Best Inherent Characteristic

Wide Range of Flow Set Point

Small Range of Flow but Large AP Change at Valve with Increasing Load

Proportional To Flow

In Series

Linear

Equal-Percentage

in Bypass*

Linear

Equal-Percentage

Proportional To Flow Squared

In Series

Linear

Equal-Percentage

In Bypass *

Equal-Percentage

Equal-Percentage

' Whan control valve closes. How rate increases m measuring element

Figure 10-14 Guidelines for control valve applications. (From Fisher Controls, 1987.)

single coefficient, resulting in the following equation for incompressible fluids:

This equation defines the flow coefficient, Cv. Here, SG is the fluid specific gravity (relative to water), pw is the density of water, and hv is the "head loss'' across the valve. The last form of Eq. (10-29) applies only for units of Q in gpm and hv in ft. Although Eq. (10-29) is similar to the flow equation for flow meters, the flow coefficient Cv is not dimensionless, as are the flow meter discharge coefficient and the loss coefficient (Kf), but has dimensions of [L3][L/M]1/2. The value of Cv is thus different for each valve and also varies with the valve opening (or stem travel) for a given valve. Values for the valve Cv are determined by the manufacturer from measurements on each valve type. Because they are not dimensionless, the values will depend upon the specific units used for the quantities in Eq. (10-29). More specifically, the "normal engineering" (inconsistent) units of Cv are gpm/ (psi)1/2. [If the fluid density were included in Eq. (10-29) instead of SG, the dimensions of Cv would be L2, which follows from the inclusion of the effective valve flow area in the definition of Cv]. The reference fluid for the density is water for liquids and air for gases.

The units normally used in the United States are the typical "engineering'' units, as follows:

Q = volumetric flow rate (gpm for liquids or scfh for gas or steam) SG = specific gravity [relative to water for liquids (62.3 lbm/ft3) or air at 60°F and 1 atm for gases (0.0764 lbm/ft3)] Pj = density at upstream conditions (lbm/ft3) P1 = upstream pressure (psia)

APv = total (net unrecovered) pressure drop across valve (psi)

Typical manufacturer's values of Cv to be used with Eq. (10-29) require the variables to be expressed in the above units, with hv in ft. [For liquids, the value of 0.658 includes the value of the density of water, pw = 62.3lbm/ft3, the ratio g/gc (which has a magnitude of 1), and 144 (in./ft)2]. For each valve design, tables for the values of the flow coefficients as a function of valve size and percent of valve opening are provided by the manufacturer (see Table 10-3, pages 318-319). In Table 10-3, Km applies to cavitating and flashing liquids and Cj applies to critical (choked) compressible flow, as discussed later.

a. Valve-System Interaction. In normal operation, a linear relation between the manipulated variable (valve stem position) and the desired

variable (flow rate) is desired. However, the valve is normally a component of a flow system that includes a pump or other driver, pipe and fittings characterized by loss coefficients, etc. In such a system the flow rate is a nonlinear function of the component loss coefficients. Thus the control valve must have a nonlinear response (i.e., trim) to compensate for the nonlinear system characteristics if a linear response is to result. Selection of the proper size and trim of the valve to be used for a given application requires matching the valve, piping system, and pump characteristics, all of which interact (Darby, 1997). The operating point for a piping system depends upon the pressure-flow behavior of both the system and the pump, as described in Chapter 8 and illustrated in Fig. 8-2 (see also Example 8-1). The control valve acts like a variable resistance in the piping system, that is, the valve loss coefficient Kf increases (and the discharge coefficient Cv decreases) as the valve is closed. The operating point for the system is where the pump head (Hp) characteristic intersects the system head requirement (Hs):

Pg g

where the last term in brackets is the head loss through the control valve, hv, from Eq. (10-29), and Cv depends upon the valve stem travel, X (see, e.g., Fig. 10-13):

A typical situation is illustrated in Fig. 10-15, which shows the pump curve and a system curve with no control valve and the same system curve with a valve that is partially closed. Closing down on the valve (i.e., reducing X) decreases the valve Cv and increases the head loss (hv) through the valve. The result is to shift the system curve upward by an amount hv at a given flow rate (note that hv also depends on flow rate). The range of possible flow rates for a given valve (also known as the "turndown" ratio) lies between the intersection on the pump curve of the system curve with a "fully open" valve (Qmax, corresponding to Cv max) and the intersection of the system curve with the (partly) closed valve. Of course the minimum flow rate is zero when the valve is fully closed. The desired operating point should be as close as practical to Qmax, because this corresponds to an open valve with minimum flow resistance. The flow is then controlled by closing down on the valve (i.e., reducing X and Cv, and thus raising hv). The minimum operating flow rate (Qmin) is established by the turndown ratio (i.e., the operating range) required for proper control. These limits set the size of the valve (e.g., the required Cv max), and the head flow rate characteristic of the system w 00

Table 10-3 Example Flow Coefficient Values for a Control Valve with Various Trim Characteristics

Linear

0 0