scholarly journals Approaching of the solution of a static compressible medium to the solution of an incompressible medium

2019 ◽  
Vol 95 (3) ◽  
pp. 19-25
Author(s):  
M.M. Bukenov ◽  
◽  
А.A. Adamov ◽  
D.K. Koikelova ◽  
◽  
...  
Keyword(s):  
Compressible Medium ◽  
Incompressible Medium

Comparison of the numerical and self-similar solutions of Sedov’s problem on a point explosion in gas

2020 ◽  
Vol 15 (3-4) ◽  
pp. 212-216
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Korobchinskaya
Keyword(s):  
Gas Dynamics ◽  
Numerical Solutions ◽  
Similarity Theory ◽  
Compressible Medium ◽  
Initial Moment ◽  
Point Explosion ◽  
Perfect Gas ◽  
Gas Dynamics Equations ◽  
Self Similar ◽  
Similar Solutions

Comparative analysis of solutions of Sedov’s problem of a point explosion in gas for the plane case, obtained by the analytical method and using the open software package of computational fluid dynamics OpenFOAM, is carried out. A brief analysis of methods of dimensionality and similarity theory used for the analytical self-similar solution of point explosion problem in a perfect gas (nitrogen) which determined by the density of uncompressed gas, magnitude of released energy, ratio of specific heat capacities and by the index of geometry of the explosion is given. The system of one-dimensional gas dynamics equations for a perfect gas includes the laws of conservation of mass, momentum, and energy is used. It is assumed that at the initial moment of time there is a point explosion with instantaneous release of energy. Analytical self-similar solutions for the Euler and Lagrangian coordinates, mass velocity, pressure, temperature, and density in the case of plane geometry are given. The numerical simulation of considered process in sonicFoam solver of OpenFOAM package built on the PISO algorithm was performed. For numerical modeling the system of differential equations of gas dynamics is used, including the equations of continuity, Navier-Stokes motion for a compressible medium and conservation of internal energy. Initial and boundary conditions were selected in accordance with the obtained analytical solution using the setFieldsDict, blockMeshDict, and uniformFixedValue utilities. The obtained analytical and numerical solutions have a satisfactory agreement.

Elbows for Accelerated Flow

1947 ◽  
Vol 14 (2) ◽  
pp. A108-A112
Author(s):  
G. F. Carrier
Keyword(s):  
Fluid Mechanics ◽  
Incompressible Fluid ◽  
Compressible Medium ◽  
Two Dimensional ◽  
Volume Relation ◽  
Accelerated Flow

Abstract It is of interest in the field of fluid mechanics to determine the shape of that two-dimensional channel which will most effectively turn a stream of fluid through an angle β while simultaneously increasing its velocity by a factor r. In the present paper, criteria which such a channel should satisfy are suggested and an elbow which meets these requirements is obtained. The solution is carried out first for a nonviscous incompressible fluid and then for the compressible medium using the Karmen-Tsien linearized pressure-volume relation.

Acoustic energy radiated by nonlinear spherical oscillations of strongly driven bubbles

2010 ◽  
Vol 466 (2118) ◽  
pp. 1829-1847 ◽  
Author(s):  
Joachim Holzfuss
Keyword(s):  
Wave Model ◽  
High Amplitude ◽  
Compressible Liquid ◽  
Acoustic Energy ◽  
Compressible Medium ◽  
Relevant Parameter ◽  
Wafer Cleaning ◽  
Viscous Compressible Liquid ◽  
Shock Wave Model ◽  
Polytropic Exponent

Based on the theory of F. Gilmore ( Gilmore 1952 The growth or collapse of a spherical bubble in a viscous compressible liquid ) for radial oscillations of a bubble in a compressible medium, the sound emission of bubbles in water driven by high-amplitude ultrasound is calculated. The model is augmented to include expressions for a variable polytropic exponent, hardcore and water vapour. Radiated acoustic energies are calculated within a quasi-acoustic approximation and also a shock wave model. Isoenergy lines are shown for driving frequencies of 23.5 kHz and 1 MHz. Together with calculations of stability against surface wave oscillations leading to fragmentation, the physically relevant parameter space for the bubble radii is found. Its upper limit is around 6 μm for the lower frequency driving and 1–3 μm for the higher. The radiated acoustic energy of a single bubble driven in the kilohertz range is calculated to be of the order of 100 nJ per driving period; a bubble driven in the megahertz range reaches two orders of magnitude less. The results for the first have applications in sonoluminescence research. Megahertz frequencies are widely used in wafer cleaning, where radiated sound may be implicated as responsible for the damage of nanometre-sized structures.

scholarly journals Elastic Settlement Analysis of Rigid Footings Relying On The “Characteristic Point” Concept

2021 ◽  
Author(s):  
Lysandros Pantelidis
Keyword(s):  
Finite Element Analysis ◽  
Characteristic Point ◽  
Compressible Medium ◽  
Tabular Form ◽  
Element Analysis ◽  
3D Finite Element ◽  
Influence Area ◽  
Elastic Settlement ◽  
Rigid Footing ◽  
Settlement Analysis

Abstract In the present paper, the problem of finding the location of the so-called “characteristic point” of flexible footings is revisited. As known, the settlement at the characteristic point, is equal to the uniform settlement of the respective rigid footing. The cases of infinitely long strips and circular footings are studied fully analytically. For the case of rectangular footings, analytical results (for flexible footings) are compared with the respective numerical results (for rigid footings) obtained from 3D finite element analysis (210 cases were examined). As shown, the location of the characteristic point may greatly deviate from the well-known values reported in the literature, as it strongly depends on the thickness and Poisson’s ratio value of the compressible medium. For rectangular footings this location also depends on their aspect ratio, L/B. The location of the characteristic point with respect to the center of footing for the various cases examined is given in tabular form. Strain influence area values (Aj=ρjEs/qB) are also given for the convenient calculation of the settlement (ρj) of footings, especially the rigid, rectangular ones; q is the uniform surcharge of footing and Es the soil modulus.

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