Component 206: Damper or Valve by HVACSIM+
General Description
A damper or valve is essentially a variable fluid resistance. The
manner in which the flow rate varies with damper or valve position is known as
the damper or valve characteristic, or inherent characteristic. The inherent
characteristic is always measured in practice with a constant pressure drop
across the damper or valve. For a linear valve, for example, the flow rate is
directly proportional to the valve stem position when the pressure drop across
the valve is constant.
This model represents dampers or valves having inherent characteristics
which are linear, exponential, or intermediate between linear and exponential.
The characteristic is determined by the value of the third parameter, Wf. When
Wf is zero, the model represents an exponential valve or damper. When Wf is
one, a linear valve or damper is modeled. Intermediate values of Wf produce
intermediate characteristics.
The model computes the inlet pressure as a function of mass flow rate
and relative damper or valve position. A non-zero leakage parameter is
required to prevent infinite flow resistance when the damper or valve is fully
closed. Parameter values for modeling opposed leaf dampers and parallel leaf
dampers are given in the model validation section below.
It is important to distinguish between the inherent characteristic of a
damper or valve and the installed characteristic. The latter depends on both
the inherent characteristic and the authority of the damper or valve (as
discussed in section 4.0 of reference [3]). The installed characteristic of an
inherently linear valve is strictly linear only when the authority is one, that
is, when the valve represents the only pressure drop in the system. A valve
with low authority has little effect on the flow rate over most of its
operating range. When used in a system with other components, the Component
506 accurately models the effects of authority.
Nomenclature
C - relative position
K - flow resistance coefficient [0.001/ (kg-m)]
M - mode: M = 0 => damper closed when C = 0.
M = 1 => damper closed when C = 1.
P - pressure (kPa)
w - mass flow rate (kg/s)
Wf - weighting factor for linear term of flow resistance coefficient
y - leakage parameter: fractional leakage when DeltaP = 1 kPa.
Subscripts
o - full open
1 - inlet
2 - outlet
Mathematical Description
If M does not equal zero, then C = 1. - C
K = Wf*Ko / [(1 - y)*C + y]^2 + (1 - Wf)*Ko*y^(2C - 2)
P1 = P2 + sign(w)*K*w^2
K is the flow resistance as a function of C, the relative position
(0 <= C <= 1). The inherent characteristic of the damper or valve model is
determined by the parameter Wf. When Wf is zero, the model represents and
exponential valve or damper. When Wf is one, a linear valve or damper is
modeled. Intermediate values of Wf produce intermediate characteristics.
Model Validation
Reference [1] gives curves of dimensionless flow resistance versus
damper position for parallel leaf dampers and for opposed leaf dampers, which
are the two types of dampers most commonly used in HVAC control applications.
The above equation for K was converted to dimensionless form (as described in
section 4.0 of reference [3]), and a nonlinear regression program was used to
find values for the parameters Ko, y, and Wf which minimized the difference
between the above equation for K and the published curves. The following
values were obtained:
Opposed Parallel
2*p*A^2*Ko 0.52274 0.54205
y 0.01091 0.012214
Wf 0.61785 0.8689
Reference [2] contains curves of flow versus position at several authorities
for parallel leaf and opposed leaf dampers. As an independent check on the
model, a simulation was run with the inlet conduit model (Component 511) joined
to the Component 506 with the parameters given above, and the authority was
varied by varying the conduit resistance. For parallel leaf dampers, agreement
between the model and the published curves is excellent. For opposed leaf
dampers, the results are less dramatic, but better agreement might be obtained
by decreasing the leakage parameter used in the simulations.
Component 506 Configuration
Inputs Description
1 w - mass flow rate (kg/s)
2 P2 - outlet pressure (kPa)
3 C - relative position of damper or valve ( - )
Outputs Description
1 P1 - inlet pressure (kPa)
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 ( - )
4 M - mode: M = 0 => damper closed when C = 0.
M = 1 => damper closed when C = 1.
References:
1. Croome, J.D. and Roberts, B.M., Airconditioning and Ventilation of
Buildings. Pergamon Press Inc., p. 310, 1981.
2. Haines, Roger W., Control Systems for Heating, Ventilating and Air
conditioning. Van Nostrand Reinhold Company Inc., pp. 67-68, 1983.
3. 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