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Transient behavior of natural circulation for boiling two-phase flow (flow after pump trip)
ELSEVIER
Nuclear Engineering and Design 152 (1994) 263-275
Nuclear E neer]ng andD gn
Transient behavior of natural circulation for boiling two-phase flow (flow after pump trip) J i n g - H s i e n C h i a n g a'l, M a s a n o r i
A r i t o m i ~, M i c h i t s u g u
Mori b
aResearch Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-10hokayama, Meguro-ku, Tokyo 152, Japan bTokyo Electric Power Company, I-I-3 Uchisaiwai-cho, Chiyoda-ku, Tokyo 100, Japan
Abstract
The idea of a flow diode has been proposed to improve the pump coastdown characteristics of the internal recirculation pumps adopted by the ABWR. In this paper, the transient behavior from forced to natural circulation was experimentaUy investigated by simulating a pump coastdown condition for the purpose of providing an available source of information that is necessary for designing the flow diode. The results of the study showed that the transient behavior after pump coastdown was influenced by the coastdown period, the trigger velocity and the initial driving force of natural circulation. The potential of each driving factor was governed by the delay time for boiling, which is a very important parameter in natural circulation of boiling two-phase flow. In consequence, a guide for the designing of a flow diode was proposed.
1. Introduction
Nuclear energy is an available major source of electricity generation, which has the potential to provide a substantially increased share of future electricity needs. In the development of nuclear energy, the fast breeder reactor (FBR) is expected to be an evolutionary reactor in the twenty-first century; however, the introduction of commercial FBRs has been held up because of cost-benefit considerations and the availability of plutonium fuel. Therefore, it is likely that light water reactors *This paper is a revised version of the paper originally presented at the Second International Conference on Nuclear Engineering, on March 24, 1993.It receivedreprint permission from ASME. Present address: Japan NUS Co. Ltd., Loop -X Building 7F, 3-9-15 Kaigan, Minato-ku, Tokyo 108, Japan.
(LWRs) will still be a major nuclear source in the early twenty-first century. Development of LWRs is now focused on the enhancement of safety and utility by the introduction of passive functions; the advanced L W R (ALWR) is such an example. In the development and project application of the ALWR, there are several promising conceptual designs, such as the use of the passive functions to replace active ones, selected for the next generation of LWRs. In the meantime, in Japan, the advanced boiling water reactor (ABWR) and the advanced pressurized water reactor (APWR) are foreseen as the next generation of LWRs in the 2010 time frame. The authors have made an effort based on fundamental research to concern themselves with the next generation of BWRs by investigating the transient behavior of natural circulation for boiling two-phase flow. The study has been separated
0029-5493/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSDI 0029-5493(94)00730-M
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into two fields: the feasibility of natural-circulation BWRs such as the simplified BWR (SBWR) (McCandless, 1989) a n d the sophistication of forced-circulation BWRs such as the ABWR. In the case of the evolution of natural circulation, the thermal hydraulics relating to the SBWR was considered as an objective. First, the authors provided a discussion about the advantages and disadvantages of eliminating the recirculation pumps, and the authors pointed out that thermal hydraulic instabilities might occur according to reactor configuration and start-up procedure (Aritomi, 1990). Next, the instabilities, geysering, natural-circulation oscillation and density-wave instability were observed by conducting simulated experiments under the conditions in insufficient vapor generation. The driving mechanisms of geysering induced by condensation and of naturalcirculation oscillation induced by hydrostatic head fluctuation in long vertical non-heated channels such as a steam separator and divided chimney were clarified experimentally (Aritomi, 1992a,b; Chiang, 1993). Finally, the authors proposed a rational procedure of start-up to prevent the instabilities from occurring, and an effective reactor configuration (Aritomi, 1992b). On the other hand, the authors have focused on the ABWR design to study the dynamic behavior in transition from forced convection to natural circulation. One distinctive feature of the ABWR is that it employs internal recirculation pumps instead of external recirculation pumps used in current BWRs to enhance safety. However, the use of internal pumps may make the pump coastdown characteristics worse and introduce a large throttling effect in the natural circulation path. Since the ABWR design was optimized for 1350 MWe and employed ten internal recirculation pumps, it seemed not to be an issue in this design. To expand the ABWR design into a unit in the power range 600 MWe to 900 MWe and an improvement in simplifying maintenance, it is said that the reduction in the number of internal recirculation pumps can meet the objective. From the fact that the pump coastdown characteristics of the ABWR are worse than those of current BWRs, because of the smaller inertia of the internal pump impeller, it is therefore agreed that the
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Natural circulatiOnpa~a
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Flowhole Guide
Pump is working
Seat
Stopper After pump tripped
Fig1.. Concept offlowdiode.
compensating system, to improve the characteristics, will be very complex for a plant with fewer internal recirculation pumps. To address this question, the authors have proposed the idea of the flow diode as shown in Fig. 1. A key feature of the flow diode is that a valve with passive function would serve a natural circulation path with a free throttling effect. It is expected that this idea could ease the current internal recirculation pump that has the worst pump coastdown characteristics and therefore prevent the undesirable event of a "power/flow mismatching" when the pump trip occurs. While the pump is working, the valve is lifted to close the natural circulation path. If the pump unintentionally stops working, the valve will fall when its own weight exceeds what the flowing force can support, thus opening the natural circulation path. To design such a device, the timing of the opening of the natural circulation path is of the utmost importance. In other words, it is necessary to determine what the flow condition is in order to predetermine when the valve should fall. The purpose of this study is to investigate experimentally the dynamic behavior of the flow after pump coastdown for providing the information that would be required by the flow diode design. Experiments were conducted with a loop that could carry boiling fluid in both natural and forced circulation by controlling a "flow-diodelike" valve. An inverter was installed at the pump to provide variable pump speed, which simulated the MG motor used in the ABWR design to control the recirculation flow. The heat input, the
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Fig. 2. The loop could carry boiling fluid in both natural and forced circulation, driven by a centrifugal pump, by switching a flow-diode-like valve. The valve was simulated by a pneumatic valve whose switch was equipped with a relay connected to a comparator that could be used to control the opening/closing of the flow-diode-like valve. A flow control valve, placed downstream of the pump, was used to set the desirable flow rate. A flowmeter was placed between the inlet plenum and flow control valve, which was used to measure the total flow rate. The measured results were fed in parallel to the data acquisition system and the comparator. There was a predetermined value set in the comparator, which
"trigger velocity" to activate a natural circulation path, and the coastdown period were selected as experimental parameters. The means of the flowdiode-like valve and of the trigger velocity are described in the next section.
2. Experimental methods
2. I. Experimental apparatus In order to investigate the transient behavior of natural circulation after the pump trip, an experimental flow loop was constructed as shown in
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Fig. 2. Experimental apparatus.
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J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
was used to compare with the measured results of the total flow rate. Once the measured total flow rate was lower than that of the set value, the comparator would serve as a signal to switch the flow-diode-like valve. That is, the signal controlled the circulated mode of flow, in natural circulation and/or in forced circulation. In this paper, the predetermined value in this comparator is used as a parameter, which is called trigger velocity. To simulate the characteristics of pump coastdown, the pump was equipped with an inverter (within a setting period, 0.1-100 s) for variation of frequency of the pump. Water was used as test fluid. Circulating fluid temperature was achieved through controlling a pre-heater and a cooler that were installed in the separator tank. The twophase mixture leaving the test section was condensed by a c6ndenser installed in the separator tank. The test section comprised a twin parallel channel between the inlet and outlet plenum. Each channel consisted of a heater, a pair of electrodes and an orifice flowmeter for measuring flow fluctuation. The heater rod (6 mm outside diameter, 1 m long) was made of thin stainless steel, and it was installed concentrically in the test section, and was heated by a d.c. power supply. The temperatures of the inlet, outlet and separator tank were measured by CA thermocouples, and the total flow rate was measured upstream of the test section by an orifice flowmeter. The differential pressures between the inlet and outlet plenums and between the outlet plenum and separator tank were measured by differential transducers. All measured data were acquired by a computer-based data acquisition system, which consisted of a data logger (sampling interval, 1 s), an analyzing recorder (sampling interval, 10 ms) and a personal computer. The differential pressures, flow rate, and temperature in the outlet plenum that would vary temporally, were recorded with the analyzing recorder. Temperatures in the inlet plenum and the separator and heat input in the test section were measured with the data logger to control the desirable experimental conditions. All of the acquired data were transferred to the personal computer. The personal computer was connected with the data acquisition recorders, the trigger generator (comparator) and the pump frequency con-
troller (invertor), to play the role of surveillance and regulation to keep the experimental parameters constant during one test.
2.2. Experimentalprocedure From our previous studies on the behavior of natural circulation in parallel channels (Aritomi, 1992b), flow instabilities, geysering and naturalcirculation oscillation would be induced under conditions of insufficient vapor generation. Based on this information, the stable region of natural circulation was selected for the present experiment. Different sets of experiments, corresponding to various heat inputs and trigger velocities, were conducted at one given inlet velocity. In order to clarify the effect of pump coastdown characteristics on transient behavior from forced circulation to a natural one, a series of pump coastdown periods was experimentally investigated in each set of experiments. All experiments were rendered under computer-controlled operation; that is, measured data were monitored in an RGB device, fine adjustment of heat input was achieved through a D/A converter installed via the personal computer to a d.c. power supply. For each trigger velocity, a preliminary experiment was conducted without any heat inputs to figure out the delay time for opening the natural circulation path and to realize the characteristics of flow in the loop. The procedure for actual tests can be outlined as follows: 1. The inlet velocity and circulation fluid temperature in the loop, the coastdown period of the pump, and the trigger velocity in the comparator were set to the desired value. 2. Heat input increased gradually to the desired value, and the system was allowed to become steady enough, as indicated by the recording and monitoring system. 3. Once the system was confirmed to ~e in a steady state, the data acquisition system started to record the measuring data. Simultaneously, a signal was sent to trigger the invertor to decelerate the pump operation. 4. After the flow rate regained a steady enough level, the test was completed.
J.-H. Chiang et al. [ Nuclear Engineering and Design 152 (1994) 263-275
0.8
Table 1 Experimental conditions Test fluid System pressure Inlet temperature Heat flux Length of riser Inlet velocity P u m p coastdown period Trigger velocity
Water Atmospheric pressure 90°C 2 0 0 - 4 0 0 k W m -2 250 m m 0.5-0.6 m s -1 0.1-30 s 0.25-0.56 m s -t
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267
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gger velOcity0'56 m/s
0.4 .o
g Table 2 Accuracies for measurements Differential pressure Flow rate Temperature Heat flux
+ 0.15 kPa _0.01 m s -1 +0.5 K +2.5 k W m -2
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0
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2
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4
I
6
Time (s) Fig. 3. Typical flow changes after pump coastdown without heat input.
As for the reproducibility of a test, the data were obtained by repeating the test under the same conditions three to five times. The experimental conditions are summarized in Table 1, and the accuracies for the measurements are tabulated in Table 2.
3. Results and discussion
3.1. Characteristics of pump coastdown and natural circulation path In the preliminary experiment, the behavior of flow after the opening of the natural circulation path was studied without any heat inputs. Fig. 3 shows a typical result of the changes in flow after pump coastdown. The dashed line is the change without opening the natural circulation path under the deceleration of the pump. The solid line is the change while the natural circulation path was opening. Here, the trigger velocity is 0.56 m s- t as shown in the figure. This means that the natural circulation path was opened at the point when the total flow rate was lower than that predetermined value, 0.56 m s-1, in the comparator. It can be seen from the figure that the flow was rapidly reduced when the natural circulation path opened. This flow reduction was caused when flow reversal
occurred in the natural circulation path. The pump would not stop immediately until the coastdown period was reached, even if the natural circulation path opened. The coastdown pumping was responsible for the flow reversal. Consequently, the resulting flow to the total flow rate in the test section was reduced owing to the flow reversal. Another preliminary test was conducted to examine the opening time of the natural circulation path for a given predetermined value of trigger velocity after the pump started the decelerating operation. Fig. 4 shows the "delay time for opening natural circulation path" vs. the coastdown period for various trigger velocities. The delay time for opening the natural circulation path was evaluated by the time difference from the time of starting coastdown to the time of opening the flow-diode valve. For a given circulating rate, if the trigger velocity in the comparator is set at a higher value then the natural circulation path will open more quickly. The results shown in the figure give the response time of the flow-diode-like valve and are useful to find a suitable trigger velocity setting. Fig. 5 demonstrates the typical measured results of the pump coastdown experiment with heat input, by means of the changes in the differential
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
268
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Fig. 5. Typical measured result of experiment. pressure of the riser section and in the circulation rate. The APup is defined from the true differential pressure, between the inlet plenum and separator tank, minus the hydrostatic head, i.e. A P , p = APtrue -- pigH. This is because the differential pressure between the inlet plenum and separator tank had been reset to zero before the experiment started. The symbols ts and t t mean the time of starting the experiment
and the time of response on the natural circulation path respectively. The symbol tmin is the time when flow decreased to a limit value, referred to as "minimum velocity". The remaining symbols td and t r are the time when flow became increased, and the time when flow rose to be equal to the circulation rate of a steady state Usteady , respectively. The differential pressure Psteady and the circulation rate Usteady a r e the values at which the system reached another steady state. The utngger is the trigger velocity set in the comparator. In all of the experiments, the dynamic behavior of the flow was almost the same as shown in Fig. 5; observed differences appeared only in the timing of each occurring aspect and on the value of minimum velocity. In addition, when the new steady state was obtained, the esteady and Ust~,dywere independent to the extent of the experimental conditions used in the present study. The dynamic behavior of flow as shown in Fig. 5 is considered as follows. The circulation rate becomes decreased when the pump starts its decelerating operation at the time ts, and the differential pressure scarcely fluctuates by that time. Again, the differential pressure shown in Fig. 5 is the resultant pressure drop between the inlet plenum and the separator tank. When the natural circulation path is opened at the setting trigger velocity, Utngg~r,the flow continues decreasing. This decrease is caused by the flow reversal occurrence in the natural circulation path as mentioned above. Subsequently, the flow reaches the minimum velocity Umin at the time tmin. After that, no specific changes in the flow rate appear till the pressure drop of the riser section becomes decreased at the time td. For low flow rates in the upward boiling system, the head drop is expected to be dominant over the friction and acceleration drops. Consequently, the increase in void fraction results in a decrease in head drop to make the total driving force become increased. Accordingly, the flow rate begins to turn up toward recovery when the pressure drop decreases. Finally, a new steady state of natural circulation is obtained.
3.2. Minimum velocity The minimum velocity is a very important criterion for the margin of safety of a heated system.
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
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Fig. 6. Effect of pump coastdown period on minimum velocity.
Fig. 7. Relationship between minimum velocity and coastdown period.
The BWR is especially susceptible to reactivity instabilities when operated at a low flow condition according to results of stability tests (Waaranpera, 1981; Sandoz, 1983) and numerical analysis (March-Leuba, 1986). To design the flow diode, therefore, the function of providing a rational minimum velocity should be established. In order to understand the effects of the coastdown period on transient behavior of flow, the minimum velocity corresponding to the coastdown period was investigated by using various heat inputs. Fig. 6 shows a typical relationship between the minimum velocity and coastdown period. Overall, the minimum velocities increased with an increase in the coastdown period. In addition, it seems that the tendency of an increase in the minimum velocity was separable by a turning point (coastdown period between 3 and 10 s): a smooth increase in shorter coastdown periods and a rapid one in longer coastdown periods. Further, when the coastdown period was set long enough, the minimum velocity had reached the trigger velocity in this case. The same tendency was observed at other heat inputs, although higher heat inputs induced moderately higher minimum velocity. The time when the circulation rate dropped down to a minimum value for various heat inputs is shown in Fig. 7. It indicates
that tmin only depends on coastdown period. If we make a comparison between the trnin and the tt, as shown in Fig. 4, we will find that train is very close to tt. The difference was caused by the flow reversal as mentioned earlier. This means that the t,ni, can be controlled by manipulating the coastdown period. The uncertainty of the minimum velocities shown in the figures was estimated within ___10%.
3.3. Driving force for natural circulation Another important parameter, driving force, is also dominant in the system under natural-circulation operation. The initial driving force for natural circulation is commonly defined by: APforc e = APdown - APup
(1)
where APdown, AP,p are the pressure drops in the downcomer and the riser section respectively (Aritomi, 1990). In this study, the experiments were conducted from forced circulation to a natural one, and the system had still been in forced circulation operation before the natural circulation path responded. Therefore, the initial driving force for natural circulation was calculated by the measured pressure detected at the point, tt, using the above definition. A typical result of driving force
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
270
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1 I~'Tin = 90 °C ~-q" = 230 kW/m2 I Uin = 0.60 m/s Uugger = 0.34 m/s
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. . . . . . . .
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. . . . . . . .
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100 101 Coastdown period (s)
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102
Fig. 8. Effect of pump coastdown period on driving force.
vs. coastdown period is shown in Fig. 8. From the figure, driving force increases slowly with an increasing coastdown period at shorter coastdown periods, but it increases dramatically when the periods pass over the turning point (the same as Fig. 6). Generally, in the natural circulation loop the driving force is directly related to the vapor generation in the boiling channel. To gain a relatively larger driving force requires a sufficient boiling condition in the heated channel. From the figure of dynamic behavior of flow, as shown in Fig. 5, we can find that the flow rate does not change availably around the minimum value of the circulation rate for a while. This aspect indicates that boiling in the heated channel was insufficient to contribute additional driving force. Fig. 9 shows a result of the arrangement of the "delay time for flow recovery" vs. the coastdown period. Delay time for flow recovery was calculated from the time difference between the time that flow begins to increase at available circulation rate, ta, and the time of natural circulation path opening, t t. The figure indicating the delay time for flow recovery is clarified into two categories: smoothly decreased and rapidly decreased, corresponding to the coastdown period. It is considered that the thermal response of the flow in the heated channel dominates in contributing to
1~_ 1 . . . . . . i'O0 . . . . 101 Coastdown period (s)
02
Fig. 9. Delay time for flow recovery vs. pump coastdown period.
the driving force. In other words, these results indicate that the opening of the natural circulation path would be unable to gain a large driving force until the circulating fluid reached the saturated condition. It is supposed that the thermal response time will be the turning point we have sought after. Therefore, we introduced a parameter which is the delay time f o r boiling to find out the turning point. Delay time for boiling was quoted from the authors' previous work (Aritomi, 1990), and it was defined by z B = p](i' -- i i , ) / q "
(2)
where q" is the calorific power per unit volume, p~ is the liquid density, i' is the liquid saturated enthalpy and ii, is the inlet liquid enthalpy. Delay time for boiling for the conditions shown in Figs. 6 to 9 was 1.86 s; using this 1.86 s as the opening time for the natural circulation path, the coastdown period can be calculated from the relationship shown in Fig. 4 to be 5 s. Further, the relationship between the delay time for boiling and the delay time for flow recovering at various heat flux values is shown in Fig. 10. A correlation can be found between both. Therefore, the delay time for boiling may be a good judge of what is a suitable coastdown period. From Figs. 6 to 10, the following circumstances are significant.
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J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275 i
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Fig. 10. Relationship between delay time for flow recovery and delay time for boiling.
Fig. 11. Relationship between minimum velocityand driving force for extremelyshort pump coastdown period.
In a longer coastdown period, after the pump has begun its decelerating operation, the boiling in the heated section is enhanced due to a decreasing flow rate. A large amount of vapor will be generated, causing a decrease in the hydrostatic head; consequently, the driving force becomes larger at the time the natural circulation path is opened. Conversely, the shorter coastdown period will not allow too much vapor to be induced because the natural circulation path is opened quickly (here the opening times were within 0.01 to 1.15 s), so the driving force for it should be mainly contributed by the initial driving force of natural circulation.
is shown in Fig. 11. It can be seen from the figure that the minimum velocity becomes zero for negative initial driving forces, but not for positive ones, and that it increases with an increase in the positive ones. This investigation is in agreement with the results concluded by the previous work. Under the condition that the pump stopped instantly, there is no longer any extra force to act on the flow except for the initial driving force. However, in a longer pump coastdown period, the pump does not instantly stop operation, i.e. the flow rate induced by the decelerating operation of the pump is still available when the natural circulation path is activated. Therefore, the effect of a higher trigger velocity will become more apparent in the longer coastdown period. Fig. 12, for example, shows the minimum velocity in relation to trigger velocity at a coastdown period of 3 s. Here, the Uste,dyis used to make the minimum velocity dimensionless, because the Usteady is independent of various conditions as mentioned before. The figure indicates that the minimum velocity became higher with the increasing of the trigger velocity. By the same conditions, the relationship between the driving force and trigger velocity is shown in Fig. 13. Similarly, the P~te,dy is also used to make a dimensionless arrangement. It can be seen that the driving force of
3.4. Minimum velocity and driving force for natural circulation
From the previous study (Aritomi, 1990), the minimum velocity appearing in a transient process where the pump trip occurred was dependent upon the initial driving force of natural circulation and did not show an evident difference between various trigger velocities. Note that the pump speed had not been controlled in those cases, i.e. the pump was stopped immediately. The relationship between the initial driving force and the minimum velocity for coastdown period 0.1 s
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1.2
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_ Coastdown period = 3 s P = 0.10 MPa ,~1 Tin = 90 °C >, 0 . 8 - q ' = 230 RW/m 2
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pump is still working when the natural circulation path is opened, the flow rate in the circulation loop will be higher at a higher trigger velocity, then the resulting minimum velocity as shown in Fig. 12 is the resultant of the initial driving force and the residual flow driven by the pump. It is the reason why the driving force decreases but the minimum velocity increases with an increase in trigger velocity. The difference of driving force and/or minimum velocity shown in Figs. 12 and 13 are not significantly obvious. Fig. 14 shows the relationship between the initial driving force and the minimum velocity obtained for coastdown periods within 0.1-3 s. Although some deviations can be seen, it seems that the correlation found from Fig. 11 is still available in the coastdown period up to 3 s. The deviation appearing in Fig. 14 is expected to be affected by different trigger velocities. It is then significant that in short-life transition of pump trip and/or pump coastdown, the transient behavior is dependent upon the driving force of natural circulation at the time of opening of the natural circulation path. This fact helps to postulate that the transient behavior of flow after the pump trip could be classified into (a) transition in short coastdown period and (b) transition in long coast-
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Fig. 13. Effect of trigger velocity on driving force for a short coastdown period.
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natural circulation somewhat decreased when the trigger velocity was increased. It can be explained that, if the natural circulation path opens at a high trigger velocity, the change in the pressure drop of the riser will be small. It seems to be inconsistent with the investigation on minimum velocity, shown in Fig. 12. If we consider that the
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Driving force for natural circulation (kPa) Fig. 14. Relationship between minimum velocity and driving force for short coastdown periods.
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275 0.6
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down period, and the judgment may be based on the delay time for boiling. To verify this postulate, furthermore, the same arrangement as in Fig. 14, plus longer coastdown periods, with various trigger velocities is shown in Fig. 15. A correlation is no longer to be found between these. Obviously, both the coastdown period and the trigger velocity influence the transient behavior of flow in a longer pump coastdown period. For a longer coastdown period, on the other hand, the driving forces as a function of trigger velocity are shown in Fig. 16. Obviously, for the same coastdown period, the driving force decreased with increasing trigger velocity. At lower trigger velocity the longer-period cases gained a large driving force, but at higher trigger velocity the driving force no longer changed with the coastdown period, as shown in the figure. From Fig. 4, we know a higher trigger velocity opened the path more quickly than a lower one for the same coastdown period. Fig. 17 shows the minimum velocity vs. the trigger velocity for a longer coastdown period. It is made clear that at lower trigger velocity the minimum velocity is closer to trigger velocity as long as the pump coastdown period is long, but when the trigger velocity is set beyond a certain value the minimum velocity starts to decrease. From this investigation, we
I
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1.2
Utrigger / Usteady (-)
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Fig. 15. Relationship between minimum velocity and driving force for various coastdown periods.
I
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Fig. 16. Effect of trigger velocity on driving force for long coastdown periods.
1.2
i
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i
i
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~ /~
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:
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then know that if the trigger velocity is set at an excessively high value, the minimum velocity will no longer be higher than the steady circulation rate u~teady, regardless of coastdown period, because the minimum velocity would be unable to rise higher than the steady circulation rate. To design the flow diode, it is desirable that the minimum velocity be as close as possible to the
274
J.-H. Chiang et aL / Nuclear Engineering and Design 152 (1994) 263-275
setting trigger velocity for the effective handling of the transient behavior after pump coastdown. From the investigations, it can be found that a trigger velocity about 0.5-0.8uste~dy and a coastdown period about 1.0-2.0 times the delay time for boiling will provide a rational minimum velocity and a quick flow recovery time. However, this suggestion does not indicate that there is only one way to design the flow diode. Nevertheless, it indicates a method of decision for designing the flow diode.
c. Longer coastdown period (longer than the delay time for boiling). Even a longer coastdown period will allow a large amount of vapor to be generated in the heated section to induce large driving force. Therefore, a longer coastdown period can promote a minimum velocity as high as the setting trigger velocity. . Although a higher trigger velocity will produce greater flow rates than a shorter one in the circulation loop, it will need a longer time for flow recovery. In contrast, a lower trigger velocity will cause quick flow recovery, but the minimum velocity will become lower. . The delay time for boiling greatly influences transient behavior of natural circulation after pump coastdown. . The natural circulation path of the flow diode should be designed to be opened before the flow rate has reached about half the velocity in a steady natural circulation. However, a much higher trigger velocity will cause the delay time for flow recovery to become longer, so it is logical to set a suitable trigger velocity and pump coastdown period with consideration of the delay time for boiling.
4. Conclusions The idea of a flow diode was proposed to improve the pump coastdown characteristics and the natural circulation path of internal recirculation pumps adopted by the ABWR. The transient behavior occurring in the transition from forced circulation to a natural one was experimentally investigated. The following insights were obtained: 1. An additional natural circulation path will provide a margin for unforeseen transient behavior of flow after pump trip and will avoid the throttling effects that might occur on the internal recirculation pump accepted by the ABWR. 2. According to coastdown period, the transient behavior of flow after pump coastdown will be divided into three transition regions: a. Extremely short coastdown period (shorter than the delay time for boiling). The minimum flow rate induced after the pump trip is dependent on the driving force of natural circulation in the conditions of a coastdown period shorter than 0.1 s. When the initial driving force is negative, the minimum flow rate becomes zero. b. Shorter coastdown period (around the delay time for boiling). This region is more complicated than the others. The initial driving force and the residual flow, which is caused by the deceleration of the pump, influence the flow behavior simultaneously. If the coastdown period is close to an extremely short one, the initial driving force will be superior to residual flow.
Acknowledgments The present work has been performed at the Research Laboratory for Nuclear Reactors, the Tokyo Institute of Technology in collaboration with the Tokyo Electric Power Company. The authors thank ASME for giving permission to reprint this paper.
Appendix A: Nomenclature g H
~n i' q; q "~
P AP
acceleration due to gravity (m S-2) height of riser (m) inlet liquid enthalpy (kJ kg-~) liquid saturated enthalpy (kJ kg-l) heat flux (kW m -2) calorific power per unit volume (kW m -3) system pressure (MPa) pressure drop (kPa)
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275 td
Tin tmin
elapsed time for flow increase (s) inlet temperature (°C) elapsed time for flow decrease to the limit value (s) elapsed time for flow rising to be equal to the circulation rate of a new steady state
(s)
Uin Utrigger
time of starting the experiment (s) elapsed time of response on the natural circulation path (s) initial inlet velocity (m s-~) trigger velocity set in comparator (m s - 1)
Greek letters
zB Pl
delay time for boiling (s) density of liquid (kg m-3)
Subscripts
min steady force true up
minimum value value at steady state initial driving force actual value upward section
275
References M. Aritomi, T. Nakahashi, J.H. Chiang, M. Wataru and M. Mori, Transient behavior of natural circulation for boiling two-phase flow (experimental results), Proc. 6th Nuclear Thermal Hydraulics, ANS 1990 Winter Meeting, Washington, DC, pp. 313-320. M. Aritomi, J.H. Chiang, T. Nakahashi, M. Wataru and M. Mori, Fundamental study on thermo-hydraulics during start-up in natural circulation boiling water reactors, (I) Thermo-hydraulic instabilities, J. Nucl. Sci. Technol. 29(7) (1992a) 631-641. M. Aritomi, J.H. Chiang and M. Moil, Geysering in parallel boiling channels, Proc. Seminar on Two-Phase Flow Dynamics, 1992b, CA, pp. 277-288. J.H. Chiang, M. Aritomi and M. Mori, Fundamental study on thermo-hydraulics during start-up in natural circulation boiling water reactors, (II) Natural circulation oscillation induced by hydrostatic head fluctuation, J. Nucl. Sci. Technol. 30(3) (1993) 203-211. R.J. McCandless and J.R. Redding, Nucl. Eng. Int. 34 (1989) 20. J. March-Leuba et al., Nonlinear dynamic and stability of boiling water reactors, Nucl. Sci. Eng. 93 (1986) 111-123. S.A. Sandoz and S.F. Chen, Trans. Am. Nucl. Soc. 45 (1983) 727. Y. Waaranpera and S. Anderson, Trans. Am. Nucl. Soc. 39 (1981) 868.
Nuclear Engineering and Design 152 (1994) 263-275
Nuclear E neer]ng andD gn
Transient behavior of natural circulation for boiling two-phase flow (flow after pump trip) J i n g - H s i e n C h i a n g a'l, M a s a n o r i
A r i t o m i ~, M i c h i t s u g u
Mori b
aResearch Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-10hokayama, Meguro-ku, Tokyo 152, Japan bTokyo Electric Power Company, I-I-3 Uchisaiwai-cho, Chiyoda-ku, Tokyo 100, Japan
Abstract
The idea of a flow diode has been proposed to improve the pump coastdown characteristics of the internal recirculation pumps adopted by the ABWR. In this paper, the transient behavior from forced to natural circulation was experimentaUy investigated by simulating a pump coastdown condition for the purpose of providing an available source of information that is necessary for designing the flow diode. The results of the study showed that the transient behavior after pump coastdown was influenced by the coastdown period, the trigger velocity and the initial driving force of natural circulation. The potential of each driving factor was governed by the delay time for boiling, which is a very important parameter in natural circulation of boiling two-phase flow. In consequence, a guide for the designing of a flow diode was proposed.
1. Introduction
Nuclear energy is an available major source of electricity generation, which has the potential to provide a substantially increased share of future electricity needs. In the development of nuclear energy, the fast breeder reactor (FBR) is expected to be an evolutionary reactor in the twenty-first century; however, the introduction of commercial FBRs has been held up because of cost-benefit considerations and the availability of plutonium fuel. Therefore, it is likely that light water reactors *This paper is a revised version of the paper originally presented at the Second International Conference on Nuclear Engineering, on March 24, 1993.It receivedreprint permission from ASME. Present address: Japan NUS Co. Ltd., Loop -X Building 7F, 3-9-15 Kaigan, Minato-ku, Tokyo 108, Japan.
(LWRs) will still be a major nuclear source in the early twenty-first century. Development of LWRs is now focused on the enhancement of safety and utility by the introduction of passive functions; the advanced L W R (ALWR) is such an example. In the development and project application of the ALWR, there are several promising conceptual designs, such as the use of the passive functions to replace active ones, selected for the next generation of LWRs. In the meantime, in Japan, the advanced boiling water reactor (ABWR) and the advanced pressurized water reactor (APWR) are foreseen as the next generation of LWRs in the 2010 time frame. The authors have made an effort based on fundamental research to concern themselves with the next generation of BWRs by investigating the transient behavior of natural circulation for boiling two-phase flow. The study has been separated
0029-5493/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSDI 0029-5493(94)00730-M
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J.-H. Chiang et aL / Nuclear Engineering and Design 152 (1994) 263-275
into two fields: the feasibility of natural-circulation BWRs such as the simplified BWR (SBWR) (McCandless, 1989) a n d the sophistication of forced-circulation BWRs such as the ABWR. In the case of the evolution of natural circulation, the thermal hydraulics relating to the SBWR was considered as an objective. First, the authors provided a discussion about the advantages and disadvantages of eliminating the recirculation pumps, and the authors pointed out that thermal hydraulic instabilities might occur according to reactor configuration and start-up procedure (Aritomi, 1990). Next, the instabilities, geysering, natural-circulation oscillation and density-wave instability were observed by conducting simulated experiments under the conditions in insufficient vapor generation. The driving mechanisms of geysering induced by condensation and of naturalcirculation oscillation induced by hydrostatic head fluctuation in long vertical non-heated channels such as a steam separator and divided chimney were clarified experimentally (Aritomi, 1992a,b; Chiang, 1993). Finally, the authors proposed a rational procedure of start-up to prevent the instabilities from occurring, and an effective reactor configuration (Aritomi, 1992b). On the other hand, the authors have focused on the ABWR design to study the dynamic behavior in transition from forced convection to natural circulation. One distinctive feature of the ABWR is that it employs internal recirculation pumps instead of external recirculation pumps used in current BWRs to enhance safety. However, the use of internal pumps may make the pump coastdown characteristics worse and introduce a large throttling effect in the natural circulation path. Since the ABWR design was optimized for 1350 MWe and employed ten internal recirculation pumps, it seemed not to be an issue in this design. To expand the ABWR design into a unit in the power range 600 MWe to 900 MWe and an improvement in simplifying maintenance, it is said that the reduction in the number of internal recirculation pumps can meet the objective. From the fact that the pump coastdown characteristics of the ABWR are worse than those of current BWRs, because of the smaller inertia of the internal pump impeller, it is therefore agreed that the
~ Ive
Natural circulatiOnpa~a
I
~
Flowhole Guide
Pump is working
Seat
Stopper After pump tripped
Fig1.. Concept offlowdiode.
compensating system, to improve the characteristics, will be very complex for a plant with fewer internal recirculation pumps. To address this question, the authors have proposed the idea of the flow diode as shown in Fig. 1. A key feature of the flow diode is that a valve with passive function would serve a natural circulation path with a free throttling effect. It is expected that this idea could ease the current internal recirculation pump that has the worst pump coastdown characteristics and therefore prevent the undesirable event of a "power/flow mismatching" when the pump trip occurs. While the pump is working, the valve is lifted to close the natural circulation path. If the pump unintentionally stops working, the valve will fall when its own weight exceeds what the flowing force can support, thus opening the natural circulation path. To design such a device, the timing of the opening of the natural circulation path is of the utmost importance. In other words, it is necessary to determine what the flow condition is in order to predetermine when the valve should fall. The purpose of this study is to investigate experimentally the dynamic behavior of the flow after pump coastdown for providing the information that would be required by the flow diode design. Experiments were conducted with a loop that could carry boiling fluid in both natural and forced circulation by controlling a "flow-diodelike" valve. An inverter was installed at the pump to provide variable pump speed, which simulated the MG motor used in the ABWR design to control the recirculation flow. The heat input, the
265
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
Fig. 2. The loop could carry boiling fluid in both natural and forced circulation, driven by a centrifugal pump, by switching a flow-diode-like valve. The valve was simulated by a pneumatic valve whose switch was equipped with a relay connected to a comparator that could be used to control the opening/closing of the flow-diode-like valve. A flow control valve, placed downstream of the pump, was used to set the desirable flow rate. A flowmeter was placed between the inlet plenum and flow control valve, which was used to measure the total flow rate. The measured results were fed in parallel to the data acquisition system and the comparator. There was a predetermined value set in the comparator, which
"trigger velocity" to activate a natural circulation path, and the coastdown period were selected as experimental parameters. The means of the flowdiode-like valve and of the trigger velocity are described in the next section.
2. Experimental methods
2. I. Experimental apparatus In order to investigate the transient behavior of natural circulation after the pump trip, an experimental flow loop was constructed as shown in
Data feeding i
II I II
I °a'a I Acqusition
AC source . . . . . . . . .
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Legend : Current : Flow rate : Pressure : Temperature :Volt
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Fig. 2. Experimental apparatus.
.
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.
266
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
was used to compare with the measured results of the total flow rate. Once the measured total flow rate was lower than that of the set value, the comparator would serve as a signal to switch the flow-diode-like valve. That is, the signal controlled the circulated mode of flow, in natural circulation and/or in forced circulation. In this paper, the predetermined value in this comparator is used as a parameter, which is called trigger velocity. To simulate the characteristics of pump coastdown, the pump was equipped with an inverter (within a setting period, 0.1-100 s) for variation of frequency of the pump. Water was used as test fluid. Circulating fluid temperature was achieved through controlling a pre-heater and a cooler that were installed in the separator tank. The twophase mixture leaving the test section was condensed by a c6ndenser installed in the separator tank. The test section comprised a twin parallel channel between the inlet and outlet plenum. Each channel consisted of a heater, a pair of electrodes and an orifice flowmeter for measuring flow fluctuation. The heater rod (6 mm outside diameter, 1 m long) was made of thin stainless steel, and it was installed concentrically in the test section, and was heated by a d.c. power supply. The temperatures of the inlet, outlet and separator tank were measured by CA thermocouples, and the total flow rate was measured upstream of the test section by an orifice flowmeter. The differential pressures between the inlet and outlet plenums and between the outlet plenum and separator tank were measured by differential transducers. All measured data were acquired by a computer-based data acquisition system, which consisted of a data logger (sampling interval, 1 s), an analyzing recorder (sampling interval, 10 ms) and a personal computer. The differential pressures, flow rate, and temperature in the outlet plenum that would vary temporally, were recorded with the analyzing recorder. Temperatures in the inlet plenum and the separator and heat input in the test section were measured with the data logger to control the desirable experimental conditions. All of the acquired data were transferred to the personal computer. The personal computer was connected with the data acquisition recorders, the trigger generator (comparator) and the pump frequency con-
troller (invertor), to play the role of surveillance and regulation to keep the experimental parameters constant during one test.
2.2. Experimentalprocedure From our previous studies on the behavior of natural circulation in parallel channels (Aritomi, 1992b), flow instabilities, geysering and naturalcirculation oscillation would be induced under conditions of insufficient vapor generation. Based on this information, the stable region of natural circulation was selected for the present experiment. Different sets of experiments, corresponding to various heat inputs and trigger velocities, were conducted at one given inlet velocity. In order to clarify the effect of pump coastdown characteristics on transient behavior from forced circulation to a natural one, a series of pump coastdown periods was experimentally investigated in each set of experiments. All experiments were rendered under computer-controlled operation; that is, measured data were monitored in an RGB device, fine adjustment of heat input was achieved through a D/A converter installed via the personal computer to a d.c. power supply. For each trigger velocity, a preliminary experiment was conducted without any heat inputs to figure out the delay time for opening the natural circulation path and to realize the characteristics of flow in the loop. The procedure for actual tests can be outlined as follows: 1. The inlet velocity and circulation fluid temperature in the loop, the coastdown period of the pump, and the trigger velocity in the comparator were set to the desired value. 2. Heat input increased gradually to the desired value, and the system was allowed to become steady enough, as indicated by the recording and monitoring system. 3. Once the system was confirmed to ~e in a steady state, the data acquisition system started to record the measuring data. Simultaneously, a signal was sent to trigger the invertor to decelerate the pump operation. 4. After the flow rate regained a steady enough level, the test was completed.
J.-H. Chiang et al. [ Nuclear Engineering and Design 152 (1994) 263-275
0.8
Table 1 Experimental conditions Test fluid System pressure Inlet temperature Heat flux Length of riser Inlet velocity P u m p coastdown period Trigger velocity
Water Atmospheric pressure 90°C 2 0 0 - 4 0 0 k W m -2 250 m m 0.5-0.6 m s -1 0.1-30 s 0.25-0.56 m s -t
I
I
Pump coastdown
267
I
~
i
Decelerationtime3 sac MeasuredTemperature: 29 °C q" = 0 kW/m2
"-" "~ --
~ n = 0'60 m/s
~
~~ii
gger velOcity0'56 m/s
0.4 .o
g Table 2 Accuracies for measurements Differential pressure Flow rate Temperature Heat flux
+ 0.15 kPa _0.01 m s -1 +0.5 K +2.5 k W m -2
I
0
I
I
2
I
4
I
6
Time (s) Fig. 3. Typical flow changes after pump coastdown without heat input.
As for the reproducibility of a test, the data were obtained by repeating the test under the same conditions three to five times. The experimental conditions are summarized in Table 1, and the accuracies for the measurements are tabulated in Table 2.
3. Results and discussion
3.1. Characteristics of pump coastdown and natural circulation path In the preliminary experiment, the behavior of flow after the opening of the natural circulation path was studied without any heat inputs. Fig. 3 shows a typical result of the changes in flow after pump coastdown. The dashed line is the change without opening the natural circulation path under the deceleration of the pump. The solid line is the change while the natural circulation path was opening. Here, the trigger velocity is 0.56 m s- t as shown in the figure. This means that the natural circulation path was opened at the point when the total flow rate was lower than that predetermined value, 0.56 m s-1, in the comparator. It can be seen from the figure that the flow was rapidly reduced when the natural circulation path opened. This flow reduction was caused when flow reversal
occurred in the natural circulation path. The pump would not stop immediately until the coastdown period was reached, even if the natural circulation path opened. The coastdown pumping was responsible for the flow reversal. Consequently, the resulting flow to the total flow rate in the test section was reduced owing to the flow reversal. Another preliminary test was conducted to examine the opening time of the natural circulation path for a given predetermined value of trigger velocity after the pump started the decelerating operation. Fig. 4 shows the "delay time for opening natural circulation path" vs. the coastdown period for various trigger velocities. The delay time for opening the natural circulation path was evaluated by the time difference from the time of starting coastdown to the time of opening the flow-diode valve. For a given circulating rate, if the trigger velocity in the comparator is set at a higher value then the natural circulation path will open more quickly. The results shown in the figure give the response time of the flow-diode-like valve and are useful to find a suitable trigger velocity setting. Fig. 5 demonstrates the typical measured results of the pump coastdown experiment with heat input, by means of the changes in the differential
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
268
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........
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........
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Q. t--
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10 1
10 2
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¢O
P = 0.10 MPa
0
1~0
210
j
30
Time (s)
Fig. 5. Typical measured result of experiment. pressure of the riser section and in the circulation rate. The APup is defined from the true differential pressure, between the inlet plenum and separator tank, minus the hydrostatic head, i.e. A P , p = APtrue -- pigH. This is because the differential pressure between the inlet plenum and separator tank had been reset to zero before the experiment started. The symbols ts and t t mean the time of starting the experiment
and the time of response on the natural circulation path respectively. The symbol tmin is the time when flow decreased to a limit value, referred to as "minimum velocity". The remaining symbols td and t r are the time when flow became increased, and the time when flow rose to be equal to the circulation rate of a steady state Usteady , respectively. The differential pressure Psteady and the circulation rate Usteady a r e the values at which the system reached another steady state. The utngger is the trigger velocity set in the comparator. In all of the experiments, the dynamic behavior of the flow was almost the same as shown in Fig. 5; observed differences appeared only in the timing of each occurring aspect and on the value of minimum velocity. In addition, when the new steady state was obtained, the esteady and Ust~,dywere independent to the extent of the experimental conditions used in the present study. The dynamic behavior of flow as shown in Fig. 5 is considered as follows. The circulation rate becomes decreased when the pump starts its decelerating operation at the time ts, and the differential pressure scarcely fluctuates by that time. Again, the differential pressure shown in Fig. 5 is the resultant pressure drop between the inlet plenum and the separator tank. When the natural circulation path is opened at the setting trigger velocity, Utngg~r,the flow continues decreasing. This decrease is caused by the flow reversal occurrence in the natural circulation path as mentioned above. Subsequently, the flow reaches the minimum velocity Umin at the time tmin. After that, no specific changes in the flow rate appear till the pressure drop of the riser section becomes decreased at the time td. For low flow rates in the upward boiling system, the head drop is expected to be dominant over the friction and acceleration drops. Consequently, the increase in void fraction results in a decrease in head drop to make the total driving force become increased. Accordingly, the flow rate begins to turn up toward recovery when the pressure drop decreases. Finally, a new steady state of natural circulation is obtained.
3.2. Minimum velocity The minimum velocity is a very important criterion for the margin of safety of a heated system.
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
0.4
. . . . . . . .
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. . . . . . . .
'
. . . . . . .
P = 0.10 MPa
.
Tin = 90 °C Uin = 0.60 m/s Utrigger = 0.34 m/s o 220 kW/m 2 q" : ~ 230 kW/m 2
101
°y
E v 0.2 ~_ E
=J:] ~ / D ' B
/ _
/
10 -1
Tin = 90 °C P = 0.10 MPa
q" = 230 kW/m2 uin = 0.60 m/s
,
1CI -1
i
i
i
Jill]
i
10 0
i
. . . . . .
I
. . . . . . .
101
10 2
Coastdown period (s)
~
10
i
2
i i illtll
I
i
i .....
J
........
I
. . . . . .
10-1 100 101 Coastdown pedod (s)
102
Fig. 6. Effect of pump coastdown period on minimum velocity.
Fig. 7. Relationship between minimum velocity and coastdown period.
The BWR is especially susceptible to reactivity instabilities when operated at a low flow condition according to results of stability tests (Waaranpera, 1981; Sandoz, 1983) and numerical analysis (March-Leuba, 1986). To design the flow diode, therefore, the function of providing a rational minimum velocity should be established. In order to understand the effects of the coastdown period on transient behavior of flow, the minimum velocity corresponding to the coastdown period was investigated by using various heat inputs. Fig. 6 shows a typical relationship between the minimum velocity and coastdown period. Overall, the minimum velocities increased with an increase in the coastdown period. In addition, it seems that the tendency of an increase in the minimum velocity was separable by a turning point (coastdown period between 3 and 10 s): a smooth increase in shorter coastdown periods and a rapid one in longer coastdown periods. Further, when the coastdown period was set long enough, the minimum velocity had reached the trigger velocity in this case. The same tendency was observed at other heat inputs, although higher heat inputs induced moderately higher minimum velocity. The time when the circulation rate dropped down to a minimum value for various heat inputs is shown in Fig. 7. It indicates
that tmin only depends on coastdown period. If we make a comparison between the trnin and the tt, as shown in Fig. 4, we will find that train is very close to tt. The difference was caused by the flow reversal as mentioned earlier. This means that the t,ni, can be controlled by manipulating the coastdown period. The uncertainty of the minimum velocities shown in the figures was estimated within ___10%.
3.3. Driving force for natural circulation Another important parameter, driving force, is also dominant in the system under natural-circulation operation. The initial driving force for natural circulation is commonly defined by: APforc e = APdown - APup
(1)
where APdown, AP,p are the pressure drops in the downcomer and the riser section respectively (Aritomi, 1990). In this study, the experiments were conducted from forced circulation to a natural one, and the system had still been in forced circulation operation before the natural circulation path responded. Therefore, the initial driving force for natural circulation was calculated by the measured pressure detected at the point, tt, using the above definition. A typical result of driving force
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
270
m
a.
6
. . . . . . . . '"1
. . . . . . . .
I
. . . . . . . .
I
I
Pump coa~down
v
I
. . . . . . .
I
- Pump coastdown
t-
.o o
4
- P = 0.10 M P a Tin = 90 ° C = 0.34 m/s Uqt.rigge2r30 = kW/m2
o
o
Uin = 0.60 m/s
c
.-t
~o o
E
0
"~ I
2
P = 0.10 M P a
1 I~'Tin = 90 °C ~-q" = 230 kW/m2 I Uin = 0.60 m/s Uugger = 0.34 m/s
\ \ o
o~ ¢..
I
I , [
10 -+
. . . . . . . .
l
. . . . . . . .
I
. . . . . . . .
100 101 Coastdown period (s)
l
102
Fig. 8. Effect of pump coastdown period on driving force.
vs. coastdown period is shown in Fig. 8. From the figure, driving force increases slowly with an increasing coastdown period at shorter coastdown periods, but it increases dramatically when the periods pass over the turning point (the same as Fig. 6). Generally, in the natural circulation loop the driving force is directly related to the vapor generation in the boiling channel. To gain a relatively larger driving force requires a sufficient boiling condition in the heated channel. From the figure of dynamic behavior of flow, as shown in Fig. 5, we can find that the flow rate does not change availably around the minimum value of the circulation rate for a while. This aspect indicates that boiling in the heated channel was insufficient to contribute additional driving force. Fig. 9 shows a result of the arrangement of the "delay time for flow recovery" vs. the coastdown period. Delay time for flow recovery was calculated from the time difference between the time that flow begins to increase at available circulation rate, ta, and the time of natural circulation path opening, t t. The figure indicating the delay time for flow recovery is clarified into two categories: smoothly decreased and rapidly decreased, corresponding to the coastdown period. It is considered that the thermal response of the flow in the heated channel dominates in contributing to
1~_ 1 . . . . . . i'O0 . . . . 101 Coastdown period (s)
02
Fig. 9. Delay time for flow recovery vs. pump coastdown period.
the driving force. In other words, these results indicate that the opening of the natural circulation path would be unable to gain a large driving force until the circulating fluid reached the saturated condition. It is supposed that the thermal response time will be the turning point we have sought after. Therefore, we introduced a parameter which is the delay time f o r boiling to find out the turning point. Delay time for boiling was quoted from the authors' previous work (Aritomi, 1990), and it was defined by z B = p](i' -- i i , ) / q "
(2)
where q" is the calorific power per unit volume, p~ is the liquid density, i' is the liquid saturated enthalpy and ii, is the inlet liquid enthalpy. Delay time for boiling for the conditions shown in Figs. 6 to 9 was 1.86 s; using this 1.86 s as the opening time for the natural circulation path, the coastdown period can be calculated from the relationship shown in Fig. 4 to be 5 s. Further, the relationship between the delay time for boiling and the delay time for flow recovering at various heat flux values is shown in Fig. 10. A correlation can be found between both. Therefore, the delay time for boiling may be a good judge of what is a suitable coastdown period. From Figs. 6 to 10, the following circumstances are significant.
271
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275 i
i
i
i
i
i
+
i
i
I
i
i
I
i
i
i
i
i
0.6
~,/
I
i
F
1
I
Pump coastdown
Pump coast(down P = 0.10 MPa Tin = 90 °C ui. = 0.60 m/s Utrigger= 0.34 m/s
j
-.....
._c
Coastdown period = 0.1 s 0 . 4 = P = 0.10 MPa Tin = 90 eC Uin = 0.60 m/s
/ / +
E
~ 1,
I
I
l
11
.= 0 . 2 -sE
/
O"
nm ~xo
I
I
IdylL
/"
o 220 kW/m 2 q" : A 230 kW/m 2 [] 240 kW/m 2
L
I
I
Delay time for boiling
I
I
t
11
. . . .
3
(s)
0 . . . . .
-0.2 5 t L -4-3-2-1
,
O"
t
- --0
I
0
t
1
,
2
,
3
I
4
5
Initial d r i v i n g f o r c e f o r n a t u r a l c i r c u l a t i o n ( k P a )
Fig. 10. Relationship between delay time for flow recovery and delay time for boiling.
Fig. 11. Relationship between minimum velocityand driving force for extremelyshort pump coastdown period.
In a longer coastdown period, after the pump has begun its decelerating operation, the boiling in the heated section is enhanced due to a decreasing flow rate. A large amount of vapor will be generated, causing a decrease in the hydrostatic head; consequently, the driving force becomes larger at the time the natural circulation path is opened. Conversely, the shorter coastdown period will not allow too much vapor to be induced because the natural circulation path is opened quickly (here the opening times were within 0.01 to 1.15 s), so the driving force for it should be mainly contributed by the initial driving force of natural circulation.
is shown in Fig. 11. It can be seen from the figure that the minimum velocity becomes zero for negative initial driving forces, but not for positive ones, and that it increases with an increase in the positive ones. This investigation is in agreement with the results concluded by the previous work. Under the condition that the pump stopped instantly, there is no longer any extra force to act on the flow except for the initial driving force. However, in a longer pump coastdown period, the pump does not instantly stop operation, i.e. the flow rate induced by the decelerating operation of the pump is still available when the natural circulation path is activated. Therefore, the effect of a higher trigger velocity will become more apparent in the longer coastdown period. Fig. 12, for example, shows the minimum velocity in relation to trigger velocity at a coastdown period of 3 s. Here, the Uste,dyis used to make the minimum velocity dimensionless, because the Usteady is independent of various conditions as mentioned before. The figure indicates that the minimum velocity became higher with the increasing of the trigger velocity. By the same conditions, the relationship between the driving force and trigger velocity is shown in Fig. 13. Similarly, the P~te,dy is also used to make a dimensionless arrangement. It can be seen that the driving force of
3.4. Minimum velocity and driving force for natural circulation
From the previous study (Aritomi, 1990), the minimum velocity appearing in a transient process where the pump trip occurred was dependent upon the initial driving force of natural circulation and did not show an evident difference between various trigger velocities. Note that the pump speed had not been controlled in those cases, i.e. the pump was stopped immediately. The relationship between the initial driving force and the minimum velocity for coastdown period 0.1 s
272
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275
1.2
l
I
I
i
I
Pump coastdown
/
_ Coastdown period = 3 s P = 0.10 MPa ,~1 Tin = 90 °C >, 0 . 8 - q ' = 230 RW/m 2
/
/
! E
= 0.4
I
0
I
I
O.4
I
I"
O.8
1.2
Utrigger / Usteady ( - )
Fig. 12. Effect of trigger velocity on minimum velocity for a shorter coastdown period.
1.2
u
I
Pump countdown - Coastdown period = 3 s P = 0.10 MPa Tin = 90 °C ~ 0 . 8 - q" = 230 kW/m 2 ¢= I
pump is still working when the natural circulation path is opened, the flow rate in the circulation loop will be higher at a higher trigger velocity, then the resulting minimum velocity as shown in Fig. 12 is the resultant of the initial driving force and the residual flow driven by the pump. It is the reason why the driving force decreases but the minimum velocity increases with an increase in trigger velocity. The difference of driving force and/or minimum velocity shown in Figs. 12 and 13 are not significantly obvious. Fig. 14 shows the relationship between the initial driving force and the minimum velocity obtained for coastdown periods within 0.1-3 s. Although some deviations can be seen, it seems that the correlation found from Fig. 11 is still available in the coastdown period up to 3 s. The deviation appearing in Fig. 14 is expected to be affected by different trigger velocities. It is then significant that in short-life transition of pump trip and/or pump coastdown, the transient behavior is dependent upon the driving force of natural circulation at the time of opening of the natural circulation path. This fact helps to postulate that the transient behavior of flow after the pump trip could be classified into (a) transition in short coastdown period and (b) transition in long coast-
Uin = 0.60 m/s
I1.
<1 0.6
d
i
,
i
I
Pump coastdown
0.4
<1
P = 0.10 MPa
0.4 -Tin = 90°C I
0
I
0.4
I
l
0.8
I
1.2
Utrigger / Usteady ( - )
v
E .~ 0.2
Uin = 0.60 m/s Coastdown period o0.1s A 1.0s o 3.0s
o,/
E
Fig. 13. Effect of trigger velocity on driving force for a short coastdown period.
O" /" /" ....
natural circulation somewhat decreased when the trigger velocity was increased. It can be explained that, if the natural circulation path opens at a high trigger velocity, the change in the pressure drop of the riser will be small. It seems to be inconsistent with the investigation on minimum velocity, shown in Fig. 12. If we consider that the
0 .....
- 0 " 9"-5 - ' - ' 34- L - ' 1
2
0.---0
0'
1'
2'
3'
4'
5
Driving force for natural circulation (kPa) Fig. 14. Relationship between minimum velocity and driving force for short coastdown periods.
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275 0.6
i
i
i
i
[
I
i
1.2
I
I
273
i
i
I
Pump coastdown o
Pump coastdown
O A
0.4
P = 0.10 MPa Tin = 90 °C
o~
ui, = 0.60 m/s
~ ~ o
I
P = 0.10 MPa Tin = 90 °C 0 . 8 -q" = 230 kW/m2 uin = 0.60 m/s EL
~
¢:)
E
._= 0.2
z~
O
o
a
O
t~
%
E
88
O
o 0.4 EL 0
O
O
O
,, 10.0s Coastdown period : o 20.0 s o 30.0 s -0.2 5 ' i I -'4-3-2-1
i
I 0
, 1
, 2
i 3
D r i v i n g f o r c e for n a t u r a l c i r c u l a t i o n
, 4
I
/
0
5
down period, and the judgment may be based on the delay time for boiling. To verify this postulate, furthermore, the same arrangement as in Fig. 14, plus longer coastdown periods, with various trigger velocities is shown in Fig. 15. A correlation is no longer to be found between these. Obviously, both the coastdown period and the trigger velocity influence the transient behavior of flow in a longer pump coastdown period. For a longer coastdown period, on the other hand, the driving forces as a function of trigger velocity are shown in Fig. 16. Obviously, for the same coastdown period, the driving force decreased with increasing trigger velocity. At lower trigger velocity the longer-period cases gained a large driving force, but at higher trigger velocity the driving force no longer changed with the coastdown period, as shown in the figure. From Fig. 4, we know a higher trigger velocity opened the path more quickly than a lower one for the same coastdown period. Fig. 17 shows the minimum velocity vs. the trigger velocity for a longer coastdown period. It is made clear that at lower trigger velocity the minimum velocity is closer to trigger velocity as long as the pump coastdown period is long, but when the trigger velocity is set beyond a certain value the minimum velocity starts to decrease. From this investigation, we
I
I
0.8
1.2
Utrigger / Usteady (-)
(kPa)
Fig. 15. Relationship between minimum velocity and driving force for various coastdown periods.
I
0.4
Fig. 16. Effect of trigger velocity on driving force for long coastdown periods.
1.2
i
i
i
i
Pump coastdown A
P = 0.10 MPa
"
T,o = 90 °c
i
/
~"
0.8 q = 230kW/m 2 •~ U,n = 0.60 m/s
~ /~
o t~ 9
[]
zx 10.0S °
"1o
g
._
E = 0.4
~
0
L
:
~
coa L
0.4
o,
por,od : ° I
|
O,8
:os
1.2
Utrigger / Usteady (-) Fig. 17. Effect of trigger velocity on minimum velocity for long coastdown periods.
then know that if the trigger velocity is set at an excessively high value, the minimum velocity will no longer be higher than the steady circulation rate u~teady, regardless of coastdown period, because the minimum velocity would be unable to rise higher than the steady circulation rate. To design the flow diode, it is desirable that the minimum velocity be as close as possible to the
274
J.-H. Chiang et aL / Nuclear Engineering and Design 152 (1994) 263-275
setting trigger velocity for the effective handling of the transient behavior after pump coastdown. From the investigations, it can be found that a trigger velocity about 0.5-0.8uste~dy and a coastdown period about 1.0-2.0 times the delay time for boiling will provide a rational minimum velocity and a quick flow recovery time. However, this suggestion does not indicate that there is only one way to design the flow diode. Nevertheless, it indicates a method of decision for designing the flow diode.
c. Longer coastdown period (longer than the delay time for boiling). Even a longer coastdown period will allow a large amount of vapor to be generated in the heated section to induce large driving force. Therefore, a longer coastdown period can promote a minimum velocity as high as the setting trigger velocity. . Although a higher trigger velocity will produce greater flow rates than a shorter one in the circulation loop, it will need a longer time for flow recovery. In contrast, a lower trigger velocity will cause quick flow recovery, but the minimum velocity will become lower. . The delay time for boiling greatly influences transient behavior of natural circulation after pump coastdown. . The natural circulation path of the flow diode should be designed to be opened before the flow rate has reached about half the velocity in a steady natural circulation. However, a much higher trigger velocity will cause the delay time for flow recovery to become longer, so it is logical to set a suitable trigger velocity and pump coastdown period with consideration of the delay time for boiling.
4. Conclusions The idea of a flow diode was proposed to improve the pump coastdown characteristics and the natural circulation path of internal recirculation pumps adopted by the ABWR. The transient behavior occurring in the transition from forced circulation to a natural one was experimentally investigated. The following insights were obtained: 1. An additional natural circulation path will provide a margin for unforeseen transient behavior of flow after pump trip and will avoid the throttling effects that might occur on the internal recirculation pump accepted by the ABWR. 2. According to coastdown period, the transient behavior of flow after pump coastdown will be divided into three transition regions: a. Extremely short coastdown period (shorter than the delay time for boiling). The minimum flow rate induced after the pump trip is dependent on the driving force of natural circulation in the conditions of a coastdown period shorter than 0.1 s. When the initial driving force is negative, the minimum flow rate becomes zero. b. Shorter coastdown period (around the delay time for boiling). This region is more complicated than the others. The initial driving force and the residual flow, which is caused by the deceleration of the pump, influence the flow behavior simultaneously. If the coastdown period is close to an extremely short one, the initial driving force will be superior to residual flow.
Acknowledgments The present work has been performed at the Research Laboratory for Nuclear Reactors, the Tokyo Institute of Technology in collaboration with the Tokyo Electric Power Company. The authors thank ASME for giving permission to reprint this paper.
Appendix A: Nomenclature g H
~n i' q; q "~
P AP
acceleration due to gravity (m S-2) height of riser (m) inlet liquid enthalpy (kJ kg-~) liquid saturated enthalpy (kJ kg-l) heat flux (kW m -2) calorific power per unit volume (kW m -3) system pressure (MPa) pressure drop (kPa)
J.-H. Chiang et al. / Nuclear Engineering and Design 152 (1994) 263-275 td
Tin tmin
elapsed time for flow increase (s) inlet temperature (°C) elapsed time for flow decrease to the limit value (s) elapsed time for flow rising to be equal to the circulation rate of a new steady state
(s)
Uin Utrigger
time of starting the experiment (s) elapsed time of response on the natural circulation path (s) initial inlet velocity (m s-~) trigger velocity set in comparator (m s - 1)
Greek letters
zB Pl
delay time for boiling (s) density of liquid (kg m-3)
Subscripts
min steady force true up
minimum value value at steady state initial driving force actual value upward section
275
References M. Aritomi, T. Nakahashi, J.H. Chiang, M. Wataru and M. Mori, Transient behavior of natural circulation for boiling two-phase flow (experimental results), Proc. 6th Nuclear Thermal Hydraulics, ANS 1990 Winter Meeting, Washington, DC, pp. 313-320. M. Aritomi, J.H. Chiang, T. Nakahashi, M. Wataru and M. Mori, Fundamental study on thermo-hydraulics during start-up in natural circulation boiling water reactors, (I) Thermo-hydraulic instabilities, J. Nucl. Sci. Technol. 29(7) (1992a) 631-641. M. Aritomi, J.H. Chiang and M. Moil, Geysering in parallel boiling channels, Proc. Seminar on Two-Phase Flow Dynamics, 1992b, CA, pp. 277-288. J.H. Chiang, M. Aritomi and M. Mori, Fundamental study on thermo-hydraulics during start-up in natural circulation boiling water reactors, (II) Natural circulation oscillation induced by hydrostatic head fluctuation, J. Nucl. Sci. Technol. 30(3) (1993) 203-211. R.J. McCandless and J.R. Redding, Nucl. Eng. Int. 34 (1989) 20. J. March-Leuba et al., Nonlinear dynamic and stability of boiling water reactors, Nucl. Sci. Eng. 93 (1986) 111-123. S.A. Sandoz and S.F. Chen, Trans. Am. Nucl. Soc. 45 (1983) 727. Y. Waaranpera and S. Anderson, Trans. Am. Nucl. Soc. 39 (1981) 868.