Modelling of heat addition to near-critical and supercritical fluids

Abstract

Abstract This work presents a coupled flow model to describe heat addition to near-critical and supercritical fluids. In a first approximation only forced convection is considered, while buoyancy forces, viscous and volume expansion losses are neglected. The steady, one-dimensional balance equations are solved simultaneously through an iterative procedure, taking into account real gas effects. The analysis shows that the intrinsic high compressibility of near-critical fluids strongly reduces the region of validity for the incompressible flow assumption. Indeed, depending on the initial conditions, compressible flow effects may occur at Mach numbers below 0.1. For a given mass flux, the occurrence of heat transfer deterioration (HTD) correlates directly with the maximum amount of heat ( $$Q_{max}$$ ) that a compressible flow can absorb at a specific local Mach number. For near-critical fluids, $$Q_{max}$$ depends upon two parameters, namely the heat flux to mass flux ratio and the thermal dilatation. The latter induces not only the early inception of compressibility effects, but it also poses an additional volumetric constraint to $$Q_{max}$$ . Indeed, in confined flows the enhancement of the thermal dilatation parameter strongly limits the capability of the flow to increase the local mass flux by expanding the flow, which eventually decreases the $$Q_{max}$$ value. These findings provide a generalization of the well-known dependence of $$Q_{max}$$ upon the local Mach number for an ideal gas. The local enhancement of the thermal dilatation also explains the counterintuitive cooling of the fluid upon heat addition. Overall, our analysis advocates for a more comprehensive flow analysis in the design of regenerative cooling systems.