The Properties of Gas Flows for Different Flow Conditions Through Laval Nozzles

For all possible types of gas flow through a Laval nozzle, a group of “operating” conditions are distinguished with particular properties characteristic for these conditions, which open up the possibility of effectively solving the problems involved in designing instruments for measuring gas flow rate and their metrological facilities.__________Translated from Izmeritel’naya Tekhnika, No. 4, pp. 40–44, April, 2005.     

Two Primary Standards for Low Flows of Gases

We describe two primary standards for gas flow in the range from 0.1 to 1000 μmol/s. (1 μmol/s ≅ 1.3 cm³/min at 0 °C and 1 atmosphere.) The first standard is a volumetric technique in which measurements of pressure, volume, temperature, and time are recorded while gas flows in or out of a stainless steel bellows at constant pressure. The second standard is a gravimetric technique. A small aluminum pressure cylinder supplies gas to a laminar flow meter, and the integrated throughput of the laminar flow meter is compared to the weight decrease of the cylinder. The two standards, which have standard uncertainties of 0.019 %, agree to within combined uncertainties with each other and with a third primary standard at NIST based on pressure measurements at constant volume.     

Modelling of the break up mechanism in gas atomization of liquid metals Part II. The gas flow model

An analytical model for the gas flow produced by a close coupled atomization assembly is described. The algorithm is based on physical arguments and it fully accounts for the expansion of compressible gas from cylindrical gas jets and the convergence/divergence of the subsequent turbulent flow. A critical input parameter of the model, the radius of the convergence area of the individual jet flows, established elsewhere [G. Antipas, PhD Thesis, University of Surrey, UK, 1995] to be 3 mm by high speed photography, is in tight agreement with the predictions of the model. Pitot tube gas velocity measurements compared well with model predictions.     

Detonation gas model for combined finite‐discrete element simulation of fracture and fragmentation

The equation of state for expansion of detonation gas together with a model for gas flow through fracturing solid is proposed and implemented into the combined finite‐discrete element code. The equation of state proposed enables gas pressure to be obtained in a closed form for both reversible and irreversible adiabatic expansion, while the gas flow model proposed considers only 1D compressible flow through cracks, hence avoiding full 2D or 3D gas flow through the fracturing solid. When coupled with finite‐discrete element algorithms for solid fracture and fragmentation, the model proposed enables gas pressure to be predicted and energy balance to be preserved. Copyright © 2000 John Wiley & Sons, Ltd.     

The Area of Application of Laval Nozzles in Flow-Rate Measurement Technique

Using examples of their use in standard and working instruments for measuring mass flow rate and a variety of gas volume flow rates, it is shown that critical nozzles and, particularly the Laval nozzle, can occupy an important place in the system of metrological facilities for this form of measurement.__________Translated from Izmeritel’naya Tekhnika, No. 4, pp. 48–52, April, 2005.     

Effective Thermal Conductivity in a Radial-Flow Packed-Bed Reactor

In this work a theoretical and experimental study of the heat transfer process in a radial flow reactor was carried out under steady- and non-steady-state conditions in order to determine the effective thermal conductivity (k _e). One of the mathematical models proposed was a pseudohomogeneous model in which the effective thermal conductivity varies with radial position. The second model studied was a two-phase model with different thermal conductivities for gas and solid. For the pseudohomogeneous model, an analytical solution was obtained using the method of separation of variables and series approximation. In the two-phase model, the gas and solid temperature profiles were obtained by two numerical methods: orthogonal collocation and Runge–Kutta. Several experiments were performed by changing particle diameter, gas flow and temperature input, and reactor size and time-operation condition: steady and nonsteady. Theoretical results were compared with experimental data in order to calculate the effective thermal conductivity. The values of k _e agree in general with the literature data. At low Reynolds numbers there is no appreciable difference between a pseudohomogeneous model and a two-phase equation model. Constant thermal properties can be used at Re;5 with enough accuracy to predict the thermal behavior of a radial-flow reactor.     

Dynamics of airflow in a short inhalation

During a rapid inhalation, such as a sniff, the flow in the airways accelerates and decays quickly. The consequences for flow development and convective transport of an inhaled gas were investigated in a subject geometry extending from the nose to the bronchi. The progress of flow transition and the advance of an inhaled non-absorbed gas were determined using highly resolved simulations of a sniff 0.5 s long, 1 l s⁻¹ peak flow, 364 ml inhaled volume. In the nose, the distribution of airflow evolved through three phases: (i) an initial transient of about 50 ms, roughly the filling time for a nasal volume, (ii) quasi-equilibrium over the majority of the inhalation, and (iii) a terminating phase. Flow transition commenced in the supraglottic region within 20 ms, resulting in large-amplitude fluctuations persisting throughout the inhalation; in the nose, fluctuations that arose nearer peak flow were of much reduced intensity and diminished in the flow decay phase. Measures of gas concentration showed non-uniform build-up and wash-out of the inhaled gas in the nose. At the carina, the form of the temporal concentration profile reflected both shear dispersion and airway filling defects owing to recirculation regions.     

Simulation and numerical investigations of the kinetics of atmospheric aerosol droplets in the wake behind a flat plate

Within the framework of the physicomathematical model of evolution of a polydisperse condensate, numerical investigations of the kinetics of atmospheric aerosol droplets in a supersonic two-phase flow past a flat plate were carried out. The gas flow was described by the Reynolds equations with the use of the two-parameter turbulence model. In view of the smallness of the condensate mass fraction in the incoming flow, the inverse effect of the dispersed phase on the gas was not considered. For various regimes of exposure to a flow, the characteristic features of the spatial distribution of the main parameters of the condensate fractions have been studied: the number densities, radii, temperatures, and averaged velocities of microdrops. The dependence of the dispersed phase dynamics on the Mach number and the incoming flow angle of attack has been investigated and the influence of the allowance for the processes of coagulation/fragmentation on the mass spectrum of droplets is shown. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 331–341, March–April, 2009.     

A quadrature of the two-dimensional equations of the hydrodynamics of an incompressible ideal liquid and a model of the flow around convex symmetric bodies with suction or injection

A class of solutions of the steady-state hydrodynamic equations of an incompressible liquid has been considered in the Euler approximation when the pressure field is described by an additive function of the form P(x; y)=F(x)+G(y). It turns out that this class of solutions includes potential flows such as wave motion of a liquid with a finite depth, a flow inside a right angle, and a hypersonic gas flow around a sphere in the approximation of constant density near the stagnation point. Among nonpotential flows, this class includes, in particular, a hypersonic flow around a cylinder. The results obtained are used to construct a model of a flow around convex symmetric bodies with suction or injection. This model can be of interest in solving some problems of physicochemical technology, for example, separation of gas mixtures and isotopes.V. E. Firsov Saratov State Pedagogical Institute, Saratov, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 1–2, pp. 59–65, July–August, 1994.     

Design and Uncertainty Analysis for a PVTt Gas Flow Standard

A new pressure, volume, temperature, and, time (PVTt) primary gas flow standard at the National Institute of Standards and Technology has an expanded uncertainty (k = 2) of between 0.02 % and 0.05 %. The standard spans the flow range of 1 L/min to 2000 L/min using two collection tanks and two diverter valve systems. The standard measures flow by collecting gas in a tank of known volume during a measured time interval. We describe the significant and novel features of the standard and analyze its uncertainty. The gas collection tanks have a small diameter and are immersed in a uniform, stable, thermostatted water bath. The collected gas achieves thermal equilibrium rapidly and the uncertainty of the average gas temperature is only 7 mK (22 × 10⁻⁶ T). A novel operating method leads to essentially zero mass change in and very low uncertainty contributions from the inventory volume. Gravimetric and volume expansion techniques were used to determine the tank and the inventory volumes. Gravimetric determinations of collection tank volume made with nitrogen and argon agree with a standard deviation of 16 × 10⁻⁶ V_T. The largest source of uncertainty in the flow measurement is drift of the pressure sensor over time, which contributes relative standard uncertainty of 60 × 10⁻⁶ to the determinations of the volumes of the collection tanks and to the flow measurements. Throughout the range 3 L/min to 110 L/min, flows were measured independently using the 34 L and the 677 L collection systems, and the two systems agreed within a relative difference of 150 × 10⁻⁶. Double diversions were used to evaluate the 677 L system over a range of 300 L/min to 1600 L/min, and the relative differences between single and double diversions were less than 75 × 10⁻⁶.     

Reliability of Measurements of the Natural Gas Flow Rate and Volume in Gas Distribution Organizations

The proposed new approach to the procedure for measuring the flow rate and volume of gas under standard conditions in gas distribution organizations increases the reliability of the measurements. It is based on identical transformations of the Clapeyron-Mendeveleev equation, with modifications, and takes into account the composition of the natural gas and the recommendations of Federal Law No. 69-FZ (article 19) of March 31, 1999, about natural gas certification by Gosstandart of the Russian Federation. Use of the modified Clapeyron–Mendeleev equation is shown to changes the form of the transformation functions of various primary measuring transducers (turbine, rotary, vortex, ultrasonic, etc.) under the conditions of actual measurements.     

Solution of the conjugate problem of the gas flow in the pulling of fluoride fiber light guides

A mathematical model is suggested for the congugate problem of the inert gas flow in a furnace channel during stretching of fluoride glass billets into optical fiber. Based on an analysis of preliminary results of a numerical investigation of gas supply from top to bottom and from bottom to top it is shown that the second variant is more effective for creating a protective atmosphere.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 3–4, pp. 319–323, September–October, 1994.     

Certain Aspects of Computer Simulation of Hypersonic Flows: Stability, Nonuniqueness, and Bifurcation of Numerical Solutions of the Navier–Stokes Equations

A number of problems associated with the nonuniqueness of numerical solutions of the Navier–Stokes equations used for simulating processes of a hypersonic real gas flow past blunt bodies are considered. The processes of evolution of a stationary pattern of flow perturbed by a single pulse at an initial time instant are considered at different values of the governing parameters of the problem. The instability of the bifurcation type resulting in transition of the nonstationary process from one branch of solution to another and the attainment of a stationary regime is investigated.     

基于收缩流动的气体超声流量计声道稀疏化及测量方法

为了提高低声道数超声流量计的准确度水平,在传统超声流量计的基础上设计了一种具有收缩流动结构的低声道数超声流量计。采用数值模拟研究了渐缩管中收缩流动的流场特征,确定了渐缩管的几何参数及超声探头的安装方式。通过空气实流实验,研究了单声道及双声道在收缩流动条件下流量计量的基本特性。在流量范围27~432m3/h,管径范围100~150mm进行了实验验证。结果表明:收缩流动的数值模拟结果与理论模型相吻合,当渐缩管的收缩比由2增大为6,被测流场均匀区占比显著增大;当收缩比固定不变时,随着流量的增大,边界层厚度显著降低。通过实流实验比较不同结构和配置超声流量计的测量结果,发现单声道收缩管超声流量计的准确度水平显著优于传统单声道气体超声流量计,与传统双声道气体超声流量计的准确度水平相当。     

横板型稳压罐气液两相流场数值模拟及流量稳定性研究

依据湍流模式理论中的标准k-ε湍流模型及流体体积函数多相流模型,实现了水流量标准装置中横板型稳压罐多相湍流流场的数值研究,采用PISO方法求解离散控制方程,并使用UDF编写入口速度脉动信号。获得稳压罐压力场、速度场、流线等关键信息,分析了入口脉动频率、气液比、竖隔板位置因素对流量稳定性的影响,并通过实验验证了计算结果的有效性。结果表明:低频脉动对稳定性影响较大,当泵出口脉动5Hz时,气液比1:3,竖板位于罐体D/3处,稳定性最好,流量波动系数为0.058%。     

Investigation on the pressure drop characteristics of cryocooler regenerators under oscillating flow and pulsating pressure conditions

This paper proposes a new oscillating flow model of the pressure drop in oscillating flow through regenerator under pulsating pressure. In this oscillating flow model, pressure drop is represented by the amplitude and the phase angle with respect to the inlet mass flow rate. In order to generalize the oscillating flow model, some non-dimensional parameters, which consist of Reynolds number, Valensi number, gas domain length ratio, oscillating flow friction factor and phase angle of pressure drop, are derived from a capillary tube model of the regenerator. Two correlations in the model are obtained from the experiments for the twill square screen regenerators under various operating frequencies and inlet mass flow rates. It is found that the oscillating flow friction factor is a function of Reynolds number while the phase angle of pressure drop is a function of Valensi number and the gas domain length ratio. Experiment also shows the effect of the mesh weave style on the oscillating flow friction factor and the phase angle. Proposed oscillating flow model can accurately describe the amplitude and the phase angle of the pressure drop through the regenerator.     

油气水三相段塞流引起的海洋立管耦合振动响应

海洋立管是海上油气集输系统的重要组成部分，用于连接海底油气井口与海上油气集输站。在油气储运工程中，海洋油气集输介质多为油气水三相流体。为了研究油气水三相流海洋立管系统在严重段塞流作用下产生的耦合振动问题，进行了数值计算与实证研究。基于多相流体力学与动力学理论，构建了油气水三相严重段塞流模型和海洋立管结构动力学模型，结合这2个模型，模拟了立管耦合振动响应过程，并设计了下倾管倾斜角度为3°的L型油气水三相流立管系统进行实验。对模型计算值和实测值进行对比，结果表明：所提出的耦合振动响应模型比现有严重段塞流瞬态数学模型更适用于油气水三相段塞流引起的海洋立管耦合振动响应问题的研究，计算结果与实验结果较吻合；立管底部压强与底部位移呈周期性变化，且变化周期基本一致；流体压强是引发立管系统耦合振动响应问题的关键因素。研究结果为油气水三相流海洋立管系统在严重段塞流作用下的耦合振动响应特性分析及其结构设计提供了参考。     

The permeability of alumina over an extended temperature range

A semiempirical mathematical model has been developed to predict the permeability of porous alumina over a wide temperature range at atmospherie pressure. Although the thermal expansion of the alumina is of the order of 1 % over the range of temperatures considered, the apparent permeability of the sample to gas flow varies by over 400%. This behavior is due to the dependence of the mean free path of a gas on temperature and to the corresponding slip conditions that occur in the pores of the solid. The model developed correlates the apparent permeability data with temperature, true permeability, gas viscosity, and gas molecular weight, variables suggested by kinetie theory on mean free path and slip. Apparent permeability was found to be a very strong function of temperature. It exhibited both a direct thermal dependence and an indirect dependence, manifest through thermally driven variations in the gas viscosity. A mathematical model from the literature was used for gas viscosity. The inverse correlation with gas molecular weight, suggested by kinetie theory, is demonstrated. The model covers the temperature range between 250 and 1600 K. Small molelcule gases including air, nitrogen, argon, and helium were used in the development.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Mass transfer between the gas and solid particles in a fluidized bed

A model of the boundary layer and condition of suspension of a solid particle by a gas flow is used to formulate analytical correlations, which are then compared with experiment.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 6, pp. 1067–1072, December, 1981.