Estimation of the Possibility to Equalize the Fluid Temperature in a Hydrolevelling System by Mixing

Abstract

Measurement systems that are based on the hydrostatic leveling method under ideal conditions allow one to determine vertical displacements with accuracy on the order of a micron. Heterogeneous and time-varying environmental conditions have a significant effect on the measurement error. One method to increase the accuracy of results is to equalize the temperature of the fluid in the hydrostatic level by mixing the liquid inside it before taking measurements. In this paper, the possibility to perform this operation by forced circulation of the fluid is estimated. For this purpose, a model problem of the circulation flow created by a pump in a simplified analog of the hydrostatic level with allowance for the heat transfer through the hose wall is solved. The fluid dynamics is described by the Reynolds averaged Navier-Stokes equations which are closed by the Menter shear stress transport model. The analytically obtained estimates of heat transfer coefficients on the lateral surface of the hose are refined based on experiments at two values of the flow rate of water flowing through the pipe. The evolution of the temperature field is found from the numerical solution of the coupled heat transfer problem by the finite volume method. In a test example, in which two parts of the hydrostatic level are located in areas with markedly different temperature, the spatial inhomogeneity of the temperature field at different times is calculated. The mixing time sufficient to achieve a temperature distribution close to the homogeneous distribution of the flowing fluid in the hose at different volumes of the mixer joint with the hydrostatic level is determined. The proposed approach can be used under real external conditions for the selection of optimal operation parameters: the pump flow rate, mixing time, and mixing tank volume. The temperature field obtained in the calculation can serve as a basis for estimating the achievable accuracy of the measurement system.