⚡ electrical engineering

Active throttling and dual‑thrust capability of 3D‑printed swirl‑star fuel grains for hybrid rocket engines

This study demonstrates that 3D-printed 5-point swirl-star fuel grains with reverse ports significantly enhance the throttling responsiveness and dual-thrust stability of hybrid rocket engines, achieving rapid stabilization and minimal pressure fluctuations during active oxidizer flow modulation.

Original authors: Mostafa El-Naggar, Ahmed F. A. Hassan, Mahmoud Y. M. Ahmed, Anwer Hashish

Published 2026-06-29

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CC BY 4.0

Original authors: Mostafa El-Naggar, Ahmed F. A. Hassan, Mahmoud Y. M. Ahmed, Anwer Hashish

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a hybrid rocket engine as a car with a unique engine: it carries solid fuel (like a stick of wood) and liquid oxidizer (like oxygen gas). To make the car go, you spray the gas onto the wood to make it burn. The problem with traditional "wood" fuel is that it burns in a messy, unpredictable way. If you try to slow down the gas flow to slow the car down, the wood doesn't always react quickly or smoothly. It might sputter, shake, or take too long to adjust, making it hard to steer precisely.

This paper is about a team of engineers who decided to fix this "wood" by carving it into very specific, fancy shapes using a 3D printer. They wanted to create a fuel grain that could instantly switch between a "boost" mode (fast acceleration) and a "sustain" mode (steady, slower cruising) without shaking or stalling.

Here is how they did it, explained simply:

1. The "Swirl" Trick

Instead of just blowing oxygen straight at the fuel, they used a special nozzle that spins the oxygen like water going down a drain. This creates a strong swirl. Think of it like stirring a pot of soup; the spinning motion helps the heat spread evenly and makes the fuel burn faster and more consistently.

2. The Shape Matters: Stars vs. Tubes

They tested different shapes for the hole in the middle of the fuel stick:

The Tube: A simple round hole (like a straw). This is the old, boring way. It burns okay, but it's not very responsive.
The Star: They carved the hole into a star shape with points sticking out. This increases the surface area, like having a crinkled piece of paper instead of a flat one. More surface area means more burning.
The "Swirl-Star-Reverse": This is their secret sauce. It's a star shape where the points are twisted to match the spinning oxygen. It's like a corkscrew designed to catch the spinning wind perfectly.

3. The Experiment: 66 Test Fires

The team printed these fuel grains out of a plastic called ABS (the same kind used in LEGO bricks) and tested them in a small 1-inch motor. They ran 66 tests in total.

60 tests were to see how fast they burned at a steady speed.
6 special tests were to see if they could switch from "fast" to "slow" instantly (throttling).

They tested stars with 5 points, 7 points, and 9 points to see which was the "Goldilocks" size—not too few, not too many.

4. The Results: Finding the Perfect Star

Here is what they found, using a simple analogy:

The 5-Point Star: This one burned the fastest, but it was like a race car with a loose steering wheel. When they tried to slow down the oxygen flow, the engine got jittery and unstable. It reacted too violently to the change.
The 9-Point Star: This one was too crowded. The points were so close together that the spinning oxygen couldn't do its job properly. It acted almost like the simple round tube, burning slowly and taking too long to react when they tried to change speeds.
The 7-Point Star (The Winner): This was the perfect balance. It burned fast, but more importantly, it was stable. When they switched from "Boost" to "Sustain," the pressure in the engine dropped smoothly and settled down almost immediately. There was very little shaking or "undershoot" (a dip in power before it stabilizes).

5. Why This Matters

The main goal was Active Throttling. Imagine a rocket that needs to blast off quickly to escape a planet's gravity (Boost), and then immediately slow down to gently land on the surface (Sustain).

With old fuel, this switch is risky and bumpy. With their new 3D-printed 7-point Swirl-Star fuel, the switch is clean and precise. The engine responds almost exactly like a liquid rocket engine, which is the "holy grail" of rocket design.

The Bottom Line

The paper concludes that by 3D printing fuel grains with a specific 7-point twisted star shape, they created a hybrid rocket engine that can be "programmed." It can switch between high power and low power smoothly and safely, without the dangerous shaking that usually happens. This opens the door for future rockets that can perform complex maneuvers, like landing on other planets or changing orbits, with much greater precision.

Note: The paper only tested this on a small scale (a 1-inch motor) and with a specific plastic fuel. They did not test it on full-size rockets or with other materials in this specific study, but the results suggest the concept works.

Technical Summary: Active Throttling and Dual-Thrust Capability of 3D-Printed Swirl-Star Fuel Grains

Problem Statement
Hybrid rocket motors (HRMs) offer a unique combination of the safety and storability of solid propellants with the throttling and restart capabilities of liquid systems. However, the practical realization of fast, stable thrust modulation is often hindered by the non-linear, diffusion-limited combustion behavior of conventional polymeric fuel grains. Specifically, the regression rate ( $\dot{r}$ ) of standard fuels typically follows a power law dependence on oxidizer mass flux ( $G_{ox}$ ) with an exponent $n$ ranging from 0.5 to 0.8. This non-linearity causes significant thermal lag and mixture ratio excursions during active throttling, making precise trajectory control difficult for applications such as planetary landers, orbital transfer vehicles, and guided missiles. There is a critical need for fuel grains that exhibit a regression rate approaching a linear dependence on oxidizer flux ( $n \to 1$ ) to enable responsive, low-oscillation dual-thrust (boost–sustain) operations.

Methodology
This study investigated the use of additively manufactured (3D-printed) fuel grains with complex internal geometries to enhance regression rates and improve throttling stability.

Fuel and Fabrication: Acrylonitrile butadiene styrene (ABS) was selected as the fuel due to its processability and stability with gaseous oxygen. Grains were fabricated using a Prusa i3 MK3 printer with 100% infill.
Grain Geometries: The study compared a baseline tubular grain against star-shaped variants: Basic Star (BS), Swirl Star (SS), and Swirl-Star-Reverse (SSR). These were tested with varying numbers of star points ( $N = 5, 7, 9$ ).
Injector Design: A tangential swirl injector ( $S=0.7$ ) was employed to impart high angular velocity to the oxidizer, creating a strong vortex to enhance convective heat transfer and mixing.
Experimental Setup: A 1-inch test motor was used for 66 static fire tests. The system utilized a dual-line oxidizer delivery architecture with parallel solenoid valves to achieve rapid, step-wise transitions between a high-thrust "boost" phase (5 g/s) and a low-thrust "sustain" phase (2.5 g/s).
Data Analysis: Regression rates were calculated from mass loss, and empirical laws ( $\dot{r} = a G_{ox}^n$ ) were derived using least-squares regression. Throttling performance was evaluated based on pressure transient response, undershoot magnitude, and oscillation levels during the boost-to-sustain transition.

Key Results

Steady-State Regression: The study confirmed that complex geometries significantly alter the combustion exponent. The tubular grain exhibited a classical exponent of $n \approx 0.617$ . The introduction of swirl and star geometries increased $n$ , with the 5-point Swirl-Star-Reverse (5SSR) achieving the highest exponent ( $n = 1.080$ ). However, the 7-point Swirl-Star-Reverse (7SSR) configuration offered a balanced performance with $n = 0.911$ and a high regression coefficient.
Throttling Dynamics:
- 5SSR ( $N=5$ ): While providing the highest raw regression rate, the 5SSR grain exhibited an unstable transient response during throttling, characterized by pressure overshoots and oscillations due to unstable vortex structures.
- 9SSR ( $N=9$ ): The 9-point configuration resulted in a lower exponent ( $n \approx 0.57$ ) and a sluggish pressure response, effectively behaving like a circular port where the star points failed to sustain a strong vortex.
- 7SSR ( $N=7$ ): This configuration demonstrated the optimal dynamic behavior. It achieved a clean transition from boost to sustain with minimal pressure undershoot (<5%) and no significant oscillations. The coupling between oxidizer flux and fuel regression was near-linear, allowing for stable, well-controlled throttling.
Repeatability: The dual-line throttling architecture provided repeatable, near-instantaneous step transitions, as evidenced by the close overlay of pressure traces from repeated tests.

Key Contributions

Optimization of Grain Geometry: The paper identifies the 7-point Swirl-Star-Reverse (7SSR) geometry as the optimal design for throttleable hybrid rockets, successfully resolving the trade-off between maximizing regression rates and maintaining stable combustion ( $n < 1$ ).
Active Throttling Demonstration: The study provides empirical evidence that 3D-printed grains with optimized swirl geometries can support responsive dual-thrust operations with low oscillation, a capability often limited in conventional hybrid systems.
Additive Manufacturing Validation: The research validates additive manufacturing as a viable route for creating complex internal port geometries that manipulate internal flow dynamics to achieve programmable thrust profiles.

Significance and Claims
The authors claim that this work provides a tractable route to programmable hybrid propulsion systems capable of performing complex thrust profiles required for future aerospace missions. By achieving a regression exponent close to unity ( $n \approx 0.911$ ) with the 7SSR grain, the motor response becomes more predictable and linear, facilitating the design of closed-loop controllers without the need to compensate for highly non-linear, hysteretic plant dynamics.

The study positions the 2:1 throttling ratio (5 g/s to 2.5 g/s) demonstrated in the 1-inch motor as a proof of concept for larger motors. The authors note that while deeper throttling ratios are necessary for applications like planetary landing, the combination of additive manufacturing, swirl injection, and the 7SSR geometry offers a new design paradigm for throttleable hybrid rockets. The use of thermoplastic ABS also highlights potential logistical advantages for in-situ resource utilization (ISRU) concepts.

Limitations
The authors modestly acknowledge that the results are based on a single motor scale (1-inch) and a specific throttling ratio (2:1). They caution that extrapolation to larger motors or deeper throttling ratios requires further validation. Additionally, the use of time-averaged burning surface area introduces a systematic uncertainty, and the assumption of uniform axial regression requires future validation via CT-based reconstruction or multi-port instrumentation. Future work is proposed to scale the concept to higher thrust levels (500–5000 N) and incorporate energetic additives.