Advanced Building Simulation

Node n
Figure 4.6 An example two zone connected system.
are the �v 2 /2 terms, and total pressure is defined to be the sum of static pressure and
dynamic pressure; that is, P � p � (�v 2 )/2. If nodes n and m represent large volumes
(e.g. a room), the dynamic pressures are effectively zero. If the nodes represent some
point in a duct or pipe network, there will be a positive dynamic pressure. Equation
(4.4) thus reduces to
�P � P n � P m � PS nm (Pa) (4.5)
where Pn, Pm are the total pressure at nodes n and m (Pa); and PSnm, the pressure
difference due to density and height differences across connection n through m (Pa).
Equations (4.4) and (4.5) define a sign convention for the direction of flow: positive
from point 1 to point 2 (or n to m). The flow within each fluid flow component
is described by a relation of the form m˙ � f(�P) . The partial derivatives needed
for the establishment of the Jacobian matrix (representing nodal pressure corrections
in terms of all branch flow partial derivatives) are thus related by
�m˙ /��Pnm ���m˙ /��Pmn. 4.2.2 Flow calculation
As an example of flow calculation, consider the power law component types (A, B,
or C). These flow components use one of the following relationships between flow
and pressure difference across the component:
Type A: m˙ � �a�P b
(kg/s)
Type B: m˙ � a�P b
(kg/s)
Type C: m˙ � a���P b
(kg/s)
z n
1
z 1
Integrated building airflow simulation 95
Reference height
Node m
(4.6a)
(4.6b)
(4.6c)
where is the fluid mass flow rate through the component (kg/s); a, the flow coefficient,
expressed in m3 /s Pab (type A), kg/s Pab (type B), (kg m3 ) 1/2 /s Pab m˙
(type C) �P,
the total pressure loss across the component (Pa); and b, the flow exponent.
2
z 2
z m