Tdyn reference manual


Near wall-modelling

In wall-attached boundary layers, the normal gradients in same flow variables become large as the wall distance reduces to zero. A large number of mesh points packed close to the wall is required to resolve these gradients. Furthermore, as the wall is approached, turbulent fluctuations are suppressed and eventually viscous effects become important in the region known as the viscous sub-layer (see Figure 35). This modified turbulence structure means that many standard turbulence models are not valid all the way through to the wall. Thus special wall modelling procedures are required.

Figure 34. Boundary layer regions.

In order to overcome the above-mentioned limitations, Tdyn incorporates several wall functions models. The difficult near-wall region is not explicitly resolved with the numerical model this way, but is bridged using so-called Law of the Wall functions (see Figure 35). In order to construct these functions the region close to the wall is characterized in terms of variables rendered dimensionless with respect to conditions at the wall.

Figure 35. Law of the wall approximation (right).

The wall friction velocity uτ is defined as (τw)1/2 where τw is the wall shear stress. Let y be normal distance from the wall and let U be time-averaged velocity parallel to the wall, Then the dimensionless velocity, U+ and dimensionless wall distance, y+ are defined as U/uτ and y·ρ·uτ/μ respectively. If the flow close to the wall is determined by conditions at the wall then U+ can be expected to be a universal (wall) function of y+ up to some limiting value of y+. This is indeed observed in practice, with a linear relationship between U+ and y+ in the viscous sub-layer, and a logarithmic relationship, known as the Law of the Wall, in the layers adjacent to this (so-called log-layer). For rough walls, this law of the wall must be modified by scaling y on the equivalent roughness height, zo (i.e. y+ is replaced by y/zo), and also by adjusting the coefficients. The y+-limit of validity depends on external factors such as pressure gradient and the penetration of far field influences. In some circumstances the range of validity may also be affected by local influences such as buoyancy forces if there is strong heat transfer at the wall.

The standard wall functions are valid for smooth walls, but can be modified to take into account roughness effects by adjustment of the constants in the Law of the Wall. If a rough wall is being modelled the wall distance in the Law of the Wall is non-dimensionalised with an equivalent roughness height. Tdyn includes a specific Law of the Wall model to take into account this effect (see RoughWall field).

These universal functions can be used to relate flow variables at the first computational mesh point, displaced some distance y from the wall, directly to the wall shear stress without resolving the structure in between.

Standard Law of the Wall functions are one of the biggest sources of misconceptions in turbulent flow computations, even for experienced users. Their purpose is to bridge the extremely thin viscous layer near the surface. They do not free the user from the need to adequately resolve the turbulent portion of the boundary layer.

The following constraints should be observed when using wall functions: