Geometric Wave Engineering of Compressible Gas Flows: A Candidate Class of Valve-Type Passive Gas-Dynamic Elements Based on Wave-Mediated Switching in PHB and ZPHB Chambers

Can the exact shape of a stationary gas chamber influence when gas enters or leaves through two permanently open ports after a single pressure impulse? We investigate this question within Geometric Wave Engineering (GWE), a proposed geometry-first framework for studying wave-mediated transport using analytically specified boundaries and established conservation laws. We introduce two related constructions: pseudohyperboloidal (PHB) chambers, assembled from exact hyperbolic meridional branches, and mirrored pseudohyperboloidal (ZPHB) chambers, assembled from prescribed reflections of those branches. Compressible-flow calculations identify finite intervals of net upper-port intake concurrent with net lower-port exhaust, without mechanical closure. This is a transient flow state, not proof of a self-recharging engine cycle. Under matched conditions, oppositely signed small profile variations near a PHB produce strongly different responses. By contrast, the tested ZPHB perturbation family retains the simultaneous intake–exhaust state while its timing varies. In a three-grid OpenFOAM comparison with ports represented by open boundaries, PHB exhibits greater filtered mixed-state intensity than a matched bicone, although the magnitude is grid-sensitive. A separate OpenFOAM comparison resolves the surrounding gas explicitly. All three geometries—PHB, ZPHB and the matched bicone—again exhibit simultaneous intake and exhaust, but their intensity ranking changes. In that calculation, upper-port inflow is not equivalent to verified replenishment by gas originating in the upper external region. The results support analytic geometry as a means of tuning the onset, duration and intensity of finite-time gas transport. They do not establish universal PHB superiority, a uniquely focal flow mechanism, or experimental device performance.