Critical Nozzle Research Articles

Dependence of Pressure Characteristics of Pressurized Pulse Water Jet Chamber on Nozzle Diameter

The nozzle is the key element of the water jet generator for energy conversion. In order to explore the influence of the nozzle diameter on the pressure characteristics of the supercharged pulsed water jet plenum chamber, a supercharged pulsed water jet pressure acquisition system was established, and the equations of motion and theoretical pressurization ratio equations of the supercharged pulsed water jet generator were established. The pressurization chamber pressure acquisition experiments under different nozzle diameters were carried out. The research results show that the pressurized pulsed water jet generator has a critical nozzle diameter of 0.6 mm. When the nozzle diameter is less than the critical diameter, the pressure in the boost chamber is equal to the product of the driving pressure and the boost ratio. As the nozzle changes, there is no significant change in the peak pressure and frequency of the boost chamber. When the nozzle diameter is greater than the critical diameter, there is a non-linear relationship between the boost chamber pressure and the driving pressure. As the nozzle diameter gradually increases, the actual boost ratio gradually decreases, and the peak pressure of the boost chamber further decreases. The nozzle diameter can no longer provide a load for the establishment of fluid pressure in the boost chamber. The results of this research provide a research basis for further controlling the pressure characteristics of the boost pulse water jet.

Experimental speed-of-sound data and a fundamental equation of state for normal hydrogen optimized for flow measurements

Speed-of-sound measurements for normal hydrogen (n-hydrogen) in a temperature range between 273 K and 323 K were carried out using a cylindrical resonator at pressures from 1 MPa to 10 MPa and a dual-path pulse-echo system at pressures from 20 MPa to 100 MPa. The relative expanded uncertainties (k = 2) of the measurements range from 0.04 % to 0.08 %. Based on these measurements and data from the literature, a fundamental equation of state (EOS) was developed for the calculation of thermodynamic properties of n-hydrogen. It is expressed in terms of the Helmholtz energy with the independent variables temperature and density. Due to the fundamental nature of the Helmholtz energy, the equation can be used to calculate all thermodynamic properties from one mathematical expression. In contrast to typical EOS of this kind, the boundary conditions are somewhat more restricted. The relevant temperature and pressure ranges are limited to typical pipeline and storage conditions of gaseous hydrogen, including temperatures relevant for measurements with critical nozzles (140 K to 370 K with pressures up to 100 MPa). The computational speed for the implementation of the correlation in measurement sensors plays a superior role. Therefore, the equation is kept as short as possible, and exponents are of integer-kind. Most of the experimental data are still reproduced within their measurement uncertainties.

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

Critical 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-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega$$\\end{document} SST model predicts the discharge coefficient well for high and low Reynolds numbers, but not in the intermediate regime. The γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document}-Reθ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re_{\ heta }$$\\end{document} 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.

Analytical methodology for calculating discharge coefficients of critical flow nozzles for high-pressure hydrogen

Hydrogen is gaining attention as a clean energy source for the sustainable development of the global economy and mitigation of global warming. Flow rate measurements are vital for ensuring the accuracy of hydrogen transaction volumes. As a widely accepted standard for gas flow rate, critical flow nozzles are expected to fulfill this role. However, the discharge coefficient associated with the calibration tests of critical flow nozzles for high-pressure hydrogen does not align with the semi-empirical formula of ISO 9300 (ISO curve). This discrepancy has not yet been resolved. In this study, we conducted 3D numerical simulations of the nozzle discharge coefficients for high-pressure hydrogen. Based on our simulations and experimental results from the previous study, we investigate the cause of the deviation of the discharge coefficient from the ISO curve at high pressure. We also propose a method for calculating the discharge coefficient based on real-gas effects and demonstrate that the discharge coefficient aligns with the ISO curve at high pressures.

Ensuring metrological traceability of the gas flow measurements at high pressure in Ukraine

Described is the PVTt primary measurement standard used to calibrate primary standard critical flow nozzles with throat diameters from 2 mm to 8 mm over a flow rate range of 100 m3/h up to 1800 m3/h. Means and methods of the working standard critical flow nozzles calibration are considered. The metrological traceability chain for the gas flow measurements is presented. In the metrological traceability chain, the primary standards are the primary standard critical flow nozzles, the metrological characteristics of which are established through calibration using the primary measuring system and the primary measurement procedure. The secondary standards are working standard critical flow nozzles, the metrological characteristics of which are established by comparing them with primary standard nozzles. The metrological traceability chain has a branched structure, as the measurement model includes various physical quantities: pressure, temperature, volume, time, and gas properties.

Transonic flow field in critical flow Venturi nozzle

In this paper, theoretical and numerical analysis of a~transonic flow field of critical flow Venturi nozzles according to the ISO~9300 standard is performed. Deviations of the flow field from an estimate based on one dimensionality are clarified. While the theoretical analysis allows prediction of these deviations, the numerical analysis allows quantification of their influence. The main studied phenomena include the local supersonic compression in transonic expansion and the Prandtl-Meyer expansion. The tendency of the flow field to spatial oscillations is shown, alongside the ability of the system to damp these oscillations.

Global stability of supersonic Euler flows in quasi-one-dimensional convergent nozzles

In this paper, we investigate the global well-posedness and stability of steady supersonic Euler flows in a quasi-one-dimensional convergent nozzle. First, we show that there exists a critical nozzle length L1, the global well-posedness of steady supersonic flows can be obtained and the explicit solution is given as long as the nozzle length L < L1. Then we prove the global stability of steady supersonic flows under small perturbations of initial-boundary values by wave decomposition.

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.

Failure analysis of a rotary satellite kiln located in a cement production line

The work herein presented aims to analyse the existing failures in a rotary satellite kiln of a cement production line, more specifically, the last 32 m of the equipment, which is responsible for the abrupt forced cooling of the clinker (cement component) throughout satellite coolers.This device undergoes pronounced temperature variation and, consequently, is subjected to high thermal induced stresses which are superimposed, due to its large dimensions, to structure’s deadweight and the influence of a reduced angular rotation speed.The main failures observed in the equipment were the existence of cracks along the circumferentially weld bead of the outside nozzle to the kiln ferrule and the cracking of the kiln ferrule near the openings that allow the clinker to exit into the satellite coolers. The solution proposed to mitigate these failures was the implementation of reinforcement collars around the critical nozzles, in order to achieve a better local distribution of stresses. Through the numerical simulations carried out using the Finite Element Method, it was verified that the average value of the first principal stress without the reinforcement collars was about 176 MPa. In the simulation with the implementation of the reinforcement collars, this value decreased to 75 MPa (approximately 57% lower). This should increase the equipment’s durability.

Flow field characteristic of water jet with air ring protective layer under submerged environment and the orthogonal optimization of nozzle structure

AbstractA water jet with an air ring protective layer is a promising rock‐breaking and cutting rate improvement method in submerged environment, such as oil–gas drilling. The jet flow field characteristic determines the jet impinge performance and is affected by nozzle structure parameters. In this study, the water jet flow with air ring under submerged environment was numerically simulated. The jet flow field structure with air ring was obtained by analyzing the distributions of jet velocity and air content at different cross sections. The effects of several critical nozzle structure parameters on jet isokinetic core length and axial velocity were investigated by adopting the orthogonal design method. The results show that the jet flow field structure with air ring in radial direction includes a high‐speed water jet zone, air ring protective layer, and air–water mixed zone, having the advantages of concentrated energy in axis region, long core section length, and low‐velocity attenuation. The influence degrees of nozzle structure parameters on jet core section length and axial velocity at X = 0.3 m are: length‐diameter ratio > outlet diameter > conic angle > air nozzle diameter > water‐air nozzle spacing and outlet diameter > length‐diameter ratio > conic angle > water‐air nozzle spacing > air nozzle diameter, respectively. The jet core section length and axial velocity both increase exponentially with the increasing outlet diameter, both first increase rapidly and then slowly decreases with the increase of conic angle and water–air nozzle spacing. There is the optimal conic angle of 15° and appropriate water–air nozzle spacing of 3–5 mm. With the increase of length–diameter ratio, they both first decrease rapidly and then slow down, indicating that conical nozzle is more suitable for water jet with air ring. And 0.9–1.2 mm is proper for the air nozzle diameter.

The Effects of the Structural Tuning on the Sensing Performance of Extinguishant Detector Based on the Differential Pressure Principle

The research of the spatial and temporal distribution of the extinguishant concentration is necessary for the design of a fire extinguishing system. The detection technique based on the differential pressure principle is very suitable for the extinguishant concentration measurement. This paper focused on studying the effect of sensing structure on sensing performance. It was found that due to the solid sensing structure, the sensor had good stability and reproducibility, and the response/sensitivity would increase with the increase of the throat diameter of the critical flow nozzle and temperature, and with the decrease of the inner diameter and the number of the tubes of the vascular bundles, which were in good agreement with the theoretical prediction. For the response rate, it could be improved by increasing the throat diameter and decreasing the external diameter of the vascular bundles, but these also caused the great increase in the response fluctuation, which could lead to the decrease in measuring accuracy despite the improvement in response and sensitivity, especially for the high concentration. However, the increase of the temperature would efficiently reduce the response fluctuation while improving the response and sensitivity. The research results can provide good theoretical suggestions for the sensor design.

Flow velocity measurement using thermocouple and its response estimation

Gas flow measurement is indispensable for social activities. Critical flow nozzles used for flow standards have been improved in ISO 9300 in 1990 and 2005. However, there are still issues regarding their rational shape. The main reason is that it is difficult to measure the flow velocity in the nozzle with low disturbance and high accuracy, although various velocity measurement methods have been proposed.

A systematic approach to calibrate spray and break-up models for the simulation of high-pressure fuel injections

A novel calibration methodology is presented to accurately predict the fundamental characteristics of high-pressure fuel sprays for Gasoline Direct Injection (GDI) applications. The model was developed within the Siemens Simcenter STAR-CD 3D CFD software environment and used the Lagrangian–Eulerian solution scheme. The simulations were carried out based on a quiescent, constant volume, computational vessel to reproduce the real spray testing environment. A combination of statistic and optimisation methods was used for spray model selection and calibration and the process was supported by a wide range of experimental data. A comparative study was conducted between the two most commonly used models for fuel atomisation: Kelvin–Helmholtz/Rayleigh–Taylor (KH–RT) and Reitz–Diwakar (RD) break-up models. The Rosin–Rammler (RR) mono-modal droplet size distribution was tuned to assign initial spray characteristics at the critical nozzle exit location. A half factorial design was used to reveal how the various model calibration factors influence the spray properties, leading to the selection of the dominant ones. Numerical simulations of the injection process were carried out based on space-filling Design of Experiment (DoE) schedules, which used the dominant factors as input variables. Statistical regression and nested optimisation procedures were then applied to define the optimal levels of the model calibration factors. The method aims to give an alternative to the widely used trial-and-error approach and unveils the correlation between calibration factors and spray characteristics. The results show the importance of the initial droplet size distribution and secondary break-up coefficients to accurately calibrate the entire spray process. RD outperformed KH–RT in terms of prediction when comparing numerical spray tip penetration and droplet size characteristics to the experimental counterparts. The calibrated spray model was able to correctly predict the spray properties over a wide range of injection pressure. The work presented in this paper is part of the APC6 DYNAMO project led by Ford Motor Company.

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.

Behaviors of discharge coefficients of small diameter critical nozzles

The discharge coefficients of 59 small diameter toroidal throat Venturi critical nozzles were measured by the static gravimetric method. The throat diameter is from 0.014 mm to 2.35 mm and the Reynolds number is 4 × 102 to 2 × 105. These nozzles were manufactured by the normally processing method base on the same design drawing, but their discharge coefficients were scattered widely. The purpose of this paper is to explain the behavior of discharge coefficient scattered. In the correction procedure used here, while comparing the discharge coefficient obtained experimentally and the reference theoretical model, the throat diameter is corrected and the optimal radius of curvature of nozzle inlet is determined so that both discharge coefficients match. Resultantly, most of the behaviors of the discharge coefficient of 59 critical nozzles could be explained well.

Improving the Estimates of Methodological Errors when Reproducing Volumetric Air Flow Rates Using a Critical Nozzle as a Standard

Improving the Estimates of Methodological Errors when Reproducing Volumetric Air Flow Rates Using a Critical Nozzle as a Standard

Improving the estimation of methodological errors in reproducing the volumetric air flow rate by reference critical nozzle

In the development of the previously obtained results a more accurate estimate of the methodological error in reproducing the volumetric air flow rate by reference critical nozzle is given, associated with the choice of the gas flow model and due to taking into account the initial kinetic energy of the flow at the nozzle inlet. Based on improved flow model an analytical evaluation of the methodological error in reproducing the volumetric air flow rate by reference critical nozzle, which is due to a change in the humidity of the working air, has been carried out. It is shown that the methodological error in reproducing the volumetric air flow rate by reference critical nozzle, associated with a change in the air humidity, as well as the analogies methodical error caused by the existence of the initial kinetic energy of the flow, must be taken part in accuracy characteristics at the real operating conditions of the standard volumetric air flow rate using critical nozzles.