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A rational design procedure for two-phase natural circulation systems
P. K. Vijayan, M.R. Gartia, A.K. Nayak, D.Saha and R.K. Sinha Reactor Engineering Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India. E-mail: [email protected]
Abstract Design of two-phase natural circulation systems is somewhat complicated due to the existence of two constraints, i.e. stability and critical heat flux (CHF). Depending on the system geometry and operating conditions, the design of natural circulation systems can be stability controlled or CHF controlled. The design procedures for two-phase natural circulation systems are not well documented and unavailable in the open literature. This paper describes a rational design procedure developed in-house based on the state of the art knowledgebase available. 1. INTRODUCTION Natural circulation systems are essentially fluid filled systems employed to transport heat from a source to a sink. In such systems, the fluid circulation is caused by the buoyancy force which in turn is caused by the density gradients resulting from the heat transport process itself. The heat transport is achieved noiselessly without the use of fluid moving machineries and is considered to be more reliable as it relies on a natural physical law which is not expected to fail. Due to these advantages these systems find extensive applications in industry. Two-phase natural circulation systems (NCS) are capable of generating larger density gradients and hence flow rates resulting in larger heat transport capability. Two-phase natural circulation systems (NCS) are extensively used in both thermal and nuclear power plants. Traditional applications include thermosyphon reboilers, steam generators in nuclear power plants and boilers in fossil fuelled power plants. Emerging applications include computer cooling and cooling of electronic components. These systems are essentially mini loops capable of transporting a few tens to a few hundred Watts and contain only a few cubic centimeter of fluid. In contrast, the NCS used in power plants has a few hundred cubic meters of fluid and is capable of transporting a few thousand MW of power. Two-phase natural circulation is the proposed coolant circulation mode in many innovative reactors such as AHWR, ESBWR and VK-300. Two-phase natural circulation systems are susceptible to several kinds of instability. The instabilities could be static or dynamic and is influenced by a large number of geometric and operating parameters. A common geometric characteristic of most industrially important two-phase NCSs is that they consist of a large number of parallel channels.
Indian Nuclear Society - Paper
2
Typical examples are BWRs, NCBs in fossil fired power plants and thermosyphon reboilers. Parallel channel instability is a characteristic of such systems. An acceptable design must avoid all instabilities. This is done by identifying the controlling instability (instability with least stable zone) and restricting operation within its stable zone. Besides instability, avoidance of the critical heat flux (CHF) is also essential for the safe operation of two-phase natural circulation systems used in nuclear and thermal power plants. Depending on the geometry of the NCS, the maximum power could be limited by instability, CHF or both. A rational design procedure for such systems is described in this paper. 2. STEADY STATE CHARACTERISTICS OF TWO-PHASE NC SYSTEMS Knowledge of the steady state characteristics is essential for the design of NCSs. By design, it is usually meant as the establishment of the geometry (of the complete system including riser height, inlet and exit loss coefficients) and operating conditions (pressure, inlet subcooling and sink conditions) of the NCS to achieve a specified heat transport capability. Since the heat transport capability depends strongly on the flow generated, the most important steady state characteristic that needs to be established is the flow rate achievable in a NCS of specified geometry and operating characteristics. For simplicity we consider a uniform diameter loop (UDL) shown in Fig. 1.
Assuming balance of the driving buoyancy force to the retarding frictional forces at steady state, the following equation was derived to estimate the steady state flow rate in a UDL [1].
b
Gbl
hb
hlb
ss NzQgAD
pW
−−
⎥⎦
⎤⎢⎣
⎡ ∆=
31
222µβρ
(1)
where p
h h⎟⎠⎞
⎜⎝⎛∂∂
=v
v1β and ( ) ( ) ( ) ( )[ ]
CeffLOtpeffLOBeffLOspefft
G llllDLN 222 φφφ +++= (2)
Lh
S=0, St
S=Sh
S=SSD
S=SSD
DowncomerHeater
Steam Drum
H
Feed Water
Steam
S=Ssp Lh
S=0, St
S=Sh
S=SSD
S=SSD
DowncomerHeater
Steam Drum
H
Feed Water
Steam
S=Ssp
Fig.1: Schematic of a two-phase NCS
∆z
3
with
b
g
le
e
lLO
x⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛−+
=
11
12
µµρ
ρφ and
b
g
lem
lLO
x⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛−+
=
12
1
12
µµρ
ρφ (3)
This correlation was derived using the basic definition of 2
LOφ and McAdam’s model for two-phase viscosity [2]. It may be noted that for single-phase flows 12 =LOφ and equation (2) reduces to that applicable to single-phase natural circulation. Also, similarity in the definitions of the thermal expansion coefficients βh ( ( ) ( ) pTP
pP CTCh β=∂∂=∂∂= vv
1vv1 ) and βT (= ( )PT∂∂vv
1 ) valid for two-phase
and single-phase flows respectively may be noted. Also, if local losses are negligible, then the effective lengths in Eq. (2) become the corresponding physical lengths. Gartia et al. [1] also checked the adequacy of this correlation by comparing it with test data from several loops and found that the data are within + 40% of the above correlation. The loops considered differed in diameter but had the same length scale (see Fig. 2). 2.1 Two-phase NC Flow Regimes The steady state flow in two-phase loops is significantly influenced by the pressure, power and loop diameter. Based on the nature of the variation of the steady state flow with power, three different natural circulation flow regimes can be observed for two-phase loops [3]. These flow regimes are designated as gravity dominant, friction dominant and the compensating regimes. In a natural circulation loop, the gravitational pressure drop (being the driving pressure differential) is always the largest component of pressure drop and the sum of all other pressure drops (friction, acceleration and local) must balance the gravity (or buoyancy) pressure differential at steady state. However, the natural circulation flow regimes are differentiated based on the change of the pressure drop components with quality (or power).
Fig.2: Schematic of experimental loop Fig.3: Variation of void fraction with quality
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.01 bar
220 b
ar 221.2
bar17
0 bar
70 bar15
bar
Voi
d fra
ctio
n
Quality
575
Condenser
Separator
Heater
2445
2020
2210
2036
4
2.1.1 Gravity Dominant Regime The gravity dominant regime is usually observed at low qualities. In this regime, for a small change in quality there is a large change in the void fraction (see Fig. 3) and hence the density and buoyancy force. The increased buoyancy driving force is to be balanced by a corresponding increase in the retarding frictional force that is possible only at a higher flow rate. As a result, the gravity dominant regime is characterized by an increase in the flow rate with power (see Figs. 4). 2.1.2 Friction Dominant Regime Friction dominant regime is observed at low to moderate pressures when quality is high. At higher qualities and low to moderate pressures, the increase in void fraction with quality is marginal (Fig. 3) leading to almost constant buoyancy force. However, the continued conversion of high density water to low density steam due to increase in power requires that the mixture velocity must increase resulting in an increase in the frictional force and hence a decrease in flow rate. Thus the friction dominant regime is characterized by a decrease in flow rate with increase in power (see the curve for 15 bar in Fig. 4a and b). 2.1.3 Compensating Regime Between the gravity dominant and friction dominant regimes, there exists a compensating regime, where the flow rate remains practically unaffected with increase in power. In this regime, the increase in buoyancy force is compensated by a corresponding increase in the frictional force leaving the flow unaffected (see the curve for 7 MPa in Fig. 4a) in spite of increase in quality. The compensating regime exists only for moderate to high pressure in small diameter loops. 2.1.4 Effect of pressure and loop diameter The NC flow regimes depend strongly on the system pressure. In fact, at high pressures only the gravity dominant regime (as in single-phase natural circulation) may be observed if the power is low. The friction dominant regime shifts to low pressures with increase in loop diameter (see Fig. 4b, 4c). Knowledge of the flow regimes is important to understand the stability behaviour of two-phase loops.
0 20 40 60 80 1000
1
2
3
4
5
6
Predicted by Eq. (1)Loop Diameter= 9.1 mm
170 bar
70 bar
15 bar
GDR
Compensating Regime
Friction Dominant Region
GDR
Flow
nor
mal
ised
to 1
00%
FP
Power (%)0 20 40 60 80 100
0.0
0.4
0.8
1.2
1.6
2.0
Predicted by Eq. (1)Loop Diameter: 19.86 mmGDR: Gravity Dominant Regime
Compensating Regime
170 bar
50 bar
15 bar
GDR
Friction Dominant RegionGDR
Flow
nor
mal
ised
to 1
00%
pow
er
Power (%)
0 20 40 60 80 1000.0
0.4
0.8
1.2
1.6
2.0
170 bar
8 bar
2 bar
GDR
Compensating Regime
Friction Dominant RegimeGDR
Predicted by Eq. (1)Loop Diameter= 49.3 mmGDR: Gravity Dominant Regime
Flow
nor
mal
ised
to 1
00%
pow
er
Power (%)
(a) 9.1 mm loop (b) 19.86 mm loop (c) 49.3 mm loop Fig. 4: Effect of power, pressure and loop diameter on steady state two-phase NC flow
5
3. STABILITY BEHAVIOUR Two-phase natural circulation systems are susceptible to a large number of instabilities. Instability is undesirable as sustained flow oscillations may cause forced mechanical vibration of components [4]. Further, premature CHF (critical heat flux) occurrence can be induced by flow oscillations as well as other undesirable secondary effects like power oscillations in BWRs. Instability can also disturb control systems and pose operational problems in nuclear reactors. The instabilities are broadly classified into three groups; static, dynamic and compound dynamic instabilities. A more detailed description of natural circulation instabilities can be found in Nayak and Vijayan [5]. 3.1 Experimental Stability Map Generally, two unstable regions are observed for two-phase NCSs as illustrated by the stability map given in Fig. 5 for a 9.1 mm i.d. UDL (the geometry of the loop is shown in Fig. 2). The first unstable zone occurs at a low power and hence at low quality and is named as type-I instability by Fukuda and Kobori [6]. Similarly, the second unstable zone in the two-phase region (Fig. 5) occurs at high powers and hence at high qualities and is named as type-II instability [6]. Theoretical analysis by the same authors has shown that the gravitational pressure drop plays a dominant role in type-I instability where as frictional pressure drop is dominant in type-II instability. In other words, type-I instability occurs in the gravity dominant regime whereas type-II instability occurs in the friction dominant regime. Instability is not reported so far in the compensating regime. 3.2 Parametric Effects on DWI Both type-I and type-II instabilities are affected by a large number of parameters out of which the effects of power, pressure and loop diameter are studied both experimentally and theoretically in the present work.
0 3000 6000 9000 12000 150000.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5Boiling inception
Stable 1-φ flow
Type-II instability
Type-I instability
Loop diameter: 9.1 mmPressure: 1.37 MPa
∆P -
Pa*0
.1;
∆T su
b - K
Pow
er -
kW
Time - s
Power
0
20
40
60
80
100
∆P ∆Tsub
(a) Stability Map (b) Type-I oscillations c) Type-I oscillations Fig. 5: Typical experimental stability map and characteristics of type-I instability
1200 1600 2000 2400 2800 3200 36000.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Stable 2-φ flow
Boiling inception
Stable 1-φ flow
Loop diameter: 9.1 mmPressure: 1.37 MPa
∆P -
Pa*0
.1;
∆T su
b - K
Pow
er -
kW
Time - s
Power
0
20
40
60
80
100
∆P ∆Tsub
13000 13500 14000 14500 15000-500
0
500
1000
∆P -
Pa
Time (s)
7.4 bar (g) pressure9.1 mm ID tube
6
3.3 General Observations on Type-I instability A general characteristic of type-I instability is that it occurs right from boiling inception. Flashing and geysering induced instability also belong to this category. Broadly speaking, with increase in power the amplitude of type-I oscillations first increases, reaches a peak and then decreases eventually leading to stable flow (Fig. 5b). However, amplitude variation is a complex function of power presumably due to flow pattern transitions (Fig. 5b). For certain type-1 unstable regions, the flow alternates between a stable and oscillatory regime (Fig. 5c). The dynamics of type-I instability is quite rich showing many different oscillatory patterns. The amplitude of type-I oscillations reduce significantly with increase in pressure (see Figs. 6). Further, type-I instability is not observed beyond a critical value of the system pressure (Fig. 6d). While experimenting with uniform diameter loops, it was observed that the critical value of pressure beyond which the instability disappears is found to decrease with increase in the loop diameter (Fig. 7). Most practical application of natural circulation systems employs non-uniform diameter loops. A typical example is the Advanced Heavy Water Reactor (AHWR) being designed in India (Fig. 8). A test facility simulating the AHWR has been set up in BARC (Fig. 9). Extensive experimentations have been carried out to study the characteristics of Type-I instability encountered during the start-up in ITL which is a non-uniform diameter loop. In non-uniform diameter loops also, it is found that type-I instability disappears at high pressure (see Fig. 10).
0 3000 6000 9000 12000 150000.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
(d) Type-I Instability disappears at 2.5 MPa(c) Type-I instability at 2.1 MPa
(b) Type-I instability at 1.85 MPa(a) Type-I instability at 1.37 MPa
∆P
Pre
ssur
e -b
ar
Pressure
Time - s
∆P -
Pa
Loop diameter: 9.1 mmPressure: 2.5 MPa
0 4000 8000 120000
200
400
600
800
1000
0
20
40
60
80
100
6000 8000 10000 12000 14000 160000
200
400
600
800
1000
0
2
4
6
8
10
Loop diameter: 9.1 mmPressure: 2.1 MPa
Time - s
Pre
ssur
e - M
Pa
∆P
- P
a
Stable 2-φ flow
Stable 1-φ flow
Type-I instability
∆P
Pressure
0 4000 8000 12000 160000
200
400
600
800
1000
0
20
40
60
80
100
Time - s
Pres
sure
- ba
r
∆P -
Pa
Loop diameter: 9.1 mmPressure 1.85 MPa
Stable 2-φ flow
stable 1-φ flow
Type-I instability
1667 W1660 W
1450 W
1309 W
Pressure
Boiling inception
Stable 1-φ flow
Type-II instability
Type-I instability
Loop diameter: 9.1 mmPressure: 1.37 MPa ∆P
- Pa
*0.1
; ∆
T sub -
K
Pow
er -
kW
Time - s
Power
0
200
400
600
800
1000
∆P ∆Tsub
Fig.6: Effect of pressure on type-I instability
7
4000 5000 60000
250
500
750
1000
Pressure
∆P -
Pa
∆P -
Pa
∆P
Pressure
-4
-2
0
2
4
Pres
sure
- ba
r (g)
Pre
ssur
e - b
ar (g
)
∆P
(b) Start-up at 5.4 barTime - sTime - s
(a) Start-up at 3.1 bar
2000 3000 4000 5000 60000
250
500
750
1000
-2
0
2
4
6
Fig.7: Type-I instability in a 19.86 mm UDL
0 20000 40000 60000 800000
50
100
150
200
250
Flow
(lpm
)
Time (s)
0 20000 40000 60000 800000
50
100
150
200
250
Flow
- lp
m
Time - s
0 20000 40000 60000 800000
50
100
150
200
250
Flow
- lp
m
Time - s
0 20000 40000 60000 800000
50
100
150
200
250
Flow
- lp
m
Time - s
(a) Pressure: 0.1 MPa (b) Pressure: 1 MPa
(c) Pressure: 1.5 MPa (b) Pressure: 3.5 MPa
Fig.10: Type-I instability in ITL at 52 kW power
Down Comer
Steam Drum
FeederCalandria Housing
Active Core
Distribution Ring Header
Tail Pipe
Steam to Turbine
Feed Water in
Down Comer
Steam Drum
FeederCalandria Housing
Active Core
Distribution Ring Header
Tail Pipe
Steam to Turbine
Feed Water in
Fig. 8: Schematic of AHWR Fig.9: Isometric layout of ITL
ICSD
GD
WP
FCS
BFST
QOVHEADER
PBC
SFP
JC SB
AA
ICSD
GD
WP
FCS
BFST
QOVHEADER
PBC
SFP
JC SB
AA
FCS : Fuel channel simulator BFST : Break flow storage tank QOV : Quick opening valve GDWP : Gravity driven water poolSFP : Secondary feed pump JC : Jet condenser SB : Star-up boiler AA : Advanced accumulator SD : Steam drum IC : Isolation condenser
8
3.4 General Observations on Type-II instability Type-II instability is found to occur after the flow starts to decrease with increase in power as in Fig. 11 (characteristic of friction dominant regime). The threshold of type-II instability is found to increase with pressure as well as loop diameter. Type-II instability is observed in large diameter loops only at low pressures. A general characteristic of the type-II instability is that the oscillation amplitude keeps increasing monotonically with power. When the amplitude reaches a critical value, CHF occurs causing test section burnout. Burnout of the test section occurred only in the small diameter loops. 3.5 Analysis of Instability Apart from dynamic instability, two-phase loops can experience static instabilities. Examples of static instability are Ledinegg and flow pattern transition instabilities. Nayak et al. [7] showed that the Ledinegg instability is observable only at low pressures. Similarly, flow pattern transition instability also occurs only at low pressures [8]. Both these analysis were conducted for the simple uniform diameter loop as well as for the AHWR geometry. The results indicated that the instability is significantly influenced by
0 2000 4000 6000 8000 10000 12000 14000-20
0
20
40
60
80
100
Pressure: 13.5 bar- ∆P Across bottom horizontal leg
1385 W
1470 W 1598 W1689 W
2995 W
3969 W
1091 W
Upper threshold
Lower thrshold
L d U th h ld t bilit
∆P m
m o
f wat
er c
olum
n (1
-φ)
Pre
ssur
e (g
)-bar
Time (s)18000 20000 22000 24000 26000
0
20
40
60
80
100
4052 W
3634 W2803 W2225 W
1629 W
1400 W
1400 W
1400 W
∆P m
m w
ater
col
umn
Pres
sure
(g)-b
ar
Time (s)4000 6000 8000 10000 12000 140000
20
40
60
80
100
5060 W
4611 W
2957 W2680 W
2355 W
2068 W
1105 W
∆P m
m w
ater
col
umn
Pre
ssur
e (g
)-bar
Time (s)
(a) 1.3 MPa (b) 1.8 MPa (c) 2.5 MPa Fig. 11: The upper threshold of instability at different pressures
0.00 0.01 0.02 0.03 0.04 0.050.00
0.01
0.02
0.03
0.04
0.05
Driving head
Neutrally stable
Unstab
le
Stable
Pressure = 1 barI.D. = 9.1 mm∆Tsub = 35 K
Pre
ssur
e dr
op (M
Pa)
Flow rate (kg/s)
2 kW 2.7 kW 3 kW
0.00 0.02 0.04 0.06 0.080.00
0.02
0.04
0.06
0.08
0.10
UnstableNeutrally stable
Stable
Driving head
Pressure = 1 barI.D. = 9.1 mm∆Tsub = 35 K
Pre
ssur
e dr
op (M
Pa)
Flow rate (kg/s)
4 kW 5.5 kW 6.9 kW
(a) Lower threshold at 0.1 MPa (b) Upper threshold at 0.1 MPa
0.00 0.02 0.04 0.06 0.08 0.100.00
0.01
0.02
0.03
0.04
0.05
Neutrally stable
Unstable
Stable
Driving head
Pressure = 5 barI.D. = 9.1 mm∆Tsub = 35 K
Pre
ssur
e dr
op (M
Pa)
Flow rate (kg/s)
8.5 kW 9.5 kW 12.5 kW
0.00 0.02 0.04 0.06 0.08 0.100.00
0.01
0.02
0.03
0.04
0.05
Neutrally stable
Stable
Driving headUnstable
Pressure = 10 barI.D. = 9.1 mm∆T
sub = 35 K
Pre
ssur
e dr
op (M
Pa)
Flow rate (kg/s)
10 kW 15.4 kW 17 kW
(c) Lower threshold at 0.5 MPa (d) Lower threshold at 1 MPa Fig. 12: Ledinegg type instability
9
the pressure (Fig. 12) confirming the trend predicted by Nayak et al. [7] for AHWR. The dynamic stability of the uniform diameter loops were studied with a linear stability code TINFLO-S. The code uses the homogeneous and the drift flux models and a detailed write-up on the linear stability analysis can be had from Nayak et al. [9] and Nayak et al. [10]. 3.5.1 Stability analysis based on Homogeneous Equilibrium Model (HEM) Using the HEM incorporated in the code TINFLO-S, stability analysis was carried out using the length scales given in Fig. 2. The results for various diameters are given in Fig. 13. The CHF profile shown is predicted using the mass flux and quality corresponding to the type-II threshold with the look-up table method [11]. The stable zone is found to increase with loop diameter. The upper threshold is found to disappear with increase in loop diameter at high subcooling values (Fig. 13d). For 40 mm loop, the upper threshold does not exist as shown by Fig. 13e. 3.5.2 Stability analysis based on Drift Flux Model (DFM) The drift flux parameters (Co and Vgj) for slug flow were used as it was the most frequently observed flow pattern during the tests. The Martinelli-Nelson two-phase
(a) 4 mm loop (b) 7 mm loop (c) 9.1 mm loop
0 5 10 15 200
2
4
6CHF (Type-II threshold)
Type-I thresholdUnstable
Type-II threshold
Stable
Loop diameter = 4 mmPressure = 70 bar
Pow
er (k
W)
Subcooling (K)0 5 10 15 20
0
5
10
15
20
25
CHF (Type-II threshold)
Type-I thresholdUnstable
Type-II threshold
Stable
Loop diameter = 7 mmPressure = 70 bar
Pow
er (k
W)
Subcooling (K)4 8 12 16
0
10
20
30
40
CHF (type-II threshold)
Type-I threshold
Type-II threshold
Stable
Unstable
Pressure:7MPaLoop diameter:9.1mm
Pow
er (k
W)
Subcooling (K)
(d) 10 mm loop (e) 40 mm loop Fig.13: Effect of loop diameter on stability using the homogeneous model
0 5 10 15 20 250
50
100
150
200
250
300
Power at which CHF occurs
Type-I threshold
Pressure:7 MPaLoop diameter: 40mm
Stable
Unstable
Pow
er (k
W)
Subcooling (K)
0 5 10 15 20 25 300
10
20
30
40
50
Type-II threshold
Type-I threshold
Power at which CHF occurs
x = 1
Unstable
Unstable
Stable
Loop diameter = 10 mm; Pressure = 70 bar
Pow
er (k
W)
Subcooling (K)
10
friction multiplier model was used in the computations. Nayak et al. [10] compared the predicted stability map with experimental data. Fig. 14a reveals that the stability is enhanced by increasing the loop diameter which is consistent with the test results. The effect of loop diameter on the lower threshold of instability (type-I instability) is less significant compared to that on the upper threshold (type-II instability). However, when plotted in terms of power (Fig. 14b) both the lower and upper thresholds are found to be significantly influenced by the loop diameter. Increase in inlet subcooling destabilizes type-I instability irrespective of the loop diameter. For type-II instability, however, similar behaviour is observed only at low loop diameter. For large loop diameters, (see the stability map for 25 mm) type-II instability stabilizes initially and then destabilizes. Similar behaviour is also reported by Boure et al. [4]. For 40 mm loop diameter, the type-II threshold is not found in the two-phase region (i.e. 0<quality<1). Experiments by Mochizuki [12] indicate that this instability occurs when the quality is close to unity at high pressure and large inlet subcooling. It may be noted that the stable zone (difference in power between the upper and lower thresholds) is very low for small diameter loops whereas it is significantly large in large diameter loops (Fig. 14b). Compared to the results of homogeneous model, it is evident that the predicted trends are similar. However, significant quantitative differences exist. 3.5.3 Parallel Channel Instability So far only single channel systems were considered. Parallel channels can significantly modify the stability behaviour. Hence a twin channel system as shown in Fig. 15a was analysed using the homogeneous model and the results are given in Fig. 15b. Since the length scales of the single channel system given in Fig. 2 is same as the twin channel system considered, the results obtained with the single channel system is also given in Fig. 15b for comparison. It is found that the twin channel system is considerably less stable than single channel system. Similar observation was also made by Nayak et al. [9] in respect of AHWR.
(a) Stability map in terms of quality (b) Stability map in terms of power Fig. 14: Effect of loop diameter on stability
7 14 21 28 35
0
30
60
90Unstable
Unstable
Stable
loop diam eter
Pressure = 70 bar
exit
qual
ity
subcooling (K)
7 mm 10 mm 15 mm 20 mm 25 mm 40 mm
6 12 18 24 30
0
50
100
150
200
Unstab le
Unstablestable
pressure = 70 bar
Pow
er (k
W)
subcoolng (K)
7 m m 10 m m 15 m m 20 m m 25 m m
11
4. DESIGN CONSIDERATIONS Most static instabilities including Ledinegg and flow pattern transition instabilities are observed only at low pressures. Only the density wave instability is observed at high pressures. For parallel channel systems, the density wave oscillations can be in-phase (characteristics of single-channel system) or out-of-phase (characteristics of parallel channel system). For such systems, generally, the controlling instability (instability with least stable zone) is found to be the out-of-phase parallel channel instability (Fig. 15b). Both in-phase and out-of-phase instabilities exhibit two unstable regions designated as type-I and type-II instabilities. Single channel experiments show that it is possible to avoid type-I instability by a pressurized start-up (Figs. 6, 7 and 10). Fig. 14a shows that the type-II instability threshold shifts to higher qualities with increase in loop diameter. For large diameter two-phase loops, it is possible to entirely eliminate the type-II instability. The above results are significant to the design of two-phase NC systems like boilers and pressure tube type BWRs. 4.1 Design Types for NCSs Since both instability and CHF (critical heat flux) needs to be avoided in the design of two-phase natural circulation systems two types of designs are possible depending on which of them is limiting the maximum power that can be extracted. These are designated as stability controlled and CHF controlled designs. Both the homogeneous and the drift flux models predict these design types albeit at different loop diameters. In view of this, only the drift flux model predictions are used for explaining this concept. 4.1.1 Stability Controlled Design In this type of NCSs, the maximum power is limited by the stability, as the threshold of type-II instability is lower than the CHF threshold. Fig. 16a shows that this is normally the case in small diameter loops. These predictions were obtained by incorporating the
Condenser
Separator
Heater
2445
2020
2036
575
2210
Condenser
Separator
Heater
2445
2020
2036
575
2210
4 6 8 10 12 14 160
5
10
15
20Pressure: 70 barLoop dia: 9.1 mm
Pow
er (k
W)
Subcooling (K)
Single-channel Parallel channel (2 Ch.)
(a) Schematic of parallel channel loop (b) Stability map for parallel channel loop Fig. 15: Comparison of stability map for single-channel and parallel channel loop
12
look-up table [11] in the TINFLO-S code. The direct substitution method (DSM) was used for the CHF prediction. In Fig 16b, stability controlled design is found on the right of the dotted line. 4.1.2 CHF Controlled Design Characteristic of this design is that the CHF threshold is much below the type-II instability threshold and hence CHF limits the maximum power that can be extracted. Fig. 16c shows that this situation arises in large diameter loops. In Fig. 16b, the design is CHF controlled only to the left of the vertical dotted line while in Fig. 16c the design is CHF controlled over the entire subcooling-power plane. By appropriate choice of the loop diameter, the design of a NCS can shift from stability controlled to CHF controlled (Figs. 16). Design of forced circulation BWRs is usually CHF controlled where inlet throttling is effective in stabilising. In contrast, inlet throttling may not be the preferred option in NCSs due to the associated reduction in flow and heat transport capability. 4.1.3 CHF Controlled Designs without type-II threshold Large diameter loops do not usually have a type-II threshold in the two-phase region. Both the homogeneous and the drift flux models predict this trend although the value of the loop diameter beyond which type-II instability disappears is significantly different. From Fig. 14a, it is found that this occurs if the loop diameter is greater than 35 mm based on the drift flux model. The design of such loops is controlled only by CHF. 5. OPERATING LINE CONCEPT Two-phase NCSs are not completely stable over the entire subcooling-power map. With the help of stability analysis techniques one could identify the stable and unstable zones as described above. Operation at the threshold of stability is not desirable as the system continues to oscillate with the same amplitude indefinitely. Besides, a small disturbance can land the system in the unstable zone. To guard against this and to provide stable operation some sort of a stability margin is desirable.
(a) Stability controlled NCS (b) Partly stability and CHF (c) CHF controlled NCS controlled NCS
7 14 21 28 350
5
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25
Stability map CHF
Loop diameter = 10 mmPressure = 70 bar
Stable
Pow
er (k
W)
Subcooling (K)
Unstable
7 14 21 28 350
20
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60Loop diameter : 15 mmPressure : 70 bar
Stability map CHF
Stable
Pow
er (k
W)
Subcooling (K)
Unstable
0 7 14 21 28 350
40
80
120Loop diameter : 20 mmPressure : 70 bar
CHF
Stable
Pow
er (k
W)
subcooling (K)
stability map
Unstable
Fig. 16: Stability and CHF controlled systems predicted using the drift flux model
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Decay ratio (defined as the ratio of amplitudes of the succeeding to the preceding oscillation) was considered to provide an indication of the stability margin. However, several instabilities are simultaneously present with each of them having decay ratio of unity at the threshold condition. In addition, there is a minimum practically achievable value of decay ratio that is different at different subcooling even for the controlling instability. Besides, the decay ratio is sensitive to the way we approach the operating point (rate of power rise or set back rate, etc.). Thus choice of a single value of decay ratio as a stability margin is not straightforward. Besides, NCSs are to be started up from cold low pressure stagnant conditions. During power and pressure raising the NCS may pass through the Type-I unstable zone. Thus specifying an operating line is a logical way to provide required stability margin. The adopted operating line must ensure stability for all anticipated operations like start-up, power raising, and step back. 5.1 Operating line for stability controlled Designs One would expect the decay ratio to go through a minimum while moving from the lower to the upper threshold for a fixed subcooling (Fig. 17). Ideally, the operating line shall pass through the minimum decay ratio (MDR) line (locus of all minimum decay ratio points i.e. points A, B, C and D in Fig. 17) so that all oscillations will die down in the quickest possible manner. The MDR line is plotted in Fig. 18 which shows that it is closer to the type-I threshold. In stability-controlled designs, one could choose the operating line as the MDR line if low power operation is adequate. A drawback of the MDR line is that it is closer to the lower threshold and does not utilize much of the high power stable zone. Another approach is to use the line corresponding to the mean of thresholds (MOT) (Fig. 18). The MOT line is midway between the type-I and type-II thresholds and the stability margins with respect to the lower and upper thresholds are equal. Even with the MOT line, the high power stable zone is not utilized. With the constant decay ratio (CDR) line as shown in Fig. 19 much of the low subcooling high power stable zone can be utilized. Care must be exercised, however, as constant decay ratio lines with very low DR will not allow operation with large inlet subcooling. For example, with CDR line of 0.7 operation is possible only with inlet subcooling less than 10 K (Fig. 19). It may be noted that the feasibility of all the operating lines need to be established from feed water inlet temperature considerations [13].
0 4 8 12 16
0.4
0.6
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C
B
A
Pressure: 7MPaLoop dia: 9.1mm
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ay R
atio
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∆Tsub - 5K ∆Tsub - 7.5K ∆Tsub - 10K ∆Tsub -12K
4 8 12 160
6
12
18
DR=1
Type-II threshold
Type-I threshold
MDR line MOT line
DR=0.91
DR=0.89
DR=0.73DR=0.57
DR=0.4
DR=1
DR=0.92DR=0.9DR=0.8
DR=0.67DR=0.56
Pow
er (k
W)
Sub-cooling (K)
Fig. 17: Variation of decay ratio Fig.18: MDR and MOT lines
14
5.2 Operating line for CHF Controlled Designs Even for this case, it may be feasible to select the MDR, MOT or CDR line as a possible operating line if sufficient thermal margin (in terms of critical heat flux ratio or critical power ratio) is there. However, more work is needed to establish this. 5.3 Operating line for CHF controlled designs without Type-II threshold In this case, the decay ratio is found to go through a minimum and subsequently, it is found to rise and stabilise at a constant value (Fig. 20). This constant value is found to be only marginally different for different subcooling. Thus for this case, a constant DR could be an appropriate option to provide adequate stability margin.
0 40 80 120 1600.0
0.2
0.4
0.6
0.8
1.0
2 K 5 K 10 K 20 K
Apsara loop I.D. = 40 mm IDPressure = 70 bar
Dec
ay R
atio
Power (kW) Fig. 20: Decay ratio for 40 mm loop (Type II instability is absent)
6. START-UP PROCEDURE Several options have been studied for the cold start-up of NC BWRs. Since the cold start-up is usually carried out at a very small fraction of the nominal full power, the main
4 8 12 160
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MDR line
Type-II threshold
Type-I threshold
DR = 0.7
DR = 0.8
DR = 0.9
Pressure:7MPaLoop diameter:9.1mm
Pow
er (k
W)
Subcooling (K)
Fig. 19: Constant decay ratio lines
15
objective of all cold start-up procedures is the avoidance of neutronics coupled power oscillations during the type-I instability observed during boiling inception. Different start-up procedures followed in BWRs are (i) Pressurised start-up, (ii) Start-up at atmospheric pressure with self pressurisation and (iii) start-up with an initial forced flow. 6.1 Pressurized Start-up In this case, during the initial heat-up low pressure instability is avoided by pressurising using an external boiler in a stage-wise manner. In this procedure boiling is initiated only at a pressure which completely eliminates type-I instability. For example, type-I instability is found to disappear at 3.5 MPa for the integral test loop simulating AHWR (Fig. 10). Thus start-up at pressures above 3.5 MPa is required for ITL. Since type-I instability is completely eliminated there is no question of neutronic coupled power oscillations. Both calculation and experiments have shown that this option is suitable for avoiding the type-I instability. Although, pressurising up to 3.5 MPa is sufficient for eliminating type-I instability, stage-wise pressurisation to the nominal operating value is adopted for AHWR as a measure of abundant caution. Although this requires an external boiler, this results in a very stable start-up. 6.2 Start-up at atmospheric pressure with self pressurisation The method appears to be feasible for NCSs with tall risers. The main advantage in systems with tall risers is that the pressure at the core exit is significantly higher than atmospheric even if the pressure at the top of the riser is atmospheric. For example, the pressure at the core exit in AHWR is ∼ 4 bar when the pressure in the stem drum is atmospheric. As a result, boiling in the core will not be initiated at temperatures below 140 0C where as boiling at 100 0C will occur in the SD. Thus, there is a strong possibility that type-I instability will not induce power oscillations as boiling is not there in the core or the void fraction in the core is too small to cause significant power oscillations. This approach has been adopted in the ESBWR. Experiments in ITL show that the void fraction at the core exit is too small to have significant power oscillations (Fig. 21). Thus this approach does not avoid type-I instability, but avoids power oscillations during the instability. The main advantage of this method is that it eliminates the start-up boiler and thus improves economy.
Fig. 21: Start-up at atmospheric pressure in ITL
0 20000 40000 600000
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Void fractionat FCS exitPower
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)Vo
id F
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)
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6.3 Start-up with Initial Forced flow In both the above procedures for cold start-up, the initial heat-up is achieved with the reactor critical at a few percent (1-2%) of the nominal full power. This calls for reactor start-up with stagnant flow. Although, this is almost the case in NC BWRs like Dodewaard and ESBWR where a small flow was provided by the purification pumps, a simulation calculation was carried out with the thermal hydraulic code RELAP5/MOD3.2 to understand the effect of initial forced flow on the cold start-up for AHWR. The initial forced flow was provided with the help of the feed water pumps by taking suction from the tail pipe region of the SD. The study showed that the type-I instability cannot be totally avoided in this case. However, the power oscillations can be avoided as in 6.2 above (Figure 22a & b).
0 5000 10000 15000 20000 25000 30000 35000 40000 450000.0
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s flo
w ra
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ar)
Fig. 22(a): Start-up at 1 bar from stagnant condition
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ssur
e (b
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ass
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Fig. 22(b): Start-up at 1 bar with initial flow of 1.2 kg/s
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7. CONCLUDING REMARKS A rational design procedure has been proposed based on the knowledgebase created in-house. The operating line concept and the rationale behind the minimum decay ratio, mean of thresholds and the constant decay ratio lines have been discussed along with their relative merits and demerits. Different options for start-up have been described. NOMENCLATURE A : flow area, m2 b : exponent in the friction factor equation D : hydraulic diameter, m f : Darcy-Weisbach friction factor g : gravitational acceleration, m/s2 h : enthalpy, J/kg l : dimensionless length, ti LL L : length, m p : constant in the friction factor equation P : pressure, Pa Qh : total heat input rate, W v : specific volume, m3/kg W : mass flow rate, kg/s x : quality ∆z : Centre line elevation difference, m Greek symbols α : void fraction βT : thermal expansion coefficient, K-1 βh : thermal expansion coefficient, (J/kg)-1
2LOφ : two-phase friction multiplier 2LOφ : mean value of 2
LOφ ρ : density, kg/m3 µ : dynamic viscosity, Ns/m2 Subscripts B : boiling length C : cooler/condenser e : heater exit eff : effective g : vapor h : heater i : ith segment l : liquid
18
m : mean sp : single phase t : total tp : two-phase REFERENCES [1] Gartia, M.R. Vijayan P.K. and Pilkhwal, D.S., 2006, A generalized flow correlation
for two-phase natural circulation loops, Nuclear Engineering and Design, 236, 1800-1809.
[2] IAEA-TECDOC-1203, Thermohydraulic relationships for advanced water cooled
reactors, International Atomic Energy Agency, April 2001, Chapter 5, 109-162. [3] Vijayan, P.K. Nayak, A.K. Saha, D. and Gartia M.R., 2008, Effect of loop diameter
on the steady state and stability behaviour of single-phase and two-phase natural circulation loops, Science and Technology of Nuclear Installations, Accepted for publication.
[4] Boure, J.A. Bergles A.E. and Tong, L.S. 1973, Review of two-phase flow instability,
Nuclear Engineering and Design 25, 165-192. [5] Nayak, A. K. and Vijayan P. K., 2008, Flow instabilities in boiling two-phase natural
circulation systems – a review, Science and Technology of Nuclear Installations, Accepted for publication.
[6] Fukuda, K and Kobori, T. (1979) Classification of two-phase flow stability by
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analysis of thermo-hydraulic instabilities of the Advanced Heavy Water Reactor (AHWR), Journal of Nuclear Science and Technology 35 (1998) 768-778.
[8] Nayak, A.K. Vijayan, P.K. Jain, V. Saha D. and Sinha, Study on the flow-pattern-
transition instability in a natural circulation heavy water moderated boiling light water cooled reactor, Nuclear Engineering and Design 225 (2003) 159-172.
[9] Nayak, A.K. Vijayan, P.K. Saha, D., Venkat Raj, V., and Aritomi, M. (2002) Study
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[10] Nayak, A.K., Dubey, P., Chavan, D.N., and Vijayan, P.K. (2006) Study on the
stability behavior of two-phase natural circulation systems using a four-equation drift flux model, HMT-2006-C084, 7th ISHMT-ASME Heat and Mass Transfer Conference, Jan 4-6, IIT, Guwahati.
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[11] Groeneveld, D. C., Leung, L.K.H., Kirillov, P.L., Bobkov, V.P., Smogalev, I.P., Vinogradov, V.N., Huang, X.C., Royer, E. 1996, The 1995 look-up table for critical heat flux in tubes, Nuclear Engineering and Design 163, pp.1-23.
[12] Mochizuki, H. (1992) Experimental and analytical studies of flow instabilities in
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