Introductory FLUENT Notes Fluent User Services cente ANSYS LUENT v6. 3 December 2006 wwfluentusers. com FLUENT RANS Modeling- Time Averaging Ensemble(time)averaging may be used to extract the mean flow properties from the instantaneous ones n(x)=mN∑x) l(x,) (x, t) (x) l4(x,)=l(x,)+(xt) Example: Fully-Developed Ins tantaneous Time-average fluctuating Turbulent Pipe Flow component component component Velocity profile he Reynolds-averaged ntum equations are OWS 0|,Dl t ax ax. a (Reynolds stress tensor) The Reynolds stresses are additional unknowns introduced by the averaging procedure, hence they must be modeled (related to the d flow quantities) order to close the system of governing equations C 2006 ANSYS. nc All ANSYS, Inc. Proprietar© 2006 ANSYS, Inc. All rights reserved. 6-7 ANSYS, Inc. Proprietary Fluent User Services Center www.fluentusers.com Introductory FLUENT Notes FLUENT v6.3 December 2006 RANS Modeling – Time Averaging ◆ Ensemble (time) averaging may be used to extract the mean flow properties from the instantaneous ones: ◆ The Reynolds-averaged momentum equations are as follows ⚫ The Reynolds stresses are additional unknowns introduced by the averaging procedure, hence they must be modeled (related to the averaged flow quantities) in order to close the system of governing equations. ( ) ( )  ( ) = → = N n n i N i u t N u t 1 , 1 x, lim x u ( t) u ( t) u ( t) i i i x, = x, +  x, Fluctuating component Time-average component Example: Fully-Developed Turbulent Pipe Flow Velocity Profile u ( t) i x, u ( t) i  x, Instantaneous component Rij ui uj = −   j i j j i k i j i k i x R x u x x p x u u t u   +              +   = −           +    (Reynolds stress tensor) u ( t) i x