De Laval Nozzle Optimization & Thrust Analysis
Investigating how exit cone geometry (\(10^{\circ}\) to \(30^{\circ}\)) influences supersonic exhaust efficiency.
Overview
As a 10th-grade researcher, I designed and executed a study to analyze how the exit angle of a de Laval nozzle affects the conversion of thermal energy into kinetic thrust. This project required building a custom thrust-testing stand from scratch and developing a C++ numerical model to bridge the gap between theoretical fluid dynamics and empirical data.
Methodology & Testing Hardware
- Numerical Baseline: Used the Rocket Thrust Equation to fix nozzle top area (25x throat width) and entrance angles at \(30^{\circ}\) to isolate the exit angle as the independent variable.
- Static Fire Test Stand: Constructed a cube-shaped aluminum frame housing a 20kg Load Cell sensor and HX711 amplifier.
- Propellant Synthesis: Formulated KNSB fuel (65% Potassium Nitrate, 35% Sucrose) and utilized specialized cellophane molds to ensure consistent grain geometry.
- Data Capture: Built an Arduino-based data logger that sampled thrust values every 0.1 seconds, recording over 200 data points per static fire.
Engineering Log: Fabrication & Testing
Structural Design: CAD modeling of the 240mm aluminum profile test stand, ensuring precise alignment for vertical thrust vectoring.
Rapid Prototyping: 3D-printed PLA molds used for casting the final cement-based de Laval nozzles to withstand combustion temperatures.
Data Acquisition (DAQ): Integrating an Arduino Nano with the HX711 amplifier to log real-time force data at 10Hz frequency.
Combustion Chamber: A high-temperature boiling tube mounted with nichrome wire, containing 20g of solidified KNSB propellant.
Static Fire Operations: The final integrated assembly at the lab bench prior to ignition for independent thrust variable testing.
Technical Struggles & Engineering Mitigations
1. High-Temperature Material Failure
Initial tests used PLA 3D-printed nozzles which would deform under the extreme heat of KNSB combustion.
Mitigation: Used 3D-printed designs only as molds for cement-cast nozzles. This allowed for the complex internal geometry of a de Laval nozzle while providing the necessary thermal resistance.
2. Numerical Precision & Latency
The initial C++ code and Load Cell setup suffered from signal noise and measurement latency, making it difficult to capture the exact peak of the thrust curve.
Mitigation: Implemented Standard Deviation analysis to quantify "radicalness" (combustion intensity) and used a line of best fit to determine a correlation coefficient of $-0.98$ for thrust efficiency.
Reflections & Modern Re-Analysis
- Historical Context: This project taught me that engineering is a compromise between parameters like weight, mechanical strength, and performance.
- The Lesson of 15°: My results corroborated professional findings that exit angles near \(15^{\circ}\) optimize the conversion of subsonic to supersonic flow while minimizing turbulence.
- Current Goal: I am currently re-processing this 2022 dataset using Savitzky-Golay Filter to replace the original linear approximations.
- Growth: Moving from 10th-grade "basic" C++ to my current work at USC RPL reflects a shift from empirical "guessing" to high-fidelity numerical simulation.