Use of Simplified Mathematical Formulations in Multi-phase Thermal Pump (MPTP) for Theoretical Prediction of Working Conditions

Abstract

In this work mathematical expressions have been formed and solved to get predictions of working parameters of multi
phase thermal pump (MPTP). MPTP is a simple pump which uses steam to pump water. The results have been compared
with data found experimentally. Experimental and theoretical values for a range of pressures versus velocity differed by
approximately 8.7% up 12% Through dimensional analysis dimensionless parameters were found Re, Eu, Fo and h/d pmp .
These helped to further elucidate the pump’s pumping phenomenon. It was experimentally shown that the Reynolds
number found theoretically gave limit of flow operating regime of the pump that it is in the transition regime. Above this
the pump failed to operate. The Euler dimensionless number gave the dependency of interface velocity on pressure
relation, when pressure was raised the velocity increased. The relation between the two parameters was found to be
approximately quadratic. The Fourier dimensionless number gave the influence of heat transfer properties of the
material of the pump to the operating characteristics. It was experimentally found that the influence of the overall heat
transfer coefficient and heat transfer were the main driving forces behind the operation of the pump. Average interface
velocities in the pump were found using pipe flow energy and mass conservation equations. Conditions for operation
(pumping and suction) of the pump have been established based on the formed mathematical formulations.