Analysis of Two-Phase Liquid Metal MHD Induction Converter

An analysis is made on the performance characteristics of a liquid-metal MHD induction converter with liquid-gas two-phase mixture as working fluid. The equivalent electrical conductivity and the velocity vary along the generator channel in this kind of induction converter.

Two important parameters which represent the variations of the equivalent electrical conductivity and the velocity respectively are defined. With these parameters the induction equation is analytically solved with the perturbation technique.

Quantities representing generator performance, such as power densities and generator efficiency, are obtained from the perturbed magnetic field and the parameters mentioned above.

Suitable combination of values for these parameters will tend to let the effects brought by the variations of electrical conductivity and of velocity cancel each other, and the relation between these parameters is analytically derived that assures the non- perturbation of the magnetic field and of the gross output power density. In this condition of non-perturbation, the generator efficiency approaches that for the unperturbed case when the velocity variation and the inlet slip ratio are small.     

Electrical Conductivity of Liquid Metal Two-Phase Mixture in Bubbly and Slug Flow Regime

A correlation function for reactor noise is determined through a conditional polarity-correlation technique in which the polarity of neutron-counting fluctuations is analyzed with the start condition that the counting rate reaches a preset level. This technique, evidently, is an example of flash-start technique, developed for the purpose of improving the efficacy of reactor noise analysis. In the present case, the conditional polarity-correlation function is described mathematically assuming that the counting fluctuations of the detector conform with a Gaussian distribution. The expression thus derived reveals that this function is approximately proportional to a cross-correlation function and is a differential type of polarity-correlation function.

In order to examine the validity of the obtained expression, an experiment was performed in a graphite-moderated reactor at slightly subcriticai state to measure the conditional polarity-correlation function. A novel contrivance was adopted in the experiment to eliminate the dead-time effect created during the busy time of the multi-channel time analyzer. The dependence on the preset level—i.e. flash-start condition—exhibited by the conditional polarity—correlation function showed good agreement with that expected from the mathematical expression. The prompt mode neutron decay constants were determined from the experimental data within statistical error of 3～4 %.     

Void Fraction and Pressure Drop in Liquid Metal Two-Phase Flow

This paper describes a new correlation for predicting a two-phase frictional pressure drop multiplier, and discusses the pressure level effects and the mass velocity effects. This correlation predicts satisfactorily the frictional pressure drop not only for liquid metals but also for ordinary fluid two-phase flow in a wide range of flow variables.

The authors' void fraction correlation previously proposed is also compared with published data of void fraction for liquid metal two-phase flow, and is found to represent well the mass velocity effects. Wettability and magnetohydrodynamic effects are discussed briefly in relation to the hydrodynamic characteristics of liquid metal two-phase flow.     

强磁场作用下液态锂在矩形通道中的流动研究

对高速液态金属锂在强磁场作用下沿着非扩散矩形型通道的流动进行了分析研究 ,通过解析分析 ,推导得到了控制电场和流场的由泊松 (Poisson)方程和亥姆霍兹 (Helmholtz)方程组成的方程组 ,并且编制了求解该方程组的程序 PHsolver;根据边界的壁面函数处理 ,用PHsolver求解得到了强磁场作用下在非扩散型矩形通道中电流密度场的分布和流场的分布 ,其中流速分布呈现为马鞍型分布。     

Heat Transfer and Temperature Fluctuation of Lithium Flowing under Transverse Magnetic Field

For providing background information on the liquid metal cooling of fusion reactors, the MHD effects on heat transfer of flowing lithium was experimentally studied with an emphasis on temperature fluctuations. The test section was constituted of a 15.8 mm I.D., 1.65 mm thick, 316-SS tubing and a 7.6 mm O.D. heater pin with nine 0.5 mm thermocouples. The experiment covered the range of B=0–1.0 T, U=0.2–4.0m/s, T=320–390°C and q=0–68 W/cm². The results are summarized as follows:

(1) With increasing magnetic flux density B, Nusselt number Nu decreases to a value of flat flow velocity model: 6.38 but rises in B=0.1–0.4T. (2) The RMS of temperature fluctuation has strong dependence on B and presents a peak near B=0.25T. (3) The singular rise of Nu is inferred to result from enhanced turbulence due to steepening of radial gradient of velocity near the wall as a result of MHD effect. (4) The transit velocity estimated from temperature cross-correlation in the parallel sector coincides with the mean velocity when B=0 but deviates toward a lower value with applying B. (5) Local flow velocity is decelerated in the magnetically-parallel sectors and accelerated in the perpendicular.     

Study on Refractive Index Matching Liquid of Polymethyl Methacrylate Employed in Flow Field Visualization Experiment

In order to reduce the impact induced by the difference in refractive index between the working fluid and fuel assembly model on the visualization flow field measurement, tetralin and ethyl alcohol were mixed to produce a new refractive index matching (RIM) liquid. The refractive index, density, dynamic viscosity, and Reynolds number of the mixed solutions with different concentrations were measured, and the sensitivities of these four variables to temperature were investigated. The results show that, the refractive index of the mixed solution of tetralin (72.2%)-ethyl alcohol (27.8%) is equal to that of polymethyl methacrylate at 25 ℃, and the Newton equation has the smallest deviation from experimental data when the refractive index of mixed solution is predicted. Since the Reynolds number is sensitive to temperature, it is suggested to set up heat exchange equipment in the experimental facility to control the temperature of the working fluid. This RIM liquid has the advantage of low cost, moderate density, low dynamic viscosity, and high stability, which can be used in the flow field visualization experiment.     

Experimental Studies on Heat Transfer by Natural Convection and Pool Boiling of Sodium in a Strong Magnetic Field

This report deals with an experiment on the heat transfer of liquid sodium, with particular reference to the effects brought by the application of a magnetic field on pool boiling. The test section, a heater pin of 6.5 mm diameter, was inserted vertically into the center of a sodium tank. The heating surface of the pin was parallel to the magnetic field as well as to the direction of gravity.

Under conditions of natural convection in a magnetic field, a sharp rise of the heating surface temperature was always seen to occur at some point when the heat flux was gradually increased, accompanied by the onset of sharp temperature oscillations.

The surface superheat required for the initiation of boiling decreased with increasing intensity of the applied magnetic field, reached a minimum, then increased again.

The surface temperature fluctuations in nucleate boiling was higher under magnetic field than when free of such influence. The critical heat flux for burn-out was not appreciably affected by magnetic field.     

Frictional Pressure Drop for NaK-N2 Two-Phase Flow in Rectangular Cross Section Channel of Large Aspect Ratio

In this paper, the frictional pressure drop in an isothermal liquid metal-gas two-phase flow through a rectangular channel with large width-to-height ratio is treated semiempirically for a NaK-N₂ two-phase flow system.

The frictional pressure drop in the two-phase flow is compared with the following two reference values :

1. The frictional pressure drop in the liquid flowing alone in single phase with the same velocity as that of the liquid in the two-phase mixture.

2. The frictional pressure drop in the liquid flowing alone in single phase with the same mass flow rate as that of the liquid in the two-phase mixture.

The comparison with the former reference value is necessary for the prediction of friction loss in a liquid metal MHD generator channel whose medium would be two-phase mixture.

The semiempirical analysis was performed assuming the two-phase mixture to be a continuous medium with its properties, e.g. viscosity and density, defined by void fraction and the velocity determined by the total mass flow rate.

In the region of low slip and density ratio ρ_g/ρ_l the frictional pressure drop in the two-phase flow appeared to be smaller than that due to the liquid flowing alone with the same velocity as that of the liquid in the two-phase flow.

The experiments have been undertaken with the NaK-N₂ two-phase mixture flowing through a rectangular channel (4 × 60 mm²).

Data were taken over the following parameter range:

NaK velocity: 5～30 m/sec, Void fraction: 0～70%

Density ratio: 0.006～0.013, Quality: 0.07～1.10%.     

Influence of Transverse Magnetic Field on Heat Transport Characteristics of Potassium Heat Pipe

The influence of a transverse magnetic field on the heat transport characteristics of a potassium heat pipe was experimentally studied in the range of field strength 0~0.6 T. The wick was constituted of a multilayer mesh screen, and the adiabatic section, to which the magnetic field was applied, was made up of a concentric double-wall rectangular tube, with the inner wall completely separating the vapor and liquid flows.

The magnetic field was applied perpendicularly to the heat pipe, upon which the axial temperature distribution of the heat pipe was observed to be affected, and the heat transport rate to be reduced with increasing field strength.

The effect of the magnetic field on the heat transport rate is analyzed in terms of the liquid pumping ability of the wick and of the magnetohydrodynamic (MHD) effect on the liquid flow through the wick. The MHD effect on the flow through wick is shown to be expressible by a formula similar to that for flow between parallel plates.

The heat transport rate measured in magnetic field are compared with values calculated assuming that the wick pumping ability was not influenced by the magnetic field but that it was the MHD effect on the liquid flow through the wick that affected the heat transport. The calculated results well explained the experimental data.