Unlimited cumulation under one-dimensional unsteady compression of an ideal gas

Various methods of unlimited cumulation (UC) of an ideal (inviscid and non-heat-conducting) gas subject to one-dimensional unsteady compression by a plane, cylindrical, or spherical piston are considered. The most perfect method, namely, UC with isentropic compression from rest to rest, which is referred to as “ideal” (IUC), is compared with three other methods of UC, which correspond to well-known self-similar solutions of one-dimensional gas compression. The most effective of these is UC with a reflected shock wave, behind which the compressed gas is homogeneous and at rest, as in IUC. The efficiency of various methods of UC is estimated by the ratio of the work done during compression to the work in the case of IUC, the ratio of the internal energy to the total energy of the compressed gas, and the degree of gas homogeneity with respect to the Lagrangian variable. Computations of these characteristics are carried out for a perfect gas with various adiabatic exponents.