Turbulent stratified open channel flow with solar heating up to Pr=7 using Direct Numerical Simulation

This paper investigates the turbulent structure of stratified open-channel flow subjected to a radiative volumetric heat source modelled by the Beer–Lambert law, for Prandtl numbers ($Pr$) varying from 0.07 to $Pr=7$. Direct Numerical Simulation (DNS) was employed to model the open-channel flow. To overcome the increased computational resources required to resolve the thermal fields when $Pr>1$, a multi-resolution method using quadratic interpolation was employed to resolve the temperature and momentum fields on different spatial and temporal resolutions. This scheme was implemented in an in-house computational fluid dynamics (CFD) code. To further reduce the computation cost, the DNS of $Pr=2.2$ and 7 fluids were initialised using the outputs of minimal channel simulations. The simulations were conducted for $Pr=0.07$, 0.22, 0.71, 2.2, and 7 under neutral ($\lambda =0$), near-neutral ($\lambda =0.1$), and stable ($\lambda =0.5$) thermal stratification. The results demonstrate that $Pr$ significantly affects the flow structure and turbulence characteristics of stratified flows, particularly near the free surface. This includes higher velocity, temperature gradient, and buoyancy effects for $Pr=7$ compared to lower $Pr$ values. For stratified $Pr=7$ flow, examination of the Reynolds stresses and turbulent heat flux reveals significant damping of turbulence near the surface, with flow displaying near-laminar behaviour.