# APPENDIX A CONTROL VALVE TESTING PROCEDURES AND EQUATIONS FOR LIQUID FLOWS

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1 APPENDIX A CONTROL VALVE TESTING PROCEDURES AND EQUATIONS FOR LIQUID FLOWS

2 Section A.1. Flow Coefficients Definition The flow coefficient or pressure loss coefficient is used to relate the pressure loss of a valve to the discharge of the valve at a given valve opening. The most widely used flow coefficient is of equation A1, where Q is in gpm, P is the pressure drop in psi, and Sg is the specific gravity of the fluid. Q gpm P / Sg A1 The definition of or used in this report is per Instrument Society of America S39. testing specifications for control valves. The main consideration in determining is that the pressure drop P is measured from static wall taps upstream and downstream of the test valve and in locations of fully developed, uniform pipe flow. The pressure drop is then calculated by subtracting from the measured pressure drop, the amount of pressure drop that was caused by the pipe wall friction between the pressure taps. The corrected pressure drop is then pressure drop and is due only to the effect of the valve on the piping system. Downstream Pressure Taps Upstream Pressure Taps FLOW 8 to 10 pipe diameters 1 to pipe diameters Another form of or 75 used is from the ISA S75.0 testing specifications where the pressure drop is measured from static wall taps located pipe diameters upstream and 6 pipe diameters downstream of the valve. 75 Q P gpm 75 /Sg A The pressure drop is not corrected for the effect of the pipe wall friction between the upstream and downstream pressure taps. Equations A3 and A4 can be used to convert based on ISA S39. and 75 based on ISA S75.0 specifications. The variable f is the pipe wall friction factor and d is the inside diameter of the pipe in inches. 75 will always be less than 39 because of the additional pressure loss from pipe friction. At

3 values of /d greater than 40, the difference between and 75 can be over 40%. For valves with /d less than 0, the difference between and 75 can be ignored. d 75 d d Sg f d 75 d Sg f d A3 A4 Another common flow or pressure coefficient is K of equation A5. It is also a form of the Euler number and often used as a pressure loss coefficient for many types of piping components. dh K V g A5 Where V is the average pipe velocity in fps, g is the gravitation constant 3. fps, and dh is the pressure differential in feet of fluid. K is dimensionless and can be converted to (ISA S39.) by equation A6. The variable d is the inside pipe diameter in inches. d K A6 is not dimensionless or independent of the size of the valve. Dividing by d creates a coefficient that is independent of valve size and constant for geometrically similar valves. However, the units of /d are still not dimensionless. Further information on flow coefficients can be found in the publication "Control Valve Flow Coefficients" by Rahmeyer and Driskell and published in the Pipeline Journal of ASCE. Testing Procedures The flow coefficient is experimentally determined for different valve openings or positions. For a constant valve opening, three to five test runs are made at different flow rates and pressure drops. The test runs are made at high Reynolds numbers and turbulent 3

4 flows such that the flow coefficient should remain constant. Runs made at levels of heavy cavitation are avoided because of the effect of cavitation on. The flow coefficient is then calculated from the average of the test runs at a constant valve opening. The valve position is usually measured from either the valve shaft or the valve operator. For quarter turn valves, a large protractor is attached to the valve to indicate valve opening in degrees of rotation. The valve in a fully open position measures as an opening of 90 degrees, and should correspond to the maximum value of. For valves that open with linear displacement of the control element, the position can be measured in units of linear travel. Valve position is usually expressed in terms of % of full open. For the purpose of repeatability in testing, valve opening is always set and measured by opening the valve to a given position. 4

5 Section A.. Dynamic Flow Torque Definition Dynamic flow torque is the valve shaft torque produced by the flow passing through the valve. Friction torque is the valve shaft torque produced by the valve components in response to the movement of the valve being opened or closed. Friction torque is itself a combination of torque produced by the shaft bearings and the shaft packing. Opening or closing a valve with flow through the valve then produces both dynamic and friction torque. By measuring both the opening and closing torques at a given flow rate and valve opening, and by assuming that the friction torque has the same magnitude for both the opening and closing directions, it is possible to calculate the dynamic flow torque. The dynamic flow torque is the average of the opening and closing torques, equation A7. The friction torque is determined as the difference shown in equation A8. Dynamic Torque, T d T open + T close A7 Friction Torque, T f T open T close A8 The dynamic torque coefficient,c TPD, equation A9, is independent of the size of the valve; but it uses the units of foot pounds for torque, psi for pressure drop, and inches for the diameter. For a given valve opening it is used to calculate the dynamic flow torque for geometrically similar valves with different pressure drops. Td is the dynamic flow torque in ft-lbs, P is the pressure drop in psi, and d is the pipe diameter in inches. Other forms of torque coefficients may use different units. C TPD P T d d 3 A9 A friction torque coefficient, C TPF can be calculated from equation A10 by using the friction torque from equation A8. The pipe diameter squared, d 3, is used in this equation. American Water Works Association Standards AWWA C-504 states that the bearing or friction torque should be related to the diameter of the valve shaft and to a coefficient of shaft friction. A change in either shaft diameter or coefficient of shaft friction should then result in a proportional change in friction torque and C TPF. C TPF Tf P d 3 A10 5

6 It must be cautioned that there are many other factors which affect the dynamic and friction torques of a valve. Sound judgment and experience should be used in applying torque coefficients, especially for different sizes of valves. Different sizes of the same model of valves are usually not geometrically similar. Even similar valves of the same size can have different friction torques. The seating torques required to operate a valve can well exceed the opening and closing torques. Testing Procedures The procedure to determine the torque induced onto a valve shaft is to measure the torque from strain gages attached to the valve shaft between the valve operator and the valve body. Four strain gages are mounted in different directions such that they measure only torque and be temperature compensating. The output of the gages is read from a nulling circuit on a strain indicator. After the strain gages have been attached to the valve shaft, the valve is clamped to a blind flange to immobilize the valve. The valve operator is removed, and different known torques are applied to the end of the shaft to calibrate and zero. Care must be taken not to load the end of the shaft with a bending moment at the same time. The valve is then installed into the test line and the operator connected. Before testing, the position indicator is installed and adjusted. The test piping is filled, and the strain gages are again zeroed. For each given valve position the valve is tested with at least three different flow rates at high Reynolds numbers. Flows at heavy cavitation are avoided because of the effect of cavitation on lessening dynamic flow torque. The opening and closing torques, the flow rate, and the pressure drop across the valve are measured for each flow. The dynamic flow torque and torque coefficients are then calculated for each flow or test run. The torque coefficients are then averaged for the different test runs at each valve position. 6

7 Section A.3. Incipient Cavitation Definition Cavitation is a liquid phenomena based on the formation and collapse of vapor cavities in the fluid passing through a valve. The vapor cavities begin to grow in low pressure regions such as areas of separation and collapse downstream of the low pressure regions. Cavitation can produce the effects of noise, vibration, and erosion or damage to the valve and downstream piping. Incipient cavitation is defined as the flow conditions at which cavitation is first noticeable. Usually incipient cavitation can be described as very intermittent popping sounds. Incipient cavitation can be detected aurally or electronically with hydrophones and accelerometers. The cavitation parameter or index is a dimensionless ratio used to relate the conditions which inhibit cavitation to the conditions which cause cavitation. There are several common forms of the cavitation parameter σ that are used. Equation A11 is used for this report and can be converted to the other forms of the parameter of equations A1 and A13 by the use of equation A14. σ P1 Pv P A11 σ P Pv P A1 Kc P P P v A13 1 σ 1 + σ Kc A14 Where P 1 is the upstream pressure, P is the downstream pressure, and P v is the vapor pressure of the fluid. The units of the parameters are such that the parameters are dimensionless. It is extremely important to note that Kc and K I have often been used to represent cavitation levels of incipient choking. The level of incipient choking is determined as the level or limit in which the intensity of the cavitation is intense enough to begin to interfere with the flow passage and affect the pressure loss coefficient. The limit of incipient choking is not the same as incipient cavitation, and usually represents 7

8 conditions of extremely heavy cavitation. It must also be cautioned that some past publications have mistakenly referred the level of incipient choking as the limit of incipient cavitation. Incipient cavitation is experimentally determined and represented by the value of σ for the conditions at which incipient cavitation occurs. For equations A11 and A1, flow conditions which represent a system σ value greater than the σ of incipient cavitation will not produce any effects of cavitation. Most valves can operate with system σ at 10 to 15 percent less than the incipient σ without any undesirable effects of cavitation. σ can be used to calculate the flow rates and pressure drops for a given valve opening and pressure that will not cause cavitation. Usually the value of incipient σ will increase for an increase in valve opening and flow coefficient. For most control valves, incipient cavitation has a small pressure and size scale effect. That is, the value of incipient σ will increase or cavitation will begin sooner than expected for higher system pressures and for larger sized valves. Because the value of σ can vary with pressure, the reference pressures, P 1 -P v, need to be listed with values of σ. The level or limit of σ can then be scale to a set of different pressures by the use of Equation A15. A typical value of n for incipient or critical cavitation is 0.. σ ( P1 Pv ) σ v ( P1 Pv ) different P1 P v reference P1 P different reference n A15 The relationship between incipient σ, valve size, and upstream pressure can be experimentally determined for each different type and style of valve. Further information can be found in the publications "Cavitation Testing of Control Valves" by William Rahmeyer and published by ISA, and in "Test Procedures for Determining Cavitation Limits in Control Valves" by William Rahmeyer and published by AWWA. The procedures for testing cavitation limits and the procedures for scaling cavitation limits with pressure and valve size can also be found in the Instrument Society of America ISA RP75.3 Considerations for Evaluating Control Valve Cavitation. Testing Procedures The flow conditions for incipient cavitation are for a given upstream pressure, valve opening, and pressure drop. The flow is usually set at a large σ value, greater than 0, where there are no effects of cavitation. The testing procedures is to then increase the flow rate or pressure drop in small increments for a constant upstream pressure and valve opening until cavitation can first be detected. Incipient σ is then calculated for the flow conditions at which cavitation began. Data is usually corrected for summary tables to compare incipient σ at the same upstream pressure for all valve openings. 8

9 Section A.4. Constant or Critical Cavitation Definition Constant or Critical cavitation is another level or limit of cavitation. It can also be mathematically represented by the cavitation parameters of equations A11 and A1. Equation A11 is the form of the cavitation parameter used in this report for constant cavitation. Pressure and size scale effects also apply for constant cavitation. For further information, see the discussion and publications referenced in section A.3. Generally, constant cavitation is about 80% of the value of the cavitation parameter for incipient cavitation. Constant or critical cavitation occurs at a light to moderate level of cavitation. It can be experimentally determined by the use of accelerometers and vibration meters as the set of conditions at which the cavitation suddenly becomes CONSTANT and increases at a slower rate with increased pressure drop than for the incipient cavitation. Constant cavitation is a good design limit for the operation of most valves, because the cavitation effects of noise and vibration are still light and not objectionable. The noise level associated with constant cavitation is usually less than 80 decibels A-scale. There is no cavitation damage associated with constant cavitation. However, testing for constant cavitation is some what subjective, and for some valve types and designs, it is not always possible to define or to test for. The testing procedures for constant cavitation are similar to those of incipient cavitation in section A.3. The procedures for testing cavitation limits and the procedures for scaling cavitation limits with pressure and valve size can also be found in the Instrument Society of America ISA RP75.3 Considerations for Evaluating Control Valve Cavitation. 9

10 Section A.5. Pressure Recovery Factor Definition The pressure recovery factor F L is the ratio of the theoretical discharge to the actual discharge through a valve for a given upstream pressure and geometric shape. For a given upstream pressure and valve opening, the pressure recovery factor calculates the maximum possible flow that can pass through the valve for a given upstream pressure. Equation A16 shows the pressure recovery factor F L as a function of the maximum possible flow Q in gpm, the average flow coefficient calculated previously (per Section A.1 and ISA S39.) for the valve at high Reynolds numbers without any effects of cavitation, the upstream pressure P 1 in psig, and the vapor pressure Pv of the fluid in psig. Qgpm FL P1 Pv A16 F L is dimensionless and independent of valve size. It varies with valve opening, and usually decreases as the valve opening increases. There is no pressure scale effect for choking cavitation or the pressure recovery factor. In liquid flows, the flow conditions corresponding to the limits of the pressure recovery factor are those of choking and flashing cavitation. Pressures inside or downstream of the valve are at vapor pressure, and any further decrease in downstream pressure of the valve will not increase the flow through the valve. It is not recommended to operate most control valves under the conditions of choking cavitation. A valve that is experiencing choking cavitation is operating at the most severe level of cavitation. Equation A17 shows the correlation between F L and the cavitation parameter of equation A11. σ CHOKED 1 FL A17 More information is available on F L in the publications "Test Procedures for Determining Cavitation Limits in Control Valves" by William Rahmeyer and published by AWWA, and in "The Pressure Recovery Factor" by Rahmeyer and Rau and published by ISA. Testing Procedures The procedures to determine the pressure recovery factor are to set the flow conditions of a valve, for a given valve opening, with the downstream control valve of the test setup full open and the upstream pressure high enough so that vapor pressure will occur in or downstream of the test valve. The flow can be verified as choked if the flow 10

11 does not decrease by slightly increasing the pressure downstream of the test valve, or it can be verified if vapor pressure is measured downstream of the test valve. 11

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