We consider global-in-time evolution of irrotational, isentropic, compressible Euler flow in $3$-D, for a broad class of $H^4$ classical Cauchy data without assuming symmetry, prescribed on an annulus surrounded by a constant state in the exterior. By giving a sufficient condition on the initial data,  we construct global exterior solutions in $H^4$ for the broad class of data, with a rather general subclass forming rarefaction at null infinity. Our result does not require smallness on the transversal derivatives of classical data, thus applies to data with a total energy of any size. This is on my work arXiv:2407.13649.