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Dynamic Application and Analysis of Control Valve Pressure Recovery Coefficient FL in Engineering Design

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    In engineering design, it is necessary to select and calculate the control valve to achieve the purpose of stable control. However, it is difficult to consider FL in the selection and calculation of the control valve. This article will analyze the general laws of FL, and at the same time analyze the possible blocking flow conditions through examples.

    I. The Generation of Blocked Flow

    In the calculation formula of the flow coefficient Cv, the measuring pressure position of the inlet pressure P1, outlet pressure p2, pressure drop changes of the fluid passing through the control valve are shown in Figure 1.

    control valve pressure recovery coefficient fl
    Figure 1: control valve pressure recovery coefficient FL

    The pressure drop on the valve ΔP=P1-P2. According to the law of conservation of energy, the flow velocity is the largest and the pressure is the lowest at the fluid contraction, so the pressure drop is the largest, which is called ΔPvc=P1-Pvc. After the contraction, the fluid velocity decreases again until most of the static pressure at P2 is restored, at which time the pressure drops to ΔP.

    When the medium is a liquid, when the differential pressure is large enough, part of the liquid vaporizes at this operating temperature and flashing occurs. Steam is entrained in the liquid, resulting in a two-phase flow. The liquid is no longer incompressible. At this time, even if the differential pressure is increased, the flow rate will no longer increase. This limiting flow phenomenon is called liquid blocking flow.

    fl for control valve
    fl for control valve

    II. Specific analysis of FL

    a. Definition of FL

     FL=SqtΔPcr/ΔPvcr)=Sqt(P1-P2)/(P1-Pvc)  (1)

    In the formula, ΔPcr–valve pressure drop when blocking flow is generated, that is, the difference between the valve inlet pressure and the pressure of the contraction flow section when blocking flow, ΔPcr=(P1-P2)cr

    b. The meaning of FL

    FL is an experimental data that shows the recovery ability of the control valve to convert kinetic energy into static pressure energy after the liquid passes (see Figure 1), so it is called the pressure recovery coefficient, and it also shows the critical condition for the liquid to produce a blocked flow, also known as the critical condition. Flow Coefficient. The purpose of proposing FL is to determine whether a blocked flow occurs when the liquid passes through the control valve, and to calculate the maximum allowable pressure difference of the control valve.

    c. Judgment of blocked flow

    In theory, the relationship between the size of Pvc and Pv is used to determine whether a blocked flow is generated, but Pvc cannot be measured, so the differential pressure is used to judge in engineering calculations. Figure 2 shows the relationship between the flow through the control valve and the differential pressure.

    figure 2
    figure 2: flow capacity with differential pressure

    The maximum allowable differential pressure is defined as ΔPvc, and its calculation formula is:
    Δpc=FL2(P1-rcpv)     (2)

    rc

    Pv–liquid saturated vapor pressure at operating temperature;
    Pc–the critical pressure of the liquid.
    Once Δp is greater than Δpc, it indicates that the flow of liquid has been blocked.

    d: Factors that determine blocked flow

    From equation (2), once the operating conditions are determined, the maximum allowable differential pressure Δpc has a linear relationship with the square of FL. The generation of blocked flow has nothing to do with the size of the flow through the control valve and the diameter of the control valve.

    III. The general rule of FL value

    1. The size of the FL value is related to the structure, flow direction and opening of the control valve. In general, the larger the valve opening, the smaller the FL value. The FL value provided by the manufacturer refers to the value when the control valve is fully opened. …
    2. The FL value of the control valve with exactly the same geometric structure is the same, and has nothing to do with the caliber. For the same type of control valve, the FL is slightly different due to the different structure of each manufacturer. …
    3. Internationally renowned manufacturers provide the FL value of each series of control valves, and there are also recommended values in China. See Table 1~4 for details. Km=FL2 in Table 2.
    4. The general relationship between FL value and control valve form and opening. In general, the FL value of a linear control valve is larger than that of a rotary control valve, and the FL value decreases as the opening of the control valve increases. See Figure 5-5-8 on page 912 of “Petrochemical Automatic Control Design Manual” 3rd Edition.

    Table 1: Masoneilan single-seat control valve

    fl of control valves masoneilan 2
    fl of control valves masoneilan 2

    Note: 1 inch = 25.4mm.

    Table 2:  Fisher single-seat control valve

    fisher control valve fl
    fisher control valve fl

    Table 3:  Neles V-port ball valves

    v port ball valves
    v port ball valves

    IV. The consideration of FL value in engineering design

    1. There are not many cases of blocked flow encountered in engineering design. Sometimes the process requires blocked flow, such as liquid phase change and gas phase as refrigerant. However, in most operating conditions, it is desirable to avoid blocking the flow.
    2. To avoid blocking the flow, a control valve with a larger value can be selected, so that Δpc is also correspondingly large. Choosing a large diameter does not avoid blocking the flow.
    3. The FL of the single-seat valve is larger than that of the rotary valve. For the large-diameter rotary valve, the correction of the FL value by the size of the pipe should be considered.
    4. When the manufacturer does not provide the FL value of the control valve, the FL value listed in Table 4 can be used as an estimation reference.
    5. Dynamic correction of FL when the valve opens at different degrees. Since the calculation of the control valve Cv value only considers a certain point of the operating conditions, it cannot guarantee that all operating conditions will avoid blocked flow, so when calculating Δpc, it is necessary to analyze it from a dynamic perspective.
      When estimating, the FL value can be the smallest value in the entire opening, which is generally the FL value in the product manual. The pressure p1 in front of the valve generally decreases (or is constant) with the increase of the opening, so it is safer to use the p1 under the maximum flow to calculate ΔPc.
      If it is found that FL and p1 do not conform to the above rules during the calculation of the control valve, Δpc shall be checked for the selected control valve at the operating point required by each process to check whether there is a possibility of blocking the flow.

    V. Project example

    Design conditions: The fluid medium is quenched oil with high viscosity. The valve body is required to be simple in structure and capable of online maintenance. Secondly, the CV value of the control valve is relatively large, which is more economical. Calculate according to the process parameters, and the results are shown in the calculation book listed in Table 5.
    Intuitively speaking, there is a potential blocking flow in this working condition. It is best to choose a control valve with a large FL, but it is generally a straight-stroke valve, which has a relatively large diameter and a high price. Therefore, at this time, especially for large-diameter valves, the selection of valve structure is very important.

    1. After comparing the products of various manufacturers, the author finally recommends NELES-CONTROL’s V-type control ball valve with a spool mounted on the top. The FL data provided by the manufacturer is: 30° opening is 0.92; 45° opening is 0.85; 80° opening is 0.72. From the calculation results, the control valve just avoids blocked flow under normal and maximum flow, and the valve structure also meets the requirements of process online maintenance.
    2. Because the differential pressure required by the process at the minimum flow rate is relatively large (0.534 MPa), and Δpc is 0.501 MPa at this time, a blocked flow is still generated. Considering that the control valve is extremely important to the device, the valve body, valve core, and valve seat are all hardened, and the actual use is good. 3. From the above examples, once the valve is selected, it is necessary to check the Δpc of the process operation point, and the manufacturer is required to provide the FL value of the valve at each opening, especially for the FL value that changes greatly with the opening. Pay special attention to valves, such as ball valves. Secondly, when the valve differential pressure changes greatly with the flow rate, Δp should be the value at the corresponding flow rate, which also corresponds to the valve opening. In the example, the blocking flow due to the large differential pressure at the minimum flow rate just illustrates this problem.

    VI. Conclusion

    There are many ways to deal with the blocked flow in the project, such as cage type control valves, multi-stage pressure reduction, installing orifice plate at the downstream of valves, etc., but the purpose is to increase the Pvc to avoid blocked flow. It is the simplest and most convenient method to choose a control valve with a larger FL value.

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