Component 515: Three-Way Valve with Actuator by HVACSIM+
General Description
This component represents a valve with two inlet ports and one outlet
port. The position of the valve is determined by an input control signal, C.
Port 1 of the valve is closed when C=0 and open when C=1. The sixth parameter,
MODE, determines the inherent characteristics of the two inlet ports. If
MODE=0, both ports are linear. If MODE=1, port 1 is exponential (equal
percentage) and port 2 is linear. If MODE=2, both ports are exponential. As
discussed in section 4.0 of reference [1], the actual behavior of the valve
model in a system simulation will depend on the valve's authority over the
system.
Nomenclature
C - requested relative valve position (0 < C < 1)
Ca - relative actuator position (0 <= Ca <= 1)
Ch1 - relative opening of port 1 (0 <= Ch <= 1)
Ch2 - relative opening of port 2 (0 <= Ch <= 1)
hys - fraction of actuator's range over which Ch remains constant when
actuator's direction of travel reverses
K1 - flow resistance parameter for inlet port 1,
when port 1 is open (Ch=1)
K2 - flow resistance parameter for inlet port 2,
when port 2 is open (Ch=0)
MODE - determines port 1 / port 2 inherent characteristics:
0 => linear / linear
1 => exponential / linear
2 => exponential / exponential
w1 - mass flow rate at inlet port 1
w2 - mass flow rate at inlet port 2
w3 - mass flow rate at outlet port 3
y - leakage parameter: fractional leakage when DeltaP = 1.
Toll - actuator time constant
Mathematical Description
The relationship between the input control signal, C, and the actuator
position, Ca, is defined by:
d(Ca)/dt = (C - Ca) / Toll
This differential equation is solved by MODSIM, the main HVACSIM+ program,
unless the time constant, Toll, is less than one second, in which case the
following solution is used:
IF (Toll/Deltat) < 0.05 OR | Css - C- | < 10^(-10) THEN
Ca = C
ELSE
Ca = C - (C - Ca-)*exp(-Deltat/Toll)
where Ca- is the value of Ca one time step ago.
The actuator position differs from the valve position due to hysteresis
effects, which are determined by the utility function HYSTER (described in section 3.2 of reference [1]).
Ch1 = HYSTER(Ca, hys)
Ch2 = 1. - Ch1
The outlet flow rate is the sum of the inlet flow rates, and the outlet
temperature is a weighted average of the inlet temperatures:
w3 = w1 + w2
T3 = (w1*T1 + w2*T2) / w3
Calculation of the inlet pressures depends upon the mode.
Mode = 0:
P1 = P3 + sign(w1)*K1*w1^2*[(1 - y)*Ch1 + y]^(-2)
P2 = P3 + sign(w2)*K2*w2^2*[(1 - y)*Ch2 + y]^(-2)
Mode = 1:
P1 = P3 + sign(w1)*K1*w1^2*y^(-2*Ch2)
P2 = P3 + sign(w2)*K2*w2^2*[(1 - y)*Ch2 + y]^(-2)
Mode = 2:
P1 = P3 + sign(w1)*K1*w1^2*y^(-2*Ch2)
P2 = P3 + sign(w2)*K2*w2^2*y^(-2*Ch1)
Component 515 Configuration
Inputs Description
1 w1 - mass flow rate, inlet port 1
2 w2 - mass flow rate, inlet port 2
3 P3 - pressure at outlet
4 T1 - temperature, inlet port 1
5 T2 - temperature, inlet port 2
6 C - input control signal (0 <= C <= 1)
7 Ca - actuator relative position
Outputs Description
1 Ca - actuator relative position
2 w3 - outlet mass flow rate
3 P1 - pressure at inlet port 1
4 P2 - pressure at inlet port 2
5 T3 - temperature at outlet
Parameters Description
1 K1 - port 1 flow resistance when port 1 is open
2 K2 - port 2 flow resistance when port 2 is open
3 y - leakage parameter
4 Toll - actuator time constant
5 hys - hysteresis parameter
6 Mode - determines characteristics of ports 1 and 2:
0 => linear / linear
1 => exponential / linear
2 => exponential / exponential
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