Ethalox Engine Design
June-August 2020
Overview:
The intent of this project was to learn how to design a liquid engine from performance parameters (thrust and impulse) with rigorous justification for all design choices.
General Design Parameters:
The thrust and impulse of this engine is designed to be identical to the solid motor my rocketry team designed last year to lift a 100lb launch vehicle (LV) to 10,000ft at the Spaceport America Cup. The impulse needed (calculated by OpenRocket) is 17,000 Ns. In order to get enough speed for the LV to be aerodynamically stable off the launch rod, the engine should provide 850lbf of thrust.
The combustion cycle that will be used for this engine will be pressure-fed. It is much more feasible at this scale than using fuel pumps of any sort. Additionally, I have opted against using any active cooling methods such as regenerative cooling, due to the manufacturing challenges it poses.
Design Parameters:
Selection of Fuel Parameters:
Ethanol and Liquid Oxygen have been selected as the fuel and oxidizers due to ethanol's low cost and ability to be diluted with water to fix any thermal problems that could arise. Liquid oxygen has been chosen due to its excellent performance as an oxidizer. Now, an oxidizer to fuel mixture ratio and an ethanol concentration need to be chosen.
In order to determine these two parameters, I used NASA's online Chemical Equilibrium with Analysis (CEA) tool. I ran 567 independant combustion simulations. I varied 3 parameters (chamber pressure, O/F ratio, and ethanol concentration). My friend wrote a parsing script for me that extracted key data like c* and combustion temperature from the raw CEA output into an organized csv file from which I could use Matlab to plot the data. I generated the following graphs.
Since my team's solid motor burned at around 2900K, in the interest of not deviating far from an already untested combustion temperature (no static fire was performed due to Covid), I will set a cap on the temperature at 3000K.
I will also set a pressure cap at 350psi. Since the engine will be pressure-fed, the highest pressures will be in the flight tanks, which will roughly have a max pressure of 800psi. With a 350psi engine, we can achieve the thrust and impulses needed, so there is no point in running at a higher than needed pressure. Having a chamber pressure too low can result in the loss of fully supersonic flow (choked flow could be lost and/or normal shocks will develop in the nozze). Since a higher pressure engine will be more efficient, I will choose 350psi for the chamber pressure.
In order to choose the O/F ratio and ethanol concentration within the pressure and temperature constraints, I plotted c* vs O/F ratio for all simulations with a chamber pressure of 350psi with combustion temperatures below 3000K. This plot is below.
I chose 95% Ethanol with an O/F Ratio of 1.25. This combination results in a combustion temperature of 2955K, and this combination yields the highest efficiency under the temperature and pressure constraints.
Fuel Properties:
Mass Flow Rate/Firing Time:
Using the chemical properties of the fuel and mixture ratio (taken from CEA), I built a Matlab model that allows you to determine fuel and oxidizer mass flow rates as well as firing time in order to meet thrust and impulse constraints. This model solves a differential equation for chamber pressure as a function of time and from chamber pressure and chemical properties, thrust can be determined. I have attached a PDF below where I go over the derivation of the equations my model uses.
From this model, I determined that the engine needs a fuel mass flow rate of 0.670kg/s, an oxidizer mass flow rate of 0.838kg/s and firing time of 4.5s.
Mass Flow Rate Table
Nozzle:
The nozzle should expand the gases to the ambient pressure about halfway into flight. From OpenRocket simulations by my team, a 100lb LV will be at an altitude of 5197ft above sea level (when launched from Las Cruces) 2.5s into the flight. The ambient pressure at this altitude is 12.14psi. Thus, an exit pressure of 12.14psi constitutes the design condition of the nozzle.
The thrust coefficient of the nozzle will be 1.4841. (Using thrust coefficient formula)
To achieve the desired 850lbf of thrust with the determined chamber pressure and thrust coefficient, the throat area must be 1.636 in^2. (Using Thrust Formula)
To expand the gases to the desired exit pressure, from 350psi, the expansion ratio of the nozzle must be 4.9712. (Using Isentropic flow relations)
Nozzle Parameter Table:
To design the nozzle contour, I decided on utilizing Rao's Thrust Optimized Parabolic (TOP) nozzle. I chose this over the more efficient Method of Characteristics (MOC) since Rao's method will generate a shorter, lighter nozzle with ~98% of the efficiency of a MOC nozzle. I wrote a Matlab script to plot the TOP nozzle contour from the throat area and expansion ratio. Additionally, I generated graphs of temperature, pressure, and mach number along the length of the nozzle. These plots are below:
The melting point of steel is around 1600K to 1800K. As can be seen from the Temperature graph for the nozzle, no part of the nozzle will experience temperatures below the melting point of steel. As a result, I have chosen graphite for the nozzle material. Graphite is an ablative, so it will slowly shed and take some heat with it. Since the firing time of the engine is ~4.5 seconds, not enough graphite will shed to significantly affect performance. This conclusion was reached after reading multiple NASA papers that conducted experiments on ablative nozzles.
However, a graphite nozzle cannot be bolted onto the combustion chamber due to its brittle nature. So, I have designed a steel carrier that will house the graphite nozzle and be bolted into the combustion chamber. Screenshots of the two parts are shown below.
Combustion Chamber:
The combustion chamber will be made out of 6061 T6 aluminum due to its low weight. Since this chamber houses the intense heats of combustion, it will need an ablative liner along its walls for thermal protection. I have decided to use G10 phenolic, since my team has used this material before.
From Design of Liquid Propellant Rocket Engines by Huzel and Huang, a contraction ratio of at least 5 should be used for small pressure-fed engines to facilitate mixing. This would correspond to having a combustion chamber diameter of at least 3.25". Using a larger contraction ratio doesn't have any consequences in terms of fuel mixing. In the interest of interfacing the engine with the airframe easier, an outer diameter of 4.25" has been chosen. In order to minimize weight, a thickness of 0.125" has been chosen for the combustion chamber. Since the G10 phenolic liner is 0.125" thick, the diameter of the combustion region is 3.75", which corresponds to a contraction ratio of 6.75.
Based on a quick, back of the envelope calculation, the factor of safety against yield at operating conditions would be 6.72. This gives enough room to account for pressure spikes (for example, during ignition) and stress concentrations from bolt holes. This hand calculation will be verified using ANSYS Static Structural.
The length of the combustion chamber is a very critical quantity to get right. The length of the combustion chamber is important to ensure proper mixing of fuel and oxidizer. The optimal length is usually chosen via experimental testing, but my team does not have the resources to conduct a multitude of experimenal tests. From Huzel Huang, typical characteristic lengths for Lox engines run from 30-50in. No number is given specifically for an ethalox engine, so I will just pick 50 inches to err on the side of safety (having a better mixture). This gives a combustion chamber length of 6.67".
Combustion Chamber Dimensions:
*This length is the distance between the injector face and the beginning of the converging section.
Below is a preliminary diagram of the engine:
I also conducted a Finite Element Analysis simulation in ANSYS for the chamber. The mesh, load conditions, and stress results are shown below. I used a finer mesh around the bolt holes, since that is where I expected the highest stresses. I used a coarser mesh in the middle of the chamber, since the stress there closely follows the hand calculation of hoop stress, due to St. Venant's principle.
To ensure that the stress converged with an increase in mesh density, I refined the mesh around the bottom holes (area of max stress) twice and the maximum stress went from the initial 17,666 psi to 17,855psi, to 17,862psi, so I am confident that the results from this simulation are accurate. This FEA suggests a factor of safety of 2.24, which is greater than the FOS of 2 that the Spaceport America Cup requires.
Injector:
I have decided to use like-on-like impinging doublet for the injector in the interest of simplicity. While other injectors may result in better atomization and mixing, it is my opinion that they are more complicated in their mechanics and that choosing a simpler design would be better to start off with.
In order to achieve the best atomization and mixing in an impinging injector, the injector orifices must have the smallest possible diameter. I will select 1/16", since this is the smallest feasible drillbit we can use on the CNC mill without a large possibility of a drillbit snapping. A snapped drillbit means scrapping the entire part, so this should be prevented.
An impinging injector usually consists of two parts, the dome, and the injector face, connected by axial bolt holes. One important feature of an injector is to prevent any extreme hotspots due to high oxygen concentration. For this reason, I will have the oxygen doublets in the center of the injector, and the fuel doublets closer to the walls of the injector. Additionally, an adequate pressure drop needs to occur across the injector face to prevent pogo oscillations (a type of combustion instability) and backflow of combustion products. According to Huzel Huang, a good pressure drop is around 25% of the chamber pressure. Additionally, an even number of orifices for both the oxidizer and fuel is desired.
Using a discharge coefficient of 0.9, and the previously calculated mass flow rates for fuel and oxidizer, I calculated that the injector needs 12 fuel orifices and 12 oxidizer orifices. This results in fuel and oxidizer pressure drops of 27.1% and 25.3% respectively. Having 12 orifices is also ideal since the holes must be drilled using a 3rd or 4th axis CNC rather than the ideal 5th axis, which my team doesn't have access to. To do this, a jig of sorts must be created which inclines the injector plate with respect to the vertical. Having 6 pairs of orifices means that the part must be rotated 60 degrees before drilling each set of orifices.
Since much of injector design is empirical and these equations mainly provide a guide, multiple cold flow tests should be conducted with the injector to determine the actual discharge coefficient and actual pressure drop.
I now need to determine the orifice length (l_0), impingement angle (2*theta), and impingement length (l_i). Below is a diagram showing these dimensions.
Impingement angle is the acute angle between the two streams from the doublets. A larger impingement angle leads to better mixing and smaller drop size, however, it also leads to backsplash which can cause injector face burnout. In order to balance these two factors, for like-on-like impingement, an angle of 60 degrees is typically chosen. As for orifice length, usually, the length is 3x the orifice diameter. A larger impingement length can lead to misimpingement due to the amplification of manufacturing errors, so usually the impingement length is 5x the orifice diameter. All of this information (including the diagram) is from Brian Sweeney's dissertation titled: LIKE-DOUBLET INJECTORS: THE EFFECTS OF VARYING THE IMPINGEMENT DISTANCE AND AN ANALYSIS OF THE PRIMARY ATOMIZATION ZONE.
Injector Parameters:
The injector has two parts: the dome, and the injector face. The injector face contains the orifices and dividers to separate the ethanol and lox manifolds. The dome contains the lox and ethanol ports, as well as radial bolt holes for mounting onto the combustion chamber. The two are connected by eight axial bolts and additionally, they interface via the lox/ethanol manifold dividers. The injector face is made of 1018 steel, since it will have to be in direct contact with the heats of combustio , and the injector top is made of 6061 Aluminum to save mass. Below are screenshots of the dome, face, and the entire assembly. I have put in two O-Ring grooves into the injector dome for dash number 240 O-Rings.
I am currently in the process of conducting CFD of Ethanol and Lox flow through the injector, as well as conducting a static structural analysis on the injector face
Now, the entire engine has been designed, and a labeled cross-section is shown below. There are 12 radial bolt holes in the injector dome, both sides of the engine casing, and on the nozzle carrier, but this cross-section doesn't show them.
