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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, you can feel free to check the FL value as below sheet from THINKTANK control valves.
    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.

    THINKTANK HCB Series Cv vs Travel Standard Trim (CAGE) Linear%

    Size: 2 ” ~ 16″ Flow Characteristic: Linear Percentage Class: 150# ~ 600#

    Valve Travel [%]102030405060708090100
    FL0.940.940.930.930.920.920.910.910.900.90
    Valve SizeOrifice Dia.TravelRated Cv
    InchmmSignInchmmInchmm
    250FC2.564.51.6404.913.922.230.339.548.657.364.769.574
    1A3.57.612.517.322.427.633.138.543.648
    2A2.65.27.710.312.915.418.020.623.226
    3A1.63.24.86.37.99.511.112.714.316
    380FC3.589.02.0508.022.039.059.075.090.0105.0119.0130.0142
    1A6.216.626.936.946.656.867.478.087.898
    2A4.511.116.622.227.733.338.844.449.956
    3A3.46.710.113.516.820.223.626.930.334
    4100FC4.4111.52.05019.341.574.4105.3133.4164.5187.6206.4219.3230
    1A8.025.443.160.477.293.8110.7127.6143.9160
    2A6.017.025.534.142.651.159.668.176.686
    3A5.210.315.420.625.730.936.041.246.352
    6150FC5.3133.62.46023.062.0123.5181.0229.1269.3315.2349.9370.1380
    1A12.040.971.4101.4130.6158.9186.7214.7242.2275
    2A9.529.744.659.474.389.1104.0118.8133.7150
    3A8.017.826.735.644.653.562.471.380.290
    8200FC6.9175.52.87028.294.2185.6288.0377.1449.1514.1571.9590.0600
    1A14.552.5108.0172.0232.0299.0365.0417.0430.0455
    2A10.045.075.4100.6125.7150.9176.0201.2226.3254
    3A9.030.145.160.275.290.3105.3120.4135.4152
    10250FC8.4214.23.18045.9189.3329.3461.8583.3689.9778.5847.7897.9950
    1A25.0103.6183.3260.7337.5414.1489.4562.3631.5700
    2A17.078.8118.2157.6197.0236.4275.8315.2354.6398
    3A12.046.770.193.5116.8140.2163.6186.9210.3238
    12300FC10.4264.84.712093.2250.0463.3660.0840.0990.01115.01205.01250.01270
    1A66.7167.8276.8382.9485.5586.9692.1796.9893.0970
    2A25.0108.9163.4218.0272.3326.7381.2435.6490.1550
    3A17.067.3101.0134.6168.3202.0235.6269.3302.9340
    14350FC12.4315.55.5140127.4407.5673.4915.61128.51316.51474.21593.11671.41740
    1A91.3233.3393.0548.1696.8838.0976.41105.41221.21300
    2A52.0153.7230.5307.3384.1460.9537.8614.6691.4776
    3A27.091.9137.8183.7229.7275.6321.6367.5413.4464
    16400FC14.1357.76.3160189.0497.0891.81248.01535.41791.51950.02063.02161.62215
    1A101.3276.5448.1615.0779.1941.91101.61255.71398.91530
    2A71.0186.1279.2372.2465.3558.4651.4744.5837.5940
    3A47.0112.5168.7224.9281.2337.4393.6449.9506.1568

    NOTE
    Cv: Valve flow coefficient
    FL: Liquid pressure recovery factor
    FC: Full Capacity 1A: 1-Step reduction
    2A: 2-Step reduction 3A: 3-Step reduction

    THINKTANK HCB Series Cv vs Travel Standard Trim (CAGE) EQ%

    Size: 2 ” ~ 16″ Flow Characteristic: Equal Percentage Class: 150# ~ 600#

    Valve Travel [%]102030405060708090100
    FL0.940.940.930.930.920.920.910.910.900.90
    Valve SizeOrifice Dia.TravelRated Cv
    InchmmSignInchmmInchmm
    250FC2.564.51.6402.004.006.009.0014.0021.0033.0050.0066.0071
    1A1.073.285.457.579.7512.7917.8626.2839.6850
    2A0.591.191.602.484.578.1612.8817.7421.5924
    3A0.340.700.941.452.674.767.5110.3512.5914
    380FC3.589.02.0504.008.5014.5022.0033.5051.0075.00108.00128.00138
    1A2.503.726.6111.1018.3529.4345.5667.6591.99110
    2A1.222.483.345.179.5217.0026.8236.9744.9850
    3A0.781.592.143.316.0910.8817.1723.6628.7932
    4100FC4.4111.52.0505.6012.9023.4036.9059.6086.50128.20163.90188.60210
    1A2.756.6811.6817.9228.5946.2171.85105.81141.21160
    2A2.004.075.488.4815.6127.8843.9960.6273.7682
    3A1.222.483.345.179.5217.0026.8236.9744.9850
    6150FC5.3133.62.4606.5015.0027.7047.1077.10123.80198.50265.20316.00340
    1A3.4011.1222.0032.2550.3581.67126.81187.40246.30270
    2A3.326.769.0814.0625.8946.2472.95100.54122.34136
    3A2.004.075.488.4815.6127.8843.9960.6273.7682
    8200FC6.9175.52.8706.5023.0045.0083.00138.00220.00325.00445.00510.00560
    1A5.6019.0039.0058.0094.00148.00222.00310.00405.00450
    2A4.0011.7215.7624.3944.9280.23126.59174.47212.29236
    3A3.007.059.4814.6827.0348.2776.17104.98127.73142
    10250FC8.4214.23.1808.1033.2065.70124.40216.80350.10493.20619.90747.60830
    1A6.5226.5047.1476.22126.33219.81343.21460.04566.24655
    2A6.1318.5824.9738.6671.19127.15200.62276.49336.42374
    3A5.4711.1314.9623.1542.6476.15120.16165.60201.50224
    12300FC10.4264.84.712022.4064.30111.10179.80303.10546.80795.00996.001155.001240
    1A15.5444.6573.67110.47174.20277.57441.34650.51837.52960
    2A12.7926.0334.9954.1699.74178.14281.08387.39471.35524
    3A7.6715.6020.9732.4559.77106.75168.43232.14282.45314
    14350FC12.4315.55.514024.7082.30158.30266.70427.00693.901015.801277.201514.701650
    1A18.9460.21103.15164.81260.61405.54630.90903.931141.451275
    2A16.2137.0649.8177.10142.00253.61400.17551.51671.05746
    3A10.8922.1629.7846.1084.89151.62239.24329.72401.19446
    16400FC14.1357.76.316035.10100.40167.00268.40471.00849.301265.101603.901911.602090
    1A26.3273.03119.55175.70286.98477.71773.091125.401432.441680
    2A20.8542.4257.0388.27162.55290.33458.10631.35768.20854
    3A12.5025.4334.1952.9297.46174.06274.65378.52460.56512

    NOTE
    Cv: Valve flow coefficient
    FL: Liquid pressure recovery factor
    FC: Full Capacity 1A: 1-Step reduction
    2A: 2-Step reduction 3A: 3-Step reduction

    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 above sheets 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.
    6. 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.
    7. 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. 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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    Picture of Will Don

    Will Don

    After earning my bachelor's degree in mechanical engineering from Zhejiang Normal University in 2008, l was fortunate enough to begin my career with Siemens, Fisher, and YTC, focusing on control valve accessories. Over the past dozen years, l've poured my heart and energy into understanding technology and fluid solutions for control valves.
    Now, as the marketing director for THINKTANK, a trusted branch of the Taiwan STONE valve group, I can't help butf eel proud of how far we've come. Our knowledge isn't just reaching professionals like engineer and valve distributors; it's also inspiring the next generation of automation college students.
    l genuinely hope you're enjoying our articles and finding them helpful.Your thoughts, questions, and feedback mean the world to me, so please don't hesitate to reach out to marketing[at]cncontrolvalve.com. Whether you're a seasoned expert or just curious about the field, I'm here to connect, share, and learn together.

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    I am the author of this article, and also the CEO and marketing director of THINKTANK, with 15 years of experience in the industrial valve industry. If you have any questions, you can contact me at any time.

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