Intake quality is crucial to gas turbines’ operation. The cartridge filter in the gas turbine intake system filters the gas and outputs a highly clean gas into the gas turbine, while pulse cleaning technology ensures the continuous and efficient operation of cartridge filters. While the current cylindrical pleated filter cartridge used in pulse cleaning usually suffers from insufficient upper cleaning, the conical pleated filter cartridge can effectively solve this issue by providing a greater upper cleaning area with significant application prospects. Despite the existing potential, research on conical filter cartridge cleaning performance is limited; thus, this paper aims to investigate the advantages of pulse cleaning using a conical filter cartridge via numerical simulation. Results demonstrate that while the conical filter cartridge enhances the cleaning strength, cleaning uniformity decreases slightly. To address this shortcoming, this paper innovatively proposes a combination of scattering nozzles and conical filter cartridges to explore the impact of the installation position of scattering nozzles on the cleaning. The modeling and cleaning performance analysis in our research illustrates that the optimal cleaning effect can be achieved under specific conditions when the scattering nozzle is installed parallel to the conical filter cartridge’s inlet. The research work in this paper provides a solution for optimizing the pulse cleaning performance of conical filter cartridges.