scholarly journals Flows of ideal and real gases in channels of variable cross section with unsteady localized energy supply

Author(s):  
Н.А. Брыков ◽  
К.Н. Волков ◽  
В.Н. Емельянов ◽  
И.В. Тетерина

Проводится моделирование течений газа в технических устройствах, в которых протекают процессы, связанные с нестационарным локализованным подводом энергии. Для численного моделирования нестационарных сопловых течений с интенсивным энергоподводом используется метод конечных объемов и векторизованный подход к расчету потоков. Для моделирования термодинамических процессов в высокотемпературных потоках воздуха применяется приближенная модель равновесной термодинамики воздуха. Приводятся результаты численного моделирования одномерных и двумерных сопловых течений с подвижной зоной энерогоподвода. На основе данных численного моделирования обсуждается качественная картина газодинамических и тепловых процессов в сопле при нестационарном подводе энергии. Устанавливается зависимость расходных характеристик сопла, а также смещение соплового скачка уплотнения при перерасширенном истечении газа из сопла от интенсивности и цикличности энергоподвода в дозвуковой части сопла. Gas flows are simulated in technical devices where processes associated with unsteady localized energy supply are proceeded. The finite volume method and the vectorized approach to the calculation of numerical fluxes are applied to the simulation of unsteady nozzle flows with intense energy supply. An approximate model of equilibrium thermodynamics of air is used to simulate thermodynamic processes in high-temperature air flows. The numerical results obtained for one-dimensional and two-dimensional nozzle flows with moving zones of energy supply are analyzed. A qualitative picture of gasdynamic and thermal processes in a nozzle with unsteady energy supply is discussed on the basis of the results of numerical simulation. A dependence of the nozzle flow rate and the displacement of nozzle shock wave on the intensity and cyclicity of energy supply is considered for overexpanded nozzle flow.

2013 ◽  
Vol 8 (4) ◽  
pp. 103-109
Author(s):  
Vladimir Zamuraev ◽  
Anna Kalinina

In this paper the pulse energy supply into the channel of variable cross section was studied. The approximate formulas were obtained for the value of the input energy, corresponding to the maximal distance which the shock wave from a pulsed power source reached upstream, as well as full power, energy supply period corresponding to the conditions of closing the channel. The applicability of the analytical relationships is confirmed by numerical calculations based on the Euler equations in a quasi one-dimensional approximation


2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.


2019 ◽  
Vol 14 (2) ◽  
pp. 82-88
Author(s):  
M.V. Alekseev ◽  
I.S. Vozhakov ◽  
S.I. Lezhnin

A numerical simulation of the process of the outflow of gas under pressure into a closed container partially filled with liquid was carried out. For comparative theoretical analysis, an asymptotic model was used with assumptions about the adiabaticity of the gas outflow process and the ideality of the liquid during the oscillatory one-dimensional motion of the liquid column. In this case, the motion of the liquid column and the evolution of pressure in the gas are determined by the equation of dynamics and the balance of enthalpy. Numerical simulation was performed in the OpenFOAM package using the fluid volume method (VOF method) and the standard k-e turbulence model. The evolution of the fields of volumetric gas content, velocity, and pressure during the flow of gas from the high-pressure chamber into a closed channel filled with liquid in the presence of a ”gas blanket“ at the upper end of the channel is obtained. It was shown that the dynamics of pulsations in the gas cavity that occurs when the gas flows into the closed region substantially depends on the physical properties of the liquid in the volume, especially the density. Numerical modeling showed that the injection of gas into water occurs in the form of a jet outflow of gas, and for the outflow into liquid lead, a gas slug is formed at the bottom of the channel. Satisfactory agreement was obtained between the numerical calculation and the calculation according to the asymptotic model for pressure pulsations in a gas projectile in liquid lead. For water, the results of calculations using the asymptotic model give a significant difference from the results of numerical calculations. In all cases, the velocity of the medium obtained by numerical simulation and when using the asymptotic model differ by an order of magnitude or more.


2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.


Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 772
Author(s):  
Xianming He ◽  
Dongxiao Li ◽  
Hong Zhou ◽  
Xindan Hui ◽  
Xiaojing Mu

The piezoelectric vibration energy harvester (PVEH) based on the variable cross-section cantilever beam (VCSCB) structure has the advantages of uniform axial strain distribution and high output power density, so it has become a research hotspot of the PVEH. However, its electromechanical model needs to be further studied. In this paper, the bidirectional coupled distributed parameter electromechanical model of the MEMS VCSCB based PVEH is constructed, analytically solved, and verified, which laid an important theoretical foundation for structural design and optimization, performance improvement, and output prediction of the PVEH. Based on the constructed model, the output performances of five kinds of VCSCB based PVEHs with different cross-sectional shapes were compared and analyzed. The results show that the PVEH with the concave quadratic beam shape has the best output due to the uniform surface stress distribution. Additionally, the influence of the main structural parameters of the MEMS trapezoidal cantilever beam (TCB) based PVEH on the output performance of the device is theoretically analyzed. Finally, a prototype of the Aluminum Nitride (AlN) TCB based PVEH is designed and developed. The peak open-circuit voltage and normalized power density of the device can reach 5.64 V and 742 μW/cm3/g2, which is in good agreement with the theoretical model value. The prototype has wide application prospects in the power supply of the wireless sensor network node such as the structural health monitoring system and the Internet of Things.


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