Luận án Nghiên cứu hiện tượng chuyển pha trong vùng hoạt lò phản ứng

 
15 
63.00 Termination of boron 
solution injection into the 
reactor from HA-1 
63.00 Termination of boron solution 
injection into the reactor from 
HA-1 
0 
117.00 Beginning of supply from 
HA-2 
115.00 Beginning of supply from HA-
2 
2 
500.00 End of the calculation 500.00 End of the calculation 0 
51 
The graph on the left of Figure 3.4 shows cladding temperature of the calculation at the hot 
channel with different location of break and the graph at the right of Figure 3.4 shows SAR 
calculation with different sensitivity study. 
Figure 3.4 (a) Cladding temperature from calculations, (b) Cladding temperature from SAR 
Thus, the comparison results of steady-state and DBA with Event number 3 mentioned above 
shown that deviation of results in Table 3.3 and Table 3.4 have no significant gap. The graphs 
in Figure 3.4 also show our calculation similar to SAR results in term of peaking cladding 
temperature and timing to cool down cladding temperature. Thus, the simulation model of this 
study is appropriate with reference model from the SAR. 
3.3 CTF models verification and assessment with BM ENTEK tests 
As mentioned in Ref. [26], the study of CTF void fraction prediction for PSBT single channel 
exercises shows that CTF predictions stay within the error bound of 0.1 void. The conclusion 
in Ref. [29] shows that the heat transfer models in CTF were inappropriate for simulations of 
subcooled boiling conditions. It is necessary to validate CTF void fraction prediction with an 
experiment in high pressure condition to verify its accuracy and the ENTEK BM tests suitable 
for this study. CTF, a COBRA-TF version with inhomogeneous models of two phase flow, is 
developed by Pennsylvania State University and is transferred to Vietnam Agency for 
Radiation and Nuclear Safety (VARANS) through bilateral cooperation. Therefore, CTF is 
considered as a tool at sub channel scale to investigate core thermal hydraulics by technical 
support organizations (TSOs). This study focuses on two points: (a) accuracy assessment 
between CTF’s void fraction predictions versus experiment distributions along the channel 
and (b) uncertainty of void fraction prediction due to propagation of input uncertainty caused 
by measured accuracy. 
3.3.1 ENTEK BM facility 
As mentioned in [33], Figure 3.5 provides a vertical and cross-section view of the test section 
which is also called as Heated Release Zone (HRZ). For the cross section view, the diameters 
are shown in millimeters. The HRZ contains a 7-rod bundle made by stainless steel 
(X18H10T). All the rods are hollow with outer diameter of 13.5 mm, 1.25 mm wall thickness, 
and 7 m length. The bundle is contained within a stainless steel pressure tube (80 mm outer 
diameter and 5 mm wall thickness) with inner diameter of 49 mm and 10.5 mm wall 
52 
thickness. The coolant flow area is 8.84×10
-4 
m
2
 and the hydraulic diameter is 7.84 mm. There 
are 20 honeycomb-type pin spacing grids along the length of the HRZ, starting 30 mm from 
the beginning of the HRZ and repeated every 350 mm. Thus, these spacing grids are similar to 
the spacers in the RBMK-1000 with a hydraulic loss coefficient of 0.4 based on 
measurements. 
The uncertainties of the measurements for each parameter are following for all tests: 
- Pressure at HRZ outlet: ±1.5 %; 
- Coolant mass flow rate : ±0.0018 kg/s; 
- Coolant temperature at HRZ inlet: ±1 K; 
- Electrical power: ±2 kW; 
- Void fraction: ±0.03; (void is calculated rather than measured). 
Figure 3.5 Test section (Heat Release Zone, φ is diameter in mm) 
with vertical and cross section view (source [33]). 
The test section, called Heat Release Zone, is illustrated from point “B” to point “C” in the 
Figure 3.5. Measurement readings were obtained at 10 axial locations (i.e., 0.385, 0.948, 
1.573, 2.322, 2.947, 4.010, 4.823, 5.448, 6.135, and 6.760 m from bottom of heated length) by 
moving the equipment during a test. The density was converted to a void fraction ( ) using 
the formula: 
The report [33] presents 25 tests together with RELAP5 calculation results. Since the input 
parameters such as pressure, mass flow rate, power and temperature are somehow not 
consistent with behavior of a flow because they are not measured at the same time in 10 
locations along the channel in test section, but measured in sequence during the test, then to 
simulate this test it is essential to setup base case for simulation and to perform sensitivity 
analysis. 
53 
3.3.2 Modeling by CTF 
Figure 3.6 shows the CTF modeling of BM ENTEK with 12 channels numbered from 1 to 12 
at the left and 18 gaps numbered from 1 to 18 at the right. The geometry data is taken from 
the Ref. [33] and the initial data is taken from tests presented in Table 3.5. 
3.3.3 Results and discussions 
 Setting for base case and sensitivity analysis 
Ten tests were selected to study. The tests: T01, T04, T08, T10 and T14 were implemented at 
pressure of 3 MPa. The five other tests: T17, T18, T22, T24 and T25 are performed at 
pressure of 7 MPa. The input for base case is selected by the average values of input 
parameters measured at ten locations. The sensitive study includes two cases for each test. 
The first is maximum voiding case by selection of maximum pressure, mass flow rate and 
minimum power and temperature measured. The second is minimum voiding case by 
selection of minimum pressure, mass flow rate and maximum power, temperature. 
Figure 3.6 BM ENTEK modeling by CTF 
Table 3.5 Setting for base case and sensitivity cases according to test 01 and test 17 
Test No P (MPa) G (kg/s) N (kW) T (K) Z (m) Void exp 
T01 
3.13 0.4364 305.6 373 0.385 0.0 
3.16 0.4353 305.1 388 0.948 0.0 
3.16 0.4344 305.1 388 1.573 0.0 
3.11 0.4336 300.8 389 2.322 0.0 
3.06 0.4481 302.3 389 2.947 0.0 
3.13 0.4403 296.7 389 4.010 0.0 
3.08 0.4339 296.8 388 4.823 0.027 
3.11 0.4389 297.0 388 5.448 0.178 
3.13 0.4344 297.8 388 6.135 0.493 
3.09 0.435 296.0 388 6.760 0.635 
Base case 3.12 0.4370 303 387 
Min void 3.16 0.4389 296 373 
Max void 3.06 0.4336 305.6 389 
54 
T17 
7.21 0.8956 308.0 496 0.385 0.0 
7.22 0.8794 303.1 498 0.948 0.004 
7.24 0.8797 302.4 501 1.573 0.006 
7.09 0.8722 303.3 494 2.322 0.0 
7.11 0.8825 301.6 494 2.947 0.009 
7.18 0.8853 302.1 496 4.010 0.002 
7.20 0.8781 301.4 497 4.823 0.017 
7.17 0.8814 302.0 497 5.448 0.033 
7.16 0.8822 301.6 494 6.135 0.079 
7.16 0.8850 302.2 493 6.760 0.194 
Base case 7.17 0.8821 302.8 496 
Min void 7.24 0.8956 301.4 493 
Max void 7.09 0.8722 301.4 501 
For remaining tests, the experiment data can be found in [33] and the base case setting and 
sensitivity cases are similar to Table 3.5. 
 Along channel void fraction distribution discussion 
Table 3.6 and Table 3.7 show the void fraction distribution calculation results versus 
experiment distribution along the channel. Table 3.8 shows the difference between void 
fraction distribution calculation results versus experiment distribution. It is observed that 
CTF’s void fraction distribution predictions for base cases are good agreement with 
experiment distribution with mainly deviation around 0.03 of void. The maximum deviations 
with value around 0.1 occurred just one or two locations of the tests T04 and T08. Especially, 
for the five tests at 7 MPa (T17, T18, T22, T24 and T25), the very good void fraction 
distribution calculations are agreed with experiment distribution with deviation not more than 
0.03 void along the channel. 
Table 3.6 Base case void fraction distribution calculations versus experiment for cases at 3MPa. 
Z T01x T01c T04x T04c T08x T08c T10x T10c T14x T14c 
0.385 0 0 0 0 0.003 0 0 0 0.002 0 
0.948 0 0 0.006 0 0.01 0 0.001 0 0.001 0 
1.573 0 0 0.015 0 0.001 0 0.006 0 0 0 
2.322 0 0 0 0 0 0 0 0 0 0 
2.947 0 0 0.002 0 0 0 0.006 0 0 0 
4.01 0 0 0.002 0 0.206 0.088 0.165 0.067 0.24 0.183 
4.823 0.027 0.003 0.043 0.022 0.621 0.574 0.398 0.342 0.484 0.441 
5.448 0.178 0.155 0.136 0.157 0.756 0.759 0.541 0.608 0.594 0.588 
6.135 0.493 0.591 0.299 0.459 0.83 0.842 0.652 0.723 0.646 0.673 
6.76 0.635 0.706 0.472 0.584 0.86 0.877 0.74 0.771 0.718 0.714 
(x = Experiment, c= Calculation) 
Table 3.7 Base case void fraction distribution calculations versus experiment for cases at 7MPa. 
Z T17x T17c T18x T18c T22x T22c T24x T24c T25x T25c 
0.385 0 0 0 0 0.001 0 0 0 0 0 
0.948 0.004 0 0.003 0 0.018 0 0 0 0 0 
1.573 0.006 0 0 0 0.015 0 0 0 0 0 
2.322 0 0 0.009 0 0.085 0.03 0 0 0 0 
2.947 0.009 0 0.089 0.005 0.22 0.134 0 0 0 0 
4.01 0.002 0 0.275 0.179 0.446 0.496 0.1027 0.076 0 0.001 
4.823 0.017 0 0.405 0.381 0.579 0.616 0.2814 0.25 0.1548 0.123 
55 
5.448 0.033 0 0.485 0.503 0.654 0.694 0.3973 0.406 0.4021 0.364 
6.135 0.079 0.056 0.553 0.585 0.733 0.75 0.4834 0.512 0.5178 0.591 
6.76 0.194 0.17 0.612 0.628 0.79 0.781 0.5585 0.564 0.6398 0.67 
It is found that CTF tends to give under prediction when experiment void fraction below 0.2 
corresponding with heat transfer in sub cooled boiling mode and flow regime map in small 
bubble. At the near outlet of the channel where the experiment void is more above 0.2 and 
heat transfer in nucleate boiling mode, CTF tends to give over prediction. Thus, CTF boiling 
model is still needed to be improved for both sub cooled and nucleate boiling regimes in order 
to generate more void in sub cooled region and reduce void at nucleate boiling region. 
Table 3.8 Deviation of void fraction distribution calculation results versus experiment 
Z D(T01)* 
Heat 
mode 
D(T04) 
Heat 
mode 
D(T08) 
Heat 
mode 
D(T10) 
Heat 
mode 
D(T14) 
Heat 
mode 
0.385 0 spl 0 spl -0.003 spl 0 spl -0.002 spl 
0.948 0 spl -0.006 spl -0.01 spl -0.001 spl -0.001 spl 
1.573 0 spl -0.015 spl -0.001 spl -0.006 spl 0 spl 
2.322 0 spl 0 spl 0 spl 0 spl 0 subc 
2.947 0 spl -0.002 spl 0 spl -0.006 spl 0 subc 
4.01 0 spl -0.002 subc -0.118 subc -0.098 subc -0.057 nucb 
4.823 -0.024 subc -0.021 subc -0.047 nucb -0.056 nucb -0.043 nucb 
5.448 -0.023 subc 0.021 nucb 0.003 nucb 0.067 nucb -0.006 nucb 
6.135 0.098 nucb 0.16 nucb 0.012 nucb 0.071 nucb 0.027 nucb 
6.76 0.071 nucb 0.112 nucb 0.017 nucb 0.031 nucb -0.004 nucb 
Z D(T017) 
Heat 
mode 
D(T18) 
Heat 
mode 
D(T22) 
Heat 
mode 
D(T24) 
Heat 
mode 
D(T25) 
Heat 
mode 
0.385 0 spl 0 spl -0.001 spl 0 spl 0 spl 
0.948 -0.004 spl -0.003 spl -0.018 spl 0 spl 0 spl 
1.573 -0.006 spl 0 spl -0.015 subc 0 spl 0 spl 
2.322 0 spl -0.009 subc -0.055 subc 0 subc 0 spl 
2.947 -0.009 spl -0.084 subc -0.086 nucb 0 subc 0 spl 
4.01 -0.002 
 spl 
-0.096 
nucb 
0.05 nucb 
-
0.0267 
nucb 0.001 subc 
4.823 -0.017 
subc 
-0.024 
nucb 
0.037 nucb 
-
0.0314 
nucb -0.0318 subc 
5.448 -0.033 subc 0.018 nucb 0.04 nucb 0.0087 nucb -0.0381 nucb 
6.135 -0.023 subc 0.032 nucb 0.017 nucb 0.0286 nucb 0.0732 nucb 
6.76 -0.024 nucb 0.016 nucb -0.009 nucb 0.0055 nucb 0.0302 nucb 
* D (T01) = (T01C-T01X), c = calculation, x = experiment 
 Radial void distribution and turbulent mixing and void drift discussion 
For radial void distribution, it is shown in Figure 3.7 that higher void fraction exist inside the 
centric channels and lower void fraction exist in the surrounded channels. 
56 
Figure 3.7 Radial void distribution of the test T04 
The literal transportation of masses due to turbulent mixing and void drift are presented in the 
Ref. [38]. Based on output of CTF for total mass cross flow from channel to channel, it is 
estimated the cross mass flows in term of flow rates caused by turbulent mixing or void drift 
separately for the liquid phase as in Figure 3.8. 
Figure 3.8 Cross mass flow due to turbulent mixing and void drift 
for test 01 (left) and test 17 (right) 
It is shown that the cross transportation do not occur neither within the centric channels 
(channel 7 to 12) nor within surrounded channels (channel 1 to 6) but only between the 
surround channel and the centric channel. The literal mass transportation for void fraction is 
not significant in comparison with liquid transportation. The sudden change of cross flow of 
turbulent mixing and void drift is caused by change of heat transfer mode in one channel. 
 Sensitivity analysis discussion 
As mentioned above, two sensitivity cases with maximum and minimum voiding are setup for 
each test. CTF boiling modeling is assessed to be appropriate with experiment if the 
maximum and minimum voiding curves wrap the experiment void fraction curve and its 
uncertainty curves with measured accuracy of ±0.03 void. The uncertainty curves are called 
upper or under curves if they are derived from experiment curve with adding +0.03 or -0.03 of 
void, respectively. In Figure 3.9 and Figure 3.10, T*exp, T*max, T*min, T*Upper and T*under are 
57 
corresponding to experiment, maximum voiding, minimum voiding, upper uncertainty 
(+0.03) and under uncertainty (-0.03) curves. It is obviously seen that for two tests T01 and 
T14 with pressure around 3MPa, the maximum and minimum voiding curves wrap 
experiment and its uncertainty curves as desired. 
Looking at the test T25 with pressure around 7 MPa, the sensitivity curves do not wrap the 
experiment curves completely. In this case, the minimum voiding curve is even over the upper 
uncertainty curve at the downstream of the channel where the measured void fraction above 
0.5. Thus, through the right graph of Figure 3.10, it is shown clearly that CTF gives over void 
prediction even in case of minimum voiding. This is due to CTF boiling models with void 
fraction over 0.2 tend to over prediction. 
Figure 3.9 Maximum and minimum voiding curves versus experiment 
and its uncertainty curves for tests T01 and T14 
Figure 3.10 Maximum and minimum voiding curves versus experiment 
and its uncertainty curves for tests T17 and T25 
 Propagation of the experiment uncertainty 
The experiment uncertainties on the input parameters for all tests are mentioned above. To 
investigate the experiment uncertainty, the calculations are performed with each base case for 
each test to get nominal void fraction distribution column, αnom, then each parameter will be 
independently changed to upper bound or lower bound of uncertainty to investigate the 
deviation of its void fraction distributions with its base cases distributions. 
58 
Table 3.9 Deviation of void fraction distributions on input uncertainties 
versus nominal void fraction and experiment distributions for test T01 
Z T01x T01b T01P+ T01P- T01G+ T01G- T01N+ T01N- T01T+ T01T- 
0.385 0 0 0 0 0 0 0 0 0 0 
0.948 0 0 0 0 0 0 0 0 0 0 
1.573 0 0 0 0 0 0 0 0 0 0 
2.322 0 0 0 0 0 0 0 0 0 0 
2.947 0 0 0 0 0 0 0 0 0 0 
4.01 0 0 0 0 0 0 0 0 0 0 
4.823 0.027 0.003 0.002 0.008 0.002 0.002 0.008 0.002 0.009 0.002 
5.448 0.178 0.155 0.131 0.181 0.143 0.143 0.177 0.133 0.181 0.131 
6.135 0.493 0.591 0.578 0.604 0.584 0.584 0.602 0.579 0.602 0.579 
6.76 0.635 0.706 0.698 0.713 0.702 0.702 0.712 0.699 0.712 0.699 
(x=experiment, b= base case, P±, G±, N±, T± = pressure, mass flow rate, power and temperature changed) 
Table 3.9 and Figure 3.11 show the deviation of void fraction distribution results from 
nominal void fraction distribution due to change of input parameter for test T01. Thus, it is 
observed that the uncertainty cases are not significant discrepancy with base case. 
Figure 3.11 Uncertainty void fraction distributions for test T01 
Table 3.10 shows the maximum deviation compared in 10 measured locations along with the 
channel between nominal void fraction distribution and void fraction distributions for each 
change on input parameters with the tests: T01, T08, T17 and T25. It is observed that the 
change of pressure and temperature is more sensitive than mass flow rate and power, except 
case of T01. 
Table 3.10 Maximum deviation of void fraction distribution on input parameters versus base case 
for tests: T01, T08, T17 and T25 
 Z (m) T01 Z (m) T08 Z (m) T17 Z (m) T25 
Pressure 
±1.5% 
5.448 αnom ± 
0.026 
4.823 αnom ± 
0.014 
6.76 αnom ±0.03 5.448 αnom 
±0.028 
Inlet Temp ± 
1K 
5.448 αnom ± 
0.026 
4.823 αnom ± 
0.012 
6.76 αnom 
±0.023 
5.448 αnom ±0.02 
Mass flow 
rate ± 0.0018 
kg/s 
5.448 αnom ± 
0.012 
4.823 αnom ±0.01 6.76 αnom 
±0.004 
5.448 αnom 
±0.005 
Power ± 2kW 5.448 αnom ± 
0.022 
4.823 αnom ±0.01 6.76 αnom 
±0.012 
5.448 αnom 
±0.008 
59 
In overall, it is concluded that the deviations between nominal void fraction distribution and 
its void fraction distributions due to uncertainties of measured input parameter are within 
measured void fraction accuracy (± 0.03). So that, CTF boiling models is stable enough with 
uncertainty from measured input parameters. 
 Conclusions 
It is summarized some assessment of CTF boiling model for ENTEK BM tests as following: 
 CTF gives void fraction distribution predictions with deviation from experiment 
distribution mainly within measured accuracy (0.03 of void) for most all base cases. 
Maximum deviations with 0.1 of void between CTF prediction and experiment occur 
at downstream of channel in some tests. 
 CTF boiling model tends to give under predict void fraction in sub cooled region 
where void fraction below 0.2 and to give over predict void fraction at nucleate boiling 
region where void fraction above 0.2. 
 The deviations between nominal void fraction distribution and its void fraction 
distributions due to uncertainties of measured input parameter are within measured 
void fraction accuracy (± 0.03) and CTF boiling model is rather sensitive with the 
change of pressure and inlet temperature than change of power and mass flow rate 
based on experimental measured accuracy. 
 Turbulent mixing and void drift effects only occur between surrounded channels and 
centric channels, the sudden change of cross mass flow in liquid phase happens due to 
the change of heat transfer mode in one channel. 
 Finally, CTF can simulate ENTEK BM tests with the appropriate results. 
3.4 Verification CFX models with PSBT sub channel tests 
Recently, an extension of CFD code application for two-phase flow is implemented as a part 
of multi-scale of thermal hydraulic safety analysis. Two-phase flow CFD used for safety 
investigations may predict small scale flow processes, which are not seen by system thermal 
hydraulics codes. It is shown that at least six Nuclear Safety Reactor (NSR) problems and 
many other NRS issues may benefit from study at the CFD scale. More detail about CFD code 
application on NSR problems can be found at [10], [6]. 
To support numerical simulation of two-phase flow, an international project of OECD/NRC 
PWR sub channel and bundle tests (PSBT) benchmark is implemented based on a database 
provided by the Nuclear Power Engineering Corporation (NUPEC), Japan from an 
experimental campaign carried out at NUPEC from 1987 to 1995 and based on that 
time state-of-art computer tomography (CT) technology for void measurements. 
According to [46], the NUPEC PSBT benchmark consists of two phases with different 
exercises. The first phase focuses on void distribution benchmark with four exercises. The 
first exercise is steady-state single sub channel benchmark with different geometry (S1, S2, 
S3 and S4). 
60 
3.4.1 PSBT test section for single sub channel 
Figure 3.12 shows the test section used for the typical center sub channel (S1) with the heated 
length of 1555 mm and the measurement position of void fraction is at 1400 mm elevation 
from inlet located at the bottom. It is seen at cross section that the diameter of the rod is 9.5 
mm and the rod pitch and rod gap is 12.6 mm and 3.1 mm, respectively. The uncertainty of 
measurement for input parameters as well as average void fraction at the measuring location 
is given in T