**4. Method of mass increment**

#### **4.1 Experimental apparatus and procedure**

The method of the mass increment was used for the investigations. Figure 7 shows a rough sketch of the apparatus. It consists of a test chamber, an electronic balance and a personal computer for data acquisition. The experimental procedure is mentioned in Sec. 2.1. Air enters the test chamber and the mass of the gas mixture in the test chamber increases.

The mass increment m is automatically measured by the electronic balance with high accuracy. From mass increment data, the density increment of the gas mixture ρL = m/V is calculated. The density increment means the difference of densities of the gas mixture from the density of pure helium in the test chamber. Then, volumetric exchange flow rate is evaluated by the following equation:

Herium-Air Exchange Flow Rate Measurement Through a Narrow Flow Path 55

**7. Nomenclature** 

T: elapsed time (s)

**Greek** 

**Subscripts** 

He: helium

**8. References** 

A: flow passage area (m2)

D: inner diameter of the tube of the flow path (m)

Fr: densimetric Froude number defined by eq.(3)

Q :volumetric exchange flow rate defined by eq.(l) (m/s)

r: radius of flow path of the horizontal direction (m)

Dc: inner diameter of test chamber (m)

g :acceleration of gravity (m/s )

Hc: inner height of test chamber (m)

U: exchange-velocity (=Q/A) (m/s)

V: volume of test chamber (m )

L : lighter fluid (gas mixture)

Wakil, 1982)

H : heavier fluid (air)

U0: maximum exchange-velocity (m/s)

m: mass increment in test chamber (kg)

ρ: mean density ( =ρH +ρHe)/ 2 (kg/m3)

ρL : density increment (= m/V) (kg/m3)

7, Track 1-7-1 (Fumizawa, 2005)

Kang,T. et al., NURETH-5, pp541-546 (Kang, 1992)

θ: inclination angle if flow path from perpendicular line (deg)

El-Wakil, M.M., Nuclear Energy Conversion, Thomas Y. Crowell Company Inc., USA (El-

Fumizawa,M.; Proc. HT2005 ASME Summer Heat Transfer Conference, HT2005-72131, pp.1-

Juni-1965, "Sicherheitsbericht fuer das Atom-Versuchskraftwerk Juelich", Arbeitsgemein-

Fumizawa,M. et. al., J. At. Energy Soc. Japan, Vol.31, pp1127-1128 (Fumizawa, 1989)

Epstein,M., Trans. ASME J. Heat Transfer, 110, pp885 -893 (Epstein, 1988)

schaft Versuchs-Reactor AVR (Juni-1965, 1965)

L: height of the tube of the flow path (m)

$$Q = \frac{V}{\rho\_H - \rho\_L} \cdot \frac{d(\Delta \rho\_L)}{dt} \tag{2}$$

The densimetric Froude number is defined by the following equation derived from the dimensional analysis suggested by Keulegan (Merzkirch, 1974):

$$Fr = \frac{Q}{A} \sqrt{\frac{\rho}{gD\Delta\rho}}\tag{3}$$

In the above equations, V is the volume of test chamber, ρH the density of air, ρL the density of gas mixture in the test chamber, ρL ( =ρH -ρHe) = the density increment of the gas mixture, t the elapsed time, U(=Q/A) the exchange-velocity, ρ( =ρH +ρHe)/ 2, D the diameter and g the acceleration of gravity. The experiments are performed under atmospheric pressure and room temperature using the vertical and inclined round tubes, and using the vertical annular tube. The density of the gas mixture is close to that of helium in the present experiment. The sizes of the tubes are as follows. The diameter of the round tube D is 20 mm, which is much smaller than that of the test chamber. The inclination angle θ ranges from 15 to 90 deg and the height L ranges from 0.5 to 200 mm.

#### **4.2 Results and discussion**

It is already known that it is regarded as constant within a time duration when the gas in the upward flow can be assumed helium (Fumizawa, 1989). Figure 10 shows the relationship between Fr and inclination angle θ with L/D as a parameter. For inclined tubes, Fr is larger than that for vertical tubes. The black circles show the experimental data for the orifice (i.e. L/D =0.05) and the black rhombuses for the long tube (i.e. L/D = 5). Densimetric Froude number reaches the maximum at 60 deg for the orifice and 30 deg for the long tube. It is found that the angle for the maximum Fr decreases with increasing L/D in the helium-air system. On the other hand, Mercer's experiments with water and brine indicated that the inclination angle for the maximum Fr was about 80 deg in the several long tubes investigated. It may depend on the difference of dynamic viscosity between the gas and the liquid.

#### **5. Conclusion**


#### **6. Acknowledgements**

The authors are deeply indebted to Dr. Makoto Hishida, who is professor of Chiba University in Japan, and Mr. Akira Furumoto who is manager of Digimo CO.,LTD for their unfailing interest and many helpful corporations to this study.
