A method for manufacturing a metallic component is disclosed. The method includes forming a metallic component with a support structure using an additive manufacturing process. The support structure includes support walls arranged to form flow passages with a predetermined cross-sectional area. The method also includes placing the metallic component with the support structure into a chamber and sealing the chamber. The method further includes introducing a fuel mixture into the chamber after sealing the chamber. The method still further includes igniting the fuel mixture in the chamber to remove one or more of the support walls of the support structure from the metallic component.