An analysis of the possibility of the isentropic compression of hydrogen with a real equation of state

Abstract

The possibility of the isentropic compression of hydrogen with a real equation of state up to high values of the density at which an anomaly, associated with the transition of hydrogen from the molecular phase to the atomic phase, is observed in the behaviour of the isentrope, is investigated. The possibility of penetrating the above-mentioned part of the change in the density during the compression of the gas in a shock-free manner is analysed. The problem is not about obtaining very high degrees of compression, which greatly exceed the value of the density in the anomalous range; when necessary, it is also assumed that density values which are less than, but close, to the anomalous range have already been obtained by a preliminary shock-free compression. It is shown that, in the case of the shock-free compression of plane, cylindrical and spherical layers of a uniform gas, which is initially at rest, an infinite density gradient of the gas arises in the flow before the final instant of compression if the density has reached values in the anomalous range. Self-similar solutions which describe the shock-free compression of initially uniform cylindrical and spherical volumes of hydrogen at rest are investigated. It is shown, using a numerical solution of the corresponding systems of ordinary differential equations, that isentropic compression up to density values both in the anomalous range and even higher is possible in this case. A unified approach to the mathematical investigation of the shock-free, strong compression of a gas was proposed in [1]. In particular, an analogue of a centred Riemann wave, which is continuously adjacent to the quiescent, uniform gas, is constructed for a gas with an arbitrary equation of state. The possibility of the shock-free compression of a gas with an arbitrary equation of state up to a certain density, which is greater than the initial density, is thereby proved. The form of the equation of state of the gas has to be specified for a more detailed description of the process of isentropic compression. The strong compression of hydrogen with a real equation of state, which is determined in appropriate physical experiments, is of the greatest interest in solving the problem of controlled thermonuclear synthesis [2].