Using small sonic nozzles as secondary flow standards

When using sonic nozzles as secondary laboratory standards they must be calibrated. Standard methods of calculating discharge coefficient values are not useful with small nozzles of uncertain geometries. Calibration against primary standards is discussed. Alternatively, one nozzle can be directly compared with another by several techniques using ratios of pressure and temperature and sometimes flow. Several factors change the nozzle coefficient. Estimates of the changes due to pressure and humidity are given. Adiabatic cooling produces temperature changes that affect the nozzle coefficient by changing the throat area. Depending on the nozzle holder the inlet gas can also be cooled with an effect on the flow. Nozzles may be made by metal machining or by shrinking glass tubes. Sapphire cutting heads, which may be bought, can be used as sonic nozzles. An example of a promising but unsuitable form of nozzle having a square throat is given. The pressure dependence of these is discussed. The use of nozzles in arrays, for automatic operation as flow standards, is described.     

The evaluation of critical pressure ratios of sonic nozzles at low Reynolds numbers

A sonic nozzle is presently used as a reference flow-meter in the area of gas flow-rate measurement. The critical pressure ratio of the sonic nozzle is an important factor in maintaining its operating condition. ISO 9300 suggested that the critical ratio of a sonic nozzle should be a function of area ratio. In this study, 13 nozzles designed according to ISO 9300, with diffuser half angles of 2°–8° and throat diameters of 0.28 to 4.48 mm were tested. The testing result for the angles of 2°–6° are similar to that of ISO 9300. But the critical ratio for the nozzle of 8° decreases by 5.5% in comparison with ISO 9300. However, ISO 9300 does not predict the critical pressure ratio at Reynolds numbers lower than 10⁵. To express the critical pressure ratio of sonic nozzles at low Reynolds numbers, it is found that the critical pressure ratio should be related as a function of Reynolds number rather than area ratio, as used by ISO 9300. A correlated relation of critical pressure ratios and low Reynolds numbers for small sonic nozzles is suggested in this investigation, with an uncertainty of ±3.2% at 95% confidence level.     

Experimental verification and numerical simulation of a vortex flowmeter at low Reynolds numbers

This study presents experimental verification and numerical simulations of a vortex flow meter in the Reynolds number range between 8300 and 50,000. A custom-designed bluff body with a wedge back shape was used in the flowmeter. A shedding frequency of the flowmeter was measured in an air duct using a hot-film probe. To evaluate the accuracy of the flowmeter, a measurement uncertainty analysis was performed. Numerical simulations of the vortex flowmeter were performed with the open source code OpenFOAM. Transient simulations of periodic vortex shedding behind the bluff body were performed using different simulation methods depending on the pipe Reynolds number, such as Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and Unsteady Reynolds Averaged Navier Stokes (URANS) method. The simulated vortex shedding frequencies matched the experimental data very well. Experiments and simulations demonstrated a clear linear dependence of the shedding frequency on the volumetric flow rate over the entire range of Reynolds numbers. In addition, numerical simulations were used to study the main mechanisms of vortex formation and shedding behind the considered bluff body.     

Development of a transfer standard with sonic Venturi nozzles for small mass flow rates of gases

We have developed a transfer standard system with sonic Venturi nozzles for small mass flow rates of gases. The system is composed of a newly developed automatic pressure controller, two pressure sensors and one temperature sensor to measure the flow conditions in the upstream and downstream sides of a nozzle. The whole system is packed in a portable aluminum trunk. The data are sent to a laptop computer, and the results are displayed on the screen and are written to files. The system can calibrate a flow meter in the flow rate range from 10 mg/min to 100 g/min using ten different sonic Venturi nozzles with the expanded standard uncertainty (k=2) being less than 0.2% for nitrogen. Examples of mass flow controller calibrations are given.     

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 100 mm 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.     

Influence of divergent section on flow fields and discharge coefficient of ISO 9300 toroidal-throat sonic nozzle

The effect of divergent section of ISO 9300 toroidal-throat nozzle on discharge coefficient was analyzed based on the inviscid transonic flow model and laminar boundary layer theory. A series of numerical simulations were conducted to verify the results of theory, and investigate the effect of divergent section length L and diffuser angle θ operated at different Reynolds numbers. Combined with the numerical results in this study and the experimental data reported by Nakao, it showed the discharge coefficient increases with the rise of diffuser angle θ or the drop of divergent section length L. A lot of new results about the effect of divergent section were obtained. It indicated that the effect of divergent section on discharge coefficient of ISO 9300 toroidal-throat nozzle should be considered when Re<1.1×10⁴. At last, a concept of effective critical flow was proposed to discuss the effect of divergent section on discharge coefficient.     

Inter-laboratory comparison of sonic nozzles at KRISS

KRISS has recently participated in two inter-laboratory comparisons of the discharge coefficients, C_d, for sonic nozzles. All laboratories involved in these inter-laboratory comparisons have primary facilities, either volume or mass based systems, for calibration of nozzles. The first one is the North American inter-laboratory comparison of the NOVA 10-mm nozzle. The second one is an inter-comparison of ISO 9300 toroidal throat nozzle package from Ford Motor C. The recent KRISS results of these tests will be reported, and recommendation will be made for future inter-laboratory comparisons.     

A novel comprehensive correlation for discharge coefficient of square-edged concentric orifice plate at low Reynolds numbers

Among various differential pressure flow meters, the orifice meter has gained its publicity in applications where cost, space, and ease of maintenance are of high priority. A major problem associated with the use of orifice flow meters at low Reynolds number flows is the significant variation of discharge coefficient (C_d) as a function of orifice geometry and the Reynolds number. In this work, a two-dimensional axisymmetric numerical model was applied to the investigation of viscous, incompressible flow through square-edged concentric orifice plate for the purpose of studying the performance of discharge coefficient consequent to variations of Reynolds number (Re), orifice/pipe diameter ratio (β), and orifice thickness ratio (t*). The analysis of numerical results by means of multiple regression method has yielded a new correlation incorporating the effect of the parameters under study on orifice meter discharge coefficient for orifice bore Reynolds numbers (Re_o) < 250. Results of relevant investigations from the literature are used in the present work as references for the validation of the numerical model as well as the proposed correlation for discharge coefficient.     

Enhancement of inline mixing with lateral synthetic jet pairs at low Reynolds numbers: The effect of fluid viscosity

In this paper, mixing between two liquid streams of the same flow rate in a planar mixing channel enhanced by means of three lateral synthetic jet pairs is examined using PLIF and PIV at net flow Reynolds numbers of Re_n=2, 10 and 83. The changes in the flow Reynolds numbers are produced with the use of fluids with different dynamic viscosities. The synthetic jet pairs are operated 180° out-of-phase and at a range of actuation frequencies (characterized by the dimensionless Strouhal number Str) and displacements (characterized by the dimensionless stroke length L). It is found that at a sufficiently high frequency or dimensionless stroke length, a homogenous mixing can be achieved. Our experimental evidence shows that the synthetic jet pairs enhance mixing via two key mechanisms, i.e. vortex interaction and entrainment; tearing and stretching of liquid interface. A functional relationship among Re_n, Str and L to ensure a nearly homogenous mixing is also obtained by best fitting the experimental data. It can be used for selecting the synthetic jet operating conditions to ensure a good mixing for a scaled version of this fluid mixer. This correlation indicates that the effectiveness of mixing has a weak dependence on Re_n, implying that the fluid mixers of such a design can be effective over a wide range of net flow Reynolds numbers and for fluids of different viscosities.