Question: I have a 2002 buick century custom that makes a growling noise off and on at low speeds. I can be going straight or turning, speeding up or slowing down, foot on brake or on gas pedal or not touching either pedal. The only constant is at a slow speed under 30. It will growl for about 3 seconds.
Answer: Growling is usually a front hub bearing, but the way you are describing the noise, it does not sound like it. The noise should be steady and increase with vehicle speed.
You may have a worn engine mount causing the engine to make the growling sound. Try a brake torque to see if you can get it make the noise. If so, do it in reverse. If the noise goes away or changes, then it is for sure and engine mount.