Component 513: Mixing Dampers and Merge by HVACSIM+
General Description
Component 513 represents a pair of mixing dampers, mechanically linked
so that one damper opens as the other closes. The first inlet is closed when
the input control signal, C, is zero, and open when C is one. The reverse is
true for the second inlet. Hysteresis effects and an actuator time constant
are not included in the model.
Flow resistances are calculated in the same manner as in the Component
506 damper or valve model. For a discussion of damper characteristics and
recommended parameter values, see section 4.5 of reference [1].
Component 513 takes three pressures as inputs and calculates three flow
rates. In this respect, it is similar to Component 510 flow split and
Component 511 inlet conduit, both of which also compute an inlet flow rate
rather than an inlet pressure.
Nomenclature
C - control signal (0 <= C <= 1)
Ko - flow resistance coefficient when damper is open
P - pressure
R - flow resistance as a function of damper position
T - temperature
w - mass flow rate
Wf - weighting factor for linear term of flow resistance
Subscripts
1 - first inlet
2 - second inlet
3 - outlet
Mathematical Description
R1 and R2 are the flow resistances of the two inlets:
R1 = {(Wf*Ko) / [(1 - y)*C + y]^2} + (1 - Wf)*Ko*y^(-2*(1 - C))
R2 = {(Wf*Ko) / [(1 - y)*(1 - C) + y]^2} + (1 - Wf)*Ko*y^(-2*C)
These equations model linear damper characteristics when Wf is one, exponential
characteristics when Wf is zero, and intermediate characteristics for
intermediate values of Wf. These flow resistances are used to find two of the
three flow rates:
w1 = sign(P1 - P3)*[|P1 - P3| / R1]^0.5
w2 = sign(P2 - P3)*[|P2 - P3| / R2]^0.5
The third flow rate is the sum of the first two:
w3 = w1 + w2
The outlet temperature is a weighted average of the two inlet temperatures:
T3 = (w1*T1 + w2*T2) / w3
Component 513 Configuration
Inputs Description
1 P1 - pressure at first inlet
2 P2 - pressure at second inlet
3 P3 - pressure at outlet
4 T1 - temperature at first inlet
5 T2 - temperature at second inlet
6 C - input control signal
Outputs Description
1 w1 - flow rate at first inlet
2 w2 - flow rate at second inlet
3 w3 - flow rate at outlet
4 T3 - temperature at outlet
Parameters Description
1 Ko - full open resistance (0.001/(kg-m))
2 y - leakage parameter ( - )
3 Wf - weighting factor for linear term of
flow resistance ( - )
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