Turbulence modeling

Turbulence modeling must be carefully assessed, starting with cases where the analytical theory allows to be quantitative. The first test case is a turbulent channel.

turbulent channel
Stream-wise velocity (sides) and wall-shear stress (top) of turbulent flow between two parallel plates SC13 Research Highlight: Petascale DNS of Turbulent Channel Flow

Turbulent flow between two parallel plates, Reynolds=10 000

The first turbulent channel is defined in the POF article of Moser: Robert D. Moser, John Kim, and Nagi N. Mansour. “Direct numerical simulation of turbulent channel flow up to Reτ = 590”. In: Physics of Fluids 11.4 (1999), pp. 943–945.

Coarse mesh – regular
Shape LxHxWπH/2 x H x 0.289πH/2
Dimensions LxHxW0,314 x 0,2 x 0,09 m
Resolution Dx0,001m
Cells5,652 Millions (1314x200x90)
Turbulent flow between two parallel plates
Domain Height0.2
Density1.1608 Kg/m3
Temperature300 Kelvins
Pressure10^5 Pascals
Bulk Reynolds10 000
Bulk Velocity1,61268091 m/s
Skin Friction coef.5.908e-3
Tau wall8,92E-03
Forcing term0,089179448 kg/m2/s2
friction Reynolds5,44E+02

Turbulent atmospheric boundary layer – Reynolds > 300 000 000

This second test comes fromLarge eddy simulation study of fully developed wind-turbine array boundary layers, Physics of Fluids 22, 015110 (2010); Marc Calaf, Charles Meneveau, and Johan Meyers.

Coarse mesh – regular
Shape LxHxW11H x H x 0.31H
Resolution Dx10m
Cells34.1 Millions (1100 x 100 x 310)
Atmospheric boundary layer
Domain Height1000m
Density1.1608 Kg/m3
Temperature300 Kelvins
Pressure10^5 Pascals
Bulk Reynolds3,63E+08
Bulk Velocity5,85 m/s
Skin Friction coef.1,25E-02
Tau wall2,48E-01
Forcing term0,000248284 kg/m2/s2
friction Reynolds2,87E+07

Article originally written by Antoine Dauptain (CERFACS), research scientist focused on computer science and engineering topics for HPC.