An Experimental Model Study of Steam Generator Tube Loading

Journal of Pressure Vessel Technology. Received July 18, 2015; Accepted manuscript posted December 8, 2015. doi:10.1115/1.4032198 Copyright (c) 2015 by ASME ASME Journal of Pressure Vessel Technology

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Ouajih Hamouda1 McMaster University Mechanical Engineering Department 1280 Main Street West, JHE-316, Hamilton, ON, L8S 4L7 Canada [email protected] ASME Student Member

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An Experimental Model Study of Steam Generator Tube Loading During a Sudden Depressurization

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David S. Weaver McMaster University Mechanical Engineering Department 1280 Main Street West, JHE-316, Hamilton, ON, L8S 4L7 Canada [email protected] ASME Fellow

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Jovica Riznic Canadian Nuclear Safety Commission (CNSC) Operational Engineering Assessment Division 280 Slater, P.O.B. 1046, Station B, Ottawa, ON, K1P 5S9 Canada [email protected] ASME Fellow

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ABSTRACT

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This paper presents the results of an experimental model study of the transient loading of steam generator

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tubes during a postulated Main Steam Line Break (MSLB) accident in a nuclear power plant. The problem involves complex transient two-phase flow dynamics and fluid-structural loading processes. A better

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understanding of this phenomenon will permit the development of improved design tools to ensure steam generator tube integrity. The pressure and temperature were measured upstream and downstream of a sectional model of a tube bundle in cross-flow and the transient tube loads were directly measured using dynamic piezoelectric load cells. High-speed videos were taken to observe and better understand the flow 1

Corresponding author telephone: +1 (905) 902-3735.

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Journal of Pressure Vessel Technology. Received July 18, 2015; Accepted manuscript posted December 8, 2015. doi:10.1115/1.4032198 Copyright (c) 2015 by ASME ASME Journal of Pressure Vessel Technology phenomena causing the tube loading. The working fluid was R-134a and the tube bundle was a normal triangular array with a pitch ratio of 1.36. The flow through the bundle was choked for the majority of the transient. The transient tube loading is explained in terms of the associated fluid mechanics. An empirical model is developed that enables the prediction of the maximum tube loads once the pressure drop is

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known.

Keywords: Main Steam Line Break, dynamic blowdown load, steam generator tube integrity

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1. INTRODUCTION

In nuclear steam generators, primary side reactor coolant inside the tubes heats

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the water on the secondary shell side to produce steam for power production. The

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steam generator tubes are exposed to aggressive thermal and mechanical loads during

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their normal operating life, especially in the U-bend region where the secondary side

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flows are across the tubes. In this region, potentially destructive vibrations are

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minimized by the installation of anti-vibration bars, typically designed to have small clearances between the tubes and their supports to allow for manufacturing tolerances and assembly, as well as for thermal expansion during operation. As a result, the tubes

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vibrate against their supports and, if the vibrations are significant, mechanical wear may

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occur. This reduces the tube wall thickness at the points of contact.

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The degradation of the tube wall integrity during the lifetime operation of steam

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generators due to mechanical wear and corrosion lowers the design margin of safety against structural failure. Tube wall thinning is especially problematic in nuclear power plants because the steam generator tubes represent the boundary between the irradiated primary side coolant (deuterium or heavy water, D2O, in CANDU reactors) and 2



the secondary side coolant (light water, H2O). The primary side reactor coolant is at a higher pressure than the secondary side coolant and any leakage through defects or tube rupture can therefore lead to the escape of irradiated primary side coolant out of

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containment. A main concern of reactor safety is to ensure that radioactive materials produced by nuclear fission during operation are safely contained. The loss of the

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structural integrity of steam generator tubes is therefore of utmost importance and a sufficient design margin against tube failure must always be ensured.

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In practice, tube wall thinning is regularly monitored and controlled during

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scheduled power plant outages. Excessively worn tubes are taken out of service so that

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the steam generators continue to function reliably over their design life, if not longer. In

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the event that the steam pipe between the steam generators and the turbine

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generators were to break, referred to as a Main Steam Line Break (MSLB), the

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pressurized heated water in the secondary side of the steam generators would suddenly be exposed to surrounding atmospheric conditions. In CANDU steam generators, the secondary side operating conditions are typically around 4.69MPa and 260°C. The rapid

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reduction in pressure to atmospheric conditions would cause the water to flash to

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vapor, producing what is called a ‘blowdown’.

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Since the tubes of a vertical U-bend type steam generator are oriented

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perpendicular to the direction of the flow in the U-bend region, they could be subjected to a significant and potentially dangerous transient hydraulic loading during a blowdown. The risk of structural tube failure is exacerbated if the tube wall thickness has been reduced due to long-term fretting wear and corrosion. If the structural 3



integrity of the tubes is compromised, a leakage pathway is created that could possibly result in the escape of radioactive materials from reactor containment. Thus, knowing the tube loading during such an event is an important input for safe design.

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Steam generator transient thermal hydraulics was the focus of several largescale nuclear safety related experimental programs in the 1970s, with emphasis placed

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on modeling postulated critical Design Basis Accident (DBA) events. Large Steam-LineBreak (SLB) simulations were performed in scaled model facilities of typical commercial

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U-tube steam generators by Framatome in collaboration with CEA [1], as well as by EPRI

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[2]. The purpose of the tests was to develop numerical capabilities to evaluate hydraulic

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loading on steam generator internals during blowdown transients.

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The Framatome tests were performed on a scaled facility of a Model 51 steam

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generator with a total height of 3.5m, maximum cross-section of 0.2m2, and an outlet

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flow restrictor area of 13.6cm2 through which the MSLB was simulated. The transients were initiated from ‘hot standby’ (0% power) initial conditions with saturated liquid water at 7MPa. The experimental vessel was filled such that the stratified liquid free

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surface was initially located between the top of the tube bundle and the bottom of the

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steam separators before the blowdowns were initiated. Transient temperature and

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pressure measurements were collected and a peak pressure difference of about 70kPa

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was recorded at the uppermost tube support plate. It was concluded from this research that investigations that are more fundamental were required to study the initial transient stages of the blowdowns during which thermodynamic non-equilibrium effects were strongly influential. 4



The tests at EPRI were carried out on a 1:7 scale prototypical steam generator facility using Freon-11 as a working fluid. An in-line square tube bundle with 1:1 scale tube diameter was employed consisting of 76 U-tubes with 0.75-inch (1.905cm) outside

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diameter and 1.05-inch (2.667cm) tube spacing. The MSLB simulations were performed through a 4-inch diameter outlet nozzle (81.1cm2 flow area) from subcooled liquid initial

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conditions of around 1013kPa and 82°C. Transient blowdown pressure and temperature measurements were obtained with a response time of 10ms and 500ms respectively.

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The results indicated a transient increase in the pressure drop across the steam

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separators, but no similar rise in pressure drop was recorded in the tube bundle. In

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addition, the build-up of backpressure in a receiver dump tank of 2270L volume was

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found to influence the transient depressurization inside the modeled steam generator

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vessel significantly.

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The US Nuclear Regulatory Commission (NRC) investigated the issue of steam generator tube vulnerability during a MSLB and concluded from dynamic response calculations that the predicted loads are not expected to pose a structural integrity risk

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for steam generator tubes [3]. The NRC study considered the thermal hydraulics of the

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initial stages of steam generator blowdown during which pressure waves propagate at

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acoustic velocities and did not include a detailed investigation of the loads developed

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because of the discharge flow present following the initial rapid transient effects. In addition, the analysis relied on calculations performed using one-dimensional thermal hydraulics codes (RELAP and TRAC-M), which do not account for three-dimensional cross-flow induced forces on the tubes. In order to evaluate the behavior of the cross5



flow in the tube bundle region numerically, a three-dimensional fluid model must be applied to the transient discharge flow during the steam generator blowdown. The application of Computational Fluid Dynamics (CFD) codes in nuclear safety

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analysis is not as well established as numerical codes such as ATHOS [4], RELAP [5], and TRACE [6]. CFD codes offer the advantageous capability of incorporating complex

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geometries and three-dimensional flow effects, which are not properly predicted by one-dimensional system codes. However, the huge degree of sophistication intrinsic to

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transient two-phase flow phenomena makes CFD codes difficult to use in the evaluation

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of nuclear accident events. An analysis of the transient thermal hydraulic response of a

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steam generator secondary side to a MSLB was performed using CFD with the steam

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modeled as a real gas [7]. The results suggested that the steam in the region inside the

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steam generator above the tube bundle accelerates from a normal operational velocity

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of 2m/s to a peak velocity of about 18m/s during a MSLB. The load is expected to scale with the velocity squared. If the fluid density is reduced by a factor of about 10, due to the rapid depressurization, then the hydraulic loading on the tubes could increase by a

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factor of nine as was concluded in the study. The problem continues to be the focus of

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some numerical investigations but, to the authors’ knowledge, no thorough

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experimental study has ever been performed.

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The purpose of the present experimental study was to simulate a MSLB,

investigate the physical phenomena causing the transient loading on a sectional model of steam generator tubes, measure the loading directly, and ultimately, to develop a predictive model for tube loading. To better understand the physics of the transient 6



two-phase blowdown tube loading, pressure drop and temperatures were also measured and high-speed video was used to observe the flow phenomena. No predictive model is presently available that can be used to evaluate the dynamic loading

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of a tube bundle during a transient two-phase blowdown. This is due to a lack of

experimental data and physical understanding of the phenomena. To the authors’

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knowledge, there are no published accounts that accurately simulate two-phase

transient blowdown pressure drop across tube banks or provide detailed measurements

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of tube loading during such events. Therefore, steam generator tube loading during a

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2. EXPERIMENTAL FACILITY

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MSLB accident remains difficult to predict with any precision.

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A purpose-designed facility was built for this experimental investigation, which

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uses R-134a as the working fluid to simulate steam-water in a vertical U-bend type steam generator. R-134a is a non-CFC refrigerant which boils essentially at standard temperature and pressure, scales reasonably well with steam, and therefore provides a

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relatively inexpensive method to carry out these experimental simulations. The system

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consists of four main components, illustrated in Fig. 1a: (1) a vertical reservoir at the

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bottom which holds the liquid refrigerant before the blowdown commences; (2) a test

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section which is filled with tubes representing a sectional model of the steam generator U-bends and has sighting glasses above and below the tube bundle for studying the twophase transient flow entering and exiting the bundle; (3) a rupture disc which is used to provide the sudden depressurization; and (4), a vacuum reservoir at the top of the rig of 7



sufficient volume that it acts as a downstream boundary condition with nearly constant pressure during the blowdown. The pipe above and below the test section is standard 6inch Schedule 40 pipe which has an internal diameter of 155mm. The pressure reservoir

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at the bottom of the rig is 457mm long with an intermediate flange providing internal reservoir lengths of 102mm and 356mm. In this way, simply turning over the pressure

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reservoir permits a change of 4.6 liters of liquid initially in the reservoir. Since the tube bundle model is square, transition sections were designed with internal dimensions of

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138mm square, so that the cross-sectional area, 186cm², remains the same as that of

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the upstream and downstream circular pipes. The transition sections are each 311mm

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long and are fitted with 4 quartz glass sight windows, 76mm x 191mm x 32mm thick.

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These windows permit visualization of the two-phase transient flow upstream and

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downstream of the test section using 2 synchronized video cameras. The test section is

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149mm long and contains a normal triangular array of 12.7mm diameter tubes, 6 rows deep, with a pitch ratio of 1.36, arranged so that the bundle is in cross-flow, as would be the case for tubes at the top of an inverted U-bend type steam generator. Half-tubes are

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welded to the test section walls to minimize boundary effects. The pipe downstream of

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the test section is 622mm long and contains the rupture disc located 235mm from the

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exit (vacuum tank). The rupture disc opens in a few milliseconds to provide the requisite

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rapid pressure relief for each experiment. The aluminum rupture discs are 155mm in diameter, the same as that of the pipe, and open completely such that there is no obstruction of the blowdown flow.

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The loading on steam generator tubes during a blowdown is basically a fluid drag force and is expected to scale with the dynamic pressure drop across the bundle. Thus, fluid density and velocity are important scaling parameters. In two-phase flows, the

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ratio of liquid-to-vapor densities is important. R-134a has a density ratio of 35 at a

temperature of 26°C and a pressure of 690kPa, which is very close to the water-steam

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density ratio of 34 at a steam generator operating condition of 257°C and 4.5MPa. The tube diameter, array geometry, and pitch ratio for the sectional model tube bundle are

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full scale and close to those used in CANDU nuclear steam generators.

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The fluid loading on the tube bundle was measured using 4 piezoelectric load

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cells, one located in each corner of the test section, shown as location 4 in Fig. 1a. The

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test section was designed such that the only load path from the bottom fluid reservoir

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to the test rig above the test section was through the load cells. Therefore, the

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synchronized sum of the signals for the 4 load cells provided the total dynamic fluid force of the flow on the tubes. An illustration of the test section design is provided in Fig. 1b. The load cells were carefully calibrated, were linear with an R² fit of 0.9993, had

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a resonant frequency of 65khz and a rise time of 38µs.

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Transient temperatures and pressures were measured upstream and

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downstream of the test section (locations 1 and 2 in Fig. 1a respectively) as well as

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downstream of the rupture disc (location 3 in Fig. 1a) during the blowdown experiments. The pressures were all measured in the absolute frame of reference and the pressure drop across the tube bundle was determined from the difference between the synchronized pressures measured at locations 1 and 2. It was considered that the 9



flow losses in the test section due to wall friction were negligible compared to those across the tube bundle itself. Commissioning tests demonstrated that the off-the-shelf instruments proved

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unsuitable for the shock load environment produced at disc rupture and a

comprehensive program of instrumentation development became a necessary

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component of the study. The instruments so developed were validated, calibrated, and synchronized to prove their reliability for the experiments undertaken. The

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measurement uncertainties are ±17.2kPa for the dynamic pressure, ±0.9°C for the

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temperature, and ±0.4kN for the dynamic load. The details of the instrument problems

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and the remedial actions taken, as well as the validations, calibrations, synchronization,

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and uncertainty determinations are described in detail in references [8] and [9].

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Each experiment began with charging the pressurized section of the rig which

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had entirely been brought down to a vacuum (99.9% or 70Pa). The charging process had to be carried out very carefully in order to ensure that the rupture disc did not burst prematurely because of pressure transients produced in the process. The specified

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pressure difference across the disc to cause rupture was 584kPa with an uncertainty of

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±5%. The system was charged to a pressure close to the specified rupture point and

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then rupture was triggered using an accumulator charged with nitrogen and having a

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distensible bladder separating the nitrogen from the refrigerant. In this way, the accumulator pressure could be very precisely controlled and the blowdown triggered with no danger of contamination of the refrigerant. 10



3. OVERVIEW OF TWO-PHASE TRANSIENT PHENOMENA In order to understand the physics of the transient tube loading during a

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simulated blowdown, a comprehensive set of experiments were conducted, varying initial liquid level and the number of tube rows. Measurements were taken of pressure

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and temperature upstream and downstream of the tube bundle as well as the tube loading. At the same time, high-speed videos were taken above and below the test

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section to observe the flow phenomena. For brevity, only those details from a typical experiment which are essential for understanding the phenomena presented in this

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paper will be summarized here. More detailed results are provided in [10] and complete details are available in [9].

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A sample set of transient pressures measured at the three sensor points along

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the pipe are shown in Fig. 2 for an experiment performed with six rows of tubes in the

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test section and 21% of the pressure vessel filled with liquid R-134a. The pressure sensors at locations 1 and 2 below the rupture disc were in the regions initially filled with subcooled liquid and saturated vapor respectively. Initially, the liquid was at

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600kPa and 19°C and the vapor was at 594kPa and 20°C. Location 3 above the rupture

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disc was initially in a vacuum. The general transient behavior observed is typical of all

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the two-phase blowdown experiments carried out. The pressure amplitudes and event durations varied from one experiment to the next due to changes in the initial conditions, the pressure vessel dimensions, and the number of rows of tubes in the test section.

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The transient pressure traces show distinct features that can be split into three main segments, which in Fig. 2 are observed to occur between 0 – 80ms, 80 – 300ms, and from 300ms onwards. The rupture disc opens in a couple of milliseconds, with a

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rarefaction wave propagating upstream towards the tube bundle and a positive

pressure wave propagating downstream towards the vacuum tank. The arrival time of

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these waves at the various transducer locations depends on the speed of sound in the fluids and no significant phase transition occurs in the first 10 milliseconds or so. The

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phenomena during this period are acoustic. The rapid pressure decrease at location 1,

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upstream of the tube bundle, is halted by the initiation of rapid phase transition from

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liquid to vapor at about 25ms. This is followed by a period of vigorous boiling in which

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the ratio of vapor to liquid in the pressure vessel increases rapidly, limited initially by

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fluid inertia. This process slows down when the rate of vapor generation becomes

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controlled by the rising pressure drop across the tube bundle, as seen at about 40ms in Fig. 2.

At about 80ms, the rate of vaporization is sufficient to produce the critical

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pressure ratio in the tube bundle and the flow is choked. At this point, the flow velocity

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in the tube bundle is sonic and no further decrease in pressure downstream of the tube

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bundle can increase the flow rate. Thus, a quasi-steady condition is established between

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80ms and 300ms in which the pressure drop across the tube bundle remains nearly constant. High-speed photographs obtained simultaneously upstream and downstream of the test section at t = 100ms are also presented in Fig. 2. The images show a densely populated bubbly mixture boiling rapidly below the tubes, at relatively higher pressure, 12



and a well-mixed homogeneous two-phase flow exiting the tube bundle at a lower pressure. Transient temperature measurements indicated that the fluid emerging from the tube bundle was in a saturated two-phase state, whereas the fluid below the tubes

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was in a prolonged state of thermal non-equilibrium, in some cases spanning practically the entire duration of the experiment. At about 300ms, the liquid in the reservoir is

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becoming depleted and the rate of vapor generation cannot be sustained. Thus, the pressure drop across the tube bundle reduces, the mass flow rate decreases

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accompanied by high void fractions, and equilibrium conditions are eventually

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established, signaling the end of the blowdown. These 3 distinct flow regimes observed

4. PRESSURE DROP ACROSS THE TUBE BUNDLE

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loading as discussed in the sections below.

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during the blowdown control the pressure drop across the tube bundle and the tube

The tube bundle in the test section imposes a significant restriction to the flow during the transient blowdown. The transient pressure drop across the tube bundle,

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obtained from Fig. 2 by subtracting the pressure measured at location 2, downstream of

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the tube bundle, from the pressure measured at location 1, upstream of the tube

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bundle, is plotted in Fig. 3. A logarithmic time scale is used to emphasize the details at

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small times. The initial static pressure drop of 5.9kPa across the test section consists primarily of the elevation head difference of the R-134a (3.2kPa) between the two sensors, and the pressure boost supplied by the compressed gas accumulator just before disc rupture (2.7kPa). The upstream propagation of the rarefaction wave from 13



the rupture disc produces a transient pressure drop across the test section, which is labeled as the ‘acoustic’ pressure drop in Fig. 3. The pressure drop begins to rise at about 2ms, when the rarefaction wave passes location 2 (above test section), and peaks

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at about 8ms, when the wave arrives at location 1 (below test section).

Following the initial pressure wave propagation effects, the pressure drop across

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the test section increases due to vapor generation, expansion, and acceleration of the two-phase flow. The small peak in the pressure drop observed at 11ms was produced by

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the flashing of a small amount of liquid which had condensed on the steel surfaces in

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the tube bundle before the transient began. The increase in the pressure drop at about

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23ms is caused by the upward acceleration of the flashing two-phase fluid front that

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originated at the liquid surface below the tubes. The flow restriction imposed by the

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tube bundle limits the rate of vapor generation below the tubes as does the inertia of

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the accelerating fluid below the tubes. This region of vapor generation, following the ‘acoustic’ wave propagation phase, from about 10ms to about 80ms, has been defined as the ‘acceleration’ phase of the blowdown.

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At about 80ms after blowdown initiation, the pressure drop across the tube

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bundle flattens out and becomes essentially constant until about 300ms. Thus, the rate

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of vapor generation of the liquid below (upstream of) the tube bundle is limited by the

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pressure drop across the tube bundle. Indeed, this pressure drop has reached a critical value at which the flow has become ‘choked’. This gives rise to the ‘quasi-steady’ flow region. At about 300ms, the liquid upstream of the tube bundle is sufficiently depleted that it can no longer sustain the mass flow rate and the pressure drop across the bundle 14



begins to fall until the blowdown is complete and equilibrium conditions have been established. Since this portion of the blowdown is dominated by the pressure drop through and downstream of the tube bundle, it has been designated as the

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‘form/friction drag’ phase.

When the flow through the tube bundle is choked, the discharge of the two-

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phase fluid below the tubes is controlled by the restriction imposed by the tubes. This is the result of form drag of the tube bundle as friction effects are expected to be

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negligible at high Reynolds numbers. This is confirmed by pressure drop measurements

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obtained across the rupture disc, which basically diminished to zero when the two-

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phase flow inside the tube bundle was choked. During this quasi-steady discharge

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portion of the transient, the pressure drop measured across the test section is

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dominated by the sharp pressure gradient at the tube bundle due to form drag losses.

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The sonic velocities produced at flow choking prevent any further increase in mass flux and, therefore, pressure drop. A schematic diagram illustrating the instantaneous pressure profile along the pressure vessel at a point during the quasi-steady stage of the

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blowdown, t = 0.25s, is shown in Fig. 4. The static pressure drop component between

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the bottom pressure transducer and the tube bundle is also included in the

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measurement. The amplitude of the initial static head was never greater than 3% of the

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overall pressure drop across the tube bundle. In order to better understand the transient pressure, it is instructive to plot the

pressure drop, Δp1-3, measured across the bottom and top of the pressure vessel, normalized by the upstream pressure (location 1), pu, according to Eq. (1), 15



Δp1−3 pu − pd p = = 1 − d , pu pu pu

(1)

where pd is the downstream pressure (location 3). The transient normalized pressure

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ratio obtained from Eq. (1) is plotted for 3 experiments with similar initial conditions in Fig. 5. The pressure downstream of the rupture disc is initially 0kPa (vacuum) and the

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initial pressure ratio is therefore equal to one at t = 0. The pressure ratio converges to zero when the upstream and downstream pressures approach other towards the end of

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the blowdown.

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The non-dimensional pressure ratio parameter collapses the three experimental

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curves quite well. This is especially true for the most important time segment during which the pressure ratio remained nearly constant and the pressure drop across the

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tube bundle was maximum (0.1s to 0.25s). The pressure ratio is directly related to the mass flow rate in the pressure vessel, which remains constant when the flow is choked

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and the fluid properties and discharge flow area are the same. Hence, the difficulty in precisely controlling all the initial conditions and the additional random boiling effects

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did not influence the quasi-steady pressure ratio when the flow rate was maximum.

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Generally, measurement repeatability was excellent and variations in the details of the

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pressures in the initial stages had little discernible influence on the average transient

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measurements over the full blowdown durations.

5. TUBE LOADING

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The two-phase flow across the tube bundle during the blowdown transient produces a significant hydraulic drag loading on the tubes. The dynamic loads on the tube bundle were measured and can be interpreted in terms of the two-phase fluid

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mechanics discussed in the previous section. The maximum pressure drop across the tube bundle was established early during the blowdown experiments after the initial

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unsteady effects were complete. These were associated with the propagation of

pressure waves and the subsequent rate of change of momentum of the flashing two-

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phase fluid.

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About 0.1s or so into the transients, the rate of vapor generation below

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(upstream of) the tubes was stabilized by the rate of fluid discharge through the tube

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bundle, producing a quasi-steady pressure drop condition. During this stage of the

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blowdown, the flow through the tube bundle was choked and the pressure drop was

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maximum. This persisted until the liquid inventory upstream of the tube bundle was depleted to the point that the maximum rate of vapor generation could not be sustained. The two-phase flow through the bundle then displayed increasing liquid

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entrainment, which was accompanied by a reduction in the upstream pressure. The

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result was a deceleration of the flow and a decrease of the pressure drop across the

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tube bundle, which eventually diminished to zero at the end of the transient blowdown

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discharge.

A sample transient load measurement obtained during an experiment performed

with a tube bundle containing 6 rows of tubes is presented in Fig. 6. The initial volume of liquid in the pressure vessel was 12.1L, which corresponds to a liquid column height 17



of 670mm. The liquid free surface level was visible at the upper window in the pressure vessel, above the tube bundle. The low-frequency decaying oscillations in the first 0.1s of the load signal were caused by vibrations of the pressure vessel at its lowest axial

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natural frequency of about 35Hz, as determined by simultaneous accelerometer measurements.

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The mean tube loading trend seen in Fig. 6 is representative of the general load behavior observed in all of the experiments. The load increases rapidly as the vapor

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downstream of the tube bundle accelerates away from the tubes and the two-phase

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fluid upstream of the tubes accelerates through the tube bundle. At about 150ms, the

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tube loading begins to level off at about 7.9kN as the flow rate through the tube bundle

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becomes established. The tube bundle loading then attains a maximum value of about

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8.5kN. This continued at a nearly constant amplitude for about 100ms, the result of the

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flow having become choked. The two-phase mixture flow rate then begins to decrease when the liquid inventory upstream of the tubes becomes depleted and the initial rapid rate of vapor generation cannot be sustained. As the two-phase flow through the

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bundle continues to decelerate, the load tapers off and converges towards 0kN at the

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end of the blowdown.

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The maximum tube loading occurred when the two-phase fluid flow rate (and

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pressure drop) through the tube bundle was maximum. This ‘quasi-steady’ discharge is associated with two-phase flow choking through the tube bundle. In order to examine this phenomenon more closely, the upstream and downstream pressures, measured for the same case as that in Fig. 6, are plotted as a function of time over the period from 18



0.25s to 1s in Fig. 7 for comparison with idealized theory. Calculations were performed to estimate the critical pressure ratio for choking using the assumptions of the Homogeneous Equilibrium Model (HEM) and Homogeneous Frozen Model (HFM) [11].

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The HEM calculation was performed assuming initially saturated liquid, as well as initially saturated vapor conditions upstream of the tubes. In both cases, the critical flow

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was assumed to be in thermal and mechanical equilibrium. The measurements obtained immediately downstream of the bundle were assumed to represent critical flow

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conditions. This is not expected to introduce any significant errors since flow losses

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become negligible once the flow is choked. The critical pressure was obtained by solving

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νc

2 ( h0 − hc ) ,

(2)

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Gc =

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iteratively for the maximum critical mass flux, Gc, according to Eq. (2),

where h0 is the stagnation enthalpy, hc is the enthalpy at the critical flow conditions, and

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νc is the specific volume at the critical flow conditions. On the other hand, the HFM assumes that the liquid is incompressible and that the quality remains constant (no

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vaporization). Choking occurs when the ratio of downstream to upstream pressure is

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η=

pc ⎛ 2 ⎞ =⎜ ⎟ p0 ⎝ γ + 1 ⎠

γ γ −1

,

(3)

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less than the critical pressure ratio given by Eq. (3),

where η is the choked pressure ratio, pc is the critical pressure, p0 is the stagnation pressure, and γ is the specific heat ratio. In reality, the quality does not remain constant, but does not change as much as would be predicted by the equilibrium model. The

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critical pressure ratio is expected to be between the two limiting cases. The predictions of the two models are usually similar when the flow quality is high and the HFM generally provides better predictions for the critical mass flux [11].

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The maximum tube load at 0.25s during the quasi-steady stage of the blowdown in Fig. 6 is associated with an upstream pressure of 430kPa. The critical downstream

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pressures for choking, computed using Eqs. (2) and (3), are shown in Fig 7. As expected, the critical pressure predictions of the two models are similar when the assumed quality

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is high. In any case, the measured downstream pressure is well below that required for

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choking which means that the flow rate through the tube bundle is independent of the

tN

downstream pressure. The pressure ratio remains below the critical value well into the

ip

transient.

sc r

A small ‘hump’ appears in the upstream pressure in Fig. 7 at about 0.66s,

Ma nu

towards the end of the transient when the flow quality is relatively high. The upstream pressure at this time is 285kPa and the downstream pressure is 169kPa. This gives a pressure ratio of 0.59 which is essentially the same as the critical pressure ratio

ed

predicted by the HFM. Based on these observations, the two-phase flow through the

pt

tube bundle appears to remain choked well into the transient blowdown after the quasi-

ce

steady stage. The ‘hump’ at 660ms appears to represent the transition from choked

Ac

flow to subsonic flow through the tube bundle. High-speed flow visualizations obtained above the tube bundle also indicated a change in the flow pattern at around the same pressures and stages during the transient. This ‘hump’ is also seen in the simultaneously measured load shown in Fig. 6 and is typical of observations in all of the experiments. 20



6. EFFECT OF LIQUID LEVEL In order to understand the effects of initial volume and level of liquid on the

ite d

two-phase transient and associated tube loading during a blowdown, a number of

experiments were carried out with essentially identical conditions while varying the

py ed

initial amount of liquid R-134a in the pressurized reservoir. Of particular interest was the influence of the initial location of the liquid free surface with respect to the tube

Co

bundle on the transient loading of the tubes. Steam generators are typically designed

ot

such that the tube bundle is submerged in water during operation but the tubes may

tN

become uncovered if the water level falls sufficiently. The quality of the saturated

ip

steam-water mixture also varies at different locations in the steam generator and with

sc r

different amounts of heat transferred from the tubes.

Ma nu

Figure 8 shows a comparison of the measured tube bundle loading for two experiments, one with the liquid free surface initially below the tube bundle and the other with the liquid level above the tubes (tube bundle submerged). The decaying high

ed

frequency fluctuations seen in the load measurements, up to about 0.5kN in magnitude,

pt

are the result of rig response to the shock loading from the bursting rupture disc, as

ce

demonstrated by simultaneous test section acceleration measurements. The pressure

Ac

measurements during the ‘acoustic’ phase of the initial pressure transients, as seen in Fig. 2, contain rapid changes that are associated with unsteady wave propagation, but these do not produce any significant effect on the tube bundle loading. Not unexpectedly, the acoustic waves pass through the tube bundle with no effect on the 21



loading and no detectable effect on the acoustic propagation velocity. The rapid increase in the measured load, which began at about 25ms for the case with the liquid initially below the tubes and 55ms for the case with the liquid surface initially above the

ite d

tubes, was produced by fluid acceleration as rapid vapor generation begins.

Very interestingly, the magnitude of the tube loading plateau during the quasi-

py ed

steady stage of the blowdown is also not significantly affected by the initial liquid level. A maximum tube bundle loading of about 7.8kN was established during the blowdown

Co

between 0.22 – 0.35s when the liquid level was initially above the tubes and between

ot

0.11 – 0.27s when the liquid was below the tubes. This can be explained by the fact that

tN

the maximum flow through the tube bundle is dependent only on there being sufficient

sc r

bundle to produce choking.

ip

vapor generation upstream to maintain the critical pressure ratio through the tube

Ma nu

Study of Fig. 8 suggests that the primary effects of the initial liquid level are the initial rate of increase of tube loading and the duration of the blowdown. The latter is simply a function of the initial liquid inventory, 4.9L and 15.4L in the case of the lower

ed

and higher initial liquid levels respectively. Everything else being the same, more liquid

pt

takes longer to boil off. The reason for the difference in initial rate of load increase is a

ce

little more subtle. The rate of vapor generation near the liquid-vapor interface will

Ac

depend on the pressure there. When the initial liquid level is below the tube bundle and flashing begins, the void fraction in the tube bundle is high and the resistance to flow through the bundle is therefore relatively low. Thus, the initial rate of vapor generation is very high. This continues until the pressure drop across the tube bundle becomes the 22



controlling factor in the rate of vapor generation. Indeed, the load for this case in Fig. 8 indicates a small, brief overshoot in load to approximately 8.1kN at about 65ms. This is probably an inertial effect as the rate of vapor generation is reduced and represents a

ite d

4% increase in the maximum load over that measured during the quasi-steady part of the blowdown. It is noted that the initial liquid level in an operating steam generator is

py ed

expected to be above the tubes.

On the other hand, when the initial liquid level is above the tube bundle, the

Co

increased pressure resulting from the flashing of the liquid, accompanying expansion

ot

and rapidly accelerating two-phase flow, occurs above the tube bundle. Thus, the

tN

pressure drop across the tube bundle and the associated loading are substantially

ip

reduced during these initial stages of the blowdown. As the nominal liquid-vapor

sc r

interface passes through the tube bundle, the pressure drop approaches the critical

Ma nu

value for choked flow and the quasi-steady conditions are established, at about 200ms in the present case. The important observation here is that the maximum load of about 7.8kN is the same during the quasi-steady stage of the transient, regardless of the initial

ed

liquid level.

pt

Close examination of the dynamic load for the case of initial liquid level below

ce

the tube bundle shows a peak of nearly 5kN was observed at about 12ms. This load

Ac

measurement was produced by the acceleration of a flashing two-phase mixture inside the tube bundle which was due to liquid condensation on the surface of the tubes before the blowdown began. This phenomenon was also demonstrated in Fig. 3 where it was shown that an isolated flashing front had developed between 9 – 13ms. The 23



corresponding rise in the load signal matches the timing of the acceleration of this fluid mixture. This gives an indication of the rapidity of the flashing phenomenon, which took place immediately after the passage of the rarefaction wave. The measurements also

ite d

demonstrate the response time adequacy of the load instrumentation system for measuring flow-induced loads on the tube bundle. The dynamic load amplitude

py ed

decreased briefly at about 14ms and increased again beginning at about 21ms. This was also shown in Fig. 3 to be related to the acceleration of the flashing two-phase fluid

ot

7. EFFECT OF NUMBER OF TUBE ROWS

tN

Co

front initially below the tubes.

ip

In order to extract practical information from the results, it was important to

sc r

study the quantitative relationship between the measured pressure drop and tube

Ma nu

bundle loading. Given that the relationship was constant for the same number of rows of tubes in the bundle, a parametric study of the effect of the number of rows of tubes was thought to be useful. Varying the number of rows of tubes reveals additional

ed

information about the underlying physics, which is valuable for developing a predictive

pt

methodology for tube loading during a blowdown.

ce

It has been demonstrated that under similar initial thermodynamic conditions

Ac

and various initial liquid volumes, the tube bundle was subjected to the same maximum load amplitudes (refer to Fig. 8). The maximum loads occurred during the quasi-steady two-phase discharge stage and remained the same regardless of whether the initial liquid level was below or above the tube bundle. It was also determined that a sufficient 24



liquid inventory is required below the tubes in order to sustain the maximum rate of vapor generation. By having the initial liquid level inside the tube bundle, quasi-steady flow conditions were reached reasonably quickly and the duration of the quasi-steady

ite d

drag loading was long enough to obtain reliable and repeatable measurements. Thus, the effects of the number of tube rows on the bundle loading were studied with an

py ed

initial liquid level of about 50% for the 27.8L vessel. The liquid surface was inside the tube bundle for this case. The test section had been designed so that the number of

Co

rows of tubes could be readily modified between each test run.

ot

A comparison of the transient tube loads obtained in two separate experiments

tN

performed with six and three rows of tubes in the tube bundle is presented in Fig. 9. The

ip

trends of the transient tube load measurements were observed to be very similar. In

sc r

particular, the rates of the change in the transient drag loading and the timing of the

Ma nu

flow transition from the initial acceleration to the quasi-steady flow through the tubes were almost the same in both tests. The main difference between the two measurements was the amplitude of the maximum load. The maximum amplitude was

ed

about 8.1kN for six tube rows and about 6.6kN for three tube rows. It is noted that the

pt

tube loading with 6 rows of tubes was slightly higher for the larger vessel volume than

ce

when the smaller vessel was used in Fig. 8 (8.1kN compared to 7.8kN). When the vessel

Ac

volume is increased relative to the discharge area, greater overall mixing allows the pressures to recover to higher amplitudes during rapid phase transition relative to the downstream pressure. The lower pressure for the smaller vessel is due to a greater departure from thermodynamic equilibrium. For blowdowns performed with similar 25



discharge areas and downstream pressures, the pressure difference between the vessel and the downstream ambient conditions is higher when the pressure vessel is larger. Quantitatively, the relationship between the amplitude of the maximum pressure drop

ite d

across the tube bundle and tube loading was observed not to be affected by the vessel volume as long as the number of rows of tubes in the bundle remained the same.

py ed

It is seen that the duration of the transient loading was also different between the two experiments in Fig. 9, with the deeper tube bundle producing a longer

Co

blowdown. The restriction imposed on the discharging two-phase flow is greater when

ot

the tube bundle contains a larger number of rows. The flow through the bundle during

tN

the quasi-steady stage is controlled by two-phase flow choking inside the tube bundle.

ip

Calculations indicate that, even for the case with only 2 rows of tubes, the ratio of

sc r

downstream to upstream pressure, 0.32, was substantially lower than the critical

Ma nu

pressure ratio, 0.59, required to choke the flow. The mass hold-up increases with additional rows of tubes as more flow losses are encountered and more liquid vaporization takes place inside the tube bundle. The flashing retards the flow discharge

ed

and results in an increased build-up of pressure upstream. Even with only 2 tube rows

ce

8. DRAG LOAD COEFFICIENT

Ac

pt

the critical pressure ratio for choking is achieved.

The drag load measured for an experiment performed with six rows of tubes and

67% of the vessel initially filled with liquid is compared to the simultaneously measured pressure drop across the tube bundle in Fig. 10. The pressure drop was computed 26



simply by subtracting the pressure above the tubes (location 2) from that below the tubes (location 1). These ‘raw’ measurements clearly show the qualitative similarity between the two independent measurements of pressure drop and load. Following the

ite d

first 55ms of the transient, in which the acoustic and inertial effects downstream of the tube bundle were significant, the trends in the pressure drop measurement followed

py ed

the load signal very closely for the remaining duration of the transient. Note that the large peak in the pressure drop measurement at about 15ms, resulting from the flashing

Co

and acceleration of vapor downstream (between the top of the tube bundle and the

ot

sensor at location 2), produces no discernible loading on the tubes.

tN

Under steady-state conditions, the drag force exerted on the tube bundle, Fdrag,

ip

is directly proportional to the form drag pressure drop established across the full array

sc r

of tubes, Δpdrag. The proportionality constant is a product of the cross-sectional flow

Ma nu

area, Acs, and a drag coefficient, Cdrag, as given by Eq. (4),

Fdrag = Cdrag ⋅ Acs ⋅ Δpdrag .

(4)

The flow area Acs in these equations is the full cross-sectional flow area of the empty

ed

pipe and Cdrag is an empirical coefficient that relates the pressure drop measured across

pt

the tubes with the overall drag force. In the present experiments, the cross-sectional

ce

area was constant, the drag load on the tube bundle was measured directly, and the

Ac

pressure drop was measured between locations 1 and 2. The pressure drop measured during the quasi-steady stage of the transient, Δpmeasured, basically consisted of the steep pressure gradient across the tube bundle due to the flow losses, Δpdrag, and the static head of the flow between the pressure sensors, Δpstatic, as shown by Eq. (5), 27



Δpmeasured = Δpdrag + Δpstatic .

(5)

Hence, the drag coefficient was related to the transient measurements as given by Eq.

C drag =

Fdrag

A ( Δpmeasured − Δpstatic )

ite d

(6), .

(6)

py ed

It is difficult to determine precisely the magnitude of the static pressure drop during the transient blowdown since this changes as the liquid flashes off. For

Co

calculation purposes, the static pressure drop component was assumed to remain

ot

constant and equal to the initial static pressure drop. This was computed based on the

tN

initial density and height of the liquid above the measurement location. Given that the

ip

liquid column observed in the high-speed flow visualizations remained relatively

sc r

unperturbed well into the quasi-steady stage of the transient, the constant static head

Ma nu

assumption was deemed reasonable. As this static head was small compared with the total pressure drop measured across the tube bundle, typically less than 3%, any error introduced by this assumption would be very small.

ed

A value for the tube loading drag coefficient was computed by matching the

pt

values of the tube load and pressure drop curves for a time segment of the quasi-steady

ce

stage of the transient over which the load was essentially constant, Δt, as indicated by

Ac

the dashed vertical lines in Fig. 10. During this time, the flow through the bundle was choked and the vapor generation rate below the tubes was maximum, producing maximum amplitudes in both the load and pressure drop measurements. Essentially, this procedure gives mean values of the results over the measurement period. The static 28



head computed for the experiment presented in Fig. 10 based on the initial liquid density of 1,222kg/m3 and height of 524mm was 6.3kPa. The traces for the measured load and pressure drop and the instantaneous drag coefficient over the time interval

ite d

indicated in Fig. 10 are shown in Fig. 11. The computed mean value of the drag

coefficient over this time period is 1.4046 and the standard deviation, indicated by the

py ed

dotted lines on the load graph of Fig. 11, is 0.0108. Thus, the drag coefficient for this experiment is taken as 1.405 ± 0.011.

Co

The procedure outlined above for computing the drag coefficient was intended

ot

to eliminate as much as possible any subjective bias in determining the drag coefficient.

tN

This value has been used in Eq. (4) to compute the load over the entire transient and the

ip

computed and measured loads are compared in Fig. 12. It is seen that the transient load

sc r

on the tubes, computed using the drag coefficient obtained from a segment of the

Ma nu

quasi-static portion of the blowdown, agrees remarkably well with the measured load over the entire blowdown following the initial acoustic transient. This supports the assumption that the maximum loading on the tubes during a blowdown can be

ed

computed from the pressure drop across the tubes and the empirical drag coefficient

pt

using the simple static relationship given by Eq. (4).

ce

The fluid drag loading on the tube bundle depends on the two-phase mass flow

Ac

rate, the tube bundle geometry, and the number of rows of tubes. By determining the drag coefficient for the array with different numbers of tube rows, the measured dynamic load can be related to the measured transient pressure drop across the tubes as a function of the number of tube rows. Thus, a number of experiments were 29



conducted with the number of tube rows varying over the range from 2 to 6 and the computed drag coefficients are shown in Table 1. These results are plotted against the number of tube rows in Fig. 13. The ‘error bars’ shown in Fig. 13 represent the standard

ite d

deviations of the data computed as indicated above and therefore are associated with instantaneous fluctuations in the load and pressure measurements (not measurement

py ed

uncertainties). Four different experiments were conducted with 6 rows of tubes and various initial conditions. The computed drag coefficients in these cases indicate

Co

remarkable agreement in Fig. 13 and Table 1.

ot

The drag load on the tube bundle is clearly proportional to the number of rows

tN

of tubes in the bundle. The mean pressure drop per tube row can be determined by

ip

dividing the pressure drop across the entire tube bundle by the number of rows of

sc r

tubes. If the number of rows of tubes in a tube array is small, the pressure drop per tube

Ma nu

row may increase as the number of transverse rows is reduced [12]. Downstream wake effects dominate the overall pressure drop and are not typical of the fully established flows in the tube bundle.

ed

In steady-state incompressible flow calculations for tube bundles in cross-flow,

pt

correction factors are typically employed to determine the drag coefficient for the

ce

leading rows of tubes. For high velocity flows (Re > 105) in a staggered bank of tubes the

Ac

correction factor is about 50% for the 1st row, 17% for the 2nd row, and 2% for the 3rd row. The flow becomes fully developed by about the fourth row at which point the pressure drop per tube row is expected to increase proportionally with the number of tube rows. Thus, a linear relationship between the drag load coefficients and the 30



number of tube rows was computed using the data for 4 to 6 tube rows inclusively and is shown by the dashed line in Fig. 13 and is given by Eq. (7),

Cdrag = 1.17 + 0.04 z ,

(7)

ite d

where z is the total number of tube rows. The linear regression provided an excellent fit

py ed

with an R2 value of 0.996. As expected, the drag coefficient for two rows does not fall on the line and this trend is also seen for the case of three rows of tubes although the departure from the linear fit is smaller.

Co

The ‘error bars’ in Fig. 13 are the standard deviation of the fluctuations around

ot

the mean computed coefficients and, as mentioned above, are not an indication of the

tN

measurement uncertainty. The larger fluctuations in the case of the experiment with 4

ip

tube rows reflects the fact that the maximum flow rate was established earlier in the

sc r

transient and rig dynamics increased the apparent magnitude of the fluctuations. These

Ma nu

clearly had little effect on the mean values of the pressure drop and load measurements.

The drag loads computed from Eqs. (4) and (7) based on the measured pressure

ed

drops are compared to the measured dynamic loads for experiments carried out with

pt

different numbers of tube rows in Fig. 14. The experiments were all performed using the

ce

same pressure vessel volume, similar initial conditions, and an initial liquid fill of about

Ac

50%. The results show that the drag load coefficient computed from Eq. (7) scales the pressure loading measured for all of the tests quite well, even in the case of 2 tube rows for which a poorer fit is expected. It is seen that the measured load is dropping off slightly below the computed load, later during the quasi-steady stage of the blowdown 31



near about 0.35s. This is the result of the piezoelectric characteristics of the dynamic load transducers and data acquisition system which tend to discharge after about 0.2s at a constant load. It is important to recognize that this load reduction is within the

ite d

experimental uncertainty of the measurements and gives a conservative prediction of the load at this stage of the blowdown. Despite having been developed using only the

py ed

brief quasi-steady stage of the transient, the computed pressure loads matched the measured tube loading trends very well for the majority of the blowdown durations.

Co

Results from these experiments as well as previous experiments presented in the

ot

literature indicate that at high flow velocities, the pressure drop across the tube bundle

tN

is Reynolds Number independent. Hence, as long as the two-phase fluid density ratio is

ip

representative (which in this case is very similar between water and R-134a), the

sc r

physical relationship between the drag load and the pressure drop is expected to

Ma nu

remain the same. The pressure drop across the tubes for choked flows will depend on the choking velocity of the fluid, which is related to the sonic velocity of the fluid and is extremely complex. The results are expected to be applicable to steam-water provided

ed

that the pressure drop is provided as an input to the developed empirical model.

pt

Ac

ce

9. STEADY STATE FLOW COMPARISONS As one of the goals of the present research was to develop a predictive model

for the dynamic loading on a tube bundle during a MSLB incident, it was considered useful to determine whether any of the existing steady-state models for the pressure drop across a tube bundle might be useful for this purpose. There has been much work 32



in the fields of heat transfer, fluid dynamics, and flow-induced vibrations of tube bundles investigating the steady drag of a tube within a bundle in cross-flow. The drag force is generally formulated as a function of pressure drop and empirical drag

ite d

coefficients. These depend on the tube array pitch and pattern, as well as the fluid properties.

py ed

Two-phase drag coefficients for tube bundles are determined from experimental investigations. One of the most widely adopted correlations [13] uses two-phase friction

Co

multipliers for the liquid and vapor phases. The pressure drop so determined does not

ot

approach the natural limits for single-phase liquid and vapor flows, and contains an

tN

unrealistic step discontinuity at the transition Reynolds number of 2000 [14].

ip

Furthermore, the two-phase friction multipliers only depend on an empirical two-phase

sc r

turbulence correction parameter, which does not account for void fraction or mass flow

Ma nu

rate. Generally, the accuracy of two-phase pressure drop correlations for tube bundles presented in the literature is limited by the range of the experimental mass flow, fluid properties, and tube bundle geometries for which the models were developed. The

ed

predictive capabilities of currently available models are not yet fully resolved and the

pt

prediction of two-phase pressure drop across tube bundles continues to be the focus of

ce

much research [15, 16]. There are several predictive tools published in the literature

Ac

dealing with the steady-state pressure drop through a tube bundle for an incompressible flow. In particular, the three models of Zukauskas [12], Idel’chik [17] and Martin [18] were investigated and compared to the present blowdown results.

33



An average Reynolds number was computed from the transient ‘quasi-steady’ blowdown results based on estimates of the average blowdown mass flux and intertube velocity. From this, a steady-state pressure drop coefficient was estimated

ite d

assuming sonic single-phase saturated vapor flow conditions. The vapor velocity was assumed equal to the speed of sound. The Martin model predictions were generally

py ed

found to be unsatisfactory. The Idel’chik model was also found to give poor pressure drop predictions for all of the experiments in this study. On the other hand, the

Co

Zukauskas model predictions were generally conservative for the experiments

ot

performed with six rows of tubes. For five rows, the Zukauskas prediction did not

tN

provide a conservative estimate, and the predictions continued to deteriorate as the

ip

number of tube rows decreased. These comparisons suggest that current models for

sc r

steady-state pressure drop across a tube bundle do not provide a reliable estimate of

Ma nu

the maximum dynamic pressure drop during a two-phase blowdown such as that of the present study. Details of these comparisons may be found in [9].

10. CONCLUSIONS

ed

ce

pt

An experimental model study was carried out to determine the tube loading

Ac

during a postulated Main Steam Line Break (MSLB) in a vertical U-bend type steam generator. For this purpose, a special rig was designed and built using refrigerant R-134a as the working fluid and a rupture disc to simulate the sudden depressurization. The pressure drop across the tube bundle as well as high-speed video was used to explain the flow phenomena causing the tube loading. Parametric studies were carried out to 34



examine the effects of initial fluid level and the number of tube rows in the array on the resulting load. A constant drag coefficient was determined to provide an estimate of the tube loading once the dynamic pressure drop across the tube bundle is known. The

1.

ite d

specific conclusions drawn from this study are as follows:

The initial stage of the blowdown was marked by the propagation of

py ed

acoustic waves which generated peaks in the pressure drop across the tube bundle but no appreciable tube loading.

The second stage of the blowdown was dominated by a quasi-steady

Co

2.

ot

pressure drop across the tube bundle caused by choking of the flow. Flow choking is the

tN

result of the development of sonic velocities which limit flow rates. During this stage,

ip

the maximum pressure drop occurs and this produces the maximum tube loading during

sc r

the blowdown.

Varying the initial liquid level for the experiments significantly changed

Ma nu

3.

the duration of the blowdown and the time at which the quasi-steady stage occurred because of the differences in liquid inventory, but had no significant effect on the

ed

maximum load measured as long as the initial liquid inventory was sufficient to generate

Varying the number of tube rows permitted the development of a linear

ce

4.

pt

choked flow.

Ac

expression for load per tube row which can be used to predict the total tube loading on a tube bundle once the pressure drop is known.

35



5.

Calculations using simplified models for steady-state pressure drop

across tube bundles in the literature indicated that they were not generally reliable predictors of the transient maximum pressure drops measured in the present study.

ite d

The present results are expected to be qualitatively representative of the flow phenomena, pressure drop, and tube loading during two-phase blowdowns in tube

py ed

arrays with different pitch ratios and patterns. This is because changing the array pitch and pattern, within the range typical of nuclear steam generators, will change the

Co

pressure drop but not the transient flow phenomena observed during a blowdown.

ot

However, more research is required to determine the quantitative behavior, and in

tN

particular, the empirical drag coefficient relationship found for tube loading for such

ip

tube arrays.

sc r

Ma nu

ACKNOWLEDGMENT The authors gratefully acknowledge the financial support of the Canadian Nuclear Safety Commission (CNSC) and the Natural Sciences and Engineering Research Council (NSERC).

ed

FUNDING

ce

pt

Canadian Nuclear Safety Commission (CNSC)

Ac

Natural Sciences and Engineering Research Council (NSERC)

36



NOMENCLATURE A area [m2] flow coefficient

F

force [N]

G

mass flux [kg/m2s]

h

specific enthalpy [J/kg]

p

pressure [kPa]

z

number of tube rows

specific heat ratio

η

choked pressure ratio

ν

specific volume [m3/kg]

Subscripts

c

critical

u 0

py ed Co ot

Ma nu

ed

pt ce

cross-sectional downstream

Ac

d

sc r

γ

cs

tN

ip

Greek symbols

ite d

C

upstream stagnation

37



Ac

ce

pt

ed

Ma nu

sc r

ip

tN

ot

Co

py ed

ite d

REFERENCES [1] Sireta, X., 1979, “Experimental and Theoretical Study of the Blowdown of the Secondary Side of a Steam Generator,” Transactions of the American Nuclear Society, 31, pp. 392-394. [2] Kalra, S., and Adams, G., 1980, “Thermal Hydraulics of Steam Line Break Transients in Thermal Reactors - Simulation Experiments,” Transactions of the American Nuclear Society, 35, pp. 297-298. [3] Reichelt, E., 2009, “Resolution of Generic Safety Issue 188: Steam Generator Tube Leaks or Ruptures Concurrent with Containment Bypass from Main Steam Line or Feedwater Line Breaches,” NUREG-1919, U.S. Nuclear Regulatory Commission, Washington, DC. [4] Singhal, A. K., Keeton, L. W., Przekwas, A. J., and Weems, J. S., 1982, “ATHOS: a Computer Program for Thermal-Hydraulic Analysis of Steam Generators. Volume 3. User's Manual,” EPRI-NP-2698-CCM-Vol. 3, CHAM of North America, Huntsville, AL. [5] Fletcher, C. D., and Schultz, R. R., 1995, “RELAP5/MOD3 Code Manual Volume V: User’s Guidelines,” NUREG/CR-5535-Vol.5, Idaho National Engineering Laboratory, Idaho Falls, ID. [6] Odar, F., Murray, C., Shumway, R., Bolander, M., Barber, D., and Mahaffy, J., 2004, “TRACE v4.0 User’s Manual,” U.S. Nuclear Regulatory Commission, Washington, DC. [7] Jo, J., and Moody, F., 2015, “Transient Thermal-Hydraulic Responses of the Nuclear Steam Generator Secondary Side to a Main Steam Line Break,” Journal of Pressure Vessel Technology, 137(4). doi:10.1115/1.4028774 [8] Hamouda, O., Weaver, D., and Riznic, J., 2015, “Instrumentation Development and Validation for an Experimental Two-Phase Blowdown Facility,” submitted to the Journal of Pressure Vessel Technology – revised manuscript under review, Paper No. PVT-151176. [9] Hamouda, O., 2015, “An Experimental Study of Steam Generator Tube Loading During a Two-Phase Blowdown”, Ph.D. Thesis, McMaster University, Hamilton, ON, available from MacSphere: http://hdl.handle.net/11375/17474. [10] Hamouda, O., Weaver, D., and Riznic, J., 2015, “An Experimental Study of Steam Generator Tube Loading During Blowdown,” PVP2015-45250, ASME Pressure Vessels and Piping Conference, Boston, MA. 38



Ac

ce

pt

ed

Ma nu

sc r

ip

tN

ot

Co

py ed

ite d

[11] Whalley, P., 1987, Boiling, Condensation and Gas-Liquid Flow, Clarendon Press, Oxford, UK. [12] Zukauskas, A., 1987, “Heat Transfer from Tubes in Cross-Flow,” Advances in Heat Transfer, 18, pp. 87-159. [13] Ishihara, K., Palen, J., and Taborek, J., 1980, “Critical Review of Correlations for Predicting Two-phase Flow Pressure Drop Across Tube Banks,” Heat Transfer Engineering, 1(3), pp. 23-32. [14] Consolini, L., Robinson, D., and Thome, J., 2006, “Void Fraction and Two-phase Pressure Drops for Evaporating Flow over Horizontal Tube Bundles,” Heat Transfer Engineering, 27(3), pp. 5-21. [15] Ribatski, G., and Thome, J., 2007, “Two-phase Flow and Heat Transfer Across Horizontal Tube Bundles – A Review,” Heat Transfer Engineering, 28(6), pp. 508- 524. [16] Sim, W. and Mureithi, N, 2013, “Drag Coefficient and Two-Phase Friction Multiplier on Tube Bundles Subjected to Two-Phase Cross-Flow,” Journal of Pressure Vessel Technology, 135(1), doi: 10.1115/1.4007285. [17] Idel’chik, I., 1996, Handbook of Hydraulic Resistance (3rd Ed.). Begell House, New York, NY. [18] Martin, H., 2002, “The Generalized Lévêque Equation and its Practical Use for the Prediction of Heat and Mass Transfer Rates from Pressure Drop,” Chemical Engineering Science, 57(16), pp. 3217-3223.

39



Figure Captions List

Fig. 1

(a) Experimental apparatus for simulating a steam generator blowdown

ite d

(b) Test section design Sample transient blowdown pressures

Fig. 3

Transient pressure drop measured across the tube bundle

Fig. 4

Illustration of instantaneous pressure measurements at t = 0.25s

Fig. 5

Transient pressure ratio across the tube bundle for 3 experiments with

Co

py ed

Fig. 2

ot

similar initial conditions Sample tube load transient

Fig. 7

Critical HEM and HFM pressure estimates based on p = 430kPa at t =

ip

tN

Fig. 6

sc r

0.25s and p = 285kPa at t = 0.66s

Comparison of the effect of the initial liquid level on tube loading

Fig. 9

Comparison of tube bundle load with different numbers of tube rows

Fig. 10

Comparison of measured tube load and pressure drop across the tube

ed

Ma nu

Fig. 8

Graphical representation of drag load coefficient: tube loading (top),

ce

Fig. 11

pt

bundle

Ac

pressure drop (center), numerically determined drag coefficient (bottom)

Fig. 12

Comparison of measured tube loading and computed pressure loading

Fig. 13

Tube bundle drag load coefficient

40



Fig. 14

Comparison of computed pressure loads and measured loads

Ac

ce

pt

ed

Ma nu

sc r

ip

tN

ot

Co

py ed

ite d

41



Table Caption List

Table 1

Computed tube bundle drag load coefficient values from two-phase blowdown experiments

Ac

ce

pt

ed

Ma nu

sc r

ip

tN

ot

Co

py ed

ite d

42


ip

tN

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

sc r

Fig. 1

(a) Experimental apparatus for simulating a steam generator blowdown (b) Test section design

43


ip

Sample transient blowdown pressures

sc r

Fig. 2

tN

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

44


sc r

Transient pressure drop measured across the tube bundle

Ac

ce

pt

ed

Ma nu

Fig. 3

ip

tN

ot

Co

py ed

ite d


45


Illustration of instantaneous pressure measurements at t = 0.25s

tN

Fig. 4

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

sc r

ip

46


ip

Transient pressure ratio across the tube bundle for 3 experiments with

sc r

Fig. 5

tN

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

similar initial conditions

47


ip

tN

ot

Co

py ed

ite d


sc r

Sample tube load transient

Ac

ce

pt

ed

Ma nu

Fig. 6

48


Critical HEM and HFM pressure estimates based on p = 430kPa at t =

sc r

Fig. 7

ip

tN

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

0.25s and p = 285kPa at t = 0.66s

49


ip

tN

ot

Co

py ed

ite d


sc r

Comparison of the effect of the initial liquid level on tube loading

Ac

ce

pt

ed

Ma nu

Fig. 8

50


sc r

Comparison of tube bundle load with different numbers of tube rows

Ac

ce

pt

ed

Ma nu

Fig. 9

ip

tN

ot

Co

py ed

ite d


51


ip

Comparison of measured tube load and pressure drop across the tube

sc r

Fig. 10

tN

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

bundle

52


Graphical representation of drag load coefficient: tube loading (top),

sc r

Fig. 11

ip

tN

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

pressure drop (center), numerically determined drag coefficient (bottom)

53


Comparison of measured tube loading and computed pressure loading

sc r

Fig. 12

ip

tN

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

54


Tube bundle drag load coefficient

ip

Fig. 13

tN

ot

Co

py ed

ite d


Ac

ce

pt

ed

Ma nu

sc r

55


sc r

Comparison of computed pressure loads and measured loads

Ac

ce

pt

ed

Ma nu

Fig. 14

ip

tN

ot

Co

py ed

ite d


56



Computed tube bundle drag load coefficient values from two-phase

Table 1

blowdown experiments 3

4

5

6

6

1.230

1.285

1.328

1.370

1.405

1.410

6

6

1.408

1.405

ite d

2

py ed

Number of tube rows Drag load coefficient

Ac

ce

pt

ed

Ma nu

sc r

ip

tN

ot

Co

57
