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.     

PVTt法气体流量标准装置参数的选择与确定

本文基于PVTt法气体流量标准装置的流量基本方程及装置的基本特征,详细分析与论证了装置主要参数,如标准容器容积V、充气初态Pi与终态压力Pf、质量流量qm或体积流量qv的选择与确定,特别对于该装置在整体上为非定常流中要保持流经流量计为定常流的基本特征、措施与气动设计方法作了全面、系统而深入的分析,涉及确定充气终态压力Pf的流动阻力系数的概念是首次由作者明确地引入的。     

低雷诺数旋翼翼型设计及气动仿真

研究了低雷诺数下薄圆弧旋翼的翼型,考虑其对高气动性能、高结构强度和便于制造和轻量化的要求,提出一种具有上凸结构的薄圆弧翼型。通过在翼型上表面增加凸起结构,增加部分弦长的翼型厚度并安装加强筋来提高翼型延展向的结构强度;设计出了最大厚度为4.3%、圆弧均匀厚度为2.5%、最大弯度为5.5%和均匀弯度为4.5%的薄圆弧翼型。采用基于二维定常、不可压缩Navier-Stoke方程的数值仿真方法计算了该翼型在雷诺数为40,000~100,000,迎角为-4°~12°下的气动性能,并获得了该翼型上下表面的压力系数分布线和速度矢量图。采用该翼型制作了直径为40cm,质量为15g,桨距为15.7cm的碳纤维旋翼;在悬停状态下完成了它的升力和结构强度试验。实验结果显示其性能满足使用要求。目前,研制的旋翼已成功地应用于某型多旋翼飞行器。     

Analysis of low Reynolds number flow around a heated circular cylinder

The objective of this study is to investigate the forced convection from and the flow around a heated cylinder. Experimental and computational results are presented for laminar flow around a heated circular cylinder with a diameter of 10 mm. The experiments were carried out using Particle Image Velocimetry (PIV) in a wind tunnel, and numerical simulations using an in-house code and a commercial software package, FLUENT. This paper presents comparisons for vorticity and temperature contours in the wake of the cylinder. Experimental and computational results are compared with those available in the literature for heated and unheated cylinders. An equation is suggested for a temperature-dependent coefficient defining a reference temperature to be used in place of the constant used in other studies. An attempt is also made to correct differences between average cylinder surface temperature and measured interior temperature of the cylinder. This paper was presented at the 7th JSME-KSME Thermal and Fluids Engineering Conference, Sapporo, Japan, October 2008. László Baranyi received his MEng degree from the Technical University for Heavy Industry, Hungary, in 1975 and his PhD in 1990. He worked as an associate professor at Nagaoka University of Technology, Japan, from 1995 to 1997. Dr. Baranyi is currently an associate professor at the University of Miskolc, Hungary. He serves as an editor of the Journal of Computational and Applied Mechanics. His research interests include bluff body aerodynamics and fluid-structure interaction. Szilárd Szabó, PhD (1995, University of Miskolc), professor, head of Department of Fluid and Heat Engineering University of Miskolc, Hungary. He earned his MSc degree in mechanical engineering in 1975 from the Technical University for Heavy Industry. He serves as an editor of the Journal of Computational and Applied Mechanics and a deputy editor-in-chief of the Hungarian journal GéP. Dr. Szabó’s research fields are supersonic gas ejectors, turbomachines, CFD, power engineering. Betti Bolló, assistant at the Department of Fluid and Heat Engineering, University of Miskolc, Hungary. She received her MSc degree from the University of Miskolc in Information Engineering (Systems of Power Engineering) in 2003. Ms Bolló’s research interests include CFD and internal combustion engines. Róbert Bordás, PhD student at the Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg “Ottovon-Guericke” in Germany. He received his MSc degree from the Budapest University of Tech-nology in Integrated Engineering (Faculty of Mechanical Engineering) in 2005. His research interests include optical measurements in engineering flows.     

Effect of spanwise flexibility on propulsion performance of a flapping hydrofoil at low Reynolds number

Spanwise flexibility is a key factor influencing propulsion performance of pectoral foils.Performances of bionic fish with oscillating pectoral foils can be enhanced by properly selecting the spanwise flexibility.The influence law of spanwise flexibility on thrust generation and propulsion efficiency of a rectangular hydro-foil is discussed.Series foils constructed by the two-component silicon rubber are developed.NACA0015 shape of chordwise cross-section is employed.The foils are strengthened by fin rays of different rigidity to realize variant spanwise rigidity and almost the same chordwise flexibility.Experiments on a towing platform developed are carried out at low Reynolds numbers of 10 000,15 000,and 20 000 and Strouhal numbers from 0.1 to 1.The following experimental results are achieved: (1) The average forward thrust increases with the St number increased;(2) Certain degree of spanwise flexibility is beneficial to the forward thrust generation,but the thrust gap is not large for the fins of different spanwise rigidity;(3) The fin of the maximal spanwise flexibility owns the highest propulsion efficiency;(4) Effect of the Reynolds number on the propulsion efficiency is significant.The experimental results can be utilized as a reference in deciding the spanwise flexibility of bionic pectoral fins in designing of robotic fish prototype propelled by flapping-wing.     

Static pressure measurement error for wall taps with high Reynolds number turbulent pipe flow

An experimental study on a static pressure measurement errors in wall taps was conducted using a high Reynolds number actual flow facility (Hi-Reff). The bulk Reynolds number Re_D examined was up to 1.3 × 10⁷ and tap Reynolds number Re_t was up to 8.5 × 10⁴. The behavior of the static pressure measurement error at high Reynolds numbers was clarified experimentally. The static pressure measurement error normalized by wall shear stress increases with Reynolds number and reaches an asymptotic value. Its maximum value is 7.1 at Re_t = 8470. The asymptotic value increases with the size of the tap diameter up to 6 mm and then becomes constant for tap diameters exceeding 6 mm. The universal curve reported in previous studies is observed for only a limited range of tap Reynolds numbers of below 700 and of tap diameters below 4 mm.     

高雷诺数下有限长圆柱绕流阻力特性研究

针对不同长径比的有限长圆柱模型,采用大涡模拟及雷诺平均的方法,对高雷诺数下有限长圆柱绕流阻力特性进行数值模拟和分析,得到了圆柱阻力系数随长径比和雷诺数的变化规律,讨论端面效应对绕流阻力系数的影响。结果表明：在亚临界区内,相同雷诺数下阻力系数随长径比的增大而增大,呈线性变化规律,L/D的对阻力系数的影响明显大于Re对阻力系数的影响;在阻力危机区内,相同雷诺数下阻力系数随长径比的增大而增大,呈二次函数的变化规律,但各工况达到阻力系数“转折点”对应的雷诺数各不相同,基本呈现随雷诺数的增大向前推移的趋势,Re对阻力系数的影响明显大于L/D对阻力系数的影响;在阻力回升区,阻力系数回升的“转折点”随着雷诺数的逐渐增大而向后推移。在各分区内,端面效应对阻力系数的影响随雷诺数增大而更加明显,在高度方向上的最大影响区域约占圆柱总高度的16%。研究结果对有限长圆柱绕流特性的研究及应用具有重要意义和价值。     

高雷诺数水流中悬空输油管道安全性数值分析

穿越河流的输油管道在长距离输油管道工程中占相当比例,在水流长期作用下容易裸露悬空。悬空管道在水流作用下可能产生共振或锁频现象,造成管线失效。通过交错网格系统中的SIMPLE算法求解N-S方程,对均匀来流中的静止管道绕流场进行模拟,验证了模型的可靠性;并应用动网格技术对高雷诺数均匀来流中悬空的横向振动管道绕流场进行了数值模拟,得到不同频率比下的升力系数、阻力系数随时间的变化曲线以及涡量等值线分布图。通过分析涡量等值线分布图得到管道在给定雷诺数流体中的"锁频频率"以及高雷诺数下管道临界长度曲线,结论可用于水流作用下管线的安全分析。     

High-pressure rheology of lubricants and limitations of the Reynolds equation

A review of high pressure rheology leads to the conclusion that the results from rheometers may be used to generate empirical rate equations which are useful in modelling elastohydrodynamic traction. However, an analytical treatment of piezoviscous liquids reveals that the Reynolds equation adequately captures the mechanics of the piezoviscous liquid only when the shear stress is much less than the reciprocal of the pressure viscosity coefficient. Otherwise the cross film pressure gradient may be significant and secondary flows result.