Numerical Simulation of Friction and Heat Exchange in Viscous-Gravitational Fluid Flow in a Loop Thermosiphon

Numerical simulation of velocity and temperature fields with laminar liquid flow in a laboratory experimental loop thermosiphon (natural circulation loop) has been made. A vertical electrically heated pipe served as a lift section. Calculations were carried out for the case of heating the entire length of the pipe under conditions of constant heat flux density on the wall. The construction of the loop is considered, in which local pressure losses and friction losses of pressure in the descending pipe are negligibly small in comparison with friction losses of pressure in the ascending section.

The object of the analysis is the laminar mode of flow. In this regime, in the flows originating exclusively under the action of thermogravitational forces, the skin-friction coefficient varies in the most sophisticated way along the flow. Using the results of calculation of velocity and temperature fields, the longitudinal changes of the skin-friction coefficients and of heat transfer coefficients are determined. As a whole, according to the results of 2D numerical simulation, the skin-friction coefficients depend in the main on the change of the velocity gradient on the wall along the flow as a result of practically continuous rearrangement of velocity profile along the entire heating zone. The form of the velocity profiles and the degree of their deformation depend in turn on the heat flow density on the wall and on the hydraulic diameter. It is shown that in a single-phase loop of natural circulation (i.e., under conditions where the liquid moves exclusively under the action of thermogravitational forces) the shear stresses on the wall change along the heating zone in a complex way, and the skin-friction coefficient cannot be described by the simple dependence of the form ξ = a/Re^b for being used in one-dimensional calculations. In all of the calculated regimes, including the one with the least (of those considered) heat flux density on the wall, the Nusselt numbers exceeded the stabilized values under the conditions of forced flow with constant thermophysical properties. With increase in distance from the entrance into the zone of heating, the Nusselt numbers first decrease monotonically, attain minimum values, and then begin to increase.