A self-actuated bleed valve assembly for assisting start-up of a gas turbine engine, comprising: a flow duct comprising: an inlet; and an outlet downstream from the inlet; a piston housing inside the flow duct between the inlet and the outlet so as to form an annular flow passage between the flow duct and the piston housing, wherein the piston housing is axially aligned with a center axis of the flow duct; a piston inside the piston housing and configured to extend downstream of the piston housing in a closed position; a spring at least partially inside the piston, wherein the spring contacts the piston and biases the piston to an open position; a fluid chamber between the piston and an upstream end of the piston housing; a control opening extending through the upstream end of the piston housing, wherein the control opening fluidically communicates with the flow duct and the fluid chamber, and characterized by: a control piston and a control spring inside the piston housing, wherein the control spring biases the control piston toward a first position that obstructs the control opening; a control seat in contact with the control spring opposite the control piston, wherein a position of the control seat is adjustable relative the control piston; a guide tube inside the piston housing, wherein the guide tube extends from the upstream end of the piston housing towards the outlet of the flow duct along a center axis of the piston housing, and wherein the piston is configured to slide on the guide tube; a first hole extending through a wall of the guide tube, wherein the first hole fluidically connects the fluid chamber with an interior of the guide tube; a second hole extending through the wall of the guide tube, wherein the second hole is positioned axially between the control seat and the first position of the control piston; and a third hole extending through the wall of the guide tube, wherein the third hole is positioned axially on the guide tube between the piston housing and the outlet of the flow duct, wherein the control piston blocks the first hole from the control opening in a first position, and wherein the second hole and the third hole fluidically connect the fluid chamber with the interior of the guide tube and the outlet of the flow duct when the piston is in the closed position and the control piston is in the first position. a flow duct comprising: an inlet; and an outlet downstream from the inlet; an inlet; and an outlet downstream from the inlet; a piston housing inside the flow duct between the inlet and the outlet so as to form an annular flow passage between the flow duct and the piston housing, wherein the piston housing is axially aligned with a center axis of the flow duct; a piston inside the piston housing and configured to extend downstream of the piston housing in a closed position; a spring at least partially inside the piston, wherein the spring contacts the piston and biases the piston to an open position; a fluid chamber between the piston and an upstream end of the piston housing; a control opening extending through the upstream end of the piston housing, wherein the control opening fluidically communicates with the flow duct and the fluid chamber, and characterized by: a control piston and a control spring inside the piston housing, wherein the control spring biases the control piston toward a first position that obstructs the control opening; a control seat in contact with the control spring opposite the control piston, wherein a position of the control seat is adjustable relative the control piston; a guide tube inside the piston housing, wherein the guide tube extends from the upstream end of the piston housing towards the outlet of the flow duct along a center axis of the piston housing, and wherein the piston is configured to slide on the guide tube; a first hole extending through a wall of the guide tube, wherein the first hole fluidically connects the fluid chamber with an interior of the guide tube; a second hole extending through the wall of the guide tube, wherein the second hole is positioned axially between the control seat and the first position of the control piston; and a third hole extending through the wall of the guide tube, wherein the third hole is positioned axially on the guide tube between the piston housing and the outlet of the flow duct, wherein the control piston blocks the first hole from the control opening in a first position, and wherein the second hole and the third hole fluidically connect the fluid chamber with the interior of the guide tube and the outlet of the flow duct when the piston is in the closed position and the control piston is in the first position.