# Effect of Loop Diameter on the Steady State and  Stability

Authors: P. K. Vijayan; A. K. Nayak; D. Saha; M. R. Gartia
Journal: Science and Technology of Nuclear Installations
 (2008)

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## Abstract

In natural circulation loops, the driving force is usually low as it depends on the riser height which is generally of the order of a few meters. The heat transport capability of natural circulation loops (NCLs) is directly proportional to the flow rate it can generate. With low driving force, the straightforward way to enhance the flow is to reduce the frictional losses. A simple way to do this is to increase the loop diameter which can be easily adopted in pressure tube designs such as the AHWR and the natural circulation boilers employed in fossil-fuelled power plants. Further, the loop diameter also plays an important role on the stability behavior. An extensive experimental and theoretical investigation of the effect of loop diameter on the steady state and stability behavior of single- and two-phase natural circulation loops have been carried out and the results of this study are presented in this paper.


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## Body

## 1. Introduction

Natural circulation systems find application
in many nuclear reactor systems. Single-phase natural circulation is the mode
of coolant circulation in the current pressurized water and heavy water
reactors (PWRs and PHWRs) following a pumping power failure. Certain reactor
systems like the heating reactors (normally referred to as district heating
reactors [1]) and the CAREM PWR [2] use single-phase natural circulation as the
normal mode of coolant circulation in the primary system. Two-phase natural
circulation systems are extensively used in fossil-fuelled power plants,
thermosyphon reboilers, and steam generators including those in nuclear power reactors
like PWRs, VVERs, and PHWRs. Two-phase natural circulation is the mode of
coolant circulation in the current generation of nuclear power plants following
a small break LOCA associated with pumping power failure. It was used as the
normal mode of coolant circulation in low power boiling water reactors (BWRs)
like Humbholdt Bay 3 (63 MWe), Dodewaard (65 MWe), and VK-50 (50 MWe). In many
new designs under development like the ESBWR, AHWR [3], and VK-300 [4],
two-phase natural circulation is the normal mode of coolant circulation.
Natural circulation based reactor designs are being studied even with
supercritical water as coolant [5, 6].In view of their wide application, both
single-phase and two-phase natural circulation systems are being extensively
studied. State-of-the-art reviews on single-phase [7, 8] and two-phase [9, 10]
natural circulation have been provided by several authors. Most studies are
concerned with instability as natural circulation systems are more unstable
than forced circulation systems. For example, both single-phase and two-phase
NCSs exhibit instability whereas only two-phase forced circulation systems are
known to exhibit instability. Apart from the steady-state performance, operational
transients like start-up, power raising and step back are also required to be
stable for natural circulation reactors. This requires specification of a
stable operating procedure which in turn requires deeper understanding of the parametric
trends due to the operational (i.e., inlet subcooling, pressure, and power) and
the geometric parameters (i.e., height, diameter, and orientation of source;
and sink) affecting natural circulation.In the present paper, the effect of loop
diameter on the steady state and stability behavior of single- and two-phase
natural circulation loops was studied both experimentally and theoretically.
Single-phase natural circulation is found to destabilize with increase in loop
diameter. On the other hand, the two-phase natural circulation is found to
stabilize with increase in loop diameter. Both the type-I and type-II
instabilities in two-phase loops are found to be significantly influenced by
the loop diameter. For example, the threshold value of pressure at which type-I
instability disappears is found to decrease with increase in loop diameter.
Type-II instability was observed only in small diameter loops. Linear analysis
showed that type-II instability does not occur in the two-phase region
(0 < quality < 1) if the loop diameter is above a critical value. Depending
on the loop diameter, the maximum operating power of a natural circulation
system can be either stability controlled or critical heat flux (CHF)
controlled. For stability controlled systems, the minimum decay ratio (DR) line
can be an ideal operating line. Premature occurrence of CHF and burnout is a
serious concern during low-frequency and high-amplitude oscillatory flows in
small diameter loops.


## 2. Single-Phase Natural Circulation

Even for natural circulation based boiling
water reactors, single-phase natural circulation is encountered during the
heat-up phase. Hence experiments were carried out in four single channel
uniform diameter loops (UDLs) of rectangular shape made of borosilicate glass
tube having horizontal heater and cooler with diameter varying from 6 mm to
26.9 mm. These studies were carried out at near atmospheric conditions. Three of
the loops studied had the general dimensions as shown in Figure1(a) and the
dimensions of the fourth loop are shown in Figure 1(b). The cooler was
tube-in-tube type and the heater was made by winding nichrome wire uniformly on
the outside of the tube. The experimental loops had a small expansion tank open
to the atmosphere to accommodate the swell and shrinkage. The measurements
included the heater power, loop temperatures and the cooling water flow rate
and its inlet temperature. For the loop shown in Figure 1(b), the pressure drop
across 1075 mm of the bottom horizontal pipe was also measured. A data logger
with a scanning time of 1.5 seconds recorded all the measurements. The
measurement accuracy was 0.4% (±1.1°C) for thermocouples, ±2% for flow rate and ±0.5%
of the span (0–1250 W) for power and
pressure drop (−100 to +100 Pa).Schematic of the experimental loops.
(a)(b)


### 2.1. Steady State Behavior

Steady state flow prevails when the driving
buoyancy force is balanced by the retarding frictional force, that is,ρ0βg∮Tdz=(fLt/D)(W2/2ρ0A2).   Integrating over the closed loop and
replacing ΔTh=Qh/WCp and f=p/Reb=pAbμb/DbWb, we obtain(1)W=[2Dbρ2βTgA2−bQhΔzpCpμbNG]1/(3−b).The above equation is valid for uniform
diameter loops with negligible local pressure losses filled with an incompressible
Boussinesq fluid, where(2)βT=1v(∂v∂T)p.From the steady state experimental data, a
heat balance using the measured heater power and the temperature difference
across the heater yielded the mass flow rate. For the same operating conditions
(heater power, coolant flow rate and its inlet temperature), the flow rate is
found to increase with power and loop diameter (Figure 2). The steady state
flow rate can be expressed by the following dimensionless correlation [11]:The steady state flow rate variation with power for different loop diameters.
(a)
Measured and predicted flow(b)
Effect of loop diameter on predicted flow rate(3)Ress=C[(Grm)ΔzNG]r,where Ress=DWss/Aμ,(Grm)ΔZ=D3ρ2βTgQhΔZ/Aμ3Cp,NG=Lt/D,C=(2/p)r,r=1/(3−b),p
and b are the constants in the friction factor correlation of the form f = p/Reb.
The p and b values for laminar, transition and turbulent flows were,
respectively, 64 & 1, 22.3 & 0.67, and 0.316 & 0.25. Corresponding
C and r values for laminar, transition and turbulent flow are, respectively,
0.1768 & 0.5, 0.3568 & 0.43, and 1.96 & 0.364. The dimensionless steady state flow rate data
is compared with (3) for various flow regimes in Figure 3. The literature data
on rectangular natural circulation loops [12–19] are also
included in Figure 3. The steady state flow rate data agrees
reasonably well with the proposed steady state correlations.Figure 3
Steady state performance of single-phase loops differing in diameter.


### 2.2. Stability Behavior

Both theoretical and experimental studies
were carried out to understand the stability behavior.


#### 2.2.1. Test Results

Before stability runs the fluctuations in the
loop instrument readings at zero power and steady state operation were
established. The fluctuations in the controlled coolant flow rate and its inlet
temperature were also noted. The experiments showed that the loops with small
diameters were highly stable. However, instability could be observed in 23.2 mm
and 26.9 mm diameter loops. Extensive investigations of the unstable behavior
were carried out for the 26.9 mm i.d. loop [20–22]. An
interesting observation is that the instability threshold is not a unique value
but depends on the operating procedure (characteristic of the hysteresis
phenomenon). Based on the operating procedure, the natural circulation flow can
be classified as unconditionally stable, conditionally stable, and
unconditionally unstable (Figure 4). In the conditionally stable (hysteresis) region,
stable or unstable flow can prevail depending on the operating procedure.Figure 4
Unstable oscillatory regions in single-phase loops.Three different
oscillatory modes are observed in the experiment depending on the power. These
are unidirectional pulsing (UDP), bidirectional pulsing (BDP), and chaotic
switching. UDP is characterized by a bean-shaped limit cycle, whereas BDP is
characterized by a dumbbell-shaped limit cycle (Figure4). Between the two, an
oscillatory regime with chaotic switching between UDP and BDP is observed. At
high powers, the BDP becomes chaotic. The loop resistance and the coolant flow
significantly affect the thresholds of a specified oscillatory flow regime.


#### 2.2.2. Stability Analysis

Derivation of the characteristic equation for
the stability parametern (n is a complex variable) and its solution procedure
are described based on the linear stability method in Vijayan and Nayak [23].
The characteristic equation for the loop shown in Figure 1 can be expressed as(4)n−(p/2)1+m(GrmIss)m(D/Lt)1+m[(I¯ω¯)-(2−b)]=0,where (5)m=b3−b,Iss=∮θssdZ,I¯ω¯=φn(1−e−n/φ)e−nLx/Lt{θ¯h−θ¯cω¯},(6)θ¯h−θ¯cω¯=Stm(θhl)ssα+(Lt/Lh)α*n(e(StmLc+nLt)/Lt−1),where α={enLhl/Lt(enLc/Lt−1)−en(1−e−nLc/Lt)} and α*={e(StmLc+nLt)/Lt(e−nLh/Lt−1)−enLcl/Lt(1−enLh/Lt)}. Using the characteristic equation, the stability map was generated for
the loops with different diameters. Figures 5(a) and 5(b) show a comparison of
the predicted stability map with test data. Considering that the effects of
wall conduction, axial conduction in the fluid, the local pressure losses, the
heat losses, and multidimensional effects are neglected in these calculations,
the agreement with test data is reasonable. The unstable zone is found to shift
up with reduction in loop diameter. Thus, increasing the loop diameter is found
to destabilize single-phase natural circulation. A literature review has
revealed that the Lt/D ratio is an important parameter affecting
instability. In fact to our knowledge, instability has not been observed experimentally
in uniform diameter loops with Lt/D>300. The stability map,
however, is a strong function of the friction correlation (Figure 5(b)).Comparison of predicted stability map with data.
(a)
6, 11 and 23.2 mm loops(b)
26.9 mm loop


## 2.1. Steady State Behavior

Steady state flow prevails when the driving
buoyancy force is balanced by the retarding frictional force, that is,ρ0βg∮Tdz=(fLt/D)(W2/2ρ0A2).   Integrating over the closed loop and
replacing ΔTh=Qh/WCp and f=p/Reb=pAbμb/DbWb, we obtain(1)W=[2Dbρ2βTgA2−bQhΔzpCpμbNG]1/(3−b).The above equation is valid for uniform
diameter loops with negligible local pressure losses filled with an incompressible
Boussinesq fluid, where(2)βT=1v(∂v∂T)p.From the steady state experimental data, a
heat balance using the measured heater power and the temperature difference
across the heater yielded the mass flow rate. For the same operating conditions
(heater power, coolant flow rate and its inlet temperature), the flow rate is
found to increase with power and loop diameter (Figure 2). The steady state
flow rate can be expressed by the following dimensionless correlation [11]:The steady state flow rate variation with power for different loop diameters.
(a)
Measured and predicted flow(b)
Effect of loop diameter on predicted flow rate(3)Ress=C[(Grm)ΔzNG]r,where Ress=DWss/Aμ,(Grm)ΔZ=D3ρ2βTgQhΔZ/Aμ3Cp,NG=Lt/D,C=(2/p)r,r=1/(3−b),p
and b are the constants in the friction factor correlation of the form f = p/Reb.
The p and b values for laminar, transition and turbulent flows were,
respectively, 64 & 1, 22.3 & 0.67, and 0.316 & 0.25. Corresponding
C and r values for laminar, transition and turbulent flow are, respectively,
0.1768 & 0.5, 0.3568 & 0.43, and 1.96 & 0.364. The dimensionless steady state flow rate data
is compared with (3) for various flow regimes in Figure 3. The literature data
on rectangular natural circulation loops [12–19] are also
included in Figure 3. The steady state flow rate data agrees
reasonably well with the proposed steady state correlations.Figure 3
Steady state performance of single-phase loops differing in diameter.


## 2.2. Stability Behavior

Both theoretical and experimental studies
were carried out to understand the stability behavior.


### 2.2.1. Test Results

Before stability runs the fluctuations in the
loop instrument readings at zero power and steady state operation were
established. The fluctuations in the controlled coolant flow rate and its inlet
temperature were also noted. The experiments showed that the loops with small
diameters were highly stable. However, instability could be observed in 23.2 mm
and 26.9 mm diameter loops. Extensive investigations of the unstable behavior
were carried out for the 26.9 mm i.d. loop [20–22]. An
interesting observation is that the instability threshold is not a unique value
but depends on the operating procedure (characteristic of the hysteresis
phenomenon). Based on the operating procedure, the natural circulation flow can
be classified as unconditionally stable, conditionally stable, and
unconditionally unstable (Figure 4). In the conditionally stable (hysteresis) region,
stable or unstable flow can prevail depending on the operating procedure.Figure 4
Unstable oscillatory regions in single-phase loops.Three different
oscillatory modes are observed in the experiment depending on the power. These
are unidirectional pulsing (UDP), bidirectional pulsing (BDP), and chaotic
switching. UDP is characterized by a bean-shaped limit cycle, whereas BDP is
characterized by a dumbbell-shaped limit cycle (Figure4). Between the two, an
oscillatory regime with chaotic switching between UDP and BDP is observed. At
high powers, the BDP becomes chaotic. The loop resistance and the coolant flow
significantly affect the thresholds of a specified oscillatory flow regime.


### 2.2.2. Stability Analysis

Derivation of the characteristic equation for
the stability parametern (n is a complex variable) and its solution procedure
are described based on the linear stability method in Vijayan and Nayak [23].
The characteristic equation for the loop shown in Figure 1 can be expressed as(4)n−(p/2)1+m(GrmIss)m(D/Lt)1+m[(I¯ω¯)-(2−b)]=0,where (5)m=b3−b,Iss=∮θssdZ,I¯ω¯=φn(1−e−n/φ)e−nLx/Lt{θ¯h−θ¯cω¯},(6)θ¯h−θ¯cω¯=Stm(θhl)ssα+(Lt/Lh)α*n(e(StmLc+nLt)/Lt−1),where α={enLhl/Lt(enLc/Lt−1)−en(1−e−nLc/Lt)} and α*={e(StmLc+nLt)/Lt(e−nLh/Lt−1)−enLcl/Lt(1−enLh/Lt)}. Using the characteristic equation, the stability map was generated for
the loops with different diameters. Figures 5(a) and 5(b) show a comparison of
the predicted stability map with test data. Considering that the effects of
wall conduction, axial conduction in the fluid, the local pressure losses, the
heat losses, and multidimensional effects are neglected in these calculations,
the agreement with test data is reasonable. The unstable zone is found to shift
up with reduction in loop diameter. Thus, increasing the loop diameter is found
to destabilize single-phase natural circulation. A literature review has
revealed that the Lt/D ratio is an important parameter affecting
instability. In fact to our knowledge, instability has not been observed experimentally
in uniform diameter loops with Lt/D>300. The stability map,
however, is a strong function of the friction correlation (Figure 5(b)).Comparison of predicted stability map with data.
(a)
6, 11 and 23.2 mm loops(b)
26.9 mm loop


## 2.2.1. Test Results

Before stability runs the fluctuations in the
loop instrument readings at zero power and steady state operation were
established. The fluctuations in the controlled coolant flow rate and its inlet
temperature were also noted. The experiments showed that the loops with small
diameters were highly stable. However, instability could be observed in 23.2 mm
and 26.9 mm diameter loops. Extensive investigations of the unstable behavior
were carried out for the 26.9 mm i.d. loop [20–22]. An
interesting observation is that the instability threshold is not a unique value
but depends on the operating procedure (characteristic of the hysteresis
phenomenon). Based on the operating procedure, the natural circulation flow can
be classified as unconditionally stable, conditionally stable, and
unconditionally unstable (Figure 4). In the conditionally stable (hysteresis) region,
stable or unstable flow can prevail depending on the operating procedure.Figure 4
Unstable oscillatory regions in single-phase loops.Three different
oscillatory modes are observed in the experiment depending on the power. These
are unidirectional pulsing (UDP), bidirectional pulsing (BDP), and chaotic
switching. UDP is characterized by a bean-shaped limit cycle, whereas BDP is
characterized by a dumbbell-shaped limit cycle (Figure4). Between the two, an
oscillatory regime with chaotic switching between UDP and BDP is observed. At
high powers, the BDP becomes chaotic. The loop resistance and the coolant flow
significantly affect the thresholds of a specified oscillatory flow regime.


## 2.2.2. Stability Analysis

Derivation of the characteristic equation for
the stability parametern (n is a complex variable) and its solution procedure
are described based on the linear stability method in Vijayan and Nayak [23].
The characteristic equation for the loop shown in Figure 1 can be expressed as(4)n−(p/2)1+m(GrmIss)m(D/Lt)1+m[(I¯ω¯)-(2−b)]=0,where (5)m=b3−b,Iss=∮θssdZ,I¯ω¯=φn(1−e−n/φ)e−nLx/Lt{θ¯h−θ¯cω¯},(6)θ¯h−θ¯cω¯=Stm(θhl)ssα+(Lt/Lh)α*n(e(StmLc+nLt)/Lt−1),where α={enLhl/Lt(enLc/Lt−1)−en(1−e−nLc/Lt)} and α*={e(StmLc+nLt)/Lt(e−nLh/Lt−1)−enLcl/Lt(1−enLh/Lt)}. Using the characteristic equation, the stability map was generated for
the loops with different diameters. Figures 5(a) and 5(b) show a comparison of
the predicted stability map with test data. Considering that the effects of
wall conduction, axial conduction in the fluid, the local pressure losses, the
heat losses, and multidimensional effects are neglected in these calculations,
the agreement with test data is reasonable. The unstable zone is found to shift
up with reduction in loop diameter. Thus, increasing the loop diameter is found
to destabilize single-phase natural circulation. A literature review has
revealed that the Lt/D ratio is an important parameter affecting
instability. In fact to our knowledge, instability has not been observed experimentally
in uniform diameter loops with Lt/D>300. The stability map,
however, is a strong function of the friction correlation (Figure 5(b)).Comparison of predicted stability map with data.
(a)
6, 11 and 23.2 mm loops(b)
26.9 mm loop


## 3. Two-Phase Natural Circulation

Two-phase natural circulation experiments
were conducted in four uniform diameter loops of inside diameter 7, 9.1, 15.74,
and 19.86 mm with the length scales as shown in Figure6(a). The steam separator, the
condenser, and the associated piping (the portion inside the rectangular box in
Figure 6(a)) were the same for all the loops. The steam separator was made of
59 mm inside diameter pipe. The vertical heater section was directly heated
with a high current low voltage power supply. The steam-water mixture produced
flows to the separator and the separated steam was condensed and the condensate
returns to the steam drum by gravity. The loop was extensively instrumented to
measure heater power, temperatures (of heater surface and fluid), steam drum
pressure, differential pressure at various sections of the single-phase and
two-phase pipes, SD level, flow rates (loop, condensate, and cooling water
flows), void fraction and its distribution. The void fraction was measured
using both neutron radiography (NRG) and conductance probe (CP). The neutron
radiography also helped to visualize the flow patterns. To facilitate neutron
radiography, the loop was installed in the Apsara reactor hall in front of the
neutron beam hole (Figure 6(b)). With the neutron radiography, void fraction
was measured at the outlet of the heated section, whereas conductance probes
were located at the center line in the vertical tube above the neutron window
as well as in the top near horizontal tube. During the experiments, the system
was initially pressurized in the cold condition to the required value with the
help of nitrogen cylinders. During the heat-up and boiling, the system pressure
increase was compensated by bleeding nitrogen-steam mixture from the condenser.
Further details of the loop are available in Vijayan et al. [24] and Dubey et
al. [25]. In addition, experimental data were generated in a 49.3 mm inside
diameter loop shown in Figure 6(c). The inside diameter of the heated section
was 53.4 mm in this loop. Further details of this facility are available in
Kumar et al. [26].Schematic of the different test loops.
(a)(b)(c)


### 3.1. Steady State Behavior

Steady state
data on flow pattern, void fraction, and flow rate were collected for the
various loops as a function of power at different pressures. The 7 mm loop was mostly
unstable and reliable steady state data could not be generated due to frequent
burnout of the heated section. The steady state data generated in all other loops
fall in the following range of parameter: loop diameter: 9.1–49.3 mm,
circulation length: 8.7 and 13.5 m, SD level: 90%  ± 5%, pressure: 0.1–7
MPa, quality: 0.4–24%, and power: 0.3–40 kW.


#### 3.1.1. Flow Patterns

Steady state
flow patterns at the exit of the heated section were recorded with a CCD
camera, details of which are available in Sinha et al. [27]. The predominant
flow pattern observed in all the loops (of geometry given by Figure 6(a)) was
bubbly or bubbly-slug. Typical recorded images and the expected flow pattern
change with increase in power are shown in Figures 7(a) and 7(b), respectively.Flow patterns obtained for a typical run.
(a)
Typical slug flow pattern(b)
Flow patterns predicted with various flow pattern maps


#### 3.1.2. Void Fraction

The void
fraction measured by the neutron radiography and the conductance probe were close
to each other. The void fraction data were compared with various correlations
giving reasonable agreement. A typical comparison with Ishii correlation [31] is
shown in Figure 8. More results on the void fraction are available in [24, 32].Figure 8
Comparison of measured void fraction with that predicted using Ishii model [31].


#### 3.1.3. Steady State Flow

The steady state
flow rate was measured with the help of calibrated pipe taps located in the
single-phase bottom horizontal pipe. 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 [33]:(7)Wss=[2pDbρl2β¯hgA2−bQhΔzμlbNG]1/(3−b),which can be expressed in
dimensionless form as (8)Ress=C(GrmNG)r,
where (9)Grm=D3ρl2β¯hgQhHAμl3;β¯h=1v(∂v∂h)p;(10)NG=LtD[(leff)sp+ϕ¯LO2(leff)B+ϕLO2(leff)tp+ϕ¯LO2(leff)C]  with (11)ϕLO2=ρlρe[11+xe(μl/μg−1)]b,φ¯LO2=ρlρm[11+(xe/2)(μl/μg−1)]b. It may be noted
that for single-phase flows ϕLO2=1,
and (8) reduces to that applicable to single-phase natural circulation. Also,
similarity in the definitions of the thermal expansion coefficients βh and βT valid for two-phase and single-phase flows, respectively, may
be noted. The constants C and r have the same definitions as in single-phase
flow. The measured steady state flow rate data from the present test loops are
plotted in Figure 9 in dimensionless form. The data are found to be within ±40% of the above theoretical correlation from Figure 9.Figure 9
Comparison of steady state data with correlations.


### 3.2. Parametric Effects on Steady State Flow

One of the drawbacks of dimensionless
correlations is that it often masks the parametric trends. In fact the
steady state performance of two-phase loops is significantly influenced by the
pressure, power, and loop diameter. Effect of pressure on two-phase NC flow was
studied experimentally and theoretically in the 49.3 mm i.d. loop and the
results are shown in Figure10. The results are in agreement with the
predictions of (7). The measured flow rate as a function of power is plotted in
Figure 11 for various loops. The predictions with (7), TINFLO-S [34], and
RELAP5/MOD3.2 are also given in Figure 11. Again, the data are in reasonable
agreement with the predictions.Figure 10
Effect of pressure on flow rate.Effect of power on the two-phase NC flow rate.
(a)
9.1 mm i.d. loop(b)
49.3 mm i.d. loop(c)
9.1 mm i.d. loop


### 3.3. Two-Phase NC Flow Regimes

Unlike
single-phase natural circulation, it is observed that the trend of the steady
state data can be significantly different for two-phase loops. 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. 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 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).


#### 3.3.1. 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 Figure12) 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 Figures 13 and 14).Figure 12
Effect of quality on void fraction.Figure 13
Effect of pressure on flow regime.Effect of pressure on flow regime for different loop diameter.
(a)(b)


#### 3.3.2. Friction Dominant Regime

Friction dominant regime is observed at low to moderate pressures when
quality is high. At higher qualities and moderate pressures, the increase in
void fraction with quality is marginal (Figure12) 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 Figure 13).


#### 3.3.3. 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 Figure11(a) and the curve for 7 MPa in Figure
13) in spite of increase in quality.


#### 3.3.4. 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 Figure14).
Knowledge of the flow regimes is important to understand the stability behavior
of two-phase loops.


### 3.4. Stability Behavior

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. Further, premature critical heat flux (CHF) 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 seen in [23].


#### 3.4.1. Experimental Stability Map

An experimentally
generated stability map for the 9.1 mm i.d. loop is shown in Figure15(a),
which shows two unstable regions for two-phase natural circulation. It may be
noted that all the two-phase loops tested had stable single-phase natural
circulation flow. However, it appears possible to get an unstable zone in the
single-phase region also for certain loop geometries. Thus overall, three
unstable zones (one in the single-phase region and two in the two-phase region)
are possible for natural circulation loops with increase in power (excluding
the single-phase vapour region). The first unstable zone in the two-phase
region (Figure 15(a)) occurs at a low power and hence at low quality and is
named as type I instability by Fukuda and Kobori [35]. Similarly, the second
unstable zone in the two-phase region (Figure 15(a)) occurs at high powers and
hence at high qualities and is named as type II instability. 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 found in the compensating regime
during the present tests.Experimental stability map and some typical type-I oscillation.
(a)
Experimental stability map(b)
Nature of type-I oscilation(c)
Type-I oscilation


#### 3.4.2. 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.


#### 3.4.3. Characteristics of 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, the amplitude of type-I oscillations first
increases, reaches a peak and then decreases with increase in power eventually
leading to stable flow (Figure15(b)). However, amplitude variation is a
complex function of power presumably due to flow pattern transitions (Figure 15(b)).
For certain type-1 unstable regions, the flow alternates between a stable and
oscillatory regime (Figure 15(c)). For large diameter loops, a unidirectional
oscillation depicting a bean shaped limit cycle is observed (Figure 16).
However, the dynamics is quite rich showing many different oscillatory patterns
(see Figures 15(c), 16(a), and 16(c) for a few sample patterns).Some typical type-1 oscillations and the limit cycle for observed for 49.3 mm i.d. loop.
(a)
Power = 20 kW(b)
Limit cycle at 2.2 bar(c)
Typical oscillationsThe amplitude of type-I oscillations reduces significantly with increase
in pressure (see Figures15(a) and 17(a)). Further, type-I instability is not
observed beyond a critical value of the system pressure (Figure 17(c)). 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 (Figure 18). However, beyond a certain
diameter, the effect of loop diameter on the critical pressure is found to be
marginal.Effect of pressure on the type-I instability in the 9.1 mm inside diameter loop.
(a)(b)(c)Effect of pressure on the instability due to boiling inception in 19.86 mm i.d. loop.
(a)
Start-up at 3.1 bar(b)
Start-up at 5.4 bar


#### 3.4.4. Characteristics of Type-II Instability

In the present experiments, type-II
instability (Figure19) is found to occur after the flow starts to decrease
with increase in power (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 frequently in the 7 mm loop and less
frequently in the 9.1 mm loop.The upper threshold of instability at different pressures.
(a)
13 bar(b)
18 bar(c)
25 bar


### 3.5. Theoretical Results

The stability of the test loops was studied
with a linear stability code TINFLO-S based on the drift flux model (Nayak et
al. [36]). The drift flux parameters (Co and Vgi) for
slug flow were used as it was the most frequently observed flow pattern during
the tests. The Martinelli-Nelsontwo-phase
friction multiplier model was used in the computations. Figures 20(a) and 20(b)
compare the predicted stability map with experimental data. Figure 21(a)
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 (Figure 21(b)) 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 behavior 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 behavior is also reported
by Boure et al. [37].Comparison of measured and predicted stability maps.
(a)
Effect of drift velocity(b)
Effect of subcoolingPredicted stability map for various loop diameters.
(a)(b)


## 3.1. Steady State Behavior

Steady state
data on flow pattern, void fraction, and flow rate were collected for the
various loops as a function of power at different pressures. The 7 mm loop was mostly
unstable and reliable steady state data could not be generated due to frequent
burnout of the heated section. The steady state data generated in all other loops
fall in the following range of parameter: loop diameter: 9.1–49.3 mm,
circulation length: 8.7 and 13.5 m, SD level: 90%  ± 5%, pressure: 0.1–7
MPa, quality: 0.4–24%, and power: 0.3–40 kW.


### 3.1.1. Flow Patterns

Steady state
flow patterns at the exit of the heated section were recorded with a CCD
camera, details of which are available in Sinha et al. [27]. The predominant
flow pattern observed in all the loops (of geometry given by Figure 6(a)) was
bubbly or bubbly-slug. Typical recorded images and the expected flow pattern
change with increase in power are shown in Figures 7(a) and 7(b), respectively.Flow patterns obtained for a typical run.
(a)
Typical slug flow pattern(b)
Flow patterns predicted with various flow pattern maps


### 3.1.2. Void Fraction

The void
fraction measured by the neutron radiography and the conductance probe were close
to each other. The void fraction data were compared with various correlations
giving reasonable agreement. A typical comparison with Ishii correlation [31] is
shown in Figure 8. More results on the void fraction are available in [24, 32].Figure 8
Comparison of measured void fraction with that predicted using Ishii model [31].


### 3.1.3. Steady State Flow

The steady state
flow rate was measured with the help of calibrated pipe taps located in the
single-phase bottom horizontal pipe. 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 [33]:(7)Wss=[2pDbρl2β¯hgA2−bQhΔzμlbNG]1/(3−b),which can be expressed in
dimensionless form as (8)Ress=C(GrmNG)r,
where (9)Grm=D3ρl2β¯hgQhHAμl3;β¯h=1v(∂v∂h)p;(10)NG=LtD[(leff)sp+ϕ¯LO2(leff)B+ϕLO2(leff)tp+ϕ¯LO2(leff)C]  with (11)ϕLO2=ρlρe[11+xe(μl/μg−1)]b,φ¯LO2=ρlρm[11+(xe/2)(μl/μg−1)]b. It may be noted
that for single-phase flows ϕLO2=1,
and (8) reduces to that applicable to single-phase natural circulation. Also,
similarity in the definitions of the thermal expansion coefficients βh and βT valid for two-phase and single-phase flows, respectively, may
be noted. The constants C and r have the same definitions as in single-phase
flow. The measured steady state flow rate data from the present test loops are
plotted in Figure 9 in dimensionless form. The data are found to be within ±40% of the above theoretical correlation from Figure 9.Figure 9
Comparison of steady state data with correlations.


## 3.1.1. Flow Patterns

Steady state
flow patterns at the exit of the heated section were recorded with a CCD
camera, details of which are available in Sinha et al. [27]. The predominant
flow pattern observed in all the loops (of geometry given by Figure 6(a)) was
bubbly or bubbly-slug. Typical recorded images and the expected flow pattern
change with increase in power are shown in Figures 7(a) and 7(b), respectively.Flow patterns obtained for a typical run.
(a)
Typical slug flow pattern(b)
Flow patterns predicted with various flow pattern maps


## 3.1.2. Void Fraction

The void
fraction measured by the neutron radiography and the conductance probe were close
to each other. The void fraction data were compared with various correlations
giving reasonable agreement. A typical comparison with Ishii correlation [31] is
shown in Figure 8. More results on the void fraction are available in [24, 32].Figure 8
Comparison of measured void fraction with that predicted using Ishii model [31].


## 3.1.3. Steady State Flow

The steady state
flow rate was measured with the help of calibrated pipe taps located in the
single-phase bottom horizontal pipe. 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 [33]:(7)Wss=[2pDbρl2β¯hgA2−bQhΔzμlbNG]1/(3−b),which can be expressed in
dimensionless form as (8)Ress=C(GrmNG)r,
where (9)Grm=D3ρl2β¯hgQhHAμl3;β¯h=1v(∂v∂h)p;(10)NG=LtD[(leff)sp+ϕ¯LO2(leff)B+ϕLO2(leff)tp+ϕ¯LO2(leff)C]  with (11)ϕLO2=ρlρe[11+xe(μl/μg−1)]b,φ¯LO2=ρlρm[11+(xe/2)(μl/μg−1)]b. It may be noted
that for single-phase flows ϕLO2=1,
and (8) reduces to that applicable to single-phase natural circulation. Also,
similarity in the definitions of the thermal expansion coefficients βh and βT valid for two-phase and single-phase flows, respectively, may
be noted. The constants C and r have the same definitions as in single-phase
flow. The measured steady state flow rate data from the present test loops are
plotted in Figure 9 in dimensionless form. The data are found to be within ±40% of the above theoretical correlation from Figure 9.Figure 9
Comparison of steady state data with correlations.


## 3.2. Parametric Effects on Steady State Flow

One of the drawbacks of dimensionless
correlations is that it often masks the parametric trends. In fact the
steady state performance of two-phase loops is significantly influenced by the
pressure, power, and loop diameter. Effect of pressure on two-phase NC flow was
studied experimentally and theoretically in the 49.3 mm i.d. loop and the
results are shown in Figure10. The results are in agreement with the
predictions of (7). The measured flow rate as a function of power is plotted in
Figure 11 for various loops. The predictions with (7), TINFLO-S [34], and
RELAP5/MOD3.2 are also given in Figure 11. Again, the data are in reasonable
agreement with the predictions.Figure 10
Effect of pressure on flow rate.Effect of power on the two-phase NC flow rate.
(a)
9.1 mm i.d. loop(b)
49.3 mm i.d. loop(c)
9.1 mm i.d. loop


## 3.3. Two-Phase NC Flow Regimes

Unlike
single-phase natural circulation, it is observed that the trend of the steady
state data can be significantly different for two-phase loops. 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. 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 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).


### 3.3.1. 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 Figure12) 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 Figures 13 and 14).Figure 12
Effect of quality on void fraction.Figure 13
Effect of pressure on flow regime.Effect of pressure on flow regime for different loop diameter.
(a)(b)


### 3.3.2. Friction Dominant Regime

Friction dominant regime is observed at low to moderate pressures when
quality is high. At higher qualities and moderate pressures, the increase in
void fraction with quality is marginal (Figure12) 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 Figure 13).


### 3.3.3. 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 Figure11(a) and the curve for 7 MPa in Figure
13) in spite of increase in quality.


### 3.3.4. 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 Figure14).
Knowledge of the flow regimes is important to understand the stability behavior
of two-phase loops.


## 3.3.1. 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 Figure12) 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 Figures 13 and 14).Figure 12
Effect of quality on void fraction.Figure 13
Effect of pressure on flow regime.Effect of pressure on flow regime for different loop diameter.
(a)(b)


## 3.3.2. Friction Dominant Regime

Friction dominant regime is observed at low to moderate pressures when
quality is high. At higher qualities and moderate pressures, the increase in
void fraction with quality is marginal (Figure12) 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 Figure 13).


## 3.3.3. 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 Figure11(a) and the curve for 7 MPa in Figure
13) in spite of increase in quality.


## 3.3.4. 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 Figure14).
Knowledge of the flow regimes is important to understand the stability behavior
of two-phase loops.


## 3.4. Stability Behavior

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. Further, premature critical heat flux (CHF) 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 seen in [23].


### 3.4.1. Experimental Stability Map

An experimentally
generated stability map for the 9.1 mm i.d. loop is shown in Figure15(a),
which shows two unstable regions for two-phase natural circulation. It may be
noted that all the two-phase loops tested had stable single-phase natural
circulation flow. However, it appears possible to get an unstable zone in the
single-phase region also for certain loop geometries. Thus overall, three
unstable zones (one in the single-phase region and two in the two-phase region)
are possible for natural circulation loops with increase in power (excluding
the single-phase vapour region). The first unstable zone in the two-phase
region (Figure 15(a)) occurs at a low power and hence at low quality and is
named as type I instability by Fukuda and Kobori [35]. Similarly, the second
unstable zone in the two-phase region (Figure 15(a)) occurs at high powers and
hence at high qualities and is named as type II instability. 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 found in the compensating regime
during the present tests.Experimental stability map and some typical type-I oscillation.
(a)
Experimental stability map(b)
Nature of type-I oscilation(c)
Type-I oscilation


### 3.4.2. 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.


### 3.4.3. Characteristics of 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, the amplitude of type-I oscillations first
increases, reaches a peak and then decreases with increase in power eventually
leading to stable flow (Figure15(b)). However, amplitude variation is a
complex function of power presumably due to flow pattern transitions (Figure 15(b)).
For certain type-1 unstable regions, the flow alternates between a stable and
oscillatory regime (Figure 15(c)). For large diameter loops, a unidirectional
oscillation depicting a bean shaped limit cycle is observed (Figure 16).
However, the dynamics is quite rich showing many different oscillatory patterns
(see Figures 15(c), 16(a), and 16(c) for a few sample patterns).Some typical type-1 oscillations and the limit cycle for observed for 49.3 mm i.d. loop.
(a)
Power = 20 kW(b)
Limit cycle at 2.2 bar(c)
Typical oscillationsThe amplitude of type-I oscillations reduces significantly with increase
in pressure (see Figures15(a) and 17(a)). Further, type-I instability is not
observed beyond a critical value of the system pressure (Figure 17(c)). 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 (Figure 18). However, beyond a certain
diameter, the effect of loop diameter on the critical pressure is found to be
marginal.Effect of pressure on the type-I instability in the 9.1 mm inside diameter loop.
(a)(b)(c)Effect of pressure on the instability due to boiling inception in 19.86 mm i.d. loop.
(a)
Start-up at 3.1 bar(b)
Start-up at 5.4 bar


### 3.4.4. Characteristics of Type-II Instability

In the present experiments, type-II
instability (Figure19) is found to occur after the flow starts to decrease
with increase in power (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 frequently in the 7 mm loop and less
frequently in the 9.1 mm loop.The upper threshold of instability at different pressures.
(a)
13 bar(b)
18 bar(c)
25 bar


## 3.4.1. Experimental Stability Map

An experimentally
generated stability map for the 9.1 mm i.d. loop is shown in Figure15(a),
which shows two unstable regions for two-phase natural circulation. It may be
noted that all the two-phase loops tested had stable single-phase natural
circulation flow. However, it appears possible to get an unstable zone in the
single-phase region also for certain loop geometries. Thus overall, three
unstable zones (one in the single-phase region and two in the two-phase region)
are possible for natural circulation loops with increase in power (excluding
the single-phase vapour region). The first unstable zone in the two-phase
region (Figure 15(a)) occurs at a low power and hence at low quality and is
named as type I instability by Fukuda and Kobori [35]. Similarly, the second
unstable zone in the two-phase region (Figure 15(a)) occurs at high powers and
hence at high qualities and is named as type II instability. 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 found in the compensating regime
during the present tests.Experimental stability map and some typical type-I oscillation.
(a)
Experimental stability map(b)
Nature of type-I oscilation(c)
Type-I oscilation


## 3.4.2. 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.


## 3.4.3. Characteristics of 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, the amplitude of type-I oscillations first
increases, reaches a peak and then decreases with increase in power eventually
leading to stable flow (Figure15(b)). However, amplitude variation is a
complex function of power presumably due to flow pattern transitions (Figure 15(b)).
For certain type-1 unstable regions, the flow alternates between a stable and
oscillatory regime (Figure 15(c)). For large diameter loops, a unidirectional
oscillation depicting a bean shaped limit cycle is observed (Figure 16).
However, the dynamics is quite rich showing many different oscillatory patterns
(see Figures 15(c), 16(a), and 16(c) for a few sample patterns).Some typical type-1 oscillations and the limit cycle for observed for 49.3 mm i.d. loop.
(a)
Power = 20 kW(b)
Limit cycle at 2.2 bar(c)
Typical oscillationsThe amplitude of type-I oscillations reduces significantly with increase
in pressure (see Figures15(a) and 17(a)). Further, type-I instability is not
observed beyond a critical value of the system pressure (Figure 17(c)). 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 (Figure 18). However, beyond a certain
diameter, the effect of loop diameter on the critical pressure is found to be
marginal.Effect of pressure on the type-I instability in the 9.1 mm inside diameter loop.
(a)(b)(c)Effect of pressure on the instability due to boiling inception in 19.86 mm i.d. loop.
(a)
Start-up at 3.1 bar(b)
Start-up at 5.4 bar


## 3.4.4. Characteristics of Type-II Instability

In the present experiments, type-II
instability (Figure19) is found to occur after the flow starts to decrease
with increase in power (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 frequently in the 7 mm loop and less
frequently in the 9.1 mm loop.The upper threshold of instability at different pressures.
(a)
13 bar(b)
18 bar(c)
25 bar


## 3.5. Theoretical Results

The stability of the test loops was studied
with a linear stability code TINFLO-S based on the drift flux model (Nayak et
al. [36]). The drift flux parameters (Co and Vgi) for
slug flow were used as it was the most frequently observed flow pattern during
the tests. The Martinelli-Nelsontwo-phase
friction multiplier model was used in the computations. Figures 20(a) and 20(b)
compare the predicted stability map with experimental data. Figure 21(a)
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 (Figure 21(b)) 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 behavior 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 behavior is also reported
by Boure et al. [37].Comparison of measured and predicted stability maps.
(a)
Effect of drift velocity(b)
Effect of subcoolingPredicted stability map for various loop diameters.
(a)(b)


## 4. Design Considerations

The above results are significant to the
design of the pressure tube type BWRs. For example, the experiments show that
it is possible to avoid type-I instability by a pressurized start-up (Figure17).
Figure 21(a) shows that the type-II instability threshold shifts to higher
qualities with increase in loop diameter. For 40 mm loop diameter, the upper
threshold is not found in the two-phase region (i.e., 0 < quality ≤ 1).
Thus, by the appropriate choice of the loop diameter, it is possible to
entirely eliminate the type-II instability in the two-phase loops. However,
this is yet to be established experimentally as the maximum test section power
was limited to 40 kW. Experiments by Mochizuki [38]
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
(Figure 21(b)).


### 4.1. Design Types for NCSs

Since both instability and CHF (critical heat
flux) need 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.


#### 4.1.1. Stability-Controlled Design

In this type of loops, the maximum power is
limited by the stability, as the threshold of type-II instability is lower than
the CHF threshold. Figure22 shows that this is normally the case in small
diameter loops. These predictions were obtained by incorporating the look-up
table (Groeneveld et al. [39]) in the TINFLO-S code. The heat balance method was
used for the CHF prediction. In Figure 22(c), stability-controlled design is
found on the right of the dotted line.Stability controlled designs and loop diameter.
(a)(b)(c)


#### 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. Figure23 shows that this situation
arises in large diameter loops. In Figure 23(a), the design is CHF controlled
only to the left of the vertical dotted line, while in Figures 23(b) and 23(c)
the design is CHF controlled over the entire subcooling-power plane. Design of
forced circulation BWRs is usually CHF controlled. By appropriate choice of the
loop diameter, the design of an NCS can shift from stability controlled to CHF
controlled (Figures 22 and 23).CHF controlled designs and loop diameter.
(a)(b)(c)


#### 4.1.3. Operating Line for Stability-Controlled Designs

Two-phase NCSs are not completely stable over
the entire subcooling-power map and an operating line needs to be specified for
ensuring stability for all anticipated operations like start-up, power raising,
and step back. One would expect the decay ratio to go through a minimum while
moving from the lower to the upper threshold for a fixed subcooling (Figure24).
Ideally, the operating line shall pass through the minimum decay ratio line
(locus of all minimum decay ratio points (see also Figure 24)) so that all
oscillations will die down in the quickest possible manner. In
stability-controlled designs, one could choose the operating line as the
minimum decay ratio line if found feasible from feed water inlet temperature
considerations (see also Vijayan et al. [40]).Figure 24
Variation of decay ratio (DR).


#### 4.1.4. Unstable Oscillations and CHF

Premature occurrence of CHF and test section
burnout can be an issue during oscillatory flows in two-phase loops. In the
present experiments, premature CHF occurrence was observed
only at low pressures when the amplitude of flow oscillation is large. Although
Figures22(a) and 22(b) show that the CHF threshold is significantly higher
than the instability threshold, burnout occurred only for the test section
diameters of 7 and 9.1 mm in the present experiments. The occurrence of burnout
during instability was more frequent in 7 mm diameter loop than in 9.1 mm loop.
A typical observed temperature excursion following the occurrence of CHF in the
7 mm diameter test section is shown in Figure 25(a), where a heater trip based
on high heater surface temperature terminated the transient. However,
occurrence of CHF away from the thermocouple locations resulted in the burnout
of the test section. Inspection of the burntout test sections revealed that the
burnout is not restricted to the test section outlet. Premature occurrence of
CHF was studied using RELAP5/MOD3.2 code for sinusoidal fluctuations in flow
rate. The effect of amplitude and frequency was also studied for the 9.1 mm
i.d. test section. Figure 25(b) shows that premature occurrence of CHF is a
concern at low frequencies and high amplitudes.Premature CHF occurrence with flow oscillatory flow.
(a)
Premature CHF occurrence(b)
Effect of amplitude and frequency


## 4.1. Design Types for NCSs

Since both instability and CHF (critical heat
flux) need 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.


### 4.1.1. Stability-Controlled Design

In this type of loops, the maximum power is
limited by the stability, as the threshold of type-II instability is lower than
the CHF threshold. Figure22 shows that this is normally the case in small
diameter loops. These predictions were obtained by incorporating the look-up
table (Groeneveld et al. [39]) in the TINFLO-S code. The heat balance method was
used for the CHF prediction. In Figure 22(c), stability-controlled design is
found on the right of the dotted line.Stability controlled designs and loop diameter.
(a)(b)(c)


### 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. Figure23 shows that this situation
arises in large diameter loops. In Figure 23(a), the design is CHF controlled
only to the left of the vertical dotted line, while in Figures 23(b) and 23(c)
the design is CHF controlled over the entire subcooling-power plane. Design of
forced circulation BWRs is usually CHF controlled. By appropriate choice of the
loop diameter, the design of an NCS can shift from stability controlled to CHF
controlled (Figures 22 and 23).CHF controlled designs and loop diameter.
(a)(b)(c)


### 4.1.3. Operating Line for Stability-Controlled Designs

Two-phase NCSs are not completely stable over
the entire subcooling-power map and an operating line needs to be specified for
ensuring stability for all anticipated operations like start-up, power raising,
and step back. One would expect the decay ratio to go through a minimum while
moving from the lower to the upper threshold for a fixed subcooling (Figure24).
Ideally, the operating line shall pass through the minimum decay ratio line
(locus of all minimum decay ratio points (see also Figure 24)) so that all
oscillations will die down in the quickest possible manner. In
stability-controlled designs, one could choose the operating line as the
minimum decay ratio line if found feasible from feed water inlet temperature
considerations (see also Vijayan et al. [40]).Figure 24
Variation of decay ratio (DR).


### 4.1.4. Unstable Oscillations and CHF

Premature occurrence of CHF and test section
burnout can be an issue during oscillatory flows in two-phase loops. In the
present experiments, premature CHF occurrence was observed
only at low pressures when the amplitude of flow oscillation is large. Although
Figures22(a) and 22(b) show that the CHF threshold is significantly higher
than the instability threshold, burnout occurred only for the test section
diameters of 7 and 9.1 mm in the present experiments. The occurrence of burnout
during instability was more frequent in 7 mm diameter loop than in 9.1 mm loop.
A typical observed temperature excursion following the occurrence of CHF in the
7 mm diameter test section is shown in Figure 25(a), where a heater trip based
on high heater surface temperature terminated the transient. However,
occurrence of CHF away from the thermocouple locations resulted in the burnout
of the test section. Inspection of the burntout test sections revealed that the
burnout is not restricted to the test section outlet. Premature occurrence of
CHF was studied using RELAP5/MOD3.2 code for sinusoidal fluctuations in flow
rate. The effect of amplitude and frequency was also studied for the 9.1 mm
i.d. test section. Figure 25(b) shows that premature occurrence of CHF is a
concern at low frequencies and high amplitudes.Premature CHF occurrence with flow oscillatory flow.
(a)
Premature CHF occurrence(b)
Effect of amplitude and frequency


## 4.1.1. Stability-Controlled Design

In this type of loops, the maximum power is
limited by the stability, as the threshold of type-II instability is lower than
the CHF threshold. Figure22 shows that this is normally the case in small
diameter loops. These predictions were obtained by incorporating the look-up
table (Groeneveld et al. [39]) in the TINFLO-S code. The heat balance method was
used for the CHF prediction. In Figure 22(c), stability-controlled design is
found on the right of the dotted line.Stability controlled designs and loop diameter.
(a)(b)(c)


## 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. Figure23 shows that this situation
arises in large diameter loops. In Figure 23(a), the design is CHF controlled
only to the left of the vertical dotted line, while in Figures 23(b) and 23(c)
the design is CHF controlled over the entire subcooling-power plane. Design of
forced circulation BWRs is usually CHF controlled. By appropriate choice of the
loop diameter, the design of an NCS can shift from stability controlled to CHF
controlled (Figures 22 and 23).CHF controlled designs and loop diameter.
(a)(b)(c)


## 4.1.3. Operating Line for Stability-Controlled Designs

Two-phase NCSs are not completely stable over
the entire subcooling-power map and an operating line needs to be specified for
ensuring stability for all anticipated operations like start-up, power raising,
and step back. One would expect the decay ratio to go through a minimum while
moving from the lower to the upper threshold for a fixed subcooling (Figure24).
Ideally, the operating line shall pass through the minimum decay ratio line
(locus of all minimum decay ratio points (see also Figure 24)) so that all
oscillations will die down in the quickest possible manner. In
stability-controlled designs, one could choose the operating line as the
minimum decay ratio line if found feasible from feed water inlet temperature
considerations (see also Vijayan et al. [40]).Figure 24
Variation of decay ratio (DR).


## 4.1.4. Unstable Oscillations and CHF

Premature occurrence of CHF and test section
burnout can be an issue during oscillatory flows in two-phase loops. In the
present experiments, premature CHF occurrence was observed
only at low pressures when the amplitude of flow oscillation is large. Although
Figures22(a) and 22(b) show that the CHF threshold is significantly higher
than the instability threshold, burnout occurred only for the test section
diameters of 7 and 9.1 mm in the present experiments. The occurrence of burnout
during instability was more frequent in 7 mm diameter loop than in 9.1 mm loop.
A typical observed temperature excursion following the occurrence of CHF in the
7 mm diameter test section is shown in Figure 25(a), where a heater trip based
on high heater surface temperature terminated the transient. However,
occurrence of CHF away from the thermocouple locations resulted in the burnout
of the test section. Inspection of the burntout test sections revealed that the
burnout is not restricted to the test section outlet. Premature occurrence of
CHF was studied using RELAP5/MOD3.2 code for sinusoidal fluctuations in flow
rate. The effect of amplitude and frequency was also studied for the 9.1 mm
i.d. test section. Figure 25(b) shows that premature occurrence of CHF is a
concern at low frequencies and high amplitudes.Premature CHF occurrence with flow oscillatory flow.
(a)
Premature CHF occurrence(b)
Effect of amplitude and frequency


## 5. Concluding Remarks

Effect of loop diameter was studied for both
single-phase and two-phase natural circulation loops.Single-Phase Loops
Four single-phase loops
differing in diameter were studied. Instability was observed only in the two
large diameter loops. The instability threshold is found to decrease with
increase in loop diameter. Also, the threshold of instability is not a unique
value as it depends on the operating procedure (hysteresis phenomenon). Linear
analysis showed that the unstable region shifts up with decrease in loop
diameter. Thus, small diameter loops are more stable than large diameter loops.Two-Phase Loops
The steady state and
stability behaviour of five loops differing in diameter were studied. Besides,
the well known gravity and friction dominant regimes a compensating regime,
where the flow is practically invariant with power is also observed under
steady state. Both type-I and type-II instabilities are observed in small
diameter loops, whereas only type-I instability was observed in large diameter
loops. Type-I instability can be avoided by a pressurized start-up. However,
the pressure beyond which the type-I instability disappears is found to decrease
with increase in the loop diameter. Contrary to the observations in
single-phase loops, the stability of two-phase loops is found to enhance with
increase in loop diameter. Linear analysis showed that increase in subcooling
destabilized type-I instability irrespective of loop diameter whereas type-II instability
is found to destabilize for small diameter loops. For large diameter loops,
type-II instability stabilizes initially with increase in subcooling and then
destabilizes with further increase in subcooling. Stability analysis also
revealed that the type-II instability is not observable in the two-phase region
(0<x<1) for large diameter loops at moderate pressures (70 bar).
Premature occurrence of CHF and burnout is a serious problem at low-frequency
high-amplitude oscillatory flow in small diameter loops. The study also shows
that the maximum operating power of NCSs can be CHF controlled or instability
controlled depending on the loop diameter. For stability controlled designs,
the minimum decay ratio (DR) line could be a feasible operating line.



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*Source: 672704-2008-06-01.xml*