The Otto cycle requires an A/F ratio close to stoichiometric to run. If you want less fuel, you can lean it out some, but you really need to have less air flow into the cylinders. One way to do that is to warm up the intake charge and make it less dense.
With the Diesel cycle, it will run with a much wider range of A/F ratio, and there is no need to reduce airflow into the cylinders. A WAI should do either nothing, or possibly reduce efficiency if there isn't enough air to burn all the fuel.
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