SCALED EXPERIMENT ON GRAVITY DRIVEN EXCHANGE FLOW FOR THE VERY HIGH TEMPERATURE REACTOR

Transcription

1 The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering SCALED EXPERIMENT ON GRAVITY DRIVEN EXCHANGE FLOW FOR THE VERY HIGH TEMPERATURE REACTOR A Thesis in Mechanical Engineering by Suchismita Sarangi Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2010

2 ii The thesis of Suchismita Sarangi was reviewed and approved* by the following: Seungjin Kim Assistant Professor of Mechanical and Nuclear Engineering Thesis Advisor Fan-Bill Cheung Professor of Mechanical and Nuclear Engineering Karen Thole Professor of Mechanical Engineering Head of the Department of Mechanical and Nuclear Engineering *Signatures are on file in the Graduate School

3 iii ABSTRACT The process of lock-exchange and gravity driven exchange flow for fluids of differing densities is of particular interest in the postulated Depressurized Loss of Forced Convection (D-LOFC) for the Very High Temperature Gas-Cooled Reactor (VHTR). This event involves the gravity driven ingress of air into the helium filled reactor vessel, ultimately leading to a possible oxidation of graphite components in the vessel. The present study performs a scoping experiment using water and brine as simulant fluids to study the exchange phenomena. To design the test apparatus, a scaling analysis is performed to maintain the exchange time ratio to be unity with the Gas Turbine Modular Helium Reactor (GT-MHR) reference system for the vertical standpipe break. The apparatus consists of two rectangular acrylic compartments connected by pipes and is designed to investigate the effects of the break angle and break length. The break angle is varied from horizontal to vertical at every 15 degrees for L/D = 0.63, 3.0 and 5.0. The volumetric exchange rate is obtained by measuring the time rate of change of mixture density using a hydrometer. A flow visualization study is performed to gain physical understanding of the phenomenon. In general, the present results show similar characteristic phenomena to those found in previous studies for the initial stage of ingress, where the mixture density changes linearly with time. As the ingress progresses, however, it is found that the mixing phenomena inside the compartment and the compartment geometry make significant impacts on the ingress rate. Unlike the previous

4 studies, the present results show that the average exchange rate for the entire ingress event can be up to 70% lower than that obtained from the initial stage alone. iv

5 v TABLE OF CONTENTS LIST OF FIGURES..... LIST OF TABLES... NOMENCLATURE. ACKNOWLEDGEMENTS. vii ix x xii CHAPTER 1 Introduction Research background and motivation Literature review Gravity driven lock exchange flows Exchange flow rate estimation Objectives of present study CHAPTER 2 Scaling Analysis Identification of scaling parameters Scaling methodology Design of test facility CHAPTER 3 Effects of geometric parameters on exchange flow Experimental setup Test apparatus Experimental procedure Experimental results Flow visualization study Density measurement Data Analysis Initial region Non-linear region Mathematical treatment for final region Volumetric flow rate and Froude number analysis... 76

6 vi CHAPTER 4 Conclusions and recommendations for future Work Conclusions Future work. 91 REFERENCES. 94 APPENDIX A1 Derivation of equations APPENDIX A2 Exchange Volume Calculations APPENDIX A3 Experimental data and correlation for L/D = APPENDIX A4 Experimental data and correlation for L/D = APPENDIX A5 Experimental data and correlation for L/D = APPENDIX A6 Volumetric flow rate and Froude number for L/D = APPENDIX A7 Volumetric flow rate and Froude number for L/D = APPENDIX A8 Volumetric flow rate and Froude number for L/D =

7 vii LIST OF FIGURES Figure 1-1: Schematic diagram of the two categories of lock-exchange flow... 9 Figure 1-2: Effect of inclination angle on Froude number Figure 1-3: Effect of mixing length on Froude number Figure 2-1: Schematic of VHTR Figure 2-2: Schematic diagram of inclined test facility Figure 3-1: Schematic diagram of test facility Figure 3-2: Complete experimental test facility Figure 3-3: Components of test facility Figure 3-4: Interface at the break for L/D = 5, Figure 3-5: Global mixing phenomena for L/D = 5, Figure 3-6: Mixing interface at the break for inclined and vertical pipe Figure 3-7: Global mixing phenomena for vertical and inclined break Figure 3-8: Time rate of change of density for L/D = 3, Figure 3-9: Data and correlation in initial region for L/D = 3, Figure 3-10: Effect of Break Angle and Length on C i Figure 3-11: Effect of Break Angle on t tr,i for L/D = Figure 3-12: Effect of Break Angle and Length on ρ * tr,i Figure 3-13: Volumetric exchange rate in initial region for L/D = 3, Figure 3-14: Experimental data and correlation for L/D = 3, 60 0 on regular axes Figure 3-15: Experimental data and correlation for L/D = 3, 60 0 on log axes Figure 3-16: Effect of Break Angle and Length on C tr... 64

8 Figure 3-17: Normalized density and time in non-linear region for L/D = Figure 3-18: Comparison of experimental data with correlation for L/D = 3, Figure 3-19: Variation of density with time with multiple time steps for L/D = 5, vertical break Figure 3-20: Experimental data and correlation for θ Figure 3-21: Experimental data and correlation for θ Figure 3-22: Effect of Break Length and Angle on ρ * tr,f Figure 3-23: Volumetric exchange rate for L/D = 3, Figure 3-24: Froude number for L/D = 3, Figure 3-25: Effect of break angle on volumetric exchange rate for L/D = Figure 3-26: Effect of break angle on Froude number for L/D = Figure 3-27: Effect of Break Length and Break Angle on Froude number of entire mixing period Figure 3-28: Comparison of average Froude number with previous studies Figure 3-29: Comparison of initial region Froude number Figure 3-30: Effect of Break Length on Froude Number Figure 4-1: Conceptual design of slit break viii

9 ix LIST OF TABLES Table 2-1: Reynolds and Froude numbers for the horizontal lock exchange flow Table 2-2: Scaling parameter ratios in vertical break for various break lengths Table 2-3: Scaling parameter ratios for various break angles Table 3-1: Test Matrix for current study.. 40

10 x NOMENCLATURE A = area of cross section of break pipe C = constant for slope C D = discharge coefficient D = diameter of break pipe D h = hydraulic diameter of pipe Fr = Froude number g = gravitational constant L = length of break pipe Q = volumetric flow rate Re = Reynolds number t = time j = local superficial exchange velocity V = Mixing volume Greek Letters ρ = density of fluid µ = dynamic viscosity of fluid γ = density ratio θ = Angle of inclination above horizontal Δ = difference (in density)

11 xi Subscripts/Superscripts f = final condition H = Higher density fluid (brine) i = initial condition k = fluid L = Lower density fluid (water) HA = Helium-Air R = Ratio tr = transition WB = Water-brine

12 xii ACKNOWLEDGEMENTS The author would like to express gratitude to her advisor, Professor Seungjin Kim for his valuable guidance and encouragement. Prof. Kim not only imparted indispensable technical knowledge but also continuous inspiration throughout the period of research work. Sincere thanks to all the students in the Advanced Multiphase Flow Laboratory for their help and cooperation during author s period of research. The author would like to acknowledge Dr. Fan-Bill Cheung for reviewing this work. The research work presented is supported by the U.S Nuclear Regulatory Commission. Finally, the author would like to express deep indebtedness to her family members and friends for their continued support, motivation and encouragement. Sincere gratefulness is extended to the author s parents, to whom this thesis is dedicated.

13 1 CHAPTER 1 Introduction

14 2 1.1 Research background and motivation The Depressurized Loss of Forced Circulation (D-LOFC) is one of the most important design based events for the Very High Temperature Gas-Cooled Reactor (VHTR). This event is caused due to the accidental rupture of the primary pipe or maintenance standpipe in a VHTR, leading to a depressurization of the reactor vessel. Once the vessel pressure reaches atmospheric pressure, air may ingress into the reactor with a simultaneous outflow of helium by different mechanisms depending on the location of the break. For the horizontal primary pipe break connected to the lower section of the vessel, after the initial depressurization, the density difference between helium and air may cause the ingress of air into the reactor by lock exchange phenomenon as described by Reyes et al. (2007). In this process, cold air enters through the horizontal pipe break and fills the lower plenum of the vessel while hot helium simultaneously escapes through the break. As the heavy air settles at the bottom of the vessel, molecular diffusion process promotes further ingress of air. This causes the density of the gas mixture to increase and after a sufficiently long time of about hrs (Oh et al., 2006) when the temperature difference of the gas mixture is large enough, natural circulation is initiated. An abrupt increase in the rate of ingress is observed at the onset of natural circulation (Takeda and Hishida, 1992). On the other hand, for the vertical maintenance standpipe at the top of the reactor vessel, following the initial depressurization, the unstable layer of heavy airhelium mixture above the light helium gas triggers immediate gravity driven air ingress

15 3 into the vessel. Once the reactor vessel is filled with the gas mixture, the temperature difference of the gas mixture causes the onset of natural circulation (Hishida et al., 1993). Since the VHTR core design consists of fuel located within a graphite matrix, the oxidation from an air-ingress event could compromise the structural integrity of the graphite, leading to a possible release of fission products. The bulk natural circulation causes extensive graphite oxidation and generates a large amount of heat which increases the core temperature (Oh et al., 2006). Hence, it is essential to determine the time available for mitigative actions before the onset of natural circulation. The present study focuses on the gravity-driven exchange stage since it is an essential mechanism of air ingress before the onset of natural circulation. The air ingress following the initial depressurization could be caused due to molecular diffusion as well as gravity driven exchange flow due to the difference in density between the helium and air. The most dominant mechanism causing this ingress phenomenon has been widely debated in the past. Earlier studies (Takeda, 1997, Takeda & Hishida, 1996 and Oh et al., 2006) focused on molecular diffusion ignoring the effects of gravity driven exchange flow. Similarly, No et al. (2007) performed numerical simulations for the assessment of the GAs Multi-component Mixture Analysis (GAMMA) code to analyze the proposed molecular diffusion following a guillotine pipe break. The onset of natural circulation was predicted to be at hours after the rupture of the primary pipe. The importance of gravity driven flow as a dominant ingress mechanism was described by Oh et al (2008) by performing CFD analysis using both FLUENT and GAMMA codes to take into account the effect of density difference driven stratified flow and molecular diffusion respectively. It was observed that the ingress of

16 4 air due to the stratified flow assumption occurred very rapidly and the entire bottom part of the vessel was filled with air within about seconds, after which the flow stabilized and molecular diffusion predominated. Based on this analysis, the onset of natural circulation was predicted to be at ~160 seconds, which is significantly earlier than the predicted time for molecular diffusion. Furthermore, in a recent study conducted by Oh et al. (2009), it has been suggested by computational simulation as well as mathematical formulation using species transport equations, that the time scale for density driven exchange is nearly 800 times longer than that of molecular diffusion. Therefore, the present study focuses on the gravity-driven exchange stage since it is crucial in determining the rate of air ingress before the onset of natural circulation. 1.2 Literature Review Gravity driven lock exchange flows The density gradient driven flow discussed above has been widely studied in the past due to its varied applications like waste water discharge into rivers, oil spills, smoke movement, indoor air flow etc. apart from the proposed accident scenario. Several experimental studies have been performed to investigate the flow pattern caused by the intrusion of a heavy fluid mass into a fluid of lower density on a horizontal plane, referred to as gravity driven lock exchange flow.

17 5 Front shape and speed The earliest theory for predicting the speed and shape of the propagating front was developed by von Kármán (1940). This theory was developed by considering energy conserving heavier current propagating in an ambient lighter fluid of infinite depth. The flow was considered relative to a coordinate system moving with the heavier fluid. The speed of the front was predicted as a function of the depth of the current and the density ratio between the mixing fluids. Furthermore, the slope of the front at the point of stagnation was predicted to be Benjamin (1968) developed a theory for the propagation of the front using momentum and mass conservation in a frame of reference moving with the current for inviscid flow. This theory suggested various possible solutions for the speed of the front depending on the depth of the current. It was also shown that the depth of the current would be half the depth of the channel for an energy conserving flow. The front speed and the shape of the front were found to agree with those obtained by von Karman (1940) for the energy conserving assumption. It was shown that if the gravity current occupied less than half the depth of the channel, the current is not energy conserving and the maximum energy flux is reached when h = H, where h is the depth of the current and H is the depth of the channel. Interface shape The shape of the interface between the two layers of fluid flow has also been studied extensively in the past. A mathematical formulation was developed by Yih and Guha (1955) to predict the interface between the two fluid layers. It was shown that fluid

18 6 motion in such stratified flows results in the formation of a hydraulic jump described by a change in depth of the propagating front. Mathematical formulations were developed utilizing conservation of momentum for the two layers of fluids to determine the jump conditions and the depth downstream from the jump. The interfacial shear was neglected and the pressure distribution was assumed to be hydrostatic in order to model the change in depth of each layer due to the occurrence of the aforementioned jump. The predictions were subsequently validated with an oil and water mixing experiment. Further studies on the horizontal exchange flow were performed by Keller & Chyou (1991) covering the complete range of density ratios between 0 and 1. The hydraulic theory was formulated using mass and momentum conservation for the two layers and two models were predicted depending on the density ratio γ between the mixing fluids. The assumption of hydrostatic pressure distribution in this case was replaced with the assumption that the static pressure difference and the stagnation pressure difference upstream and downstream of the hydraulic jump are proportional, with the constant of proportionality limited between 0 and 1. For small density differences (γ 0.281), both the gravity currents were assumed to be energy conserving and connected by a long expansion wave and an internal hydraulic jump, whereas for larger density differences (0 < γ 0.281), the heavier current was assumed to be dissipative in nature and the two currents were connected only by a long expansion wave. Experiments were also performed using several different fluid pairs, covering a density ratio range of to 0.9 to validate the results obtained from the proposed model by flow visualization studies. However, some discrepancies between the model predictions and the experiments were found due to the effects of viscosity and surface tension.

19 7 Lowe et al. (2005) performed experiments and developed models to investigate the shape of the front as well as the interface for fluids having small density differences, i.e. Boussinesq lock exchange, as well as large density differences, i.e. non-boussinesq lock exchange. It was seen that for the Boussinesq case, the speed of both the currents are constant and nearly equal and the flow is symmetrical about the centerline such that the front of each current occupies half the depth of the channel as described earlier by Benjamin (1968). For the non-boussinesq case, it was seen that the heavier current travels at a higher speed than the lighter current although both the currents still move at constant speed. The flow is not symmetric as was seen for the Boussinesq case and the depth of the heavier current is found to be slightly smaller than half the depth of the channel. In order to model the shape of the interface, the theory proposed by Keller & Chyou (1991) was derived again in this study and experiments were performed using water and brine to cover a density ratio range of 0.6 to 1. The two proposed flow configurations as suggested by Keller & Chyou (1991) are shown in Fig. 1 (Lowe et al., 2005). Fig. 1-1 (a) shows the flow configuration for < γ 1 and Fig. 1-1 (b) shows the flow configuration for 0 < γ as discussed earlier. This study was extended to propose a second possible solution considering only an expansion wave connecting the two gravity currents as shown in Fig. 1-1 (b) for the entire range of density ratios for the non-boussinesq exchange flow. The data obtained from the experiments were compared with the results from computational simulations by Birman et al. (2005) and the results from the two proposed models with and without the internal hydraulic jump for the entire range of density ratios. It was found that the theory in which the two gravity currents are connected only by a long expansion wave, with the

20 8 heavy current being dissipative in nature was found to be most representative of the non- Boussinesq lock exchange flow. This contradicted the theory proposed by Keller & Chyou (1991) for the range of density ratios < γ 1 which assumed both the currents to be energy conserving and connected by both an expansion wave and an internal hydraulic jump.

21 9 Figure 1-1: Schematic diagram of the two categories of lock exchange flow: (a) Both currents energy conserving, connected by an expansion wave and an internal hydraulic jump and (b) light current energy conserving and heavy current dissipative, connected by a long expansion wave (Lowe et al., 2005).

22 Exchange flow rate estimation In order to understand the effects of geometric parameters on the general flow characteristics resulting from gravity driven exchange, several previous studies have been performed using water and brine as simulant fluids. Leach and Thompson (1975) performed experiments using both water-brine and carbon dioxide-air as simulant fluids to investigate the accident scenario for a Magnox reactor. These experiments were performed for the horizontal pipe, covering a break development length-to-diameter ratio (L/D) range of 0.5 to 20. The water-brine experiments were performed using a sealed box containing brine connected by a pipe to a tank containing water and recording the weight of the brine box with time by using a force transducer. The carbon dioxide-air experiments were performed using a pipe with a quick release valve at one end to start the ingress of air, connected to a box containing carbon dioxide and measuring the change in concentration of gas sample in the box. A dimensional analysis was also performed in order to estimate the volumetric flow rate in terms of the measurable parameters as discussed above. It was suggested that after the start of the ingress, the reactor vessel can be purged with an external supply of carbon dioxide (coolant gas) in order to prevent further ingress of air. The purging flow rate required to replace the air in the vessel and prevent further ingress was also determined. The results were expressed in terms of a non dimensional parameter referred to as the discharge coefficient of the flow which scales the effect of inertia force to buoyancy force and is essentially similar to the Froude number that has been used in several studies later. This discharge coefficient was given as (Leach & Thompson, 1975):

23 11 (1-1) where Q is the measured volumetric exchange rate, D is the diameter of the pipe, Δρ is the density difference between the two and g is the acceleration due to gravity. Due to the very small density difference, ρ can be the density of either fluid, without making an effect on the calculated value. It was seen that for the case of horizontal pipes, the exchange flow is not significantly affected by the L/D ratio and the discharge coefficient is constant. To investigate the effect of inclination of tubes on gravity driven flows, Mercer & Thompson (1975) performed experiments using ducts inclined at various angles between the horizontal and vertical for a range of L/D = 3.5 to 18. The test apparatus consisted of a sealed tank containing brine connected to a duct. The open end of the duct was immersed in an open tank of water and a quick release seal at the end of the duct was employed to start the ingress. Two experiments were performed for various orientations of the inclined break, namely, tilting the entire system with the pipe connected normal to the compartments, and tilting only the break with the pipe connected to the compartments at the orientation angle. The exchange flow rate was determined by measuring the change in weight of one compartment with time. The results obtained were expressed in terms of a non-dimensional volumetric flow rate q * similar to the discharge coefficient described in Eq (1-1). The value of q * was given by Mercer & Thompson (1975) as:

24 12 (1-2) where ρ H is the density of the heavier fluid. It was observed that the value of q * obtained for the horizontal ducts was independent of the L/D ratio and was found to agree with the value of discharge coefficient obtained in previous studies (Leach & Thompson 1975). Furthermore, it was seen that q * increases as the duct angle is increased above the horizontal until it reaches a maximum value at a peak angle dependent on L/D. Thereafter, q * starts decreasing as the duct angle is increased until it reaches a minimum value for the vertical duct. The q * value in general was also found to decrease with increasing L/D. To further investigate the effect of break length in vertical tubes Epstein (1988) conducted experiments using tubes having L/D range of 0.01 to 10 connecting two compartments containing water and brine respectively. A rubber stopper at the end of the tube was used to start or stop the ingress as desired. The volumetric flow rate was calculated by measuring the density of the brine filled compartment at regular intervals of time (~ 2 min). It was observed that the density of the fluid in upper compartment decreased linearly with time. The results of these experiments were presented in terms of the non-dimensional Froude number which scales the effect of inertia force to buoyancy force and is similar to the non-dimensional parameters used in previous studies. The Froude number was defined as: (1-3)

25 13 where is the mean density of the two fluids and A is the area of cross section of the pipe. The area of cross section of the pipe is given by: (1-4) and the mean density is given by: (1-5) It was found that the Froude number increases with L/D until it reaches a maximum value at L/D = 0.6 and thereafter decreases with increase in L/D. Based on L/D, four exchange regimes were observed, namely the oscillatory flow regime for small L/D described by Taylor wave theory (I), the Bernoulli flow regime described by an inviscid counter current exchange flow model by the application of Bernoulli equation (Brown, 1962), the turbulent diffusion flow regime for very high L/D described by chaotic mixing of the two fluids leading to slower exchange between the compartments and the intermediate flow regime between II and IV described by Bernoulli type flow at the ends of the tube and turbulent diffusion at the center of the tube (III). The maximum exchange flow rate was found to occur in regime III. Finally, a suitable formulation was developed to predict the Froude number in each condition and this was found to compare well with that obtained from the experimental data.

26 14 To study the exchange flow parameters for fluids having higher density differences, various studies have also been performed in the past utilizing two gases as simulant fluids. An experimental study on the effect of break length and angle using helium and air was performed by Hishida et al. (1993) in order to understand the air ingress processes during the primary pipe and stand pipe rupture accidents of the High Temperature Engineering Test Reactor (HTTR). The test apparatus for the stand pipe rupture experiment consisted of a pipe connected to a box containing helium, with a cover plate that could be removed to start the ingress of air. These experiments covered a wide range of inclination angles from horizontal to vertical for L/D = 0.05 and L/D = 10. The effect of break length on the exchange rate was also investigated for the vertical break. The exchange flow rate was obtained by measuring the change in weight of the helium compartment during the exchange by using an electronic weight balance and was expressed in terms of Froude number. The variation of Froude number with L/D was found to agree well with previous data (Mercer et al., 1975 and Epstein, 1988) as shown in Figs 1-2 and 1-3. It was observed that the Froude number is constant for L/D < 0.1, increases with increasing break length upto L/D = 0.6 and decreases thereafter. However, although the overall trend of variation of Froude number with pipe angle was similar to what was observed by Mercer et al., the peak Froude number occurred at much higher angles as shown in Fig.1-2. The peak Froude number for L/D = 10 was found to occur at 60 0 for the helium-air exchange, whereas that for the water-brine experiment from previous studies occurred at angles less than 15 0 for L/D = 8 and 13.

27 15 Figure 1-2: Effect of inclination angle on Froude number (Hishida et al., 1993). Figure 1-3: Effect of mixing length on Froude number (Hishida et al., 1993).

28 16 Furthermore, the differences in exchange flow pattern and flow rate for different fluid pairs including air-helium, Ar-air and SF 6 -air were studied by Tanaka et al. (2002) using similar experimental procedure as Hishida et al. (1993). Here, the effects of inclination and fluid properties on exchange flow parameters in a rectangular channel were investigated. The axial velocity profile was obtained using Laser Doppler velocimeter and flow visualization was performed to analyze the flow pattern for different break angles varying from 15 0 to The exchange flow rate was obtained by measuring the change in weight of one compartment with time and found to depend on both of the break angle and initial density difference between the mixing fluids. It was found that the exchange flow rate increases with the increase in density difference between mixing fluids. Furthermore, it was also observed that the exchange flow increases with an increase in pipe angle, reaching a peak value at about 75 0 and decreases thereafter. 1.3 Objectives of present study For all pairs of mixing fluids it has been reported that the exchange rate strongly depends on both the L/D and angle. Furthermore, the Froude number is identified as the major non-dimensional parameter to account for to account for these effects. Based upon the previous works, the present study seeks to perform an adiabatic scoping study using a scaled water-brine tests to observe the two dimensional mixing phenomena and investigate the effect of geometric parameters on the exchange rate during the postulated D-LOFC in VHTR. The exchange rate and Froude number are calculated by measuring density of heavier fluid for each L/D and angle and the results obtained are analyzed in

29 17 comparison with previous studies. The results of the scoping study performed are crucial to understand the exchange mechanism for gravity driven exchange flow in order to assist in the design of a heated helium-air test facility to aid in the future licensing of helium cooled gas reactors.

30 18 CHAPTER 2 Scaling Analysis

31 Identification of scaling parameters The present study aims at performing a scoping experiment to establish database and provide understanding of the gravity driven exchange flow phenomena occurring during the postulated accident scenario. The experiments are performed using water and brine as simulant fluids in a scaled test apparatus. The design of the water-brine test apparatus is developed based on the scaling analysis and other practical considerations. The scaling analysis described below has been performed in a previous study by Kim & Talley (2009). Since the water-brine test is a scoping experiment, the test apparatus is designed taking the following factors into consideration: To be able to perform scaled experiments over a wide range of geometric parameters as given in previous studies, To be able to perform detailed flow visualization studies on a local as well as global scale, To be able to observe the two dimensional mixing phenomena during the process of ingress of heavier fluid To be simple to implement different pipe lengths, To be light in weight so as to easily perform experiments for the inclined conditions.

32 20 The scaling of the water-brine test apparatus is based on the General Atomics Gas Turbine Modular Helium Reactor as given in INEEL/EXT (2003) design. As shown in Fig. 2-1, this reactor vessel consists of two pipelines connected to the vessel; the horizontal coaxial primary core inlet/exit duct, and the vertical refueling standpipe. For initiation of air-ingress into the reactor vessel, these entry points of different size and orientation are considered.

33 21 Standpipe Primary Pipe Figure 2-1: Schematic of VHTR (INEEL/EXT , 2003).

34 22 In the scaling of adiabatic gravity-driven exchange phenomenon, the previous studies by Turner (1973) and Epstein (1988) suggest that Froude number is the dimensionless number that accounts for the effect of both the break length and orientation. The Froude number scales the effect of the inertia force of the ingressing fluid with respect to the buoyancy force induced by the fluid density difference and is given by: (2-1) where k denotes the fluid (k = H for heavier fluid and k = L for lighter fluid), D denotes the break diameter, g denotes the acceleration due to gravity, Δρ denotes the density difference between the two fluids and denotes the mean density of the two fluids as given by Eq (1-5). Here, j k is the superficial fluid exchange velocity given by: (2-2) where u denotes the fluid exchange velocity and α is the fraction of the total crosssectional area occupied by the fluid k, at the break, which is given by: (2-3)

35 The Froude number can also be rewritten in terms of the volumetric exchange flow rate given by: 23 (2-4) where Q and A are volumetric exchange rate and break area, respectively. Here, the volumetric flow rate can be measured in the experiment by monitoring the density change with respect to time as given by Epstein (1988): (2-5) where V H and V L are the volumes of heavy and light fluids, respectively, and ρ H is the density of the heavier fluid at a given time, t. The subscript i denotes the initial time, i.e., t=0. This expression for Q is obtained by mass balance of the two mixing compartments as given in Appendix A1-1. Based on the Froude Number and volumetric flow relations, the following ratios are identified as key scaling parameters for the water-brine test: : Froude Number Ratio (2-6) : Global Exchange Ratio (2-7)

36 : Local Exchange Ratio (2-8) 24 : Exchange Time Ratio (2-9) where the subscripts WB and HA denote water-brine and helium-air, respectively. The fluid exchange rate has been taken into consideration through two scaling parameters, namely a global scale,, and a local scale,. The volumetric exchange rate ratio for each fluid-pair can be deduced from Eq (2-4) by: (2-10) As such, can vary based on the Fr number and break size. Similarly, the local exchange rate ratio is obtained from Eq (2-1) by: (2-11)

37 Scaling Methodology In order to calculate the scaling parameters, the Froude number for a given simulant fluid pair for a particular case is estimated from previous studies based on the effect of break angle from Fig. 1-2 and break development length from Fig To take into account the effect of the break angle, the data for air-helium is taken from the L/D = 10 experiment by Hishida et al. (1993) while the data for water-brine experiment is taken from the L/D = 8 experiment by Mercer & Thompson (1975). The break angles are varied at 15 intervals between horizontal and vertical. To take into account the effect of break length, Froude number is obtained only for the vertical pipes over a range of break lengths between L/D = 0 to L/D = 10. To determine the break size, the pipe diameter for water-brine test apparatus is varied over a range of L/D ratios comparable with previous experiments for both the break angle and break length effects. The pipe size for heliumair is taken to be a prototypic VHTR hot-leg diameter value of approximately 1.5 meters for the break angle effect, and a standpipe diameter of approximately 0.75 meters for the break length effect. Hence, the global and local exchange rate ratios are calculated by substituting the Froude number ratio and break size obtained as described above, in Eqs (2-10) and (2-11). The exchange time ratio that scales the total time required for complete exchange of the fluids for a given exchange volume is given by:

38 26 (2-12) where V HA and Q HA are the volume and the volumetric flow rate based on the reference GT-MHR dimensions. Based on the two entry locations in the GT-MHR vessel, different amounts of fluids are exchanged, depending upon the volume below the break location. In the vertical standpipe case, a complete volume exchange is assumed, approximately 351,000 liters, such that the heavier air in containment will completely displace the lighter helium in the reactor vessel. The volume of the core is excluded from the vessel volume to obtain the available volume of the annular region between the vessel and core. In the primary break case, the air is assumed to displace any helium below the plane parallel to the top of the primary pipe break, approximately 94,000 liters or 27% of the total vessel volume. The volume of the lower plenum which includes the shutdown cooling system has been neglected for calculating the exchange volume. Furthermore, the support structures under the core and any internals in the upper hemisphere are also neglected in the volume calculations. The detailed volume calculations are described in Appendix A2. To estimate the exchange time for water-brine experiment, it is noted that the volume of fluid to be exchanged also varies with the break angle. In the case of the vertical break the entire volume will mix, whereas in the horizontal break approximately half of the volume will be exchanged. The volume that will remain unmixed, for a break angle θ, is obtained based upon the planes that are perpendicular to the direction of gravity and touch the highest and lowest point of the breaks as shown in Fig The

39 volume not located within this region will always be exchanged. The detailed volume calculation for the present study is included in Appendix A2. 27 Water-brine mixture in upper compartment Unmixed water Unmixed brine Water-brine mixture in lower compartment Figure 2-2: Schematic diagram of inclined test facility (showing unmixed volume for inclined break).

40 28 It should be noted that the exchange time ratio thus calculated by Eq (2-12) represents the time ratio for complete exchange of fluids between the two compartments under adiabatic conditions as opposed to a local exchange time ratio based on the local front velocity at the break. The global timescale is chosen as the primary scaling parameter due to its importance in determining the timescale for mitigative actions. Here, the prototypic exchange time can be estimated as a function of break angle and L/D based on the previous adiabatic Froude number measurements. As such, the parameters of test apparatus volume and break size are varied to make the global time scale,, of order unity. In view of scaling the inertia force of the exchange fluid with respect to the viscous force, the Reynolds number is also examined. It is noted, however, that both Epstein (1988) and Hishida (1993) showed the flow structure and exchange mechanisms of the exchange fluid are primarily determined by the L/D ratio in a vertical break. Hence, only the lock-exchange flow in the horizontal break is considered in examining the Reynolds number. The Reynolds number for a fluid is given by: (2-13) where D h denotes the hydraulic diameter and µ k denotes the viscosity of the fluid. Since each fluid occupies half the depth of the channel as discussed by Benjamin (1968) and Lowe et al. (2005), the hydraulic diameter for the front of a fluid is given by:

41 29 (2-14) Based on the available Froude number data from previous studies, the fluid superficial velocity can be calculated from Eq (2-1). Hence, the Reynolds number can be obtained as: (2-15) Assuming that each lock-exchange fluid will occupy exactly half of the pipe cross-section, the length scale in the Reynolds number is chosen as the hydraulic diameter of half of the pipe cross-section. The Reynolds number obtained for water-brine and helium-air is shown in Table 2-1. The subscript H refers to the heavier fluid while L refers to lighter fluid. As can be found in the Table, while the Reynolds number ratios are far from unity, the exchange flow is laminar for all the cases. Hence, the flow structures and exchange mechanisms can be scaled reasonably well in the adiabatic water-brine scoping tests ensuring that the exchange time ratio is near unity. Fluid temperatures for the heated condition are chosen as C and 43 0 C for helium and air, respectively. For unheated conditions, the fluid temperatures are chosen as 20 0 C for all the fluids.

42 Table 2-1: Reynolds and Froude numbers for the horizontal (θ=0 ) lock-exchange flow. 30 Condition Fr D [m] Re H Re L Heated Helium-Air Unheated Helium-Air Water-Brine Design of test facility Based on the scaling approach described above, the dimensions for the test apparatus are determined. From the calculated scaling ratios, a break size of mm is selected in order to maintain the exchange time ratio between the water-brine scoping apparatus and the prototypic VHTR, close to unity. The scaling ratios for this break size are given in Tables 2-2 and 2-3 for the various tilt angles and L/D values, respectively. From the scaling tables it is clear that the exchange time can vary significantly based on the tilt angle and L/D value. It can also be found that for a fixed L/D the exchange rate increases as the break is tilted more towards horizontal. In the vertical standpipe break, the exchange time increases as the mixing length increases. Since the L/D ratio captures the break size effects, the separate-effects scoping studies have been performed with one break size. The height of the tank is chosen to be the same as the width for simplicity. Based on the dimensions determined from the scaling analysis the water-brine test facility is designed as described in Section 3.1.

43 31 Table 2-2: Scaling parameter ratios in vertical break for various break lengths Pipe Size [mm] L/D Fr] R Q] R j] R t G ] R E E E E E E E Table 2-2: Scaling parameter ratios for various break angles Pipe Size [mm] Tilt Angle [deg] Fr] R Q] R j] R t G ] R (horizontal) E E E E E (vertical) E

44 32 CHAPTER 3 Effects of geometric parameters on exchange flow

45 Experimental Setup Test Apparatus The test apparatus for the water-brine experiments is designed as shown in Fig The apparatus consists of two narrow rectangular acrylic tanks of dimensions 25.4 x 25.4 x 3.81 cm where the narrow rectangular geometry is chosen to highlight the twodimensional mixing and enhance flow visualization studies. Figure 3-1: Schematic diagram of test facility. All dimensions are in cm.

46 34 The complete test facility is shown in Fig In order to investigate the effect of break angle, the test apparatus is attached to a pivoting support, which can be locked at any position between vertical and horizontal as shown in Fig. 3-2 (b). The tilt angles are monitored by a digital level, accurate to ±0.1, attached to the test apparatus. The compartments are connected by break pipes of various lengths as shown in Fig. 3-3 (a). To minimize optical distortion, the break pipes are machined from solid rectangular acrylic blocks by boring holes of the break size into the pieces. As such, the present test section provides an ideal condition for detailed flow visualization study. To initiate the ingress at the beginning of a test, a careful consideration is made in designing a manual shutter mechanism. Unlike most of the previous studies as described by Epstein (1988), Cholemari & Arakeri (2005) and Kuhn et al (2001) where a simple rubber plug has been employed as a stopper, the present study employs a sliding gate mechanism. The gate employed is shown in Fig 3-3 (b). The method employed in previous studies may induce unwanted agitation in the tank that can affect the initial stage of the ingress pattern. Therefore, the sliding gate shutter mechanism reduces the disturbance to the flow at the beginning of ingress.

47 35 (a) Experimental setup, vertical (b) Experimental setup, inclined Figure 3-2: Complete experimental test facility

48 36 (a) Pipe break component (L/D = 5) (b) Manual sliding shutter Figure 3-3: Components of test facility

49 Experimental Procedure The experiments are performed separately for flow visualization and data collection. In determining the density difference between the fluids, values in the range of = are chosen to be consistent with the previous studies of Mercer & Thompson (1975) and Epstein (1988). Since the density difference between the mixing fluids is small (γ = ρ L /ρ H = 0.97), the flow can be categorized as Boussinesq exchange. However, it may be noted that the exchange flow for the prototypic condition, using air and helium is non-boussinesq due to the larger density difference (γ = ρ L /ρ H = 0.15). The implication of this density difference is discussed in Section 4.1. The detailed setup procedure is as follows: a. The break piece of interest is installed between the two compartments. b. The test apparatus is cleaned and tested for leakage. c. The density of brine is measured using hydrometer and the brine is dyed a darker color using food dye. d. The bottom compartment is filled with water and the shutter is closed. e. The top compartment is filled with dyed brine and the top lid is installed to close the top compartment. f. The setup is inclined to the desired angle accurate to ±0.1 0 indicated by the digital level. Thereafter, the experiment is performed in two steps, i.e flow visualization and data collection, as described below:

50 38 Flow Visualization In order to perform the flow visualization, the setup is prepared by following steps a through f above. The experiment is then performed as follows: g. The video camera is installed in position depending on whether the local or global mixing phenomenon is being investigated. Both a high-speed and regular speed movie camera is used to capture the local and global mixing phenomena in the break and the compartments, respectively. For the high-speed movies, a capture rate of 125 frames per second is employed to allow observation of the flow structure in detail. h. The camera is turned on, the shutter is opened and the stopwatch is started simultaneously. i. After the ingress is completed as seen by visual observation, the shutter is closed. j. The test facility is set back into vertical position, a sample is collected from the upper compartment and the final density is measure using hydrometer. The time on the stopwatch is recorded. k. The video is investigated to record the time at which the mixture interface reaches the break height. Data Collection After the flow visualization is performed, the data collection experiment is conducted to obtain the rate of change of density in the upper compartment as and hence evaluate the volumetric exchange rate as described in Sections and 3.3. The test

51 39 facility is setup as described in steps a through f and then the experiment is conducted as follows: l. The shutter is opened to start the ingress and the stopwatch is also started simultaneously. m. After a fixed time determined from flow visualization, the shutter is closed and the test facility is set back to vertical position. The time intervals are very close initially and then spread out as the ingress progresses. n. A sample is taken from the upper compartment and the density is measured with the hydrometer. The time interval and density are recorded. o. The sample is returned into the top compartment and the fluid is stirred thoroughly. p. The top lid is closed and the facility is set back into the inclined position. q. A wait time is allowed for the interface to be stable again at the inclined position and then the steps l through p is repeated. r. After the completion of the ingress, the final density is recorded and the graph is plotted to obtain the rate of change of density with time. In order to investigate the ingress phenomena for the break length and angle effect, the test matrix shown in Table 3-1 is developed. The break length is varied with L/D = 0.63, 3.0 and 5.0 to account for the prototypic reactor condition where the length of the primary pipe between the GT-MHR reactor vessel and the power conversion unit is approximately 4.5 meters or 3 diameters. In addition, this range allows comparison to the

52 previous experiments. For each of the three L/D ratios, the break angle is adjusted from vertical to horizontal in 15 increments to observe the effect of break angle. 40 Table 3-1: Test Matrix for Current Study L/D Degree from horizontal , 15, 30, 45, 60, 75, , 15, 30, 45, 60, 75, , 15, 30, 45, 60, 75, Experimental Results The experimental results are divided into two categories. The first set of results consists of observation of the flow phenomena and exchange mechanism from flow visualization, for different break lengths and angles. The second set consists of the results obtained from density measurement experiments for all conditions of the test matrix.

53 Flow Visualization Study The flow visualization study is performed in two ways, i.e using a high speed camera to capture the local mixing phenomena at the break and using a regular speed camera to capture the global mixing phenomena in the compartment. It is observed that the mixing phenomenon depends greatly on the angle of inclination. For the case of 0 (horizontal break) when the gate is opened, the fluid propagates from the brine compartment to the water compartment, with a well defined front or nose as shown in Fig. 3-4 (a). The slope of this nose at the stagnation point is found to be approximately 60 which is in agreement with the shape of the front as predicted by von Karman (1940) and Benjamin (1968). Following the nose, a stable and well defined interface between the brine and the water is observed as shown in Fig. 3-4 (b). It is seen that the propagation fronts of brine and water are symmetric about the middle of the pipe with each fluid layer occupying approximately half the depth of the pipe. This observation is consistent with the predicted interface characteristics for a Boussinesq lock exchange flow as described by Wilkinson (1986) and Lowe et al (2005). Furthermore, it is also seen that the interface is sloping downwards as it reaches the end of the break. This phenomenon can be described by considering an expansion wave typical of the lock exchange process, as described by Keller & Chyou (1991) and Lowe et al (2005).

54 42 θ ~ 60 0 Flow direction of brine Flow direction of brine (a) Front shape at start of ingress (b) Interface at a later stage of ingress Figure 3-4: Interface at the break for L/D = 5, 0 0 : (a) front shape and (b) mixing interface

55 43 As the brine ingresses into the lower compartment it forms a traveling layer along the bottom as shown in Fig. 3-5 (a). This traveling layer is seen to have a greater thickness at the front as compared to the trailing edge. This can be considered as an internal hydraulic jump that is typically formed when a high density fluid ingresses into a channel containing low density fluid as discussed by Yih & Guha (1954) and Keller & Chyou (1991). Once the brine reaches the opposite wall, it is forced upward by the ingressing brine as shown in Fig. 3-5 (b). Since denser brine is continuously filling below the nose, the brine that is forced upward cannot fall back down and begins to propagate back across the compartment towards the break. This characteristic wavy mixing phenomenon as shown in Fig. 3-5 (c) occurs until the denser fluid reaches the height of the break.

56 44 (a) initial ingress stage (b) increase in height of brine (c) backward wave propagation. Figure 3-5: Global mixing phenomena for L/D = 5, 0 0.

57 45 For the case of inclined angles, the interface is no longer stable at the break as seen in Fig. 3-6 (a). From the figure, several layers can be seen corresponding to a counter-current flow. The ingress rate is generally higher compared to the horizontal condition due to the force of gravity enhancing the exchange as explained in previous studies by Hishida et al. (1993). It is also seen that the region of interfacial mixing increases as the angle of inclination is increased from the horizontal as discussed by Tanaka et al (2002). Due to this interfacial mixing the symmetry of the propagation fronts seen for the horizontal case is absent. However, in the case of the vertical pipe break, it is observed from Fig. 3-6 (b) that there is no clear stable interface between the fluids and the mixing phenomena is highly three-dimensional. The upward water stream and downward brine stream interact strongly and fluctuate irregularly similar to what was reported for air and helium by Hishida et al. (1993). These flow characteristics for the vertical pipe with L/D = 5 are found to be similar to the characteristics of the turbulent diffusion flow regime (IV) described by Epstein (1988). Moreover, this threedimensional mixing causes a reduction in the ingress rate.

58 46 Water flow Brine flow (a) Interface at the break: L/D = 5, 45 0 (b) Interface at the break: L/D = 5, 45 0 Figure 3-6: Mixing interface at the break for inclined and vertical pipe.

59 47 Similar mechanisms are observed in the mixing phenomena for the inclined and vertical break cases based on global compartment observations. As the brine ingresses into the lower compartment, the plume spreads and the outer region is slowed by the shear flow with the stagnant water. This slower region is then displaced outward by the continuously ingressing plume as seen in Figs. 3-7 (a) and 3-7 (b), and the brine spreads throughout the compartment rapidly. Additionally, when the plume reaches a wall, the slower fluid at the wall is displaced upwards by the ingressing brine, after which it cannot move downward due to the presence of the heavier fluid below. It is noted that such mixing of the brine throughout the compartment occurs rather quickly on the order of 1 to 2 minutes depending on the break length and angle. In all cases, it is observed that the ingress rate decreases after the brine has spread throughout the compartment.

60 48 Brine flow Brine flow (a) Global mixing for L/D = 0.63, 45 0 (b) Global mixing for L/D = 0.63, vertical Figure 3-7: Global mixing phenomena for vertical and inclined break.

61 49 The flow visualization study also allows for determination of density measurement time based on the rate and pattern of ingress observed. The time at which the mixture interface reaches the break is recorded from the flow visualization. Then the time intervals at which density measurements need to be recorded are determined from the flow visualization study to obtain reliable measurements within the resolution of the hydrometer and also obtain sufficient number of data points to be able to capture the nature of ingress. As shown in Section 3.2.2, the measurement frequency is initially higher when the ingress is faster, but lower as the ingress slows down Density Measurement As described in Section 3.1.2, the density change in the upper compartment is measured throughout the exchange using a hydrometer by stopping and restarting the ingress. An example of the density measurement is shown in Fig. 3-8 for L/D=3, 60. From the figure it can be seen that the data can be clearly divided into two regions. In the initial region the change of density is linear with respect to time, while in the subsequent region this density change becomes non-linear. It is found from the flow visualization study that initiation of this transition corresponds to the time when the brine reaches the break height. After the transition occurs, the ingress rate slows as the density difference between the fluids in the two compartments decreases.

62 ρ H [kg/m 3 ] Measured Data Time brine reaches break Theoretical final density Figure 3-8: Time rate of change of density for L/D = 3, 60 0.

63 51 This result of two characteristic regions is different from the findings in the previous water-brine studies, which reported the density change to be linear throughout. It is speculated that such differences in mixing characteristics are attributed to the difference in mixing compartment volumes. In the previous studies by Mercer & Thompson (1975) and Epstein (1988), the lower compartment volumes were much larger than the upper compartment, such that the mixing phenomena may have had little effect on the overall ingress characteristics. It is speculated that due to the larger volume of the lower compartment, the density of the lower compartment is not affected by the ingress of heavier fluid. As a result, ρ L in the denominator of Eq (2-4) can be treated as a constant. In the present study, the mixing volume is much smaller and the results highlight the effects of mixing of the fluids on the rate of ingress. It is important to note that the present study is more pertinent to the reactor condition, because the reactor vessel volume is finite and smaller compared to the containment building volume. 3.3 Data Analysis Based on the two characteristic regions observed during the exchange, each region is treated separately for analysis of volumetric flow rate and the Froude number.

64 Initial Region (0 < t t tr,i ) In the initial portion of the exchange, a constant rate of density decrease in the upper compartment is observed. For this region the density data can be fit using an equation of the form: (3-1) where C i is the slope of the initial region and ρ H,i is the intercept based on the initial density measurement. For each break length and angle, the values of C i are varied to obtain the best fit to the experimental data. The data for the initial region is shown in Fig. 3-9 for L/D = 3, 60 0 where the straight line represents Eq (3-1) for this condition.

65 ρ H [kg/m 3 ] 53 Measured Data 1027 ρ = t Linear (Initial Correlation) 1022 ρ tr,i Time brine reaches break Figure 3-9: Data and correlation in initial region for L/D = 3, (Error bars are ±0.1%)

66 54 The value of C i found for various break angles and lengths is shown in Fig From the figure, it can be seen that C i increases, i.e. ingress rate increases in general, as the break angle increases from the horizontal up to a maximum angle for a given break length. This is due to the increase in the effective buoyancy force as the component of gravity in the flow direction increases. Furthermore, from the flow visualization, the angles within this region are found to promote counter-current flow which can lead to an increased flow rate. For all experiments it is found that the maximum ingress rate occurs at an angle between 30 and 45. For higher break angles, it is observed that the ingress rate decreases with increasing break angle. This is due to the mixing structure occurring within the break which becomes chaotic and three-dimensional as the counter-current flow no longer occurs in two distinct layers. As can be seen from the figure, the ingress rate in the initial region is slowest for the vertical case where the three dimensional mixing is the most extreme.

67 Ci, L/D=0.63 Ci, L/D=3 Ci, L/D= Slope in initial stage, C i Angle of Inclination (deg) Figure 3-10: Effect of Break Angle and Length on C i

68 Transition time t tr,i [sec] 56 In investigating the transition time, t tr,i, where the density change becomes nonlinear, it is found that the time is not affected by inclination for break angles less than 45 as shown in Fig However, at angles above 45, the transition time increases with break angle because the ingress rate is decreasing, as shown by the decreasing C i values Break Angle (deg) Figure 3-11: Effect of Break Angle on t tr,i. for L/D = 3.

69 Furthermore, it is found that the transition point can be related to a density difference ratio given by: 57 (3-2) where ρ L is the density of the lower compartment and ρ * tr,i is the density difference at the point of transition normalized with respect to the initial density difference. The value of this parameter is found to be within the same range for all 21 break angle and break length combinations as shown in Fig

70 % Density difference ratio at transition ρ * tr,i % L/D = 0.63 L/D = Break angle (deg) L/D = 5 Figure 3-12: Effect of Break Angle and Length on ρ * tr,i.

71 Using the derivative of Eq (3-1) to obtain the rate of change of density, the volumetric flow rate in the initial region can be expressed as: 59 (3-3) where is the initial density difference between the two fluids. Based on this expression, it can be noted that the volumetric flow rate will increase as time progresses as shown in Fig This occurs since the numerator is constant due to the constant density change, while the denominator becomes smaller as time progresses. However, additional experimental studies are necessary to validate this result.

72 Volumetric flow rate Q [m 3 /s] 60 5.E-06 4.E-06 3.E-06 2.E-06 1.E-06 0.E Figure 3-13: Volumetric exchange rate in initial region for L/D = 3, 60 0.

73 Non-linear Region (t tr,i < t t f ) For the non-linear region of the exchange, the time rate of change for density is found to decrease as the exchange progresses. This is physically consistent as the density difference driven flow should cease when there is no density difference. The change in density for this region is found to be well represented by a logarithmic decay relation of the form: (3-4) where t, t tr,i and C tr are the time into the exchange, the time at which the transition occurs and a constant to fit the experimental data. The values of C tr are varied to obtain the best fit to the experimental data for each break length and angle. Additionally, an effort was made to minimize the slope difference between the linear and logarithmic fits near the transition in the selection of C tr values to represent a continuous exchange. An example of the data and correlation for L/D = 3, 60 0 is shown in Figs and 3-15 on regular and logarithmic scale respectively.

74 ρ H [kg/m 3 ] Data 1025 ρ = t 1020 ρ tr,i ρ = ρ tr,i - C tr ln(t/t tr,i ) where C tr = Time dye interface reaches Break Theoretical final density Figure 3-14: Experimental data and correlation for L/D = 3, 60 0 on regular axes. (Error bars are ±0.1%)

75 ρ H [kg/m 3 ] 63 Data ρ = t ρ tr,i ρ = ρ tr,i - C tr ln(t/t tr,i ) where C tr = 3.6 Time dye interface reaches Break Figure 3-15: Experimental data and correlation for L/D = 3, 60 0 on log axes. (Error bars are ±0.1%)

76 64 It can be seen from Fig that the value of C tr does not vary greatly in the range of 3 to 4 for all break angles and lengths. This implies that in the transient region the dependence of ingress rate on break angle and length may not be as significant as in the initial region. The average value of C tr for all experiments is found to be 3.43 ± 9% % Slope of non linear region, C tr % L/D= L/D=3 L/D= Angle of Inclination (deg) Figure 3-16: Effect of Break Angle and Length on C tr.

77 65 Since the values of C tr and ρ * tr are found to be constant for all break angles and break lengths, the density as well as the time scales can be normalized with respect to the transition density and time respectively, in the non linear region so as to follow similar trend as shown in Fig Transition Region Normalized Density, ρ norm Correlation 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg Transition Region Normalized Time, t norm Figure 3-17: Normalized density and time in non-linear region for L/D = 3.

78 66 An example of the curve fit for density measurement in both regions is shown in Figs (a) and (b) for the vertical case with L/D = 3 on a regular and logarithmic scale respectively. It is clearly seen that the linear and logarithmic fits obtained from Eq (3-1) and (3-4) respectively, describe the experimental data very well within ±0.1%. Similar graphs showing the data and correlation for density measurement for all the conditions of the test matrix are available in Appendices A3, A4 and A5.

79 Upper compartment density ρ H [kg/m 3 ] Upper compartment density ρ H [kg/m 3 ] ρ = t 1025 (ρ H ) tr,i (ρ H ) tr,i 1020 ρ = (ρ H ) tr,i - C tr ln(t/t tr,i ) where C tr =3.4 ρ = t 1015 ρ = (ρ H ) tr,i - C tr ln(t/t tr,i ) where C tr = Theoretical end of ingress (t f ) Ingress time [sec] Ingress time [sec] (a) Data and correlation, L/D = 3, 90 0, regular scale. (b) Data and correlation, L/D = 3, 90 0, log scale. Figure 3-18: Comparison of experimental data with correlation for L/D = 3, 90. Error bars shown are ±0.1%.

80 68 Since in the prototypic condition, the ingress is continuous, it is necessary to ensure that the current method of stopping the ingress to take measurement and starting it again, has minimal effect on the ingress rate. In order to take into account, the effect of starting and stopping of the ingress in small time intervals, additional experiments have been performed with larger time intervals of continuous ingress. The results of these experiments are shown in Fig for L/D = 5, vertical break. The data has been collected in three separate experiments with the smallest time intervals of 30s, 120s and 300s respectively. In order to compare the results, the data has been normalized with respect to the initial density for each experiment. As can be seen from the figure, the results are found to be within ±0.1% of the value from the proposed correlation in all cases. The data points match well with the correlation in the initial region but start deviating towards the end of the experiment. In this region, however, the density measurement becomes less reliable as the change in density may be lower than the 0.5 kg/m 3 resolution of the hydrometer. Furthermore, the values of C i, ρ * tr and C tr are found to be within the limits described above, for all the three runs. Overall, the data is repeatable and little effect of the static measurement procedure is observed.

81 Normalized density Smallest time interval 30 s Normalized density = 120 s s Proposed Correlation Figure 3-19: Variation of density with time with multiple time steps for L/D = 5, vertical break. Error bars are ±0.1%.

82 Normalized density 70 The variation of normalized density with time for different break angles is shown in Figs and 3-21 for L/D = 3. The density is normalized with respect to the measured initial density of the upper compartment, ρ H,i. As can be seen from Fig. 3-20, the rate of change of density increases as the angle of inclination is increased for smaller angles up to 30 0 due to the increased counter-current flow. However, the reverse trend is observed in Fig for angles above 45 0 due to the mixing structure inside the break deg 15 deg deg Normalized density = Increasing break angle Figure 3-20: Experimental data and correlation for L/D = 3, θ (Dotted lines represent correlations).

83 Normalized density deg 60 deg 75 deg 90 deg Normalized density = Increasing break angle Figure 3-21: Experimental data and correlation for L/D = 3, θ (Dotted lines represent correlations).

84 Using the derivative of Eq (3-4) to evaluate the rate of change of density, the volumetric flow rate in the transient region can be expressed as: 72 (3-5) where is the lower compartment density at the transition time estimated through a mass balance of the fluid in the apparatus. The mass balance of the fluid in the apparatus can also provide the final theoretical density in the system when the compartments are completely mixed. When this density is substituted into Eq (3-4), the total mixing time, t f, can then be estimated. The derivation of the theoretical final density and time is included in Appendix A Mathematical treatment for final region (t tr,f < t t f ) A mathematical evaluation of Eq (3-5) shows that as the exchange progresses in time, it reaches a point of inflexion where the derivative of Q becomes zero. Similarly, the Froude number evaluated from Q also reaches a point of inflexion at time t tr,f such that (3-6)

85 The solution of Eq (3-6) results in the value of the time t tr,f at which this inflexion 73 occurs. The density difference ratio at this point of inflexion is evaluated by the expression (3-7) where is the density difference between the two fluids at the point of inflexion. The values of obtained for all the conditions of the test matrix are shown in Fig It is observed from Fig and Eq 3-7 that the density ratio at which inflexion occurs is constant for all break angles and lengths.

86 74 1 L/D = 0.63 L/D = 3 Density difference ratio at inflexion ρ * tr,f 0.5 L/D = Tilt angle (deg) Figure 3-22: Effect of Break Length and Angle on ρ * tr,f

87 75 Since this inflexion occurs while mixing is continuing, the application of Eq (3-5) after this inflexion point is non-physical. Furthermore, as the exchange approaches completion, i.e, as t approaches t f, both the numerator and denominator terms in Eq (2-4) for Q approach zero. This denotes a point of singularity in the expression. Hence, a suitable mathematical treatment needs to be applied to evaluate Q for the later stage. Therefore, L Hospital s Rule is applied in the treatment of Eq. (3-5) to evaluate the value of Q at the limiting condition. Furthermore, it is known that at t f the volumetric exchange is zero since the density difference is zero. Utilizing this boundary condition and the L Hospital s rule, the expression for Q for the final mixing stage is given by: for t tr,f < t t f (3-8) Hence, the Froude number can be obtained for the final mixing stage by: for t tr,f < t t f (3-9) The detailed derivation of this formulation is included in Appendix A1-3.

88 Volumetric Flow Rate and Froude Number Analysis The volumetric flow rate and Froude number values obtained are shown in Figs and 3-24, respectively, for the vertical break with L/D=3. In each figure, there exist three different time regions as shown by the vertical lines. These are, the initial region with increasing exchange flow rate i.e. 0 < t t tr,i, the intermediate region with non linearly decreasing exchange rate i.e. t tr,i < t t tr,f and the final region after the inflexion occurs i.e. t tr,f < t t f. Similar graphs of the variation of exchange parameters with time for all conditions of the test matrix are included in Appendices A6, A7 and A8.

89 Figure 3-23: Volumetric exchange rate for L/D = 3,

90 78 Figure 3-24: Froude number for L/D = 3, 90. Volumetric Flow Rate and Froude number for entire mixing period The variation of volumetric flow rate and Froude number with time for the horizontal, inclined and vertical pipes for L/D = 3 are shown in Figs and As can be seen from the figures, the exchange rate Q and Froude number are found to increase very rapidly in the initial region for the inclined break (45 0 ) and also decrease

91 Q [m 3 /s] 79 rapidly in the non linear region. The Q and Froude number for the vertical break are seen to increase very slowly in the initial region and also decrease slowly in the non-linear region. In case of the horizontal break, the rate of change of Q and Froude number are intermediate between the vertical and inclined pipes. This is consistent with the ingress mechanism for different break angles as discussed in Section E-06 0 deg 5.E deg 4.E deg 3.E-06 2.E-06 1.E-06 0.E Figure 3-25: Effect of break angle on volumetric exchange rate for L/D = 3.

92 Froude Number deg 45 deg deg Figure 3-26: Effect of break angle on Froude number for L/D = 3.

93 81 The time averaged Froude number for the entire mixing period is obtained by numeric integration. The average Froude number for all conditions of the test matrix is shown in Fig The Froude number in general is found to increase as the break angle is increased from the horizontal, until a peak value is reached. This peak Froude number is found to occur at an angle between 30 to 45 depending on the break length. For angles higher than the peak angle, the Froude number decreases until it reaches a minimum value for the vertical break where the mixing is slowed down due to the threedimensional flow structure.

94 Froude Number Avg Fr, L/D = Avg Fr, L/D = 3 Avg Fr, L/D= Angle of Inclination (deg) Figure 3-27: Effect of Break length and angle on Froude number of entire mixing period.

95 83 The average Froude number values from the present study are shown in Fig in comparison with the previous studies by Mercer & Thompson (1975) and Hishida et al (1993). From the figure it can be seen that the general trend of the current results are similar to those of the previous studies. The Froude number is found to gradually increase as the break angle is increased from the horizontal until a peak value is reached and thereafter decreases until reaching a minimum value for the vertical break. It can be seen from the figure that the peak Froude number in case of previous experiments using water and brine by Mercer & Thompson (1975) was found to occur at an angle smaller than 15 for all break lengths, whereas for experiments using air and water by Hishida et al. (1993), the peak Froude number for L/D = 10 is found to occur at an angle of 60. For the present study the peak Froude number occurs at angles between 30 to 45 for the break lengths under consideration, which is closer to the air-water experiments by Hishida et al. (1993). It is also observed that the Froude number predicted is lower in general than the values previously obtained for the smaller angles, but compares well with the data of Mercer & Thompson (1975) for angles above 30. Furthermore, it can be seen that the Froude number is almost constant for the horizontal break for all the three L/D ratios under consideration, as observed in previous studies (Leach & Thompson, 1975).

96 Froude Number Avg Fr, L/D = 0.63 Avg Fr, L/D = 3 Avg Fr, L/D= 5 Mercer, L/D = 8 Hishida, helium-air, L/D = 0.05 Hishida, helium-air, L/D = Angle of Inclination (deg) Figure 3-28: Comparison of average Froude number with previous studies.

97 Froude Number 85 Froude number of initial region for all conditions The Froude number calculated by considering only the initial linear region is shown in Figure 3-29 for all conditions of the test matrix. The Froude number of the initial region is found to compare well with previous studies as can be seen from the figure L/D=0.63, Initial region L/D=3, Initial region L/D=5, Initial region Mercer, L/D = 5.5 Hishida, helium-air, L/D = Angle of Inclination (deg) Figure 3-29: Comparison of initial region Froude number.

98 86 The effect of break length on Froude number for the vertical break is shown in Fig The Froude number is found to decrease as the break length increases, similar to what was observed in previous studies by Epstein (1988) and Hishida et al. (1993) for the range of break lengths under consideration. However, the values of Froude number obtained in the current study are lower than previously reported values. The time averaged Froude number obtained by considering only the initial linear region is also plotted in Fig As can be seen from the Figure, these values match very well with the Froude number reported in previous studies. Since the average value of Froude number for entire mixing period includes both the linear and non linear regions, the Froude numbers calculated based on complete exchange are much smaller than those calculated based on only the initial region. Similar behavior is also seen from the calculated values of exchange rate. The time averaged volumetric exchange rate calculated over the entire exchange period is found to be upto 70% lower than the value obtained by considering only the initial linear region.

99 Froude Number "Current: Entire Stages" "Current: Initial Stage" Water-brine, Epstein 0.10 Air-He, Hishida et al Break L/D Figure 3-30: Effect of Break Length on Froude Number

100 88 CHAPTER 4 Conclusions and Recommendations for Future Work

101 Conclusions The current study aims at performing a scoping study to investigate the effects of the geometric parameters on the gravity driven exchange phenomena. The experiment is performed using water and brine having density ratio, = , as the mixing fluids. The geometric parameters under consideration are the break angle and the break development length-to-diameter (L/D) ratio. This work is performed to establish database to aid in the design of a heated helium-air facility to investigate the D-LOFC event for the VHTR. Flow visualization and density measurement studies are performed to estimate the ingress rate which is important for mitigative actions in the postulated accident event. It is observed that the break angle has a significant effect on the ingress mechanism. Furthermore, it is found that the finite mixing volume and the mixing phenomena make significant impact in overall ingress characteristics. As such, the rate of ingress is steady initially, but after the mixing phenomenon occurs and the brine reaches the break height, the rate of ingress decreases. It is found that the transition occurs at a critical density ratio of ρ* tr,i = 0.74 ± 5% for all conditions of the test matrix. Furthermore, the slope of the change of density for the transient region was found to be a constant value given by C tr = 3.43 ± 9% for all the 21 test conditions under consideration. The estimated Froude number, based on averaging of the entire ingress, for the various conditions is compared to the previous studies. It is found that the average Froude number in general follows similar trend as reported previously. However, the angle at which the peak Froude number occurs is higher than previous data. The overall exchange

102 90 rate is found to be of the order of 70% lower than the exchange rate obtained by considering only the initial linear region of the exchange. Furthermore, the Froude number values of the initial region are found to match better with previous studies than the average Froude number of the complete exchange. Thus, it is seen that the volume of the mixing compartments as well as the break angle plays a major role in determining the ingress mechanism and rate of ingress. However, it is possible that there may be some distortion of the density data since the resolution of the hydrometer is limited to 0.5 kg/m 3. The flow visualization experiments performed using water and brine provides a reliable estimation of the expected ingress mechanism in the proposed helium-air experiments. However, there may be some differences in the flow phenomena for the helium-air exchange flow due to the much higher density difference. The lock exchange flow for the prototypic case is expected to follow the flow pattern described for non- Boussinesq lock exchange flow as opposed to the present study which follows the Boussinesq exchange flow pattern (Lowe et al., 2005). Furthermore, the molecular diffusion may have a more significant effect than in the current study, since the diffusivity of the helium-air system is about 10 4 times higher than the water brine system. The dynamic viscosity of the helium air system is also about 10 2 times higher than the current study and could have an effect on the ingress rate (Fumizawa, 1992). Although the Froude number may be higher than what is predicted for water-brine exchange flow, the overall exchange rate is expected to be lower than earlier predictions, since the exchange rate is found to decrease after the initial rapid linear ingress stage.

103 Recommendations for Future Work Future studies are recommended to perform experiments to obtain a continuous measurement of the change in density during the exchange by using other instrumentation in order to validate the results obtained in current study. Further experiments are recommended to investigate other break geometries such as slit break, to simulate a crack in a pipe and other break locations, such as primary pipe located close to the bottom of the compartments. The scaling study needs to be performed to design the break in a similar manner as in the current study, to maintain the exchange time close to that of a prototypic VHTR. The conceptual design of such a slit break is shown in Figure 4-1. The slit break should be designed in a manner that allows flow visualization without optical distortion. The experiments for slit break need to be designed so as to obtain continuous measurement of ingress rate during the exchange.

104 92 Pipe: rectangular block Slit: crack in pipe Figure 4-1: Conceptual design of slit break.

105 93 Future studies are recommended to utilize the results obtained from the current study to design a heated helium-air test facility. The scaling analysis is performed for the proposed test facility, similar to the scaling study for the water-brine test. Based on the scaling study, the dimensions of the test apparatus are determined so as to maintain the exchange time ratio between the test apparatus and the prototypic VHTR close to unity. The test facility will consist of a cylindrical carbon steel vessel with the various breaks installed on the top cover and on the vessel wall at various locations to simulate the standpipe and primary pipe. The breaks will be installed with flanges that can be altered to accommodate pipes at various inclined angles. To monitor the rate of air ingress through the break, several instrumentations will be utilized. Detailed temperature measurements can be taken at different radial and axial locations within the vessel using thermocouples. Air concentration can be monitored by an oxygen analyzer and local sampling probe at different axial levels. The flow velocity in the break pipes can be acquired by a Laser Doppler Anemometer to relate local oxygen concentration and velocity profiles to obtain the rate of air ingress. Since the mixing is found to occur very rapidly until the mixture interface reaches the height of the break, the proposed air-helium test facility needs to be designed in such a manner that the measurement locations are more detailed up to the height of the break and spread out thereafter. These experiments will provide reliable database for the rate of air ingress and hence will aid in the future licensing of Very High Temperature Gas Cooled Reactors.

106 94 REFERENCES Benjamin, T. B., 1968, Gravity currents and related phenomena, J. Fluid Mech, 31 (2), pp Birman, V., Martin, J. E. & Meiburg, E., 2005, The non-boussinesq lock-exchange problem. Part 2.High-resolution simulations. J. Fluid Mech. 537, Cholemari M. R., and Arakeri, J. H., 2005, Experiments and a model of turbulent exchange flow in a vertical pipe, Int. J. Heat and Mass Transfer, 48, pp Epstein, M., 1988, Buoyancy-driven exchange flow through small openings in horizontal partitions, J. of Heat Transfer, 110, pp Fumizawa, M., 1992, Experimental study of helium-air exchange flow through a small opening, Kerntechnik, 57 (3), pp Hishida, M., Fumizawa, M., Takeda, T., Ogawa, M., and Takenaka, S., 1993, Researches on air ingress accidents of the HTTR, Nuc. Eng. Des., 144, pp Karman, T. von, 1940, The engineer grapples with non-linear problems, Bull. Am. Math. Soc., 46, pp Keller, J. J., and Chyou, Y.-P., 1991, On the hydraulic lock-exchange problem. J. Appl. Math. Phys., 42, pp

107 95 Kim, S. and Talley, J.D., 2009, Quick Look Report Task 5: Air exchange and air ingress experimental data, Scaling analysis and test apparatus design for water-brine scoping experiments, prepared for the U.S Nuclear Regulatory Commission. Kuhn, S.Z., Bernardis, R.D., Lee, C.H., and Peterson, P.F., 2001, Density stratification from buoyancy-driven exchange flow through horizontal partitions in a liquid tank. Nuc. Eng. Des., 204, pp Leach, S.J., and Thompson, H., 1975, An investigation of some aspects of flow into gas cooled nuclear reactors following an accidental depressurization, J. Br. Nucl. Energy Soc., 14 (3), pp Lowe, R. J., Rottman, J. W. and Linden, P. F., 2005, The non-boussinesq lock-exchange problem. Part 1. Theory and Experiments, J. Fluid Mech., 537, pp Mac Donald P. E. et al., September 2003, NGNP Point Design Results of the Initial Neutronics and Thermal Hydraulic Assessments during FY-03, Idaho National Engineering and Environmental Laboratory, INEEL/EXT Rev. 1. Mercer, A., and Thompson, H., 1975, An experimental investigation of some further aspects of the buoyancy-driven exchange flow between carbon dioxide and air following a depressurization accident in a Magnox Reactor, Part I: The exchange flow in inclined ducts, J. Br. Nucl. Soc., 14, pp NO, H. C. et al., Multicomponent Diffusion Analysis and Assessment of GAMMA Code and Improved RELAP 5 Code, Nuclear Engineeringand Design, 237, Oh, C. H., Kim, E. S., Kang, H. S., No, H. C., and Cho, N. Z., December 2009, Experimental validation of stratified flow phenomena, graphite oxidation and mitigation

108 96 strategies of air ingress accidents, FY-09. Idaho National Laboratory INL/EXT Rev. 1. Oh, C. H., Kim, E. S., NO, H. C., and Cho, N. Z., December 2008, Experimental Validation of Stratified Flow Phenomena, Graphite Oxidation, and Mitigation Strategies of Air Ingress Accident, INL/EXT Oh, C.H., et al., March 2006, Development of Safety Analysis Code and Experimental Validation for a Very High Temperature Gas-Cooled Reactor, INL/EXT Reyes, Jr., J. N., Groome, J. T., Woods, B. W., Jackson, B., and Marshall, T. D., 2007, Scaling analysis for the high temperature gas reactor test section (GRTS), NURETH-12, Proceedings, Pittsburgh, PA. Richards, M. B., et al, April 2006, H2-MHR Pro-Conceptual Design Report: SI-Based Plant, General Atomics, GA-A Takeda, T., 1997, Air Ingress Behavior during a Primary-pipe Rupture Accident of HTGR, JAERI-1338, Japan Atomic Energy Research Institute. Takeda, T., and Hishida, M., 1996, Studies on Molecular Diffusion and Natural Convection in a Multicomponent Gas System, International Journal of Heat and Mass Transfer, 39 (3), Takeda, T., and Hishida, M., 1992, Studies on diffusion and natural convection of two component gases, Nucl Eng Des, 135, Tanaka, G., Zhang, B., and Hishida, M., 2002, Effects of Gas Properties and Inclination Angle on Exchange Flow through a Rectangular Channel, JSME Int. J. Ser. B, 45 (4), pp

109 97 Turner, S., 1973, Buoyancy Effects in Fluids, Cambridge University Press, London. Wilkinson, D. L., 1986, Buoyancy driven exchange flow in a horizontal pipe, J. Engrg. Mech., 112 (5), pp Yih, C.S., and Guha, C.R., Hydraulic jump in a fluid system of two layers. Tellus 7 (3),

110 98 APPENDIX A1 Derivation of equations

111 99 Appendix A1-1: Volumetric exchange rate calculation (Epstein, 1988) Mass balance of the two compartments gives: (A1-1) (A1-2) Solving Eq. (A1-1) for Q gives: (A1-3) Adding Eq. (A1-1) and Eq. (A1-2) and integrating the result: (A1-4) (A1-5) (A1-6) Substituting Eq. (A1-6) in Eq. (A1-3) results in:

112 100 (A1-8) Appendix A1-2: Theoretical final density Initial condition at the start of experiment: Density of upper compartment fluid = ρ H,i Density of lower compartment fluid = ρ L,i Final condition at the end of experiment: Density of upper compartment fluid = ρ H,f Density of lower compartment fluid = ρ L,f Mass balance of the total volume of fluids between initial and final conditions gives: (A1-9) At the end of ingress, the densities of the two fluids are equal. Hence, (A1-10) Substituting Eq. (A1-10) in Eq. (A1-9) gives: Since the compartment volumes are equal, this gives the expression for the theoretical final density of the upper compartment as: (A1-11)

113 101 Theoretical final time The expression for change in density of the upper compartment in the non-linear region is given by Eq. 3-4 in section as: (A1-12) At t = t f, the theoretical final density is obtained from Eq. (A1-11) as discussed above. Substituting this into Eq. (A1-12), we get: (A1-13) Hence, the theoretical final time for complete exchange to occur is obtained as: (A1-14) Appendix A1-3: Mathematical treatment for final region (t tr,f t t f ) The volumetric exchange rate is given by Eq. (A1-8) as: Since the volumes of the mixing compartments are equal, this expression changes to: (A1-15) where = constant throughout the exchange As t t f, and Hence, the limit of the expression for Q can be evaluated from Eq. (A1-15) as:

114 102 (A1-16) Using L Hospital s rule, the volumetric exchange rate is evaluated as: (A1-17) Taking the derivative of the correlation for density given by Eq. (A1-12): (A1-18) (A1-19) Furthermore, it is also known that as the density difference between the two compartments approaches zero, the exchange approaches completion and hence, Q 0 as t t f (A1-20) Hence, substituting Eqs (A1-18) and (A1-19) in Eq. (A1-17) and utilizing the boundary condition given by Eq. (A1-20) the expression for volumetric exchange rate in the final stage is obtained as:, for t tr,f t t f (A1-21) The Froude number in this final stage can thus be obtained from Eq. (A1-21) as:, for t tr,f t t f (A1-22)

115 103 APPENDIX A2 Exchange Volume Calculations

116 104 Appendix A2-1: Exchange Volume calculation of prototypic GT-MHR (Quick Look Report, 2009) In order to calculate the global exchange time ratio for the current study as given by Eq. (2-11), the prototypic GT-MHR (INEEL/EXT , (2003)) is used as reference to determine the total volume to be exchanged. A schematic diagram of the reactor vessel is shown in Fig. A2-1 (a) and A2-1 (b). To simplify calculations, the internal structures in the core and upper hemisphere and the shutdown cooling system in the lower hemisphere are neglected. In case of the rupture of the primary pipe, the ingressing air will replace the helium in the vessel upto the highest point of connection between the primary pipe and the vessel, as shown in Fig. A2-1 (b). This volume is given by: where d vessel is the diameter of the vessel, and H is the diameter of the primary pipe. (A2-1)

117 105 Highest level for primary pipe (a) Reactor Vessel (dimensions are in inches) (b) Internal Structures Figure A2-1: Schematic diagram of reference GT-MHR

118 106 For the standpipe, the volume to be exchanged is the total free volume in the vessel for any inclination of the break. This volume includes the core region for which the cross-sectional layout is given in Fig. A2-2 and the fuel block dimensions are given in Fig. A2-3. Figure A2-2: Cross-sectional view of core layout

119 Figure A2-3: Fuel Block (all dimensions are in inches) 107