Rankine-Hugoniot шарттары: соққы толқындары мен жану толқындарының физикасы

Concept in physics

The Rankine–Hugoniot conditions, also referred to as Rankine–Hugoniot jump conditions or Rankine–Hugoniot relations, describe the relationship between the states on both sides of a shock wave or a combustion wave (deflagration or detonation) in a one dimensional flow in fluids or a one dimensional deformation in solids. They are named in recognition of the work carried out by Scottish engineer and physicist William John Macquorn Rankine and French engineer Pierre Henri Hugoniot. The basic idea of the jump conditions is to consider what happens to a fluid when it undergoes a rapid change. Consider, for example, driving a piston into a tube filled with non reacting gas. A disturbance is propagated through the fluid somewhat faster than the speed of sound. Because the disturbance propagates supersonically, it is a shock wave, and the fluid downstream of the shock has no advance information of it. In a frame of reference moving with the wave, atoms or molecules in front of the wave slam into the wave supersonically. On a microscopic level, they undergo collisions on the scale of the mean free path length until they come to rest in the post shock flow (but moving in the frame of reference of the wave or of the tube). The bulk transfer of kinetic energy heats the post shock flow. Because the mean free path length is assumed to be negligible in comparison to all other length scales in a hydrodynamic treatment, the shock front is essentially a hydrodynamic discontinuity. The jump conditions then establish the transition between the pre and post shock flow, based solely upon the conservation of mass, momentum, and energy. The conditions are correct even though the shock actually has a positive thickness. This non reacting example of a shock wave also generalizes to reacting flows, where a combustion front (either a detonation or a deflagration) can be modeled as a discontinuity in a first approximation.

Most solid materials undergo plastic deformations when subjected to strong shocks. The point on the shock Hugoniot at which a material transitions from a purely elastic state to an elastic plastic state is called the Hugoniot elastic limit (HEL) and the pressure at which this transition takes place is denoted pHEL. Values of pHEL can range from 0.2 GPa to 20 GPa. Above the HEL, the material loses much of its shear strength and starts behaving like a fluid.

Rankine–Hugoniot conditions in magnetohydrodynamics are interesting to consider since they very relevant to astrophysical applications. Across the discontinuity the normal component of the magnetic field and the tangential component of the electric field (infinite conductivity limit) must be continuous. We thus have

where difference between the values of any physical quantity on the two sides of discontinuity. The remaining conditions are given by

These conditions are general in the sense that they include contact discontinuities tangential discontinuities , rotational or Alfvén discontinuities and shock waves .