Linear valve

The range of flow rates possible with the control valve can be estimated by inserting the linear valve trim [i.e., Cv max/(T) = 64X] into Eq. (10-33) and calculating the system curves for the valve open, half open, and one-fourth open (X = 1, 0.5, 0.25). The intersection of these system curves with the pump curve shows that the operating range with this valve is approximately 150-450 gpm, as shown in Fig. 10-17. 

Actual, inherent gain characteristics of linear valve... 

In order to stay within 25% of the theoretical valve gain, the maximum flow should not exceed 60% in a linear valve and 70% of full flow in an equal-percentage valve. In terms of valve lift, these flow limits correspond to 85% for an equal-percentage and 70% for linear valves. 

The gain components of a linear controller (plain proportional) and a linear transmitter (for temperature Gs = 100%/°F) are both constant. Therefore, if the process gain (Gp = °F/GPM) is also constant, a linear valve is needed to maintain the total loop gain at 0.5 (Gv = 0.5/GPGcGs = constant). 

FIGURE 19.14 (a) Inherent flow characteristics of valves at constant pressure drop (b) effective characteristics of a linear valve (c) effective characteristics of a 50 1 equal-percentage valve. 

Figure 19.14b and c give definite criteria for the amount of pressure drop the control valve should handle in the system. This pressure drop is not an arbitrary value, such as 5 lb/in2, but rather a percent of the total dynamic drop. The control valve should take at least 33 percent of the total dynamic system pressure drop if an equal-percentage valve is used and is to retain its inherent characteristics. A linear valve should not take less than a 50 percent pressure drop if its linear properties are desired. 

What size valve will be required to control the flow rate of 50 gaFmin (0.169 m /min) of brine (p = 1.2), if the frictional pressure drop in the system, excluding the valve, is 15 psi (1.03 bar) Assume a linear valve. 

For adequate process control, the pressure drop across the valve for a linear valve is... 

So far, the frictional head does not include the frictional pressure drop across the control valve. To insure good process control, the designer specifies the pressure drop across the valve. The pressure drop should be about 33% of the frictional pressure drop for a linear valve. 

For many process control applications it is possible that the pressure drop across the valve will have more effect on flow rate than will the valve position. The relationship between pressure drop and flow rate at constant valve position is the square-root expression for flow through an orifice. This relation introduces a nonlinearity in the control system which complicates the analysis of the system except insofar as it can be linearized. For equal-percentage valves the effect of changing pressure drop in the lift-flow characteristic of the valve is small, but for linear valves the effect is large. 

Figure 15.18 shows how7(x) varies with stem position for three types of valves a quick opening valve, an equal percentage valve, and a linear valve, where... 

FIGURE 15.20 Installed valve characteristics for a typical equal percentage (=%) valve and linear valve. 

But the relationship between state variables arising from different mathematical descriptions of the same process does not have to be linear. Let us assume that we wish to recast our equations in terms of valve openings rather than valve travels. This is a simple business for the linear valves I and 2, where fractional valve openings are identical with fractional valve travels (equations (2.6) and (2.7)). But the outlet valve has a square-law characteristic ... 

The two most common globe valve characteristics are the linear valve and the equal percentage valve. The linear valve has the characteristic... 

Linear valve, so valve opening, y = x, valve travel. Valve limiting gas conductance at valve travel, x, Cg =... 

This derivative may be found from the valve characteristic. For example, for a linear valve, dy,/dx = 1, while for a square-law valve, dy,/dx = 2x. 

An alternative approach, also shown in Figure 5.25, is the use of an equal percentage valve. This may be manufactured to behave in a specified nonlinear behaviour or it may be a conventional linear valve fitted with a positioner in which the engineer can define the valve... 

For a linear valve Cy is constant, but for an equal percentage valve... 

If the pressure drop across the valve exceeds the pressure drop across the rest of the process then it will change relatively little as the flow changes. A linear valve will then provide better linearity. If the pressure drop across the valve is relatively small then an equal percentage will perform better. But oversizing a linear valve has a more detrimental effect than oversizing an equal percentage valve so the latter is often chosen to provide more robust control as process conditions vary. 

Linear Valves. In a linear valve, the flowrate is proportional to the valve position. This is given by the relationship v = kz, where v is the volumetric flow and z is the vertical position of the disk or valve stem. 

The gain of a valve can be defined as the change in delivered flow vs. percent change in stem position. The gain of a linear valve is simply the rated flow under nominal process conditions at full stroke ... 

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