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