I wonder if a combustion engine with oxygen in air as oxidant can be net energy efficient by oxygen enriching the air before using it? This is the same as asking if the net mechanical energy output of such an engine would increase if some of its energy (mechanical or thermal, whatever is useful) is used to enrich the oxygen in the air intake.
A car with variable valve timing would automatically adjust the engine compression ratio based on the oxygen level detected by the oxygen sensor. (If oxygen levels increase, variable valve timing close the intake valves earlier.)
One way of answering this question is to show the efficiency of increasing oxygen content in the intake and combine that with the energy needed to do the oxygen enrichment from air.
Some clues can be had from
Engineering Science and Technology, Volume 19, Issue 1, March 2016, Pages 438-443 Effects of oxygen enriched combustion on pollution and performance characteristics of a diesel engine P.Baskar, A.Senthilkumar
THE EFFECT OF OXYGEN-ENRICHED AIR ON THE PERFORMANCE AND EXHAUST EMISSIONS OF INTERNAL COMBUSTION ENGINES ,VARADARAJA SETTY, B.E. MASTER THESIS IN MECHANICAL ENGINEERING , Texas Tech University
Reports like the following are less interesting, since spark timing is the regulating mechanism with increased oxygen levels.
J.X. Zhou, B. Moreau, Christine Mounaïm-Rousselle, Fabrice Foucher. Combustion, Performance and Emission Analysis of an Oxygen-Controlling Downsized SI Engine. Oil & Gas Science and Technology - Revue d’IFP Energies nouvelles, Institut Français du Pétrole, 2016, 71 (4), pp.49. ff10.2516/ogst/2015035ff. ffhal-01597165f