Analytical Method of Profiling Axial-Radial Compressor Impellers

A new analytical method for constructing axial-radial compressor impellers with compound lean leading and trailing edges is proposed allowing us to describe a wide class of flow paths based on a limited (small) number of parameterized quantities. With the aid of this method there has been designed a new flow path with a typical axial radial impeller for turbo-expander aggregate compressors with flow coefficients in the range from 0.03 to 0.06. To test the method, a numerical study of spatial viscous flows was carried out in the existing and new modifications of the flow path for the typical axial-radial compressor of a low-temperature turbo-expander aggregate. To do that, the IPMFlow software package was used, which is the development of the FlowER and FlowER-U programs.Запропоновано новий аналітичний метод побудови осерадіальних робочих коліс компресорів зі складними навалами вхідних і вихідних кромок, який дозволяє описувати широкий клас проточних частин на основі обмеженої (невеликої) кількості параметризованих величин. За допомогою цього методу створено нову проточну частину типового осерадіального робочого колеса для компресорів турбодетандерних агрегатів із коефіцієнтами витрати в діапазоні від 0,03 до 0,06. Для апробації методу виконано чисельне дослідження просторових в'язких течій у існуючій та новій модифікації проточної частини типового осерадіального компресора низькотемпературного турбодетандерного агрегату з використанням програмного комплексу IPMFlow, що є розвитком програм FlowER і FlowER-U.Предложен новый аналитический метод построения осерадиальних рабочих колес компрессоров со сложными навалами входных и выходных кромок, который позволяет описывать широкий класс проточных частей на основе ограниченного (небольшого) количества параметризованных величин. С помощью этого метода создана новая проточная часть типичного осерадиального рабочего колеса для компрессоров турбодетандерних агрегатов с коэффициентами расхода в диапазоне от 0,03 до 0,06. Для апробации метода выполнено численное исследование пространственных вязких течений в существующей и новой модификации проточной части типичного осерадиального компрессора низкотемпературного турбодетандерного агрегата с использованием программного комплекса IPMFlow, который является развитием программ FlowER и FlowER-U

Conceptual aspects of line tensions

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid--fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition,however, the line tension does depend on the choice of the Gibbs dividing interfaces. We provide equations for the equilibrium contact angles which are form-invariant with respect to notional shifts of dividing interfaces which only change the description of the system. Conceptual consistency requires to introduce additional stiffness constants attributed to the line. We show how these constants transform as a function of the relative displacements of the dividing interfaces. The dependences of the contact angles on lens or drop volumes do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness constants of the line.Comment: 34 pages, 9 figure

Plasma flow past a two-dimensional magnetic dipole

Plasma flow past a two dimensional magnetic dipol

Capillary pressure of van der Waals liquid nanodrops

The dependence of the surface tension on a nanodrop radius is important for the new-phase formation process. It is demonstrated that the famous Tolman formula is not unique and the size-dependence of the surface tension can distinct for different systems. The analysis is based on a relationship between the surface tension and disjoining pressure in nanodrops. It is shown that the van der Waals interactions do not affect the new-phase formation thermodynamics since the effect of the disjoining pressure and size-dependent component of the surface tension cancel each other.Comment: The paper is dedicated to the 80th anniversary of A.I. Rusano

All speed scheme for the low mach number limit of the Isentropic Euler equation

An all speed scheme for the Isentropic Euler equation is presented in this paper. When the Mach number tends to zero, the compressible Euler equation converges to its incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficulty in the low Mach regime. The key idea of our all speed scheme is the special semi-implicit time discretization, in which the low Mach number stiff term is divided into two parts, one being treated explicitly and the other one implicitly. Moreover, the flux of the density equation is also treated implicitly and an elliptic type equation is derived to obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared with previous semi-implicit methods, nonphysical oscillations can be suppressed. We develop this semi-implicit time discretization in the framework of a first order local Lax-Friedrich (LLF) scheme and numerical tests are displayed to demonstrate its performances

Grand potential in thermodynamics of solid bodies and surfaces

Using the chemical potential of a solid in a dissolved state or the corresponding component of the chemical potential tensor at equilibrium with the solution, a new concept of grand thermodynamic potential for solids has been suggested. This allows generalizing the definition of Gibbs' quantity $\sigma$ (surface work often called the solid-fluid interfacial free energy) at a planar surface as an excess grand thermodynamic potential per unit surface area that (1) does not depend on the dividing surface location and (2) is common for fluids and solids.Comment: 6 page