg, a development of the four-vortex secondary flow structure is observed. Figs. 3(b) and 4(b) show such flow pattern at different cross-section planes, i.e. 15° , 30 ° and 45 ° bend angles from bend entrance towards the steam generator. Two small vortexes (one vortex in the half cross-section) develop near the outer side of the curvature, whereas the other two are larger and appear near the side region. The vortex centers move slightly towards the outside of the bend when the flow changes from laminar to turbulent.
3.2. Cocurrent stratified flow during natural circulation A second part of the numerical research is the development of the cocurrent stratified two-phase flow and the water transport mechanisms in the hot leg during natural circulation. According to the U P T F Test A2 (Sonnenburg, 1993), stratified
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643 652
depth unchanged, leads to the formation of a critical flow, when the velocity of the disturbance traveling upstream becomes zero. Further increasing the fluid velocity gives supercritical flow when all small disturbances travel downstream. Gardner (1989) gave a criterion for this critical condition, which corresponds to a water mass flow rate of 300 kg s 1 in the U P T F Test A2 (Sonnenburg, 1993). Based on this knowledge, computational conditions covering the two flow patterns were chosen from the transient runs of U P T F - A 2 Run 03C. Table 2 lists the specific boundary conditions used. Here HI,in represents the water level at the entrance of the hot leg from the upper plenum, determined from the U P T F measurements near that region. The velocities of two phases were calculated based on this water level and the mass flow rates. They were then used as the inlet velocities for computations. The simplified interfacial friction model was used as the standard interphase m o m e n t u m transfer model.
SC
UP
HOW
i1
f t~V~r~dl
regqon
2 7 0 5 E+OO
1.0587E+00 0 8470E+00 0.6325E+00 0 4235E+00 0.2118E+00 0.O000E+00
(a)
/
/
iy / outer 15 °
30 °
647
45 °
(b) Fig. 4. Single-phase turbulent flow in the 3-d hot leg, Re = 108 800: (a) velocity field on the symmetric plane; (b)
3.2. I. Behavior of subcritical stratified flow
secondary flow in the bend region.
Fig. 5 shows a typical two-dimensional simulation of the subcritical stratified flow in the hot leg under the condition of U P T F - A 2 Run 03C, time interval 380-473 s. As the flow in this time interval is unstable, the boundary condition was taken specifically around the time 450s. The U P T F measurements of water level and vapor velocity along the hot leg are also presented in the figure for comparison. The water level was measured at two locations using the 7-densitometer and five other locations using the differential pressure transducers. It is seen from Fig. 5 that both the water level and the vapor velocity agree with the U P T F measurements quite satisfactorily. Fig. 5(a) shows a predicted void fraction field, in which a wavy
flow is a typical flow pattern during the natural circulation m o d e within the water mass flow rates up to 400 kg s - ' and a constant steam mass flow rate of about 10 kg s - l . Depending on the water flow rate, two different patterns m a y exist, i.e. the subcritical stratified flow and the supercritical stratified flow. Here the terminologies subcritical and supercritical flow originate from the hydraulic engineer's analysis of small surface disturbances in one-dimensional channel flow, where two disturbances are found traveling at different velocities (Gardner, 1989). In subcritical flow, one disturbance travels upstream and another downstream. Increasing the fluid velocity, with the Table 2 Boundary conditions for cocurrent flow computations UPTF Test
Time (s)
p (bar)
/f/g (kgs i)
/I)/I (kgs 1)
Vg.in (ms -I)
Vi.i,, (ms -I)
Ht,i, (m)
A2 Run 03C A2 Run 03C
380 473 585-672
15 15
9.5 10.0
125 390
7.41 8.75
0.528 1.54
0.445 0.47
648
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643-652
SG
UP
cx Measurement of water level:
~ +: from Ap-signals
X: from ~-signals
1.0000E+00 8.3333E-01 6.6667E-01 5.0000~: o l 3.3333E Ol 1.6667E Ol 4 7441E 09
(a) SG
UP
steam generator. This is again qualitatively in agreement with the U P T F observation that a strong entrainment exists in the bend and in the riser part. Fig. 5(b) shows the predicted vapor velocity field along the hot leg. Owing to the existence of the ECC-injection pipe, steam is accelerated in that region. The same phenomenon is also observed in the riser part because of the reduction of the vapor passage. Fig. 5(c) shows an amplified flow structure in the bend and the riser part. It is interesting to find a clear, though not large, water circulation: water near the interface flows upward in the same direction as the vapor, whereas it flows downward near the outer wall of the bend and the riser. This phenomenon has been revealed by the U P T F experiment as another peculiar feature of the subcritial stratified flow.
v, [m/s] U: Position of velocity measurement
.... ~
I
Vl, M : 8.7 m/s V2, M = 6.9 m/s V3, M = 14.1 m/$
(b)
2,3847E+01 1.9872E+0[ 1.5898E+01 1.1923E+01 7.9489E+00 3.9744E÷00 o ooo0E+OO
SG
horizontal
part
iiiiii
(c) Fig. 5. Cocurrent stratified flow in the hot leg during the natural circulation condition, UPTF-A2 Run 03C, time interval 380-473 s: (a) void fraction field; (b) vapor velocity field; (c) flow structure in the bend and the riser part. interface is revealed in the horizontal part of the hot leg. Downstream of the ECC-injection pipe water level increases. This behavior is consistent with the experiment (Sonnenburg, 1993), and can be regarded as a characteristic of the subcritical flow pattern. At the end of the hot leg, void fraction is found somewhat less stratified, implying probably a higher phase interaction near the
3.2.2. Behavior o f supercritical stratified flow Increasing the water mass flow rate, the flow becomes supercritical. Fig. 6 shows a simulation of this flow pattern in the hot leg under the condition of UPTF-A2 Run 03C, time interval 585-672 s. Since the flow in this region was shown to be rather stable in the measurement, the assumption of steady state is reasonably adopted in the simulation. Again, the computation agrees well with the U P T F experiment both on the water level and on the vapor velocity. Compared with the subcritical flow, the supercritical stratified flow exhibits different behavior. The most important behavior is a decrease in water level downstream from the ECC-injection pipe, correctly predicted in the present study. This feature may cause a change in the water transport mechanism towards the steam generator. In addition, Fig. 6(c) indicates that the flow structure in the elbow and the riser part differs completely from that in the subcritical flow. Both liquid and vapor flow in the same direction, and no water circulation is found under this condition. Similar velocity effects on the flow structure have already been revealed in the single-phase simulation. 3.2.3. Effect of different &terphase transfer models Different interphase momentum transfer models were studied regarding their reliability for stratified flow simulation. Compared with the
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643 652
U P T F experiments, FLOW3D interphase momentum models did not provide reasonable results. In most cases they led to quick divergence, obviously due to their unrealistic physics. On the contrary, the interfacial friction model incorporated into FLOW3D code gave rather satisfactory results. It was found that the Ohnuki interfacial friction correlation provided very similar flow patterns to
j,~/2 0.8 j,gl/2 + j,~/2 = 0.7 0.6
?
+: from Ap-signals x: from
~-signals
(a)
~
1
al. 1978)
; 39
0.4: 37 0.2
Measurement o f water level:
(Richteret
./
L = 0.639 m A = 0.3974 m 2
SG
up
649
0
0.05
0.1
0.15
0.2
0.25 j.~/2
Fig. 7. Numerical and UPTF experimental runs on the Wallis diagram.
~r t O000E+OO 8 . 3 3 3 3 E Ol 6 6667E-01
those presented above from the simplified Lee and Bankoff correlation. Therefore the interfacial friction model can be satisfactorily used in two-dimensional stratified flow simulation.
5 ooooz-ol 3 3333E-01 I 6667E-01 2.9716E 09
SG
uP
v, {m/s] 2.257 IE+01 [3: P o s i t i o n o f v e l o c i t y m e a s u r e m e n t
Vt, M = 13.7 m/s V2, M :
8 9 m/s
V3, M = 2 5 . 1 m / s
(b)
i
I
1.8809E+01 1.5047E+01 1.1285E+01
7 5235E+00 3 7618E+00 o O000E+O0
5G
horizontal
part
(c) Fig. 6. Cocurrent stratified flow in the hot leg during the natural circulation condition, UPTF-A2 Run 03C, time interval 585-672 s: (a) void fraction field; (b) vapor velocity field; (c) flow structure in the bend and the riser part.
3.3. Countercurrent stratified flow during reflux condensation The last part of the numerical study is the countercurrent flow during reflux condensation mode, corresponding to the conditions of the U P T F Test 11 (Weiss, 1988). Numerous experiments indicated that the countercurrent flow has its l i m i t - - a t each particular gas flow rate there is a maximum liquid flow rate, and vice versa. Such phenomenon, called countercurrent flow limit (CCFL) or flooding, can be best described by the Richter correlation in PWR hot legs (Richter, 1978). In the Wallis diagram of Fig. 7, three computational points of different flow status relative to the Richter line were chosen from the U P T F Test 11, and they are listed in Table 3. Here the Wallis parameter in Fig. 7 is defined as Jk--Jk[pk/gL(pl--pg)] 1'2, where the length scale L is taken as the hydraulic diameter in the ECC pipe region. In Table 3, h)/j is the measured water mass flow rate from the hot leg to the reactor vessel, whereas h;/Li,j is the total water mass flow rate injected from the steam generator during the experiment.
650
M.J. Wang, F. Mayinger / Nuclear Engineering and Design 155 (1995) 643-652
Table 3 Boundary condition for countercurrent flow computations UPTF Test 11
p (bar)
Mg (kg s - 1 )
/~/I (kg s -I)
~/i,i.j (kg s -~)
Status
Run 37 Run 38 Run 39
15 15 15
8.3 18.1 24.0
9.8 29.4 25.2
9.8 29.4 29.6
Without CCFL Without CCFL With CCFL
3.3.1. Behavior o f countercurrent flow without CCFL Fig. 8 shows the predicted flow structure of U P T F Test 11 Run 37 under the typical reflux condensation condition using the simplified interfacial friction model. As illustrated in Fig. 7, Run 37 is far away from the C C F L in the hot leg, and was shown to be a stable point (Sonnenburg, 1993). Owing to lack of information on the water level near the steam generator, three steady runs SG
UP
a) HLin = 0.1875 In SG
UP
b) HLi. = 0.375 m
of different inlet void fractions were performed. It can be seen that the three computations reveal some c o m m o n features. There is a gradual increase in water level in the direction from the upper plenum towards the steam generator, obviously due to the retardation effect of the interfacial shear force. Such hydraulic phenomenon has also been observed in the hot leg model experiments of Ohnuki (1986). It is also found in this study that the ECC-injection pipe brings about an appreciable disturbance on the flow structure in the horizontal part, although the two-dimensional assumption may amplify such an effect. The greatest water level under this condition is found in the bend region, where flooding might eventually be initiated under favorable hydraulic conditions. Application of other interphase m o m e n t u m models to simulate the countercurrent flow was also tried. Again, it was found that the interphase models provided by FLOW3D code failed to give the right flow pattern, or even convergent results. On the contrary, the interfacial friction model with the Ohnuki correlation provided similar convergent results to the simplified Lee and Bankoff correlation.
5G
UP
c) HLio = 0.5625 nl ce 10000E+00 Mg = 8.3 kg/s
i
8.3333E-01 6.6667E-01 5.0OOOE-Ol
M I = 9.8 kg/s
3.3333E OI 1.6667E-01 1.0000E-08
Fig. 8. Void fraction field of the countercurrent stratified flow in the hot leg during typical reflux condensation condition, UPTF Test 11 Run 37 with different inlet water levels.
3.3.2. Behavior o f countercurrent flow near and with CCFL Fig. 9 illustrates the numerical simulation of U P T F Test 11 Run 38, at which the countercurrent stratified flow is still maintained, but is already near the flooding line. Fig. 10 presents the numerical result of U P T F Test 11 Run 39, at which flooding takes place and there is only partial delivery of liquid to the upper plenum of the reactor vessel. In the j~l/2_j,l/2 diagram of Fig. 7, Runs 38 and 39 are very close to each other. It can be found from Figs. 9 and 10 that the flow structures of these two runs exhibit a very similar
M.J. Wang, F. Mayinger /Nuclear Engineering and Design 155 (1995) 643-652 SG
uP
~ooooE+oo 8.3333E-01
Hlin = 0.5625 m
1
6.6667E OI
bag =
I
5.OO00Eol
18.1
kg/s
3.3333E-01
bAI : 29,4 kg/s
1.6667E OI I OOOOE-O8
Fig. 9. Void fraction field of the countercurrent flow in the hot leg during the reflux condensation condition, U P T F Test 11 R u n 38 near C C F L .
behavior. Downstream of the liquid inlet, water level decreases rapidly. Only a very thin liquid film was found in the bend region and the horizontal region. This implies a strong interphase momentum exchange. Between the pure liquid layer at the bottom and the pure vapor layer at the top of the hot leg, there is a relatively large region where void fraction lies between one and zero. This could be explained by the fact that under these conditions part of the liquid may be entrained in the vapor stream, forming a chaotic pattern in the core region.
4. Conclusions Thermal-hydraulic phenomena in the hot leg of a PWR during SBLOCA are simulated and analyzed in this paper. The main conclusions are
651
given as follows. The present study has shown, in principle, the applicability of the computational fluid dynamics method to the analysis of the thermal-hydraulic processes related to the SBLOCA as long as the relevant constitutive equations are well formulated. Thus, the numerical simulation provides an alternative to the reactor safety study. The hot leg configuration of the PWR presents a strong multi-dimensional effect which has not been properly considered in some one-dimensional thermal-hydraulic codes (Cappiello, 1988; Dillistone, 1992). Fundamental study of the single-phase laminar and turbulent flows reveals a remarkable flow distortion along the hot leg in the ECC pipe region, the elbow and the riser regions, and a four-vortex flow structure in the cross-section of the elbow. Steady state co- and counter-current flows in the hot leg are successfully simulated under the boundary conditions of UPTF Test A2 and Test 11 for natural circulation mode and reflux condensation mode. Interfacial friction models based on the Lee-Bankoff correlation and the Ohnuki correlation were implemented into the code FLOW3D for the interfacial momentum transfer. Satisfactory results were obtained in the subcritical and supercritical regions of the cocurrent stratified flow under the natural circulation conditions, where the same water transport mechanisms as shown in the UPTF experiment were predicted. Under the reflux condensation conditions, numerical computations reveal that different flow structures appeared in the region away from the CCFL line and in the region near the CCFL line.
SG
up
1.0000E+OO
Hlln = 0.5625 m bag = 24.0 kg/s
i
The authors acknowledge with great gratitude the financial support of the German Ministry of Research and Technology (BMFT) for this study.
6.6667E8"3333EO ' Io[ ~0oooE-ol 3 3333E~01
M~= 25.2 kg/s
Acknowledgment
1.6667E-01
Appendix A: Nomenclature
1 O000E-O8
Fig. 10. Void fraction field of the countercurrent flow in the hot leg during the reflux condensation condition, U P T F Test l l R u n 39 with C C F L .
A CD di
area drag coefficient interfacial length scale
M.J. Wang, F. May&ger / Nuclear Engineering and Design 155 (1995) 643-652
652 D
D
f g H
J J* L
M
if/ P
Ap Re
V(V)
tube diameter generalized drag i n t e r f a c i a l f r i c t i o n coefficient gravitational acceleration w a t e r level superfacial velocity Wallis parameter l e n g t h scale t o t a l i n t e r f a c i a l s h e a r stress mass rate pressure pressure drop Reynolds number velocity (vector)
Greek letters volume fraction dynamic viscosity density s h e a r stress
Subscripts g i in inj k 1 M t w
vapor interface inlet injection phase k liquid measurement turbulent wall
References AEA, FLOW3D 3.2 user manual, AEA Industrial Technology, Harwell Laboratory, UK, October 1992.
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