A system is provided for an aerial vehicle. This system includes a splash plate, a fuel nozzle and a gas circuit. The splash plate includes a splash plate surface. The fuel nozzle includes a nozzle orifice. The fuel nozzle is configured to direct fuel out of the nozzle orifice to impinge against the splash plate surface. The gas circuit includes a gas passage and a gas outlet. At least a portion of the gas passage is formed by and embedded within the splash plate. The gas passage extends through the splash plate to the gas outlet.