CFD Online Discussion Forums

Exactly. Expanding on other posts here I present the following:

I.) Motivation and Situations A.) 2-equation model B.) Wall bounded-flows C.) Need B.C.'s for velocity, k, and D.) Many 2 eqn. models fail to predict the law of the wall constant, C, satisfactorily E.) Consequently one CANNOT apply no-slip B.C., integrate through the viscous sublayer (y --> 0), and expect to yield satisfactory results for predicting the log-layer solution

II.) One method for 2-Equation Wall Treatment is the use of wall functions ("a matching procedure") – HIGH REYNOLDS APPROACH -- Simply matching to the law of the wall using a suitable value of C

WALL FUNCTIONS III.) "Law of the Wall" as the Constitutive Relation A.) Generally, it is a constitutive relation between velocity and shear stress 1.) The velocity we are focusing on is that for the "matching point" 2.) "Matching point" relates to the mesh point closest to the surface or the first point outside the viscous sublayer. B.) More specifically, it is a transcendental equation for the friction velocity and hence shear stress (see Turbulence Modeling textbooks like that of Wilcox) C.) Assumptions to wall functions 1.) constant pressure boundary layer 2.) incompressible boundary layer 3.) far from the case of internal combustion engine flows!!!

IV.) a.) It's empirical b.) Near wall cell placement 1.) Placed in regions where the underlying hypothesis of the 2-eqn. models are satisfied 2.) In the log-law region where turbulent Reynolds number is > 150

=== Why Wall Functions Need to Be Used With Caution === A.) Assumptions to wall functions do not hold for many practical flows 1.) constant pressure boundary layer 2.) incompressible boundary layer

B.) Cannot predict the computational domain to fit the high Reynolds number approach in complex flows 1.) High Reynolds number approach requirement y+ between 30 and 100 inclusive 2.) Those velocities are tough to predict --> tough to predict proper grid resolution 3.) Even if local velocity measurements were available, it is not feasible to satisfy the high Reynolds number requirement a.) Complex flows --> wide range of velocities throughout domain b.) Separation, curvature, rotation, or stagnation points occur throughout the domain c.) Even if alternative formulations of wall functions are used, they cannot escape the strongest limitation of wall functions i.) Namely, that is the evaluation of y+ based on friction velocity ii.) In complex flows (e.g., separated and recirculating flows), friction velocity varies locally throughout the domain iii.) In separated flow, fric. vel. changes sign!!! iv.) The changeover of sign of fric. vel. implies it is less than or equal to zero. Also note that omega and epsilon in the 2 eqn. models are odd functions of fric. vel. and omega and epsilon are positive definite quantities. v.) A neg. fric. velocity --> y+ < 0 which is clearly not feasible

C.) Turbulence anisotropy which characterizes near boundary regimes are neglected as well -- Significant lack of accuracy

D.) Very sensitive to the choice of the first grid point from the wall 1.) Calculations of Pattjin, S., "Niet lineaire, laag-Reynolds, tweevergelijkingen turbulentiemodellen", Ph.D. Thesis, Universiteit Gent, 1999. 2.) He/she mentioned that the first grid point must be located at y+ between 40 and 50 inclusive to get agreement with DNS-data 3.) y+ > 50 can lead to discrepancies

E.) Therefore wall functions provide totally nonsense results for complex flows -- more accurate alternatives are the low-Reynolds and two-layer approach for these cases