The valve characteristic

The positions of the flow restrictors inside both globe and rotary valves depend on the action of a piston actuator, either directly or through a gear mechanism. As noted in Section 7.2, the stroke of this piston is called the valve travel . We have already given this the symbol, x, with the convention that 

The flow area will depend on the valve travel, with a characteristic dictated by the geometry of the plug and cage in a globe valve or by the detailed shape of the disc or notched ball in a rotary valve. Hence, in general, the valve opening is a function of the valve travel y = / (x). The geometrical basis for the valve characteristic means that the function, /, is applicable equally to liquid and gas flow. 

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

The equal percentage valve has the characteristic behaviour that equal increments of valve travel give rise to equal percentage increases in valve opening. We may describe this behaviour mathematically by the differential equation  

Substituting back into (7.28) allows us to write the relationship between valve opening, y, and valve travel, x, as  

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Relief Yalve normally selected for liquid relief service such as hydraulic systems, fire and liquid pumps, marine services, liquefied gases, and other total liquid applications. The valve characteristically opens on overpressure to relieve its rated capacity, and then reseats. 

In reality, the valve characteristic curve is likely nonlinear and we need to look up the technical specification in the manufacturer s catalog. After that, the valve gain can be calculated from the slope of the characteristic curve at the operating point. See Homework Problem 1.33 and the Web... 

The relation between the valve stem position and the flow through the valve at constant pressure drop is termed the valve characteristic. Two characteristics must be evaluated for valve selection, the inherent and the installed characteristics 67. ... 

Figure 2.63 illustrates the effect of the distortion coefficient (Dc) on the characteristics of a linear and an equal-percentage valve. As the ratio of the minimum to maximum pressure drop increases, the Dc drops and the equal-percentage characteristics of the valve shift toward linear and the linear characteristics shift toward QO. In addition, as the Dc drops, the controllable minimum flow increases, and therefore, the rangeability (the flow range within which the valve characteristic remains as specified) of the valve also drops. 

Final elements must provide the desired capacity with the required precision of flow throttling over the desired range, usually 10% to 95% of maximum flow. The valve characteristic should provide a linear closed-loop gain, except choose linear or quick-opening characteristics for valves that are normally closed but must open quickly. Select the valve failure position for safety. The valve body should satisfy such requirements as required flow at 0% stem position, plugging, pressure drop, or flashing. The nonideal final element behavior, such as friction and deadband, should be small, as required by each application. Control valves should have manual bypass and block valves to allow temporary valve maintenance when short process interruptions are not acceptable. However, the bypass should never compromise safety interlock systems. 

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. 

A steam trap is essentially a control valve and the valve characteristic is described by the Cy factor. How can one estimate steam trap losses via Cy factor Calculation steps are explained below... 

To do this, the first step is selection of which equation to use based on either choke flow or nonchoke flow. The second step is to apply the equation selected to calculate the steam flow according to Cy and then incorporate the flows into the valve characteristic table and expand it to Table 15.2. The last step is to develop a correlation for steam flow based on the valve position. 

For Steam Pressure Reduction Valve Letdown valves (PRV) are used to supplement steam demands at lower pressures for operational flexibility. Modeling of PRV is based on the valve characteristics, which are expressed in the general form... 

Cascade control also removes any control valve issues from the primary controller. If the valve characteristic is nonlinear, the positioner poorly calibrated or subject to minor mechanical problems, all will be dealt with by the secondary controller. This helps considerably when tuning the primary controller. 

Although a pH process is nonlinear, its characteristic curve cannot be corrected with an equal-percentage valve, because the valve acts on the output of the controller, not on the input. The valve characteristic, in fact, made matters worse. Sot only did the loop gain become variable, but it was higher than it would have been witli an cquivnlcnt linear valve. 

There essentially two major valve types one with a hnear characteristic and one with an exponential characteristic. One should keep in mind, however, that a hnear valve may not behave linearly when installed in a pipeline circuit. The flow rate is not determined solely by the valve characteristics, but also depends on the resistanee of the pipehne and the pump characteristics. It is therefore essential to evaluate the entire eincuitiy in which the valve is installed. Figure 31.14 shows how the pump pressure varies with the flow through the system. At F = 0 the pump head is APp o- The maximrrm flow without valve is F. The range of the valve covers only a part of the total possible range and varies from F ose. to F... 

Here q is the flow rate, f ) is the valve characteristic, APy is the pressure drop across the valve, and gg is the specific gravity of the fluid. This relation is valid for nonflashing liquids. See Edgar et al. (2008) for other cases such as flashing liquids. 

Specification of the valve size is dependent on the valve characteristic /. Three control valve characteristics are mainly used. For a fixed pressure drop across the valve, the valve characteristic/(O < / < 1) is related to the lift (0 < 1) that is, the extent of valve opening, by one of the following relations ... 

An alternative method for estimating Ky is to use the tangent to the valve characteristic curve (see Chapter 9). Now that all of the gains and the time constant in Fig. 11.16 have been calculated, we can calculate the closed-loop gain K and time constant T] in Eq. 11-41. Substituting these numerical values into Eqs. 11-38 and 11-39 for the three values of Kc gives... 

This matching of the valve characteristic to that of the process is only relevant if the operating point of the process does not vary over the whole range, i.e. it is not subject to large disturbances. In this case, there may be no way of matching the valve to the process if there is more than one variable that produces appreciable changes to the operating point. This is because the best characteristic for the compensation of the... 

The minimum flow often corresponds to maximum pressure drop and vice versa and these actual pressure drops are determined by system hydraulics (as discussed earlier). Also note that there are Cy corrections for viscous flow for cases where the valve Reynolds numbers are less than 5000. Finally, note that the valve characteristic type and rangeability should be checked, as detailed earlier. Although sizing equations in this sections use Fisher nomenclature, they are equivalent to ANSI/ISA versions if fI (where L signifies liquid) is substituted for Km-... 

In Equation 2.17,7 is an expansion factor (ratio of flow coefficient for a gas to that for a liquid) that plays a similar role to Ci, G is specific gravity and Z is a compressibility factor. Although the form of this equation seems much different than the Fisher one, the results are equivalent. Again, the valve characteristic type and rangeability should he checked. 

The flow Gout is determined by the valve characteristic VlXp), with Xp being the valve plug-stem expressed in per cent opening, the valve flow constant Cv, and the square root of the pressure drop across the valve as given in... 

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