d11

• Chris Nkinthorn, $\texttt{20190810}$

Prompt: Please discuss the relevance of having turbulence flow and heat transfer being modeled using RANS and LES approaches combined.

Discussion:

Reynolds Averaged Navier-Stokes (RANS) refers to application of a mean and transient component of the velocity field. These introduce Reynolds stresses which correspond to dispersion of turbulent kinetic energy (TKE). Application of TKE is dependent on the Komolgorov hypothesis of turbulent viscosity: quantification of the diffusion of momentum due to turbulent flow. This diffusive constant is a property of the flow: unlike the momentum's viscous quantity, $\mu$, is a property of the fluid. Large Eddy Simulation (LES) is used to track the fluctuating macro scale movement of energy and momentum. This allows for modeling of diffusion of TKE as eddies fall tiers until they approach isotropy. At which point, the mean shear disappears. It is the combination of both RANS and TKE to track the distribution of the conserved momentum quantity.

Response to:

Using this to respond (to my self): It is important to bring up the effect of periodicity in LES which quantified by the wave number . As mentioned, the diffusion of TKE is a flow property rather than a fluid property, quantified by . This additionally brings up the topic of the closure problem introduced in the application of RANS to LES.