2011 Honda Civic EX Coupe is making a gurgling/rattling noise when accelerating only?

I own a 2011 Honda Civic EX Coupe with only about 30,000 miles, well maintained and regular maintenance. For about a year, the car has been making a weird gurgling/rattling noise ONLY when accelerating. As soon as I take my foot off the pedal, it stops. Also it seems to only do it when I'm on D-drive. In the morning, I go up some pretty steep hills, and on Drive it takes the loud sounds, but when I lower my gear to D3, going at the same speed limit, it doesn't make the noise. It doesn't happen when I'm turning or braking. Only when accelerating. I have complained to the shop for months but they say they do not see what is causing it. Can anyone help? Also I only use 93 octane gas.

Air in heater core. Gurgling sound under dashboard. Some 2007-11 Civic/ Fit compact cars may emit a gurgling noise from under the dashboard at idle, under light acceleration or during deceleration.

One likely cause of the annoyance, reports Honda, is an air-bound heater core. Giving the core a good burp should alleviate the condition immediately.

Start by loosening the radiator cap a tad. Next, start the engine and allow it to idle until the electric cooling fan has cycled on and off twice. Now turn the ignition off and carefully remove the radiator cap. Fill the radiator with coolant until it reaches the base of the filler neck, then add coolant to the reservoir until it aligns with the MAX mark.

Install and tighten the radiator cap, then allow the engine to cool to the ambient temperature. Once it does, check the coolant level in the reservoir. It should be down near the MIN mark. If it didn't drop, check for a leak or a bad radiator cap. If the level did drop, fill the reservoir to the MAX mark.

To complete the fix, go on a road test to verify that the gurgling noise has been eliminated. If it hasn't, repeat the bleed procedure.