First-Stage Rocket Design
The purpose of this study was to model the performance characteristics of the first stage of a multistage rocket. The objective was to carry an upper stage and payload of 5,000 kg to an altitude of 45 km, achieving a velocity of 5,000 km/hr at that point. This goal was achieved through an iterative numerical model that specified the propellant, combustion chamber and nozzle geometry, propellant feed turbomachinery, and associated thermodynamics of the system. This project showed that a minimal rocket design can achieve this mission, both with a simple trajectory and a more complex flight path that responds to aerodynamic pressure.
This was my final project completed for ME 4040 at Cal State LA in Spring 2020 with Dr. Jeffrey Santner.
Drag-free, constant velocity first approximation of trajectory
The NASA Chemical Equilibrium with Applications (CEA) solver was utilized to establish the baseline thermodynamic properties required to achieve performance values. One of these values, specific impulse (Isp) enabled finding the key parameters of engine burnout time and overall mass ratio.
Numerical integration yields a solution for the 1/MR term in the integrated position equation and sets a first approximation for engine cutoff time, initial vehicle mass, and propellant mass. This calculation also produces time-step data for altitude and velocity, making it possible to introduce drag into the approximation.
Propulsion Thermodynamics
The liquid propellant RP-1 with Liquid Oxygen oxidizer (LOX) was selected on the basis of its prevalence in existing engine systems, its documented performance characteristics, and ability to store and handle with relative ease. Though a fuel with lower molecular mass has the potential to perform slightly better, the practical advantages of RP-1 often outweigh the difficulties associated with higher-Isp fuels such as liquid hydrogen or methane.
The engine runs on a fuel-lean oxidizer-to-fuel ratio of 2.36, approximately equal to similar first-stage engines and the stoichiometric ratio for LOX/RP-1, but lower than other similar systems designed for higher altitudes.
The geometry of the combustion chamber is driven by a desire to avoid the performance reduction associated with an Ac/At ratio smaller than 4. Below this value, the gas velocity in the equivalently "infinite" chamber, v1, slows to stagnation and can be discounted. Due to a competing need to maximize the nozzle throat area to increase mass flow while maintaining a nozzle expansion ratio for a design altitude, the chamber-to-throat ratio settled on a value of 3, with only a marginal loss in Isp.
Gas generator cycle with regenerative cooling that diverts 1.26% of the RP-1 and 0.24% of the LOX flow to a gas generator cycle with a single turbine driving fuel pumps.
Flight Performance
These plots show the thrust coefficient, Cf, vs altitude in an unthrottled launch and a thrust, F, vs altitude in a launch that throttles to 70% thrust as the rocket passes through maximum dynamic pressure, max-q.
Adding drag to the model and accounting for a down-throttle for max-q both have significant propellant mass consequences, but only add a few seconds to the time to burnout, when the mission is accomplished.
These results were essentially in line with the first stage of the reference engine and rocket, Rocket Lab’s Rutherford engine on an Electron rocket.