Evaluation of the possibility of equalizing the fluid temperature in a hydrolevelling system by mixing

Measurement systems that are based on the hydrostatic leveling method in ideal conditions allow one to control vertical displacements with accuracy of the order of one micrometer. Heterogeneous and time-varying environmental conditions have a significant effect on the measurement error. One way to reduce it is to equalize the temperature of the fluid in a hydrostatic level by mixing liquid inside it before taking measurements. In this paper, it is estimated that this operation can be performed by modeling the fluid circulation process in a simplified analog of the hydrostatic level taking into account a heat transfer through the hose wall. The fluid dynamics is described by the Reynolds averaged Navier-Stokes equations, which are closed by the SST turbulence model. The given analytical estimates of heat transfer coefficients on the side surface of the hose are refined on the basis of 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 conjugate heat transfer problem by the finite volume method. In the test example, in which two parts of the hydrostatic level are located in the areas with markedly different temperature, the heterogeneity of the temperature field at different times has been estimated. The mixing time sufficient to achieve a temperature close to the homogeneous distribution of the flowing fluid in the hydrostatic level is determined at different volumes of the mixer. The proposed approach can be used under real external conditions for the selection of optimal parameters of 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.