Unsteady Heat Transfer Analysis of an Impinging Jet

Unsteady heat transfer caused by a confined impinging jet is studied using direct numerical simulation (DNS). The time-dependent compressible Navier-Stokes equations are solved using high-order numerical schemes together with high-fidelity numerical boundary conditions. A sixth-order compact finite difference scheme is employed for spatial discretization while a third-order explicit Runge-Kutta method is adopted for temporal integration. Extensive spatial and temporal resolution tests have been performed to ensure accurate numerical solutions. The simulations cover several Reynolds numbers and two nozzle-to-plate distances. The instantaneous flow fields and heat transfer distributions are found to be highly unsteady and oscillatory in nature, even at relatively low Reynolds numbers. The fluctuation of the stagnation or impingement Nusselt number, for example, can be as high as 20 percent of the time-mean value. The correlation between the vortex structures and the unsteady heat transfer is carefully examined. It is shown that the fluctuations in the stagnation heat transfer are mainly caused by impingement of the primary vortices originating from the jet nozzle exit. The quasi-periodic nature of the generation of the primary vortices due to the Kelvin-Helmholtz instability is behind the nearly periodic fluctuation in impingement heat transfer, although more chaotic and non-linear fluctuations are observed with increasing Reynolds numbers. The Nusselt number distribution away from the impingement point, on the other hand, is influenced by the secondary vortices which arise due to the interaction between the primary vortices and the wall jets. The unsteady vortex separation from the wall in the higher Reynolds number cases leads to a local minimum and a secondary maximum in the Nusselt number distribution. These are due to the changes in the thermal layer thickness accompanying the unsteady flow structures.