How to model a damper in a system simulation software tool as a control valve with an approximated flow coefficient profile.
Editor’s Note: Jeff Sines is a member of Ray Hardee’s team at Engineered Software Inc. This month, he is a guest columnist in Hardee’s place.

A damper is used extensively in the heating, ventilation and air conditioning (HVAC) industry as well as other industries that move air or compressible gases for their processes. A damper controls air flow throughout a duct system to evenly distribute air or gas. It operates by changing the size and shape of its flow path, so its flow capacity (or conversely, resistance) changes with position. This column describes how to model a damper in a system simulation software tool as a control valve with an approximated flow coefficient (Cv) profile. A damper specification datasheet is used as an example in this column.

Some damper manufacturers provide performance curves for their products. An example performance curve graph of pressure vs. air velocity is shown on the next page for fully open dampers of 16 inches, 24 inches and 36 inches.

This performance curve has velocity units in feet per minute and pressure drop in inches of water gauge. Some manufacturer curves may be in other units such as cubic feet per minute (cfm). The system simulation software needs the flow coefficient (Cv or Kv) at different throttling percentages in order to model the damper as a control valve. The first step is converting a set of data points (velocity and pressure drop) for the fully open position to a Cv value. The equation from the Crane Technical Paper TP-410 to be used to obtain the Cv values is shown as Equation 1.

Equation 1

Cv = W63.3FPYxP'1ρ1−−−−−√Cv = W63.3FPYxP1'ρ1

The equation can be re-arranged:

Cv = W63.3FPYdPρ1−−−−−√Cv = W63.3FPYdPρ1 Table 1. Calculate Cv and K from d (inches), volumetric flow rate (cfm), and dP (inches wc)

Where:
W = mass flow rate (lb/hr)
FP = piping geometry factor accounts for fittings attached to the valve
Y = expansion factor (between 0.667 at choked flow to 1.0 for no expansion)
x = pressure drop ratio dP/P'1
dP = pressure drop (psi)
P'1 = absolute inlet pressure (psia)
ρ1 = gas density (lb/ft3)

The next step is reading data from the performance curve and converting the units to accommodate the equation.

By entering the damper diameter and reading one value of dP at a select fluid velocity from the performance curve, the Cv can be determined. For example, the 36-inch damper has a pressure drop of 0.018 in water column (wc) at a velocity of 2,000 feet per minute (ft/min) air velocity. An expansion factor (Y) value of 1.0 is estimated in order to determine the Cv without considering the effect of gas expansion. The piping geometry factor (Fp) is assumed to be 1.0 to evaluate the performance of the damper without attached reducers or other fittings.

At 100 percent open, the damper has a calculated Cv of 143,649 (which corresponds to a resistance coefficient of about 0.07). Because this is an estimated value based on values taken from a curve, different points on the curve can be used to determine the Cv and an average can be defined.

Once the Cv is found, a control valve data estimator in a piping design software can be used to estimate a Cv profile for the damper. A sample control valve data estimator dialog box (Courtesy of the author)

In this example, a butterfly, center shaft body style was used with a trim type of aligned 60 degrees and equal percentage characteristic curve. Once the valve position of 100 percent and Cv value are entered, the system simulation software can estimate the remaining control valve data to fit the selected characteristic curve. Sample control valve data estimator dialog box

It will also enter an FL and xT profile based on typical butterfly valves shown in the International Electrotechnical Commission (IEC) and International Society of Automation (ISA) standards for sizing control valves.

It is important to understand that the damper performance is being estimated based on values taken from a log scale on the graph, the profile is assumed by the user, and the FL and xT values are based on typical tested valves. More accurate data should be obtained from the manufacturer or field measurements if possible.