An Exact Solution on Compression of a Cavity in a Viscous Heat-Conducting Compressible Medium

• Published in: Fluid dynamics 2022-08, Vol.57 (4), p.494-502
• Main Authors: Golubyatnikov, A. N., Ukrainskii, D. V.
• Format: Article
• Language: English
• Subjects: Classical and Continuum Physics; Classical Mechanics; Compressibility; Compressing; Density; Engineering Fluid Dynamics; Equations of motion; Equations of state; Exact solutions; Fluid- and Aerodynamics; Heat transfer; Heat transmission; Ideal gas; Lagrange coordinates; Newton's laws of motion; Newtonian liquids; Non Newtonian liquids; Physics; Physics and Astronomy; Poisson equation; Strain rate; Symmetry; Tensors
• ISSN: 0015-4628; 1573-8507
• DOI: 10.1134/S0015462822040024

A partially spherically symmetric exact solution of dynamics of a heat-conducting medium with the thermodynamic equations of state of a perfect gas for which the viscous stress tensor depends on the strain-rate tensor in an arbitrary way is given. It is assumed that the strain rates and the pressure are homogeneous and there is no acceleration; in this case, the equations of motion are identically satisfied. As a result of separation of variables in the energy equation, the three-dimensional Poisson equation is obtained for the density as a function of the Lagrangian coordinates. Its solution simulates compression of a domain of significantly variable density in the medium considered, for example, in the case of full spherical symmetry of a buble or a drop. Non-spherical constant-density surfaces are also possible. Flow can occur from the state of rest with a finite mass of the medium due to the motion of the compressing spherical piston. The power-law non-Newtonian liquids are investigated. The energy of medium is calculated and its behavior is presented in the neighborhood of the instant of compression to a point.