Mathematical model of fuel sloshing in the measuring channel of the fuel expenditure control system

Abstract

The problem of fuel sloshing in the measuring cylindrical channel of the system controlling fuel expenditure in the tank is considered in the paper. The system under consideration is a tank inside which there is a measuring channel in the form of a vertical cylindrical tube. The fuel level in the tank is recorded by the level sensors disposed within the measurement channel. It is known that the level of fuel in the tank does not match that in the channel. A mathematical model of fuel flow in the channel is constructed on the basis of parabolic equations of the heat-conduction type. The numerical solution of the model for the Crank-Nicolson scheme is presented. To confirm the results obtained by the model, the problem is solved with the help of full Navier-Stokes equations and the VOF model in the Ansys Fluid package. Construction of geometrical patterns and block grids in the ICEM CFD package is described. The problem is solved on grids differing in volume. The comparison of the results shows good agreement between them and indicates the presence of quasi-periodic oscillations of fuel in the channel. The inertia of the liquid column is the cause of the mismatch between the free surface level in the tank and that in the channel. When conditions change on the boundary, the response is late in the channel, causing vibrations. The results obtained suggest that the level sensors evenly spaced along the length of the channel will provide distorted information. The error is not systematic. The proposed model can be used to estimate the sloshing of liquid fuel in the measuring channels of fuel expenditure control system and for the development of more complex models.