Component 209: Flow Split by HVACSIM+
General Description
This component models the division of a flow stream into two flow
streams. It calculates the mass flow rates at the two outlets, and the
pressure at the single inlet. The model assumes that the flow resistance
parameter is the same for all three branches. Care has been taken to ensure
that correct results are obtained even when the flow direction of one or more
flow streams is reversed.
Nomenclature
K - flow resistance coefficient
P - pressure
w - mass flow rate
Subscripts
0 - center of component
1 - inlet
2 - first outlet
3 - second outlet
Mathematical Description
The model is derived from the following set of equations:
P1 - P0 = 0.5*K*sign(w1)*w1^2
P0 - P2 = 0.5*K*sign(w2)*w2^2
P0 - P3 = 0.5*K*sign(w3)*w3^2
w1 = w2 + w3
where P0 is the pressure at the center of the component and 0.5*K is the flow
resistance between the center and an inlet or outlet. The set of equations is
solved for w2 and w3, and the solution is expressed in the following form:
w2 = (w1 / 2) + [sign(w1)]*DeltaP / (K*w1) if S >= 0.
w2 = (w1 / 2) + [sign(DeltaP)]*[abs(DeltaP)/K - w1^2/4]^0.5 if S < 0.
where
DeltaP = P3 - P2
and
S = w1^2 - 2*abs(DeltaP)/K
w3 = w1 - w2
When S is positive, all three flow rates have the same sign, and w1 represents
the single inlet (positive) or outlet (negative) flow rate of a split or merge.
When S is negative, w2 and w3 do not have the same sign, and w1 represents one
of two inlets (w1 positive) or outlets (w1 negative). The pressure at the
nominal inlet, P1, is then calculated:
P1 = P3 + (K/2)*[sign(w1)*w1^2 + sign(w3)*w3^2]
Component 509 Configuration
Inputs Description
1 w1 - flow rate at inlet
2 P2 - pressure at first outlet
3 P3 - pressure at second outlet
Outputs Description
1 w2 - flow rate at first outlet
2 w3 - flow rate at second outlet
3 P1 - pressure at inlet
Parameters Description
1 K - flow resistance coefficient
Reference:
1. HVACSIM+ Building Systems and Equipment Simulation Program Reference
Manual (NBSIR 84-2996)
Daniel R. Clark
United States Department of Commerce
National Institute of Standards and Technology
Gaithersburg, Maryland 20899-0001