A turbomachine includes a compressor portion, and a turbine portion operatively connected to the compressor portion. The turbine portion includes a turbine casing. A combustor assembly, including at least one combustor, fluidically connects the compressor portion and the turbine portion. At least one of the compressor portion, turbine portion and combustor assembly includes a sensing cavity. A passive clearance control system is operatively arranged in the turbomachine. The passive clearance control system includes at least one passive flow modulating device mounted in the sensing cavity, and at least one cooling channel extending from the sensing cavity through the casing. The at least one passive flow modulating device selectively passes the fluid from the sensing cavity through the at least one cooling channel to adjust a clearance between stators and rotating airfoils in the turbine portion.