Void Profile Studies in Vertical Upward Co-Current Churn
Mercury-Nitrogen Flows
Liquid Metal Magnetohydrodynamic (LMMHD) power converters of gravity type have been proposed for various heat sources [1]. In these systems, two-phase flows consisting of steam and high density liquid metal (lead, lead-bismuth alloys etc.) take place in the riser and liquid metal flows in the downcomer containing MHD generator.
In general, the flow consists of multibubble, churn and slug as void fraction varies from around 0.1 to 0.8. Due to large diameter of the riser and high gas flow rates, significant length of the riser will have churn flow. The parameters of two-phase flow critically decide the overall efficiency of conversion. This requires detailed knowledge of void distribution across the cross-section.
Neal and Bankoff have studied void profiles for slug flow and developed an empirical relation for void fraction as a function of ratio of volumetric flux and Froude number of the liquid metal flow [2]. In this paper, void profiles for churn flows are studied. Empirical relations similar to that of Neal and Bankoff are developed.
Experiments have been carried out in a nitrogen-mercury simulation LMMHD loop operating at ambient temperature. The system consists of mixer, riser pipe, separator, downcomer and MHD flow meter. Nitrogen is introduced through the mixer and a two-phase mixture is established in the riser. This gives rise to density difference between the riser and downcomer and leads to the circulation of liquid metal in the loop. Nitrogen is separated and is let out to the ambient. Mercury flows through the downcomer. Gamma ray attenuation method has been employed for determining radial void profile using 60Co of activity 2775 MBq at two locations in the riser [3].
For low flow rates, the flow was bubbly and the void exhibited oscillating profile as a function of radial co-ordinate [4]. However, for gas flow rates above 4.7 g/s, the flow was churn [5] and the void profile exhibited monotonic variation with maximum value at the center.
Void fraction profile (() for churn flow has been expressed as a function of power law as follows:
EMBED Equation.2 (1)
where r is the radial distance from entrance. R is the internal radius of the pipe. p is given by
EMBED Equation.2 (2)
C1 and C2 are constants determined based on the best fitted p value. (, Nfr are the fraction of the volumetric flow rate of the gas and Froude number of the liquid metal respectively.
Best fitted p values for the experimental data varied from 2.75 to 4.75 for different flow rates. For slug flow this value is in the range of 10.9 and 12.7. The smaller values for p indicate that void fraction profiles for churn flows are less steep than those of slug flow near the walls.
The difference in the profile shape can be attributed to the difference in the flow structure between slug and churn. The slug flow consists of large bullet shaped voids extending right up to the walls of the pipe followed by bubbles distributed across the cross section. Because of the bullet shaped void, the time averaged void fraction near the walls will be larger than that for churn, making the profiles steeper.
Both C1 and C2 have been separately varied to fit with experimental values. C1 varied in the narrow range of 3.5 to 4.5. On the other hand, C2 varied from 1.19 to 2.11 for the entire flow conditions and locations. These values are five times or more as compared to those for slug flow.
References
[1] Branover, H. 1993 Liquid metal MHD research and development in Israel energy convention and Magnetohydrodynamic flows, Progress in Astronautics and Aeronautic, Edited by H .Branover and Y .Unger, 18, 209-221.
[2] Neal, L. G. and Bankoff, S. G., 1965 Local parameters in cocurrent mercury-nitrogen flow, A. I. Ch. E. Journal, 11, 624-635.
[3] Thiyagarajan, T. K., Satyamurthy, P., Dixit, N. S., Venkatramani, N., Garg, A. and Kanvinde, N. R. 1995 Void fraction profile measurements in the two-phase mercury-nitrogen flow s using gamma-ray attenuation method, Experimental Thermal and Fluid Sciences, 10, 347-354.
[4] Satyamurthy, P., Dixit, N. S., Thiyagarajan, T. K., Venkatramani, Quraishi, A. M. and Mushtaq, A., 1998, Two-fluid model studies for high density two-phase liquid metal vertical flows, Int. J. of Multiphase Flow, 24, 721-737.
[5] Taitel, Y., Bornea, D. and Duckler, A. E. 1980 Modeling flow pattern transition for steady upward gas-liquid flow in vertical tubes, A. I. Ch. E. Journal, 26, 345-354.