Exergy destruction due to mean flow and fluctuating motion in incompressible turbulent flows through a tube

The control volume method has been widely used to describe the rate of exergy destruction due to process irreversibility in a laminar fluid flow stream. In this work, we demonstrate that when the approach is applied to turbulent flows, and the fluid properties are based on averaged values, some information may be lost. We have applied the Reynolds time average method to the set of equations of exergy transfer for turbulent flows and found that the exergy destruction is mainly due to two factors, i.e. the mean flow dissipations and the fluctuating motion dissipations. As a case study, this result is used to model the incompressible turbulent flows through a duct with constant heat flux. The distributions of exergy destruction due to mean flow and fluctuating motion viscous dissipations as well as to mean flow and fluctuating motion heat transfer irreversibility in radial and in axis directions are obtained. The numerical solution of an example with water passing through the duct is obtained and the mechanisms of irreversibility analyzed. It is shown that for a given fluid, the total exergy destruction per unit length is a function of the geometrical parameters and the boundary conditions as well as the Reynolds number. It implies that the design of a thermal system can be optimized through minimizing the exergy destruction in the system.