Method of Temperature Correlations for Estimating the Large-Scale Circulation Rate in the Case of Turbulent Convection of Liquid Metals in an Inclined Cylinder

Abstract

The potentials of the temperature correlation method in determining the mean velocities of liquid metal turbulent flows are investigated. The method uses the signals from temperature sensors arranged in line in the direction of large-scale circulation motion. As distinct from other, more conventional techniques, this indirect method can be used in the measurements in melt metals, which represent aggressive opaque media. The method is based on the Taylor hypothesis of the temperature disturbance field freezing in the velocity field on a certain level of flow turbulence. By fixing the passage of such disturbances through temperature sensors it is possible to calculate the flow velocity. The flow in the actual setups is usually inhomogeneous and developed turbulence arises only locally in the cavity. For this reason, though the method is absolute and does not need calibration, its applicability should to be verified in each particular case. In this study the method is applied to the problem of turbulent convection of liquid sodium (Prandtl number Pr = 0.0083) in a cylinder, whose length is greater than its diameter by the factor of 5, heated from one end and cooled from the other. In the flow regimes considered the cylinder is inclined to the vertical by an angle β, 18° ≤ β ≤ 90°. The Rayleigh number based on the cylinder diameter was 5 × 10⁶. An analysis of the data of experimental investigations and three-dimensional numerical calculations is performed. In the latter case the flow velocity is known for a fact and can be directly compared with the estimates obtained using the cross-correlation analysis. It is shown that the method of temperature correlations not always allows one to adequately estimate the mean velocities of regular large-scale sodium flows, that is, has its own restrictions. The method performs well in the conditions of moderate turbulent fluctuations of the temperature and velocity. The greatest error of the method takes place near the heat exchangers in the flow direction: a demonstrative explanation of the reasons for this error is proposed with reference to this example. The nonlinear dependence of the large-scale circulation amplitude on the angle of inclination of the cylinder is obtained; it has a maximum near 45°. The location of the maximum of this dependence is different from that for the cylinder with the aspect ratio 20 (60°–70°).