Sanity check. Once leaned at altitude, it shouldn't matter if you change RPM, if you haven't changed altitude?? I never need to do this in normal ops, but my break-in procedure suggests a change in RPM every so often. Break-in is leaned rich of peak.
This all depends. Is there a turbo? What altitude are you at? Constant speed prop? Etc.
For example. In a turbo airplane:
- If you are leaned way out because you are crusing at 55% power, and suddenly increase to 100% power, you absolutely will need to increase the mixture (and do so prior/while making that power change). As you need a richer fuel mixture at 100% power.
- If you are leaned for 80% power, and decrease to 50% power, you would probably want to lean the mixture some more yet to save fuel. You can more safely run at leaner mixtures while at lower power settings.
Key detail: The above is not because your fuel system doesn't maintain the same fuel/air ratio at different power settings (like others incorrectly said). It is because you NEED/WANT a different fuel/air ratio at different settings and you as a pilot need to command that. In a car, your ECU is constantly changing the fuel/air ratio based on the environment, engine load, and other factors.
If you are not in a turbo airplane, fixed-pitch prop, and lets assume you are cruising at 8,000 ft:
- Most likely you'd be WOT, and leaned as appropriate for that. If you reduced RPM, you want to lean out a little more, as you can get by with a leaner fuel mixture. Leaner fuel mixtures (in the right scenario) are better for your plugs, and save you money.
- Lets say you were at 40% power, leaned for that, and decided to increase to WOT...Then you might want to go a little richer.
- That all said, without a turbo, at 8,000 ft..It doesn't really matter what you do with the mixture knob as you won't make enough power to hurt anything.
Every scenario will result in a slightly different answer. There are thousands of scenarios you will encounter as a pilot. What you should do will change depending on the equipment, and countless other factors. There is no "short cheat list" for what you should do. You need to understand the relations of power, mixture, and temperature. Once you really understand your engine you will know what you should do.