ECI International Conference on Boiling Heat Transfer Florianópolis-SC-Brazil, 3-7 May 2009

1 INTRODUCTION

Direct steam injection is a very effective way to rapidly and homogeneously heat fluids. A well-known industrial application is the sterilization process of milk. To improve the taste of the milk it is necessary to decrease the heating time and increase the process temperature during sterilization. A CFD model, based on Large Eddy Simulation and Diffuse Interface Modeling, is being developed to facilitate the determination of the optimal process conditions and the scale up from laboratory experiments to commercial production scales. Next to that, an experimental study is conducted to investigate the turbulent mixing and heating phenomena

induced by the condensation of steam in a cross-flow of water.

The findings of the experimental work are also used for the validation of the CDF model.

When steam is injected into water direct contact

condensation occurs. Depending on process conditions like steam mass flux, bulk water temperature and the injection configuration (direction of injection, nozzle diameter and

shape), different regimes of direct contact condensation can be distinguished. At high steam mass fluxes, the steam forms

either an oscillatory or stable vapor jet that collapses at a certain distance from the injector. Stable steam jets require

chocked injector flow and have been studied extensively. Theoretical expressions for vapor jet lengths injected into a stagnant pool of sub-cooled liquids of the same substance

were presented by Weimer et al. [1] and Chen & Faeth [2]. In addition, several experimental studies (Kerney et. al [3],

Weimer et. al [1], Chun et al. [4]) have been carried out to obtain correlations for the condensing steam jet length and the

average steam-water heat transfer coefficient as a function of liquid bath temperature, steam mass flux and injection nozzle diameter. At lower steam mass fluxes, the condensing steam

forms a vapor pocket that continuously grows and collapses at the steam injection hole. At very low steam fluxes and high water sub-cooling, the steam-water interface moves periodically in and out of the injection hole and this regime is indicated as chugging. Both regimes have been investigated by Nariai & Aya [5], Aya and Nariai [6], Youn et al. [7] and Chan & Lee [8]. Pressure and fluid oscillations, induced by the unstable condensation, were studied both theoretically and experimentally [5, 6]. Various sub-regimes could be recognized from the pressure oscillation patterns. A condensation regime map for steam mass fluxes less than 200

kg/m2s was constructed [5, 6]. Chan en Lee [8] presented a

regime map for steam mass fluxes less than 175 kg/m2s based

on high speed films and pressure measurements.

Previous studies of unstable steam condensation at low mass fluxes of steam merely focused on the occurring pressure oscillations and regime transitions, while the interface

topology of condensing steam jet and the intermittent character not really were investigated. In the present paper, an experimental study of unstable direct steam condensation is

carried out to determine average heat transfer coefficients, growth and waiting times and sizes and shapes of the steam

pocket . In addition, a model is developed to predict growth, total time of growth and maximum steam pocket sized. The

topology of steam condensation at low mass fluxes of steam is reminiscent of that of boiling at high heat fluxes. For this reason the model has been based on those for the detachment

of boiling bubbles. The model predictions are compared with the experimental results, not only for validation purposes but

also to facilitate interpretation of measured trends. A new feature of the experiments, never studied before to our

knowledge, is the effect of a liquid cross-flow on heat transfer and interface topology of unstable direct condensation.

EXPERIMENTAL AND ANALYTICAL STUDY OF INTERMITTENCY IN DIRECT

CONTACT CONDENSATION OF STEAM IN A CROSS-FLOW OF WATER

N. Clerx*, C.W.M. van der Geld°

* Eindhoven University of Technology, Faculty of Mechanical Engineering, P.O. Box 513, NL–5600 MB Eindhoven –The Netherlands; Tel.: +31 40 247 5906, fax: +31 40 247 5399; N.Clerx@tue.nl

° Eindhoven University of Technology, Faculty of Mechanical Engineering, , P.O. Box 513, NL–5600 MB Eindhoven –The Netherlands; Tel.: +31 40 247 2923, fax: +31 40 247 5399;

C.W.M.v.d.Geld@tue.nl

ABSTRACT The topology of a condensing steam jet, at low steam mass fluxes, injected in a cross-flow of water has been investigated

experimentally for various conditions (system pressure around 3 bar). The intermittent character of the steam pocket growth

and collapse clearly appeared from the high speed recordings. The typical pocket size grows almost linear until it reaches a

maximum penetration depth. Pocket disappearance occurs either via partial detachment and collapse or instantaneous break-up

of the entire pocket. The main effect of the liquid cross-flow is an increased heat transfer coefficient for otherwise identical

process conditions. This results in a notable reduction of both growth time and maximum penetration depth. A model has been

developed and presented to facilitate interpretation of measurement results and to increase our predictive capacity of unstable

direct steam injection. Comparison of model predictions and experimental findings shows that the steam pocket growth time

and its maximum penetration depth are generally well-predicted. The chugging regime occurring at the lowest water

temperature is atypical and has nonzero waiting times. The growth of a steam pocket in unstable condensation regimes is found

to be controlled by fluid inertia and momentum of the injected steam, while drag is negligible.

2 EXPERIMENTAL

Fig. 1 schematically shows the experimental set-up with the

steam supply system on the left and the test section in the

center. The steam generator delivers saturated steam at a

maximum pressure of 10 bar (absolute) and a maximum flow

rate of 0.33 kg/s. The reduction valve enables control of the

pressure downstream the main supply line. A large part of the

steam is bypassed to a condenser, to avoid condensation since

only a small amount of steam (at max. 4.5 kg/h) is needed in

the test section during an experimental run. The bypass heats up the steam supply lines before measuring. Two meters

upstream of the steam injection point, the diameter of the

steam supply line gradually decreases from DN40 to DN 4.

The steam flow after this convergence is measured and

controlled by a Coriolis mass flow meter (accuracy: 1% of

measured value) and a PID actuated pneumatic valve. Further

downstream, 15 cm upstream of the injection point, a pressure

transducer (accuracy: 0.1 % FS) and Pt-100 element monitor

the injection conditions of the steam. This DN4 section of the

steam line as well as the mass flow controller is covered with

an electrical heating wire and insulation to avoid

condensation.

What is called the measurement loop (the right hand side of Fig. 1) is a closed circuit, containing approximately 50 liters of demineralized water. The flow is upward in the test section and is provided by a frequency controlled centrifugal pump. The volumetric flow rate of the water is measured with an ultrasonic flow meter (accuracy: 0.25 % FS). The closed loop can be pressurized up to 8 bar (absolute) via an expansion vessel whose upper half is connected to a pressurized air supply. The expansion vessel also minimizes pressure fluctuations. Four Pt-100 elements are implemented to monitor the water temperature at various locations in the loop. The system pressure and the water temperature are kept constant during the measurements despite the injection of the steam. A PID actuated bleed valve that is connected to the pressure transducer (accuracy: 0.1 % FS), located at the inlet of the measurement section, is used to control pressure. If the pressure in the loop exceeds set point, the bleed valve opens and it closes again when the pressure again reaches the set

value. The water temperature is kept constant during steam

injection, by using a heat exchanger and a 17 kW electrical heater downstream of the test section whose output power is controlled by a PID controller. The electrical heater then heats

the water to the desired value with a maximum of 100 °C.

Figure 1: Experimental set-up

The actual measurement section, indicated in Fig. 1 with a grey color, has a square inner cross-section of 3x3 cm

2 and is

optically accessible at the location where the steam is injected. Before entering the optically accessible section, the water flows through an identical channel with a length of 1.2 m (40Dh) to obtain fully developed turbulent flow at the steam injection point. The steam is injected through a flush mounted wall injector with a circular hole with a diameter of 2 mm, which is located 10 cm upstream of the entrance of the optically accessible section. The whole set-up is thermally insulated with a 20 mm thick foam layer.

The condensing steam pocket is observed with a 10 bit high speed camera (PCO 1200 hs) at frame rates between 3333 and 3400 Hz and with a resolution of 700x536 pixels. A 250 Watt halogen lamp illuminates the pocket from the front in such away that reflections at the gas-liquid interface are minimized.

The signals of all measuring equipment are monitored and logged by means of a data acquisition system consisting of a

A/D converter and a PC. The data logging and visualization

are synchronized to correlate the process conditions and the high speed recordings of the steam pocket.

Experimental run number

1 2 3 4 5 6 7 15 16 17

Steam pressure [bar a]

3.0 3.1 3.1 3.2 3.0 2.9 2.9 2.8 2.8 2.8

Steam temperature

[°°°°C] 138.3 139 139.6 140.5 138.3 137.4 137.4 132.2 133.2 133.8

Steam mass flow [kg/m

2s]

70.74 44.21 53.05 35.37 35.37 44.21 53.05 35.37 44.21 53.05

Closed loop pressure [bar a]

2.99 3.07 3.13 3.23 3.02 2.94 2.94 2.78 2.79 2.80

Water temperature

[°°°°C] 64.2 64.5 64.4 65 64.4 64.1 64.4 26 25.9 25.9

Water flow rate [10-4 m

3/s]

1.75 1.75 1.75 1.75 0 0 0 1.75 1.75 1.75

Table 1: Process conditions of the experimental runs

The steam mass flux, the liquid flow rate and the inlet

temperature of the water have been varied. The process

conditions analyzed in this paper are listed in Tab. 1. The

steam is injected at slightly superheated conditions (Tsat =

133.55 ºC at 3 bar absolute).

3 EXPERIMENTAL RESULTS

The following results will be presented for a steam mass

flux of 35.37 kg/m2s, water flow rate of 1.75⋅10

-4 m

3/s and

water temperatures of 26ºC and 65ºC:

• Image sequences of typical condensation cycles.

• Histories of the steam pocket penetration depth.

The following results will be presented for steam mass fluxes

in the range of 35.37 kg/m2s to 70.74 kg/m

2s, water flow rates

of 0 m3/s and 1.75⋅10

-4 m

3/s and water temperatures of 26ºC

and 65ºC:

• Time-averaged maximum penetration depths of the steam

pocket.

• Time-averaged growth time of the steam pocket.

• Total heat transfer coefficients coefficient for heat

transferred from the steam to the water.

• Characterization of the steam pocket shapes at the instant of condensation.

• Initial velocity of the center of the steam pocket away from the wall.

3.1 Intermittent steam pocket growth and condensation

For each set of process conditions, 500 images have been used for the analysis of the condensing steam jet. This corresponds to a measurement time of 147 ms for experimental runs 1 to 4 and 150 ms in the case of run 5 to 7 and run 15 to 17, see Tab. 1. The image recording was started 2 minutes after changing the process conditions, to ensure that the steam injection and the conditions inside the measurement loop were at their steady state.

Figure 2 shows a sequence of 12 images of a condensing steam jet typically observed at low steam mass flux and high water temperature (run 4), see Tab. 1. The time between consecutive images is 0.294 ms and the width of one image

corresponds to 10.1 mm. The transformation of pixel sizes to

physical coordinates is done by linear scaling. The first image shown in Fig. 2 represents a steam pocket at its initial size that is growing in the subsequent images. The steam pocket

reaches its maximum size in the second last image, and this size is defined as the maximum penetration depth. Partial detachment of the steam pocket is displayed in the last image.

Note the formation of a neck in the last image of the second

row of Fig. 2. Figure 3 shows a sequence of 6 images of a typical

condensation cycle observed at a low mass flux of steam and

low water temperature (run 15), see Tab. 1. The time between consecutive images is now 0.3 ms and the width of an image corresponds to 10.1 mm. The growing steam jet is at its

maximum penetration depth in the second last image followed

by a sudden burst of the entire total pocket in the last image. Figure 4 shows two penetration depth histories of the steam

pocket during subsequent condensation cycles at a steam mass

flux of 35.37 kg/m2s and a water flow rate of 1.75⋅10

-4 m

3/s.

The water temperature is 65 ºC for the upper history and 26ºC

for the lower history. The penetration depth is defined as the

Figure 2: Image sequence of a typical condensation cycle at

a steam mass flux of 35.37 kg/m2s, water flow rate of 1.75⋅10

-4

m3/s and water temperature of 65ºC (run 4 ). The time interval

between consecutive images is 0.294 ms. horizontal position of the front of the steam pocket with respect to the position of the injection hole. The penetration depth has been determined by tracking the horizontal pixel positions of the front of the pocket for 41 subsequent images.

Figure 3: Image sequence of a typical condensation cycle at a

steam mass flux of 35.37 kg/m2s, water flow rate of 1.75⋅10

-4

m3/s and water temperature of 26ºC (run 15). The time

interval between consecutive images is 0.3 ms

10.1 mm

10.1 mm

Both histories clearly show the periodical growth of the steam

pocket from their initial size to their maximum penetration

depth. The arrows in the histories point at the moment of

condensation. It should be noted that in histories at TL = 26ºC

besides the condensation cycles also periods are observed

during which no steam pocket was present in the images. This

is indicated as waiting time in Fig. 4.

0 2 4 6 8 10 120

2

4

6

8

time [ms]

TL = 65

oC

0 2 4 6 8 10 120

2

4

6

8

time [ms]

(h

+ R

) [

mm

]

TL = 26

oC

0 2 4 6 8 10 120

2

4

6

8

time [ms]

TL = 65

oC

0 2 4 6 8 10 120

2

4

6

8

time [ms]

TL = 65

oC

0 2 4 6 8 10 120

2

4

6

8

time [ms]

(h

+ R

) [

mm

]

TL = 65

oCcycle 1 cycle 2 cycle 3 cycle 4

cycle 1 cycle 2 cycle 3 cycle 4

waiting

timecycle 5

Figure 4: Penetration depth histories of the of the steam pocket during consecutive condensation cycles at a steam

mass flux of 35.37 kg/m2s and water flow rate of 1.75⋅10

-4

m3/s and water temperatures of 26ºC and 65ºC. The arrows

indicate the instant of condensation.

3.2 Time-averaged properties of direct contact condensation

The results presented in the following have been obtained by identifying the condensation cycles and waiting times for each experimental run, with 500 images per run. The measured maximum penetration depths, growth times and heat transfer coefficients have subsequently been averaged over the total number of condensation cycles of each run. All errors in

this paper are defined for a 68% confidence interval. Figure 5 shows the maximum penetration depths of the

steam pocket for steam mass fluxes between 35.37 kg/m2s and

70.74 kg/m2s, water temperatures of 65°C and 26°C and water

flow rates of 1.75⋅10-4

m3/s and 0 m

3/s. The error bars on the

steam mass flux represent the standard deviations of the

measured fluxes. Note that the accuracy of the coriolis meter given by the manufacturer is 1% of the measured value, which is much smaller than the measured standard deviation of

around 6%. The error bars on the maximum penetration depth

represent the standard error in the mean value of the maximum penetration depth for each experimental run. This standard error is for all cases around 3 % of the mean value. It appears

that the maximum penetration depth of the steam pocket is

highest in the case for a water temperature of 65°C and a zero

water flow rate and lowest at a water temperature of 26°C and

a water flow rate of 1.75⋅10-4

kg/s. The maximum penetration

depth is first increasing and subsequently decreasing with increasing steam flux, at constant water temperature and

constant flow rate. Figure 6 presents the duration of the condensation cycles,

indicated as growth time, for steam mass fluxes between 35.37

kg/m2s and 70.74 kg/m

2s, water temperatures of 65°C and

26°C and water flow rates of 1.75⋅10-4

m3/s and 0 m

3/s. The

growth time of the steam pocket in a single condensation cycle

is calculated from multiplication of the amount of images of

which the cycle consists by the inverse of the frame rate of the

camera. The mean growth time of an experimental run is then

obtained by averaging over all condensation cycles occurring

in that run. The error bars on the steam mass fluxes have been

defined in the above. The vertical error bars represent the

standard error in the mean value of the growth time for each

experimental run. This standard error is 7% for the mean

growth times at a steam mass flux of 35.37 kg/m2s and around

4% for the other runs.

30 35 40 45 50 55 60 65 70 753

4

5

6

7

8

9

10

G [kg/m2s]

(R

+ h

) f [m

m]

TL = 65

oC + flow

TL = 26

oC + flow

TL = 65

oC no flow

Figure 5: Maximum penetration depths of the steam pocket at steam mass fluxes of 35.37 kg/m

2s, 44.21 kg/m

2s, 50.53

kg/m2s and 70.74 kg/m

2s, water temperatures of 65°C and

26°C and water flow rates of 1.75⋅10-4

m3/s and 0 m

3/s, which

are indicated in the legend as ’ + flow’ and ‘no flow’, respectively. The dashed lines are plotted to guide the eye.

Figure 6 clearly shows that the growth time is decreasing with increasing steam mass fluxes for all water temperatures and flow rates. It also appears that the growth time is highest

for the ‘no flow’ case at TL = 65°C and is shortest at TL =

26°C.

30 35 40 45 50 55 60 65 70 750

0.5

1

1.5

2

2.5

3

3.5

4

G [kg/m2s]

tf

[ms]

TL = 65

oC + flow

TL = 26

oC + flow

TL = 65

oC no flow

Figure 6: Growth times at steam mass fluxes of 35.37 kg/m2s,

44.21 kg/m2s, 50.53 kg/m

2s and 70.74 kg/m

2s, water

temperatures of 65°C and 26°C and water flow rates of

1.75⋅10-4

m3/s and 0 m

3/s, which are indicated in the legend as

’ + flow’ and ‘no flow’, respectively. The dashed lines are

plotted to guide the eye.

The heat flux from the incoming steam to the liquid is

defined by:

iLva AHHRGq /)(2 −⋅⋅⋅= π (1)

Hv is the incoming enthalpy of the steam and is well-known

during the experiments since both the inlet steam pressure and the temperature of the incoming steam, Tv, are measured. The

same holds for that of the liquid, HL. Let TL denote the bulk

temperature of the approaching liquid. By definition Tv and TL

are time-averaged values. It is noted that in our case the low

sampling rates and inertia of the sensors used would not allow

an assessment of quasi-instantaneous values of pressures and

temperatures. This implies that Hv and HL are also time-

averaged values. Ai denotes the mean interfacial contact area

and is determined by averaging the mean steam pocket surface

areas of the single condensation cycles that are observed in the

500 images for each experimental run. Since the surface area

of a steam pocket appears to grow linear in time, the mean

surface area of a steam pocket during a single condensation cycle can be approximated by:

)(5.0 TAA pocketpocket ⋅= (2)

Where Apocket (T) denotes the surface area of the steam pocket when it reaches its maximum penetration depth and is estimated from the three-dimensional surface of a contour that fits the surface area of the steam pocket. The mean surface areas calculated from Eq. 2 had to be corrected for the experimental runs at low water temperature (15, 16 and 17), because of the occurring waiting times. The time-averaged total heat transfer coefficient has been determined from:

)/( Lvtot TTqh −= (3)

The heat transfer coefficients calculated from Eq. 3 are

compared with an empirical correlation for htot found by Nariai & Aya [5] during what they named a condensation

oscillation of a spherical pocket:

( ) ( )LvFS TTGh −⋅⋅=9.0

4.66 (4)

The results for htot and hFS are shown in Figure 7 for steam mass fluxes between 35.37 kg/m

2s and 70.74 kg/m

2s, water

temperatures of 65°C and 26°C and water flow rates of

1.75⋅10-4

m3/s and 0 m

3/s. The error bar on htot defines the

standard error in the mean value of htot and accounts for the uncertainties in the measured steam mass flux, temperatures of

the steam and water and the standard error in Ai. The standard error in htot is in de range of 5% to 8.5%. The error bar on hFS

accounts for the measured fluctuations of the steam mass flux and the errors of steam and water temperatures and is in de

range of 2.5% to 5%. Both heat transfer coefficients shown in Fig. 7 are increasing with increasing steam mass flux. The values of hFS are higher than those of htot for a given water temperature.

3.3 Geometrical criterion for pocket shape at condensation

To characterize the shape of the steam pocket just before

collapsing, when the pocket reaches its maximum penetration

depth, the so called detachment ratio has been defined as

(h/R)f. Here h denotes the distance of the center of the steam

pocket to the injection wall and R is the radius of the steam

pocket. To determine R from the high speed recordings, a

contour is fitted on the surface area of the steam pocket. When

projecting this contour on the injection wall, R is taken equal

to radius of this projected contour.

30 35 40 45 50 55 60 65 70 750

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

5

G [kg/m2s]

h [W

/m2K

]

htot

: TL = 65

oC + flow

hFS

: TL = 65

oC + flow

htot

: TL = 26

oC + flow

hFS

: TL = 26

oC + flow

htot

: TL = 64

oC no flow

hFS

: TL = 64

oC no flow

Figure 7: Time-averaged heat transfer coefficients at steam mass fluxes of 35.37 kg/m

2s, 44.21 kg/m

2s, 50.53 kg/m

2s and

70.74 kg/m2s, water temperatures of 65°C and 26°C and water

flow rates of 1.75⋅10-4

m3/s and 0 m

3/s, which are indicated in

the legend as ’ + flow’ and ‘no flow’, respectively. The dashed lines are plotted to guide the eye.

Mean detachment ratios for a given set conditions are obtained by averaging the ratios of all condensation cycles occurring in each experimental run and are presented in Figure 8.

30 35 40 45 50 55 60 65 70 750.5

1

1.5

2

2.5

G [kg/m2s]

(h

/R) f

[-]

TL = 65

oC + flow

TL = 26

oC + flow

TL = 65

oC no flow

Figure 8: Detachment ratios at steam mass fluxes of 35.37

kg/m2s, 44.21 kg/m

2s, 50.53 kg/m

2s and 70.74 kg/m

2s, water

temperatures of 65°C and 26°C and water flow rates of

1.75⋅10-4

m3/s and 0 m

3/s, which are indicated in the legend as

’ + flow’ and ‘no flow’, respectively. The dashed lines are plotted to guide the eye. The contours on the right represent

typical steam pocket geometries at collapse for water

temperatures of 65°C (upper) and 26°C (lower).

The error bars on the detachment ratios represent the standard

error in the mean value of (h/R)f. The largest standard errors

occur in the experimental runs performed at a water

temperature of 26 °C and are 10% at maximum. The standard

errors for the other runs are around 4% of the mean

detachment ratio. The detachment ratios are highest for the

case of a water temperature of 65°C and the ‘no flow’ condition, while the ratios for the ‘flow’ condition at the same

water temperature are slightly lower. Note that the detachment

ratios at a water temperature of 26°C are considerably lower.

3.4 Initial wall normal pocket velocity and pocket radius

The initial wall normal velocity U0 is determined from the

high speed recordings according to:

( ) ttLtLU ∆−= /)()( 010 (5)

Where L(t0) is the penetration depth of the steam pocket in the

first image of a condensation cycle, i.e. the first image of the sequence shown in Fig. 4. L(t1) is the penetration depth in the subsequent image, i.e. the second image of the sequence of Fig. 4 and ∆t corresponds to the inverse of the frame rate. Like the other results presented in this section, is U0 determined from averaging over the single condensation cycles of each experimental run. The error bars on U0, depicted in Figure 9, are the standard error in the mean value of U0. The standard

error is around 9% of the mean U0 for the runs at TL = 26°C and 6% for the other cases. It appears from Fig. 9 that the initial wall normal velocity is increasing with increasing steam mass fluxes and that it is highest for the experimental runs

performed at TL = 26°C.

30 35 40 45 50 55 60 65 70 751

1.5

2

2.5

3

3.5

4

4.5

5

G [kg/m2s]

U0 [m

/s]

TL = 65

oC + flow

TL = 26

oC + flow

TL = 65

oC no flow

Figure 9: Initial wall normal velocity of the steam pocket at steam mass fluxes of 35.37 kg/m

2s, 44.21 kg/m

2s, 50.53

kg/m2s and 70.74 kg/m

2s, water temperatures of 65°C and

26°C and water flow rates of 1.75⋅10-4

m3/s and 0 m

3/s, which

are indicated in the legend as ’ + flow’ and ‘no flow’, respectively. The dashed lines are plotted to guide the eye.

The initial radius R0 of the steam pocket has been

determined from the first image of a condensation cycle, i.e.

the first image of the sequence shown in Fig.’s 4 and 5. The

average value of R0 per experimental run and the

corresponding error bars, as shown in Figure 10, are

calculated in the same way as described for the other results.

The standard errors in the mean vale of R0 are 1% in the case

of TL = 26°C with ‘flow’ and around 3.5% in the case of TL =

65°C at the ‘no flow’ condition. Fig. 10 shows that the steam

mass flow has no distinct effect on R0, which is most notable

for the runs with TL = 26°C with ‘flow’. At a lower water

temperature, however, R0 is distinctly smaller.

30 35 40 45 50 55 60 65 70 750.5

1

1.5

2

2.5

G [kg/m2s]

R0 [m

m]

TL = 65

oC + flow

TL = 26

oC + flow

TL = 65

oC no flow

Figure 10: Initial radius of the steam pocket at steam mass

fluxes of 35.37 kg/m2s, 44.21 kg/m

2s, 50.53 kg/m

2s and 70.74

kg/m2s, water temperatures of 65°C and 26°C and water flow

rates of 1.75⋅10-4

m3/s and 0 m

3/s, which are indicated in the

legend as ’ + flow’ and ‘no flow’, respectively. The dashed lines are plotted to guide the eye.

4 MODEL FOR INTERMITTENT STEAM INJECTION

The main feature of unstable direct condensation flow regimes is the intermittency of vapor pocket penetration into the liquid. There is a resemblance with some conditions of isothermal gas injection and there is a resemblance with boiling vapor bubble

detachment. It is therefore tempting to try to model

condensation oscillation and even chugging during direct condensation steam injection in a similar way as bubble detachment was modeled in the past. The aim of the model is

to predict growth, total time of growth and maximum penetration depth of a vapor pocket created by unstable direct steam condensation. The prediction method follows a

mechanistic approach, using expressions for forces derived for

smooth bubble interfaces even though the interface of the condensing steam pocket is more often than not wrinkled. The method employs two key elements: a force balance that holds

at all times in the direction perpendicular to the injection wall and a geometric steam pocket shape criterion that only holds at “detachment”, i.e. the moment of collapse of the pocket.

This criterion will be based on measurements presented in the

above (section 3.3). The initial conditions of bubble growth will be based on the detailed measurements presented in section 3.4. Subsequent displacement and growth of the steam

pocket will be predicted with the aid of the force balance and mass conservation, in a way detailed below.

The shape of the steam pocket is schematized to be that of

a sphere with radius R with its center at distance h from the wall (Fig. 10). If h exceeds R, a cylinder with radius Ra is

assumed to connect the sphere with the inlet. Although the

assumed bubble shape for some flow regimes is quite accurate

a description, for other flow regimes it is a crude

approximation. However, Nariai & Aya [5] analyzed

differences between the predicted bubble growth times, tf, of

mechanistic models based on quite different bubble shapes

and found tf to be fairly independent of the shape. We shall

show that also the model presented below is able to predict

not only tf, but also other prediction outcomes, fairly

accurately for various intermittent condensation flow regimes.

Figure 10: Schematic representation of the steam pocket

The model will be validated by comparing the following main outcomes of the model with experiments:

• the growth time of the bubble, tf

• the maximum penetration depth, (R+h)f

• time history of (R+h) These parameters have all been measured quite accurately, see section 3.1 and 3.2. Typical accuracies are 6% for the maximum penetration depth and 4% to 7% for the growth time. Also the geometrical criterion for “detachment”, the so-called detachment ratio (h/R)f, has been measured accurately, see section 3.3. Two main input parameters of the model,

• the initial radius, R0,

• the initial velocity of the center of the bubble normal to the wall, U0,

have also been measured. Typical accuracies are between 6% and 9% for U0 and between 1% and 3.5% for R0. Another input parameter, the initial growth rate of radius R, Ŕ0, follows from mass conservation and from R0, and is controlled by the injection mass flux, G, and the condensation rate which involves the heat transfer coefficient htot. The way to predict

condensation heat transfer has been assessed in section 3.2.

With the assumed pocket shape, conservation of mass yields

d ρv ∀ / dt = G π Ra2

– 4 π R2 htot (Tv – TL) / hcond (6)

with hcond the enthalpy of condensation and∀ the volume of

the pocket, including the neck: ∀ = 4 π R3/3 + πRa

2(h – R). If

h > R,

d ρv ∀ / dt = 4 π R2 Ŕ ρv + π Ra

2 U ρv + dρv/dp dp/dt ∀ (7)

and d ρv ∀ / dt = 4 π R2 Ŕ ρv + dρv/dp dp/dt ∀ otherwise. The

dρv/dp –term has for the process conditions of our measurements been found to be negligible, a posteriori. The occurrence of U in the above equation couples it to the

equation for dU/dt that will given below. Elimination of d ρv

∀ / dt from Eq.’s (6) and (7) yields Ŕ = Ŕ(G, h). The governing equation for the velocity U of a spherical

bubble detached from the wall has been derived by one of the authors in a previous study (van der Geld [9]). Two added mass coefficients, Cam,1 and Cam,2, have been shown to be

relevant, with values that depend on distance h to the wall. In

first order approximation these coefficients are given by:

Cam,1 = 1.07 {1.5 /[1 – (0.5 R/h)3] – 1}

Cam,2 = – 3.9 (0.5 R/h)2

if h > 1.02 R, and Cam,1 = 0.8 and Cam,2 = – 1.05 otherwise. At

the transition point, h = 1.02 R, the above calculation yields

values of the added mass coefficients that are not continuous,

but this is inessential with the present level of approximation

(the neck is neglected for the added mass coefficients) and can easily be improved. In subsequent studies, also the added mass

coefficients of a truncated sphere have been quantified; see for

example van der Geld [10]. For the present model, merely the

above mentioned values have been used.

In for example van der Geld [10] and in Duhar et al. [11], two

forces on the bubble in the direction normal to the wall are

found to be significant, usually, but counteracting. These are

the pressure correction force and the surface tension force. If a

bubble is pinned on a wall with the shape of a truncated

sphere in the vicinity of the contact line, i.e. with

homogeneous contact angle, these forces are found to be

precisely compensating. This is the case with the vapor

pockets created by steam injection if the shape near the injection point is not affected too a large extend by the approaching liquid flow. These two forces are therefore assumed to be balancing each other. The drag force has in a previous study, van der Geld [9], been shown to comprise two terms. For a sphere touching a plane

wall, the expression – 32 π µL R U + 20 π µL R Ŕ for the drag force can be shown to be in line with these published findings. Note that bubble growth is that fast that vorticity has little time to develop and gather in the downstream wake of the bubble (see van der Geld [10]). This makes the above expression for the drag to be applicable to the present circumstances. If anything, it is an overestimation of the drag, and since the contribution of this drag expression to the total force on the bubble will be found to be negligible, drag must be negligible altogether in the present circumstances.

With the mass density of the liquid, ρL, a constant, the following equation is now derived:

(Cam,1 ρL ∀) dU/dt = (– Cam,1 U – Cam,2 Ŕ/ 2) ρL d∀ /dt +

– Cam,2 ρL ∀ d Ŕ/dt /2 – 32 π µL R U

+ 20 π µL R Ŕ + – (G/π Ra2)

2 / (ρv π Ra

2)

– π R2 {h (Tv – TL) / hcond

}

2 / ρv (8)

The last term on the RHS of Eq. (8) accounts for the momentum in h-direction, i.e. normal to the wall, which

disappears due to condensation. Part of the momentum loss at the half of the sphere facing the wall is compensated by momentum gain at the other half of the sphere, furthest away

from the wall. The area πR2 used in Eq. (8) is therefore most

likely an overestimation of the actual effective area. Since the

contribution of this term will be found to be negligible, the error in the estimate of the area is negligible altogether. A second order Adams-Bashford method has been used for

integration in time, the only numerical step involved.

R h

Ra

5 ANALYIS

5.1 Intermittent steam pocket growth and condensation

The high speed recordings show that the growth and

subsequent condensation of the steam pocket happens in fairly

constant cycles. The pocket starts to grow from its initial size

until the front of its surface area has reached the maximum

penetration depth. Thereafter the steam pocket collapses due

to condensation. From the recordings, two types of pocket

collapse can be distinguished: 1. Partial detachment of the front part of the steam pocket

(far from the steam injection point) from its rear part

close to the injection point (last image of Fig. 2).

2. Instantaneous break-up and disappearance of the entire

steam pocket (last image of Fig. 3).

The first type of collapse is mainly observed at the lowest

steam mass fluxes (35.37 kg/m2s and 44.21 kg/m

2s,) and at TL

= 65°C for both the ‘flow’ and the ‘no flow’ condition. The

detachment typically occurs between 2Ra and 3Ra from the

injection hole. After detachment, the front part of the steam

pocket disappears due to condensation. The rear part stays

attached to the steam injection hole and subsequently starts to

grow again. At higher mass fluxes also the second type of collapse is observed, although less frequent than the first one. The instantaneous break up of the total steam pocket becomes the dominant collapse mechanism at a water temperature of 26°C when sub-cooling of the water is larger and condensation rates are higher.

Figure 11: Schematic representation of stagnation flow inside

the steam pocket

From Fig. 2 and 3 it can be seen that the pocket collapse is

preceded by a wrinkling of the surface area starting at the neck of the pocket. This might be caused by inhomogeneous heat transfer rates at the vapor-liquid interface. As a matter of fact,

the part of the interface that faces the steam inlet and is

farthest away from it, say part A (Fig. 11), is usually observed to be relatively smooth, with the neck and parts of the interface in the vicinity of the steam inlet, part B say, more

wrinkled and wavy. This is understood to be a consequence of inhomogeneous heat transfer in the following way. The Reynolds number of the incoming steam, based on U0 and

2Ra, is typically in the range 200-1000. The velocity in the center of the injection mouth is highest and vapor fluid

elements originating from this center penetrate the pocket in such away that a kind of stagnation flow develops at part A. Convective heat transfer coefficients at stagnation points are

known to exceed those at other places. This part A is therefore heated well by the hot vapor, which prevents condensation.

The gas flow at part B is partly flow returning from part A

which is therefore colder, whence condensation sets in earlier

at part B.

The intermittent character of the steam pocket growth

appears obviously from the penetration depth histories, shown

in Fig. 4. The steam pocket seems to grow linear in time in

case of the higher water temperature (top of Fig. 4). After

reaching its maximum penetration depth the pocket collapses

due to detachment of the front part of the pocket. The

penetration depth of the rear part, which remains attached to

the injection hole during the collapse, is the initial penetration

depth of the new condensation cycle. These penetration depths

are, for the condensation cycles shown in the upper history of Fig. 4, in the range of 2 mm to 4 mm and correspond to the

previously mentioned typical detachment distance range of

2Ra to 3Ra. Pocket growth is less linear for the low water

temperature, as shown in the lower history of Fig. 4. The

steam pocket grows until its maximum penetration depth

where after total break-up occurs. Total break-up implicates in

most cases zero initial size of the steam pocket at the

beginning of the new condensation cycle. This is in

correspondence with the penetration depth path shown in the

lower history of Fig. 4. Note the occurrence of the ‘waiting

time’ between condensation cycle 4 and 5. During such a

period no steam pocket was visible in the high-speed

recordings, probably due to water entering the steam injection hole. This phenomenon is referred to as chugging. Waiting times appear more frequently at higher steam mass fluxes (runs 16 and 17).

The type of condensation regime in direct contact condensation is mainly dependent on the steam mass flux and the temperature of the bulk liquid. Oscillatory condensation phenomena are known to occur at lower steam mass fluxes (< 200 kg/m

2s) and are classified in regime maps presented by

i.e. Chan & Lee [8] and Nariai & Aya [5]. According to Nariai & Aya [5] all of the experimental runs presented in this paper, except for run 15, are situated in the condensation oscillation region. The condensation in this region is characterized by the growth and shrink of steam bubbles at the steam injection point. Run 15 is situated in the ‘small chugging region’ which is characterized by the movement of a steam-water interface around the injection hole and periodic water entrance in the hole. The classification of condensation regimes according to

Nariai & Aya [5] is corresponding to the observations made in this paper. In here chugging in combination with intermittent growth and condensation is observed for all mass fluxes at the

low water temperature. According to the regime map of Chan

and Lee [8], runs 2, 3 and 4 would be located in the external chugging regime with encapsulated bubble. This regime is similar to the one that Nariai & Aya [5] refer to as small

chugging. Run 1 would be located in the oscillatory bubble regime which corresponds to the regime indicated by Nariai & Aya [5] as condensation oscillation. It should be noted,

however, that transitions between different condensation regimes are greatly dependent on f.e. shape and orientation of

the steam injection nozzle and the presence of a cross-flow of liquid. The regime maps presented by Nariai & Aya [5] and

Chan & Lee [8] were designed for different geometries than our set-up, which explains possible differences found.

5.2 Effects of steam mass flux, cross-flow and sub-cooling

The trends observed for U0 are explained as follow. Growth of the steam pocket implies that the LHS of the equation for

mass conservation (Eq. 7) is positive and that the source of mass G is larger than mass loss due to condensation. If the

A

B

steam mass flux, G, is increasing the loss-term, which is

proportional to G via htot (Eq. 4), is also increasing, but the

difference d (ρv ∀ )/ dt is increasing still. A higher input mass

flux of steam, G, for a given steam pocket radius R0 therefore

results in a higher value of Ŕ0. Since, see Fig. 10:

222

RRh a =+ (9)

the initial wall-normal velocity of the pocket, U0, follows

from:

0000 )/( RhRU &= (10)

With increasing G, both Ŕ0 and U0 increase. This explains the

trends of U0 observed in Fig. 9.

The experimentally determined heat transfer coefficients

htot is compared with an empirical correlation (hFS), presented

by Nariai & Aya [5] for a spherical pocket during

condensation oscillation, in Fig. 7. The only other study on

interfacial heat transfer during condensation oscillation we

found was conducted by Liang [12] for heat transfer

dominated condensation oscillations, which study is therefore

not applicable to the present study. The results shown in Fig. 7 demonstrate that the heat transfer coefficients resulting from the empirical relation of Nariai & Aya [5] are substantially higher than our values of htot. This is probably due to differences between our injection geometry and flow conditions and those for which hFS was established. Such differences are mainly: vertical injection in a stagnant pool (Nariai & Aya [5]) as opposed to horizontal injection and nonzero liquid velocities in our case. Fig. 7 shows, for TL = 65ºC, that an increase in liquid velocity results in an increase in htot, hence enhances heat transfer rates, due to additional forced convective heat transfer. Note that this effect is absent for hFS for obvious reasons. Higher water sub-cooling has the same effect on the heat transfer coefficient as the imposed cross-flow. Heat flux increases with decreasing TL, see Figs. 6 and 7. The increase of htot is more pronounced for the runs at

TL = 26°C with ‘flow’ than that of the runs at TL = 65°C with ‘flow’, due to the cumulative effects of cross-flow and sub-

cooling. For the model of section 4 an instantaneous heat

transfer coefficient, h, is needed, whereas only time-averaged values, htot, can be provided. The first source of differences between htot and h is of course the possible physical time- and

shape dependency of coefficient h. Such dependencies are

familiar for convective heat transfer. For condensation, the surface renewal model of Kim et al. [13] yields an h that is proportional to √s, with s the so-called surface renewal rate.

Since s for direct condensation mainly depends on bursts at the interface, according to these authors, s is proportional to the average interfacial stress which depends on the surface

area. This causes h to differ from htot. Fluctuations in the

steam mass flow rate are of the order of 8 % and are a second source of discrepancies between h(t) and htot.

Figure 6 shows the trends created by cross-flow and sub-

cooling of the water on the growth time of the steam pocket. These trends are easily understood from the influence these

parameters have on the heat transfer coefficient htot. Higher sub-cooling or higher liquid velocity results in a higher htot,

which yields a faster growth Ŕ and a shorter growth time tf (Fig. 6).

The temperature of the water has also a strong effect on the

measured detachment ratios, displayed in Fig. 8. This ratio is

significantly lower for the runs performed at TL = 26°C than

those of the runs of TL = 65°C. Since the detachment ratio is

used as a geometrical parameter that includes the physics

related to collapse of the steam bubble just before

condensation, it would be desirable to provide a correlation

based on the measured values shown in Fig. 8. At present,

because of the small amount of measurement points, this is not

yet possible. Within measurement accuracies, (h/R)f – values

are roughly constant for each process condition: 1.9 for TL =

65°C and no flow, 1.7 for TL = 65°C and QL = 1.75⋅10-4

m3/s

and 1 for TL = 26°C and QL = 1.75⋅10-4

m3/s.

5.3 Comparison experimental findings and model predictions

Typical predicted steam pocket growth is represented by the

histories of h and R shown in Fig. 12.

The nearly linear increase in time for (h + R) is in good

agreement with the histories of the penetration depth depicted

in Fig. 4. Note that after approximately 1 ms the growth rate Ŕ

becomes small. This is a result of an increasing pocket surface

area (R increases) and consequently more condensation of

steam while the source of mass momentum (G2-term, see Fig.

13) remains constant. The bubble foot radius rfoot is at t0 equal

to Ra and becomes zero after ± 7 ms when the neck of the steam pocket starts to form.

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

time [ms]

R, h

[m

m]

h

2R

rfoot

Figure 12: Predicted histories of h and R for a steam mass

flux of 53.05 kg/m2s, a water temperature of 65°C and a flow

rate of 1.75⋅10-4

m3/s (run 3). rfoot denotes the bubble foot

radius and is equal to (R2 – h

2)

1/2.

The corresponding force component histories are shown in Fig. 13. These typical results demonstrate that drag and momentum loss due to inhomogeneous condensation are

negligible, and that momentum gain due to steam injection yields the only positive force component.

Running the model at higher values of both G and U0, while keeping the detachment ratio (h/R)f, R0 and htot constant,

learns that the counteraction of the inertia forces increases and

that hf increases. Since the increase of G leads to a smaller h at detachment, the influence of increasing U0 is found to be dominant. Since the detachment ratio (h/R)f hardly depends on

G at constant water temperature (Fig. 8), an increase in G causes a decrease of the growth time, tf. This explains the trends shown in Fig. 6.

0 0.5 1 1.5 2 2.5-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

time [ms]

F [N

]

Drag

Condensation

Inertia

G2-term

Total

Figure 13: Predicted force histories for a steam mass

flux of 53.05 kg/m2s, a water temperature of 65°C and a flow

rate of 1.75⋅10-4

m3/s (run 3). The drag force is given by – 32

π µL R U + 20 π µL R Ŕ. The momentum loss term due to

inhomogeneous condensation is equal to π R2 {h (Tv – TL) /

hcond }

2 / ρv. The inertia force is (– Cam,1 U – Cam,2 Ŕ/ 2) ρL d∀

/dt + Cam,2 ρL ∀ d Ŕ/dt /2, where d∀ /dt is given by Eq. 6. The

source of mass momentum equals G2 / (ρv π Ra

2).

Vapor pocket growth at the fast rate found in our experiments is clearly controlled by inertia, as is confirmed by the agreement found between the predicted and measured values found of the growth time and the maximum penetration depth (Fig’s 14 and 15). The figures comprise both the experimental findings of Fig.’s 5 and 6 and model prediction results. The error bars of the latter indicate the errors propagated from the mean values of U0, R0, htot and the detachment ratio and do therefore not reflect the relatively large scatter found in these four parameters, as discussed in sections 3.3, 3.4 and 3.5. The agreement both in trend and in value between predictions and experiments is quite good.

30 35 40 45 50 55 60 65 70 750

1

2

3

4

5

6

G [kg/m2s]

tf

[ms]

Model: TL = 65

oC + flow

Exp: TL = 65

oC + flow

Model: TL = 26

oC + flow

Exp: TL = 26

oC + flow

Model: TL = 65

oC no flow

Exp: TL = 65

oC no flow

Figure 14: Experimental and model prediction results for the

growth time of the steam pocket at steam mass fluxes of 35.37 kg/m

2s, 44.21 kg/m

2s, 50.53 kg/m

2s and 70.74 kg/m

2s, water

temperatures of 65°C and 26°C and water flow rates of

1.75⋅10-4

m3/s and 0 m

3/s, which are indicated in the legend as

’ + flow’ and ‘no flow’, respectively. The dashed lines are plotted to guide the eye.

Note that a time-averaged value of the heat (and mass)

transfer coefficient is used at each instant of time; possible

resulting discrepancies have been discussed in section 5.2.

The worst predictions are those for large temperature

difference between steam and liquid and with flow. This is the

chugging flow regime (section 5.1) where for example the

heat transfer coefficient h might be affected by the waiting

time. The predicted histories for the highest steam flux (53

kg/(m2s)) are suspect, showing that the chugging regime

deserves further modeling attention.

The main conclusion is that inertia and momentum of

injected steam control growth of a vapor pocket in the unstable condensation flow patterns.

No fit parameters have been used in the model. Future

predictions with the model may utilize a correlation for h in

the form of that of Nariai & Aya [5] (section 3.2) or one that

is appropriate for the conditions investigated, as done in the

present paper. Future predictions may also utilize a prediction

criterion for the detachment ratio, in the form of a correlation

or likewise. Simple criteria were used for bubble detachment

in the past, see the introduction (section 1); the present study

shows that for intermittent steam injection a correlation is

necessary that at least accounts for TL and QL.

30 35 40 45 50 55 60 65 70 750

1

2

3

4

5

6

7

8

9

10

11

G [kg/m2s]

(R

+ h

) f [m

m]

Model: TL = 65

oC + flow

Exp: TL = 65

oC + flow

Model: TL = 26

oC + flow

Exp: TL = 26

oC + flow

Model: TL = 65

oC no flow

Exp: TL = 65

oC no flow

Figure 15: Experimental and model prediction results for the

maximum penetration depth at steam mass fluxes of 35.37 kg/m

2s, 44.21 kg/m

2s, 50.53 kg/m

2s and 70.74 kg/m

2s, water

temperatures of 65°C and 26°C and water flow rates of

1.75⋅10-4

m3/s and 0 m

3/s, which are indicated in the legend as

’ + flow’ and ‘no flow’, respectively. The dashed lines are plotted to guide the eye.

6 CONCLUSION

Unstable direct steam condensation at low mass fluxes of steam has been measured, both for injection in a stagnant

pool, a 30x30 mm2 channel actually, and for injection into a

cross-flow of water. Average heat transfer coefficients, growth

and waiting times and sizes and shapes of the steam pocket have been determined, next to other characteristic features of

intermittent steam pocket growth and collapse. The measured effects of the steam mass flux, the cross-flow and the sub-

cooling on the experimentally determined growth time, tf, heat transfer coefficient, htot, and inlet velocity, U0 are readily understood. The main effect of the liquid cross-flow is an increased heat transfer coefficient for otherwise identical

process conditions. This results in a notable reduction of both

growth time and maximum penetration depth.

A model has been developed and presented to facilitate

interpretation of measurement results and to increase our

predictive capacity of unstable direct steam injection. No fit

parameters have been necessary and recently obtained

knowledge of added mass coefficients has been utilized.

Comparison of model predictions and experimental findings

shows that:

• Model predications of the penetration depth history, (h +

R), of tf, and of the maximum penetration depth, (h + R)f,

are generally good.

• Inertia and momentum of the injected steam control the

growth of a steam pocket in the unstable condensation

regimes , while drag is negligible.

• The chugging regime, that occurs for the lowest liquid

temperature TL = 26°C, shows the largest discrepancies

and therefore needs further modeling attention.

With the aid of additional measurements is will be possible to

correlate the present findings of the heat transfer coefficient,

h. Comparison with a correlation from the literature shows

that our h-values are relatively low, which is attributed to

differences in geometries of steam injection.. A similar

observation is made for the geometrical detachment criterion, (h/R)f, that has been shown to depend on TL and QL.

ACKNOWLEDGEMENTS

This research is supported by the Dutch Technology Foundation STW, applied science division of NOW and the Technology program of the Ministry of Economic Affairs.

NOMENCLATURE Ai mean surface area of steam pocket, mm

2

Apocket(T) surface area of steam pocket at maximum penetration depth, mm

2

Āpocket mean surface area of steam pocket during a condensation cycle, mm

2

Cam,1,2 added mass coefficients, -

F Force, N G steam mass flux, kg/m

2s

H enthalpy, kJ/kg

L(t0) penetration depth of steam pocket at

condensation cycle start, mm Q flow rate, m

3/s

R radius of steam pocket, mm

(R+h) penetration depth, mm Ra radius of injection hole, mm

Ŕ growth rate of steam pocket radius, m/s T temperature, ºC

U wall normal steam pocket velocity, m/s

∀ steam pocket volume, m3

h distance of steam pocket centre to injection wall, mm

(h/R) detachment ratio, -

hcond condensation enthalpy, kJ/kg hFS heat transfer coefficient, W/m

2K

htot heat transfer coefficient, W/m2K

p pressure, bar q heat flux, W/m

2

t time, s

∆t inverse of frame rate, s

tf growth time of steam pocket, ms

rfoot bubble foot radius, mm

Greek

µ dynamic viscosity, Pa s

ρ density, kg/m3

Subscripts

o initial

f at detachment

L water V steam

sat saturation

REFERENCES 1. J.C. Weimer, G.M. Faeth and D.R. Olsen, Penetration of

vapor jets submerged in subcooled liquids, AIChE

Journal, vol. 19(3), pp. 552-558, 1973.

2. L.D. Chen and G.M. Faeth, Condensation of submerged

vapor jets in subcooled liquids, Transactions of the

ASME, vol. 104, pp. 774-780, 1982.

3. P.J. Kerney, G.M. Faeth and D.R. Olsen, Penetration characteristics of a submerged steam jet, AIChE Journal, vol. 18(5), pp. 548-553, 1972.

4. M.H. Chun, Y.S. Kim and J.W. Park, An investigation of direct condensation of steam jet in subcooled water, International Communications in Heat

and Mass Transfer, vol. 23(7), pp. 947-958, 1996. 5. Nariai and I. Aya, Fluid and pressure oscillations

occurring at direct contact condensation of steam flow with cold water, Nulcear Eng. and Design, vol. 95, pp. 35-45, 1986.

6. I. Aya and H. Nariai, Boundaries between regimes of pressure oscillation induced by steam condensation in pressure suppression containment, Nulcear Eng. and

Design, vol. 99, pp. 31-40, 1987. 7. D.H. Youn, K.B. Ko, Y.Y. Lee, M.H. Kim, Y.Y. Bae and

J.K. Park, The direct contact condensation of steam in a pool at low mass flux, J. of Nuclear Sc. And Techn., vol.

40(10), pp. 881-885, 2003.

8. C.K. Chan and C.K.B. Lee, A regime map for direct contact condensation, International Journal of

Multiphase Flow, vol. 8(1), pp 11-20, 1982.

9. C.W.M. van der Geld, On the motion of a spherical bubble deforming near a plane wall, J. Eng. Math., vol.

42 (1), pp. 91-118, 2002. 10. C.W.M. van der Geld, The dynamics of a boiling bubble

before and after detachment, Heat Mass Transfer, vol. 44 (1), pp. 1-30, DOI 10.1007/s00231-007-0254-7, 2007.

11. G. Duhar, G. Riboux and C. Colin, Vapour bubble growth

and detachment at the wall of shear flow, Heat Mass

Transfer, vol. 44 (1), DOI 10.1007/s00231-007-0287-y, 2007.

12. Kuo-Shing Liang, Experimental and analytical study of

direct contact condensation of steam in water, Ph. D. thesis, Massachusetts Institute of Technology, 1991.

13. Y.S. Kim, J.W. Park and C.H. Song, Investigation of the

steam-water direct contact condensation heat transfer coefficients using interfacial transport model,

International Communications in Heat and Mass Transfer, vol. 31(3), pp. 397-408, 2004.