Might be a dumb question but what do the flappers do ? Been without for the past 3 years. I'm thinking they help slow down water from entering back into exhaust when not running ? Or ?
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They actually work like check valves to help cancel out the exhaust pulses to prevent reversion. Reversion is when small (or not so small) amounts of water get brought back into the exhaust valve during valve overlap at idle.
Just so you can see what is happening, idle your car and take a piece of notepad paper and place or over the tip of the tailpipe.
Report back and let us know what you witness. You may be very surprised.
GT