# Measurement of Pneumatic Valve Flow Parameters on the Test Bench with Interchangeable Venturi Tubes and Their Practical Use

## Abstract

**:**

## 1. Introduction

_{1}= 6 bar (7 bar absolute pressure) and a pressure drop of 1 bar, corresponding to a downstream relative pressure p

_{2}of 5 bar (6 bar absolute pressure). The nominal diameter DN (fr. diamètre nominal) is a standard indicator that is used as a reference to evaluate valve size. The nominal diameter of the valve matches the nominal diameter of the connected pipe. The match of the nominal diameters of the valve and the pipeline avoids oversizing the valve, which could lead to the unstable operation of the pneumatic systems. Additionally, if the valve is undersized, it can cause a high-pressure drop and damage the pneumatic components.

^{3}/h (or kv in L/min) according to the VDI/VDE 2173: 2022 standard [8]. The relationship between Cv and Kv is expressed as follows, Cv = 1.16 Kv and Kv = 0.862 Cv. When applying the flow factors Cv or Kv to pneumatic valves, various complications occur as they are determined using water as a test fluid. ANSI/(NFPA)T3.21.3-1990 will provide a common reference for test methods to be used on pneumatic elements. The VDI/VDE 2173: 2022 standard summarises the essential requirements of the existing standards and makes them available for practical application. It applies to all types of industrial process control valves. The procedures for sizing industrial process control valves are based on accepted mathematical methods, such as those specified in the ANSI/ISA-75.01.01: 2012 standard [9]. ANSI/ISA-75.01.01-2012 includes equations for predicting the flow of compressible and incompressible fluids through control valves. The equations for incompressible flow are based on standard hydrodynamic equations for Newtonian incompressible fluids. They are not intended for use when non-Newtonian fluids, fluid mixtures, slurries, or liquid–solid conveyance systems are encountered. The equations for incompressible flow may be used with caution for non-vaporizing multi-component liquid mixtures. To calculate the air flow through the pneumatic valve, it is necessary to use a conversion of these factors. Using this method to calculate the air flow rate will not provide accurate results. A particular problem is the small pressure drop across the pneumatic valve, which in the valve seat is 15% of the inlet pressure. From an economic and environmental point of view, it is justified to use two flow parameters, such as sound conductance C and critical pressure ratio b recommended by the ISO 6358: 2013 standard [10]. The ISO 6358-1:2013 standard specifies requirements for the installation of the test, the test procedure, and the presentation of the results for the steady state method. Value C is the maximum valve flow rate when the air passing through reaches the sonic flow condition (choked flow). Value b is the critical pressure ratio between the downstream pressure and the upstream pressure when the flow condition changes from subsonic to sonic or vice versa. In paper [11], algorithms are presented to calculate the nominal flow rate q

_{vn}and the flow factor Kv as a function of the volume flow sonic conductance C and the critical pressure ratio b. In this paper, two methods are presented that were used to determine the sonic conductance C and the critical pressure ratio b, when the flow coefficient K

_{v}or the nominal flow rate q

_{Nnom}are known. These two approaches improve the selection of flow parameters for pneumatic control valves. The alternative flow parameter is the effective sectional area S in mm

^{2}according to the JIS B 8390: 2016 standard [12]. JIS B 8390: 2016 deals with the determination of the flow rate characteristics of components using compressible fluids. This standard is an important tool in determining the flow rate expressed by the effective area S. The S represents the maximum constant flow in choked flow. It also expresses the size of the valve in direct relation to the speed of the actuator. The conversion of the sonic conductance C in dm

^{3}s

^{−1}∙bar

^{−1}to the effective sectional area S in mm

^{2}applies: S = 5 C. The flow parameters C and b contained in the data sheets often differ from their actual values, which were confirmed by the experimental determination of the characteristic of the pneumatic control valve [13]. The object of this article is to test the properties of pneumatic elements. These elements are part of the equipment to measure the parameters of rotary air motors. A comparison of the measured data with the mathematical model revealed minor variations. The flow parameters C and b of the pneumatic valves are not always given in the manufacturer’s data sheets. Some pneumatic components manufacturers do not measure valve flow parameters, but only provide their nominal DN diameters in the data sheets.

## 2. Measurement Methods to Determine the Flow Parameters of Pneumatic Components

## 3. Test Bench with Individually Configured Flow Meter Circuits

_{vN}= 20–200 L/min (1.2–12 m

^{3}/h), proportional directional control valve q

_{vN}= 100–2000 L/min (6–120 m

^{3}/h), and directional valve q

_{vN}= 500–4200 L/min (30–252 m

^{3}/h). The purchase of several expensive thermal flow meters adapted to different flow rates of pneumatic valves usually exceeds the financial capabilities of research laboratories. Therefore, a measuring stand was built to measure the flow characteristics and parameters of pneumatic valves tested with a wide range of sizes, from very small to very large nominal flows. A wide range of flow rate measurements are possible by adopting replaceable Venturi tubes. The measuring stand contains components recommended in the ISO 6358 standard for the online testing circuit. The measuring stand has also been equipped with a flow meter circuit and HMI measurement and control panels. The flow meter circuit contains interchangeable venturi tubes, a Setaram thermal microflow meter (called Setaram) [22], and two bypass loops, main and side. The main bypass loop contains a calibrated orifice. The Setaram is placed in the side bypass loop. The heated tube of the Setaram in the side bypass loop is connected using capillary tubes to the main bypass loop. The view and diagram of the measuring test bench with replaceable venturi tubes for the automatic measurement of pneumatic valve flow rates in a wide range of sizes are shown in Figure 3.

- The interchangeable venturi tubes can be adapted to the flow measurement range of the pneumatic valves.
- Pressure losses in bypass loops depend on the choice of calibrated orifice and pipe dimensions.
- The flow measurement is independent of the gas pressure and temperature, allowing for the direct measurement of the volumetric flow rate q
_{v}in m^{3}/h. - Interchangeable venturi tubes in the nominal diameter range from 0.015 to 0.080 m significantly extend the flow rate measurement range from 2.5 to 250 m
^{3}/h for a given upstream pressure. - The upstream pressure can have a different range, up to 1, 2, and 5 MPa, depending on the dimensions of the bypass loops.

^{3}/h) to high (up to 250 m

^{3}/h) at pressures of up to 1 MPa. For the parallel connection of the side loop, the main loop, and the venturi tube, the following equation for volumetric flow rates was written.

_{vm}is the measured flow rate, q

_{S}is the flow rate in the Setaram heated tube, q

_{vt}is the flow rate through the venturi tube, and q

_{MS}is the flow rate in the main bypass loop tube section.

_{S}is the flow resistance in the side bypass loop, R

_{SM}is the flow resistance in the main bypass loop tube section, and K is the calibration constant

_{m}is the mass flow rate through the venturi tube in kg/s, q

_{vt}is the volume flow rate through the venturi tube in m

^{3}/s, C

_{d}is the discharge coefficient, C

_{d}= 0.987, ε is the expansibility factor, ε = 0.978, β is the diameter ratio, β = d/D, d is the diameter of the throat in m, D is the nominal diameter of the tube in m, Δp is upstream-to-throat differential pressure in Pa, Δp = p

_{1}− p

_{2}, p

_{1}is the static upstream pressure in Pa, p

_{2}is the static pressure in the throat in Pa, ρ

_{m}is the air density in kg/m

^{3}under measurement conditions, for the measured pressure p

_{2m}and temperature T

_{1m}, ρ

_{m}= p

_{2m}R

^{−1}T

_{1m}

^{−1}, and R is the individual gas constant of air in J kg

^{−1}K

^{−1}.

_{S}in the heated Setaram tube is inversely proportional to the temperature difference ΔT = T

_{2}− T

_{1}, as follows [25],

_{S}is the volume flow rate of the gas in the Setaram heated tube in m

^{3}/s, f

_{S}is the proportionality factor of the Setaram, P is the input power converted into heat energy in W, L is the conduction loss in W, c

_{p}is the specific heat of the gas at constant pressure in J kg

^{−1}K

^{−1}, T

_{1}is the temperature of the gas (tube wall) before the heater in K, and T

_{2}is the temperature of the gas (tube wall) behind the heater in K.

_{0}is the resistance of the windings at ambient temperature (T

_{a}= 293.15 K) in Ω, R

_{3}is the constant resistance in Ω, ${\overline{T}}_{1}$, ${\overline{T}}_{2}$ are the average temperatures of the resistance winding in K.

^{3}/h. On a calibrated measuring circuit with interchangeable venturi tubes of a specific nominal size, the flow parameters of the pneumatic valves are measured in the same range of nominal flow. In industrial pneumatics, pneumatic valves with a wide range of sizes are used, for which it is difficult to determine the flow parameters using theoretical calculations. The flow parameters of pneumatic valves have an important effect on the performance of pneumatic control systems. The correct selection of pneumatic valves depends on the type of medium, working pressure, pressure drop, flow rate, and temperature. Determining the flow rate is significant because the maximum flow rate is used to select the valve size, the minimum flow rate is used to check the turndown requirement, and the normal flow rate is used to check the valve control.

## 4. Calibration of the Individually Configured Flow Meter Circuit

_{vm}in the calibrated flow meter circuit and the reference flow rate q

_{vref}of the Molbloc flow meter. The diagram of the calibration test bench for the calibration of the flow meter circuit with the Molbloc/Molbox system is shown in Figure 6.

_{vm}in m

^{3}/h for the power change rate (PCR) in W/h (units that indicate the change in power over time). The power change rate (PCR) at W/h is the calibration parameter of the Setaram microflow meter. The calibration curves were linearly approximated. The linearization of the calibration curves increases the accuracy and repeatability of the flow rate measurement and is also essential in automating this measurement. For the purposes of determining the characteristics and flow parameters of pneumatic valves, the flow meter circuit with an interchangeable venturi tube with a nominal diameter of D = 0.065 m was calibrated. The calibration curves performed are shown in Figure 7 and Figure 8. Calibrated flow meter circuits have an accuracy of 1.5% and a repeatability of 0.5% full-scale (FS). From the calibration curve U = f(PCR) the PCR value is read, and from the calibration curve q

_{vm}= f(PCR) the volumetric flow rate value q

_{vm}is read.

## 5. Automatic Measurement of Flow Parameters

^{3}/h).

## 6. Measurement Results

^{3}/h) at pressure 7 bar.

_{vm}= f(p

_{2m}/p

_{1m}) of the pneumatic valves were carried out at a constant upstream pressure p

_{1m}set by the pressure regulator and a changing downstream pressure p

_{2m}adjustable through the flow control valve. The flow control valve sets the initial downstream pressure p

_{2}

_{m}below the critical point. Then, before changing the setting of this valve, the pressure drops in the pneumatic valve under test gradually increase. For each set pressure p

_{2}

_{m}, the flow rates q

_{v}

_{m}are read from the calibration curves, as seen in Figure 7 and Figure 8. The measurement data were limited to 17 points. Figure 10 shows the measurement data for the volume flow rate as a function of the pressure ratio, q

_{vm}= f(p

_{2m}/p

_{1m}).

_{2m}= f(q

_{vm}) obtained for different upstream pressures p

_{1m}are often presented. Figure 11 shows the downstream pressure measurement data as a function of the flow ratio, p

_{2m}= f(q

_{vm}).

_{N}= 100 kPa, temperature T

_{N}= 293.15 K, and individual gas constant R

_{N}= 288 J kg

^{−1}K

^{−1}at 65% RH (Relative Humidity).

_{v}

_{c}was determined and then the volume flow sonic conductance C was calculated according to the formula,

_{2mc}is the critical downstream pressure from the measured data.

_{0}= 0.46, as read from the measurement data. From the LSF numerical procedure, the best fitting value of the critical pressure ratio b = 0.4781 was obtained. Figure 12 shows the flow rate measurement data with a fitting curve in the flow rate ratio vs. pressure ratio coordinates.

_{i}(X

_{i},b) function with respect to the flow rate measurement data determined from the formula,

_{vc}, the upstream pressure sdp

_{1m}, and the upstream temperature sdT

_{1m}was calculated for a distribution of measured values. The uncertainty of the sonic conductance sC/C and the critical pressure ratio sb/b was calculated according to the ISO 6358-2 standard [28]. The results of the measurements and the values of the parameters calculated of the pneumatic valve tested are presented in Table 2.

## 7. Discussion

- -
- flow rate under choked flow conditions, for $\frac{{p}_{2}}{{p}_{1ma}}\le b$

- -
- flow rate under subsonic flow conditions, for $\frac{{p}_{2}}{{p}_{1ma}}>b$

_{a}. Figure 16 compares the discharge characteristics of the air tank through the pneumatic solenoid valve with the flow parameters C and b determined on the measuring stand and adopted from the catalogue (C

_{cat}= 2.6 × 10

^{−8}m

^{3}s

^{−1}Pa

^{−1}, b

_{cat}= 0.526, for adiabatic expansion, κ = 1.4).

_{m}is the density in measurement condition and ρ

_{N}is the density referred in ANR.

## 8. Practical Purpose

_{1}, b

_{1}and a proportional throttle valve with flow parameters C

_{2}, b

_{2}, the equivalent flow parameters C

_{1,2}and b

_{1,2}were determined. If each of the connected series valves has approximately the same capacity [31], then the values of the equivalent flow parameters C

_{1,2}, b

_{1,2}were determined using the simplified additive method,

_{C}from 20 MPa to 0.6 MPa. The setting of the throttle valve is adapted to the air consumption and the pressure in the air motor. Figure 19 compares the numerically calculated and experimental curves of the high-pressure compressed air tanks discharge processes through two series-connected pneumatic valves. The numerical solution to discharging the compressed air receiver tank through pneumatic valves is presented in [32]. The result of the HTB high-pressure air tank discharge tests allowed us to verify the additive method of calculating the equivalent values of the flow parameters C

_{1,2}, b

_{1,2}for two connected pneumatic valves in series. The calculation time for the tank discharging is approximately 6% shorter than the measurement time. This has no special meaning when calculating the traction time of a hybrid tricycle bike (HTB) pneumatic propulsion system, which depends on many other factors. The results presented are the basis for determining the HTB traction parameters, e.g., travel distance S and the selection of propulsion parameters. The speed of the HTB can be adjusted to the needs of the user by adjusting the airflow to the motor using a proportional throttle valve. An HTB pneumatic propulsion system allows for a wide range of speed settings.

## 9. Conclusions

_{i}(X

_{i},b) to the measurement data. A solution to a real scientific problem has been presented, which is to determine the discharge time of the compressed air receiver tank through series-connected pneumatic valves. The additive method for calculating the equivalent values of the flow parameters C

_{1,2}, b

_{1,2}for two series-connected pneumatic valves was experimentally verified. The series of connecting pneumatic valves was used in the HTB high-pressure pneumatic propulsion system.

- The proposed individually configurable flow meter circuit with the appropriate split of flow rates in the venturi/main bypass loop/side bypass loop ensures high measurement accuracy from low to large flow rates.
- Calibration should be performed for each individually configured flow meter circuit. Measurements made on a calibrated flow meter circuit are reliable and useful in practice.
- The automatic measurement procedure enables the precise and reproducible measurement and rapid sharing of the measurement results over a wireless network with industrial partners.
- The theoretical model of flow parameters was well adapted to the data measured by a numeric method. The numerical model can be used to calculate the flow parameters of air valves of different sizes. Limiting the measurement points affects the precision of the fit function.
- The discharging characteristics of the air tank through the pneumatic solenoid valve with the flow parameters C and b determined on the test bench and adopted from the catalogues were compared. The flow parameters of the valves in the catalogues do not make it possible to make accurate calculations of the discharge parameters of the compressed air tank.

## 10. Patents

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

b | critical pressure ratio |

C | sonic conductance [m^{3}/s/Pa] |

C_{d} | discharge coefficient |

D | diameter of the throat [m] |

D | nominal diameter [m] |

P | pressure [Pa] |

p_{a} | atmospheric pressure [Pa] |

q_{m} | mass flow rate [m^{3}/h] |

q_{v} | volumetric flow rate [kg/s] |

R | gas constant [J/(kgK)] |

T | temperature [K] |

V | velocity [m/s] |

Β | diameter ratio |

ε | expansibility factor |

κ | specific heat ratio |

ρ | density [kg/m^{3}] |

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**Figure 1.**A test set-up according to the ISO 6358 standard: (

**a**) circuit for the exhaust-to-atmosphere test, (

**b**) circuit for the in-line test, 1—adjustable pressure reducing valve, 2—shut-off valve, 3—mass flow meter, 4—temperature measuring tube, 5—temperature measuring instrument, 6—upsteram pressure measuring tube, 7—upstream pressure gauge, 8—pneumatic component under test, 9—downstream pressure measuring tube, 10—downstream pressure gauge, 11—flow control valve [9].

**Figure 2.**The test bench for indirect measurement of the flow parameters of pneumatic components: (

**a**) discharge test, (

**b**) charge test, (

**c**) tank-to-tank test: 1—compressor air source, 2—shut-off valve, 3—supply tank, 4—dual pressure and temperature transducer, 5—switching valve, 6—upstream pressure flow measurement tube, 7—pneumatic component under test, 8—downstream pressure measurement tube, 9—upstream pressure and temperature transducer, 10—downstream pressure transducer, 11—exhaust tank, 12—dual pressure and temperature transducer.

**Figure 3.**View (

**a**) and diagram (

**b**) of the measuring test bench with interchangeable venturi tubes: 1—digitally controlled proportional pressure regulator, 2—upstream measuring tube, 3—valve under test, 4—proportional flow control valve, 5—interchangeable venturi tube, 6—calibrated orifice, 7—main bypass loop, 8—meter bypass loop with capillary tubes, 9—heated tube, 10—Setaram thermal microflow meter, 11—power supply, 12—millivolt meter, 13—temperature meter, 14, 15—digital pressure sensors, 16—HMI measurement panel, and 17—HMI control panel.

**Figure 4.**Dimensions of the flow meter circuit with interchangeable venturi tubes, the main bypass loop, and the side bypass loop.

**Figure 5.**Setaram thermal microflow meter with electrical resistance bridge: 1—sealed cylindrical container, 2—thermal shield, 3—heated tube, 4—resistance winding on the inlet side, 5—resistance winding on the outlet side, 6—resistance bridge, 7—amplifier, 8—constant-current power supply.

**Figure 6.**Calibration test bench for the flow meter circuit: 1—pressure regulator, 2—calibrated flow meter circuit, 3—Molbloc-S, 4—Molbox1+, 5—PC with Compass calibration software.

**Figure 9.**View of the main screen (

**a**), and the sensor screens (

**b**) of the MP panel, and screen for calculation blocks (

**c**) of the CP panel.

**Figure 14.**Comparison of the measurement data and the theoretical flow characteristic of the valve under test.

**Figure 15.**Diagram of the air tank discharge measurement test bench: 1—compressor, 2—pressure regulator, 3—stand-alone air receiver tank, 4—dual pressure and temperature transducer, 5—pneumatic solenoid valve.

**Figure 16.**Comparison of the discharge characteristics of the air tank through the pneumatic valve for the flow parameters C and b, as determined on the measuring stand and adopted from the catalogue.

**Figure 18.**Diagram of the HTB high-pressure pneumatic propulsion system: 1—high-pressure air compressed tank, 2—pressure transducer, 3—high-pressure valve, 4—proportional throttle valve, 5—pressure transducer, 6—air motor, 7—chain transmission, 8—tricycle wheels.

**Figure 19.**High-pressure air compressed tank discharge processes for two series connected pneumatic valves.

Nominal Diameter D | Diameter Ratio Β | Differential Pressure Δp | Flow Rate Range q _{v} |
---|---|---|---|

m | Pa | m^{3}/h | |

0.015 | 0.5 | 150 | 2.5 |

0.020 | 0.5 | 190 | 5 |

0.032 | 0.5 | 255 | 15 |

0.040 | 0.5 | 290 | 25 |

0.050 | 0.6 | 215 | 50 |

0.065 | 0.6 | 295 | 100 |

0.080 | 0.75 | 265 | 250 |

Parameter | Value | Description |
---|---|---|

p_{1ma} | 732.014 kPa | Average upstream pressure |

sdp_{1m} | 0.835 kPa | Standard deviation of upstream pressure |

T_{1ma} | 295.52 K | Average upstream temperature |

sdT_{1m} | 0.108 K | Standard deviation of upstream temperature |

q_{vca} | 78.85 m^{3} h^{−1} | Average critical flow rate |

sq_{vc} | 0.05 m^{3} h^{−1} | Standard deviation of critical flow rate |

C | 3 × 10^{−8} m^{3} s^{−1} Pa^{−1} | Volume flow sonic conductance |

sC/C | 1.8% | Uncertainty of the sonic conductance |

b | 0.4781 | Critical pressure ratio |

sb/b | 2.6% | Uncertainty of the critical pressure ratio |

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## Share and Cite

**MDPI and ACS Style**

Dindorf, R.
Measurement of Pneumatic Valve Flow Parameters on the Test Bench with Interchangeable Venturi Tubes and Their Practical Use. *Sensors* **2023**, *23*, 6042.
https://doi.org/10.3390/s23136042

**AMA Style**

Dindorf R.
Measurement of Pneumatic Valve Flow Parameters on the Test Bench with Interchangeable Venturi Tubes and Their Practical Use. *Sensors*. 2023; 23(13):6042.
https://doi.org/10.3390/s23136042

**Chicago/Turabian Style**

Dindorf, Ryszard.
2023. "Measurement of Pneumatic Valve Flow Parameters on the Test Bench with Interchangeable Venturi Tubes and Their Practical Use" *Sensors* 23, no. 13: 6042.
https://doi.org/10.3390/s23136042