Chapter 4 Steady state behavior of natural circulation loops operating with carbon
5.4 Conclusions
During experimentation with carbon dioxide, instability has been observed for a very narrow window of power for HHHC orientation only and that too at lower secondary side chilled water flow rate i.e. 10-15 lpm. The instability in the loop was observed in the pseudo-critical temperature range of operation where the volumetric expansion coefficient of the fluid is the highest. For closed loop boundary conditions, NOLSTA code (without considering pipe wall thermal capacitance effect) predicts instability over a large range of power bounded by lower &
upper stable zones. Moreover, the instability is predicted even for very high secondary flows i.e.
135 lpm unlike experimental data where no instability was observed at 34 lpm secondary flow.
However no instability was predicted at 180 lpm secondary flow. The predictions are only
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qualitatively matching with experimental data, hence pipe wall thermal capacitance model was incorporated in NOLSTA code. Consideration of pipe wall thermal capacitance predicts SPNCL to be completely stable, but reducing the thermal capacitance by 18% and neglecting the local losses the code is able to simulate limit cycle oscillations without flow reversal as observed during experiments. As interaction of heat structure and fluid should be modeled in greater detail, hence 3D-CFD codes may be a helpful tool in understanding the stability behavior of closed loop thermo syphon with supercritical fluids.
The modified NOLSTA code with pipe wall effect was also used for studying stability behavior for an open loop i.e. Lomperski’s loop. The consideration of pipe wall thermal capacitance pushed stability threshold beyond the experimental power range and explains the reason of instability not observed during experiments. Modeling of thermal capacitance of pipe walls is strongly recommended for stability analysis of natural circulation at supercritical conditions (both open and closed loop boundary conditions) unlike two phase natural circulation flow case.
In two phase natural circulation case there cannot be any energy interaction between two phase fluid and adiabatic heat structure as both will always be at same temperature during the transient.
Any perturbation in two phase flow will give rise to a perturbation in two phase fluid enthalpy and void fraction/ density, but perturbation in enthalpy will not give rise to any perturbation in two phase fluid temperature and so there cannot be any thermal interaction of fluid with the wall.
However, perturbation in supercritical fluid flow will give rise to perturbation in enthalpy/
density and perturbation in enthalpy will also give rise to perturbation in supercritical fluid temperature and hence thermal interaction with the wall becomes possible.
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0 50 100 150
0.0650 0.0675 0.0700 0.0725
Lomperski's loop (without pipe wall effect) 8 MPa, T
in=24
oC
7500 W7800 W
Mass flow rate - kg/s
Time -s
Figure 5-1: Prediction of instability for Lomperski’s loop at 8 MPa and 24oC heater inlet temperature
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Figure 5-2: Typical unstable behavior at 500 W for HHHC orientation with SC-CO2 operation.
(a)
0 2000 4000 6000 8000 10000 12000 14000 -20
0 20 40 60 80
Pressure drop
Power - W
(p) Heater - mm WC
Time - s
0 200 400 600 800 1000
Power
9.1 MPa, 500 W
Secondary coolant flow rate - 10.1 LPM
(b)
0 2000 4000 6000 8000 10000 12000 14000 0
10 20 30 40 50
9.1 MPa, 500 W
Secondary coolant flow rate - 10.1 LPM
Heater inlet Heater out
Temperature(O C)
Time (s)
0 100 200 300 400 500 600 700 800
Power
Power (W)
(c)
2400 2500 2600 2700 2800 2900 3000 0
10 20 30 40 50
9.1 M P a, 500 W
S econdary coolant flow rate - 10.1 LP M
Tim e - s
H eater inlet H eater out
Temperature - O C
127
(c) (a)
0 1000 2000 3000 4000 5000 6000 7000 0
20 40 60 80 100
9.1 MPa, 800 W
Secondary coolant flow rate - 15.0 LPM Pressure drop
(P) Heater - mm WC
Time - s
0 300 600 900 1200 1500
Power - W
Power
(b)
0 1000 2000 3000 4000 5000 6000 7000 0
10 20 30 40 50
Heater in Heater Out
Temperature (0 C)
Time (s)
0 200 400 600 800 1000 1200
9.1 MPa, 800 W
Secondary coolant flow rate - 15.0 LPM
Power
Power (W)
Figure 5-3: Typical unstable behavior at 800 W for HHHC orientation with SC-CO2 operation.
3000 3100 3200 3300 3400 3500 0
10 20 30 40 50
9.1 MPa, 800 W
Secondary coolant flow rate - 15.0 LPM Heater in Heater Out
Temperature (0 C)
Time (s)
128
(b)
0 2000 4000 6000 8000 10000 0
10 20 30 40 50
9.1 MPa, 700 W
Secondary coolant flow rate - 15.5 LPM Heater in Heater out
Temperature (o C)
Time (s)
0 300 600 900 1200 1500
Power (W)
Power
Figure 5-4: Typical unstable behavior at 700 W for HHHC orientation with SC-CO2 operation.
(a)
0 2000 4000 6000 8000 10000
0 20 40 60 80 100
9.1 MPa, 700 W
Secondary coolant flow rate - 15.5 LPM
Pressure drop
(P) Heater - mm WC
Time - s
0 200 400 600 800 1000
Power - W
Power
(c)
4000 4200 4400 4600 4800 5000
0 10 20 30 40 50
9.1 MPa, 700 W
Secondary coolant flow rate - 15.5 LPM Heater in Heater out
Temperature (o C)
Time (s)
129
(a)
0 2000 4000 6000 8000
-40 -20 0 20 40 60 80 100
Pressure drop
(p) Heater- mm WC
Time - s
0 500 1000 1500 2000
7.7 MPa, 300 W
Secondary coolant flow rate - 10.0 LPM
Power - W
Power
(b)
0 2000 4000 6000 8000
0 20 40 60 80 100
7.7 MPa, 300 W
Secondary coolant flow rate - 10.0 LPM Heater in
Heater Out
Temperature(O C)
Time (s)
0 400 800 1200 1600 2000
Power (W)
Power
Figure 5-5: Typical unstable behavior at 300 W for HHHC orientation during power step down with SC-CO2 operation.
(c)
7000 7200 7400 7600 7800 8000 0
10 20 30 40 50
7.7 MPa, 300 W
Secondary coolant flow rate - 10.0 LPM Heater in Heater Out
Temperature(O C)
Time (s)
130
Figure 5-6: Typical unstable behavior at 700 W for HHHC orientation during power step rise with SC-CO2operation.
(a)
0 1000 2000 3000 4000 5000 6000 7000 8000 -20
0 20 40 60 80
Pressure drop
(p) Heater- mm WC
Time - s
0 200 400 600 800 1000 1200
8.1 M Pa, 700 W
Secondary coolant flow rate - 10 LPM Power
Power - W
(b)
3000 3200 3400 3600 3800 4000
10 15 20 25 30 35 40
Temperature - o C
Heater inlet Heater out
Tim e (s)
0 300 600 900 1200
8.1 MPa, 700 W
Secondary coolant flow rate - 10 LPM
Power (W)
Figure 5-7: Variation of volumetric thermal expansion coefficient of carbon dioxide with temperature at 9.1 MPa pressure
10 20 30 40 50 60 70 80
0.00000 0.00002 0.00004 0.00006 0.00008 0.00010 0.00012
Instability region in experiments
CO2 9.1 MPa
Volumetric thermal expansion coefficient - K-1
Temperature - oC
131
18 36 54 72
0.08 0.12 0.16 0.20
Mass flow rate (kg/s)
p (mm-WC) 800 W; 9.1 MPa;
15 lpm & 9.8
oC
30 40 50 60
0.12 0.14 0.16 0.18 0.20
Mass flow rate (kg/s)
p (mm-WC)
500 W; 9.1 MPa;
10 lpm & 9.8
oC
Figure 5-8: Phase plot of single cycle oscillation at 500 W corresponding to time series in figure 5-2
Figure 5-9: Phase plot of single cycle oscillation at 800 W corresponding to time series in figure 5-3
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25 50 75
0.12 0.16 0.20
Mass flow rate (kg/s)
p (mm-WC)
700 W; 9.1 MPa;
15.5 lpm & 9.8
oC
30 40 50 60 70
0.12 0.14 0.16 0.18 0.20
Ma s s flo w ra te ( k g /s )
p (mm-WC)
500 W; 9.1 MPa; 10 lpm & 9.8 oC
Figure 5-10: Phase plot of single cycle oscillation at 700 W corresponding to time series in figure 5-4
Figure 5-11: Long duration phase plot at 500 W corresponding to time series in figure 5-2
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0 25 50 75 100 125 150 175 200
0.040 0.041 0.042 0.043 0.044 0.045
0.03 s 0.06 s 0.12 s 0.24 s
500 W, 9.1 MPa, HHHC, (Bringer Smith, 1957) Secondary flow rate - 15 lpm at 9oC
M a s s fl o w ra te - k g /s
Time -s
20 30 40 50 60 70 80
0.09 0.12 0.15 0.18 0.21
Mass flow rate (kg/s)
p (mm-WC)
700 W; 9.1 MPa;
15.5 lpm & 9.8 oC
Figure 5-12: Long duration phase plot at 700 W corresponding to time series in figure 5-4
Figure 5-13: Time step sensitivity study for stability behavior of closed loop SPNCL with SC-CO2 operation
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0 25 50 75 100 125 150 175 200 225 250 0.041
0.042 0.043 0.044 0.045
node length = 0.005m node length = 0.01m node length = 0.025m node length = 0.05m
500 W, 9.1 MPa, HHHC, (Bringer Smith, 1957) Secondary flow rate - 15 lpm at 9oC
Mass flow rate - kg/s
Time -s
0 25 50 75 100 125 150 175 200
0.040 0.042 0.044 0.046
Convergence value = 0.1 Pa Convergence value = 1.0 Pa Convergence value = 10.0 Pa
500 W, 9.1 MPa, HHHC, (Bringer Smith, 1957) Secondary flow rate - 15 lpm at 9oC
Mass flow rate - kg/s
Time -s
Figure 5-14: Grid size sensitivity study for stability behavior of closed loop SPNCL with SC-CO2 operation
Figure 5-15: Effect of loop pressure closure convergence criterion on stability behavior of closed loop SPNCL with SC-CO2 operation
135
0 50 100 150 200 250 300
0.0350 0.0375 0.0400 0.0425 0.0450 0.0475 0.0500
400 W 450 W 500 W 9.1 MPa, HHHC, (Bringer Smith, 1957)
Secondary flow rate - 15 lpm at 9oC
M a s s flo w r a te - k g /s
Time -s
Figure 5-16: Stable, unstable and neutrally stable operating conditions for SPNCL with SC-CO2 operation
136
0 25 50 75 100 125 150 175 200
0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055
800 W
1000 W 500 W
1350 W 400 W
9.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) Secondary flow rate - 15 lpm at 9oC
Mass flow rate - kg/s
Time -s
Figure 5-17: Stability predictions for closed loop SPNCL for HHHC orientation at 15 lpm.
(a)
(b)
0 50 100 150 200 250 300
20 30 40 50 60 70 80 90 100 110 120
9.1 MPa, HHHC
Secondary flow rate - 15 lpm at 9oC
Heater Inlet temperature ---- Heater outlet temperature
Outlet temp. (400 W) Inlet temp. (400 W) Outlet temp. (800 W)
Inlet temp. (800 W) Inlet temp. (1350 W) Outlet temp. (1350W)
T e m per at ur e -
oC
Time -s
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Figure 5-18: Prediction of instability at 800 W by NOLSTA code in more detail.
(a)
0 100 200 300 400
0.00 0.02 0.04 0.06 0.08 0.10
800 W, 9.1 MPa, HHHC, NOLSTA (Bringer Smith , 1957) Secondary flow rate - 15 lpm at 9oC
Mass flow rate - kg/s
Time -s
(b)
0 100 200 300 400
40 42 44 46 48 50 52 54 56 58
800 W, 9.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) Secondary flow rate - 15 lpm at 9oC
Temperature - o C
Time -s
Heater Inlet temperature Heater outlet temperature
138
0 25 50 75 100 125 150
0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080
3400 W 1200 W
2000 W
2600 W
9.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) Secondary flow rate - 90 lpm at 9oC
Mass flow rate - kg/s
Time -s
0 50 100 150 200
20 30 40 50 60 70 80
9.1 MPa, HHHC
Secondary flow rate - 90 lpm at 9oC
Heater Inlet temperature ---- Heater outlet temperature
Outlet temp. (1200 W) Inlet temp. (1200 W) Outlet temp. (2000 W) Inlet temp. (2000 W)
Inlet temp. (3400 W) Outlet temp. (3400W)
Temperature - o C
Time -s
Figure 5-19: Stability predictions for closed loop SPNCL with HHHC orientation at 90 lpm.
(a)
(b)
139
0 100 200 300 400
0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090
4000 W
3400 W 1600 W
2800 W 2200 W
9.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) Secondary flow rate - 180 lpm at 9oC
Mass flow rate - kg/s
Time -s
0 20 40 60 80 100 120
0.055 0.060 0.065 0.070 0.075 0.080 0.085
2200 W
3000 W
3500 W
9.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) Secondary flow rate - 135 lpm at 9oC
Mass flow rate - kg/s
Time -s
Figure 5-20: Stability predictions for SPNCL at 135 lpm
Figure 5-21: Stability predictions for SPNCL at 180 lpm
140
0 25 50 75 100 125 150 175 200
0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080
ID - 13.88 mm ID - 15.5 mm ID - 16.5 mm
8.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) 450 W, Secondary flow rate - 10 lpm at 9oC
Mass flow rate - kg/s
Time -s
0 30 60 90 120 150 180 210 0
1 2 3 4 5 6
Power required to make loop average temp. equal
to pseudo-critical temp. at 8.1 MPa Power required to make loop average temp. equal
to pseudo-critical temp. at 9.1 MPa Stability threshold by NOLSTA, 9.1 MPa (Bringer Smith) Stability threshold by NOLSTA, 8.1 MPa (Bringer Smith) Unstable data at 7.7 MPa
Unstable data at 8.1 MPa Unstable data at 9.1 MPa Stable data at 8.1 MPa Stable data at 8.6 MPa Stable data at 9.1 MPa
Stable Stable
Unstable
Coolant flow rate - LPM
Powe r - k W
Figure 5-22: Stability maps for closed loop SPNCL with HHHC orientation at different pressures
Figure 5-23: Effect of loop inside diameter on stability behavior of SPNCL
141
0 25 50 75 100 125 150 175 200
0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070
425 W 450 W 475 W
8.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) Secondary flow rate - 10 lpm at 9oC, ID-15.5 mm
Mass flow rate - kg/s
Time -s
0 100 200 300 400 500
0.00 0.02 0.04 0.06 0.08 0.10 0.12
8.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) 450 W, Secondary flow rate - 10 lpm at 9oC ID -15.8 mm (1/2" Sch. 40 pipe)
Mas s flow rate - k g /s
Time -s
Figure 5-25: Flow reversal case obtained for ID -15.8 mm in SPNCL Figure 5-24: Effect of power on the limit cycle oscillations observed in SPNCL
142
0 25 50 75 100 125 150 175 200
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11
1800 W 1400 W
1200 W
800 W 1600 W
1000 W
8.1 MPa, HHHC, NOLSTA (Bringer Smith, 1957) Secondary flow rate - 34 lpm at 9oC
ID - 15.5 mm
Mass flow rate - kg/s
Time -s
0 25 50 75
0.050 0.055 0.060 0.065 0.070 0.075
14700 W 15000 W
Lomperski's loop (with pipe wall effect) 8 MPa, Tin=24oC
Mass flow rate - kg/s
Time -s
Figure 5-26: Completely stable behavior of SPNCL obtained by considering wall thermal capacitance at 34 lpm.
Figure 5-27: Stability threshold of Lomperski’s loop after considering thermal capacitance of pipe wall.
143