Advanced Building Simulation

New perspectives on CFD simulation 147
forced mixing of the HVAC system is eliminated, then the problem domain must
respond to the scale of each behavior, not of the building. The elimination of the dominant
mixing behavior should result in an aerodynamically quasi-calm core environment,
and therefore each thermal input will behave as an individually bounded
phenomenon (Popiolek 1993). Indeed, the growing success of displacement ventilation
strategies demonstrates that discrete buoyant behaviors will maintain their
autonomy if mixing flows are suppressed. As such, individual phenomena can be
explored accurately at length-scales relevant to their operative boundaries. Each
behavior operating within a specific environment thus determines the boundary
conditions and the length-scale of the characteristic variables.
Boundary conditions are the sine qua non of CFD simulation. In fluid flow, a
boundary is a region of rapid variation in fluid properties, and in the case of interior
environments, the important property is that of density. The greater the variation, the
more likely a distinct boundary layer will develop between the two states, and the
mitigation of all the state variables—pressure, velocity, density, and temperature—
will take place almost entirely within this layer. But a rapid variation in density is
problematic in continuum mechanics, and thus boundaries conceptually appear as a
discontinuity. In numerical and analytical models, boundary conditions provide the
resolution for these discontinuities. In buildings, the common assumption is that solid
surfaces are the operative boundaries and thus establish the definitive boundary conditions
for the simulation model. Solid surfaces establish but one of the typical
boundary conditions present—that of the no-slip condition (the tangential velocity of
the fluid adjacent to the surface is equal to the velocity of the surface, which for building
surfaces is zero). Much more complicated, and more common, are interface
boundaries and far-field boundaries. Interface boundaries occur when adjacent fluids
have different bulk properties, and as such, are dynamic and deformable. Far-field
boundaries occur when the phenomenon in question is small in relation to the
domain extents of the surrounding fluid (Figure 6.1).
In all types of buoyant flow, the temperature and velocity fields are closely coupled.
Velocities tend to be quite small such that the momentum and viscous effects are of
the same order. As a result, the outer edge along a no-slip surface’s boundary layer
edge may also be a deformable boundary, particularly if the ambient environment is
stratified or unstable. In free buoyant flow, and this is particularly so when there is a
quiescent ambient environment, one can consider that far-field boundary conditions
prevail. Within the major categories of buoyant flow—conventional, unstable, and
stable—any of the three types of boundary conditions may be present. Even for a
given flow, small changes in one of the variables may cause the flow to cycle through
different phenomena, and thus the same source might have different boundary conditions
at different times and at different locations. One of the more remarkable
properties of buoyant flows is that the key parameter for determining heat transfer—
the characteristic length (L)—is contingent upon the overall type of flow as well as
the flow phenomenon at that instant and that location. Just as the boundary conditions
are contingent, so too is the characteristic length and thus the heat transfer. This
is very different from forced convection, in which the length is a fixed geometric
entity. This contingency plays havoc with the simulation of boundary layer transfer,
so the majority of CFD simulations for indoor air environments will substitute empirically
derived wall functions for the direct determination of the boundary behavior.