Analytical Solution of the Problem of a Shock Wave in the Collapsing Gas in Lagrangian Coordinates

被引:1
|
作者
Kuropatenko, V. F. [1 ,2 ]
Shestakovskaya, E. S. [2 ]
机构
[1] Zababakhin All Russia Res Inst Tech Phys, Russian Fed Nucl Ctr, Snezhinsk 456770, Russia
[2] Natl Res Univ, South Ural State Univ, Chelyabinsk 454080, Russia
关键词
D O I
10.1063/1.4964011
中图分类号
O59 [应用物理学];
学科分类号
摘要
It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t(0) the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.
引用
收藏
页数:7
相关论文
共 50 条
  • [1] The shock convergence problem in Euler and Lagrangian coordinates
    Magazov, F. G.
    Shestakovskaya, E. S.
    Yakimova, M. N.
    [J]. XXXIII INTERNATIONAL CONFERENCE ON EQUATIONS OF STATE FOR MATTER, 2019, 1147
  • [2] Similarity solution of a collapsing cylindrical shock wave in a thermal radiating and conducting gas
    Hirschler, T
    Gretler, W
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2000, 80 : S609 - S610
  • [3] UNIFORMLY VALID ANALYTICAL SOLUTION TO THE PROBLEM OF A DECAYING SHOCK-WAVE
    SHARMA, VD
    RAM, R
    SACHDEV, PL
    [J]. JOURNAL OF FLUID MECHANICS, 1987, 185 : 153 - 170
  • [4] Analytical solution of direct dynamics problem in cylindrical coordinates
    Pala, Y
    Güney, I
    Karadere, G
    [J]. JOURNAL OF ENGINEERING MECHANICS-ASCE, 2004, 130 (09): : 1115 - 1117
  • [5] Analytical Solution of the Blast Wave Problem in a Non-Ideal Gas
    Singh, L. P.
    Ram, S. D.
    Singh, D. B.
    [J]. CHINESE PHYSICS LETTERS, 2011, 28 (11)
  • [6] The Analytical Solution of the Problem of a Shock Focusing in a Gas for One-Dimensional Case
    Shestakovskaya, E. S.
    Magazov, F. G.
    [J]. XV ALL-RUSSIAN SEMINAR DYNAMICS OF MULTIPHASE MEDIA, 2018, 1939
  • [7] Analytical solution to the problem of interaction between a shock wave and a neutron star’s magnetosphere
    S. I. Bezrodnykh
    B. V. Somov
    [J]. Doklady Physics, 2014, 59 : 355 - 359
  • [8] ON THE SIMILARITY SOLUTION OF THE PROBLEM OF A SHOCK-WAVE ARRIVING AT THE EDGE OF A-GAS
    GRASSBERG, EK
    [J]. ASTRONOMICHESKII ZHURNAL, 1981, 58 (01): : 155 - 157
  • [9] Analytical Solution to the Problem of Interaction between a Shock Wave and a Neutron Star's Magnetosphere
    Bezrodnykh, S. I.
    Somov, B. V.
    [J]. DOKLADY PHYSICS, 2014, 59 (08) : 355 - 359
  • [10] Analytical solution for a shock wave in an embedded pile
    Holeyman, A
    Bachy, X
    [J]. GEOTECHNICAL ENGINEERING FOR TRANSPORTATION INFRASTRUCTURE, VOLS 1-3: THEORY AND PRACTICE, PLANNING AND DESIGN, CONSTRUCTION AND MAINTENANCE, 1999, : 777 - 782