Mechanical Spiral-Phased Transducer (MSPT): A Geometric Principle for Deterministic Control of Travelling Boundary Conditions, Wave Forcing and Vortical Flows

This preprint presents the Mechanical Spiral-Phased Transducer (MSPT), a proposed class of mechanical devices for deterministic programming of travelling boundary conditions in fluids and gases. The principle is based on the geometric superposition of two periodic surface families: a spiral or helical aperture sequence on one moving element and an inclined finite-width shutter family on a second, relatively moving element. Their momentary coincidences form a travelling set of opened apertures. This set can impose a moving boundary condition on a working medium: local opening, pressure drop, mass injection, density perturbation, acoustic forcing or vorticity source, depending on the surrounding chamber and operating regime. The central scientific result is kinematic: the velocity of the travelling coincidence pattern is not constrained to equal the material surface velocity of the rotor. It is a phase-pattern velocity defined by geometry, pitch and rotation frequency. The work therefore distinguishes three velocities that must not be conflated: the material velocity of the rotating surface, the projected radial or axial sweep velocity, and the full spiral or helical coordinate velocity of the aperture sequence. This distinction is inserted explicitly to avoid the common but incorrect interpretation that a fast phase pattern implies superluminal, superacoustic or non-causal transport of matter or energy. Two configurations are formulated. The disk configuration (MSPT-D) uses a planar Archimedean spiral of apertures on disk A and thirty inclined shutters of finite 4 mm width on disk B. For a 150 mm disk with four turns, thirty apertures per turn and a rotation frequency of 50 rev/s, the one-pitch step time is 666.7 microseconds, the material edge velocity is 21.99 m/s, the projected radial sweep velocity is 22.50 m/s, and the full spiral-coordinate phase velocity is 2358 m/s. The cylindrical configuration (MSPT-C) uses a helical aperture sequence on an inner cylinder and axially inclined shutters on an outer cylinder. For a radius of 50 mm, length of 200 mm, eight turns, thirty apertures per turn and 50 rev/s, the projected axial sweep velocity is 300 m/s, while the material surface velocity is 15.71 m/s. The article develops the geometry, closed-form kinematics, corrected scaling relations, numerical consistency checks, wave and vortex regimes, and a validation roadmap. Application domains are presented as falsifiable hypotheses rather than demonstrated performance claims. The proposed potential includes deterministic vortex injection, broadband flow-through acoustic forcing, controlled cavitation studies, externally forced Ranque-Hilsch-type modes, sonochemistry, mixing acceleration, combustion initiation research and plasma or shock preconditioning. The novelty claimed here is not a violation of established physics but a mechanical implementation of geometric phase programming in a mass-throughput aperture system.