Dynamic Viscosity Coefficient Research Articles

Determination and Evolution of Dynamic Viscosity Coefficient of Rock Under High Water Pressure and High-Stress Conditions

Determination and Evolution of Dynamic Viscosity Coefficient of Rock Under High Water Pressure and High-Stress Conditions

STUDY OF RHEOLOGICAL PROPERTIES OF PARAFFIN OIL MIXTURE

In experiments on cavitation effect on oil, rheological properties (density, dynamic viscosity coefficient, oil composition, freezing point and shear stress on the wall) of high-viscosity, low-freezing oils from the Kalamkas and Karazhanbas fields, as well as high-freezing paraffinic oils from the Uzen and Zhetybay fields were studied. The ratio of oils in this case is: Zhetybay-Uzen - 65%, Karazhanbas-Kalamkas – 35%. From a ready mixture of oils in the volume of 10 liters, in accordance with the sampling method according to GOST 2517-85, a sample of oil in the amount of 0.5 liters is taken for the initial analysis of the mixture of oils according to the measured values. Then the ready mixture of oils, heated to the required temperature, is loaded into the receiving tank of the unit and mixed with a mixer to obtain a homogeneous mixture. The mixed oil mixture is pumped by a gear pump and fed to the cavitation unit. In this case, the movable rod regulates the oil pressure at the inlet to the confuser and changes the cavitation mode. After the oil passes through the diffuser, a sample of oil is taken for analysis using a special device. The processed oil is again fed to the receiving tank and then sent for secondary processing using a gear pump. The ultimate shear stress of oils before and after cavitation at different temperatures was determined. It was found that at temperatures below 30 oC and above, oils are Newtonian fluids. Pseudoplastic fluids have rheological characteristics that do not depend on time, and for such fluids, the yield point is not detected.

Performance characteristics of rotary lobe pumps for high viscosity food medium

Abstract This paper analyses the effects of food media with high viscosity on the performance of rotary lobe pumps. Rotary lobe pumps have long been used in the food industry for pumping highly viscous media and are designed to operate for long periods of time without replacement of any parts. The study utilised publicly available data from factory tests of the PLP 3-4 pump for pumping food media of various viscosities μ (μ above 10,000 cP). The paper presents the results of processing these data, which allow us to draw some conclusions. It is established that the power input of the pump PLP 3-4, due to the viscosity of the food medium, is directly proportional to the rotor speed and increases with its increase. Thus the power spent on overcoming back pressure depends on rotor speed nonlinearly. At the same rotor speed the increase in pressure drop and dynamic viscosity coefficient do not affect the productivity, but lead to a significant increase in power consumption. The obtained results allow to draw a conclusion that it is not necessary to connect the increase of hydraulic efficiency of rotary lobe pump with improvement of energy efficiency of unit utilisation and to take into account the reason of increase of discharge pressure.

Теплоотдача при движении воды в трубе при температурах, близких к температурам кипения в переходном режиме

Currently, there is a problem of developing effective methods to calculate heat and mass transfer processes during steam condensation from a vapor-gas mixture in industrial devices. This is due to the need to create new reliable and highly efficient designs of heat exchangers for various purposes. The finite element method has been used in the ANSYS Fluent software package during the numerical simulation. An experimental plant is tested in the pipeline of an industrial enterprise at the production site of the Technopolis KHIMGRAD industrial park (Kazan-city). The applicability of the Lee model to solve problems of water flow in a pipeline with partial evaporation is proved. This model allows you to accurately account for the processes of evaporation and condensation, which is important for the design of cooling and air conditioning systems. The authors have designed a three-dimensional model of the flow area of the experimental module and a CFD model to calculate temperatures, phase velocities and their concentrations, considering the peculiarities of the ongoing processes of heat and mass transfer. A slight effect on the heat flow of a 180° rotation during the flow of a liquid medium in the range of the Reynolds numbers 1800–2600 is shown. The developed model is verified with the results obtained at the experimental plant. It is established that the model reproduces experimental data well. An analysis of studies of heat and mass transfer processes during the fluid flow in channels in the presence of phase transitions is carried out. The problems of calculating the parameters of heat transfer during the movement of a fluid in a transient mode are revealed, especially at values of the Reynolds number close to 2000. The experimental plant diagram is presented. It is found that in the range of Reynolds numbers of 2600–3600, the calculated temperature values differ from the temperature values obtained experimentally by less than 0,42 %. During the partial transition of water into steam in the range of Reynolds numbers of 1800–2600, the deviations were less than 6 %, which confirms the adequacy of numerical modeling of calculating the heat transfer process in a pipe. It is shown that considering the influence of temperature on surface tension, the coefficient of thermal conductivity of water and the coefficient of dynamic viscosity of water is important to obtain accurate results. The proposed approach can be used to optimize the operating parameters of condensers and evaporators, as well as to accurately calculate the heat transfer coefficient and determine the areas of vapor formation. It will improve the energy efficiency of industrial installations and reduce the cost of equipment operation.

Density, thermal expansion, dynamic viscosity of halogenated arenes

Purpose. Experimental study of the density, thermal expansion and dynamic viscosity of halogenated arenes at temperatures from 293.15 to 343.15 K and atmospheric pressure 97.992 kPa.Methods. Density was determined by the pycnometric method, viscosity by the capillary method. A quartz pycnometer type PZh2 with a nominal capacity of 10 ml and a glass capillary viscometer type VPZh-2 with a nominal capillary diameter of 0.34 mm were used. The mass of liquids was measured using an electronic scale VSL-200/0.1A with a division value of 0.0001 g. Numerical methods were used to process the experimental results.Results. Experimental data were obtained on the density, coefficient of volumetric thermal expansion and dynamic viscosity of liquid o-xylene, ethylbenzene, fluorobenzene, chlorobenzene, bromobenzene, toluene, o-fluorotoluene, mfluorotoluene, p-fluorotoluene, o-chlorotoluene, m-chlorotoluene, p-chlorotoluene, 2,4-dichlorotoluene, 2,6-dichlorotoluene. Density and dynamic viscosity data are approximated by a third-degree polynomial. Data on the coefficient of volumetric thermal expansion are obtained from approximated measured density data. The maximum estimate of the measurement error for density was 0.13 %, for dynamic viscosity – 3.5 %. The maximum calculation error for the coefficient of thermal expansion is estimated at 3 %.Conclusion. Mathematical processing of the obtained experimental data on density and dynamic viscosity made it possible to obtain analytical relations in the form of power polynomials that allow calculating the values of these quantities at any temperature from the studied temperature range and atmospheric pressure with an error not exceeding the error of experimental determination. The calculated values are in good agreement with the data provided in the reference and scientific literature. The experimental data obtained complement the information on the properties of some of the liquids under consideration, for which the dependences of density and viscosity on temperature are poorly understood. The substances under study are used in various sectors of the economy and are therefore technically important liquids. The measurement results can be used in condensed matter physics, for the analysis of liquid hydrocarbons, and can be useful in the chemical industry.

Dynamic viscosity, interfacial tension and diffusion coefficient of n-hexane, cyclohexane, 2-methylpentane with dissolved CO2

In this work, n-hexane, cyclohexane and 2-methylpentane were selected to represent linear-alkane, cycloalkane and branched-alkane, respectively. Based on the dynamic light method (DLS), the viscosity, interfacial tension and diffusion coefficient of n-hexane/CO2, cyclohexane/CO2 and 2-methylpentane/CO2 systems under saturation condition were measured in order to explore the change trend of thermophysical properties of the systems with the same carbon atom number but different molecular structures. The experiments were conducted at the temperatures of 303, 343 and 383 K and at pressures up to 5.64 MPa. The expanded uncertainties（k = 2）of dynamic viscosity, interfacial tension and diffusion coefficient were 3 %, 3 % and 4.4 % respectively. The experimental results show that n-hexane and 2-methylpentane with similar molecular structure have more similar value of the properties. The effects of different alkane structures on system viscosity, interfacial tension, and diffusion coefficient were explained at the molecular level through radial distribution function, interface thickness, and CO2 coordination number. At 303.15 K and 4 MPa, the peak radial distribution function of CO2/cyclohexane is 1.845, which is greater than that of CO2/n-hexane and CO2/2-methylpentane molecules. It has been proven that the arrangement of CO2/cyclohexane is more orderly, resulting in higher viscosity and lower diffusion coefficient of the system. The interface thickness of CO2/cyclohexane is 6.13 nm, which is smaller than CO2/n-hexane (7.53 nm) and CO2/2-methylpentane (6.3 nm). The smaller the interface thickness, the more compact the structure, the stronger the intermolecular forces, and the greater the interfacial tension. At 303.15 K and 2 MPa, the number of CO2 coordination sites within 1 nm around liquid phase alkanes is 3.96, which is smaller than 4.78 for cyclohexane and 6.62 for 2-methylpentane. Prove that the coordination number is directly proportional to the diffusion coefficient and inversely proportional to viscosity and interfacial tension.

New mathematical models for the load factor of slip pairs of the ship propulsion complex for non-Newtonian lubricants

The method of boundary variation was applied to the solution of the boundary value problem with respect to the Reynolds differential equation for the lubricating layer in the sliding bearings of ship power plants and auxiliary ship equipment, which made it possible to obtain analytical representations for the hydrodynamic pressure, shear stresses, as well as the integral characteristics of the lubricating layer. This made it possible to build new, easy-to-use mathematical models for the load factor (carrying force factor) of the sliding pairs of the ship propulsion complex, considering the non-Newtonian properties of lubricants, i.e. in the case of the dependence of dynamic viscosity on pressure and temperature. Mathematical models take into account geometric parameters of bearings, operational parameters: relative radial clearance and relative eccentricity, angular velocity; as well as viscosity characteristics of lubricants, in particular, dynamic viscosity and piezo coefficient of viscosity of lubricants. A criterion for the applicability of lubricants for given operating characteristics and bearing parameters has been developed, which uses the viscosity characteristics of lubricants. The research results are illustrated in the form of tables and graphs.

Investigation of the Newtonian fluids flow in circular horizontal tubes at low inlet pressures

The issues of increasing hydrodynamic efficiency, improving the operational and technical characteristics of various apparatus and devices used in the fi eld of heat and mass transfer, as well as ensuring the required regime and flowow conditions of liquids of different viscosities do not lose their relevance. To solve these issues, in addition to studying the nature of the flowow of various liquids in round horizontal tubes (capillaries), it is necessary to determine the conditions when the flowow of liquid in capillaries and round tubes of small diameter is laminar and can be described by the Poiseuille equation. Experimental data on determining water flow ow through horizontal round tubes of various diameters are presented. Determining the patterns and features of such flow ows is mostly aimed at increasing hydrodynamic efficiency, improving the operational and technical characteristics of various apparatus and devices, as well as ensuring the required flow ow regime and conditions. Experimental data on determining the flow ow rate of water through horizontal tubes of circular cross-section with different diameters are presented in the article. The dependence of the volumetric flow ow rate on the pressure drop has been determined; it has been shown that the main parameters that determine the nature of the flow ow of liquids in horizontal tubes are the tube radius and the dynamic viscosity of the liquid. The flow ow of distilled water in tubes with diameters of 0.95, 1.6 and 2.0 mm at an overpressure of 0.266 kPa to 4 kPa is considered. It is shown that the dependence of the volumetric flow ow rate on the excess pressure remains linear at 0.95 mm in the entire considered pressure range. An increase in the tube radius increases the likelihood of velocity flow uctuations and the appearance of a radial velocity component, i.e. the occurrence of elements of a turbulent structure. In this regard, with tube diameters of 1.6 and 2.0 mm, a deviation of the water flow ow regime from the laminar character was established at pressures of more than 1.3 kPa and 1 kPa, respectively. The dependence of the volumetric flow ow rate on pressure for a 40 % aqueous solution of CaCl2, transformer, transmission and engine oils with dynamic viscosity coefficients from 0.002 Pa·s to 0.182 Pa·s remains linear up to pipe diameters of 5–6 mm. The experimental results are shown in the form of a nomogram of the dependence of the coefficient K* on the tube radius at different values of the viscosity coefficient. The results of studies of liquids of various viscosities are presented in the form of a nomogram of the dependence of the ratio of the radius of the tube to the fourth power to the viscosity of the liquid on the radius of the tube. The analysis of which makes it possible to predict the nature of the flow ow of the investigated liquid at the given values of the tube radius and the dynamic viscosity coefficient. Heat exchange devices for the design of which the presented results can be used include a variety of radiators that include tubes through which coolant circulates.

МОЛЕКУЛАЛАРДЫҢ АКТИВАЦИЯЛЫҚ ЭНЕРГИЯСЫН СИПАТТАЙТЫН ФИЗИКАЛЫҚ ПАРАМЕТРЛЕРГЕ ТӘУЕЛДІЛІГІН ЗЕРТТЕУ ӘДІСТЕРІ

The article describes the principles of operation of devices that practically determine the activation energies of molecules of liquids, discusses their advantages and disadvantages from each other. Methods for calculating the activation energy by measuring parameters that determine the dynamic and kinematic viscosity coefficients of liquids are shown. The physical meanings of formulas describing the empirical dependence of the relaxation time of molecules using the activation energies, the dynamic viscosity coefficient on the temperature with the activation energy are discussed in detail and analyzed that they have a great influence on a full understanding of the mechanisms of physical processes and phenomena. A way to calculate the kinematic viscosity coefficients using the density and dynamic viscosity coefficients of liquids is shown. Using practical measurements and formulas that express the laws of physics, it was theoretically possible to summarize what parameters the law describing activation energy depends on. Particular attention is paid to the place that the formulas obtained as a result of theoretical calculations occupy in the study of physical phenomena.

Modelling the centrifugal mixing process of minced meat to optimise the production of chopped meat semi-finished products

One of the most important problems in ensuring the quality of mincemeat preparation in the production of sausages is the effective structuring of components and mixing of their ingredients. To solve this problem, researchers added a multifunctional admixture based on whey protein in the process of centrifugal mixing of the components, which determined the composition of the factor space of the investigated process. Based on the results of the research, the effective content of whey protein, sodium alginate, and soy fiber in the developed recipe was proven, which showed high characteristics in terms of fat-retaining and moisture-retaining ability, digestibility, pH level – activity, and other parameters. The developed formulation made it possible to improve the general indicator of the balance of amino acids in the product and increase the functional-technological and quality parameters of the developed products. The physical and mechanical characteristics of the obtained meat product were evaluated based on the results of physical and mathematical modelling. Modelling was carried out using Federman-on-Buckingham's second similarity theory and the "dimension theory" method, which allows the processing of the obtained experimental data in the form of a criterion equation, which was compiled using Froude, Euler, and Sherwood criteria. The purpose of this study was to obtain dependencies between such process factors as product density, the coefficient of dynamic viscosity of the technological medium, the ultimate shear stress, the change in the concentration of the main impurities of lactic acid in the raw material, the value of the diffusion coefficient and the coefficient of mass transfer in the loading mass, the weight of one load of products, the angular frequency of rotation of the screws of the minced meat mixer, the radius of the rotating working bodies, the characteristic size of the products after grinding. Using the complex criterion equation and the developed program, we find a recommended set of operating mode parameters for preparing minced meat under the conditions of centrifugal influence on the mixing process and the action of the specified factors.

Investigation on the Lubrication Heat Transfer Mechanism of the Multilevel Gearbox by the Lattice Boltzmann Method

In a gear transmission system in a closed space, the heat transfer between gears and fluids presents highly nonlinear characteristics due to the complex physical processes involved in heat exchange and fluid motion, and constructing and solving the thermodynamic model of the gearbox becomes a task that involves considerable difficulty. This paper takes a conical–cylindrical two-stage gearbox as the research object, proposes a fluid–solid coupled dynamics model based on the lattice Boltzmann (LBM) combined with the large eddy simulation (LES) method, and the adopted lattice model is the D3Q27 velocity model, which is used to numerically simulate the distribution of the flow field inside the gearbox and undertake in-depth research on the fluid motion law of the complex gear transmission system in the enclosed space. The model is solved to reveal the laws determining the gear speed and the effects of the lubricant’s dynamic viscosity and thermal conductivity coefficient on the gear heat dissipation efficiency. By adopting the lattice Boltzmann method, we can simulate the fluid flow and heat transfer inside the gearbox more efficiently, which provides a new way to closely understand the thermodynamic behavior of closed complex gear transmission systems. The application of this method is expected to provide strong support for thermal performance optimization and the design of gear transmission systems.

ВЛИЯНИЕ ЭКСТРАКТИВНЫХ АГЕНТОВ НА ПЛОТНОСТЬ И ВЯЗКОСТЬ ЖИДКОЙ ФАЗЫ ПРИ РЕКТИФИКАЦИИ СМЕСИ ИЗОПРОПАНОЛ-ВОДА

In this work, the dynamic viscosity and density of three-component mixtures consisting of a binary azeotropic mixture of isopropanol-water and an extractive agent were investigated. Three points of the profile of concentrations in the liquid phase in the extractive separation column of isopropanol-water mixture in recalculation on the pseudobinary mixture were selected for research: the first point - 95/5 % wt. %; the second point - 5/95 % wt. %; the third azeotrope point - 88/12 % wt. %. For the selected points model mixtures were prepared to which 13 % wt. % of the extractive agent was added. The extractants used in this work were monoethylene glycol (EG), which is used in industrial processes, 1-ethyl-3-methyl imidazolium chloride ([Emim][Cl]) and triethylene glycol-based boronic acid amino ester (AEBA). Experimental data on concentration and temperature dependences of dynamic viscosity and density were obtained for these mixtures. The results showed that the viscosity of the system increases in the series of EG, AEBA, [Emim][Cl]. To carry out calculations of the investigated thermophysical properties in the work we used known expressions: for density - through the sum of volumes; for viscosity - the Kendall-Manroe model. For a three-component mixture with EG, the results of calculations of properties performed in the AspenPlus V12 package are presented. The studies carried out in this work have shown that the density modeling of the studied mixtures is quite accurate, the discrepancy between experimental and calculated data does not exceed 1%. Modeling of the dynamic viscosity coefficient of the system by the Kendall-Manroe model for isopropanol-water mixture in the presence of the studied extractive agents can lead to significant errors, the maximum value reaches 52%. The calculated values of the dynamic viscosity coefficient are underestimated, which in turn can lead to errors in modeling (on the basis of these properties) of heat and mass transfer processes occurring in the apparatus.

Temperature effect analysis of paste backfill rheological properties based on inter-particle potential and water evolution

This study focuses on investigating the rheological properties and micro-mechanisms of paste filling materials under varying temperatures, which is crucial for addressing the issue of transporting paste materials through pipelines at different temperatures. The rheological properties of Pure Tailing sand Paste Backfill (TPB) with a mass concentration set at 66% and Cement Paste Backfill (CPB) with a 1:4 ratio of the cementing agent were analyzed at different temperatures were compared and analyzed at different temperatures using rheometer, Zeta potential, and low-field nuclear magnetic resonance measurement technology. The study aims to identify the macroscopic trends in the dynamic yield stress and viscosity coefficient of paste slurry under temperature influence, and to determine the microscopic mechanisms of the competition between water activity and electrostatic interaction between particles. The study not only examines the characteristics of paste slurry at macro and micro levels but also provides a model of rheological parameters and temperature for the optimization of paste filling technology. Studies have shown that temperature has the opposite effect on dynamic yield stress and consistency factor, and both should be considered in practical applications.

Study of the Rheological Properties and Flow Process of High-Viscosity Oil Using Depressant Additives

This article analyzes the dependence of the choice of the method of transportation of high-viscosity oil on the rheological characteristics of the oil in question. An analysis of existing rheological models of high-viscosity oil was carried out, and it was found that a number of models have certain features (model coefficients, their purpose, quantity) that affect the choice of a rheological model of oil. The dependences for determining the coefficient of dynamic viscosity when pumping high-viscosity oil with the addition of pour-point depressants were studied, and the dependence of the hydraulic resistance coefficient when depressants are added to the oil was obtained. A method for choosing a rational oil heating temperature and diluent concentration to achieve the maximum pipeline performance is substantiated.

Effect of StaticMagneticand Pulsated Electromagnetic Fields On the Dynamic and Kinematic Viscosity of Metal Cutting Fluids

In this paper, authors investigated the difference between the influenceof staticmagnetic field and pulsating electromagnetic field on metal cutting fluids. Two essential physical parameters of the cutting fluids, dynamic and kinematic viscosity coefficients were analyzedduring the experiment in the same laboratory condition.The results obtained from the experimental researchshow thatthe influence of thestatic magnetic field onsample metal cutting fluids is greaterthanthe influence ofthe pulsating electromagnetic field.Such as, after magnetizing cutting fluids under the effect of three various static magnetic field strengths, the kinematic and dynamic viscosity havedecreased about 17%and 6% respectively,while they declined about 7% and 4% after magnetizing the fluidsunder the effect of the same electromagnetic magnetic field strengths. Moreover, special magnetizing devices have beendesigned to magnetize different types offluids intheirflowing condition.

Rheological Analysis of 3D Printed Elements of Acrylonitrile Butadiene and Styrene Material Using Multiparameter Ideal Body Models.

The growing application of additive technologies in various industrial fields determines the undertaking of research in this direction. The need to study mechanical properties, including rheological properties, is necessitated by the use of additively manufactured models as utility models. Furthermore, the values of mechanical properties are affected by the technological parameters of 3D printing. One of the popular engineering materials used in 3D printing is acrylonitrile butadiene and styrene, commonly known by the abbreviated name ABS, which is quite hard and resistant to high temperatures. This article presents a study of the rheological properties of ABS material using multiparameter ideal body models. Two rheological phenomena of stress relaxation and creep were evaluated. The effects of two technological parameters, layer height and printing direction, on the resulting values of elastic moduli and dynamic viscosity coefficients were also evaluated. The elastic moduli and dynamic viscosity coefficients were calculated using the Maxwell-Wiechert and Kelvin-Voight models. The study showed the effect of layer height on rheological properties. Moreover, very good fit was obtained between the multiparameter rheological models and the experimental curves, which are shown by the average value of and . The presented research can be used by designers to design machine parts or car or aircraft components. Moreover, research expands knowledge of the mechanical properties of additively manufactured parts.

Experimental Study on Overall Cooling Effectiveness of Turbine Nozzle Guide Vane with Impingement-Cutback Structure

The overall cooling performance of turbine nozzle guide vane, with the impingement-cutback structure, is experimentally studied in the actual-scale cascade. The gas with the high temperature is used to achieve the actual dynamic viscosity coefficient and the density ratios. The coolant-to-gas mass flow ratio (KG) varies between 0.034 and 0.050 and the gas-to-coolant temperature ratio (KT) varies between 1.5 and 2.4. The local Overall Cooling Effectiveness (OCE) on the middle cross-section of the vane is obtained. The experimental results reveal that the lowest value of the OCE achieves a 10% relative arc length on the suction side of the vane; however, the highest value appears at 40% relative arc length on the pressure side of the vane. The averaged values of the OCE are respectively enhanced by 19.45%, 24.22%, and 35.57% at temperature ratios equal to 1.7, 1.9, and 2.3, with an increase of the KG from 0.034 to 0.050. Added to that, it was identified that an increase of KT from 1.7 to 2.3 leads to the decrease of the OCE. The comparison results show that this characteristic becomes dramatical while KG is 0.034. The higher KT leads to a greater influence of KG, which is illustrated clearly by the compared results of the OCE.

Автоматизация теплового расчета реактора для производства серосодержащего сорбента при разогреве реакционной смеси

The article highlights the problem of automation the thermal design of a reactor for the synthesis of a sulfur-containing sorbent obtained from the use of waste products of epichlorohydrin, chlorinated lignin and sodium polysulfides is considered. Automated design helps to reduce the intensity of the process, improve the quality of design decisions, significantly reduce production costs, which has a positive effect on the cost of finished products. It has been found that due to the incompatibility of the similarity criteria of chemical and mass transfer processes there is little possibility to carry out a large-scale transition in a reactor based on physical similarity. In the course of a large-scale transition from a laboratory unit to a small production unit there were used the computational methods based on engineering experience that allow increasing the reliability of the results obtained. There have been determined the initial values, which will be used in the design for a reactor with a propeller agitator to mix a working mass having a dynamic viscosity coefficient of 6.01 sP and a solid phase content of 31.8%. The agitator type was determined by calculating the physical properties of the ingredients and selecting the mixer designs. A flowchart and a formal description of the algorithm for calculating heat transfer during a reaction mixture heating are given; the program interface is written in C# displaying the results of thermal design of the working mixture heating. As a result of the calculation, there has been calculated the amount of heat and time required to heat the working mixture, coefficient of heat transfer from the working mass to the reactor wall, mass flow rate of water and its costs, velocity of water in the thermal jacket, mode of water flow in the jacket and other similarity criteria.

Параметрические исследования течений в микросоплах

The work is devoted to parametric investigations of the krypton flow in a conical micronozzle when flowing into a region with low pressure. The features of the flows are studied at various values of the stagnation pressure in the pre-nozzle volume, including the occurrence of a condensed phase in the flow. Mathematical modeling was carried out on the basis of a numerical solution of the complete system of Navier-Stokes equations, supplemented by the equation for the mass fraction of the condensate. The mathematical model takes into account the change in the coefficients of dynamic viscosity and thermal conductivity depending on the gas temperature. The problem was solved by the control volume method on a block-structured regular grid of quadrangular elements using schemes of the second order of accuracy. The equations were integrated with respect to time using the Runge-Kutta method. The calculations were carried out at stagnation pressures of 5, 10, and 15 atm for single-phase and two-phase flows. The distribution fields of temperature and Mach number in the nozzle and in the space behind it are presented. The axial distribution of pressure, temperature, and Mach number has been studied. It is shown that in the case of a single-phase flow, self-similarity of gas flows is observed. The pressure fields were similar, but in a dimensionless form they coincided to each other. In this case, the identity of the velocity and temperature fields was observed at different values of the stagnation pressure. The self-similarity of the flow is violated in the zone of formation of condensed particles. The dimensions of the zones of local temperature increase, as well as the intensity of heat release, depend on the given stagnation pressure, which is reflected in the velocity characteristics of the flow.

Simulations of Bubble Formation and Oscillation Behavior in Micro-Leakage Measurement System

In the process of measuring micro-leakage based on the bubble method, the physical parameters of the liquid phase have a great impact on the formation and movement of bubbles, thus affecting the measurement accuracy of the system. Therefore, it is of great significance to study the physical parameters of the liquid phase. At present, it is difficult to independently study the parameters of the liquid phase by experimental methods. In this paper, based on the Cahn-Hilliard phase field model, a gas-liquid two-phase flow model for the expression of leakage is established to independently study the influence of different physical parameters on the formation and movement of bubbles in the measuring system. Firstly, the effects of liquid medium density, dynamic viscosity coefficient and surface tension on the initial shape (aspect ratio), the generation period and the shape oscillation of bubbles after they leave the nozzle are analyzed. Then, an experimental platform for visualization of bubbles in two-phase flow based on machine vision is built, through which the morphological parameters of bubbles in the liquid phase can be obtained in real time. Finally, the results of visualization experiment and numerical simulation are compared. The results show that the initial aspect ratio error of bubbles obtained by visual experiment and numerical simulation is 1.8%, and the average oscillation period error is 12.3%. The results are basically consistent, which proves the rationality and correctness of the mathematical model established. It is found that the liquid with larger dynamic viscosity coefficient μ and density ρ and smaller surface tension σ can be selected as the liquid medium of the measurement system. It is more conducive to the accurate expression of micro-leakage in the measurement system, and the bubble shape can quickly reach a stable state. It provides theoretical support for improving the accuracy and stability of the micro-leakage measurement system.