The burning of fuel (e.g., coal) in industrial equipment generates an exhaust flow containing airborne particulate. The flow is passed through a rotary heat exchanger to preheat inlet air. The heat exchanger element is subject to fouling and is cleaned by a pulsed combustion device. The device is operated by introducing a fuel and oxidizer charge to at least one conduit and initiating combustion of the charge. The combustion generates a shock wave to which the element is exposed, dislodging and/or otherwise removing the deposits.