Refined Reynolds analogy for particle-laden compressible turbulent channel flow

The Reynolds analogy is revisited and the van Driest equation is established for fully developed particle-laden compressible turbulent channel flow (CTCF). A correction function is introduced into the classical approximate solution of the van Driest equation based on numerical observations. The refined Reynolds analogy is validated in both single-phase and particle-laden CTCFs. The newly proposed mean temperature–velocity relation agrees very well with numerical results. The turbulence modulation caused by inertial particles in CTCF is also studied through two-way coupling point-particle direct numerical simulation. Similar to its incompressible counterpart, the mean velocity of background flow is unchanged in the presence of inertial particles. However, it is discovered that the mean temperature of background flow is attenuated due to the interplay between carrier flow and adiabatic particles. The temperature attenuation rate (TAR) is employed to describe this phenomenon, which is defined as the integral of mean temperature profile with respect to mean velocity normalized by the product of wall temperature and central mean velocity. The numerical results manifest that the inertial particles can cause considerable temperature attenuation across the channel. It is further found that the Reynolds analogy and recovery factors are reduced by inertial particles. The refined Reynolds analogy can reproduce the TAR obtained from numerical simulations. In addition, the energy transfer analysis reveals that the temperature attenuation caused by the motion of adiabatic particles is mainly attributed to the suppression of turbulent dissipation.