Theory and Design Principals of Hybrid Rocket Engine
Introduction
This white paper serves to outline the basic design process of hybrid rockets for amateur rocketeers, students, and those interested in the general approach for using hybrid rocket engines in projects.
DISCLAIMER: this paper is meant for educational purposes and will only discuss the theoretical concepts behind designing a hybrid rocket engine. Extreme caution should be taken when working with combustibles. While a hybrid rocket engine is safer in operation than a liquid rocket engine the author cannot accept any responsibility from injury caused from mishandling of rocket components.
Most simply explained, a hybrid rocket engine utilizes both solid and liquid components to generate heat in a combustion chamber. As heat and pressure build in the combustion chamber, the subsequent exhaust is expelled through the aft of the vehicle generating thrust.
The general concept for rocket engine performance is a hydrocarbon, which outputs any enthalpy value greater than zero, will increase its energy output with the introduction of an oxidizer. A familiar example is when one makes a campfire then fans the fire to introduce oxygen to the combustion thereby increasing the intensity of the fire. For hybrid rockets, one component of the combustion pair is a liquid and the other component is a solid. A traditional hybrid engine will utilize a solid hydrocarbon and a liquid oxidizer.
The advantages of hybrid rockets are increased safety, lower cost, and simplified fueling procedures.
We will examine the process of combustion in a hybrid engine as the Liquid Oxygen (LOX) travels through the system and reacts with the Hydroxyl-terminated Polybutadiene Resin (HTPB) within the combustion chamber.
Source: Adapted from [1]
Explanation on general rocket performance theory
Foundational to how rocket engines perform is pressure, more specifically is pressures relation to heat in calculating theoretical performance of a rocket.
The general principal behind a rocket’s movement is a rocket can vertically displace itself away from the ground by ejecting mass and energy in the opposite direction of travel.
It is imperative to remember that while designing a rocket engine, that gas created within the combustion chamber will seek a state of equilibrium, even small model rocket motors follow this principle. As the difference between gasses grow between the combustion chamber and the outside atmosphere, the higher-pressure gas inside the combustion chamber will accelerate and flow into of low pressure of the atmosphere.
A gasses desire to seek equilibrium is defined through the Equation of State:
P*V = R * T
In this equation, P is Pressure, R is the Gas Constant, V is Volume, and T is Temperature.
Now we can consider the forces which allow thrust in a rocket. The general thrust equations is derived from Newton’s second law. For the purposes of understanding the force acting upon a vehicle, rocket engine designers can utilize the following thrust equation:
F = (Ṁ * Ve)-(Ṁ*Vt)+∆P*Ae
Here, F is force in Newtons, P is pressure in bars at the throat of the nozzle, Ṁ (pronounced M Dot) is the mass flow rate in grams per second, Pe is pressure in bars at the aft of the combustion chamber, V is velocity in meters per second, and Ae is the area in cm at the exit of the nozzle bell. Through the general thrust equation, it is possible to calculate how to control the pressure within the combustion chamber by increasing temperature [2].
The explain it like I’m five version of the thrust equation is the faster the gas moves, the more force you can lift away from earth. So how can a rocketeer increase the velocity of the exhaust?
Re-arranging the equation of state from earlier allows rocketeers to understand how increased temperatures within combustion chamber can increase the overall velocity of their creation.
T= P*V / R
When the equation of state solves for temperature it becomes clear that to increase the velocity of the exhaust, rocketeers need to increase the overall temperature within the combustion chamber.
Oxidizer: Implementation of Commercial Off the Shelf Oxidizers
There is a plethora of best oxygen to fuel (O/F) ratios studies available, but this document will consider LOX as the primary oxidizer for simplicity. LOX is an inexpensive oxidizer but requires launch operators to understand safe handling of cryogenic material. Rocketeers can obtain LOX from a retailer, or by purchasing an in home O2 condenser.
The LOX container is usually made of either aircraft grade stainless steel or composite carbon fiber. Carbon fiber is easily available on the internet, and there is a very small learning curve to work with the material which makes it ideal for hobbyists. No matter which material is chosen, it must provide the robustness required to contain the LOX at operating pressures while reducing the overall weight of the vehicle.
Oxidizer fuel tanks must begin fueling once the rocket is placed on the launch pad and oriented in the direction of flight. One of the benefits of LOX is it boils at a balmy temperature of 90.19 K (−297.33 °F) at 101.325 kPa (sea level), therefore, as operators fuel the rocket the LOX begins to boil off and thereby self-pressurizing the container.
As the LOX evaporates and the desired pressurization is reached, the solid fuel core is ignited. At this stage the temperature of the fuel core is approximately 600 Celsius [3].
Other inert gasses, like helium, can help pressurize the LOX container. The oxidizer container must will also have a vent valve to prevent over pressurization.
Once the oxidizer is filled in the rocket, a valve opens for the oxidizer to flow into the Oxidizer feed line.
Oxidizer Injector Assembly: Pump / Swirl Oxidizer Injection
Source: Adapted from [3]
The Axial Feed Line consists of plumbing, a turbo pump, and an injection nozzle.
As the LOX container valve is opened, the LOX flows towards the turbo pump which pressurizes the LOX prior to injection. Depending on the performance requirements of the desired vehicle, a turbo pump may not be required if the Oxidizer container can maintain a required pressure to inject the oxidizer into the combustion chamber.
Next the LOX will travel through the injection nozzle.
The injection nozzle must be designed to meet the correct O/F ratios for the chosen combustion sources. Current research indicates that Swirling Oxidizer Flow Types (SOFT) injectors can increase the performance of combustion by normalizing the O/F ratios and providing consistent regression rates of the solid fuel core.
Solid Fuel Core: Fuel Type
Source: Adapted from [1]
As the LOX enters the combustion chamber it interacts with the combustion on the fuel core surface. The fuel core’s geometry is important, consisting of a hydrocarbon rod with the same diameter as the vehicle and a hole running the entire length. A cylinder shape is vital because it prevents axial force acting upon the gas [2]. The hollow center of the core creates the combustion chamber.
When choosing a fuel core, any material which burns may be used. Some popular core materials include paraffin wax, Hexamine, and HTPB because of their high energy density and low weight. HTPB provides an additional manufacturing advantage. Because HTPB resin cures as a solid, rocket manufactures can pour the resin into a mold of any specified geometry to improve the engines’ performance.
The rate at which the fuel disappears due to combustion is known as the regression rate. As regression continues, and the combustion chamber grows the pressure within the rocket decreases. But this performance drop can be mitigated through increasing the oxidizer flow rate.
Conclusion
Overall, hybrid rocket engines provide significant advantages towards resource constrained projects. Combined with the simplicity of the overall system design, a hybrid rocket engine allows hobbyist rocketeers to design, manufacture, and fly higher than they imagined.
References
[1] D. Altman and A. Holzman, “Overview and History of Hybrid Rocket Propulsion,” American Institute of Aeronautics and Astronautics, Reston, 2012.
[2] G. P. Sutton, Rocket Propulsion Elements, New York: Wiley Interscience Publication, 1976.
[3] K. Ozawa, “Hybrid Rocket Firing Experiments at Various,” JOURNAL OF PROPULSION AND POWER, vol. 35, no. 1, pp. 64–107, 2019.
