The practical significance of the adjustable ratio of control valves in engineering design

This issue cannot be explained clearly in just a few words. You can take a look at the calculation process for the flow coefficient; the process already specifies the maximum and minimum flow rates. As long as the regulating capacity of your control valve is sufficient to meet the process requirements, that’s fine. The adjustability ratio represents the range of adjustment available for the control valve, and it operates on a similar principle to the range of certain instruments. You can take a close look at the materials on this topic, and then you’ll understand why.

The manufacturer will usually tell you the ideal R value for the valve – it can be 30 or 50 – but the actual value is much lower, as the factor of S comes into play, making it difficult for the manufacturer to calculate the actual R value. If S is set to 0.3-0.5, then the corresponding R is 5.5-7. It can be seen that the actual R is generally around 10. Did you understand?

There are two basic flow characteristics for control valves: linear flow characteristic – research on the relationship between the flow coefficient of a control valve and its adjustment ratio – Equation 1; equal percentage flow characteristic: Ф=Ф0Rh (2), where Ф represents the flow coefficient at a certain degree of opening； R is the adjustable ratio ； h is the relative opening degree ； F0 is the flow coefficient at h=0. According to the traditional interpretation, the adjustable ratio R refers to the ratio of the maximum flow rate that can be controlled; in other words, it is the relationship between the flow coefficient of the control valve and this adjustable ratio. When designing a control valve, it is necessary to first determine a value for R, and then calculate the flow coefficient Ф at various opening degrees, using these values as a basis for designing the valve core curve and the corresponding window shapes. The two unified design efforts in China’s control valve industry both involved calculating the theoretical values of the flow coefficient for each opening degree on the premise that R=30 (see Table 1). Table 1 Flow coefficient Ф and flow characteristics Ф0 for the control valve at various relative openings when R=30; values of Ф at different relative openings: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0. For linear characteristic: 3.33, 13.00, 22.67, 32.33, 42.00, 51.67, 61.33, 71.00, 80.67, 90.33, 100.00. For equal percentage characteristic: 3.33, 4.68, 6.58, 9.25, 12.99, 18.26, 25.65, 36.05, 50.65, 71.17, 100.00. From an application perspective, it is desirable that the amplification factor KD of the control valve be high; KD is related to the adjustable ratio R. Study on the relationship between the flow coefficient of control valves with linear characteristic and the adjustable ratio – Equation 4. Study on the relationship between the flow coefficient of control valves with equal percentage characteristic and the adjustable ratio – Equation 5. Here, L represents the full-stroke opening. It can be seen that increasing KD should raise the R value; therefore, manufacturers specify a value greater than a certain threshold for the adjustability as a performance indicator. However, the larger the R value of the control valve, the greater the difficulty in design and manufacturing. For single- and double-seat control valves, if the R value is too high, root cutting occurs during the manufacturing of the valve spool in the 90%~100% opening range ； For sleeve control valves, if the R value is too large, it becomes impossible to manufacture them within the 90%~100% opening range due to the excessive width of the window. All these limit the increase in the R value. The manufacturer designed and produced the control valve products assuming R=30, but issues such as the actual R value of these control valves and the deviation from R=30 have not yet received attention. Since designers’ understanding of the R value is limited to the ratio of Qmax to Qmin, and Qmin is merely a theoretical value that cannot be measured, it is considered that the actual adjustable ratio cannot be calculated either. In the available information on control valves to date, no discussions on this aspect have been found. The standards for control valves both domestically and internationally also do not specify methods for measuring, calculating, or evaluating the R value. This is due to a one-sided understanding of the concept of adjustable ratio; it is now necessary to conduct further exploration and research starting from the relationship between adjustable ratio and flow coefficient. 1. The relationship between the comparable valve and the flow characteristic curve: As can be seen from the formula for calculating the flow coefficient, the R value depends on certain factors, but it determines the value of the flow coefficient at any given relative stroke. Therefore, this holds great practical significance from the perspectives of the design, manufacturing, and application of control valves. Because no control valve can be used at its minimum opening; in other words, it does not operate at its Qmin value. In most applications, flow rate is controlled at a certain opening degree (usually between 20% and 80% of the full stroke). At this point, the value of the flow coefficient of the control valve determines its operating degree; the change in the flow coefficient relative to the stroke determines the amplification factor of the control valve, and all these factors are related to the R value. Therefore, the R value cannot be simply understood as the ratio of Qmax to Qmin; rather, it should be regarded as a characteristic parameter of the entire flow characteristic curve. From equations (1) and (2) as well as equations (3) and (4), it can be seen that changes in the R value have little effect on the linear flow characteristics; especially when R > 1, both Ф and KD are independent of the R value ； The impact on the equal percentile property is significant; therefore, the discussion in this paper on the effect of these values on the flow coefficient is limited to the equal percentile property. When the R value serves as a characteristic parameter of the flow characteristic curve, it is possible to consider the flow characteristic curve over the entire stroke as being composed of several segments, each determined by a different R value. At openings of 0~80%, the R value is set to be higher, ensuring that the control valve has a sufficient R value within its operating range, which in turn means it has an adequate amplification factor. In the range of 80% to 100% opening, the R value should be kept low, so that it is easier to achieve the desired shape for both the valve spool and the window in the sleeve during the manufacturing process of the control valve. Increasing the R value at higher operating degrees can also serve as a way to explore ways of improving flow capacity in control valve design. The idea of using different R values for different segments is reflected in IEC534—2—4 (draft) as well as in some flow coefficient tables for control valves abroad. In this context, the concept of adjustable ratio is no longer simply the ratio of Qmax to Qmin; it should be regarded as a characteristic parameter of the flow characteristic curve, one that needs to be studied. 2 Method for calculating the R value: The actual adjustable ratio R value of a control valve can be calculated. According to equation (2), it can be derived that lnФ = lnФ0 + hlnR (6). In the lnФ–h coordinate system, the equal percentage flow characteristic curve is a straight line, and the R value actually determines the slope of this line. By actually measuring the flow characteristics of a control valve, several sets of (Ф, h) data can be obtained. Due to manufacturing and measurement errors, these values exhibit an approximately linear distribution in the lnФ—h coordinate system, and this approximate straight line is considered to be the actual flow characteristic curve of that control valve. To obtain such a line that is as close as possible to these points in the coordinate system, it is recommended to use the method of least squares. When measuring the flow coefficient of a control valve at different opening degrees, a set of data consisting of the relative stroke and the flow coefficient is obtained. By substituting these values into equation (6), an equation system is derived. Research on the relationship between the flow coefficient of a control valve and its adjustable ratio – Equation 7: In this equation, Ф0 and R represent the actual values for that control valve; their approximate values can be determined using the least squares method from equation (7). Research on the relationship between the flow coefficient of a control valve and its adjustable ratio – Equation 8: Generally, measurements are taken at 10 different opening degrees, with hi taking the values 0.1, 0.2, 0.3, …, 1.0. At this point, K=10; study on the relationship between the flow coefficient of the control valve and its adjustable range – Equation 1 = 5.5 ； Study on the relationship between the flow coefficient of a control valve and its adjustable ratio – With equation 2 equal to 3.85, substituting this value into equation (8) yields Equation 9. By inserting the measured flow coefficient Fi into Equation (9), it is possible to determine the actual adjustable ratio R of that control valve. By substituting the theoretical value of the percentage flow coefficient in Table 1 into Equation (9), it is possible to calculate R=30. The value obtained by using equation (9) represents the adjustable ratio over the entire range of operation. To accurately determine the adjustable ratio of the control valve during its operating range, values for hi can be taken as 0.2, 0.3, …, 0.8; that is, k=7. From the studies on the relationship between the flow coefficient of the control valve and its adjustable ratio – Equation 3 = 3.5, and Equation 4 = 2.03 – Equation 10 can be derived. By substituting in the flow coefficients corresponding to opening degrees of 20% to 80%, it is possible to obtain the R value for the flow characteristics within this range. Similarly, by substituting the theoretical value data from Table 1 into Equation (10), R=30 can also be calculated. Since the value of Ф in equations (9) and (10) appears in the form of a ratio, the results obtained by using either the absolute flow coefficient or the relative flow coefficient are identical. Therefore, it is very convenient to use it for calculating the R value. Similarly, when it is necessary to calculate the value of the flow characteristic curve for any given segment, the corresponding calculation formula can be derived. 3 Comparison of R values for some control valves at home and abroad: Using equation (9), the flow coefficients of domestically designed two-seat control valves and jointly designed sleeve control valves, as well as Fisher Company’s ED type sleeve valves, were used to calculate the corresponding R values; the results are shown in Tables 2 to 4. As can be seen from the table, although the two-seat control valves and sleeve control valves have R=30 preset during design, the R value of control valves of various specifications produced in practice varies. Table 2: Flow coefficient Φ values and calculated R values for two-seat control valves
Nominal diameter DN×dN | Φ values at various relative openings | Adjustable ratio R
0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0
25 | 2.65 | 4.57 | 7.84 | 12.76 | 17.96 | 25.04 | 35.00 | 49.11 | 74.53 | 103.39 | 51.5
32 | 3.09 | 6.30 | 9.90 | 13.99 | 18.90 | 24.60 | 30.10 | 42.80 | 74.40 | 100.00 | 34.6
40 | 7.44 | 10.28 | 11.52 | 13.22 | 16.88 | 21.92 | 28.82 | 52.84 | 78.92 | 92.00 | 17.4
50 | 7.68 | 11.89 | 14.90 | 18.40 | 22.90 | 29.50 | 37.80 | 53.50 | 70.40 | 98.20 | 14.6
65 | 3.95 | 7.72 | 11.36 | 15.53 | 20.20 | 26.56 | 36.51 | 50.77 | 77.53 | 99.58 | 28.9
80 | 3.34 | 7.64 | 10.49 | 14.63 | 19.85 | 28.00 | 37.75 | 50.28 | 75.49 | 97.25 | 32.4
100 | 4.70 | 7.68 | 10.32 | 14.20 | 18.81 | 27.35 | 37.02 | 52.82 | 72.39 | 97.60 | 27.1
125 | 4.14 | 6.49 | 9.47 | 12.89 | 19.37 | 27.61 | 37.34 | 51.88 | 66.66 | 103.63 | 32.3
150 | 2.55 | 5.70 | 8.50 | 12.42 | 18.17 | 25.45 | 34.98 | 48.48 | 76.74 | 96.81 | 45.7
200 | 12.20 | 16.10 | 20.10 | 25.10 | 32.00 | 46.50 | 75.80 | 100.50 | – | – | 20.0

Table 3: Flow coefficient Φ values and calculated R values for sleeve control valves
Nominal diameter DN×dN | Φ values at various relative openings | Adjustable ratio R
0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0
25 | 4.10 | 7.90 | 12.10 | 16.50 | 20.40 | 29.60 | 42.20 | 61.00 | 81.50 | 103.00 | 30.9
40 (C=16) | 2.12 | 6.06 | 10.00 | 14.31 | 18.75 | 24.75 | 34.50 | 51.06 | 73.75 | 96.88 | 45.3
60 (C=25) | 6.54 | 9.12 | 11.76 | 14.84 | 20.24 | 28.16 | 38.60 | 56.00 | 78.00 | 99.20 | 21.3
50 | 3.10 | 6.45 | 9.90 | 15.05 | 22.48 | 32.50 | 46.50 | 67.50 | 90.50 | 97.75 | 45.2
65 | 3.25 | 6.83 | 10.24 | 14.63 | 20.63 | 27.46 | 40.32 | 58.73 | 86.35 | 107.94 | 41.2
80 | 4.20 | 7.67 | 11.10 | 14.97 | 21.05 | 29.70 | 40.60 | 60.50 | 80.10 | 92.60 | 29.9
100 | 3.57 | 7.37 | 11.03 | 15.21 | 21.80 | 30.39 | 44.13 | 64.90 | 82.06 | 93.23 | 34.9
125 (C=250) | 3.69 | 7.00 | 10.80 | 15.24 | 21.20 | 29.80 | 41.60 | 59.60 | 87.60 | 102.80 | 36.9
125 (C=370) | 3.34 | 7.14 | 10.84 | 15.19 | 21.89 | 31.62 | 45.95 | 65.41 | 82.43 | 93.24 | 37.5
200 | 3.17 | 6.90 | 10.79 | 15.66 | 22.41 | 31.90 | 42.76 | 60.34 | 81.21 | 96.03 | 37.8
300 | 3.31 | 6.92 | 10.54 | 14.54 | 20.23 | 28.62 | 43.85 | 64.23 | 82.31 | 94.08 | 38.3

Table 4: Flow coefficient Φ values and calculated R values for Fisher’s ED-type sleeve valves
Nominal diameter DN×dN | Φ values at various relative openings | Adjustable ratio R
0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0
1*1/4×1*5/16 | 0.783 | 1.54 | 2.20 | 2.89 | 4.21 | 5.76 | 7.83 | 10.9 | 14.1 | 17.2 | 27.4
1*1/2×1*7/8 | 1.52 | 2.63 | 3.87 | 5.41 | 7.45 | 11.2 | 17.4 | 24.5 | 30.8 | 35.8 | 36.3
2×2*5/16 | 1.66 | 2.93 | 4.66 | 6.98 | 10.8 | 16.5 | 25.4 | 37.3 | 50.7 | 59.7 | 57.6
2*1/2×2*7/8 | 3.43 | 7.13 | 10.8 | 15.1 | 22.4 | 33.7 | 49.2 | 71.1 | 89.5 | 99.4 | 41.3
3×3*7/16 | 4.32 | 7.53 | 10.9 | 17.1 | 27.2 | 43.5 | 66.0 | 97.0 | 120 | 136 | 54.2
4×4*3/8 | 5.85 | 11.6 | 18.3 | 30.2 | 49.7 | 79.7 | 125 | 171 | 205 | 224 | 64.8
6×7 | 12.9 | 25.8 | 43.3 | 67.4 | 104 | 162 | 239 | 316 | 368 | 394 | 47.1
8×8 L=2 | 18.5 | 38.0 | 58.4 | 86.7 | 130 | 189 | 268 | 371 | 476 | 567 | 41.9
8×8 L=3 | 27.0 | 58.1 | 105 | 188 | 307 | 478 | 605 | 695 | 761 | 818 | 43.1

By comparing the R values of the two series of control valves in Table 2 and Table 3, it can be seen that the R values for various specifications of two-seat control valves exhibit relatively large deviations, whereas those for sleeve control valves show smaller deviations. This is consistent with the different error criteria used for flow characteristics in the design of these two types of valves: the double-seat control valve uses 10% of the maximum flow value as the allowable deviation range for the flow value per stroke, whereas the sleeve valve employs the slope method specified in the international IEC standards to calculate the deviation in flow characteristics. Clearly, the latter method is better than the former at ensuring that the R value meets the design requirements, which also demonstrates the superiority of the IEC standard slope method. Comparing Tables 2, 3, and 4 also shows that the R value of domestically produced control valves is lower than that of imported control valves; the average R value for domestic two-seat valves is 30.5, while the average R value for sleeve valves is 36.2 ； The average value of Fisher Company’s ED type cartridge valve R = 45.9. The R values of the domestic sleeve valves and Fisher’s ED type sleeve valves during the working stroke range (h=0.2~0.8) were calculated using equation (10), and these values were compared with those at full stroke; the results are shown in Tables 5 and 6. It can be seen that the R value during the working stroke of the domestically produced cartridge valves is close to the R value for the full stroke, with no significant change; the average value of R is 34.2. In contrast, the R value during the working stroke of Fisher’s cartridge valves is significantly higher than the R value for the full stroke, with an average value of R of 60.5. Increasing the R value of the working stroke segment has the advantage of better meeting the requirements of automatic control systems; it also increases the flow coefficient at an opening degree of 80%, thereby significantly enhancing the flow capacity of the valve when it is fully open. Through the analysis and comparison of R values, it is shown that there is a certain gap in the design level of control valves between domestic and international manufacturers. Table 5: R values of domestic sleeve control valves. Stroke stages of sleeve valves; R values for various specifications of sleeve valves. Average R value: 20, 40; C=16: 40; C=25: 50, 65, 80, 100, 125; C=250: 125; C=370: 200, 300. For full stroke: 30.9, 45.3, 21.3, 45.2, 41.2, 29.9, 34.9, 36.9, 37.5, 37.8, 38.3, 36.2. When h=0.2~0.8: 26.9, 28.9, 20.5, 49.2, 33.4, 29.5, 35.4, 33.0, 39.2, 35.2, 38.4, 34.2. Table 6: R values of Fisher company’s sleeve valves. Stroke stages of sleeve valves; R values for various specifications of sleeve valves. Average R value: 1*1/4×1*5/1, 1*1/2×1*7/8, 2×2*5/16, 2*1/2×2*7/8, 3×3*7/16, 4×4*3/8, 6×7, 8×8L=2, 8×8L=3. For full stroke: 27.4, 35.3, 57.6, 41.3, 54.2, 64.8, 67.1, 41.9, 43.1, 45.9. When h=0.2~0.8: 25.8, 41.5, 69.7, 46.2, 78.1, 99.7, 69.0, 45.0, 69.7, 60.5. 4. Understanding of IEC 534—2—4 (draft): Paragraph 3.3 of IEC 534—2—4 (draft) specifies the equal percentage flow characteristic as follows: “Between h=0.2 and h=0.8, the difference between the logarithms of any two adjacent flow coefficient values should be within the range of 0.13 to 0.2.” “For values below h=0.2, these two values are 0.13 and 0.25 respectively ； For values above h=0.8, these figures should correspond to 0.03 and 0.2”. Here, the selection of the range for deviations in flow characteristics should be considered as being determined by the range of values for R. Calculating accordingly: for R=20, 0.1×logR=0.13; for R=100, 0.1×logR=0.20; for R=300, 0.1×logR=0.25; and for R=2, 0.1×logR=0.03. In other words, the deviations in flow characteristics are actually restricted within certain ranges for R values, specifically, h=0.2~0.8 and R=20~80 ； h=0.8~1.0, R=2~100 ； h=0~0.2, R=20~300 ； This requirement of the IEC reflects the use of the R value as a characteristic parameter of the flow characteristic curve, and it implements the design concept that different R values can be adopted across the entire range of motion. The national standard GB 4213—84 \"General Technical Requirements for Pneumatic Control Valves\" differs to some extent from the IEC standard on this issue. A thorough discussion of the relationship between the R value and the flow coefficient is of significance for the design, manufacturing, and application of control valves. It is also essential for advancing the fundamental theoretical research on control valves and improving the level of design and manufacturing of such valves in our country

The flow coefficient of a control valve (referred to as the Cv value in European and American standards, and as the KV value in international standards) denotes the volumetric flow rate or mass flow rate under standard (test) conditions. The maximum flow coefficient Kv of a control valve refers to the volumetric flow rate per hour that passes through the valve, in units of m3/h, when the valve is fully open, the pressure difference ΔP across the valve is 100 KPa, and the density of the fluid is 1 gf/cm3 (i.e., water at 20°C). The regulation ratio R of a control valve is defined as the ratio of the maximum flow coefficient to the minimum flow coefficient; in other words, it is the ratio of the maximum volume flow rate of water passing through the valve under standard conditions to the minimum (controllable) volume flow rate, and it indicates the valve’s ability to regulate flow.