Experimental Study and Modelling of Spacer Grid Influence on Flow in Nuclear Fuel Assemblies

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Experimental Study and Modelling of Spacer Grid Influence on Flow in Nuclear Fuel Assemblies

Diana Caraghiaur Garrido

Licentiate Thesis

School of Engineering Sciences Department of Physics

Nuclear Reactor Technology Division Stockholm, Sweden, 2009

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TRITA‐FYS 2009:02 KTH

ISSN 0280‐316X School of Engineering Sciences

ISRN KTH/FYS/‐‐09:02‐‐SE SE‐106 91 Stockholm

ISBN 978‐91‐7415‐229‐6 Sweden

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan framlägges till offentling granskning för avläggande av teknologie licentiatexamen i energiteknik torsdagen den 26 februari 2009 klockan 10:00 i sal FA31, Albanova Universitetscentrum, Roslagstullsbacken 21, Stockholm.

Universitetsservice US‐AB, Stockholm 2009

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Abstract

The work is focused on experimental study and modelling of spacer grid influence on single‐

and two‐phase flow. In the experimental study a mock‐up of a realistic fuel bundle with five spacer grids of thin plate spring construction was investigated. A special pressure measuring technique was used to measure pressure distribution inside the spacer. Five pressure taps were drilled in one of the rods, which could exchange position with other rods, in this way providing a large degree of freedom. Laser Doppler Velocimetry was used to measure mean local axial velocity and its fluctuating component upstream and downstream of the spacer in several subchannels with differing spacer part. The experimental study revealed an interesting behaviour. Subchannels from the interior part of the bundle display a different effect on the flow downstream of the spacer compared to subchannels close to the box wall, even if the spacer part is the same. This behaviour is not reflected in modern correlations.

The modelling part, first, consisted in comparing the present experimental data to Computational Fluid Dynamics calculations. It was shown that stand‐alone subchannel models could predict the local velocity, but are unreliable in prediction of turbulence enhancement due to spacer. The second part of the modelling consisted in developing a deposition model for increase due to spacer. In this study Lagrangian Particle Tracking (LPT) coupled to Discrete Random Walk (DRW) technique was used to model droplet movements through turbulent flow. The LPT technique has an advantage to model the influence of turbulence structure effect on droplet deposition, in this way presenting a generalized model in view of spacer geometry change. The verification of the applicability of LPT DRW method to model deposition in annular flow at Boiling Water Reactor conditions proved that the method is unreliable in its present state. The model calculations compare reasonably well to air‐water deposition data, but display a wrong trend if the fluids have a different density ratio than air‐water.

Descriptors: spacer grid influence, annular flow, deposition, Lagrangian Particle Tracking

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Preface

The thesis is based on the following papers:

Paper 1. Caraghiaur, D., Frid, W. and Tillmark, N., 2004, Detailed pressure drop measurements in single‐ and two‐phase adiabatic air‐water turbulent flows in realistic BWR fuel assembly geometry with spacer grids, The 6^th International Conference on Nuclear Thermal Hydraulics, Operations and Safety (NUTHOS‐6), Nara, Japan, October 4‐8

Paper 2. Caraghiaur, D. and Anglart, H., Experimental investigation of turbulent flow through spacer grids in fuel rod bundles, Submitted to Nuclear Engineering and Design, November 2008

Paper 3. Caraghiaur, D. and Anglart, H., 2007, Measurements and CFD predictions of velocity, turbulence intensity and pressure development in BWR fuel rod assembly with spacers, The 12^th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH‐12), Sheraton Station Square, Pittsburgh, Pennsylvania, U.S.A., September 30‐

October 4

Paper 4. Caraghiaur, D. and Anglart, H., 2007, Annular flow deposition model with obstacle effect, accepted at The 6^th International Conference on Multiphase Flow, ICMF 2007, Leipzig, Germany, July 9‐13

Paper 5. Caraghiaur, D. and Anglart, H., 2009, Lagrangian particle tracking as a tool for deposition modeling in annular flow, submitted to the 17th International Conference on Nuclear Engineering ICONE17, July 12‐16, Brussels, Belgium

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Introduction

1.1 Background

Nuclear fuel bundles contain spacers, positioned to keep the fuel rods at a certain distance from each other. Acting as obstacles to the coolant flow, the spacers cause additional pressure drop, and so, they add to the economical expense both by material consumption and pumping power. To minimize the flow blockage and provide enough support to the fuel bundle structure, spacer grids have been transformed over the years to include complex geometrical details such as dimples and springs. Turbulence promoters have been added to augment the lateral momentum and energy exchange. The resultant complex geometry almost prohibits the analytical approach of the influence of spacers on the flow. To add to the complexity, the spacer design and the spacer axial position in relation to other spacers affect the Critical Heat Flux (CHF) occurrence. CHF is the major design parameter for the entire nuclear fuel assembly and its prediction with the least margins contributes to the economical and safe operation of the nuclear reactor.

From the above discussion we can distinguish two views of spacer design consideration: in the development stage of the spacer; and in safe and economical operation. In the development stage, best‐practice methods together with expensive large‐scale experiments are still a common practice. The amount of costs associated with large‐scale experiments exercises pressure on the models and correlations development. In view of safe and economical operation, the CHF phenomenon has to be correctly predicted by analysis codes.

In Boiling Water Reactor (BWR) the prediction of CHF is a two‐part model, which involves the prediction of the correct amount of void in the subchannels coupled to the liquid film flow analysis. The spacer design affects both parts of the model. To predict the amount of void, cross‐flows between subchannels due to turbulent mixing, transverse pressure gradients and void drift are to be considered. The modern spacer, with its differently blocked subchannels has an influence on all three processes. The liquid film is affected by the spacer presence, both upstream and downstream of the spacer.

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2 Chapter 1 Introduction

1.2 Spacer influence on thermal hydraulic characteristics

The influence of spacers (or flow obstacles) on CHF has been studied for more than three decades. Summarizing an extensive experimental project Pioro et al. (2002) concluded that flow obstacles can have a significant (up to 12 times) enhancement effect on CHF. The largest enhancement occurred for largest flow blockage and qualities corresponding to deposition‐driven annular flow. They also observed that the distance from an upstream obstacle has a strong effect on CHF.

In BWR systems annular flow is the predominant regime. Annular flow is characterized by the gas phase flowing in the core of the conduit and the liquid phase, which is split between thin liquid film flowing on the heater wall and liquid droplets travelling in the gas. There is a continuous mass transfer from the liquid film to the droplet field, termed entrainment, and a reverse process, termed deposition. Evaporation of the film contributes to film reduction.

The mechanism that leads to CHF in annular flow is characterized by drying out of the thin liquid film from the heater wall, even though CHF does not always occur when the liquid film is dried out in case rewetting exists. The effect of spacers on the liquid film thickness has been studied by several researchers. Mori et al. (2007) have measured the liquid film thickness and noticed three distinctive effects of spacer influence: a slight upstream increase of the liquid film thickness, a decrease along the spacer height and a downstream increase. The upstream increase is believed to be caused by stagnation of the flow. Inside the spacer, the liquid film thickness decreases due to a greater interfacial shear resulting from the acceleration of the flow. The increase downstream is supposed to be caused by turbulence enhancement which promotes droplet deposition. In addition to turbulence enhancement a collection and run‐off effect contributes to the downstream thickening of the liquid film. The collection and run‐off effect results from the fact that a fraction of droplets travelling in the gas core will be collected by the spacer surface in the form of film, which will deposit on the neighbouring surface. The amount of run‐off depends on the geometrical characteristics of the spacer and the proximity of the spacer element to the rod surface. Following the studies, which show that CHF in the fuel bundle always occurs upstream of the spacer, Shiralkar and Lahey (1973) through visualization of the flow and force balance acting on the liquid film deducted that dry patches which form upstream of the obstacle are due to the stagnation of the flow. The obstruction creates a horseshoe vortex that scrubs the liquid film. However, more recent studies e.g. of Mori et al. (2007) have a different solution for the CHF occurrence upstream of the spacer. They have analyzed the wavy structure of the liquid film upstream and downstream of the spacer and have concluded that when disturbance waves pass the spacer, the amplitude reduces and as a consequence the film thickness in between the disturbance waves becomes larger, that is why CHF never occurs downstream of the spacer. However, traces of disturbance waves still exist and further downstream they develop in typical disturbance waves, reducing the base film thickness. As a result dryout occurs further downstream from the spacer, eventually

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1.2 Spacer influence on thermal hydraulic characteristics 3

upstream of the next spacer. Consequently, they have concluded that the smaller the spacer spacing the larger the CHF enhancement.

Besides the influence on the wavy interface of the liquid film thickness, the spacer also causes an increase in turbulence intensity, as was stated above. Several experimental studies have been set up to study the turbulence downstream of the spacer. The first turbulence study was performed by Rowe and Chapman (1973). They showed that turbulence intensity for an internal subchannel significantly varied with distance downstream from the spacer grid. The high intensity observed at the trailing edge of the spacer rapidly decayed to values below the fully developed condition at a moderate distance from the spacer. Further downstream the level of intensity increased to nearly twice the level of intensity of fully developed flow before finally decaying to the developed state. In contrast to the internal subchannel, the wall subchannel had shown high turbulence intensity near the trailing edge of the spacer and a monotonical decay downstream towards a fully developed condition.

Yang and Chung (1998) and Nagayoshi and Nishida (1998) have conducted their own experiments of turbulence development downstream of the spacer. They have observed the behaviour of a sudden increase of turbulence intensity just downstream of the spacer followed by a monotonic decay – a characteristic wall subchannel behavior in the study by Rowe and Chapman. However, no other studies have shown the internal subchannel behaviour observed by Rowe and Chapman.

The interest to study the influence of the spacer on the downstream turbulence distribution is two‐fold. One reason is that turbulence mixing contributes to the cross‐flows in the subchannel analysis, discussed later. The other reasoning stems from the belief that deposition of droplets is substantially influenced by the turbulence of the core flow. Okawa et al. (2004) have conducted experiments to elucidate the effects of the obstacle on deposition rates. Okawa et al. (2007) completed the previous study by placing differently shaped obstacles in the flow. For studied tubular obstacles placed concentrically the authors measured increased deposition rates downstream of the obstacle. The deposition rate increase was up to 200 %. The droplet deposition due to obstacle increased with increased blockage ratio and with decreased diameter ratio (obstacle diameter‐to‐channel diameter).

Thus, the main phenomena responsible for the obstacle‐induced droplet deposition seem to be the turbulence enhancement downstream of the obstacle and the drift flow upstream of the obstacle.

In addition to the upstream and downstream effects, the spacer, especially due to radially non‐uniform geometry, causes transverse (radial) disturbances, compared to the reference case of a bare rod bundle. Rehme and Trippe (1980) concluded that different blockages in the subchannels give rise to a remarkable change in the mass flow rates of the subchannels.

The separation and redistribution caused by the spacer from the higher blocked subchannels into the less blocked subchannels was clearly recognized.

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1.3 Models and correlations

The transformation of the spacer from exclusively mechanical device to clear the distance between the rods into a thermal‐hydraulics‐improving device has required many steps, both in experimental evidence collection and models and correlations development. The first correlations to characterize spacers were the pressure drop correlations. For spacer design consideration it is not feasible to have an exact pressure drop correlation. However, an approximate correlation would help the decision making.

The measured single‐phase pressure drop over the spacer consists of friction of the bare rod bundle, represented by the Darcy friction factor , and spacer pressure loss, represented by the spacer pressure loss coefficient and can be calculated by the following relation:

Δ Δ 1

2

(1.1)

Rehme (1973) has deduced from his experiments that spacer pressure loss coefficient can be calculated as a function of the blockage ratio of the spacer and an empirical coefficient, which was shown to be a weak function of Reynolds number. Kim et al. (1992) have developed a more sophisticated model including the form drag of the thin strap and the friction along the spacer walls. However, their model did not include important elements, which are present in the modern spacer grid design such as mixing vanes, springs and dimples. Chun and Oh (1998) extended the Kim et al. model to include the missing geometrical details.

The two‐phase pressure loss due to the local flow obstructions of grid spacers is treated in much the same manner as frictional pressure loss. That is, the corresponding single‐phase pressure drop is multiplied by an appropriate two‐phase multiplier (Φ) to yield the local two‐

phase pressure drop:

∆ 2 2 _, Φ

(1.2)

where the functional form of the two‐phase multiplier normally is synthesized empirically.

is the total mass flux, is the density of the two‐phase mixture and _, is the density of the saturated liquid.

Up to this date, for design considerations, best practice guidelines derived from expensive full‐scale tests aided by pressure drop correlations are largely used. Computational Fluid Dynamics (CFD) analysis becomes a more common practice particularly for single‐phase flow applications, however it still requires further model development and thorough validation.

For the operational analysis, subchannel‐based computer codes are routinely used to asses the thermal hydraulic behavior of nuclear fuel assemblies. In such codes, the fuel assembly is divided into imaginary subchannels, having the coolant in the center – a more common

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1.3 Models and correlations 5

practice‐ or having the fuel rod in the center ‐ an approach adapted to film flow analysis.

These codes solve the one‐dimensional conservation of mass, momentum and energy for each interconnected subchannel. Interactions leading to inter‐subchannel exchange of mass, momentum and energy are modelled as semi‐empirical source terms to the one‐dimensional equations. Carlucci et al. (2004) have summarized the effects that contribute to the inter‐

subchannel exchange as follows:

1. Single‐ and two‐phase diversion cross flow, which is the flow caused by the net transverse pressure difference between adjacent subchannels. Lateral pressure differences can result from different subchannel hydraulic diameter, heat flux distributions and gradual and abrupt changes in flow areas caused, for example, by rod bowing and spacer grids, respectively.

2. Single‐ and two‐phase turbulent mixing, being a result of random turbulent flow and pressure fluctuations. It can be classified as natural or forced. Natural turbulent mixing occurs continuously between smooth interconnected subchannels. Forced turbulent mixing results from the non‐directional flow scattering caused by local flow obstructions, especially if the flow obstruction (spacer grid) is non‐symmetric. Under single‐phase flow conditions, density differences between interconnected subchannels at different temperatures are negligible, and thus there is a net transfer of thermal energy, but negligible mass transfer. Under two‐phase flow conditions, the turbulent fluctuations of the liquid and gas phases can result in a net mass transfer, in addition to a net energy transfer between two interconnected subchannels having different void fractions.

3. Two‐phase void drift, which is due to the tendency of the vapor phase to redistribute itself to a preferred “equilibrium” void distribution. In a bundle comprising subchannels of different sizes and shapes, the “equilibrium” void fraction in the larger subchannels tends to be higher than in the smaller ones.

Brown et al. (1975) shows how the specific terms in the transverse interchange characteristic for flow blockages could be introduced in the subchannel code. The analysis of the effect of the obstacle on the transverse interchange is based on the general transverse momentum balance and comprises a variable control volume to capture the effect of the obstacle on the flow downstream of the obstacle.

In BWR systems, the subchannel code, which predicts the flow and void distribution in the fuel assembly, is coupled to the film flow analysis. Here, the one‐dimensional film is calculated according to the equation:

1

(1.3)

where is the perimeter considered, is the change in liquid film flow rate in the axial distance . The right hand side of eq. (1.3) represents the sources (sinks) to the liquid film

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flow rate, namely, is the deposition rate of droplets, is the entrainment rate of droplets and is the evaporation of the liquid film.

An increase in deposition due to spacer is usually introduced as:

1

(1.4) In this, the deposition is regarded as a diffusion‐like process (see Chapter 3), where is the concentration of droplets and is a mass transfer coefficient. In eq. (1.4), is a function characterizing the deposition due to the turbulence increase downstream of the spacer and

is the deposition increase due to collection and run‐off effects.

Akiba et al. (2005) state that the spacer effect in CHF calculations is handled by two coefficients: the deposition enhancement coefficient and the entrainment enhancement coefficient. Subchannel analysis is unable to predict these coefficients, because the analysis mesh is too coarse to capture the effects of the spacer geometry. They state that, at present, these coefficients are arbitrarily given by the researchers so that the analyzed critical power may agree with the measured critical power. Therefore, subchannel analysis is unable to predict CHF considering the change in spacer geometry.

Several authors (e.g. Naitoh et al. 2002, Windecker et al. 1999 and Kanazawa et al. 1995) have reported the use of Lagrangian Particle Tracking technique as a tool to calculate droplet deposition in annular two‐phase flow of BWR conditions. This method has an advantage that it models the deposition as a function of the turbulent structure of the flow. However, the authors that report the use of this technique present no or little validation of the model itself.

1.4 Problem statement and objectives

Following the discussion the overall problem formulation in this subject would be development of a model able to predict the effect of the spacer on single‐ and two‐phase flow, in view of changing geometry. This is a long term perspective for aspiration, to which we chose to contribute with two aspects: an experimental data base for flow around spacer for CFD validation and an engineering solution for deposition modelling to include spacer effect. By an engineering solution is meant either a trustworthy correlation that can be included into eq. (1.4) or a cheap computational model that can be directly coupled to subchannel codes with film flow analysis.

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Chapter 2

Experimental study of spacer grid influence on single and twophase flow

2.1 Experimental arrangement

The experimental rig, schematically shown in Fig.2.1, consists of a test section, a water reservoir, a 15 kW centrifugal pump, flow control valves and stainless steel piping, forming a closed loop. The water flow is measured by an electromagnetic flow meter downstream of the pump. From the pump the water enters the plenum connected to the lower part of the vertical test section. The plenum contains a honeycomb flow rectifier suppressing large‐scale vortices generated by the pump and tube bends. An air injector mounted at the bottom centre of the plenum provides air during two‐phase flow tests. The outflow from the plenum is directed vertically and passes a nozzle with a contraction ratio of 7.4. A fast closing valve is mounted at the outlet and a transforming unit is placed between the valve and the inlet of the test section bridging the different cross sections. The upper end of the test section terminates in a quick closing valve followed by a plenum. A weir in the upper plenum maintains a constant water level and a free surface at atmospheric pressure. The water from the upper plenum returns to the reservoir passing a number of baffles giving time for air bubbles trapped in the water to rise to the surface.

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8 Chapter 2 Experimental study of spacer grid influence on single and twophase flow

water reservoir

test section

flow meter

pump lower plenum

spacers upper plenum

air vent

compressed air fast closing valve fast closing valve

Figure 2.1: Experimental rig

The test section has an asymmetric cross section corresponding to one quarter of the fuel bundle of SVEA–96, illustrated in Fig. 2.2. The same figure shows the spacer part in the studied subchannels.

Figure 2.2: The cross‐sectional view of the test section

The 24 rods are held in position by 5 spacers. The spacers are of thin plate spring construction; the details of the spacer can be seen on the photographs in Fig. 2.3.

dimple

D

B C

A spring

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2.2 Measurement techniques and procedure 9

Figure 2.3: The details of the spacer of SVEA‐96 fuel bundle

The characteristic geometric parameters of the test section are given in Table 1. The walls of the test section are made of 10 mm thick glass plates, allowing visibility techniques to be used to study the flow.

Table 2.1: Geometrical parameters of the test section

Rod diameter 10.0 mm

P/D (pitch‐to‐diameter ratio) 1.320

W/D (wall‐to‐diameter ratio) 1.305 and 1.264

Rod length 1894 mm

Cross‐section flow area 2400 mm²

Hydraulic diameter 9.86 mm

2.2 Measurement techniques and procedure

2.2.1 Pressure measurements

The pressure distribution inside the mock‐up of the fuel bundle was measured by use of pressure probes. Five pressure taps were drilled in one of the rods, aligned along a vertical straight line. The pressure sensing rod could be rotated along its axis and traversed axially within a range of ± 250 mm. The position of the holes and the traversing range enables to get a detailed vertical pressure distribution in the test section. The pressure taps are connected from the inside of the rod with plastic tubes to a set of differential pressure transducers, positioned at the level of the free surface in the upper plenum, thus compensating for the gravitational pressure head in the vertical test section. The flexible plastic tubes are translucent to ensure proper purging of air bubbles prior to testing.

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During single phase flow measurements, the first thing was to establish the desired arrangement of the pressure sensing rod: at specific radial and axial positions, which involved dismantling of the test section if the radial position was changed. The next thing was to reach steady pump rotations at the desired liquid flow rate. The accumulated air in the plastic tubes which connect the pressure taps with the transducer was properly purged.

The traversing system of the pressure sensing rod was connected to the LABVIEW programme, where the desired translation distance and the step were entered before each run. The data of each run were automatically saved to the computer. The rate was 1000 samples per second and the sampling time was set to 10 s for each position. The waiting time before sampling was set to 10 s in order to avoid the influence of rod movement.

During two‐phase flow measurements the same procedure was repeated with the addition of adjustment of desired air flow rate. To measure the void, two fast closing valves were used at the extremes of the test section. The calibration of the amount of void in the test section was performed by filling the test section starting from the lower fast closing valve with measured amounts of water.

2.2.2 Local velocity and turbulence intensity measurements

In order to have good spatial and temporal resolution and minimal probe interference with the local flow structure, Laser Doppler Velocimetry (LDV) technique was used to measure axial velocity and the turbulence intensity across the third spacer of the test section. Polytec LDV system used in the present work has been operated in dual‐beam back‐scatter mode.

The 61.178 mm beam separation and 310 mm focal‐length focusing lens result in beam waist at the measurement volume equal to 68 μm. To avoid the influence of vibrations of the test loop on the measurement equipment, the LDV with its 3‐D traverse system was installed on a separate platform.

The start of the measurement run was the adjustment of the desired water flow rate. The initial position of the LDV measurement volume was selected and carefully placed starting from a reflecting surface, such as rod surface or box wall and translating the system by known distance. Before each run a few test measurements were observed on the oscilloscope screen to make sure that the signal‐to‐noise ratio is appropriate, if not it was adjusted to satisfy the requirement. The translation algorithm was introduced into the computer. The data were automatically saved.

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2.3 Accuracy 11

2.3 Accuracy

The water flow was measured using ABB Kent‐Taylor electromagnetic MagMasterTM flowmeter with stated measuring accuracy ±0.15 %. Over the time period required to obtain a full axial pressure profile or a full velocity run, the standard deviation of the fluctuating flowmeter readings was ±1% or less. The air flow was measured and controlled by Bronkhost Hi‐Tec digital mass flowmeter and controller F‐203AC‐RBB‐44Z. The stated error of the calibrated instrument was ±1 % and the time standard deviation was calculated to be less than ±1 %.

Calibrated Motorola MPX‐5050 piezoresistive differential pressure transducer was used to sense the pressure. The calibration of the transducer showed a maximum error of 6%. The pressure tap locations were calibrated before each set of measurements against a reference point by means of a ruler. The maximum error in location reading was considered to be less than 0.5 mm.

During velocity and turbulence intensity measurements a reasonable signal‐to‐noise ratio was chosen by adjusting the shape of the probability density function curve to represent a Gaussian distribution by modifying the burst threshold. The raw signal together with the triggering of the digitized data were observed on the oscilloscope screen to make sure that the triggering occurs when the burst does. To have a reliable statistical value, at least 2000 valid counts were accumulated, which in some cases accounted for 20‐30 min measuring time in one point. The biggest source of error was considered to be the initial positioning of the LDV measurement volume. The position was measured by a ruler and sight judgment accounting for 0.5 mm error in readings, which for the subchannel width of 3 mm is a significant source of error.

2.4 Summary of results

Paper 1 reports all the pressure measurements performed in the frame of this work. The experimental bare rod friction coefficient is compared to several correlations, among which are the Blasius, McAdams and a specific correlation developed for fuel bundle. The Blasius correlation shows good prediction within experimental uncertainty. A specific spacer pressure loss coefficient is calculated as a function of Reynolds number. A large data base of detailed pressure measurements inside the spacer is presented for several subchannels with differing spacer part. Single‐ and two‐phase flow pressure measurements are included. An example of the difference in pressure distribution of single‐ and two‐phase flow is presented in Fig. 2.4.

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Figure 2.4: Pressure distribution along the length of the third spacer around middle rod ”a”

Paper 2 reports the mean local velocity and turbulence intensity measurements. An example of velocity and its rms value measurements upstream and downstream of the third spacer for different Reynolds numbers is presented in Figure 2.5.

20 25 30 35 40 45 50

‐1340

‐1350

‐1360

‐1370

‐1380

‐1390

Pressure, [kPa]

Distance from fixed reference point, [mm]

0º +45º +135º ‐45º ‐135º

a

+ 45

0

- 45 + 135

- 135

void 0%

j_l=4.5 m/s

20 25 30 35 40 45 50

‐1340

‐1350

‐1360

‐1370

‐1380

‐1390

Pressure, [kPa]

Distance from fixed reference point, [mm]

0 deg +45 deg +135 deg ‐45 deg ‐135 deg

a

+ 45

0

- 45 + 135

- 135

void 6%

j_l=4.5 m/s j_g=0.21 m/s

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inside one ation consid cer do not r

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

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Re=

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Chapter 3

Modelling of deposition of drops in annular flow.

Influence of obstacle on deposition

3.1 Experiments of deposition of drops in annular flow

On the way to experimentally establish the parameters of influence, the deposition of drops in annular two‐phase flow is often regarded as a diffusion‐like process. The droplets move from the core of the channel with a prescribed concentration towards the channel wall, where the concentration becomes zero. This movement is described by the mass transfer coefficient, named also deposition velocity, , so that the deposition rate becomes:

(3.1)

Finding of true concentration of drops presupposes knowledge of the mean drop velocity ( ) or the slip ratio ⁄ , where is the mean gas velocity:

(3.2)

where is the mass flux of entrained liquid (in form of drops). The slip ratio is rarely reported in experimental studies and there are no generally accepted correlations to calculate it, that is why is often assumed to be equal to one when correlating experimental data. An illustration on how the deposition velocity depends on homogeneous concentration ( 1) is presented in Fig. 3.1, where data from some recent and older experimental studies have been collected.

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16 Chapter 3 Modelling of deposition of drops in annular flow

Figure 3.1: Collection of experimental data of deposition velocity as a function of

homogeneous volumetric concentration of droplets

Figure 3.1 presents mostly experiments performed in air‐water, with the density ratio

⁄ 1000 300. A set of helium‐water data with ⁄ 5000 and a set of steam‐

water in BWR conditions (P=70 bar) with ⁄ 20 are included. The dependence of deposition velocity on homogeneous concentration is unclear, when the concentration is low (e.g. 1). It becomes a decreasing function when 1. The influence of the density ratio cannot be identified from this particular presentation of data.

Starting from eq. (3.1) extensive efforts were spent to find the correlation parameters of the deposition velocity. The study of Govan et al. (1988) uses a group formed by the size of the conduit , the density of the gas phase and the surface tension,

.

as a correlation parameter, even though no physical support for this choice was reported. Other correlations (e.g. Sugawara, 1990) have the gas superficial velocity as the correlation parameter. From the plot in Fig. 3.2, it is unclear how the two correlate. Some experimental sets, e.g. Jepson et al. data for helium‐water, Schadel et al. data and Cousins and Hewitt data exhibit an increasing function of deposition velocity against increasing superficial gas velocity, while the rest of experimental data sets do not present such a function.

0.001 0.01 0.1 1

0.01 0.1 1 10 100

kd, [m s‐1]

C_h, [kg m^‐3]

Jepson et al. 1989: helium‐water Jepson et al. 1989: air‐water Okawa et al. 2005: air‐water Schadel et al. 1990: air‐water Hewitt et al. 1969: steam‐water Govan et al. 1988: air‐water Cousins&Hewitt 1969: air‐water

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3.1 Experiments of deposition of drops in annular flow 17

Figure 3.2: Collection of experimental data of deposition velocity as a function of superficial gas velocity

Schadel et al. (1990) argued that the function could be clearly seen if the true concentration would be used in calculating the deposition velocity. However, the experimental studies, as mentioned above, rarely report droplet velocity in combination with measured deposition velocity.

Even though these correlations have shown acceptable predictions in flows similar to the correlating ones, it is unclear how to extrapolate their effects for the situations, which are interesting in BWR annular flow deposition, namely, the effect of the rod bundle geometry with the presence of spacer and varying cross‐section on a subchannel basis. To answer these questions a more detailed experimental investigation is needed to show how the deposition is actually happening and which local parameters are responsible for it.

Visual observations and photographic studies have shown that droplets in annular flow have different sizes (see Fig. 3.3 for references). It was also observed that droplets have a different way of depositing depending on their size and flow characteristics (e.g. Young and Leeming, 1997 and James et al. 1980), so that one correlation could hardly incorporate the complex situation in annular two‐phase flow. One way to overcome the complexity of representing a multitude of sizes is to calculate a representative mean droplet diameter. If an optical technique is used to measure the droplet diameter, then the number distribution function could be found that is described by:

⁄ (3.3)

0.001 0.01 0.1 1

0 50 100 150 200 250

kd, [m s‐1]

j_g, [m s^‐1]

Jepson et al. 1989: helium‐water Jepson et al. 1989: air‐water Okawa et al. 2005: air‐water Schadel et al. 1990: air‐water Hewitt et al. 1969: steam‐water Govan et al. 1988: air‐water Cousins&Hewitt 1969: air‐water

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where is the number of droplets in the range , , and is the total number of measured droplets. If the distribution number function is known, the commonly used mean diameters can be represented by the following formulas:

(3.4)

(3.5)

(3.6)

(3.7)

where is the mean length diameter when 1, mean surface diameter when 2 and mean volume diameter when 3. is the mean volume‐length diameter, is the mean volume‐surface diameter (named also Sauter mean diameter, or ) and is the mean mass diameter.

The number distribution function has been empirically fitted to show that the droplet size distribution in annular two‐phase flow can be represented by the Rosin‐Rammler distribution and the upper limit log normal (ULLN) distribution. Azzopardi (1997) have noted that mathematically the Rosin‐Rammler equation has no natural upper cut off resulting in a tail of infinite drop sizes and a more suitable in a physical sense would be the ULLN function.

It has to be mentioned that the experimental number distribution function as well as the reported mean droplet diameter are very sensitive to the measurement technique and statistical accuracy chosen (Azzopardi, 1997).

Liquid drops in annular flow are usually represented by the mean volume‐surface diameter (eq.3.5). In Figure 3.3 a collection of experimental Sauter mean diameter of the droplets in annular two‐phase flow is presented as a function of homogeneous droplet concentration.

The general trend, seen from the figure, is that drop size increases with concentration. The common belief among researchers is that bigger drops result from coalescence.

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3.1 Experiments of deposition of drops in annular flow 19

Figure 3.3: Collection of experimental data of Sauter mean droplet diameter as a function of homogeneous volumetric droplet concentration

Young and Leeming (1997) have summarized several experimental results of deposition of particles and based on that have differentiated three deposition regimes as a function of particle relaxation time τ , which measures the responsiveness of the particle to a change in fluid velocity:

18

(3.8)

where is the particle diameter, is the continuous flow kinematic viscosity, is the material density of the particle and is the density of the gas.

These regimes are diffusional deposition regime, diffusion‐impaction regime and inertia‐

moderated regime. Very small particles, with the non‐dimensionalized particle relaxation time τ 0.2 (τ τ u ν , u is the friction velocity) travel in the core by turbulent dispersion and move through the quiescent boundary layer by Brownian diffusion. The non‐

dimensionalized deposition velocity, k k u⁄ , in this regime has an almost constant value. In annular flow, however, the drops with such small sizes occupy a negligible mass fraction out of the total mass of drops and in the modelling this regime could be ignored. In the diffusion‐impaction regime, 0.2 τ 20, the particles have more inertia, interacting actively with turbulent eddies. They arrive at the wall by the influence of turbophoresis,

1 10 100 1000 10000

0.01 0.1 1 10

d32, [µm]

C_h, [kg m^‐3]

Hay et al. 1996: air-water Jepson et al. 1989: air-water Jepson et al. 1989: helium-water Fore&Dukler 1995: air-water Fore&Dukler 1995: air-glycerine/water Azzopardi&Teixeira 1994: air-water Pogson et al. 1970: steam-water, P=1 bar Ardron&Hall 1981: steam-water, P=1 bar Fore et al. 2000: nitrogen-water, P=3 bar Fore et al. 2000: nitrogen-water, P=17 bar

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which is the movement down the gradient of turbulence fluctuations. The non‐

dimensionalized deposition velocity in this regime increases by several orders of magnitude.

The non‐dimensionalized deposition velocity in the inertia‐moderated regime, τ 20, slightly decreases as a function of increased particle response time, as reported by Young and Leeming (1997). One of the stated reasons being the lower responsiveness to turbulent eddies, because of the high inertia. Another deposition regime, characteristic to annular flow has been first experimentally established by James et al. (1980). Their photographic studies in air‐water showed that the measured large droplets d 250 µm detached from the waves of the liquid film travel almost in straight lines to the opposite wall, unaffected by the turbulence of the flow. This regime, called direct impaction, is characterized by the dependence on the initial conditions of droplets (entrainment process). At present, however, there is no complete understanding to establish the initial momentum of the droplet, thus the limit, in terms of drop response time, when direct impaction is predominant is in principle unknown. In annular flow, as was mentioned above, the droplets have a distribution of sizes, where the deposition is likely to be a mix of different deposition regimes, which in terms of modeling is not an easy task.

In Figure 3.4 the data from Fig. 3.3 are recalculated to represent the non‐dimensional particle relaxation time (Sauter mean diameter was used). From this plot we can conclude that the deposition regimes worth modelling in annular two‐phase flow are the inertia moderated regime (τ 20) and the direct‐impaction regime with the condition that the Sauter mean diameter is a representative droplet size. The representative droplet size means in this case, the size responsible for the main deposition regime in certain annular flow conditions.

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3.2 Deposition mechanisms and deposition modelling 21

Figure 3.4: Non‐dimensional particle relaxation time of droplets in annular two‐phase flow Another parameter worth investigating in relation to deposition of droplets in annular flow is the turbulence intensity of the gas. Since all deposition regimes, except direct impaction are driven by the turbulence of the core flow, it has to be correctly represented in the model.

Annular flow is characterized by the presence of a wavy liquid film at the heated wall.

Researchers (e.g. Hay et al. 1996, Azzopardi and Teixeira 1994) have shown that the liquid film on the wall acts as a rough surface increasing the turbulence of the flow. The increase is proportional to the liquid film thickness. From the other side, Chamberlain (1967) and El‐

Shobokshy (1983) have shown that deposition increases on rough surfaces compared to smooth surfaces. It is also interesting to know how the presence of droplets influences the turbulence of the flow. For solid particles Gore and Crowe (1989) have shown that small particles decrease the turbulence intensity, while larger particles increase considerably the turbulence intensity up to 400%. Azzopardi and Teixeira (1994) and Trabold and Kumar (2000) have experimentally shown that liquid droplets always increase the turbulence intensity of the gas flow.

3.2 Deposition mechanisms and deposition modelling

The study of deposition and its modelling has been going on for more than half a century.

Herein we will refer to deposition of particles, since many researchers have dealt with solid particles. Many conclusions and models of the deposition of particles are valid for liquid drops as well. Friedlander and Johnstone (1957) have proposed one of the earliest descriptions of deposition mechanism of particles onto the wall, based on “free‐flight”

1 10 100 1000 10000 100000 1000000 10000000

0.01 0.1 1 10

τp+[-]

C_h/ρ_g, [‐]

Hay et al. 1996: air‐water Jepson et al. 1989: helium‐water Jepson et al. 1989: air‐water Fore&Dukler 1995: air‐water Fore&Dukler 1995: air‐water/glycerine Azzopardi&Teixeira 1994: air‐water Pogson et al. 1970: steam‐water, P=1 bar Ardron&Hall 1981: steam‐water P=1 bar Fore et al. 2000: nitrogen‐water, P=3 bar Fore et al. 2000: nitrogen‐water, P=17 bar

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theory. The essence of this mechanism is that particles are transported by turbulent motions to within one stop‐distance from the wall, where they acquire sufficient momentum to move through the quiescent viscous sub‐layer towards the wall. The much‐debated assumption of the model is the independence of the velocity of the particle, set on the “free‐flight”, on particle position. In the initial model this velocity was set equal to the turbulent velocity fluctuation of the gas well outside the sub‐layer region. This assumption had no physical support. Many other improved models based on this theory followed and the “free‐flight”

mechanism of deposition is still considered nowadays (e.g Brooke et al. 1994, Narayanan et al. 2003).

More detailed studies on the nature of the viscous sub‐layer gave start to a new set of deposition mechanism explanations based on the “downsweep” motion, initialized by Cleaver and Yates (1975). Later experimental studies performed first by Rashidi et al. (1990) and later by Kaftori et al. (1995) proved that the wall coherent structures (bursts) have a significant effect on the wall deposition. The interactions between the near‐wall bursts and solid particles are a strong function of particle size, particle density and flow Reynolds number.

Caporaloni et al. (1975) and Reeks (1983) proposed a new physical explanation on how the particles arrive to the wall passing through the anisotropic turbulence layer. They derived the turbulence diffusion equation on the analogy with thermal diffusion, and term it turbophoresis, which represents the movement of particles down the gradient of turbulent fluctuations. The diffusion of particles – the movement down the concentration gradient is recognized also as a possible deposition mechanism in Direct Numerical Simulation studies, due to the accumulation of particles in the viscous sublayer (see Brooke et al. 1994).

The movement of the very small particles can be described by Brownian motion and the very large particles with initial velocity deposit solely by inertia. This sums up the present knowledge about the physical process of deposition onto the wall.

Two main streams are formed to model the deposition of particles: the first is the Eulerian description of both continuous and particulate phases, and the second is the Lagrangian representation of the particulate phase coupled with the Eulerian representation of the continuous phase. Illustratively the degree of freedom in the two methods is represented in Fig. 3.5.

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3.2 Deposition mechanisms and deposition modelling 23

Figure 3.5: Degrees of freedom in Eulerian and Lagrangian representation of particulate phase

The Eulerian description for the dispersed phase assumes that particle characteristics (e.g.

velocity) can be described as a continuous process. This assumption allows the dispersed phase to be treated with the same discretization and the same numerical technique as the continuous phase, which becomes important when the dispersed phase exerts an influence on the surrounding fluid – a process termed two‐way coupling. If the dispersed phase is present with a range of sizes with individual characteristics (e.g. velocity), a set of mass, momentum and energy equations should be included for each bin of sizes, increasing substantially the computational cost. The Eulerian models proposed in the literature are dependent on the phenomenological constants that need to be estimated by experiment or costly simulations (see Cerbelli et al. 2001 and cited literature).

In the Lagrangian description the particle is represented as a single point, which moves with an independent velocity. In this way the particle individual path is calculated throughout the flow, providing an easier method to monitor turbulent diffusion and particle deposition onto the solid wall or reflection from the wall. In the point‐volume or point‐mass representation the presence of the particles is not felt by the continuous flow field or the discretization. The other Lagrangian representation of particle is to discretize its finite volume together with the continuous field. However, this method is applicable at present only for studies of one or very few particles at a time. These studies are very useful in respect of interphase terms evaluation, needed for the point‐volume representation. The spatial and temporal calculation resolution of the continuous field puts a limit in terms of the amount of physics of particulate flow that can be resolved.

The calculation of the continuous phase in the Eulerian formulation can be done in an unresolved‐ or resolved‐eddy description. See Loth (2000) for full classification of continuous flow descriptions. The Reynolds‐averaged Navier‐Stokes equations represent the basis of the unresolved‐eddy description. In order to close the system of equations turbulence modelling is required. Among the turbulence models that are applicable to engineering calculations Loth (2000) names the robust and relatively inexpensive k‐epsilon turbulence model, which can be successfully used in isotropic and homogeneous turbulent

Particle path line Particle velocity vector

Eulerian particle representation Lagrangian particle representation

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