Control Valve Characteristics

The valve’s flow characteristic is the relationship of the change in the valve’s opening to the change in flow through the valve. In general, the flow through a control valve for a specific fluid at a given temperature can be expressed as

where  Q= volumetric flow rate

            X= valve stem position
            P₀= upstream pressure
            P₁= downstream pressure

Lets us express the following quantities:

where  Q = flow rate
Q_max = maximum flow rate
X = stem position
X_max = maximum stem position

The types of valve characteristics can be defined in terms of the sensitivity of the valve, which is the fractional change in flow to the fractional change in stem position for fixed upstream and downstream pressures. Mathematically control valve sensitivity may be expressed as:

Depending on value of can be decreasing, linear or increasing the valve characteristics can be quick opening, linear, and equal percentage respectively.

The quick-opening valve is predominantly used for on/off control applications. A relatively small movement of the valve stem causes the maximum possible flow rate through the valve. For example, a quick-opening valve may allow 85 percent of the maximum flow rate with only 25 percent stem travel.

The linear valve has a flow rate that varies linearly with the position of the stem. This relationship can be expressed as follows:

where ‘α’ is constant.

The equal percentage valve is manufactured so that a given percentage changes in the stem position produces the same percentage change in flow. Generally, this type of valve does not shut off the flow completely in its limit of travel. For an equal-percentage valve, the defining equation is

Here ‘β’ is constant.

Here q₀ is the flow at x=0.

At x = 1, q=1,

Q_min represents the minimum flow when the stem is at one limit of its travel. At the fully open position, the control valve allows a maximum flow rate, Qmin. So we define a term called Rangeability (R) as the ratio of maximum flow (Qmax) to minimum flow (Qmin):

The curve in Figure 4 shows a typical equal percentage curve that depends on the rangeability for its exact form. The curve shows that increase in flow rate for a given change in valve opening depends on the extent to which the valve is already open. This curve is typically exponential in form and is represented by: