Condensation in a vertical tube bundle passive condenser – Part 1: Through flow condensation

International Journal of Heat and Mass Transfer 53 (2010) 1146–1155

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Condensation in a vertical tube bundle passive condenser – Part 1: Through flow condensation Wenzhong Zhou, Gavin Henderson, Shripad T. Revankar * School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA

a r t i c l e

i n f o

Article history: Received 26 May 2009 Received in revised form 20 October 2009 Available online 27 November 2009 Keywords: Passive condenser Tube bundle Through flow condensation Non-condensable gas Boundary layer model

a b s t r a c t An experimental study and a boundary layer analysis were performed for the steam condensation in a vertical tube bundle passive condenser operating in a through flow mode. Four condenser tubes were submerged in a water pool and the heat from the condenser tube was removed through boiling. Experimental data were obtained for various system pressures (100–170 kPa), inlet steam flow rates (15–47 g/s) and non-condensable gas concentration (0–15%). The experimental results showed substantial deterioration in condensation when non-condensable gas was present. With increase in steam flow rate and system pressure the condensate rate increased. The boundary layer thickness and non-condensable gas concentration increased along the condenser tube length. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Condensation phenomenon is an important heat transfer process in the chemical and power industry, including nuclear power plants. In nuclear power plants condensation has important safety implications. For example during a loss of coolant accident (LOCA) in the primary system of a water-cooled nuclear reactor a large amount of steam can be released into the reactor containment. As a result, the integrity of the containment can be seriously threatened [1]. There are several aspects, which have to be taken into account during such events. One of these is the possibility of over-pressurization of the reactor containment. In such condition it is very important to condense released steam as quickly as possible. Containment spray systems, suppression pool (SP) and passive containment cooling system (PCCS) condense steam in the containment during steam release scenarios. The efficiency of these systems depends not only on the type of condensation but also on the composition of the gaseous phase, which usually contains a significant amount of non-condensable (NC) gas [2]. The NC gases can be air, nitrogen, hydrogen, or oxygen or mixture of these gases. Condensation has high heat transfer coefficient. However, even small amounts of NC gases can strongly deteriorate the condensation heat and mass transfer process. NC gases tend to accumulate near the liquid–gas interface due to its impermeability to these components. This creates an additional resistance to the mass

* Corresponding author. Tel.: +1 765 496 1782; fax: +1 765 494 9570. E-mail address: [email protected] (S.T. Revankar). 0017-9310/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2009.10.039

transfer, because the condensable gas has to diffuse through the mixture gaseous layer. In the General Electric’s simplified boiling water reactor (GESBWR) the PCCS is a passive heat exchanger that allows the transfer of reactor heat via steam condensation to the outer water pool [3]. The PCCS condenser must be able to remove sufficient energy from the reactor containment to prevent containment from exceeding its design pressure following a design basis accident. Hence, a detailed knowledge of the variation of the heat transfer coefficient and its dependence on the system is necessary in order to predict the performance of the PCCS and for design optimization. A schematic flow diagram of the PCCS for the GE-SBWR is shown in Fig. 1. The PCCS condensers are immersed in a large interconnected pool of water. The pool is located outside and above the containment. The driving force of the PCCS is provided by the pressure difference between the dry-well (DW) and the SP. Condensed water produced in the PCCS drains in to the gravity driven cooling system (GDCS) pool and then to the reactor pressure vessel (RPV). The NC gas and the uncondensed steam from the PCCS are vented to the SP. There are no valves or pumps in the PCCS operation and operator actions or signals are not needed which makes the PCCS a truly passive system. The performance of the condenser degrades when the NC gases are present in the condenser tubes. The condensed water flows as an annular liquid film adjacent to the condenser tube wall and the steam–air mixture flows in the core region. Since the NC gases are impermeable to the liquid film, they accumulate at the liquid–gas interface so its concentration increases along the tube length. The high NC gas concentration region at the interface propagates to the gas core region by mass diffusion.

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Nomenclature English A Cp D d g H h hfg j00 k M m m00 N NC p, P Q q00 r R t T U u v W x z

s area specific heat diffusion constant diameter gravitational constant height heat transfer coefficient (HTC) or enthalpy latent heat of vaporization diffusion mass flux thermal conductivity molecular weight mass flow rate or mass mass flux number non-condensable pressure Heat Transfer Rate heat flux radial coordinate radius or gas constant for a specific gas time temperature overall heat transfer coefficient axial velocity radial velocity or specific volume non-condensable gas mass fraction independent variable axial or stream-wise coordinate

Greek symbols thermal diffusivity d film thickness g transformed wall coordinate l dynamic viscosity n transformed axial coordinate q density

a

Three different operational modes are possible in the PCCS depending on the NC gas concentration and the pressure difference between the DW and SP, dPVENT (= PDW  PSP). These are through flow mode, complete condensation mode and cyclic venting mode [4]. Fig. 2 shows the characteristics of these three operational modes of PCCS. The PCCS will be in through flow mode when the

shear stress

Subscripts a, air non-condensable gas b bulk c, con condensation eva evaporation g gas I interface i inside L liquid m model o outside p pool or prototype R ratio SAT saturation sec secondary side TOT total v vapor W wall Superscripts m molecular transport quantity t turbulent transport quantity Abbreviations DW dry well GDCS gravity drain cooling system GE General Electric GE-SBWR GE designed simplified boiling water reactor HTC heat transfer coefficient ICS isolation condensation system LOCA loss of coolant accident PCCS passive containment cooling system RPV reactor pressure vessel SG steam generator SP suppression pool

dPVENT is greater than the head due to the submergence of the vent line in the SP, dPHEAD. This condition is realized during the blowdown process, i.e., initial period of the accident. In this mode, uncondensed steam and NC gas pass through the PCCS condensers and are vented to the SP through the vent line. This mode of PCCS

Condenser

To GDCS

SP

SP

Through Flow

Fig. 1. PCCS operation in the SBWR.

DW

DW

Cyclic Venting

DW

SP

Complete Condensation

Fig. 2. Three operation modes of the PCCS.

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operation corresponds to forced convection. The present study covers the through flow mode of operation of PCCS. Since the work of Uchida et al.’s work [5], which provided the first practical correlation for degradation of condensation from NC gas from experiments with steam–gas condensation on vertical wall, there is substantial amount of experimental and modeling work done on condensation of steam inside a vertical tube in the presence of NC gas [6–23]. Most of these work relate to the through flow mode operation of the PCCS and were conducted with secondary heat removal through forced convention cooling except Kim and No [18] who used pool boiling, but in a large rectangular tank, and the experiments did not involve the presence of NC gas. Table 1 gives the summary of all experimental work on PCCS related studies. Oh and Revankar [24–27] performed series of experiments with single vertical tube condenser that simulated all three modes of PCCS operation: through flow, cyclic venting, and complete condensation mode and used the realistic secondary heat transfer condition – pool boiling heat transfer. A boundary layer model and heat and mass transfer analogy model were developed based on the methodology presented by Colburn and Hougen [28] to simulate PCCS condensation. Here in this work a new multi-tube test facility was designed and constructed to extend Oh and Revankar’s research [24] as well as to investigate the tube bundle effect on PCCS heat removal capabilities [29]. The present work focuses on experiments and analysis of the through flow condensation mode in a multi-tube condenser.

is the inner surface area of a condenser tube, and Tb and Tp are the steam and PCCS pool temperatures, respectively. The overall heat transfer coefficient is given by

U¼



1 lnðdo =di Þdi di þ þ hc 2kW hp do

1 ð2Þ

:

In the right-hand side of Eq. (2), the first term corresponds to the tube side condensation heat transfer coefficient, the second term corresponds to the tube wall conduction heat transfer coefficient, and the third term corresponds to the outside tube pool heat transfer coefficient. For the correct scaling of heat removal by the PCCS condensers we should have:

_ fg Þm ðQ_ pccs =mh ¼ 1; _ _ fg Þ ðQ pccs =mh

ð3Þ

p

_ is the inlet steam mass flow rate to the PCCS condenser. where m From Eqs. (1)–(3), the scaling requirement for PCCS condenser heat removal rate is given as

    _ fg R ¼ 1: N tubes Nunits UAi T b  T p mh

ð4Þ

If the prototype and model have the same operating pressure condition and use the same operating fluid (water), then the temperature difference can be preserved. From Eqs. (3) and (4) we obtain,

)          ( Q =mhfg m Nm Nm Um Am ðT b  T p Þm  pccs  ¼ Np tubes Np units U p Ap i ðT b  T p Þp Q pccs =mhfg p    ðh Þ mp fg p :  mm ðhfg Þm

2. Experiment program 2.1. Scaling and design of test facility For conduct of experiments scaling methodology can be used in the design of the test facility, analysis of the data from the scaled facility, scale up of the data from scaled model to the prototype design. Revankar and Ishii [30] proposed a scaling method for the condensation and venting phenomena in the PCCS. They modeled the mechanism of the PCCS venting into the SP and calculated the vent frequency for prototype and model of the SBWR. The PCCS condensers provide decay heat removal by condensing steam from the DW and supplying condensate water to the RPV through the GDCS tanks. The scaling of the heat transfer rate through the condenser is given by

Q pccs ¼ Ntubes Nunits UAi ðT b  T p Þ;

Eq. (5) is used for the design of the PCCS tube bundle condenser for the integral test facility. The specific design of the PCCS condenser tube bundle test section was based on the scaling analysis, and four condenser tubes are used. A full diameter and height scaling was chosen in the present design. The dimensions of the tube bundle facility are compared with the prototype in Table 2. The tube unit ratio is 62 for the scaled test facility. This number can be used to scale up the experimental condensed mass flux to the prototype condensate mass flux. 2.2. Description of experimental loop

ð1Þ

where Ntubes is the number of PCCS condenser tubes, Nunits is the number of PCCS units, U is the overall heat transfer coefficient, Ai

The schematic of the experimental set-up is shown in Fig. 3. The test loop is comprised of a steam generator (SG), instrumented condenser test section with secondary pool boiling section,

Table 1 Comparison of previous vertical tube condensation experiments.

Tube length (m) Tube bundle Tube ID (mm) Tube thickness (mm) Secondary jacket ID (mm) Non-condensable gas Secondary cooling Steam flow (g/s) Inlet air mass fraction (%) Pressure (MPa) HTC (W/m2 K)

Vierow [8]

Kuhn [10]

Siddique [9]

Park and No [16]

Kim and No [18]

Al-Shammari et al. [21]

Oh and Revankar [24]

Lee and Kim [23]

2.1 No 22 1.65 50.8

2.4 No 47.5 1.65 76.2

2.54 No 46 2.4 62.7

2.4 No 47.5 1.65 100

1.8 No 46.2 2.3 1.2 m  1.2 m square

3 No 28.25 62.7

1 No 26.6 3.38 152.4

2.8 No 13 2.5 40

Air

Air, helium

Air, helium

Air

Pure steam

Air

Air

Nitrogen

Forced convection 1.6–6.9 0–0.14

Forced convection 8.2–17 0–40

Forced convection 2.4–8.9 10–35

Forced convection 2–11 10–70

Pool boiling – 0

Forced convection 1.5–2.4 17–47

Pool boiling 2.5–5.5 0–10

Forced convection 1.8–7.8 0–40

0.03–0.45 0–16,000

0.1–0.5 500–13,000

0.1–0.5 100–25,000

0.17–0.5 100–7000

0.35–7.5 4000–7400

0.12–0.13 3500–10,000

0.1–0.4 3500–6500

0.1–0.13 300–27,900

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W. Zhou et al. / International Journal of Heat and Mass Transfer 53 (2010) 1146–1155 Table 2 Comparison between tube bundle condenser and prototype parameters.

Steam

Parameter

Experiment loop

Prototype

Ratio

Number of tubes

4

248 per module

62

Condenser tubes Length (m) Diameter (cm)

1.8 5.08

1.8 5.08

1 1

0.0126 66 67

0.78 66 67

62 1 1

Insulation

Header Volume (m3) Height (cm) Header center to pool bottom (cm)

Insulation VD1

Sight Glass LT4 Level Level Level Level Level Level

1 2 3 4 5 6

Level 7

condensate tank, suppression pool (SP), water storage tank, air supply line, and associated piping and instrumentation. The SG is a 406 mm (18 in.) diameter, 3.05 m (120 in.) long stainless steel tank. An immersion type sheathed electrical heater of 100 kW capacity was mounted at the lower flange of this vessel. The vessel is instrumented with thermocouples, a pressure gauge and a DP cell to measure and monitor temperature, pressure and water level. A relief valve was mounted at the upper shell of the SG. For the pool boiling heat removal at the secondary side, the test section was designed with two subassemblies: the primary condensing tube bundle with insulation housing and the secondary boiling tube as shown in Fig. 4. The primary condensing tubes were made of type 304 stainless steel pipes with 52.5 mm inner diameter (ID), 3.91 mm thickness, and 1.8 m length. The secondary boil-

PG

Air supply

T Flowmeters

PT T

Steam venting line

FT

Blowdown

Sight glass DP

T Steam generator

Test section

DP Water level tube

PG

PG

PG T Suppression pool

DP T

DP

Heat exchanger

Condensation tank

Storage pool

drain

Instrument sensing line

Heat exchanger

Fig. 3. Schematic of test facility.

Level 8 Level 9 Level 10 VD9 Fig. 4. Test section.

ing tube was made of type 304 stainless steel pipe with 19.1 cm (7.5 in.) diameter. Condensation occurs at the inside surface of the primary condensing tubes and boiling occurs at the outside surface. The annulus between the primary condensing tubes and the secondary boiling tube was filled with water and serves as a water pool. During the test, the secondary water level was maintained to cover the active condenser and the secondary pool was maintained at saturation condition. Steam generated in the pool is discharged through three steam exit nozzles located symmetrically at the top of the secondary boiling tube. To separate the active condenser from the upstream pipe, the insulation housing was welded at the top of the active condenser. To minimize the conduction heat transfer above the active condenser, the gap between the primary condensing tube and the insulation housing was filled with a fiber glass thermal insulation material. The effect of the heat conduction in the inlet region was investigated with the numerical analysis by solving the steady state heat conduction equation for the primary condensing tubes and the insulation housing. Due to the heat conduction, condensation can occur before the active condenser. The extended condensation length, where the condensation initiates before the inlet of the active condenser, was estimated to be less than 1.5% of the active length for the present test conditions. Therefore, the effect of the heat conduction was not accounted for in the data reduction. Another function of the insulation housing is to reduce the pool cross-sectional area of the steam rising section, which gives magnified water level difference due to evaporation. Hence, it provides more accurate measurement of evaporation heat transfer rate. To measure the local temperature along the condensation tube, 140 thermocouples were welded on the condensation tube, 14 T/Cs for each level and 10 levels altogether. Six heat flux sensors were also mounted along the tubes. To measure the secondary side temperature, eight thermocouples were installed in the secondary pool at different axial locations. The evaporation rate during the experiment was calculated by the water level measurement of the secondary pool. The steam supply line to the condenser was made of 52.5 mm stainless steel pipe and equipped with vortex flow meters to measure steam flow rate. To determine the flow condition at vortex flow meters, a pressure transducer and a thermocouple were installed at the downstream of the vortex flow meter. The sensing line to this pressure transducer was routed upward to drain the condensate in the sensing line. The air supply line was connected

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to the steam line. Before the connection to the steam line, three rotameters with different flow ranges are installed to measure the wide range of air flow rates. A pressure gauge and a thermocouple were also installed to measure pressure and temperature of air. A pre-heater was not used to heat the air since the steam is highly superheated before mixing. The condensate tank collects the condensate. It was equipped with three thermocouples, a pressure gauge and a DP cell for level measurement. Condensation rate was calculated by the measurement of the condensate water level. For the venting of the NC gas and uncondensed steam, a vent line was connected between steam space of the condensate tank and water space of the SP. The SP serves as a collector of the NC gas and the uncondensed steam. The water level in the SP can be maintained at desired level by continuous bleeding water from the tank. The condenser operating pressure was set by the pressure level in the SP. A blowdown line was connected to the water storage tank. The NC flow from SP can be controlled through the valve on the blowdown line in the through flow mode operation. This valve can be set at different opening to set the pressure in the SP. This SP pressure provides the back pressure in the test section. The steam and air inlet flow rate, the back pressure and condensation determined the operating pressure of the test section. The SP was instrumented with two thermocouples, a pressure gauge and a DP cell to measure and monitor temperature, pressure and water level. The water storage tank served as heat and mass sink and deionized water supply. The discharges from steam–gas space of the SP were routed to this tank for blowdown purposes. The discharge line was submerged into the water space of the water storage tank. The steam generated in the test section secondary side was also discharged to this tank through three independent sets of copper tubing. 2.3. Test procedure First, the instrument lines were purged. The SG, secondary pool and suppression pool were filled with de-ionized water to the required levels. The heater in SG was turned on after it is isolated from the remaining part of the system. The steam was vented several times from the SG to remove any dissolved gases and air. Using steam loop and secondary water pool is heated to required temperature. When the secondary water temperatures reach saturation condition (100 °C), the required steam flow rate and air flow rate were established. All condensation experiments were conducted in steady state mode. The first the power to the steam generator (SG) was fixed, this provided constant steam inlet flow rate. The SG was maintained at higher pressure than the condenser operation pressure. The air flow was added to steam flow at the inlet of the condenser. For these given conditions, the test section pressure was maintained at a desired level by use of the blowdown valves or air supply line valve. However, the facility reached to a steady state pressure for a given inlet steam, air flow rate and the setting of the SP valve. The steam temperature, flow rate, secondary water pool temperature and the system pressure were checked to verify the steady state. Data was taken once the steady state was established. 2.4. Data reduction The measured steam bulk temperature was slightly higher than the saturation temperature at the system pressure. It means that the state of the steam–air mixture is superheated. However, the amount of sensible heat transfer is much less than that of condensation heat transfer. For the present test conditions, the sensible heat transfer rates were evaluated to be less than 1% of the conden-

sation heat transfer rate. Therefore, the sensible heat transfer was ignored in data reduction. The overall heat transfer coefficient in condenser tubes is determined from:

U¼

Q con ; Ai ðT SAT  T P Þ

ð6Þ

where Qcon is the condensation heat transferred by condenser tubes, Ai is the heat transfer area of tube inside, TSAT is the saturation temperature at the steam partial pressure (PSAT) and TP is the secondary pool water temperature. The condensation heat transferred by the condenser tube Qcon can be calculated as follows:

Q con ¼ mcon hfg ðPSAT Þ;

ð7Þ

where meva is the condensation mass flow rate calculated from the condensate tank water level difference during the test and hfg(PSAT) is the latent heat of condensation based on the steam partial pressure PSAT. This condensation heat transfer rate should be equal to the secondary side heat removal rate, QTOT, which is the sum of the evaporative heat transfer rate and the heat loss from the secondary tube surface. The overall heat transfer coefficient is given by the following equation derived by the heat balance among the inside of the condenser tube, tube wall and outside of the tube.

 U¼

1 lnðDo =Di ÞDi Di þ þ hc 2kw hsec Do

1 :

ð8Þ

The first term of the right-hand side of the above equation corresponds to the tube side condensation heat transfer, the second term corresponds to the tube wall conduction heat transfer, and the third term corresponds to the secondary side pool boiling heat transfer. Neglecting the heat transfer along the condenser tube length, the condensation heat transfer coefficient, hc, is defined as follows:

hc ¼

Q con ; Ai ðT SAT  T Wi Þ

ð9Þ

where TWi is the tube inside wall temperature. The secondary side pool boiling heat transfer coefficient, hsec, is defined as follows:

hsec ¼

Q con ; Ao ðT Wo  T P Þ

ð10Þ

where TWo is the tube outside wall temperature and Ao is the heat transfer area of the outside of the tube. From Eq. (8), the condensation heat transfer coefficient can be expressed as follows:

1 1 lnðDo =Di ÞDi Di ¼   : hc U 2kw hsec Do

ð11Þ

Substituting Eqs. (6), (7) and (10) into Eq. (11) and rearranging to get the condensation heat transfer coefficient with the known or experimentally obtainable values is shown as follows:

hc ¼

2kw mcon hfg : 2kw pDi Htube ðT SAT  T Wo Þ  mcon hfg lnðDo =Di ÞDi

ð12Þ

Vapor partial pressure can be calculated from the Gibbs–Dalton ideal gas mixture equation as follows:

PSAT 1  W air

; ¼ PTOT 1  W air 1  Mv Ma

ð13Þ

where the air mass fraction Wair is defined as NC gas mass flow rate divided by the total inlet mass flow rate, PTOT is the total pressure which is the sum of the vapor partial pressure and air partial pres-

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sure, Mv and Ma are the molecular weights of the vapor and air, respectively. The average NC gas concentration is the arithmetic mean of the tube inlet and outlet NC gas concentration. By combining Eqs. (9) and (12), the average inside wall temperature can be calculated. Since the four condenser tubes in the secondary pool have equal positions, the calculated values of the condensation HTCs and inside wall temperatures for four tubes will be almost the same. 2.5. Experimental results During the postulated loss of coolant accident of the SBWR, initial steam flow rate and pressure are very high and the steam flow rate and pressure gradually decrease with time. This accident scenario can be roughly simulated with different steam flow rates and system pressures. The experiments were conducted under the conditions of the average calculated liquid film Reynolds number in the range 370–915. Figs. 5 and 6 show the effects of non-condensable gas mass fractions, inlet steam flow rates, and system pressures on steam condensation in a vertical tube bundle condenser with the presence of NC gas. In the experiment it was not possible obtain required pressure for given steam flow rate; the test section pressure reached steady state value for a given inlet steam, airflow rate and the setting of the SP valve. Hence the data were grouped in to small ranges of inlet mass flow rate and pressure. The condensed mass flow rates were normalized to steam inlet flow rate. The normalization of the condensation rate reduced the effect of inlet mass flow variation. Fig. 5(a) and (b) shows the effects of non-condensable gas mass fraction, inlet steam flow rate and system pressure on the normalized condensate rates. Here the normalized condensation rate,

which is defined as the ratio of condensation rate to inlet steam flow rate, is employed to study the percentage of the inlet steam flow being condensed. Fig. 5(a) shows how the steam flow rate will affect the normalized condensate rate for different steam flow rates at relatively the same system pressure. The system pressure was set at 159.2–168 kPa by adjusting the vent line from the suppression pool to the storage pool. It should be noted here that during the experiments the system pressure could not be held at one constant value, hence pressure ranges are stated. Two steam flow ranges were used for these experiments, one from 15.56 to 26.77 g/s, and the other one from 34.92 to 46.47 g/s. From the figure, we can see that the normalized condensate rate decreases with increasing NC gas mass fraction, and decreases with increasing inlet steam flow rate for a given system pressure. Thus with increasing steam flow rate the fraction of steam condensed decreases for through flow mode. In Fig. 5(b), the effect of system pressure on the normalized condensate rate is shown for inlet steam flow rates from 16.92 g/s to 36.63 g/s. The system pressure was set at two levels one at 110.3–117.2 kPa and another 127.6–131 kPa, respectively. The data show that the normalized condensate rates first decreased by 30% when pure steam was mixed with 1% of NC gas concentration and then it decreases at relatively slower rate with increase in NC concentration. However, normalized condensate rate does not change much with system pressure for the range of pressures studied. The data indicated that when the condensed mass was normalized with inlet steam flow rate the effects of non-condensable on condensation could be clearly observed irrespective of the inlet steam flow rate. With a small amount of NC (at 1%) the condensation rate decreases substantially. 40

(a)

(a)

0.8

Condensation rate (g/s)

Normalized Condensate Rate

1

0.6

0.4

SG Rate 15.56-26.77 g/s SG Rate 34.92-46.47 g/s

0.2

30

20

steam flow rate 15.56 g/s steam flow rate 21.66-26.77 g/s steam flow rate 34.92-41.35 g/s steam flow rate 46.47 g/s

10

0 0

2

4

6

8

0 0

NC Gas Mass Fraction (%)

2

4

6

8

Non-condensable gas mass fraction (%)

(b)

25

(b)

0.8

Condensation rate (g/s)

Normalized Condensate Rate

1

0.6

0.4

Flow pressure: 110.3-117.2 kPa 0.2

Flow pressure: 127.6-131.0 kPa

0

20 15 10

system pressure 113.8-129.7 kPa

5

system pressure 162.2-168.0 kPa 0

0

2

4

6

8

10

12

14

16

NC Gas Mass Fraction (%) Fig. 5. Through flow normalized condensate rate vs. air mass fraction (a) for system pressure 159.2–168.0 kPa and (b) for inlet steam flow rates of 16.92–36.63 g/s.

3

5

7

9

Non-condensable gas mass fraction (%) Fig. 6. Through flow condensate rate vs. air mass fraction (a) for system pressure 159.2–168.0 kPa and (b) for inlet steam flow rate 20.22–26.77 g/s.

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Fig. 6(a) shows the condensate rate for different steam flow rates at relatively constant pressure. The system pressure is set at 159.2–168.0 kPa. The steam flow rates have four ranges as shown in Fig. 6(a). From the figure, we can see that the condensate rate decreases with increasing NC gas mass fraction, and increases with increasing inlet steam flow rate for an almost fixed system pressure. The trends for the normalized condensate rate change and total condensate rate change are opposite with the inlet steam flow rate changes. Fig. 6(b) shows effect of the system pressure on the total condensate rate. Data were obtained for the system pressure of 113.8–129.7 kPa and 162.2–168.0 kPa and the steam flow rate was at 20.22–26.77 g/s. From the figure, we can see that the condensate rate decreases with increasing NC gas mass fraction, and slightly increases with increasing system pressure. However, with increase in NC gas mass faction, the effect of system pressure on the condensate rate is smaller. At 7.5% NC gas mass fraction the effect of system pressure on the condensate rate is negligible. Thus we see even small amounts of the NC gas can significantly degrade the performance of the condenser. Since the NC gas is impermeable to the liquid film, it accumulates at the film–gas interface. This high NC gas concentration at the interface diffuses to the gas core. So, the gas boundary layer thickness increases with higher NC concentration level along condenser tube length. In the next section, using boundary layer model the gas boundary layer thicknesses are studied. From Figs. 5 and 6, we can see that as the inlet steam flow rate and system pressure decrease, the normalized condensate rate will increase, although the condensate rate decreases. The condensate rate increases with increasing inlet steam flow rate. This is possible as the inlet steam flow rate increases, interfacial shear also increases. This results in a thinner liquid film, i.e., smaller resistance in heat transfer. The average film Reynolds numbers were calculated for the range of condensed steam mass flow rate studied and were in laminar range. The condensate rate is higher for the higher pressure condition, although there is almost no effect for system pressure on normalized condensate rate.

z U velocity

g

δ Liquid film

T temperature

δM , δ H , δ W Boundary layer for u , T, W

Fig. 7. Physical model of film condensation in a vertical tube.



00 00 00 jg and jv ¼ jg . Diffusion mass flux for NC gas can be represented by the Fick’s law as follows:

J 00g ¼ qD

oW : or

ð17Þ

Conservation of species

  oquW 1 orqvW 1 o oW þ ¼ r qD : oz r or r or or

3.1. Boundary layer model formulation The boundary layer model is based on the self similar velocity assumption. The PCCS tube is considered as a two-dimensional axisymmetric model as shown in Fig. 7. The saturated steam enters the tube and is considered turbulent. The condensed steam develops in to a laminar film on the tube surface. Boundary layer equations for the mass, momentum, energy and species in steam–gas mixture region are as follows: Conservation of mass

ð18Þ

All transport properties for momentum, energy and species are the sum of the molecular and turbulent transport terms as follows:

l ¼ lm þ lt ; m

t

ð19Þ

k¼k þk ;

ð20Þ

D ¼ Dm þ Dt :

ð21Þ

ð14Þ

For the liquid film, all the physical properties are assumed as constant and flow condition is laminar. Boundary layer equations for the mass, momentum, and energy in liquid region are as follows: Conservation of mass

ð15Þ

ouL 1 or v L þ ¼ 0: r or oz

Conservation of z-directional momentum

oquu 1 or qvu dp 1 o ou þ ¼ þ ðr l Þ þ qg: oz r or dz r or or

W NC gas mass fraction

τLτI

3. Boundary layer model

oqu 1 or qv þ ¼ 0: oz r or

r

y

ð22Þ

Conservation of z-directional momentum

Conservation of energy

i 1 o  oT  oqC p uT 1 or qC p v T 1 o h 00 þ þ rðC pg  C pv Þjg T ¼ rk : oz r or r or r or or

uL ð16Þ

The third term on the left-hand side of the energy equation represents a net enthalpy change due to the diffusion mass fluxes

  ouL ouL 1 dp mL o ouL þ r þ vL ¼ þ g: ox or qL dx r or or

ð23Þ

Conservation of energy

  oT L oT L aL o oT L : uL r þ vL ¼ oz or r or or

ð24Þ

W. Zhou et al. / International Journal of Heat and Mass Transfer 53 (2010) 1146–1155

Since the NC gas is impermeable, there is no species equation for the film region. Film region governing equations are transformed using the coordinate transformation ðz; rÞ ) ðn; gÞ as follows:

n ¼ z;

g¼

Rr : d

ð25Þ

Here, liquid film thickness, d, is only a function of the axial direction z. By this transformation, dimensional radial coordinate is changed to the non-dimensional wall coordinate where g = 0 at the wall and g = 1 at the interface. Conservation of mass

ouL g dd ouL 1 o   fðR  dgÞv L g ¼ 0: on d dz og ðR  dgÞd og

ð26Þ

Conservation of z-directional momentum

uL

  ouL g dd v L ouL 1 dp mL ¼ uL þ þgþ  on d dz d og qL dz ðR  dgÞd2  o ouL :  ðR  dgÞ og og

ð27Þ

Conservation of energy

uL

   oT L g dd v L oT L aL o oT L uL þ  : ¼ ðR  dgÞ 2 on d dz d og ðR  dgÞd og og

ð28Þ

The present problem is a two-phase, two-component flow with an annular flow regime. The two sets of nonlinear partial differential equations for the vapor–gas mixture and liquid film are coupled at the interface. To solve the two-phase flow, the following the interface jump conditions for mass, momentum, energy and species at the liquid–gas interface are used. Mass

m00c ¼ Dm00L :

ð29Þ

Momentum

sI ¼ lL

ouL

ou

¼  l : or I or I

ð30Þ

Energy

q00I ¼ kL

oT L

oT

¼ k þ m00c hfg : or I or I

ð31Þ

Species

J 00gl ¼ qD

oW

¼ m00c W I : or I

ð32Þ

Boundary conditions at the tube wall, tuber center, and interface can be specified as follows: At interface:

uLI ¼ uI ; T LI ¼ T I :

ð33Þ

At r = 0 (tube center line):

ou oT oW ¼ ¼ ¼ 0; or or or

v ¼ 0:

ð34Þ

At r = R (wall):

uL ¼ 0;

TL ¼ T W:

ð35Þ

The nonlinear partial differential equations were solved using the finite-difference scheme. The inlet conditions specified were the Reynolds number, pressure and temperature and the geometric parameters specified were tube radius and length. To start calculations initial condensate rate and interfacial shear were assumed. Using these, film thickness and velocity profiles gas and film were obtained. Then the condensate rate and interfacial shear were

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updated until all parameters were converged. The process was repeated for each axial node by satisfying the continuity, momentum and energy equations. The calculation procedure is summarized as follows: (1) Specify inlet and boundary conditions. (2) Initialize the variables and parameters for next axial node. (3) Assume interface shear, interface temperature, interface condensation mass flux and calculate relevant parameters. (4) Calculate film thickness from film mass balance. (5) Solve liquid film momentum equation. (6) Solve liquid film continuity equation. (7) Solve gas region momentum equation. (8) Solve gas region continuity equation. (9) Check the global mass balance. (10) Go to step (3) and repeat until velocity field, interface shear and global mass balance converge. (11) Solve film energy equation. (12) Solve gas energy balance equation. (13) Solve gas species balance equation. (14) Go to step (3) and repeat until temperature and NC gas mass fraction filed, interface heat flux, interface species and mass balance converge. (15) Go to step (2) for the next axial node. 3.2. Analysis results The boundary layer model was used to predict the condensation mass flow rates and HTC of a condenser tube using the same operating conditions as in the through flow experiments. First the average condensate mass flow rates using the model were calculated and were compared to the experimental results. Since the model only predicts data for a single condenser tube, the experimental average condensate mass flow rate is divided by four to obtain the average condensate mass flow rate per tube. The condensation HTCs predicted by the model were also compared with the experimental results. Fig. 8(a) and (b) shows the comparison between the experimental results and model predictions for average condensate mass flow rate and average condensation HTC, respectively. The dashed lines represent a ±25% agreement between the experiment and the model. From the trendlines, with line fits, y = 1.0987x and y = 1.0718x, respectively, we can see that the experimental condensate mass flow rates are about 10% higher than model predictions on average, and the experimental condensation HTCs are about 7.2% higher than model predictions on average. Error propagation analysis was carried out the experimental condensation HTC. The summary of the error propagation is shown in Table 3. From the table, we can see that the relative errors of condensation HTC hc vary from 1.4% to 2.3%. As it is shown in Part 2 of this paper the higher HTC is due to the tube bundle effect on condensation heat removal. The turbulent mixing on the secondary side decreases the DT between pool water and condenser tube outer wall, causing an increase in secondary HTC. This increase in secondary HTC thus results in higher condensate mass flow rates. The model predicts results for a single condenser tube and turbulent mixing in secondary boiling is not taken into account in the current model. Thus the predicted condensate mass flow rates lower than in a tube bundle experiment. Experimentally it is almost impossible to measure the condensate mass flow rate at different axial points, and the axial profile for condensation HTC could not be directly computed. To estimate the local condensation HTC, the boundary layer model was used to predict the axial condensate mass flow rates. Figs. 9 and 10 show the axial profiles of the condensate film thickness and HTC from the entrance for nominal system pressure of 260 kPa and inlet steam mass flow rate of 0.2 g/s. Fig. 9 shows that the condensate

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W. Zhou et al. / International Journal of Heat and Mass Transfer 53 (2010) 1146–1155

0.16

(a)

y = 1.0987x

30

Thickness (mm)

Condensate Mass Flow: Experimental (g/s)

40

20

0.12

0.08

0% NC 5%

10

0.04

0

0

10% 15% 20%

0

10

0

40

30

20

0.6

0.9

1.2

1.5

1.8

Axial Distance from Entrance (m)

Condensate Mass Flow : Model (g/s)

Fig. 9. Condensate film thickness vs. axial distance from entrance for different NC mass fraction.

15000

(b) y = 1.0718x

12000

40000

9000

6000

3000

0 0

3000

6000

9000

12000

15000

Condensation HTC : Model (W/m2K) Fig. 8. Comparison between experimental data and prediction from boundary layer model (a) condensate flow rate per tube and (b) condensation HTC per tube.

Average Total HTC (W/m2-K)

Condensation HTC: Experimental(W/m2K)

0.3

30000

0% NC 5% 10%

20000

15% 20% 10000

0

film thickness increases with the axial distance from the tube entrance, and decreases with the increasing NC gas mass fraction at a fixed inlet steam flow rate and a fixed system pressure. The thickness increases rapidly initially, and then slowly as the axial distance from the entrance. Fig. 10 shows that the local condensation HTC drops rapidly at first, and then decreases slowly as the axial distance from the entrance increases. The condensation HTC decreased with increase in NC gas mass fraction and impact of NC gas mass fraction is significant at the entrance region where condensation is efficient. At the region near to the inlet of the tube, the liquid film is very thin; condensation is efficient due to the small heat transfer resistance. As a result, high heat flux, condensation HTC and condensation mass flow can be reached. With the continuous condensation of steam, the film thickness increases rapidly so that the heat Table 3 Summary of error propagation analysis. Pressure (kPa)

Non-condensable gas mass fraction (%)

Relative errors in condensation HTC hc

165 166 159 165 164 162 169 168 128 132 128 134

0.45 0.94 4.50 1.74 6.03 4.64 3.07 3.55 0.67 3.60 1.01 0.80

0.016 0.015 0.022 0.021 0.014 0.017 0.016 0.019 0.023 0.022 0.018 0.018

0

0.3

0.6

0.9

1.2

1.5

1.8

Axial Distance from Entrance (m) Fig. 10. Average heat transfer coefficient vs. axial distance from entrance for different NC mass fraction.

transfer resistance is larger. With NC gas more NC gas accumulates at the gas–liquid interface along the condenser tube length. The mass transfer resistance increases even more and becomes the dominant resistance for preventing condensation. The liquid film thickness increases along the axial direction. At the entrance the film is very thin and the rate of heat transfer is generally at the entrance section. The NC gas fraction also increases with axial distance form the entrance. The increased film thickness and the NC degrade the condensation along the axial direction from the entrance. Thus the heat flux, condensation HTC and condensation mass flow drop with the increase of heat transfer resistance and mass transfer resistance along the tubes.

4. Conclusions Experiments were performed on simulated PCCS condenser with a four-tube bundle submerged in a boiling water pool. PCCS condenser tubes at a full length and full diameter scale were used to obtain the condensation data with various parameters: system pressure, inlet steam flow rate, and inlet NC gas mass fraction. A boundary layer model was used to study the steam condensation in the presence of NC gas in through flow condition. The results show deterioration in condenser performance when NC gas is present. The condensation HTC decreased with increasing NC gas mass

W. Zhou et al. / International Journal of Heat and Mass Transfer 53 (2010) 1146–1155

fraction. As the inlet steam flow rate and system pressure decreased, the normalized condensate rate increased, although the condensate rate decreases. The condensation rate is higher for the higher pressure condition. The results from boundary layer model showed that the boundary layer thickness and the NC concentration level increased along condenser tube length. Local condensation HTC decreased with condenser tube length and the condensation HTC drops sharply at the entrance indicating the entrance effect. The present experimental and theoretical data provide a new database for vertical tube bundle steam condensation with NC gas submerged in a water pool for the PCCS through flow operation condition. Acknowledgments The financial support of Department of Energy (DOE) through Nuclear Engineering Education and Research (NEER) program with award number DE-FG07-04ID14605 is gratefully acknowledged. References [1] OECD/NEA Group of Experts, SOAR on Containment Thermohydraulics and Hydrogen Distribution, OECD/NEA Report, June 1999. [2] D. Paladino, Investigation on Passive Safety Systems in LWRs, Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden, 2004. [3] GE Nuclear Energy, SBWR Standard Safety Analysis Report, Report No. 25A5113 Rev. A (1992), August 1992. [4] S. Oh, S.T. Revankar, Heat transfer modes in a passive condenser system of ESBWR reactor, in: Proceedings of the Sixth International Conference on Nuclear Thermal Hydraulics, Operations and Safety (NUTHOS-6). Nara, Japan, 2004. [5] H. Uchida, A. Oyama, Y. Togo, Evaluation of post-incident cooling systems of light water reactors, in: Proceedings of the Third International Conference Peaceful Uses of Atomic Energy, vol. 13, Vienna, Austria, International Atomic Energy Agency, 1964. [6] H.K. Al-Diwany, J.W. Rose, Free convection film condensation of steam in presence of non-condensing gases, Int. J. Heat Mass Transfer 16 (1973) 1359– 1369. [7] R.G. Krebs, E.U. Schlunder, Condensation with non-condensing gases inside vertical tubes with turbulent gas and film flow, Chem. Eng. Process. 18 (1984) 341–356. [8] K.M. Vierow, Behavior of steam–air systems condensing in concurrent vertical downflow, M.S. Thesis, Department of Nuclear Engineering, University of California, Berkeley, CA, 1990. [9] M. Siddique, The effects of noncondensable gases on steam condensation under forced convection conditions, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1992. [10] S.Z. Kuhn, Investigation of heat transfer from condensing steam–gas mixtures and turbulent films flowing downward inside a vertical tube, Ph.D. Thesis, Department of Nuclear Engineering, University of California, Berkeley, CA, 1995.

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