Built-up deposits on the top surface of a tubesheet and on adjacent tube sections in a tube bundle heat exchanger are removed by inducing vigorous turbulent flow of cleaning liquid radially along the surface of the tubesheet by repetitively and periodically injecting gas pulses into the liquid to form an expanding and retracting gas bubble proximate the plate center. The gas pulse rise time is smoothed by controlling the actuation time of a discharge valve and by a surge volume downstream of the valve to thereby avoid harmful pressure shock waves in the heat exchanger. The cleaning liquid is recirculated through an external filter loop to remove suspended foreign materials dislodged by the turbulent flow.