Discharge of ideal gas into vacuum
Abstract
Threedimensional nonisentropic flow of an ideal gas adjoining a vacuum or occurring upon instantaneous removal of a solid barrier which separates it from a vacuum is analyzed as a problem of decaying discontinuity. The solution to the corresponding system of three vector equations of motion and the equation of state, using the function sigma =sigma sub O(x)=p 1/2 (upsilon) (pdensity of gas, upsilon 1), is sought in the form of special converging series. A convergence test reveals that the gas particles move along straight lines at constant velocity until infinite gradients of gasdynamic parameters build up at the vacuum boundary. Four theorems are proved pertaining respectively to the existence of a unique analytical solution in the vicinity of the discontinuity surface, to its convergence region, to the constant velocity transient following the decay of the discontinuity, and to the corresponding Cauchy problem. The proof of the first theorem reduces to an analog of the proof of the CauchyKowalewska theorem and it yields a lemma pertaining to the coefficients and exponents in the series.
 Publication:

USSR Rept Eng Equipment JPRS UEQ
 Pub Date:
 April 1984
 Bibcode:
 1984RpEE.....R..10B
 Keywords:

 Discontinuity;
 Gas Dynamics;
 Ideal Gas;
 Three Dimensional Flow;
 Vacuum;
 Cauchy Problem;
 Coefficients;
 Convergence;
 Differential Equations;
 Equations Of Motion;
 Gas Density;
 Fluid Mechanics and Heat Transfer