Advanced Building Simulation

148 Addington
Boundary layer
thickness
Temperature
profile
Velocity
profile
No-slip boundary condition Far-field boundary condition
Figure 6.1 Schematic representation of typical buoyant boundary conditions.
In the conventional HVAC system typically used for conditioning interior environments,
the length-scales resulting from forced convection are generally an order of
magnitude higher than the length-scales from buoyant convection and so buoyant
transfer can quite reasonably be approximated from wall functions. As soon as forced
convection is removed from the picture, the wall functions currently available are no
longer adequate.
Buoyancy forces also directly produce vorticity, and as such, buoyancy-induced
flows often straddle the transition point from one flow regime to the other. The precise
conditions under which laminar flow becomes unstable has not yet been fully
determined, but a reasonable assumption is that buoyancy-induced motion is usually
laminar at a length-scale less than one meter, depending on bounding conditions, and
turbulent for much larger scale free-boundary flow (Gebhart et al. 1988). As neither
dominates, and the transition flow is a critical element, then the simulation cannot
privilege one or the other. Much discussion is currently taking place within the field
of turbulence modeling for interior environments, but the point of controversy is the
choice of turbulence models: RANS (Reynolds Averaged Navier–Stokes) in which the
��� simplification is the most commonly used, or LES (Large Eddy Simulation).
Both of these turbulence models are semiempirical. In the ��� formulation, wall
functions must be used. LES numerically models the large turbulent eddies, but treats
the small eddies as independent of the geometry at-hand. With fully developed
turbulence at high Reynolds numbers, the boundary layers can be neglected and the
turbulence can be considered as homogeneous. Again, these turbulent models are