Analysis and experimental study on flow characteristic and rangeability of plug control valve

According to the specific structure of the plug valve, a method for estimating the rated flow coefficient was proposed. Based on a variable diameter flow passage model, flow coefficient tests for four plug control valves with different specifications were carried out, and the experimental data were analyzed and researched. The results show that: (1) The proposed estimation method for calculating the rated flow coefficient of the plug valve, in which the deviation range is -6.58%∼4.10%, meets the requirement of the standard IEC 60534-2-4-2009 as not exceeding ±10%; (2) Due to the manufacturing errors, the actual inherent flow characteristic of the plug control valve is between equal percentage and parabola. The larger the flow capacity is, the more equal the flow characteristic gets; (3) The plug control valve has an outstanding feature of high rangeability, which can be up to R=979 and is obtained based on the flow coefficient test data.


Introduction
When we design a control valve, to obtain a specified rated flow coefficient, a flow coefficient test is generally adopted to revise the prototype repeatedly, or CFD software is used to carry out numerical simulation repeatedly, which is a great deal of work [1] .
Wang et al. [1][2] proposed a method for estimating the rated flow coefficient of the straight-through single-seated control valve, in which the estimation deviation is within 30.76%.However, the prerequisite to ensure the estimation accuracy is that the control valve is a straight-through single-seated type, which is not suitable for the rotary quarter turn plug control valve studied in this paper.
Yu and Wang [3] carried out a numerical simulation analysis on the flow characteristic curve of the plug control valve with triangular throttling apertures, which does not involve the flow characteristic of the plug valve featuring teardrop-shaped apertures studied in this paper.
Jin [4] calculated the rangeability of the rotary quarter turn ball valve, not giving the source of the minimum controllable flow for calculating the inherent rangeability.As a result, it cannot be used to guide the estimation of the inherent rangeability of the plug control valve studied in this paper.
A method is provided for estimating the inherent rangeability of plug control valves, which has not been applied to analyze and study, based on many flow coefficient test data [5] .Above all, this paper presented a method for estimating the rated flow coefficient of plug control valves, based on the variable diameter flow passage model.Several flow coefficient tests were carried out for various plug valves with different specifications to evaluate the estimation accuracy.Furthermore, through analyzing and processing the test data, the actual inherent flow characteristics of plug control valves were studied, and the high rangeability feature of the plug control valve was revealed.

Typical structure and principle of the plug control valve
The plug control valve adopts a bottom-installed structure, and the regulating element is a bell-shaped plug, which features teardrop-shaped apertures machined into both inlet and outlet but laterally reverses.Each teardrop-shaped aperture consists of a major arc and a gradually reduced V-notch.The typical structure schematic diagram of plug control valve is shown in Figure 1, and the image of a bell-shaped plug is shown in figure 2. The plug control valve is a rotary quarter-turn valve.During opening, this plug rotates and simultaneously uncovers the two tear drop apertures, giving fine flow adjustment with a 2-stage pressure reduction across both seats.As the plug is further rotated, the profiled apertures gradually become circular permitting an increasing flow.The apertures at full capacity are circular, and the bell-shaped plug with a slope angle outside the interlock is pressed into the valve seat through the spring force in the bottom cover.During rotation, the seat simultaneously acts as a "friction bearing", absorbing the friction forces over a wide surface area and centering the control element under the action of the spring.The structure and principle of the plug control valve were described in detail [5][6] .The flow passage structure of the fully opened plug control valve is shown in Figure 3, which consists of a gradually reduced flow passage and a gradually increased flow passage.Connecting in series, the sum of the pressure head loss of each section is the total pressure head loss of the valve [7][8] .It is very complicated to determine the flow resistance coefficient of the gradually reduced or increased flow passage based on the variable diameter flow passage model [9] , relating to not only the geometric dimensions of the flow passage but also the roughness of the inner wall, which is difficult to directly apply in engineering design.However, the equation for calculating the flow resistance coefficient of the variable flow passage featuring sudden expansion or sudden contraction is only related to the geometric dimensions, which is simple and convenient.In this paper, it is used to determine the flow coefficient of the gradually increased or reduced flow passage alternatively.
where  is the total pressure head loss of the incompressible fluid flowing through the fully opened valve;  is the total flow resistance coefficient of the fully opened valve; V is the average velocity of the incompressible fluid flowing through the fully opened valve.
where  is the volume flow rate of the incompressible fluid flowing through the fully opened valve;  is the cross-sectional area of the connecting pipe (cm 2 ).
where  is the local pressure head loss of the incompressible fluid flowing through each variable diameter flow passage section, when the valve is fully opened;  is the local flow resistance coefficient of each variable diameter flow passage, when the valve is fully opened;  is the flow velocity at the relatively small cross-section of each variable diameter flow passage, when the valve is fully opened.
where  is the cross-sectional area at the inlet of the variable diameter flow passage (cm 2 );  is the cross-sectional area at the outlet of the variable diameter flow passage (cm 2 ).
The total pressure head loss of the control valve is the sum of each local pressure head loss when the valve is fully opened, that is: For the incompressible fluid flowing through the valve, the density is constant.According to the law of conservation of mass, and by combining a system of Equations (1~5), we can obtain that: 5.09 When we use the international system of units, the rated flow coefficient of the control valve is expressed as  , which is defined as the number of cubic meters of water at a temperature of 5~40℃ that will pass through a valve with a 10 5 Pa pressure drop [10][11] .
where  can be determined by using Equation ( 9) when the variable diameter flow passage model featuring a sudden expansion is used [7][8] .
where  can be determined by using Equation (10) when the variable diameter flow passage model featuring a sudden contraction is used [7][8] .Characteristics and Rangeability specify that the rated test flow coefficient shall not deviate by more than ±10% from the manufacturer-stated flow coefficient at the rated travel.As the results listed in Table 3 above, it can be concluded that the relative error between the theoretical calculation value and the actual test value, referring to the rated flow coefficient of the test valves 1#~4#, are within the permissible deviations specified in the standard.Therefore, the accuracy of the method proposed in this paper for estimating the rated flow coefficient of the plug control valve is sufficient.

Inherent flow characteristic of the plug control valve
The theoretical inherent flow characteristic of the plug control valve is usually designed to be equal percentage [5] , however, in practice, varying degrees of deviations exist for the actual inherent flow characteristic, due to manufacturing errors primarily.According to the flow coefficient test data listed in Table 1 above, the actual flow characteristic curve of each test valve is drawn respectively, and the curve of theoretical equal percentage, parabolic curve, and linear curve are also drawn for comparison, as illustrated in Figure 6 below.For test valves 1# and 2# within the travel range of 0~75%, the flow characteristic curves which are between the equal percentage and parabolic curve are closer to the latter, and within the travel range of 75~100%, the flow characteristic curve deviates from parabola to the linear curve.For test valves 3# and 4#, the flow characteristic curves, which are between equal percentage and parabolic curve, are closer to the former.The main reason for the larger deviation of the flow characteristics of test valves 1# and 2#, compared to equal percentage flow characteristics, is that the rated flow coefficients of the two test valves are relatively smaller, bringing about machining errors of the V-shaped aperture with a greater impact on the throttling area, and resulting in a great distortion on the flow characteristic curve.

Inherent rangeability estimation of the plug control valve
A method is proposed for estimating the inherent rangeability of the plug control valve based on the flow coefficient test, which describes the equation derivation in detail [5] .The inherent rangeability R of each test valve is obtained by substituting the individual measured flow coefficient data corresponding to the ten-point valve travel (10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100%) into Equation (11) It can be seen from the equation derivation process [5] that, the inherent rangeability estimation method was proposed on the assumption that the plug control has an equal percentage characteristic.However, it can be seen from the above analysis that the inherent flow characteristics of the test valves are not equal percentages, among which the inherent flow characteristics of test valves 3# and 4# were closer to the equal percentage characteristics.As a result, their estimated inherent rangeability is more accurate.

Conclusion
(1) The proposed estimation method for calculating the rated flow coefficient of the plug valve, in which the deviation range is -6.58%~4.10%,meets the requirement of the standard IEC 60534-2-4-2009 as not exceeding ±10%.The method is convenient, practical, and accurate, which is very suitable for the engineering design of plug control valves.
(2) Due to manufacturing errors, the actual inherent flow characteristic of the plug control valve is between equal percentage and parabola.The larger the flow capacity is, the closer the flow characteristic gets to the equal percentage.
(3) The plug control valve has an outstanding feature of high rangeability.Through quantitative analysis of the flow coefficient test data, results show that the inherent rangeability of the plug control valve can be up to R=979.

Figure 1 .
Figure 1.Typical structure schematic diagram of plug control valve.Figure 2. Image of a bell-shaped plug.

Figure 2 .Figure 3 .
Figure 1.Typical structure schematic diagram of plug control valve.Figure 2. Image of a bell-shaped plug.3.A method for estimating the rated flow coefficient of the plug control valve

4 .
Flow tests of the plug control valves According to GB/T 30832-2014 Valves-Test Method of Flow Coefficient and Flow Resistance Coefficient, flow coefficients at various valve openings were measured, and the schematic diagram of the basic flow test system is shown in Figure 4. Normal temperature water flows through the upstream throttling valve, temperature measuring equipment, flow measuring device, test valve, and downstream throttling valve successively.The upstream throttling valve is used to regulate the inlet pressure of the test section.The temperature measuring equipment is used to measure the actual temperature of the water.Pressure detection instruments are set up at the upstream and downstream pressure tappings, to measure the pressure at each position.The pressure difference between the inlet and outlet of the test section is controlled by the upstream and downstream throttling valves together.Pictures of different plug valves being conducted flow coefficient test are shown in Figure 5.The measured flow coefficient data at various valve openings for each test valve 1#, 2#, 3#, and 4# are listed inTable 1 below.

Figure 5 .
Figure 5. Flow coefficient test of plug control valves.
Valve openingFlow coefficient test data at various valve opening K V (m 3 /h)

Table 2 .
Flow passage dimensions of the fully opened test valves 1#~4#.With the flow passage dimensions of the fully opened test valves 1#~4# listed in Table2, the rated flow coefficient of each test valve was calculated according to Equation(8), and then compared with the measured flow coefficient when the test valve is fully opened, analysis results are listed in Table3below.

Table 3 .
Comparison of calculated data and experimental data for test valves 1#~4#.

Table 4 .
.By substituting the measured flow coefficient corresponding to the ten-point valve opening listed in Table1into Equation(11), the calculated inherent rangeability R of test valves 1#~4# was obtained and listed in Table4below.The inherent rangeability values of test valves 1#~4#.