An engagement system (10) for a fluid-coupling device (9) may include a first engagement member (31) and a second engagement member (15) that is in operation with the first engagement member (31). A working chamber (33) is disposed between and at least partially defined by the first engagement member (31) and the second engagement member (15). The working chamber (33) has an inlet port (118) and an outlet port (120). A fluid reservoir (35) is fluidically-coupled to the working chamber (33). A scavenge valve (11) is coupled between the working chamber (33) and the fluid reservoir (35) and adjusts the fluid flow through the outlet port (120). An engagement system (10) for a fluid-coupling device (9) may in addition to or alternatively include a working chamber (33) that includes a working chamber inlet port (118) that is along an outer perimeter (126) of the first engagement member (31). A valve (11) is coupled between the working chamber (33) and the fluid reservoir (35) and adjusts the fluid flow through the working chamber.