Density in NS equation
 

Hello Friends,

I have a question (which I got during my presentation). I am doing LES of water mixing in a T-junction with high ΔT. Hot and cold fluid temperatures are 415 K and 298 K respectively. Pressure is 30 bar. The flow is incompressible. Continuity, Navier-Stokes and Energy equations are attached in the picture. < > represents filtering process for LES in the equations. The question is
(i) Where should density symbol (ρ) be placed (inside the differential bracket or outside it), and why?
(ii) Why shouldn't the density symbol be placed inside the filtered bracket, ex: <ρ> as it is not constant?

FYI: The relative density difference, Δ ρ/ ρ is calculated to be 5%. I am using IAPWS library in my simulations and If I understood correctly, this accounts for change of properties like density, viscosity etc. with temperature, right?

Thanks in advance.

Regards,
Karthick

If you are modelling it incompressible then density is constant. The buoyancy is modelled as a source term - it does not change density. If you want to have varying density then you need to use a full compressible model, but the run times will increase.

IAPWS material properties includes density, viscosity, Cp versus temperature.