Separate effects experiments for air-ingress in helium filled vessel

Experimental Thermal and Fluid Science 49 (2013) 1–13

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Separate effects experiments for air-ingress in helium filled vessel Seungjin Kim a, Mohan S. Yadav a,⇑, Justin D. Talley a, Andrew Ireland b, Stephen M. Bajorek b a b

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, 31 Hammond Building, University Park, PA 16802, United States The United States Nuclear Regulatory Commission, Washington, DC 20555, United States

a r t i c l e

i n f o

Article history: Received 5 September 2012 Received in revised form 3 January 2013 Accepted 26 February 2013 Available online 6 April 2013 Keywords: Gravity-driven flows Air-ingress

a b s t r a c t This study performs scaled separate-effects experiments to investigate the gravity-driven ingress of air into a helium filled vessel. Experiments are performed under both adiabatic and heated conditions up to 100 °C. An oxygen analyzer is employed to measure the transient oxygen concentration inside the test vessel during the ingress event. The air-ingress transient is found to be characterized by three distinct stages, namely: (a) The initial stage where the exchange flow rate linearly increases with time until it reaches its maxima and makes a transition; (b) The intermediate stage where the exchange flow rate decreases from its maximum value and varies non-linearly with time; and (c) The final stage of ingress where the exchange rate decreases asymptotically to zero towards the end of the ingress. An extensive oxygen concentration transient database is established accounting for various effects including the pipe-break size (or length-to-diameter ratios), break location, break orientation and the initial helium temperature. Predictive models are developed for the mixture density transient and the exchange flow rate during entire ingress process. Additionally, a non-dimensional critical density ratio is defined that determines the point of transition between the initial and the intermediate stages of the ingress process. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Knowledge of gravity-driven exchange flows is important to problems of various geophysical phenomena, safety requirements and accident scenarios. The gravity-driven flows for fluids with small density differences (with density ratio of heavier and lighter fluid, qH/qL, of, less than 1.2) can be considered as Boussinesq flows. A large number of previous studies focused on the Boussinesq flows due to their applications to many important geophysical flows such as sea front breezes and avalanches [1]. However, in many important environmental problems, such as the release of the dense poisonous gas in the atmosphere, the density difference can be quite large. As these flows have a density ratio greater than 1.2, they are called non-Boussinesq flows. Most studies in the past have focused on the shape and speed of the non-Boussinesq gravity currents in straight pipes [2,3]. In many practical applications, however, exchange flow occurs between two compartments connected by a single opening. A typical example of such flows includes circulation of air in a building in an event of fire [4]. Additionally, such non-Boussinesq exchange of fluids is of great interest in an air-ingress scenario for postulated event of primary coolant pipe rupture in a next generation gas reactor, or a Very High Temperature Reactor (VHTR).

⇑ Corresponding author. Tel.: +1 814 865 8429; fax: +1 814 863 4848. E-mail address: [email protected] (M.S. Yadav). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.02.022

The postulated accident scenario in a VHTR is called Depressurized Conduction Cool-down (DCC), caused by the rupture of the primary coolant pipe. After depressurization of the helium inside the reactor core vessel (RCV), this event can lead to gravity-driven ingress of air. Should such an event occur, the oxidation of graphite components of the reactor is a concern in view of the structural integrity of the core and the supporting graphite structure in the lower plenum of General Atomics designed High Temperature Gas Reactor (HGTR), and also cause a possible supporting graphite structure collapse, which might result in core collapse and fission gas release [5]. Therefore, it is essential to investigate the ingress phenomena and to gain knowledge on the time available for mitigative actions. Relatively few experimental studies have addressed the problem of non-Boussinesq gravity-driven exchange between two compartments connected by a single opening [6,7]. Some of the previous studies suggested that, following the initial helium depressurization, air-ingress can be caused due both to the gravity-driven exchange and the molecular diffusion [8–11]. In a recent study conducted by Oh et al. [5,8,9], however, it has been suggested by computational simulation, as well as by dimensional analysis using species transport equations, that the time scale for density driven exchange flow is nearly 800 times faster than that of molecular diffusion. In view of these, the objectives of the current study are to: (a) perform scaling analysis focusing on the dominant mechanisms governing the air-ingress phenomena under the DCC scenario, (b) establish an experimental facility to study the gravity-driven

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Nomenclature A C Ci Cf D Dab DH Fr g H L R j Pe Q Re Sc t V

pipe-break cross-sectional area (m2) concentration (–) slope of mixture density during initial stage (kg m3 s1) constant for intermediate stage (–) break-pipe diameter (m) mass diffusivity between species a and b (m2 s) hydraulic diameter (m) Froude number (–) gravitational constant (m s2) height (m) height of test facility (m) radius for the test facility (m) superficial velocity (m s1) Peclet number (–) volumetric flow rate (m3 s1) Reynolds number (–) Schmidt number (–) time (s) volume (m3)

Greek symbol density ratio (–) density (kg m3) l dynamic viscosity (kg m1 s1) m kinematic viscosity (m2 s1)

c q

Subscripts air air f final H heavy He helium i initial k kth phase L light m mixture O2 oxygen P prototypic R ratio S scaled tr transition

exchange between air and helium in both adiabatic and heated conditions, (c) develop experimental database for air-ingress in helium filled vessel in a simple geometry, (d) perform parametric separate-effect experiments on pipe-break size (length-to-diameter ratios, L/D), orientation, and initial helium temperature, and (e) develop simple predictive models for the gravity-driven exchange between air and helium.

where jk, D, Dq, q, Q, and A denote the superficial velocity of the kth fluid, pipe-break diameter, density difference between the heavy and light fluids, mean density, volumetric exchange rate and pipebreak cross-sectional area, respectively. In addition to the Froude number, the Reynolds number based upon the superficial exchange velocity, jk, is also considered. The Reynolds number, Rek is given by:

2. Experiments

Rek ¼

2.1. Scaling considerations

where qk and lk are the density and viscosity of the kth fluid, respectively. Here, it is noted that DH,k denotes the hydraulic diameter subject to the kth fluid. Additionally, the Schmidt and Peclet numbers are considered for the effects of molecular diffusion on ingress characteristics. The Schmidt number, Sc, scales the viscous diffusion with respect to molecular diffusion and the Peclet number, Pe, scales the convective diffusion versus molecular diffusion. The Sc and Pe are given, respectively, by:

In the current study, the General Atomics Gas-Turbine Modular Helium Reactor (GT-MHR) design [12,13] is selected as the reference system in designing the experimental facility with scaling considerations. In the GT-MHR design, there are two major pipelines connected to the vessel, namely: the horizontal coaxial primary inlet/outlet pipeline and the vertical refueling standpipe. Considerations are made for breaks at different locations and orientations occurring in both of these pipelines. The focus of this study is to preserve the major hydrodynamics of the air–helium exchange phenomena associated with the break geometry or orientation. As such, the internal RCV volume available for exchange is considered. The complicated flow paths through the internal structure of the prototypic GT-MHR are not scaled, and the RCV is simplified to be a cylindrical vessel in the experiment without upper and lower hemispherical domes. Although, the exchange rate may show some distortions compared to the prototypic GTMHR, these scaling considerations lead to simplification in the computational fluid dynamics code (CFD) analysis in future investigation. First, the Froude number is identified as the major dimensionless number that accounts for both the break geometry and orientation in gravity-driven exchange phenomenon [4,7,14]. The Froude number, Fr, scales the inertia of the heavier fluid with respect to the buoyancy force due to the density difference between the fluids. This can be written as:

jk Q Fr ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DgðDq=qÞ A Dg Dq=q

ð1Þ

Sc ¼

qk jk DH;k lk

m Dab

and Pe ¼ Re  Sc

ð2Þ

ð3Þ

where m is the kinematic viscosity and Dab is the mass diffusivity. For a given parameter, w, the scaling ratio, wR , is defined as the ratio of the scaled condition with respect to the prototypic condition. The ratio for total time required for complete exchange of the fluids, based on a given exchange volume, V is defined as:

tG R ¼

ðV=QÞS VR ¼ ðV=QÞP QR

ð4Þ

where the subscripts S and P denote the scaled and prototypic condition, respectively. In summary, the major scaling parameter ratios studied in the present work include: Froude number, FrR , Reynolds number, ReR , global exchange rate, Q R , local exchange rate, jR , exchange time, tG R , Peclet number, PeR and Schmidt number, ScR . It is assumed that air will displace helium up to the top level of the pipe-break. Hence, the geometric scaling parameters such as the height to diameter ratio of the RCV, exchange volume ratio and pipe-break length-to-diameter ratio are preserved. Both adia-

S. Kim et al. / Experimental Thermal and Fluid Science 49 (2013) 1–13

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Fig. 1. Schematic layout of the experimental setup. Inset shows the radial measurement mesh used for lower-side horizontal break (markers inside the cross-section denote the measurement position).

batic and heated conditions are considered to obtain the global and local exchange rate ratios. Based on obtaining an exchange time ratio nearest to unity, the scaled pipe-break diameter is determined to be 4.45 cm for the horizontal break and 5.72 cm for the vertical break. 2.2. Experimental setup Fig. 1 shows the schematic diagram of the experimental facility. The experimental setup has three important components, namely, (1) experimental vessel, (2) auxiliary equipment such as vacuum pump, helium supply and heaters, and (3) instrumentation. These components are discussed in detail below. The experimental vessel has a cylindrical geometry and is constructed from a carbon steel pipe with a nominal diameter of 61 cm and a height of 183 cm. The top and the bottom of the vessel are sealed by flat cover plates. The pipe-break is connected to a base flange, which can be attached to the vessel flange at the desired break location. Since the effect of the pipe-break size can be captured by the length-to-diameter ratio, L/D, all pipe-breaks are chosen to be 5.08 cm inner diameter. A total of three break locations are available on the test vessel. A break in the primary coolant pipe of the GT-MHR is simulated by the installing the pipe-break at the lower-side horizontal break location, which is

centered at 11.4 cm from the bottom of the vessel. The vertical break location, which represents the vertical standpipe of the GTMHR design, is located at the center of the top plate. Due to machining considerations the engineering design deviates from the conceptual design based on scaling analysis. As such, the time ratios deviate from near unity in the conceptual design scaling analysis, but they all remain within the order of unity (i.e. tG R  2.29 and 1.41 for vertical and horizontal pipe-break, respectively). This leads to an increase in the amount of time available for experimental measurement. Based on the engineering design considerations, the gravity-driven ingress in the present scaled experiment is expected to take approximately two times longer than the prototypic condition. In order to investigate the effect of the pipe-break length, straight pipe-breaks with development lengths of 1D, 3D are employed. Additionally, a pipe-break inclined at 45° from the horizontal and with a development length of 3D is used to investigate the effect of inclined break on air-ingress characteristics. An additional horizontal pipe-break location, centered at 34.3 cm from the bottom of the vessel, is available to investigate the effect of the exchange volume below the pipe axis on the ingress characteristics. A total of 68 instrumentation ports are available along the experimental vessel. Each of these ports consists of Swagelok tube fittings to implement sampling probes. These ports are located at

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17 axial locations along the height of the vessel. The axial positions are chosen such that more detailed measurements can be made near and below the horizontal pipe-breaks, where the highest density gradients are expected to occur. At each axial location, the ports are located along azimuthal angles of 45°, 90°, 135°, and 180° from the horizontal pipe-break axis. Prior to the experiments, a Quincy model QV-1.5 HP Rotary Vane Vacuum Pump, capable of evacuating 0.57 cubic meters per minute to a pressure of 759 mm HgV, is employed to evacuate the vessel. For the heated experiments, a combination of the gas preheater and surface heaters is employed to raise the temperature of the helium inside the vessel. The inlet helium temperature to the test vessel can be controlled between 93 °C to 287 °C by a 1.5 kW Omega GCHAI series medium temperature gas heater. The surface temperature of the vessel is controlled by a combination of Watlow resistance heaters with power ranging from 350 W to 1000 W. In order to prevent heat loss during the experiment, the test vessel is insulated by a 2.54 cm thick Unifrax Durablanket insulation. 2.3. Instrumentation The pressure inside the test vessel is measured by a Rosemount 3051S scalable coplanar pressure transmitter with an accuracy of ±1% of the full-scale reading. The pressure transducer is designed to operate up to a temperature of 232 °C. The gas temperature inside the vessel is measured by Omega manufactured type-T thermocouples with special limits of error of greater than 0.5 °C (or 0.4%) for temperatures up-to 350 °C. The temperature of the vessel surface is monitored by shim-style type-J thermocouples with an accuracy of greater than 2.2 °C (or 0.75%). The most important measurement in the current experiments is the local transient oxygen concentration measurement. The Ametek Thermox CEM O2/TM Trace Oxygen Analyzer is employed for transient oxygen concentration measurements. The analyzer has an operating range from 1 ppm (ppm) O2 to 100% O2 and can sample inlet gases with temperature up-to 204 °C. The response time of the analyzer is less than 10 s for 90% of a two-decade step change. The oxygen concentration is measured in ppm when the concentration is below 5000 ppm and as a percentage when the concentration is 0.5% and above. The accuracy and repeatability of the analyzer in both ppm and percentage mode are shown in Table 1. To ensure the reliability of the analyzer, ambient Oxygen samples were measured/compared prior to and after every experiment. The sampling probe is constructed from a 4.5 mm ID stainless tube and is connected to the aspirator of the oxygen analyzer. The aspirator’s pressure is regulated to a gage pressure of 34.5 kPa and the sample gas is drawn into the oxygen analyzer at a rate of 1 L/min. A Dwyer model RMB-49-SSV flow meter, with an accuracy of ±5% of the full-scale reading, is employed to control the sample gas flow rate. 2.4. Experimental conditions For the adiabatic experiments, a total of five pipe-break configurations, as shown in Table 2, are chosen to investigate the

Table 1 Accuracy and repeatability of the oxygen analyzer.

Table 2 Pipe-break configurations used in the helium–air experiments. L/D

Break location

Angle

Effect

3 3 3 1 3

Lower-side Higher-side Standpipe Lower-side Lower-side

Horizontal Horizontal Vertical Horizontal 45°

– Exchange-volume Pipe-break orientation Pipe-break length Pipe-break orientation

air-ingress phenomenon. The lower-side horizontal pipe-break with L/D = 3 represents the double-ended guillotine break in the primary coolant channel of the prototypic VHTR. The remaining geometries are implemented to study the effects of parameters such as pipe length, break inclination, and break location on the ingress phenomenon. 2.5. Co-ordinate system and measurement mesh A cylindrical co-ordinate system is chosen to represent the test vessel, and the center of the bottom plate is chosen as the origin. The non-dimensional radial positions of r/R = 0 and r/R = 1 represent the center and the wall of the vessel, respectively. The azimuthal direction increases in the counter-clockwise direction referenced from the horizontal pipe-break axis and the positive z-direction is along the height of the vessel. In previous studies with brine and water as simulant fluids [15,16], it was confirmed via flow visualization that during the gravity-driven exchange flow, the heavier fluid displaces the lighter fluid up to the height of the break. This phenomenon is also confirmed via oxygen concentration measurements during shakedown experiments in the current studies. As such, it is assumed that during all the experiments air will replace helium only up to the top of the pipe-break. Therefore, the measurements in the axial direction are obtained up to a height of 15.24 cm and 38.1 cm for the lowerside and higher-side horizontal breaks, respectively. In case of the standpipe break, however, measurements are obtained along the total height of the vessel. The symmetry of the ingress across the pipe-break axis is confirmed during the shakedown experiments. As such, measurements obtained in one half of the vessel cross-section are transposed to the other half. Inset of Fig. 1 shows the radial measurement mesh used for the experiments with lower-side break. Along each azimuthal direction, measurements are obtained by traversing the sampling probe to different radial positions. Further details on the measurement points for different break locations can be obtained from Baird [17], and Kim et al. [18]. In case of the vertical standpipe break configuration, the measurements are obtained along the entire axial length of the vessel. The measurement mesh is selected such that a dense axial measurement mesh is employed near the top of the vessel to capture the characteristics of the plume. A coarse axial measurement mesh is used in the bottom half of the vessel, where low concentration gradients exists in the axial direction. Moreover, the data is obtained only along the centerline (r/R = 0) in the lower half of the vessel because the air–helium mixture display near-uniform radial profiles. 2.6. Experimental procedure

Mode

Accuracy (whichever is greater)

Repeatability (whichever is greater)

Parts per million (ppm) Percentage

±2% of the reading, or 5 ppm O2 absolute ±0.05% O2 absolute, or 0.75% of the reading

±0.5% of the reading or 0.1 ppm ±0.5% of the reading or 0.1% O2

During the air ingress experiment, the transient trace of the local oxygen concentration is recorded. A set of experimental procedures are developed to ensure repeatability of the experiment and to provide identical initial conditions. First, the vessel is sealed and vacuumed to approximately 137.89 kPa (20 psi) below atmospheric pressure using the vacuum pump. The vessel is then filled

S. Kim et al. / Experimental Thermal and Fluid Science 49 (2013) 1–13

with helium and the break is initiated when the pressure inside the vessel reaches to 6.89 kPa (1 psi) above the atmospheric pressure. The gas sample from the vessel is measured and the ingress transient data collection is initiated when the O2 concentration in the vessel is approximately 1800–2000 ppm. During the experiment, a continuous trace of oxygen concentration at a measurement position in the experimental vessel is recorded. The percent oxygen concentration information is used to obtain the local air concentration as:

C air ¼

C O2 ;m C O2 ;r

 100%

ð5Þ

where C O2 ;m , C O2 ; r and Cair represent the mixture oxygen concentration, averaged room oxygen concentration and the air concentration, respectively. The gas mixture-density, qmix , can be obtained in terms of air concentration and the density of air and helium given by qair and qHe , respectively, as:

qmix ¼

  C air 1  C air qair þ qHe 100 100

ð6Þ

3. Results and discussion This section presents the results from the experiments performed to characterize the gravity driven ingress of air into the helium filled vessel. The experimental results are divided in two sections, namely, adiabatic experiments (Section 3.1), and heated experiments (Section 3.2). Furthermore, Section 3.3 details the development of predictive models. 3.1. Adiabatic experiments 3.1.1. Local characteristics In this section local measurements of transient mixture-density characterizing the air-ingress for the lower-side horizontal pipebreak with L/D = 3 and vertical pipe-break with L/D = 3 under adiabatic conditions are presented. Fig. 2 shows the transient of the mixture density measured at different radial locations aligned along the pipe-break direction and located at 7.62 cm from the bottom of the vessel. Qualitatively, the density transient at all radial locations can be divided into two characteristic stages, namely: the initial stage where the mixture density increases rapidly in an approximately linear manner and an intermediate-final stage where the mixture density rises more slowly and in a non-linear manner. Furthermore, during the initial stage of ingress, as shown in the inset of Fig. 2, it is observed that the density transient has two distinct trends depending on the radial location. At r/ R = 0.98, corresponding to the radial position nearest to the pipebreak location, the mixture density increases at a faster rate and displays oscillations. The oscillatory behavior at this radial location is confirmed by multiple measurements. It is speculated that air enters the vessel in form of a plume falling along the wall near the pipe-break location. Furthermore, r/R = 0.98 corresponds to the mixing region between the air-plume and helium. As such, the oscillations may be caused by fluctuating nature of this mixing region. However, with an increase in the radial distance from the pipe-break, the mixture density profiles at each measurement location are approximately identical. It is also found that the mixture density transient measured at different radial locations along the ports B, C and D are nearly identical. The above behavior can be explained by considering the sequence of events during the ingress. At the beginning of the ingress, the air settles to the bottom of the vessel and replaces the helium and stratifies the bottom surface. During this process

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mixing occurs at the air–helium interface. As the ingress event progresses in time, air replaces this layer of air–helium mixture at the bottom of the vessel leading to the rise of this mixture layer in the axial direction. As such, this mixture layer at a particular axial measurement location has a very small variation in density in azimuthal as well as radial directions. The axial evolution of the transient mixture density during airingress inside the vessel is shown in Fig. 3. Here, the mixture-density transients at the centerline of the vessel (i.e. r/R = 0) for ports P1, P2 and P3, located at the heights of 7.6 cm, 11.4 cm and 15.6 cm from the bottom of the vessel, respectively, are compared. As shown in Fig. 2, the variations in mixture-density across a crosssection are very small. As such, the behavior of the transient mixture density at any point in a cross-section can be represented by the behavior at the center point (i.e. r/R = 0). It is observed that the rate of change of the mixture density decreases with increasing elevation. This phenomenon can also be explained by considering the ingress process. At the beginning of the ingress event, air falls to the bottom of the vessel and stratifies along the bottom plane; during this process the air–helium mixture interface is developed. As the ingress progresses, this mixture is replaced with the heavier air continuously falling to the bottom of the vessel. As such, the layer of the air–helium mixture increases in elevation until reaching the plane corresponding to the top of the pipe-break. Hence, a sampling probe located nearer to the bottom of the vessel measures increased air content earlier, and increasing at a faster rate compared to a sampling probe located at a higher elevation. The local data measured at different radial locations in a crosssection are used to obtain the surface plots of oxygen concentration. Fig. 4 shows the surface plots of oxygen concentration for the lower-side horizontal break with L/D = 3. Here, the measurements at port P2 (1.3 cm below the break) at six different times (100 s, 200 s, 400 s, 600 s, 800 s, and 1000 s, respectively) during the ingress are shown. The magnitude of the oxygen concentration is denoted by the z-axis as well as the color. It is observed that the oxygen concentration profile at a given time step is approximately uniform across the vessel cross-section except in the near pipebreak region. In the near pipe-break region, the probe samples from the falling air plume where air and helium are not well mixed. Hence, the oxygen concentration rises at a faster rate and has a higher value compared to the rest of the cross-section. Moreover, it can be noted that the oxygen concentration rises at an approximately constant rate initially, (i.e. between t = 100 s and 200 s) and the rate of increase then slows down in the later stages of ingress (i.e. from t = 400 s to t = 1000 s). 3.1.2. Vertical standpipe break, L/D = 3 Fig. 5 shows the transient mixture-density measured at different radial locations for the vertical pipe-break with L/D = 3. The measurements are obtained at different radial locations along the plane located at a height of 178 cm from the bottom of the vessel (or 5 cm below the break). The inset of Fig. 5 shows the density transients in the initial period of ingress. The measurement locations near the pipe-break axis corresponding to r/R = 0.00, 0.03 and 0.10 show oscillations in the measurement. It is speculated that the oscillations in the measurements arise from the placement of the sampling probe in the plume of air–helium mixture. This is also supported by the flow visualization performed for the vertical break in experiments with brine and water [15]. It was shown that chaotic mixing occurs in the break region and there is no clear interface between the two fluids. As such, the oscillations in the measurement indicate mixing of the two fluids in the break region. Since, this region is the first to encounter the ingressing air, the oxygen concentration at these radial locations increases faster and to a higher value compared to the regions away from the pipe-break.

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Fig. 2. Transient mixture-density at different radial locations for lower-side horizontal break (L/D = 3) measured at port P1 (z = 7.62 cm) and aligned along the break direction h = 180°. Inset shows the zoomed-in view of the initial stage of ingress.

Fig. 3. Transient mixture-density for lower-side horizontal break (L/D = 3) measured along the centerline at ports P1, P2 and P3.

The radial profiles of mixture density transient farther away from the break location (168 cm from the bottom of the vessel) are shown in Fig. 6. It is observed that the transient mixture densities are nearly identical throughout the entire cross-section. The initial period of ingress (inset of Fig. 6) highlights the oscillations at the radial locations near the pipe-break axis. However, the magnitude of these oscillations is much smaller and they diminish much faster compared to the oscillations near the pipebreak. At axial locations away from the standpipe break it is found that the variation in the mixture density transients diminishes across the vessel cross-section, as such local measurements are obtained only at three radial locations. Furthermore, in the lower half of the vessel, the measurements show that mixture-density is very uniform across the vessel cross-section. As such the transient

mixture-density is measured only along the vessel centerline. This indicates that the mixing becomes more uniform with increasing distance from the pipe-break. 3.1.3. Volumetric-averaged characteristics In order to investigate the global behavior of air-ingress, including the volumetric exchange rate, the local transient oxygen concentration data are averaged over the exchange volume. Volume averaging is first performed in the cross-section and then averaged over a given axial height by:

q¼

1 V

Z

qðr; h; zÞdV ¼

1 H

 Z  Z 1 qðr; h; zÞdA dz A

ð7Þ

where V, H, and A refer to the volume considered, height, and area of cross-section, respectively.

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Fig. 4. Surface plots showing the transients of oxygen concentration (%) measured at 7.62 cm above the bottom of the vessel for lower-side horizontal pipe-break with L/ D = 3.

The integral for area averaging can be evaluated by approximating it as the summation of the product of the local density and corresponding area element performed over the entire cross-section given by:

1 A

Z

qðr; h; zÞdA ffi

N 1X An qn ðr; h; zÞ A n¼1

ð8Þ

Each local data point is associated with a discrete area element surrounding the measurement point. The area-averaged data obtained at different axial locations are used to obtain the volumeaveraged data as:

q¼

1 H

Z

q A ðzÞdz

 A is the area-averaged density. Where q

ð9Þ

It is assumed that during the ingress phenomena helium is replaced by air in the volume below the top of the break location. As such, H in Eq. (7) denotes the height measured from the bottom of the vessel to the top of the pipe-break. The integral for averaging in the axial direction is approximated by summation, as given by:

1 H

Z

q A ðzÞdH ¼

N 1X 1 Dzn ðqA;k þ qA;kþ1 Þ H k¼1 2

ð10Þ

where Dzn represents the height between each axial measurement location. Fig. 7 shows the volume-averaged mixture density for the lower-side horizontal pipe-break with L/D = 3. It is noted that the characteristic shape of the volume-averaged mixture density transient

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Fig. 5. Transient mixture-density at different radial locations for vertical standpipe break (L/D = 3) measured at 5 cm below the break. Inset shows the zoomed-in view of the initial stage of ingress.

Fig. 6. Transient mixture-density at different radial locations for vertical standpipe break (L/D = 3) measured at 15 cm below the break. Inset shows the zoomed-in view of the initial stage of ingress.

is similar to the local mixture density transients. This is expected because the volume-averaged behavior is dependent on the general characteristics of the local transient mixture-density, which are nearly identical at all radial locations. Generally, the volumeaveraged mixture-density transient can be divided into two characteristic stages, namely: initial stage of ingress and intermediate-to-final stage of ingress. In the initial stage, the increase in the mixture density is approximately linear. Since, the slope of the mixture-density is indicative of the flow rate in each stage, the steeper linear slope in this stage indicates a higher ingress rate. As such, most of the exchange occurs during the initial stage. In the intermediate-to-final stage of ingress, the increase in the mixturedensity is non-linear and the ingress rate slows down significantly.

A detailed explanation of this behavior is presented in the dataanalysis section. To estimate the volumetric flow rate, the time rate of change of the air volume of inside the vessel is employed. Hence the volumetric flow rate can be written as:

Q¼

  C t 2  C t1 V CO2;air t 2  t1 1

ð11Þ

where C O2 ;air is the concentration of oxygen in atmospheric air. Ct1 and Ct2 are the volume-averaged oxygen concentration in the vessel at a time of t1 and t2, respectively. The variation of volumetric flow rate, Q, and Froude number, Fr, obtained from Eq. (1), with time for the lower-side horizontal

S. Kim et al. / Experimental Thermal and Fluid Science 49 (2013) 1–13

Fig. 7. Volume-averaged mixture density versus time for lower-side horizontal break with L/D = 3.

pipe-break with L/D = 3 is shown in Figs. 8 and 9, respectively. It is observed, that the time transients of both Q and Fr are very similar because Fr is a function of Q. Similar to the volume-averaged mixture-density transient, both Q and Fr display two distinct trends, depending on the stage of ingress. In the initial stage both Q and Fr increase at a constant rate while, in the intermediate-final stage of ingress they decrease with time as the ingress approaches completion. Moreover, the peak in the profiles of both Q and Fr occurs at the time corresponding to the end of the initial period of ingress. Fig. 10 shows the effect of the pipe-break length (L/D ratio) on the ingress phenomena. In this figure the time transient of volume-averaged mixture-density for the lower-side horizontal pipe-break with two different L/D ratios, L/D = 1 and L/D = 3, are shown. It is observed that the mixture-density inside the vessel increases at a faster rate for the short pipe-break (L/D = 1). This suggests that the ingress rate increases with decreasing the length of the pipe-break. It is speculated that this is due to an increase in the wall friction and the interfacial shear between the air and helium interface with increasing pipe L/D. Fig. 10 also shows the effect of pipe-break inclination on the ingress phenomena. The comparison is made between two lowerside pipe-breaks with L/D = 3 and with inclination angles of 0° (i.e., horizontal break) and 45° from the horizontal. Similar to brine–water experiments [15], it is found the exchange flow rate is higher for a pipe-break inclined at 45° from the horizontal axis. The change in the inclination of the pipe-break from 0° to 45° changes the driving head for the exchange flow and consequently

Fig. 8. Volumetric flow rate of air versus time for lower-side horizontal break with L/D = 3.

9

Fig. 9. Froude number versus time for lower-side horizontal break with L/D = 3.

Fig. 10. Volume-averaged mixture density for lower-side horizontal breaks with L/ D = 1 and L/D = 3 and 45° break with L/D = 3.

the interfacial structure between air and helium inside the pipebreak. The interface between air and helium in the pipe-break is smooth and stable for the 0° inclination. However, for the 45° inclination the interface between the two fluids becomes highly unstable and the increased head of the gravity force promotes countercurrent flow leading to an increase in the volumetric flow rate. In addition, a comparison between the lower-side horizontal pipe-break and the vertical standpipe break (i.e., 90°), both with L/D = 3, is shown in Fig. 11. Although, the driving head for the vertical pipe-break is higher compared to the horizontal pipe-break, it is observed that the rate of increase of the mixture-density and hence the exchange flow rate is significantly higher for the horizontal pipe-break. This behavior can be attributed to the interfacial structure between air and helium inside the pipe-break. Unlike the horizontal pipe-break, the interface in the vertical pipe-break is not smooth and stable. This is due to a highly mixed countercurrent flow in the vertical standpipe break which further leads to a slower ingress. Moreover, the exchange volume for the vertical standpipe break consists of the entire vessel volume, which is approximately sixteen times larger than the exchange volume for the horizontal pipe-break. Hence, the time required to complete the ingress process is significantly longer for the vertical standpipe break. The effect of mixing volume on the ingress phenomenon is investigated by installing the horizontal pipe-breaks at two different heights of 11.4 cm and 34.3 cm from the bottom of the vessel.

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Fig. 11. Volume-averaged mixture density for lower-side horizontal break with L/ D = 3, higher side horizontal break with L/D = 3, and vertical stand pipe with L/D = 3.

Fig. 12. Radial profiles of density transients for lower-side horizontal break (L/ D = 3) measured at port P1 (z = 7.62 cm) and aligned along the break direction for helium temperature of 75 °C.

It should be noted that the volume available for exchange corresponds to the vessel volume below the top of the pipe-break. Fig. 11 shows that the comparison of the mixture-density transients for lower-side and higher-side horizontal pipe-breaks with L/D = 3. It is clear that during the initial period of ingress, the exchange rate is higher for the lower-side pipe-break. However, the exchange rates become comparable during the final period of ingress. The hydrostatic pressure head driving the ingress for both the pipe-breaks is identical. Moreover, since the pipes have the same length and orientation, a similar interface between air and helium inside the pipes is expected. As such, overall ingress rates are comparable for both the pipe-breaks. Since, the averaging is performed over a larger volume for the higher side pipe-break, it yields a lower mixture density in the initial stage of ingress. 3.2. Heated experiments In order to study the effect of density ratio on the ingress phenomena, experiments are performed by heating the helium inside the vessel up to 100 °C. An increase in the temperature from 20 °C to 100 °C decreases the density of helium and the density ratio, c (qHe/qair), by approximately 22%, as shown in Table 3. All the heated experiments are performed for lower-side horizontal pipe-break with L/D = 3. 3.2.1. Local characteristics Figs. 12 and 13 show the mixture-density transients at different radial locations aligned along the break direction at port P1 for helium temperatures of 75 °C and 100 °C, respectively. The mixturedensity inside the vessel is evaluated by considering both helium and air to be at the temperature inside the vessel. It is observed that in general the ingress behavior for heated conditions is similar to the adiabatic condition. This result is expected, because the primary effect of heating the helium to a higher temperature is to decrease the density ratio, c. As such, the hydrostatic head driving the ingress changes without changing the overall behavior of the ingress process. Moreover, the radial profiles of density transients throughout the vessel cross-section are nearly identical. This indiTable 3 Density of helium and density ratio at different temperatures. Experimental condition

qHe

c (qHe/qair)

Adiabatic (20 °C) Heated (75 °C) Heated (100 °C)

0.166 0.140 0.131

0.138 0.116 0.108

Fig. 13. Radial profiles of density transients for lower -side horizontal break (L/ D = 3) measured at port P1 (z = 7.62 cm) and aligned along the break direction for helium temperature of 100 °C.

cates that the mixing characteristics for the heated conditions are also similar to the adiabatic case. 3.2.2. Volumetric averaged characteristics The local data obtained at different radial locations and for different initial helium temperatures is volume-averaged to study the thermal effects on the global behavior of ingress. Since, mixturedensity varies with temperature, volume-averaged oxygen concentration transient is compared for experiments with different initial helium temperature, as shown in Fig. 14. As mentioned in the previous section, the change in initial helium temperature does not change the overall behavior of the ingress. The ingress phenomenon consists of an initial stage where the oxygen concentration rises rapidly in a linear manner and an intermediate to final stage where the rate of increase in oxygen concentration is significantly reduced and non-linear. It is observed that an increase in the initial helium temperature from 20 °C to 100 °C leads to a very small increase in the rate of ingress in the initial stage of ingress. 3.3. Development of predictive models It is observed in all of the experiments that the ingress process displays three characteristic transient periods. These are characterized by either linear or non-linear trends in the time rate of change

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Fig. 14. Comparison of the volume-averaged oxygen concentration for lower-side horizontal break (L/D = 3) for different helium temperatures.

of the mixture density inside the vessel. The following presents detailed discussions on these characteristic behaviors and develops simple predictive models for the mixture density transients. 3.3.1. Initial stage of ingress ð0 6 t 6 t tr;i ) It is found that during the initial transient of the air ingress the mixture density increases linearly with time such that the slope of the density transient profile remains constant. In the present study, this characteristic stage is termed as the initial stage of ingress and the change in the mixture density can be predicted by a simple linear correlation as given by:

qm;i ðtÞ ¼ q0 þ C i t for ð0 6 t 6 ttr;i Þ

ð12Þ

where qm,i, q0, Ci, and ttr,i are the mixture density at time t during the initial stage, initial density inside the vessel, the slope of the mixture density transient, and the time when the transition occurs from the initial stage to the next stage, respectively. In the initial stage of ingress, the rate of change of mixture density depends upon the pipe-break configuration. As such, for each pipe-break configuration, C i , is varied to obtain the best fit to the experimental data. Fig. 15 shows the initial stage correlation for the lower-side horizontal pipe-break with L/D = 3. The time-step between the successive data points is determined such that the change in the oxygen concentration is greater than or equal to five times the accuracy of the oxygen analyzer. The end of the initial stage of ingress is determined by considering the relative deviation of the data from the linear trend. The density at this point is denoted as the transition density, qtr,i, as indicated in the figure. 3.3.2. Point of transition A non-dimensional density ratio, qtr;i , defined to specify the point of transition between the linear and non-linear characteristics in density transients is given by:

qtr;i ¼

Dqtr;i

qi

¼

Dqtr;i  qL;i qH;i  qL;i

ð13Þ

where qH,i is the density of heavier fluid (air), qL,i is the density of the lighter fluid (Helium) and qtr,i is the mixture density at the transition point from the linear to non-linear stage. Table 4 lists the values of the non-dimensional density ratios for breaks with different lengths, orientations, and locations. As can be seen in the Table, the values of the non-dimensional transition density ratio remains nearly constant, 0.74 ± 0.05, for all of the test conditions. It should be noted that this value is identical to experiments with brine

Fig. 15. Prediction of the mixture density in the initial stage of ingress using the linear correlation for lower-side horizontal break with L/D = 3. (Error bars shown: ±5%.)

and water as simulant fluids, where the value of transition density was found to be 0.74 ± 0.03 [15]. It was shown in an ingress study employing brine and water that the transition point corresponds to the time when the brine–water mixture ingressing into the vessel fills to the height of the ingress location [15]. As such, it is speculated that the transition point for the helium–air experiments corresponds to the time when helium–air mixture in the vessel reaches the height corresponding to the bottom of the pipe-break. The point of transition as well as the general behavior of the ingress can be explained based on the balance of the driving forces. Consider the dynamics of ingress during the initial stage, transition point, and the intermediate/final stage of ingress. After the initial depressurization, the pressure balances between the inside and outside of the vessel. Therefore, the major driving force for ingress is the hydrostatic head difference between air and helium. As such the problem reduces to the lock-exchange problem between the air and helium in a hypothetical pipe, which coincides with the pipe-break. The initiation of the lock-exchange flow can be simplified as removing the wall between the pipe-break filled with helium and the hypothetical pipe extending from the end of the pipe-break filled with air. The flow in the pipe is driven by the force proportional to the difference in the hydrostatic head between the air and helium in the pipe, given by:

F / ðqair  qHe ÞgD ¼ DqgD

ð14Þ

where F is the driving force, g is the gravitational constant and D is the diameter of the pipe-break through which the ingress occurs. The flow inside the pipe-break is also affected by the viscous forces acting on the fluids along the pipe wall and the interface between the fluids. However, it is assumed that these forces remain approximately constant during the exchange and do not affect the general

Table 4 Transition density and non-dimensional transition density for different experiments. Experiment

qtr,i

qtr;i

L/D = 1, L/D = 3, L/D = 3, L/D = 3, L/D = 3, L/D = 3, L/D = 3,

0.487 0.406 0.389 0.527 0.426 0.345 0.33

0.691 0.769 0.785 0.652 0.750 0.766 0.756

Lower-side horizontal break Lower-side horizontal break Higher-side horizontal break 45° Lower-side break Vertical standpipe break Lower-side horizontal break (75 °C) Lower-side horizontal break (100 °C)

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behavior of ingress. During the initial stage of ingress, the air entering the vessel stratifies the bottom of the vessel. As the ingress time increases, the height of the interface between the helium and helium–air mixture increases. Hence, during the initial stage of ingress, the density difference in the pipe driving the exchange flow remains constants. This leads to a constant rise in the vessel mixture density with time inside the vessel.

F initial / ðqair  qHe ÞgD ¼ DqgD ¼ constant

ð15Þ

The end of the initial stage of ingress (and hence the initiation of the intermediate stage) is marked when the helium–air mixture in the vessel reaches the bottom of the pipe-break. As shown above, the driving force and hence the exchange velocity remains constant during the initial stage of ingress. This yields a constant point of transition marked by the non-dimensional transition density ratio as defined in Eq. (13). 3.3.3. Intermediate stage of ingress ðt r;i 6 t 6 t tr;f Þ After the point of transition, the rate of change in the mixture density starts to decrease significantly with respect to time. Moreover, the decrease is non-linear. Since the change in density is related to the volumetric exchange flow rate, this implies a decrease in the exchange flow rate with time. It is found that in the intermediate stage of the ingress, the data is well correlated with a logarithmic function of the form:

qm;f ðtÞ ¼ qtr;i þ C f ln



t

t tr;i



for ðtr;i 6 t 6 t tr;f Þ

ð16Þ

where qm,f is the mixture density at any time, t, into the intermediate stage of ingress, and qtr,i is the mixture density at the time of transition, ttr,i. A best fit for each experiment is obtained by varying Cf, which is a constant for the intermediate stage of ingress. Fig. 16 shows the prediction of the mixture density using the Eq. (16) for lower-side horizontal break with L/D = 3. It is evident from the figure that the correlation predicts the experimental data well during the intermediate stage of ingress. Towards the end of the intermediate stage, the experimental data starts to deviate from the logarithmic profile. This point is denoted by the transition density, qtr,f, as indicated in the figure. During the intermediate stage of ingress, the driving force is not constant and changes continuously with time. This is because the hydrostatic head is now a function of mixture density, which is a function of time. Hence, the force balance can be written as:

Fig. 16. Prediction of the mixture density in the intermediate stage of ingress using the logarithmic correlation for lower-side horizontal break with L/D = 3. (Error bars shown: ±5%.)

F intermediate / ðqair  qm ðtÞÞgD ¼ DqðtÞgD

ð17Þ

The mixture density inside the pipe-break increases with time during the intermediate and final stages of ingress. As such, the driving force, and consequently the exchange rate decreases with time. Therefore, the change in the mixture density inside the vessel during this stage is a function of the mixture density in the pipebreak region. This leads to a non-linear rise in the mixture density inside the vessel, which yields the density transient as a logarithmic function of time.

3.3.4. Final stage of ingress ðtr;f 6 tÞ During the final stage of ingress, when the ingress asymptotically approaches completion, the mixture density inside the vessel is a weak function of time. As such, the rate of change of the mixture density decreases significantly, and the volumetric exchange rate asymptotes towards zero. It should be noted that with the knowledge of initial rate of ingress and non-dimensional critical density ratio, it is possible to predict almost entire gravity-driven ingress event. This result leads to an accurate estimation of the amount of air entering the vessel during the ingress event.

4. Summary and conclusions This study performs separate effects experiments to investigate gravity-driven air-ingress phenomena in a helium filled vessel. The General Atomics design of the GT-MHR design is selected as the reference system in designing the experimental facility based on scaling considerations. The focus of the scaling considerations is to preserve the major hydrodynamics of the air–helium exchange phenomena associated with the break geometry or orientation. The experimental database on air-ingress phenomena established in this study can be valuable for validation of CFD codes or system analysis codes. An oxygen analyzer is employed to obtain local measurements of the transient oxygen concentration throughout the vessel during an ingress event. Oxygen concentration measurements are then converted to mixture density and air content information. It is observed from the data that the air-ingress phenomenon is characterized by three distinct stages: (a) The initial stage of ingress where the mixture-density inside the vessel increases linearly and the volumetric exchange flow rate increases with time, (b) an intermediate stage of ingress where the increase in the mixture-density becomes non-linear and the volumetric exchange flow rate decreases with time and (c) a final stage of ingress where the rate of change of mixture-density becomes a weak function of time and the volumetric exchange flow rate further decreases and asymptotically approaches zero. The effect of geometric parameters on the air-ingress is investigated by implementing pipe-breaks with different length, orientation and location. The exchange flow rate is found to be smallest for the vertical standpipe break due to the three-dimensional nature of mixing of air and helium inside the pipe-break, which acts against the exchange flow. For the pipe-breaks located on the side of the vessel, the exchange flow rate increases with decreasing the pipe-break length as well as increasing the inclination of pipebreak to 45° from the horizontal. Additionally, the exchange rate decreases with an increase in the height of the horizontal pipebreak from the bottom of the vessel. Heated experiments are performed to study the effect of decreasing density ratios on air-ingress, and to evaluate any effect induced by convective mixing on air-ingress. Under the current temperatures and the density ratios investigated in the present study, however, no significant effects are observed on the overall ingress phenomenon.

S. Kim et al. / Experimental Thermal and Fluid Science 49 (2013) 1–13

Simple predictive models are developed to predict the mixture density transient as well as the volumetric flow rate during the ingress, which agrees well with the data within ±5%. A non-dimensional critical transition density ratio, qtr;i , is defined to characterize the point of transition between the initial and the intermediate stages of ingress. It is found that qtr;i remains constant at approximately 0.74 ± 0.05 independent of the break location, break size, break orientation and initial temperature of helium for all of the helium–air experiments performed. The knowledge of the critical transition density ratio along with the initial rate of ingress can be utilized to predict the entire gravity driven ingress event. Acknowledgement This work is supported by the United States Nuclear Regulatory Commission Office of Nuclear Regulatory Research. References [1] J.E. Simpson, Gravity Currents in Environment and the Laboratory, Ellis Horwood, 1987. [2] H.P. Grobelbauer, T.K. Fannelop, R.E. Britter, The propagation of intrusion fronts of high density ratios, J. Fluid Mech. 250 (1993) 669–687. [3] R.J. Lowe, J.W. Rottman, P.F. Linden, The non-Boussinesq lock-exchange problem. Part1. Theory and experiments, J. Fluid Mech. 537 (2005) 101–124. [4] M. Epstein, Buoyancy-driven exchange flow through small openings in horizontal partitions, J. Heat Transfer 110 (1988) 885–893. [5] C.H. Oh, E.S. Kim, H.S. Kang, H.C. No, N.Z. Cho, Experimental validation of stratified flow phenomena, graphite oxidation and mitigation strategies of airingress accidents, FY-09, Idaho National Laboratory INL/EXT-09-16465 Rev. 1, 2009.

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