Hexa-Wankel

A Geometric and Thermodynamic Hypothesis for a Six-Apex Rotary Engine with Two-Phase Combustion

Abstract

This paper formulates the Hexa-Wankel as a hypothesis for a six-apex rotary engine intended to combine the power density of the triangular Wankel engine with the thermal- sealing predictability of the piston engine. The design definition used here is a convex six-apex rotor operating within a Wankel-like five-lobe baseline housing, not a flat hexagonal housing. Two combustion zones are fixed in housing coordinates and operate in phase- separated sequence; the total fuel dose is not doubled, but divided into two pulses, Q/2+Q/2. The design objective is not to reduce the mean engine temperature, but to render the thermal and pressure maps more stable, periodic, and predictable enough for apex-seal force to be specified more precisely. The paper derives an initial kinematic closure for an N-apex rotor, the envelope regularity condition, swept-volume scaling, friction thresholds, apex-only leakage thresholds, Fourier thermal-harmonic analysis, the relationship between phase angle and the torque kernel Ki(θ) = dVi/dθ, and the gas-exchange constraints of a six-chamber architecture. As an initial validation step, the paper also includes a two-dimensional kinematic CAD model and numerical chamber-volume calculation for the six-apex/five-lobe baseline. This validation establishes basic geometric feasibility and chamber-volume periodicity, but it does not establish performance superiority; the torque kernel, phased-combustion compatibility, port timing, CFD, FEA, and three-dimensional leakage remain subsequent tests. The principal result is therefore not a final efficiency prediction, but a set of threshold conditions: to avoid being defeated by seal friction, the six-apex candidate must satisfy λF λv < 0.5; to avoid being defeated by leakage, it must satisfy 2λA􏰈λpλt < 1; and to approach a modern petrol piston engine at approximately 40% brake thermal efficiency at a target r = 10.5, the total realisation factor must satisfy ΞH > 0.713. The Hexa-Wankel is consequently a coherent first-order design hypothesis, but it remains falsifiable: it fails if the six-apex/five-lobe housing cannot produce sealed chambers, an adequate compression ratio, a two-phase torque kernel, sufficient port timing, and measurable reductions in thermal variance and seal loss.