Critical Flow Venturi Nozzles Research Articles

Improved Prediction of the Flow in Cylindrical Critical Flow Venturi Nozzles Using a Transitional Model

AbstractCritical flow Venturi nozzles (CFVNs) are a state-of-the-art secondary standard widely used for gas flow measurements with high precision. The flow rate correlates with the type and thickness of the boundary layer (BL) inside the nozzle throat. In the cylindrical type—one of the two standard designs of CFVNs—the nozzle throat encompasses a defined axial length in which the BL develops. This numerical study is concerned with the BL effects in a cylindrical CFVN by means of two turbulence models. Compared to experimental data, the k-$$\omega$$ ω SST model predicts the discharge coefficient well for high and low Reynolds numbers, but not in the intermediate regime. The $$\gamma$$ γ -$$Re_{\theta }$$ R e θ model, on the contrary, agrees well with experimental data in the entire flow range. Relevant quantities and profiles of the BL are separately investigated in the laminar, turbulent, and transitional region. The calculated laminar and turbulent BL thicknesses correspond to predictions based on integral methods for solving the BL equations. Simple representations are proposed for the Zagarola-Smits scaled laminar and turbulent deficit BL profiles removing the effects of axial position, Reynolds number, and pressure gradient. Furthermore, the shape factor is investigated as a characteristic parameter for determining the transitional region.

Metrology infrastructure for high-pressure gas and liquified hydrogen flows. A brief outline of the MetHyInfra project, measurement challenges, and first results

This paper gives an overview of the ongoing Joint Research Project (JRP) 20IND11 “Metrology infrastructure for high pressure gas and liquefied hydrogen flows” (MetHyInfra), which will ensure traceability in the hydrogen distribution chain. For this purpose, very precise nozzles with well-defined geometries have been produced. In this project, Critical Flow Venturi Nozzles (CFVNs) will be traceably calibrated for the first time with hydrogen and pressures up to 100 MPa using a Coriolis Flow Meter (CFM) as a secondary standard. A CFM has been successfully calibrated with hydrogen against a gravimetric primary standard.Equations of State (EoS) are important for the high-pressure calibration of the nozzles, but also for Computational Fluid Dynamics (CFD) simulations. With regard to CFD, a numerical model has been developed to simulate high pressure hydrogen flow in the CFVN. In a parameter study, non-ideal nozzle shapes are investigated using a shape variation parameter. New Speed of Sound (SoS) measurements were conducted at temperatures from 273 to 323 K and pressures from 1 to 100 MPa. These new data were then used to develop a new EoS for normal hydrogen, optimized for gas phase calculations. In addition to gaseous hydrogen, the project has a strong focus on liquefied hydrogen. Here a three-pronged approach allows traceable measurements. Each of the approaches presented is based on a unique flow calibration principle and relies on independent traceability schemes. The results of the project will ensure traceable measurements and thus a higher level of confidence among end users.

Performance evaluation test of Coriolis flow meters for hydrogen metering at high pressure

This paper describes the results of performance evaluation of Coriolis flow meters from various manufacturers in high-pressure hydrogen actual flow using a calibration system with critical flow Venturi nozzles as a reference. The calibration system consisting of five nozzles was developed to calibrate the flow meters by high-pressure, high-flow-rate hydrogen gas. The performance evaluation test of the Coriolis flow meters was conducted at maximum pressure of 70 MPa, gas temperature of 0 °C and −40 °C, and flow rate range from 0.5 kg/min to 3.0 kg/min. It was confirmed that the instrumental error of most of the DUTs tested in this paper was within ±2.0 %, although the instrumental error tended to be slightly larger at −40 °C in the small flow rate range.

Investigation of the discharge coefficient in the laminar boundary layer regime of critical flow Venturi nozzles calibrated with different gases including hydrogen

This study represents the first step towards the introduction of critical flow Venturi nozzles into the traceability scheme for gaseous hydrogen and addresses the characterisation of the hydrogen discharge coefficient in the laminar boundary layer regime and the identification of a potential alternative gas for nozzle calibration. The experimental study presented was performed for two nozzles with a throat diameter of 0.175 mm and 0.436 mm. The tests were performed with six different gases, including hydrogen, covering a Reynolds number range from 1.5·103 to 6·104. The experimental results show that the discharge coefficient depends not only on the Reynolds number but also on the isentropic exponent of the gas. Based on the experimental data, theoretical models taking into account the isentropic exponent and the Prandtl number of the gas were evaluated. The study indicates possibilities to use inert gases instead of hydrogen in calibration processes.

Measurement Standards of Ukraine for Gas Volume Flow Rate at Pressures of 1 MPa to 5 MPa

The characteristics of the primary measurement standards of the volume gas flow rate at high pressure developed in various countries are considered. A hierarchical scheme for gas flow measuring instruments and a corresponding metrological traceability chain are presented. Described is a PVTt method, on which the primary standards of gas flow rate used in the USA, France, Japan, and Taiwan are based. The need to create in Ukraine primary measurement standards of gas flow rate at high pressure covering different parts of the total flow rate interval from 0,3 m3/h to 1800 m3/h at a pressure of 1 MPa to 5 MPa is substantiated. Metrological traceability of gas flow measurements is realized through a sequence of critical flow Venturi nozzles, which play a role of the reference flow rate material measures. The standards might be used to calibrate the primary reference Venturi nozzles of the most common 0,1 mm to 8 mm diameters. The characteristics and parameters of the standards are determined. By their metrological and technical characteristics, the standards will correspond to the state-of-the-art level. According to the programme of developing the measurement-standard facilities in Ukraine, in 2019 the primary standard PVTt-65 was created and work had started on the development of the primary standard PVTt-1800 and the working standard PE-5400. A detailed study of the metrological characteristics of the measurement standards will be the topic of further work.

Experimental investigations on cylindrical critical flow Venturi nozzles with roughness

In an attempt to redefine and improve the ISO9300 norm, it is possible to see the emergence of a universal (Cd) curve. For this, all the influential factors must be correctly understood within their range of variation. In recent discussions, the experimental calibration point could be limited, and a low-pressure measurement could be sufficient to extrapolate the higher part of the curve with a relatively good level of confidence. For that purpose, the cylindrical shape gives more variations and needs a higher level of measurement to understand the behavior of the curve. Roughness level is a key parameter to this understanding. Experiments have been carried out to determine the impact of cylindrical nozzle throat roughness on Cd and to demonstrate the need for precise dimensional parameters, such as diameter and roughness characterization. The results show that an increase in roughness may lead to a significant decrease in Cd, particularly at high Reynolds numbers (Red). A theorization is introduced based on Colebrook & White’s formulation which allows the thickness boundary layer to be quantified. This study highlights the need for further investigation into both cylindrical nozzles and roughness effects on the discharge coefficient in order to improve the norm.

Discharge coefficients of CFVN predicted for high Reynolds numbers based on low-Re-calibration

In 2016, PTB introduced a function for the representation of the discharge coefficient cD of critical flow venturi nozzles (CFVN) (versus the Reynolds number Re) which covers the operating range for both laminar and turbulent boundary layers. It contains the parameters a for the impact of the core flow, blam for the Re-dependency in case of laminar and bturb in case of turbulent boundary layers. These parameters are not independent from each other but have the fixed relation of bturb = 0.003654blam1.736.Furthermore, the parameter a and the parameter blam are both direct functions of the local curvature radius Rc,throat of the nozzle at the throat. These relationships to Rc,throat are described by theoretical models. Consequently, the overall dependency of the discharge coefficient cD on Reynolds number Re can be derived from only one parameter.The paper describes how these relationships can be used to extrapolate the calibration values of a CFVN determined with atmospheric air to high pressure gas flow applications covering a Reynolds range of about 1:60. It is shown in detail by examples and the reliability is demonstrated by comparison data for low and high pressure for 33 nozzles. Finally, aspects of preconditions for such extrapolation and uncertainties are discussed.

Experimental study on improving the critical back-pressure ratio using a step in a critical-flow Venturi nozzle

Critical-flow Venturi nozzles (CFVNs) are used widely as transfer standards and can measure flow rates accurately. However, previous research has reported that in some CFVNs, the pressure-recovery effect of the diffuser is poor, and it is called the premature unchoking phenomenon. In the present study, experiments were conducted to investigate the critical back-pressure ratio (CBPR) of a CFVN. Additionally, to solve the problem of premature unchoking phenomenon, we focused on the step in the diffuser and verified its effect. The diffuser step can maintain a high CBPR at values of the Reynolds number (Re) of around 22,000 and 5500. For Re = 5500, although the CBPR of a typical CFVN is 0.46, providing the step increases it to 0.75. Notably, we are able to increase the CBPR at low Re, at which previous studies could not suppress premature unchoking phenomenon. A diffuser step is believed to improve the CBPR because the shock location is fixed at the step, and the region of subsonic flow, which is important for pressure recovery, is expanded.

Gas dilution system using critical flow Venturi nozzles for generating primary trace-moisture standards in multiple gas species

Gas dilution systems are commonly used to generate calibration gas mixtures for secondary gas standards. However, if a gas dilution system is used to generate gas mixtures for primary trace-moisture standards in multiple gas species, difficulty arises; flow control with relative stability of better than 0.009% is required although the relative uncertainty of the best gas flow meter to date is around 0.3%. In this study, we developed a novel gas dilution system using critical flow Venturi nozzles to address this problem. The developed dilution system can measure and control the flow rates of gases in the range of approximately 0.05 l min−1 to 7 l min−1 (when converted to those measured at 101 325 Pa and 273.15 K) with relative stability of better than 0.007%. Using the dilution system, we developed a magnetic suspension balance/diffusion-tube humidity generator capable of generating trace moisture in N2 in the range of approximately 10 nmol mol−1 to 5 µmol mol−1 in amount fraction. The accuracy of the generated trace-moisture standard was verified by measurement with cavity ring-down spectroscopy.

Experimental and numerical investigation of the cavitation-induced choked flow in a herschel venturi-tube

Due to their simple geometry, cavitating Venturi nozzles (CV) are a long time subject of experimental as well as numerical investigations. However, research mostly focused on certain aspects like the comparison of experimental data with numerical cavitation models or the spray development of diesel injection nozzles, but rarely on the choked flow condition itself, especially with regard to liquid flow measurement.If the pressure decreases due to the local acceleration of the flow to the respective vapor pressure, a choked flow condition similar to the well-known critical flow Venturi-nozzles (CFVN) develops. For the purpose of gaining further insight into the choked flow condition with respect to liquid flow measurement, high-speed camera investigations of a transparent Herschel Venturi-tube configuration, also known as classical Venturi-tube, were performed. Together with pressure and flow rate measurements, they demonstrated the overall stable flow behavior under choked conditions. With additional numerical investigations, phenomena during the onset of the choked condition were clarified. Furthermore, a simple correlation for the calculation of the actual flow rate during the choked condition, including a temperature correction was proposed.

Thermal effect on body temperature distribution of the critical flow Venturi nozzle

The expansion of the gas through a critical flow Venturi nozzle (CFVN) leads to a 50°C temperature drop of the gas at the nozzle throat. The body of CFVN is also cooled, which produces several effects on the flow characteristics called thermal effects. Thus, there is an urgent necessary to investigate the dynamic temperature distribution of CFVN body. Firstly, experiments were conducted by a multipoint temperature acquisition system. The dynamic temperatures of 12 sampling points for each stainless steel CFVN were obtained. It is found that the dynamic response time of CFVN body temperature can be hundreds to thousands of seconds. The maximum body temperature drop of 16.5°C was observed. Then some isotherm maps of CFVN body were obtained by the Kriging interpolation method. Finally, CFD simulations were carried out to explain the experimental results because the flow field of axisymmetric nozzle is difficult to be observed. The results revealed the position of shock wave is the main influence on body temperature distribution of CFVN. All the results can be used to further analyze the thermal effect of CFVN.

Research on the Coaxial Connection between Gas Flowmeter and Critical Flow Venturi Nozzle Gas Flow Standard Device

As an important measurement instruments of trade metering, gas flowmeter has been more and more widely used, and the quantity value transfer of the flow meter is becoming increasingly significant. In order to realize the accurate measurement, the method of the coaxial connection between gas flowmeter and critical flow Venturi nozzle gas flow standard device is studied in this paper, and the coaxial error between this gas flowmeter and standard device within ±1mm is achieved.

Humidity effect on the calibration of discharge coefficients of critical flow Venturi nozzles in a pVTt facility

The available research on the humidity effect when calibrating the discharge coefficients of critical flow Venturi nozzles has mostly treated the humid air as a mixture of vapor and dry air. In this paper, atmospheric air with normal humidity was used to calibrate the discharge coefficients of critical flow Venturi nozzles in a pVTt facility. The calibration results were found to depend on the initial pressure in the collection tank, which reduced the discharge coefficient by 1.17%. The results suggest that vapor condensation in the diffuser section of the CFVN and the inventory volume or collection tank and adsorption of water molecules on the surface of the collection tank are additional humidity effects in a pVTt facility. An empirical model was developed for the humidity effect with the critical pressure for each facility determined from the experimental results. With the humidity correction, the NIM and PTB results compare very well.

Discharge coefficient equation for critical-flow toroidal-throat venturi nozzles covering the boundary-layer transition regime

A single, simple correlating equation between the discharge coefficient of critical-flow Venturi nozzles (CFVNs) having an ISO 9300 toroidal throat and their Reynolds number is proposed in the Reynolds number range from 2.1×104 to 3.2×107. The equation covers the whole Reynolds number range from laminar to turbulent boundary-layer regimes and can thus be used instead of the two correlating equations defined in ISO 9300 : 2005. The deviation of the discharge coefficients of well-made CFVNs is expected to be less than ±0.2% throughout the Reynolds number range. Tolerances for the diffuser length, inlet curvature and inlet diameter are also proposed. It is shown that the widely-accepted theories that estimate the core flow distribution result in significant error when the inlet curvature is small and that removing the third term in Hall׳s equation results in very good agreement with the experimental data regardless of the magnitude of the inlet curvature. The use of CFVNs with the inlet curvature of 1.0D is discussed in order to reduce the uncertainty owing to undefined boundary-layer transition Reynolds number. A possibility is shown that such a CFVN may not have an apparent boundary-layer transition in the investigated Reynolds number range from 1.5×104 to 2.0×106.

Discharge coefficient of small sonic nozzles

The purpose of this investigation is to understand flow characteristics in mini/micro sonic nozzles, in order to precisely measure and control miniscule flowrates. Experimental and numerical simulation methods have been used to study critical flow Venturi nozzles. The results show that the nozzle?s size and shape influence gas flow characteristics which leading the boundary layer thickness to change, and then impact on the discharge coefficient. With the diameter of sonic nozzle throat decreasing, the discharge coefficient reduces. The maximum discharge coefficient exits in the condition of the inlet surface radius being double the throat diameter. The longer the diffuser section, the smaller the discharge coefficient becomes. Diffuser angle affects the discharge coefficient slightly.

Influence of wall roughness on discharge coefficient of sonic nozzles

To research the influence of roughness on discharge coefficient of axisymmetric sonic nozzles systematically, a turbulence model was established, and standard k–ε model was used in the turbulent core region while Wall Functions was carried out in the boundary layer region. A series of numerical simulations were conducted to research discharge coefficients of 6 critical flow Venturi nozzles with throat diameter ranging from 0.5 to 100mm when Reynolds numbers ranges from 104 to 109 and relative roughness from 10−2 to 10−6. The validity of the simulation model was confirmed by both the experimental data of Stewart and ISO 9300 empirical equation. According to the simulation results and theoretical analysis, the relations between discharge coefficient and relative roughness were obtained. It is recommended that the dimensionless parameter relative roughness should be used in ISO 9300 rather than absolute roughness. Additionally, when the machining of nozzle cannot satisfy the ISO 9300 requirement or the Reynolds numbers exceed the upper limits of the ISO 9300 equation, the effect of roughness should be considered, and the relative roughness of sonic nozzle should be provided clearly in the further experiment of discharge coefficient.

Research on the measurement way of the small critical flow venturi nozzle based on the gas prover standard device

Research on the measurement way of the small critical flow venturi nozzle based on the gas prover standard device

Experimental Research on the Expansibility Factor Calculation Model of V-Cone Flowmeters

This article aims to improve the accuracy of gas flow measurement of cone flowmeter and get a high-precision expansibility factor calculation model with wide applicable pressure range and different upstream side pressure. The experimental research was based on the DN50 and DN100 two sets of V-Cone flowmeter designed by Tianjin University. As the standard gas flow facility by means of critical flow venturi nozzles was insufficient supply capacity and poor pressure stability in positive pressure method, the experimental data obtained from standard gas flow facility by using negative pressure method was used to fit out the V-Cone flowmeter expansibility factor calculation model --TJU-2012 model. The model was tested with the experimental data obtained from the standard gas flow facility and compared with other four cone flowmeter expansibility factor calculation models, its maximum relative error was better than 0.9% and square averaged root error was better than 0.6%, both of them are the least.

The humidity effect on air flow rates in a critical flow venturi nozzle

A Critical Flow Venturi Nozzle (CFVN) is usually calibrated using dry air. Yet CFVNs in industrial and calibration service centers are often used to measure flow rates of humid air. Therefore, ISO 9300 provides the calculation method for the humidity effect on discharge coefficients of CFVN. However, since this method is only due to a theoretical analysis, it is important to confirm and check the ISO calculation method for the humidity effect on CFVN with its isentropic analysis by means of an experimental method. In this experiment, three CFVNs with diameters of 0.4, 0.8 and 1.6 mm were calibrated with dry air (with the dew point −40 °C), in a primary air flow standard system with a mercury sealed piston prover, installed at the Korea Research Institute of Standards and Science (KRISS). Another piston prover, a portable dry piston prover, was used as a reference meter and was also calibrated in the primary standard system using dry air. The repeatability of this dry piston prover was confirmed with the deviation being less than 0.05%. The CFVNs were tested with this dry piston prover, using humid air. For air types with high humidity, the humidity effect on flow rates through the CFVNs showed quite significant difference between the experimental results and those from the ISO method with isentropic analysis. But for air types with low humidity, its effect was relatively insignificant.

Novel Flow Measurement/Control System in Magnetic Suspension Balance/Diffusion-Tube Humidity Generator

A novel flow measurement/control system was developed to improve the capability of measuring and controlling the flow rate of the dry gas in the magnetic suspension balance/diffusion-tube humidity generator at the National Metrology Institute of Japan. The flow rate was measured using a mass flow meter composed of multiple critical flow Venturi nozzles and was adjusted to a set value by controlling the pressure of the gas upstream of the nozzles using a feedback loop with the flow rate measured using the mass flow meter. Using this system, the uncertainty due to the instability of the flow rate was reduced to less than 0.0023 %, causing its contribution to the uncertainty of the standard value of the trace moisture generated to be insignificant. The improved capability to rapidly and stably control the flow rate of the dry gas allows the rapid change in trace moisture that is necessary to evaluate the performance of conventional and commonly used trace-moisture analyzers.