Advanced Building Simulation

38 de Wit
AIR TEMPERATURE STRATIFICATION
In the mainstream building simulation approach, it is assumed that the air temperature
in building spaces is uniform. This will generally not be the case, however. In naturally
ventilated buildings there is limited control over either ventilation rates or convective
internal heat loads. This results in flow regimes varying from predominantly
forced convection to fully buoyancy-driven flow. In the case of buoyancy-driven flow,
plumes from both heat sources and warm walls rise in the relatively cool ambient air,
entraining air from their environment in the process, and creating a stratified temperature
profile. Cold plumes from heat sinks and cool walls may contribute to this
stratification. Forced convection flow elements, like jets, may either enhance the
stratification effect or reduce it, depending on their location, direction, air stream
temperature, and momentum flow.
As in the case of the wind pressure coefficients, the simplified modeling approach
of the air temperature distribution in mainstream simulation introduces modeling
uncertainty. There is a difference however. Whereas the effect of the airflow around
the building on the ventilation flows is reduced to an empirical model with a few
coefficients, the effect of temperature stratification in a building space on heat flows
and occupant satisfaction is completely ignored. To be able to account for thermal
stratification and the uncertainty in its magnitude and effects, we will first have to
model it.
If we consider the current approach as a zero-order approximation of the spatial
temperature distribution, then it is a logical step to refine the model by incorporating
first-order terms. As vertical temperature gradients in a space are commonly dominant,
we will use the following model:
T air(z) � T air � �(z � H/2)
(2.3)
where Tair is the air temperature; Tair,
the mean air temperature; z, the height above
the floor; H, the ceiling height of the space; and �, the stratification parameter.
Dropping the assumption of uniform air temperature has the following consequences:
● the temperature of the outgoing air is no longer equal to the mean air temperature
as the ventilation openings in the spaces are close to the ceiling;
● the (mean) temperature differences over the air boundary layers at the ceiling and
floor, driving the convective heat exchange between the air and those wall components,
are no longer equal to the difference between the surface temperature
and the mean air temperature;
● the occupants, who are assumed to be sitting while doing their office work, are
residing in the lower half of the space and hence experience an air temperature
that is different from the mean air temperature.
With Equation (2.3) we can quantify these changes and modify the simulation model
to account for them. In most commercially available simulation environments this is
not feasible, but in the open simulation toolkit BFEP this can be done.
In the analysis we will assume that � in Equation (2.3) is a fixed, but uncertain
parameter. This means that we randomize over a wide variety of flow conditions in
the space that may occur over the simulated period. In, for examples, Loomans