A new wall function for indoor airflow with buoyancy effect

Convective heat transfer on interior surfaces of the building envelope is important for predicting building energy consumption. The buoyancy effect is a key factor in convective heat transfer. Reynolds-averaged Navier-Stokes (RANS) models combined with the standard wall function are often used to simulate the convective heat transfer coefficient of an interior wall. However, since the buoyancy effect is not considered in the standard wall function, the convective heat transfer is often underestimated, which in turn will affect the prediction of indoor air velocity and temperature distributions. Several researchers have modified the standard wall function by adjusting the wall Prandtl number, but this ad hoc adjustment has not always been effective and has no physical basis. This investigation developed a new wall function that accounts for the influence of buoyancy on heat transfer by adding a buoyancy source term to the Navier-Stokes equation for the near-wall region. The source term varies with the ratio of buoyancy and inertia forces and is linear to the logarithm of the Richardson number. Five typical indoor flows were then simulated with the new wall function to test its performance. The results show that the predicted profiles of air velocity and air temperature and the local Nu number were significantly better than those predicted with the standard wall function. The study concluded that the new wall function can correctly predict convective heat transfer on an interior wall.