Study on Heat Transfer Mechanism of Steam Condensation on Water Jet in Steam Injector

Abstract

In this chapter, the heat transfer characteristics in the steam injector that has been proposed to introduce into boiling water reactors as a feed water heat exchanger and a safety injection pump are examined. The temperature and the velocity distribution in the injector were measured. The heat transfer rate from the steam flow around the water jet to the water jet was greatly larger than that of the usual turbulent flow in a pipe. High-speed camera pictures revealed the surface of the water jet was very wavy. It was supposed that the wavy motion on the water jet surface created the effective large-internal circulation flow in the water jet, which resulted in the tremendously effective heat transport from the surface into the center portion of the water jet. From the high-speed camera pictures, the characteristics of waves on the surface; the wave height, the wave velocity, and the wave length were obtained. In addition, the dimensionless numbers were found from the parameters that related to the phenomena in the steam injector. By using these dimensionless numbers, a correlation for the heat transfer from steam flow to the water jet in the steam injector was proposed.

1. Introduction

By making use of the thermal energy of steam, low-pressure gas can be pressurized and liquid can be pumped up to high elevation. The former and the latter are sometimes called as an ejector and a steam injector, respectively. These equipments do not have any moving/rotating parts. Thus, these are simple and solid in structure and reliable. A large amount of fluid can be handled even if these are small in size.

Ejectors have been used as air evacuation pumps in steam turbine systems and evaporators, and as compressors in steam jet refrigerators, and so on. Ueda [1, 2] examined the flow mechanism in the ejector and presented the design guideline of the ejectors.

Injectors have also been utilized in many areas, for example as feed water pumps in steam locomotives. Because of the advantage of the simplicity in the design and no necessity of the power to drive, Narabayashi et al. [3, 4, 5] and Iwaki et al. [6] recently examined the steam injectors by introducing the injectors into nuclear reactors as feed water pumps and safety injection pumps in mind. It has been proved that the steam injectors have the possibility that low-pressure steam can pump up water to an operating pressure of boiling water reactors (BWRs). Analytical models that can be used to design steam injectors have been also proposed.

Although steam injectors are based on proven technology and have been investigated by many researchers in the past, several things are still open to be examined. The steam injectors tested by Narabayashi et al. or Iwaki et al. were small and scaling low or scaling-up methodology should be cleared. The operating condition or range is also important. When the injectors are included in BWRs, these may experience broad conditions that may be outside design conditions occasionally. It must be clarified how the steam injector may behave under various conditions and whether there is no possibility in any condition that these may be in the way, especially in the safety aspect.

In considering the above, the most important is how to estimate the normal operating condition that the injectors function as expected and how to predict the behavior of the injectors when they go outside of the normal operating condition. These should be precisely analyzed by nuclear reactor safety analysis codes.

The essential phenomenon in the steam injectors is the conversion of the thermal energy of steam to the kinetic energy, thus the dynamic interaction and the thermal interaction between steam flow and water flow as pointed out by Iwaki et al. Fully understanding about these is required. In the present study, authors have investigated the stability of a water jet with steam condensing at the surface, the condensation heat transfer at the water jet surface, and the heat transport into the water jet for the center water jet type injectors [7, 8, 9].

In this chapter, steam condensation heat transfer to the jet surface in the steam injector was examined and the characteristics of the wavy jet surface were also reported. Additionally, the heat transfer data of the steam condensation to the water jet in the steam injector were correlated focusing on the relation between the wave motion of the jet surface and heat transport in the water jet.

2. Experimental apparatus and procedures

2.1 Experimental setup

The experimental apparatus used in the present study is schematically shown in Figure 1. It is composed of a steam generator, a test section, an outlet reservoir, a water tank, circulation pumps, and instruments.

Figure 1.

Experimental apparatus. Source: Takahashi Y., Koizumi Y., Ohtake H. and Mori M., study on characteristics of thermal–hydraulic phenomena in steam injector, [internet]. Volume 4: Computational fluid dynamics, Neutronics methods and coupled codes; student paper competition. ASMEDC; 2006. Reprinted with permission.

The steam generator is electrically heated. It has 40 kg/h evaporative capacity at 0.5 MPa. Steam from the steam generator is superheated with ribbon heaters on piping between the steam generator and the test section and flows into the test section through an orifice flow meter. Water pumped out from the water tank also flows into the test section. The flow rate of water is measured with a rotameter. Water or water and steam mixture is collected in the outlet reservoir. Then, keeping the water level in the outlet reservoir constant, water is returned to the water tank by a pump. Steam goes back to the water tank and is discharged into the water to condense.

The steam flow rate is controlled by adjusting the electric power supply to the steam generator. The water flow rate is controlled by adjusting a valve. The temperature of the water is controlled by electric heaters in the water tank and cooling coils of service water.

2.2 Test section

A water nozzle has a straight part of 125 mm in length and 5 mm in inner diameter and abruptly opens to a condensing section of steam. The water jet is blown out from this nozzle into the condensing section. Details of the test section used in the present study are illustrated in Figure 2.

Figure 2.

Details of test section. Source: Takahashi Y., Koizumi Y., Ohtake H. and Mori M., study on characteristics of thermal–hydraulic phenomena in steam injector, [internet]. Volume 4: Computational fluid dynamics, Neutronics methods and coupled codes; student paper competition. ASMEDC; 2006. Reprinted with permission.

The test section has a converging condensing section as shown in Figure 2. The inner diameter of the condensing section at the outlet of the water nozzle was 13.3 mm and the condensing section length was 52.9 mm. The inner diameter of the throat was 4 mm and the throat length was 5 mm. A diffuser section followed the throat. The diffuser length and the inner diameter at the outlet were 55.2 and 13.7 mm, respectively. The test section and other parts of the apparatus were well thermally insulated.

2.3 Experimental procedures

For the specified flow rate of the water jet, steam flow was supplied to the test section. During the experiment, the supplied water temperature and the water level in the outlet reservoir were kept constant. The overflow line had a check valve. When the experiment was started by supplying steam and water for the test section, the flow state in the steam injector was unstable and excess water was exhausted through the check valve in the overflow line. After the flow was stabilized, the overflow of water from the test section was stopped by the check valve. Then, the overflow line valve was manually closed. Temperature and velocity of the water jet in the test section were measured at two positions in the axial direction; at 10 and 20 mm from the outlet of the water nozzle, as shown in Figure 2. Pressure in the test section was also measured at similar locations. The temperature of the water jet in the mixing section was measured with an Alumel-Chromel thermocouple of 0.13 mm diameter wires. The thermocouple was radially traversed at each measuring location with an increment of 0.5 mm. The velocity of the water jet was measured with a Pitot tube of 0.8 mm diameter tube. The Pitot tube was also traversed radially in a similar way to the thermocouple.

The liquid temperature and the velocity of the water jet tested were at 20 and 35°C and from 6.8 to 17 m/s, respectively. The steam flow rate also varied from 30 to 40 kg/h in the experiments. In all conditions, the ratio of the steam to the water mass flow rate is less than 10%. In the experiments, the exit pressure of the test section was atmospheric pressure.

The flow state of the water jet in the condensing section was also visually examined. The test section for the visual experiment was made of polycarbonate and had the same as that shown in Figure 2. Pictures of the flow state were taken by a high-speed video camera at the flame rate of 8000 flame/s and at the shutter speed of 1/10,000 s. The pictures were recorded for one second; 8000 flames.

Parts of this chapter were originally published as a conference paper: Takahashi, Y., Koizumi Y., Ohtake H. and, Mori, M., Study on Characteristics of Thermal–Hydraulic Phenomena in Steam Injector, [Internet]. Volume 4: Computational Fluid Dynamics, Neutronics Methods and Coupled Codes; Student Paper Competition. ASMEDC; 2006. Available from: http://dx.doi.org/10.1115/ICONE14-89365.

3. Experimental and analytical results

3.1 Temperature distribution

One example of radial temperature distributions measured in the injector-type experiments is shown in Figure 3. The velocity of water at the nozzle outlet is 8.5 m/s and the velocity of steam at the water nozzle exit position is 320 m/s. At the position close to the nozzle outlet, 10 mm from the nozzle outlet, the temperature increase is observed only in the peripheral region of the water jet. As the flow goes downstream, at 20 mm from the nozzle outlet, the temperature increase propagates to the central region of the jet. At the position of 55.4 mm from the nozzle outlet (throat position), the radial temperature distribution becomes flat; it suggests that steam condensing has been completed until there. The temperature at the center portion of the water jet increases largely in the short distance between 10 mm and 20 mm from the nozzle outlet. The condensation of all steam flowing into the injector with the velocity of 320 m/s which corresponds to 40 kW thermal energy has completed in the very short distance of just 55 mm. It is indicated that highly efficient heat transport in the radial direction of the water jet takes place.

Figure 3.

Radial temperature distribution in steam injector.

3.2 Velocity distribution

Measured water jet velocity distributions are illustrated in Figure 4. These are results for the water velocity of 8.5 m/s and the steam velocity of 320 m/s. The differential pressure measured with the Pitot tube was converted to a velocity using the density of water or the density of steam depending on the water region or the steam region, respectively. In this figure, the boundary between the water region and the steam region is expressed with a blue line. The average velocity of the water jet was derived from the measured radial velocity distribution. Assuming that the mass flow rate of the water jet was equal to the water flow rate at the nozzle outlet, the jet surface position was obtained from the average velocity and the mass flow rate.

Figure 4.

Radial velocity distribution in steam injector.

At 10 mm from the nozzle outlet, only the peripheral part of the jet is accelerated. At 20 mm from the nozzle outlet, the acceleration reached to the central portion of the jet, and the center part is largely accelerated. it is expected that the water jet becomes thinner as the results of the acceleration as the flows proceed downstream. However, it is not observed. It is amazing that the water jet is greatly accelerated in the very short distance of 10 mm.

In the figure, the sonic velocity of steam is illustrated. The steam velocity has reached the super-sonic velocity at 10 mm from the inlet. It suggests that steam molecules vigorously plunge into the water jet surface to condense there.

3.3 Condensation heat transfer coefficient and surface heat flux

Bulk temperature $T_m$ is calculated from the measured liquid velocity $u$_l and liquid temperature T distributions as follows:

$$T_m=\frac{{\int }_0^{r_0}2\pi {\rho }_l{c}_{\mathit{pl}}r{u}_l\mathit{Tdr}}{{\int }_0^{r_0}2\pi {\rho }_l{c}_{\mathit{pl}}r{u}_l\mathit{dr}}$$E1

The surface heat flux q_s of steam condensation to the jet surface can be related to the increasing rate of bulk temperature to the flow direction $x$ as:

$$\frac{d{T}_m}{\mathit{dx}}=\frac{\mathit{\pi D}{q}_s}{c_{\mathit{pl}}{m}_l}$$E2

where D is the water jet diameter and $m_l$ is the water jet flow rate. The condensation heat transfer coefficient is defined by using the local water subcooling that is defined by using the steam saturation temperature for pressure at the measuring position and the bulk water temperature at the measured position as follows;

$$h=\frac{q_s}{T_{\mathit{sat}}-T_m}$$E3

The heat fluxes $q_s$ of steam condensation to the jet surface derived with Eqs. (1) and (2) are presented in Figure 5. The horizontal axis is the local water subcooling. It was expected from Figure 5 that the condensation heat transfer coefficient would show decreasing trend for the water subcooling since the surface heat flux seems to be constant with an increase in the subcooling and the heat transfer coefficient was in inverse proportion to the subcooling; Eq. (3).

Figure 5.

Surface heat flux.

Heat transfer coefficients $h$ derived by Eq. (3) in the experiments are plotted for the local water subcooling in Figure 6. Measured heat transfer coefficients express a weakly decreasing trend for an increase in the inlet liquid subcooling. Those are much lower than the ideal condensation heat transfer coefficient [10].

Figure 6.

Heat transfer coefficient.

Figure 7 shows the Re-Nu correlation that was obtained from this experiment. The value of Nu is one or two orders as large as the Dittus-Boelter correlation. This result clearly expresses that tremendously effective heat transfer was done in the condensation area.

Figure 7.

Re-nu correlation.

3.4 Visualization

Figure 8 shows the image of the water jet in the steam injector taken by high-speed video camera. In Figure 8(a), only water flows, and steam is not supplied. The original image on the left is binarized on the right. Although there are tiny waves on the surface, the shape of the water jet is kept round and straight. When steam was provided and the steam injector functioned as a pump, the jet surface looks like the water jet is foamy; tiny vapor bubbles are dissolved into the water jet (Figure 8(b)). And it is noted that there is large-clear wave motion on the water jet surface.

Figure 8.

Water jet behavior.

From these results, it was supposed that the wavy motion on the water jet surface created the effective large-internal circulation flow in the water jet and the tremendously effective heat transport into the center portion of the water jet.

From the pictures of the water jet surface, the characteristics of waves on the surface; the wave height, the wave length, and the wave velocity, were obtained. A total of 50 large waves were randomly selected in the recorded pictures and then the wave heights were measured. The average value of these was defined as the wave height. Similarly, 50 large waves were randomly selected, and then traveling distance in a certain time period was obtained. From these, the wave velocities were calculated. The average of these was also defined as the wave velocities in the present experiments.

Figure 9 shows one example of the characteristics of the wave on the jet surface obtained in the present study. The water temperature was 20 and 35°C. The wavelength was almost constant regardless of the velocity difference between the water jet and the steam flow. The wave velocities indicate the tendency to increase with the water jet Reynolds number. The wave velocity is in the range from 20 to 30 m/s. The average water jet velocity was in the range from 15 to 20 m/s.

Figure 9.

Wave characteristics.

4. Correlation of dimensionless numbers

4.1 Non-dimensional analysis

The dimensionless numbers were derived from the non-dimensional analysis. The obtained dimensionless numbers are;

The Nusselt number: $\mathbf{Nu}=\mathit{hD}/k_{l.}$

The water jet Reynolds number: ${\mathbf{Re}}_{\mathbf{l}}=u_{l}D/{\nu }_l$

The Prandtl number: $\mathbf{Pr}={\rho }_l{\nu }_l{c}_{\mathit{pl}}/k_l$

The Weber number is defined by the difference between the average steam velocity and the average jet velocity Δu and the jet diameter: ${\mathbf{\text{We}}}_{\mathbf{∆}{\mathbf{u}}_{\mathbf{l}}}={\rho }_l\Delta u^{2}D/\sigma$

The Froude number: $\mathbf{Fr}={u_w}^2/\mathit{gD}$

The Reynolds number defined by the velocity difference between the jet and the steam flow Δu: ${\mathbf{Re}}_{\mathbf{\Delta ul}}=\mathit{\Delta uD}/{\nu }_l$

The Reynolds number is defined by the wavelength λ and the differential velocity between the jet and the steam flow Δu: ${\mathbf{Re}}_{\mathbf{\Delta u\lambda }}\mathbf{=}\mathit{\Delta u\lambda }/\nu$

The Reynolds number defined by the wave height h_W and the differential velocity between the jet and the steam flow Δu: ${\mathbf{Re}}_{\mathbf{\Delta uh}}=\mathit{\Delta u}{h}_W/\nu$

Non-dimensional wave velocity: ${\mathbf{N}}_{\mathbf{uw}}=\mathit{\nu g}/{u_W}^3$

Combinations of Dimensionless Number: ${{\mathbf{\text{We}}}_{\mathbf{∆}\mathbf{u}}}^{\mathbf{-}\mathbf{1}}{·\mathbf{Re}}_{\mathbf{\Delta ul}}$, $\mathbf{Nu}·{{\mathbf{Re}}_{\mathbf{l}}}^{\mathbf{-}\mathbf{1}}$

4.2 Heat transfer correlation

By using some of the non-dimensional numbers that were derived by the non-dimensional analysis, the best-fit correlation for the steam condensation heat transfer to the water jet in the steam injector was developed.

In Figure 10, the relation between the non-dimensional parameter groups is presented. Some trend is noticed. In the present experiments, the temperature of the water jet was varied. In order to check the effect of the physical properties, the dependency of the heat transfer on the Prandtl number is presented in Figure 11. The clear dependency of the heat transfer on the Prandtl number is noticed.

Figure 10.

Dimensionless number combination.

Figure 11.

Influence of Prandtl number.

Finally, the best-fit correlation for the steam condensation heat transfer in the steam injector is developed as

$$\mathbf{Nu}=64\left({\mathit{Re}}^{0.866}{\mathbf{Pr}}^{-1.389}{{\mathbf{\text{We}}}_{\mathbf{\Delta u}}}^{-0.237}\right)$$E4

As shown in Figure 12, the agreement between the experimental results and the proposed correlation; Eq. (4) is quite well.

Figure 12.

Heat transfer correlation.

5. Conclusions

Steam condensation heat transfer to a water jet in a steam injector was examined. Following conclusions were obtained.

1. The measured velocity distribution exhibited that the velocity of steam around the water jet was super-sonic velocity and the water velocity at the peripheral region was considerably faster than that in the central region. It suggested that the water jet was greatly accelerated by the steam flow around the jet. The radial and the axial temperature distributions expressed that the water temperature at the central region jumped up in a short distance. It implied that considerably effective-radial heat transport took place in the water jet.

2. The heat transfer coefficient showed a slightly decreasing trend for water subcooling and the condensation heat flux was almost independent of the subcooling. The heat transfer coefficient of steam condensation to the water jet surface was much higher than that of the turbulent heat transfer in the circular tube.

3. As a result of observation, it was clarified that the interface between the water jet and the steam flow was very wavy. It was supposed that the wavy motion on the water jet surface created tremendously effective heat transport into the center portion of the water jet. The wavelength, wave height, and wave velocity were measured from pictures taken by a high-speed video camera.

4. From the non-dimension analysis and the comparison with the experimental results, the heat transfer correlation of the jet flow accompanying the direct condensation of steam on the surface in the steam injector was proposed.

Acknowledgments

The present research project has been carried out by Tokyo Electric Power Company, Toshiba Corporation, and six Universities in Japan, funded by the Institute of Applied Energy (IAE) of Japan as the national public research-funded program.

Nomenclature

cp	Specific heat [J/kg·K]
D	Water jet diameter [m]
g	Gravitational acceleration [m/s^2]
h	Heat transfer coefficient [W/m^2·K]
hW	Wave height [m]
k	Thermal conductivity [W/m·K]
m	Mass flow rate [kg/s]
P	Pressure [Pa]
q	Heat flux [W/m^2]
r	Radial position [m]
T	Temperature [K], [°C]
u	Velocity [m/s]
x	Axial position [m]
y	Radial position from wall [m]

Greek Symbols

Δu	Difference between average steam velocity and average jet velocity [m/s]
λ	Wave length [m]
ν	Kinematic viscosity [m^2/s]
ρ	Density [kg/m^3]
σ	Surface tension [N/m]

Subscripts

g	Gas
l	Liquid
m	Mean
s	Surface
sat	Saturation
W	Wave