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Experimental study on fundamental phenomena in HTGR small break air-ingress accident
Annals of Nuclear Energy 87 (2016) 145–156
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Experimental study on fundamental phenomena in HTGR small break air-ingress accident Jae Soon Kim a, Jin-Seok Hwang a, Eung Soo Kim a,⇑, Byung Jun Kim b, Chang Ho Oh c a
Department of Nuclear Engineering, Seoul National University, Daehak-dong, Gwanak-gu, Seoul 151-742, Republic of Korea Korea Institute of Industry Technology, 618-230 Kangsu-gu, Busan, South Korea c Idaho National Laboratory, 2525 N. Fremont Ave., Idaho Falls, ID 83415, USA b
a r t i c l e
i n f o
Article history: Received 1 March 2015 Received in revised form 4 August 2015 Accepted 9 August 2015 Available online 9 September 2015 Keywords: HTGR Air ingress Small break Density gradient driven flow
a b s t r a c t This study experimentally investigates fundamental phenomena in the HTGR small break air-ingress accident. Several important parameters including density ratio, break angle, break size, and main flow velocity are considered in the measurement and the analysis. The test-section is made of a circular pipe with small holes drilled around the surface and it is installed in the helium/air flow circulation loop. Oxygen concentrations and flow rates are recorded during the tests with fixed break angles, break sizes, and flow velocities for measurement of the air-ingress rates. According to the experimental results, the higher density difference leads to the higher rates of air-ingress with large sensitivity of the break angles. It is also found that the break angle significantly affects the air-ingress rates, which is gradually increased from 0° to 120° and suddenly decreased to 180°. The minimum air ingress rate is found at 0° and the maximum, at 110°. The air-ingress rate increases with the break size due to the increased flow-exchange area. However, it is not directly proportional to the break area due to the complexity of the phenomena. The increased flow velocity in the channel inside enhances the air-ingress process. However, among all the parameters, the main flow velocity exhibits the lowest effect on this process. In this study, the Froude Number relevant to the small break air-ingress conditions are newly defined considering both heavy and light fluids, and break angles. Based on this definition, the experimental data can be well rearranged and collected. Finally, this study develops and proposes a non-dimensional parameter and a criteria for determination of the small break air-ingress flow regimes. As a result, the non-dimensional parameter higher than 0.49 indicates that the air-ingress is mainly controlled by density gradient effect. On the other hand, that lower than 0.47 indicates that the other effects such as inertia or diffusion are dominant air-ingress mechanisms. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction A high temperature gas cooled reactor (HTGR) is a Gen-IV reactor concept incorporating high temperature, graphite-moderated, uranium-fueled, helium-cooled features for high efficiency, safety, and usability (GA, 1996); Schultz et al., 2006; Melse and Katz, 1984). The HTGR technology has been studied and developed since the 1950s and it exhibits several advantages over light water reactors including fuel integrity, proliferation resistance, a relatively simple fuel cycle, easy refueling, and modularity to supply electricity to remote areas. Even though gas reactors have been developed in the past with limited success, the innovations of modularity and integrated state-of-the-art safety systems make the HTGR design attractive from technical and economic perspectives. ⇑ Corresponding author. E-mail address: [email protected] (E.S. Kim). http://dx.doi.org/10.1016/j.anucene.2015.08.012 0306-4549/Ó 2015 Elsevier Ltd. All rights reserved.
In spite of its inherent safety features, the HTGR concept could be detrimental if a loss of coolant accident (LOCA) occurs that results in depressurization and potential air-ingress issues related with various physical/chemical phenomena (ORNL (2007); Schultz, 2008; Oh et al., 2006, 2010). This LOCA could lead to oxidation of the in-core graphite structure and the fuel, which will accelerate heat-up of the reactor core and lead to the release of toxic gasses (CO and CO2) and fission products. Therefore, without effective countermeasures, a pipe break may lead to significant fuel damage and fission product release depending on the reactor design, break locations, and break orientations. The most recent researches on the air-ingress accident phenomena were performed and reported by Idaho National Laboratory (Oh et al., 2006, 2010). In their researches, an air-ingress scenario based on density gradient driven flow were newly proposed (Oh et al., 2010), which consists of four steps. Based on extensive CFD analyses, it was shown that the density gradient driven stratified
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flow is the dominant air-ingress mechanism regardless of the accident scenarios. Characteristics of natural circulation were also investigated by Oh and Kim (2012) in the post onset-naturalcirculation (ONC). This study showed that a natural circulation pattern consists of two flow paths and a recirculation flow rapidly drives air into the reactor vessel. An estimated air-ingress rates from 3-D CFD simulations were about an order of magnitude faster than that estimated by a 1-D system code. It indicated that the air ingress modeling should be conducted on multi-dimensional basis. Even though many researches were previously conducted for the air-ingress accident in the HTGR, they mostly focused on a double-ended guillotine break (DEGB) scenario, where the inside and the outside connecting vessels are ruptured simultaneously (Hishida et al., 1993; Xiaowei et al., 2004; INET (2006); Oh et al., 2006; KAERI, 2011). It is based on the basic assumption that the DEGB would cause highest air-ingress into the reactor and therefore it could result in the most serious consequences. However, there have been some recent discussions that a small break or leak is a much more probable accident in reality than the DEGB, and therefore this accident scenario should be also importantly considered. From this motivation, the present study is focusing on airingress phenomena that expected to occur under much smaller break accident like SBLOCA in a light water reactor (LWR). There is no clear definition on the small break accident in the HTGR, but it is generally considered to be an accident whose break size is less than 1/2 inch according to Next Generation Nuclear Plant Method Technical Program Plan (Schultz et al. (2006)). Currently, the detailed situations for the small-break are not well defined and identified yet in the existing Phenomena Identification and Ranking Tables (PIRTs). However, it is obvious that the probability of the small-break is much higher than the double-endedguillotine-break (DEGB). The possible small-break locations are coolant pipes, control rod guide tubes, instrumentation lines, heat exchanger tubes, and etc. in the primary side. Previously, few researches were carried out on the HTGR small break phenomena. Oh et al. (2010) conducted simple CFD simulations in order to understand basic phenomena. Comparing to the DEGB scenario, the most important aspect observed in the small break situation is that the flow characteristics are highly dependent on the break angles. According to their research, the flow phenomena can be divided into three regimes as shows in Fig. 1. Molecular diffusion is identified as the first flow regime. It is observed when the break is at the bottom. In this case, gravitational force keeps the air from mixing with the helium through either of the second two regimes. For this reason, only diffusion governs the exchange of helium and air. The second flow regime identified is density gradient driven stratified flow. It occurs when the break is somewhere on the side. In this case, heavier fluid flows into the lower part of the hole as a counter current manner, stratified with the lighter fluid exiting in the upper portion like shown
in the DEGB scenario. An unstable gravity-driven flow, observed when the break angle of around 180°, is the last flow regime identified. In this case, the helium exit flow is counter currently chocked with the air inlet flow. The air flow rate is not constant and will be much smaller than that in the second flow regime. Although some computational works have been previously conducted to visualize small break situations, no quantitative experimental data are now available for supporting these numerical results. From this reason, this study attempts to quantitatively measure the air-ingress rates in a small break for various flow and break conditions. Several parameters including break angle, break size, density ratio, and main flow velocity are importantly taken into account. The main objectives of this study is (1) to understand fundamental phenomena and air-ingress characteristics in the HTGR small break accident and (2) to develop a quantitative measure to determine different flow regimes.
2. Experimental loop Fig. 2 shows a schematic of the SNU small break air-ingress experimental loop which consists of the following five parts: Test section: the test section is made of a circular pipe (4 inch) with several holes around it for mimicking a small break situation in the HTGR. During the experiment, all holes except for one are closed. The test-section is made of stainless steel, and nylon caps are used to plug the holes. Circulator: the circulator flows air/helium mixture in the test loop. The circulator speed is adjustable. The circulator is designed to provide the same volumetric flows regardless of types of mixtures. Mixing tank: the mixing tank is designed to stabilize flow and enhances mixing of it. This mixing tank also contains a circulator and various instrument devices including a thermocouple, a pressure transducer, a pressure gauge, and an oxygen sensor. The mixing tank is made of acrylic. Flowmeter: the flow meter measures the flow rates of the working fluids (mainly helium). Since the mixture concentrations are changing during the experiment, the flow velocity are also separately measured using an optical technique. Oxygen sensor: two oxygen sensors measure oxygen concentrations (0–25%) in the helium/air mixture flow. These oxygen sensors are installed in the mixing tank and at the entry of the testsection, respectively. This experiment uses zirconia based sensors commercially available. The test-loop is initially filled with helium gas, and the flow is generated by a circulator. If the flow is stabilized and the system reaches a steady-state condition, a cap on the test-section is un-
Fig. 1. Three different regimes created depending on the break angle of the hole (Oh et al., 2010).
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Fig. 2. Schematic of small break air-ingress experimental facility.
Fig. 3. SNU small break air-ingress experiment set-up.
plugged to initiate air-ingress into the loop. During the experiment, oxygen concentrations, flow rates, temperatures, and pressures are monitored and recorded by a data acquisition system (DAS) and Labview software. The experiment is conducted at room temperature and atmospheric pressure by simplification. Therefore, the effect of temperature on the air-ingress needs to be further investigated in the future. Fig. 3 shows the SNU small break air-ingress experimental set-up. Fig. 4 shows the test-section, which is made of a 4 inch cylindrical pipe on which various small holes are drilled. In order to reflect various small break conditions, separate replaceable test-sections with different size holes and angles are made. The test conditions
are as summarized in Table 1. Five different hole-sizes are considered: 3 mm, 6 mm, 12 mm, 15 mm, and 18 mm. Each hole-size has seven different break angles from bottom (0°) to top (180°). Three flow velocities (0.27 m/s, 0.43 m/s, 0.37 m/s) and five oxygen concentration levels (3%, 8%, 12%, 16%, 18%) are selected. This study assumes isothermal condition while the reactor is heated in the real accident situation. In the small break situation, the heating effect is important since it affects the density of the fluids at the break which can be determined by the temperature and the pressure in the reactor inside. This study conducted the experiment on wide ranges of density ratios from 0.25 to 0.85, which covers most of the possible fluid conditions during the small break
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Fig. 4. Test-section and breaks (holes).
Table 1 Experimental Conditions. Parameters
Test conditions
Temperature Pressure Hole diameter (dhole) Break angle (u) Flow velocity (Uinside) Oxygen concentration (C O2 )
25 °C 1.0 atm 3, 6, 12, 15, 18 mm 0°, 30°, 60°, 90°, 120°, 150°, 180° 0.27, 0.37, 0.43 m/s 3%, 8%, 12%, 16%, 18%
accident. Therefore, it can be considered that the heating effect is somewhat reflected in the current experimental conditions. However, since the local temperature distribution in the reactor can affect the small break process, the further study is obviously necessary to investigate it. According to the literature⁄ (Schultz et al. (2006)), any breaks under 1/2 inch are generally regarded as a small break⁄. The break angle can be any directions from downward (0°) to upward (180°). This study maintained the break sizes and the angles compared to the real prototype. However, the test-section diameter was reduced to 10 cm diameter replicating small break probable pipes. Since the small-break air-ingress is a local phenomenon mainly affected by a break size and angle, this experiment is considered to maintain the key parameters with the prototype. Because of the fractions of the gas mixture are continuously changed, it is hard to determine gas velocity precisely. So this study used Particle Image Velocimetry (PIV) to measure the velocity in the test-section by replacing a certain section with a transparent material with injecting smoke into the loop. Smoke is generated by a commercial smoke generator. A continuous laser sheet made smoke particle easily visible on high-speed camera. Velocity was averaged and its uncertainty is an order of under 0.01 m/s. 3. Data analysis method In this experiment, the oxygen concentrations are collected and used as the final results. The types of the oxygen sensors are electrochemical partial oxygen pressure sensors with an accuracy of ±0.1%. A data acquisition system collected oxygen concentrations
at every single second. Since the timescale of the gas concentration change is very small, 1.0 s is sufficient to capture the slight changes with high quality. Fig. 5 shows the raw data of a sample test case (angle = 90°, dhole = 12 mm, Uinside = 0.37 m/s). In this study, the experiment was conducted under a couple of fixed oxygen concentration levels near 3%, 8%, 12%, 16%, 18% in order to effectively reduce total experiment time. Initially, the loop was filled with air/helium mixture with the lowest helium concentration and the steady-state condition was reached in a couple of minutes. Then, a cap was unplugged and air is introduced into the test section. After airingress data was sufficiently collected (25 min per each oxygen concentration level), the test-section was intentionally purged with air in order to increase air concentration in the loop up to the pre-defined level (i.e. 3–8%, 8–12%). One of the two oxygen sensors placed near to purge line (air injection line) and therefore the peak in Fig. 5 was monitored when the purge was started. After the purge line was closed, the air was mixed with the existing gas and the peak was reduced to a certain value. In order to analyze the data, the raw data is sliced for each oxygen concentration level as shown as red lines in this figure. Using the measured oxygen concentration, a mole fraction of the air/ helium mixture in the test loop can be estimated as follows:
f air ¼
C O2 C O2 ;1
ð1Þ
where fair = air mole fraction in the test loop, C O2 = oxygen concentration in the test loop (%), C O2;1 = oxygen concentration in the environment (21%). Therefore, the helium mole fraction can be estimated by the following expression:
f he ¼ 1 f air
ð2Þ
where fhe = helium mole fraction in the test section. The total volumes of air/helium mixture in the test loop can be estimated by the following equations:
V he ¼ V total f he ¼ V total ð1 f air Þ
ð3Þ
V air ¼ V total f air
ð4Þ
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18% 16%
12% 8% 3%
Fig. 5. Oxygen concentrations in a sample test case (angle = 90°, dhole = 12 mm, Uinside = 0.37 m/s).
where Vhe = volume of helium in the test loop (m3), Vair = volume of air in the test loop (m3), Vtotal = total flow volume of the test loop (m3). The change of air volume in the test section can be estimated by the following equation:
The density ratio of the helium/air mixture the air are defined as follows
dV air d dfair ¼ ðV total f air Þ ¼ V total dt dt dt
where qmix = helium/air mixture density in the test loop (kg/m3).
ð5Þ
Since the pressure in the test-section is maintained during the experiment, the volumetric inflow and outflow are balanced as follows:
V_ in ¼ V_ out ¼ V_ ex
ð6Þ
where V_ in = volumetric flow rate of air into the test-section (m3), V_ out = volumetric flow rate of air/helium mixture out of the test sec-
tion (m3), V_ ex = exchange volumetric flow rate through the testsection hole (m3). Therefore, the volumetric flow rate of air into the test-section (or exchange volumetric flow rate) can be obtained as follows:
dV air dfair ¼ V_ in f air V_ out ¼ ð1 f air Þ V_ in ¼ V total dt dt V_ in ¼
V total dfair ð1 f air Þ dt
ð7Þ ð8Þ
The mass flow rate of the air into the test section through the hole can be estimated by the following equation:
q V df _ air ¼ qair V_ in ¼ air total air m ð1 f air Þ dt
ð9Þ
_ air = mass flow rate of air into the test section (kg/s), where m
qair = air density in environment (kg/m3).
The average velocity of the air into the test section through the hole can be estimated by the following expressions:
U air ¼
_ air m
qair Ahole
¼
V total dfair Ahole ð1 f air Þ dt
ð10Þ
where U air = average velocity of air into the test section (m/s), Ahole = surface area of the break (m2). The break surface area in Eq. (7) can be calculated by
Ahole ¼
p
2 dhole
4
where dhole = hole diameter (m).
ð11Þ
c¼
qmix qair
ð12Þ
4. Experimental results 4.1. Effect of density ratio (c) According to the previous study (Oh et al., 2010), the density difference is the main driving force in the HTGR small break accident. The higher density difference leads to the higher air ingress rates for the other conditions fixed. Therefore, in this study, the density ratio (c) between the inside (light fluid) and the outside (heavy fluid) of the break is selected as a key parameter of the experiment. Fig. 6 shows the results on the measured air-ingress rates with respect to the density ratio. It covers the density ratios from 0.2 to 0.9 which include most of the possible accident conditions. The notable findings from this experiment (see Fig. 6) are as follows: The smaller density ratios (=higher density difference) lead to the higher air-ingress rates and the higher break angle sensitivity. The lowest air-ingress rates are found when the break angle is 0°. It is due to its physically stable condition where the heavy gas (air) is located under the light gas (air/helium mixture). The negligible effect of the density ratios in the break angle of 0° means that the density gradient is not an important physical mechanism at this condition. The effect of the density ratio also decreases as the density ratio increases due to the reduced driving force (=density difference). 4.2. Effect of break angle (u) The most dramatic change of the air-ingress rates are found with respect to the break angle. Fig. 7 shows the results. All three air-ingress regimes (diffusion-controlled regime, stratified flow regime, and intermittent flow regime) are found in this figure. The notable results are summarized as follows:
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(a) dhole = 3 mm, Uinside = 0.27 m/s
(b) dhole = 18 mm, Uinside = 0.27 m/s Fig. 6. Effect of density ratio on volumetric air ingress rate.
Fig. 7. Effect of hole orientation on volumetric air ingress flow rate (dhole = 18 mm, Uinside = 0.37 m/s).
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(a) Uinside = 0.27 m/s,
(b) Uinside = 0.27 m/s,
= 30 deg (diffusion dominant regime)
= 150 deg (density gradient driven flow regime)
(c) Uinside = 0.27 m/s,
= 180 deg (intermittent flow regime)
Fig. 8. Effect of break size on volumetric air ingress flow rate.
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Air-ingress rates gradually increases from 0° to 120° of the break angles, and then suddenly decreases to 180°. It supports the previous findings that for around u = 0, the air-ingress is controlled by molecular diffusion (or main flow instability at the break), for u = 0–150 by the density gradient driven stratified flow, and for around u = 0 by an intermittent flow (Oh et al., 2010). The maximum air-ingress rate is found at the break angle around 110°. The effect of the break angle is clearly seen for the low density ratios when the driving force (=density difference) is significant. However, it diminishes rapidly as the driving force decreases. The air-ingress rates are not significantly reduced to zero even for the 0° indicating that the air-ingress mechanism in this condition is not in the pure molecular diffusion controlled regime. It is because that the break at the bottom (angle = 0°) still has a slight curvature and there is a flow instability around the break by generating repeated flow mixing. 4.3. Effect of break size (dhole Þ The air-ingress rates increase with the break size due to the increased flow-exchange area. However, it is not directly proportional to the break area since the break size affects not only the
(a) dhole = 15 mm,
flow-exchange area but also the exchange velocity itself. According to the previous gravity current studies (Keller and Chyou, 1991; Lowe et al., 2005), the stratified flow velocity clearly increases with the break size. Fig. 8 shows the results and it finds the followings: From 30° to 150° (stratified flow regime), the air-ingress rates increases with the break area. For low density ratios (=high density difference), the increase of the air-ingress rates are slightly higher than that of the break area and vice versa. For 180° (intermittent flow regime), the density ratio below 0.6 clearly shows that the air-ingress rate increases with the break size, but that above 0.7 shows negligible effect.
4.4. Effect of flow velocity (U inside ) Among the parameters concerned with the experiments, the main flow velocity in the test section shows the lowest effect on the air-ingress rates. As shown in Fig. 9, the increase of the main flow velocity increases the air-ingress rates slightly regardless of the flow regimes. However, the variation is not noticeable compared to those from the density ratios and the break angles.
= 120 deg (density gradient driven flow regime)
(b) dhole = 15 mm,
= 0 deg (diffusion dominant regime)
Fig. 9. Effect of break size on volumetric air ingress flow rate.
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5. Determination of flow regimes This study attempts to obtain more meaningful information from the experimental data. In order to achieve it, a relevant definition of the Froude Number is developed for quantifying the small break air-ingress phenomena. Then, a criteria for determination of the air-ingress flow regimes are discussed and provided. The details are as follows.
5.1. Definitions of Froude Number (Fr) for small break air ingress Froude Number is a non-dimensional parameter which reflects a ratio of inertia force to gravitational force and therefore it is useful to quantify the density gradient driven flow in the small break
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air-ingress situations. Considering both light and heavy fluid, the Froude Number for the density gradient driven flow is defined as follows (see Fig. 10)
Fr ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qH U 2H þ qL U 2L 2ðqH qL Þg L
ð13Þ
where qH = density of heavy fluid (kg/m3), qL = density of light fluid (kg/m3), U H = velocity of heavy fluid (air) (m/s), U L = velocity of light fluid (air/helium mixture) (m/s), L = length scale (m). During the air-ingress process, the volumetric flow rates through the break are maintained as the pressure at the break is not varied. Therefore, the following equation is valid
U H AH ¼ U L AL
Fig. 10. Schematic of side and cross-sectional views.
Fig. 11. Froude Number vs. density ratio (dhole = 18 mm, Uinside = 0.27 m/s).
ð14Þ
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where AH = heavy fluid inflow area (m2), AL = light fluid outflow area (m2). By implementing Eq. (14), Eq. (13) can be rewritten as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðqH þ qL ðAH =AL Þ2 Þ U 2H Fr ¼ : 2ðqH qL Þg L
ð15Þ
By assuming that the area of the heavy fluid and the light fluid at the break is the same, the above equation can be rewritten as
Fr ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u U 2H t ðqH qL Þ g q
L
ð16Þ
ð18Þ
Therefore, the Froude number for the small break air-ingress is finally expressed by
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u U2 Fr ¼ tðq q Þ H H L g DH sin h q
ð19Þ
Fig. 11 shows the data re-arranged based on the Froude Number defined in Eq. (19) and the density ratio. As shown in this figure, the Froude numbers are well arranged in terms of the break angle. The lower Froude numbers are estimated for the lower break angles. 5.2. Determinations of flow regimes
where
q ¼
L ¼ DH sin h
qH þ qL 2
:
ð17Þ
Considering the break angle and the gravitational direction, the length scale is defined as follows (see Fig. 10)
According to the experimental observations, the air-ingress mechanisms can be divided in terms of whether the flow is controlled by density gradient or not. An important characteristic of the density gradient driven flow is that the flow is highly sensitive
(a) Froude Number vs. Density Ratio (dhole = 18 mm, Uinside = 0.27 m/s): significant angle effect
(b) Froude Number vs. Density Ratio (dhole = 3 mm, Uinside = 0.43 m/s): no angle effect Fig. 12. Determination of flow regimes from experimental data.
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velocities. In the experiment, totally 105 cases are tested by measuring variations of oxygen concentrations in the helium/air flow system using two oxygen sensors (or detectors). The following summarizes the notable results:
Fig. 13. Criteria for flow regimes.
to the break orientations since the gravitational force is dominant. Fig. 12 shows the two extreme cases. In Fig. 12(a), the Froude numbers are well arranged to the break angles sequentially. In this case, the break diameter (dhole) is large and the main flow velocity (Uinside) is small. Therefore, this is the condition where the density gradient driven flow can be easily driven. On the other hand, in Fig. 12(b), the Froude numbers are scattered with respect to the break angles. It is due to the small break diameter which leads to less density gradient driving force. Based on this idea, the data obtained from the experiment are split into two groups. One group includes the data sensitive to the density gradient and the other includes the remaining data. In order quantify the relative importance of the density gradient effect, a non-dimensional parameter is newly defined as follows:
Pgd ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qH qL q þq g dhole H
L
U inside
ð20Þ
The physical meaning of this non-dimensional parameter is a ratio of the gravitational force at the break to the main flow inertia. Therefore, it is equivalent to an inverse of Froude number. If this non-dimensional parameter has a larger value, it indicates that the flow is a more gradient driven dominant flow and vice versa. Fig. 13 exhibits the non-dimensional parameters evaluated from the experimental data. In this figure, the symbols of the circle (s) represent the data sensitive to the density gradient and the symbols of the cross () represents the data insensitive to the density gradient. According to this graph, if the non-dimensional parameter is larger than 0.49, the air-ingress mechanism is the density gradient driven dominant flow. On the other hand, if the non-dimensional parameter is less than 0.47, the other effects such as inertia or diffusion are dominant air-ingress mechanism. Between 0.47 and 0.49, the flow regime is not clear.
6. Summary and conclusions An experimental study has been performed in this paper in order to understand fundamental air-ingress phenomena in a small pipe break accident in the HTGR. This study measures the airingress rates through a circular break on a 4 inch cylindrical pipe for various density ratios, break angles, break sizes and main flow
Effect of density ratio: density difference is a main driving force in the HTGR small break accident. The higher density difference (=smaller density ratio) leads to the higher air ingress rates with the higher break angle sensitivity. The negligible effect of density ratios for the break angle of 0° is found, which means that the density gradient is not an important air-ingress mechanism at this condition. The effect of a density ratio is also decreased as the density ratio is increased due to the reduced driving force. Effect of break angle: break angle shows the most dramatic changes of air ingress mechanisms and rates. According to the experimental observation, air ingress rate gradually increases from 0° to 120° with angles and suddenly decreases to 180°. The maximum air-ingress rate is found at the break angle of around 110°. The effect of break angle looks clear for low density ratios. However, it diminishes rapidly as the driving force decreases. The air-ingress rates are not significantly decreased to zero even for 0° because of the curvature and the instability around the break. Effect of break size: the air-ingress rates increase with the break size due to the increased flow-exchange area. However, it is not directly proportional to the break area since the break size affects not only the flow-exchange area but also the exchange velocity itself. For stratified flow regime (30–150°), the airingress rates increase with the break area almost proportionally. For intermittent flow regime (180°), the density ratio below 0.6 clearly shows that the air-ingress rate increases with the break size, but that above 0.7 shows negligible effect on the air-ingress rates. Effect of main flow velocity: increased flow rate in the channel inside increases air-ingress rate. The increase of the airingress rate with the flow rate looks attributed to increase of flow instability around the hole when the flow passes through it. However, among the parameters concerned with the experiments, the main flow velocity in the test section shows the lowest effect on the air-ingress rates. In this study, Froude Number relevant to the small break airingress are newly defined considering both heavy and light fluids, and break angles. Based on this definition, the experimental data are well arranged sequentially in terms of break angles. Finally, this study developed a non-dimensional parameter and the criteria for determination of the small break air-ingress flow regimes. Based on the physical meaning of this non-dimensional parameter, which is a ratio of the gravitational force at the break to the main flow inertia, it is found that the non-dimensional parameter higher than 0.49 indicates that the air-ingress is controlled by density gradient. On the other hand, the non-dimensional parameter lower than 0.47 indicates that the other effects such as inertia or diffusion are dominant air-ingress mechanism.
Acknowledgements This work was supported by the Nuclear Safety Research Program through the Korea Radiation Safety Foundation (KORSAFe) and the Nuclear Safety and Security Commission (NSSC), Republic of Korea (Grant No. 1403005). This work was also supported by the National Research Foundation of Korea (NRF) Grant funded by the Ministry of Science, ICT & Future Planning (MSIP) (No. 0666-20150009).
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References General Atomics, Gas Turbine Modular Helium Reactor (GT-MHR) Conceptual Design Description Report, 910720, 1996. Hishida, M., Fumizawa, M., Takeda, M., Ogawa, M., Takenaka, S., 1993. Researches on air ingress accidents of the HTTR. Nucl. Eng. Des. 144, 317–325. INET, HTR-10 Experimental Report-Loss of Helium Flow without Reactor Scram, NH-JRC-P1-R06-009, KAERI/INET Internal Report, 2006. KAERI, State of Art Report for the OECD-NEA Loss-of_Forced Cooling (LOFC) Test Project using HTTR Reactor, AR-884, 2011. Keller, J.J., Chyou, Y.P., 1991. On the hydraulic lock-exchange problem. J. Appl. Math. Phys. 41. Lowe, R.J., Rottman, J.W., Linden, P.F., 2005. The non-Boussinesq lock-exchange problem. Part 1. Theory and experiments. J. Fluid Mech. 537, 101–124. Melse, G., Katz, R., 1984. Thermal and flow design of helium-cooled reactors. Am. Nucl. Soc., 181–185 Oh, C.H., Kim, E.S., 2012. Natural circulation patterns in the VHTR air-ingress accident and related issues, Recommended for Publication in Nuclear Engineering Design from NUTHOS8, 249, 228–236.
Oh, C.H., Davis, C., Siefken, L., Moore, R., NO, H.C., Kim, J., Park, G.C., Lee, J.C., Martin, W.R., 2006. Development of Safety Analysis Codes and Experimental Validation for a Very High Temperature Gas-Cooled Reactor, Final Report, INL/EXT-0601362, Idaho National Laboratory, March 2006. Oh, C.H., Kim, E.S., NO, S.H.C., Cho, N.Z., 2010. Experimental Validation of Stratified Flow Phenomena, Graphite Oxidation, and Mitigation Strategies of Air Ingress Accident, Final Report, INL/EXT-10-19289, Idaho National Laboratory, December 2010. ORNL, Next Generation Nuclear Plant Phenomena Identification and Ranking Tables (PIRTs): Volume 2. Accident and Thermal Fluids Analysis PIRTs, ORNL/TM-2007/ 147, 2007. Schultz, R.R., 2008. Meeting the thermal-hydraulic analysis needs for advanced gas reactor systems. In: Fourth International Topical Meeting on High Temperature Reactor Technology, Volume 2, 2008. 241–253. Schultz, R.R., et al., 2006. Next Generation Nuclear Plant Methods Technical Program Plan, INL/EXT-06-11804, September 2006. Xiaowei, L., Charles, R.J., Suyuan, Y., 2004. Effect of temperature on graphite oxidation behavior. Nucl. Eng. Des. 227, 273.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Experimental study on fundamental phenomena in HTGR small break air-ingress accident Jae Soon Kim a, Jin-Seok Hwang a, Eung Soo Kim a,⇑, Byung Jun Kim b, Chang Ho Oh c a
Department of Nuclear Engineering, Seoul National University, Daehak-dong, Gwanak-gu, Seoul 151-742, Republic of Korea Korea Institute of Industry Technology, 618-230 Kangsu-gu, Busan, South Korea c Idaho National Laboratory, 2525 N. Fremont Ave., Idaho Falls, ID 83415, USA b
a r t i c l e
i n f o
Article history: Received 1 March 2015 Received in revised form 4 August 2015 Accepted 9 August 2015 Available online 9 September 2015 Keywords: HTGR Air ingress Small break Density gradient driven flow
a b s t r a c t This study experimentally investigates fundamental phenomena in the HTGR small break air-ingress accident. Several important parameters including density ratio, break angle, break size, and main flow velocity are considered in the measurement and the analysis. The test-section is made of a circular pipe with small holes drilled around the surface and it is installed in the helium/air flow circulation loop. Oxygen concentrations and flow rates are recorded during the tests with fixed break angles, break sizes, and flow velocities for measurement of the air-ingress rates. According to the experimental results, the higher density difference leads to the higher rates of air-ingress with large sensitivity of the break angles. It is also found that the break angle significantly affects the air-ingress rates, which is gradually increased from 0° to 120° and suddenly decreased to 180°. The minimum air ingress rate is found at 0° and the maximum, at 110°. The air-ingress rate increases with the break size due to the increased flow-exchange area. However, it is not directly proportional to the break area due to the complexity of the phenomena. The increased flow velocity in the channel inside enhances the air-ingress process. However, among all the parameters, the main flow velocity exhibits the lowest effect on this process. In this study, the Froude Number relevant to the small break air-ingress conditions are newly defined considering both heavy and light fluids, and break angles. Based on this definition, the experimental data can be well rearranged and collected. Finally, this study develops and proposes a non-dimensional parameter and a criteria for determination of the small break air-ingress flow regimes. As a result, the non-dimensional parameter higher than 0.49 indicates that the air-ingress is mainly controlled by density gradient effect. On the other hand, that lower than 0.47 indicates that the other effects such as inertia or diffusion are dominant air-ingress mechanisms. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction A high temperature gas cooled reactor (HTGR) is a Gen-IV reactor concept incorporating high temperature, graphite-moderated, uranium-fueled, helium-cooled features for high efficiency, safety, and usability (GA, 1996); Schultz et al., 2006; Melse and Katz, 1984). The HTGR technology has been studied and developed since the 1950s and it exhibits several advantages over light water reactors including fuel integrity, proliferation resistance, a relatively simple fuel cycle, easy refueling, and modularity to supply electricity to remote areas. Even though gas reactors have been developed in the past with limited success, the innovations of modularity and integrated state-of-the-art safety systems make the HTGR design attractive from technical and economic perspectives. ⇑ Corresponding author. E-mail address: [email protected] (E.S. Kim). http://dx.doi.org/10.1016/j.anucene.2015.08.012 0306-4549/Ó 2015 Elsevier Ltd. All rights reserved.
In spite of its inherent safety features, the HTGR concept could be detrimental if a loss of coolant accident (LOCA) occurs that results in depressurization and potential air-ingress issues related with various physical/chemical phenomena (ORNL (2007); Schultz, 2008; Oh et al., 2006, 2010). This LOCA could lead to oxidation of the in-core graphite structure and the fuel, which will accelerate heat-up of the reactor core and lead to the release of toxic gasses (CO and CO2) and fission products. Therefore, without effective countermeasures, a pipe break may lead to significant fuel damage and fission product release depending on the reactor design, break locations, and break orientations. The most recent researches on the air-ingress accident phenomena were performed and reported by Idaho National Laboratory (Oh et al., 2006, 2010). In their researches, an air-ingress scenario based on density gradient driven flow were newly proposed (Oh et al., 2010), which consists of four steps. Based on extensive CFD analyses, it was shown that the density gradient driven stratified
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flow is the dominant air-ingress mechanism regardless of the accident scenarios. Characteristics of natural circulation were also investigated by Oh and Kim (2012) in the post onset-naturalcirculation (ONC). This study showed that a natural circulation pattern consists of two flow paths and a recirculation flow rapidly drives air into the reactor vessel. An estimated air-ingress rates from 3-D CFD simulations were about an order of magnitude faster than that estimated by a 1-D system code. It indicated that the air ingress modeling should be conducted on multi-dimensional basis. Even though many researches were previously conducted for the air-ingress accident in the HTGR, they mostly focused on a double-ended guillotine break (DEGB) scenario, where the inside and the outside connecting vessels are ruptured simultaneously (Hishida et al., 1993; Xiaowei et al., 2004; INET (2006); Oh et al., 2006; KAERI, 2011). It is based on the basic assumption that the DEGB would cause highest air-ingress into the reactor and therefore it could result in the most serious consequences. However, there have been some recent discussions that a small break or leak is a much more probable accident in reality than the DEGB, and therefore this accident scenario should be also importantly considered. From this motivation, the present study is focusing on airingress phenomena that expected to occur under much smaller break accident like SBLOCA in a light water reactor (LWR). There is no clear definition on the small break accident in the HTGR, but it is generally considered to be an accident whose break size is less than 1/2 inch according to Next Generation Nuclear Plant Method Technical Program Plan (Schultz et al. (2006)). Currently, the detailed situations for the small-break are not well defined and identified yet in the existing Phenomena Identification and Ranking Tables (PIRTs). However, it is obvious that the probability of the small-break is much higher than the double-endedguillotine-break (DEGB). The possible small-break locations are coolant pipes, control rod guide tubes, instrumentation lines, heat exchanger tubes, and etc. in the primary side. Previously, few researches were carried out on the HTGR small break phenomena. Oh et al. (2010) conducted simple CFD simulations in order to understand basic phenomena. Comparing to the DEGB scenario, the most important aspect observed in the small break situation is that the flow characteristics are highly dependent on the break angles. According to their research, the flow phenomena can be divided into three regimes as shows in Fig. 1. Molecular diffusion is identified as the first flow regime. It is observed when the break is at the bottom. In this case, gravitational force keeps the air from mixing with the helium through either of the second two regimes. For this reason, only diffusion governs the exchange of helium and air. The second flow regime identified is density gradient driven stratified flow. It occurs when the break is somewhere on the side. In this case, heavier fluid flows into the lower part of the hole as a counter current manner, stratified with the lighter fluid exiting in the upper portion like shown
in the DEGB scenario. An unstable gravity-driven flow, observed when the break angle of around 180°, is the last flow regime identified. In this case, the helium exit flow is counter currently chocked with the air inlet flow. The air flow rate is not constant and will be much smaller than that in the second flow regime. Although some computational works have been previously conducted to visualize small break situations, no quantitative experimental data are now available for supporting these numerical results. From this reason, this study attempts to quantitatively measure the air-ingress rates in a small break for various flow and break conditions. Several parameters including break angle, break size, density ratio, and main flow velocity are importantly taken into account. The main objectives of this study is (1) to understand fundamental phenomena and air-ingress characteristics in the HTGR small break accident and (2) to develop a quantitative measure to determine different flow regimes.
2. Experimental loop Fig. 2 shows a schematic of the SNU small break air-ingress experimental loop which consists of the following five parts: Test section: the test section is made of a circular pipe (4 inch) with several holes around it for mimicking a small break situation in the HTGR. During the experiment, all holes except for one are closed. The test-section is made of stainless steel, and nylon caps are used to plug the holes. Circulator: the circulator flows air/helium mixture in the test loop. The circulator speed is adjustable. The circulator is designed to provide the same volumetric flows regardless of types of mixtures. Mixing tank: the mixing tank is designed to stabilize flow and enhances mixing of it. This mixing tank also contains a circulator and various instrument devices including a thermocouple, a pressure transducer, a pressure gauge, and an oxygen sensor. The mixing tank is made of acrylic. Flowmeter: the flow meter measures the flow rates of the working fluids (mainly helium). Since the mixture concentrations are changing during the experiment, the flow velocity are also separately measured using an optical technique. Oxygen sensor: two oxygen sensors measure oxygen concentrations (0–25%) in the helium/air mixture flow. These oxygen sensors are installed in the mixing tank and at the entry of the testsection, respectively. This experiment uses zirconia based sensors commercially available. The test-loop is initially filled with helium gas, and the flow is generated by a circulator. If the flow is stabilized and the system reaches a steady-state condition, a cap on the test-section is un-
Fig. 1. Three different regimes created depending on the break angle of the hole (Oh et al., 2010).
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Fig. 2. Schematic of small break air-ingress experimental facility.
Fig. 3. SNU small break air-ingress experiment set-up.
plugged to initiate air-ingress into the loop. During the experiment, oxygen concentrations, flow rates, temperatures, and pressures are monitored and recorded by a data acquisition system (DAS) and Labview software. The experiment is conducted at room temperature and atmospheric pressure by simplification. Therefore, the effect of temperature on the air-ingress needs to be further investigated in the future. Fig. 3 shows the SNU small break air-ingress experimental set-up. Fig. 4 shows the test-section, which is made of a 4 inch cylindrical pipe on which various small holes are drilled. In order to reflect various small break conditions, separate replaceable test-sections with different size holes and angles are made. The test conditions
are as summarized in Table 1. Five different hole-sizes are considered: 3 mm, 6 mm, 12 mm, 15 mm, and 18 mm. Each hole-size has seven different break angles from bottom (0°) to top (180°). Three flow velocities (0.27 m/s, 0.43 m/s, 0.37 m/s) and five oxygen concentration levels (3%, 8%, 12%, 16%, 18%) are selected. This study assumes isothermal condition while the reactor is heated in the real accident situation. In the small break situation, the heating effect is important since it affects the density of the fluids at the break which can be determined by the temperature and the pressure in the reactor inside. This study conducted the experiment on wide ranges of density ratios from 0.25 to 0.85, which covers most of the possible fluid conditions during the small break
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Fig. 4. Test-section and breaks (holes).
Table 1 Experimental Conditions. Parameters
Test conditions
Temperature Pressure Hole diameter (dhole) Break angle (u) Flow velocity (Uinside) Oxygen concentration (C O2 )
25 °C 1.0 atm 3, 6, 12, 15, 18 mm 0°, 30°, 60°, 90°, 120°, 150°, 180° 0.27, 0.37, 0.43 m/s 3%, 8%, 12%, 16%, 18%
accident. Therefore, it can be considered that the heating effect is somewhat reflected in the current experimental conditions. However, since the local temperature distribution in the reactor can affect the small break process, the further study is obviously necessary to investigate it. According to the literature⁄ (Schultz et al. (2006)), any breaks under 1/2 inch are generally regarded as a small break⁄. The break angle can be any directions from downward (0°) to upward (180°). This study maintained the break sizes and the angles compared to the real prototype. However, the test-section diameter was reduced to 10 cm diameter replicating small break probable pipes. Since the small-break air-ingress is a local phenomenon mainly affected by a break size and angle, this experiment is considered to maintain the key parameters with the prototype. Because of the fractions of the gas mixture are continuously changed, it is hard to determine gas velocity precisely. So this study used Particle Image Velocimetry (PIV) to measure the velocity in the test-section by replacing a certain section with a transparent material with injecting smoke into the loop. Smoke is generated by a commercial smoke generator. A continuous laser sheet made smoke particle easily visible on high-speed camera. Velocity was averaged and its uncertainty is an order of under 0.01 m/s. 3. Data analysis method In this experiment, the oxygen concentrations are collected and used as the final results. The types of the oxygen sensors are electrochemical partial oxygen pressure sensors with an accuracy of ±0.1%. A data acquisition system collected oxygen concentrations
at every single second. Since the timescale of the gas concentration change is very small, 1.0 s is sufficient to capture the slight changes with high quality. Fig. 5 shows the raw data of a sample test case (angle = 90°, dhole = 12 mm, Uinside = 0.37 m/s). In this study, the experiment was conducted under a couple of fixed oxygen concentration levels near 3%, 8%, 12%, 16%, 18% in order to effectively reduce total experiment time. Initially, the loop was filled with air/helium mixture with the lowest helium concentration and the steady-state condition was reached in a couple of minutes. Then, a cap was unplugged and air is introduced into the test section. After airingress data was sufficiently collected (25 min per each oxygen concentration level), the test-section was intentionally purged with air in order to increase air concentration in the loop up to the pre-defined level (i.e. 3–8%, 8–12%). One of the two oxygen sensors placed near to purge line (air injection line) and therefore the peak in Fig. 5 was monitored when the purge was started. After the purge line was closed, the air was mixed with the existing gas and the peak was reduced to a certain value. In order to analyze the data, the raw data is sliced for each oxygen concentration level as shown as red lines in this figure. Using the measured oxygen concentration, a mole fraction of the air/ helium mixture in the test loop can be estimated as follows:
f air ¼
C O2 C O2 ;1
ð1Þ
where fair = air mole fraction in the test loop, C O2 = oxygen concentration in the test loop (%), C O2;1 = oxygen concentration in the environment (21%). Therefore, the helium mole fraction can be estimated by the following expression:
f he ¼ 1 f air
ð2Þ
where fhe = helium mole fraction in the test section. The total volumes of air/helium mixture in the test loop can be estimated by the following equations:
V he ¼ V total f he ¼ V total ð1 f air Þ
ð3Þ
V air ¼ V total f air
ð4Þ
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18% 16%
12% 8% 3%
Fig. 5. Oxygen concentrations in a sample test case (angle = 90°, dhole = 12 mm, Uinside = 0.37 m/s).
where Vhe = volume of helium in the test loop (m3), Vair = volume of air in the test loop (m3), Vtotal = total flow volume of the test loop (m3). The change of air volume in the test section can be estimated by the following equation:
The density ratio of the helium/air mixture the air are defined as follows
dV air d dfair ¼ ðV total f air Þ ¼ V total dt dt dt
where qmix = helium/air mixture density in the test loop (kg/m3).
ð5Þ
Since the pressure in the test-section is maintained during the experiment, the volumetric inflow and outflow are balanced as follows:
V_ in ¼ V_ out ¼ V_ ex
ð6Þ
where V_ in = volumetric flow rate of air into the test-section (m3), V_ out = volumetric flow rate of air/helium mixture out of the test sec-
tion (m3), V_ ex = exchange volumetric flow rate through the testsection hole (m3). Therefore, the volumetric flow rate of air into the test-section (or exchange volumetric flow rate) can be obtained as follows:
dV air dfair ¼ V_ in f air V_ out ¼ ð1 f air Þ V_ in ¼ V total dt dt V_ in ¼
V total dfair ð1 f air Þ dt
ð7Þ ð8Þ
The mass flow rate of the air into the test section through the hole can be estimated by the following equation:
q V df _ air ¼ qair V_ in ¼ air total air m ð1 f air Þ dt
ð9Þ
_ air = mass flow rate of air into the test section (kg/s), where m
qair = air density in environment (kg/m3).
The average velocity of the air into the test section through the hole can be estimated by the following expressions:
U air ¼
_ air m
qair Ahole
¼
V total dfair Ahole ð1 f air Þ dt
ð10Þ
where U air = average velocity of air into the test section (m/s), Ahole = surface area of the break (m2). The break surface area in Eq. (7) can be calculated by
Ahole ¼
p
2 dhole
4
where dhole = hole diameter (m).
ð11Þ
c¼
qmix qair
ð12Þ
4. Experimental results 4.1. Effect of density ratio (c) According to the previous study (Oh et al., 2010), the density difference is the main driving force in the HTGR small break accident. The higher density difference leads to the higher air ingress rates for the other conditions fixed. Therefore, in this study, the density ratio (c) between the inside (light fluid) and the outside (heavy fluid) of the break is selected as a key parameter of the experiment. Fig. 6 shows the results on the measured air-ingress rates with respect to the density ratio. It covers the density ratios from 0.2 to 0.9 which include most of the possible accident conditions. The notable findings from this experiment (see Fig. 6) are as follows: The smaller density ratios (=higher density difference) lead to the higher air-ingress rates and the higher break angle sensitivity. The lowest air-ingress rates are found when the break angle is 0°. It is due to its physically stable condition where the heavy gas (air) is located under the light gas (air/helium mixture). The negligible effect of the density ratios in the break angle of 0° means that the density gradient is not an important physical mechanism at this condition. The effect of the density ratio also decreases as the density ratio increases due to the reduced driving force (=density difference). 4.2. Effect of break angle (u) The most dramatic change of the air-ingress rates are found with respect to the break angle. Fig. 7 shows the results. All three air-ingress regimes (diffusion-controlled regime, stratified flow regime, and intermittent flow regime) are found in this figure. The notable results are summarized as follows:
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(a) dhole = 3 mm, Uinside = 0.27 m/s
(b) dhole = 18 mm, Uinside = 0.27 m/s Fig. 6. Effect of density ratio on volumetric air ingress rate.
Fig. 7. Effect of hole orientation on volumetric air ingress flow rate (dhole = 18 mm, Uinside = 0.37 m/s).
J.S. Kim et al. / Annals of Nuclear Energy 87 (2016) 145–156
(a) Uinside = 0.27 m/s,
(b) Uinside = 0.27 m/s,
= 30 deg (diffusion dominant regime)
= 150 deg (density gradient driven flow regime)
(c) Uinside = 0.27 m/s,
= 180 deg (intermittent flow regime)
Fig. 8. Effect of break size on volumetric air ingress flow rate.
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Air-ingress rates gradually increases from 0° to 120° of the break angles, and then suddenly decreases to 180°. It supports the previous findings that for around u = 0, the air-ingress is controlled by molecular diffusion (or main flow instability at the break), for u = 0–150 by the density gradient driven stratified flow, and for around u = 0 by an intermittent flow (Oh et al., 2010). The maximum air-ingress rate is found at the break angle around 110°. The effect of the break angle is clearly seen for the low density ratios when the driving force (=density difference) is significant. However, it diminishes rapidly as the driving force decreases. The air-ingress rates are not significantly reduced to zero even for the 0° indicating that the air-ingress mechanism in this condition is not in the pure molecular diffusion controlled regime. It is because that the break at the bottom (angle = 0°) still has a slight curvature and there is a flow instability around the break by generating repeated flow mixing. 4.3. Effect of break size (dhole Þ The air-ingress rates increase with the break size due to the increased flow-exchange area. However, it is not directly proportional to the break area since the break size affects not only the
(a) dhole = 15 mm,
flow-exchange area but also the exchange velocity itself. According to the previous gravity current studies (Keller and Chyou, 1991; Lowe et al., 2005), the stratified flow velocity clearly increases with the break size. Fig. 8 shows the results and it finds the followings: From 30° to 150° (stratified flow regime), the air-ingress rates increases with the break area. For low density ratios (=high density difference), the increase of the air-ingress rates are slightly higher than that of the break area and vice versa. For 180° (intermittent flow regime), the density ratio below 0.6 clearly shows that the air-ingress rate increases with the break size, but that above 0.7 shows negligible effect.
4.4. Effect of flow velocity (U inside ) Among the parameters concerned with the experiments, the main flow velocity in the test section shows the lowest effect on the air-ingress rates. As shown in Fig. 9, the increase of the main flow velocity increases the air-ingress rates slightly regardless of the flow regimes. However, the variation is not noticeable compared to those from the density ratios and the break angles.
= 120 deg (density gradient driven flow regime)
(b) dhole = 15 mm,
= 0 deg (diffusion dominant regime)
Fig. 9. Effect of break size on volumetric air ingress flow rate.
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5. Determination of flow regimes This study attempts to obtain more meaningful information from the experimental data. In order to achieve it, a relevant definition of the Froude Number is developed for quantifying the small break air-ingress phenomena. Then, a criteria for determination of the air-ingress flow regimes are discussed and provided. The details are as follows.
5.1. Definitions of Froude Number (Fr) for small break air ingress Froude Number is a non-dimensional parameter which reflects a ratio of inertia force to gravitational force and therefore it is useful to quantify the density gradient driven flow in the small break
153
air-ingress situations. Considering both light and heavy fluid, the Froude Number for the density gradient driven flow is defined as follows (see Fig. 10)
Fr ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qH U 2H þ qL U 2L 2ðqH qL Þg L
ð13Þ
where qH = density of heavy fluid (kg/m3), qL = density of light fluid (kg/m3), U H = velocity of heavy fluid (air) (m/s), U L = velocity of light fluid (air/helium mixture) (m/s), L = length scale (m). During the air-ingress process, the volumetric flow rates through the break are maintained as the pressure at the break is not varied. Therefore, the following equation is valid
U H AH ¼ U L AL
Fig. 10. Schematic of side and cross-sectional views.
Fig. 11. Froude Number vs. density ratio (dhole = 18 mm, Uinside = 0.27 m/s).
ð14Þ
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where AH = heavy fluid inflow area (m2), AL = light fluid outflow area (m2). By implementing Eq. (14), Eq. (13) can be rewritten as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðqH þ qL ðAH =AL Þ2 Þ U 2H Fr ¼ : 2ðqH qL Þg L
ð15Þ
By assuming that the area of the heavy fluid and the light fluid at the break is the same, the above equation can be rewritten as
Fr ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u U 2H t ðqH qL Þ g q
L
ð16Þ
ð18Þ
Therefore, the Froude number for the small break air-ingress is finally expressed by
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u U2 Fr ¼ tðq q Þ H H L g DH sin h q
ð19Þ
Fig. 11 shows the data re-arranged based on the Froude Number defined in Eq. (19) and the density ratio. As shown in this figure, the Froude numbers are well arranged in terms of the break angle. The lower Froude numbers are estimated for the lower break angles. 5.2. Determinations of flow regimes
where
q ¼
L ¼ DH sin h
qH þ qL 2
:
ð17Þ
Considering the break angle and the gravitational direction, the length scale is defined as follows (see Fig. 10)
According to the experimental observations, the air-ingress mechanisms can be divided in terms of whether the flow is controlled by density gradient or not. An important characteristic of the density gradient driven flow is that the flow is highly sensitive
(a) Froude Number vs. Density Ratio (dhole = 18 mm, Uinside = 0.27 m/s): significant angle effect
(b) Froude Number vs. Density Ratio (dhole = 3 mm, Uinside = 0.43 m/s): no angle effect Fig. 12. Determination of flow regimes from experimental data.
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velocities. In the experiment, totally 105 cases are tested by measuring variations of oxygen concentrations in the helium/air flow system using two oxygen sensors (or detectors). The following summarizes the notable results:
Fig. 13. Criteria for flow regimes.
to the break orientations since the gravitational force is dominant. Fig. 12 shows the two extreme cases. In Fig. 12(a), the Froude numbers are well arranged to the break angles sequentially. In this case, the break diameter (dhole) is large and the main flow velocity (Uinside) is small. Therefore, this is the condition where the density gradient driven flow can be easily driven. On the other hand, in Fig. 12(b), the Froude numbers are scattered with respect to the break angles. It is due to the small break diameter which leads to less density gradient driving force. Based on this idea, the data obtained from the experiment are split into two groups. One group includes the data sensitive to the density gradient and the other includes the remaining data. In order quantify the relative importance of the density gradient effect, a non-dimensional parameter is newly defined as follows:
Pgd ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qH qL q þq g dhole H
L
U inside
ð20Þ
The physical meaning of this non-dimensional parameter is a ratio of the gravitational force at the break to the main flow inertia. Therefore, it is equivalent to an inverse of Froude number. If this non-dimensional parameter has a larger value, it indicates that the flow is a more gradient driven dominant flow and vice versa. Fig. 13 exhibits the non-dimensional parameters evaluated from the experimental data. In this figure, the symbols of the circle (s) represent the data sensitive to the density gradient and the symbols of the cross () represents the data insensitive to the density gradient. According to this graph, if the non-dimensional parameter is larger than 0.49, the air-ingress mechanism is the density gradient driven dominant flow. On the other hand, if the non-dimensional parameter is less than 0.47, the other effects such as inertia or diffusion are dominant air-ingress mechanism. Between 0.47 and 0.49, the flow regime is not clear.
6. Summary and conclusions An experimental study has been performed in this paper in order to understand fundamental air-ingress phenomena in a small pipe break accident in the HTGR. This study measures the airingress rates through a circular break on a 4 inch cylindrical pipe for various density ratios, break angles, break sizes and main flow
Effect of density ratio: density difference is a main driving force in the HTGR small break accident. The higher density difference (=smaller density ratio) leads to the higher air ingress rates with the higher break angle sensitivity. The negligible effect of density ratios for the break angle of 0° is found, which means that the density gradient is not an important air-ingress mechanism at this condition. The effect of a density ratio is also decreased as the density ratio is increased due to the reduced driving force. Effect of break angle: break angle shows the most dramatic changes of air ingress mechanisms and rates. According to the experimental observation, air ingress rate gradually increases from 0° to 120° with angles and suddenly decreases to 180°. The maximum air-ingress rate is found at the break angle of around 110°. The effect of break angle looks clear for low density ratios. However, it diminishes rapidly as the driving force decreases. The air-ingress rates are not significantly decreased to zero even for 0° because of the curvature and the instability around the break. Effect of break size: the air-ingress rates increase with the break size due to the increased flow-exchange area. However, it is not directly proportional to the break area since the break size affects not only the flow-exchange area but also the exchange velocity itself. For stratified flow regime (30–150°), the airingress rates increase with the break area almost proportionally. For intermittent flow regime (180°), the density ratio below 0.6 clearly shows that the air-ingress rate increases with the break size, but that above 0.7 shows negligible effect on the air-ingress rates. Effect of main flow velocity: increased flow rate in the channel inside increases air-ingress rate. The increase of the airingress rate with the flow rate looks attributed to increase of flow instability around the hole when the flow passes through it. However, among the parameters concerned with the experiments, the main flow velocity in the test section shows the lowest effect on the air-ingress rates. In this study, Froude Number relevant to the small break airingress are newly defined considering both heavy and light fluids, and break angles. Based on this definition, the experimental data are well arranged sequentially in terms of break angles. Finally, this study developed a non-dimensional parameter and the criteria for determination of the small break air-ingress flow regimes. Based on the physical meaning of this non-dimensional parameter, which is a ratio of the gravitational force at the break to the main flow inertia, it is found that the non-dimensional parameter higher than 0.49 indicates that the air-ingress is controlled by density gradient. On the other hand, the non-dimensional parameter lower than 0.47 indicates that the other effects such as inertia or diffusion are dominant air-ingress mechanism.
Acknowledgements This work was supported by the Nuclear Safety Research Program through the Korea Radiation Safety Foundation (KORSAFe) and the Nuclear Safety and Security Commission (NSSC), Republic of Korea (Grant No. 1403005). This work was also supported by the National Research Foundation of Korea (NRF) Grant funded by the Ministry of Science, ICT & Future Planning (MSIP) (No. 0666-20150009).
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