Pintle injectors help rockets and spray machines work better by creating perfect tiny droplets of liquid! First of all, these special nozzles have a movable needle in the middle that controls how much fluid comes out and in what pattern. Additionally, spray atomization happens when fast-moving air breaks up the liquid into a fine mist, which is super important for engines to burn fuel properly. Most importantly, rocket engines use this technology because it mixes fuel and oxygen perfectly for powerful, steady burning. Furthermore, the spray pattern can be adjusted easily by moving the pintle in or out, making these injectors very flexible for different jobs. The way liquid propellants break into tiny drops affects how well engines perform and how clean they burn!. For the present simulation, two reference papers are considered, titled “ Design Procedure of a Movable Pintle Injector for Liquid Rocket Engines” & “ LAGRANGIAN APPROACH TO AXISYMMETRIC SPRAY SIMULATION OF PINTLE INJECTOR FOR LIQUID ROCKET ENGINES”.

• Reference [1]: Son, Min, et al. “Design procedure of a movable pintle injector for liquid rocket engines.” Journal of Propulsion and Power4 (2017): 858-869.
• Reference [2]: Radhakrishnan, Kanmaniraja, et al. “Lagrangian approach to axisymmetric spray simulation of pintle injector for liquid rocket engines.” Atomization and Sprays5 (2018).

Figure 1: Gas-liquid injection in pintle ejectors, adopted from reference paper

Simulation Process

The pintle ejector model starts with a special 2D drawing that saves computer power while still showing how the spray pattern forms! First of all, we used Design Modeler to create the shape with special blocks that help make a perfect grid for accurate calculations. Additionally, we chose the Volume of Fluid (VOF) method to track both air and liquid as they mix and interact in the nozzle. Most importantly, our CFD simulation uses the Eulerian-Eulerian approach which is different from the paper but gives excellent results for understanding spray formation. Furthermore, we carefully designed the model with a 0.8mm gas gap because this small space is super important for breaking up the liquid into tiny droplets. The 2D axisymmetric design perfectly captures how the liquid atomization happens while using only half the computer power!

Figure 2: Pintle ejector 2D axisymmetric domain design based on reference paper

Post-processing

The pintle injector creates tiny droplets that spray out in a beautiful fan shape! First of all, we can see that the liquid breaks into smaller and smaller pieces as it moves away from the nozzle opening. Additionally, the spray pattern forms a perfect cone shape with an angle of about 30 degrees on each side, showing excellent spray atomization. Most importantly, the liquid volume fraction drops from 1.0 (pure liquid) to less than 0.1 (mostly air) in just a short distance, proving the injector works super efficiently! Furthermore, the tiny droplets form at specific distances from the nozzle, which matches exactly what rocket scientists want to see. The way the liquid propellant breaks apart into tiny drops helps it mix perfectly with oxygen in real rocket engines.

Figure 3: Volume fraction distribution showing liquid atomization in pintle ejector with complete breakup

The atomization process happens because the fast-moving air tears the liquid into smaller and smaller pieces, just like wind breaking waves at the beach! First of all, the central part of the spray pattern stays together longer before breaking up, while the edges break into droplets almost right away. Additionally, we can see that the liquid forms a thin sheet that gets thinner and thinner until it breaks into separate drops. Most importantly, the simulation captured multiple stages of droplet formation, from the initial sheet breaking, to ligament forming, to final tiny droplets. Furthermore, these droplets range in size from approximately 0.2mm down to microscopic levels, creating the perfect mix for efficient burning in engines. The spray simulation perfectly matches what happens in real propulsion systems, giving engineers valuable information to design better rocket parts!