Design and test of a student hybrid rocket engine with an external carbon ﬁber composite structure

: The development of hybrid rockets offers excellent opportunities for the practical education of students at universities due to a high safety and a relatively low complexity of the rocket propulsion system. During the German educational program STERN, students of the Technische Universität Braunschweig obtain the possibility to design and launch a sounding rocket with a hybrid engine. The design of engine HYDRA 4X is presented and results of ﬁrst engine tests are discussed. Results for measured regression rates are compared to results from literature. Furthermore, the impact of the lightweight casing material CFRP on the hybrid engine mass and ﬂight apogee altitude is examined for rockets with different total impulse classes (10 to 50 kNs). It is shown that the beneﬁt of a lightweight casing material on engine mass decreases with an increasing total impulse. However, a higher gain on apogee altitude, especially for bigger rockets with a comparable high total impulse is shown. writing–original F.H. and writing–review and L.K., R.S. and visualization, and


Design of Faust rocket and HYDRA 3X engine
Faust is a sounding rocket, which is propelled by a hybrid rocket engine. A schematic of the rocket is shown in Figure 2 and its main characteristics are listed in Table 1. Faust has a modular design of eight segments. The nose cone is part of the two-staged recovery system that is located on top of the electronics section. The complete propulsion system consists of a pressure vessel for pressurization of the oxidizer vessel, valves, feeding lines, and the hybrid engine. Fins for flight stability are connected to the body tube that accommodates the engine [25]. A successful launch with a maximum altitude of 5400 m was performed in 2015.

Pressure vessel (helium) Electronics
Oxidizer vessel (nitrous oxide) Hybrid rocket engine Nose cone Fins Figure 2. Design of the sounding rocket Faust A hybrid engine was chosen for the Faust rocket because of the advantages of the propulsion concept. The operational safety is suitable for a student project and the propellants are storable and relatively safe to use. The hybrid engine HYDRA 3X uses a propellant combination of liquid N 2 O as oxidizer and a solid mixture of 70 % hydroxyl-terminated polybutadiene (HTPB) and 30 % aluminum powder as fuel [26]. The aluminum was added to increase the fuel regression rate. Engine test runs with HYDRA 3X showed an increase in regression rate of about 20 % compared to tests without the addition of aluminum powder [26]. The engine design shows typical components of a hybrid engine, such as an injector for feeding and vaporizing oxidizer into the following combustion chamber ( [27]). It is based on a shower-head injector that additionally uses a cone for diverting the oxidizer to ensure a better distribution of the mass flow. The propellant fuel is cast directly into the combustion chamber, which uses a star-shaped mold for creating the required fuel geometry that is presented in Figure 3. The fuel grain ends at the vortex disk that generates a large vortex flow. This provides the required mixture of both propellants. Subsequently, a conical convergent-divergent nozzle is located at the end of the engine [26,28,29].  Most parts of the engine structure are manufactured from phenolic paper due to advantageous ablative cooling characteristics. The nozzle throat is additionally reinforced with graphite to withstand high thermal loads during combustion. The engine is encapsulated by a steel casing for resistance of combustion pressure loads. The engine outer diameter is 0.09 m and therefore smaller than the rocket diameter. Hence, an additional structure tube is necessary that is added to the engine casing mass. Structural and performance data of HYDRA 3X are given in Table 2. A successful flight of the Faust rocket was performed with the HYDRA 3X engine. It burned for 10 s with a mean thrust of 1.25 kN. After 37 s flight time an apogee altitude of 5.4 km was reached [23]. The following objectives for Faust II engine, HYDRA 4X, within the STERN II project were chosen:

Injector
• Apogee altitude of 10 km • Increased engine thrust and total impulse • Improved engine power to mass ratio • Integrated lightweight casing made from carbon fiber reinforced plastic (CFRP)

Design of hybrid rocket engine HYDRA 4X
After the successful application of the HYDRA 3X engine, the HYDRA 4X engine for the Faust II propulsion system was planned. It uses pure HTPB as fuel, waiving additional aluminum powder. This propellant is cast into the engine at a liquid state. It cures by using hardener and therefore gets solid. The grain geometry is created by using a casting mold that is removed after the curing process.
The structure parts are made from phenolic paper while the nozzle throat is additionally supported with graphite. The structure must be able to withstand the combustion pressure loads. Thus, the engine is equipped with a CFRP laminate coating that resists the operational pressure. The injector head is based on the design of HYDRA 3X. It is a shower-head injector with channel orifices of 0.8 mm.
A diverting cone is added as shown in Figure 4b. The oxidizer flow impinges on this cone that diverts the flow and directs it to the fuel grain. The current design of HYDRA 4X is presented in Figure 4a and key data in Table 2

Performance calculations
The technical design of the HYDRA 4X is built upon a first evaluation of an ideal ratio of N 2 O and HTPB for a maximum specific impulse. NASAs CEA-Code (Chemical Equilibrium with Applications) suggests an oxidizer to fuel mass ratio of O/F = 7, using input data from Table 3 with a frozen composition assumed after the nozzle throat. The O/F is used to calculate combustion characteristics for the combustion chamber pressure and nozzle exit pressure. Since the ambient pressure of the rocket changes with altitude, a value for nozzle exit pressure needs to be defined. In this case, the nozzle is adapted to ambient pressure at half of the maximum flight altitude. Input data and relevant results of CEA are shown in Table 3. Based on former flight tests experience, a lift-off acceleration of around 5 g should be achieved to ensure a reliable launch. This is the boundary condition to determine the required thrust F and thus, mass flowṁ. This results in a thrust of 2.25 kN for the overall rocket mass of 46 kg. From [1] andṁ the required fuel mass flowṁ f can be calculated. A global engine efficiency of η engine = 91% was determined via engine tests during the first STERN program. This is a preliminary design assumption. Different star-shaped fuel grain geometries were iterated regarding number of star spikes and shape. A constant regression, perpendicular to the fuel grain geometry over full burn time was assumed. The regression rate for the preliminary design is approximated toṙ = 0.6 mm/s from previous measurements of HYDRA 4. It was adapted with every hot fire test of HYDRA 4X for the design iteration. The mean regression rate of a hot fire test was obtained through weighing the engine before and after the test. The weight difference is converted into a geometric regression, by dividing the weight difference with burn time and fuel grain surface area prior to testing. An optimization was carried out for burn time t b , thrust profile according to burn time and initial mass flow levels, given by Equation 2. This leads to a star shaped fuel grain with parameters shown in Figure 7a and Table 6. Using fuel grain geometry and mass flowṁ f , the O/F-ratio determines the subsequent oxidizer mass flowṁ ox :ṁ The propulsion system of Faust II is designed to inject liquid oxidizer into the engine. A pressure of 5 MPa is chosen for pressurization of the oxidizer vessel. This pressure level ensures a liquid state of the nitrous oxide and thus operational temperatures up to 293 K [30]. This temperature agrees with ambient temperature requirements set by a planned launch from ESRANGE Space Center. With combustion chamber pressure p c and oxidizer vessel pressure p ox , the theoretical injection speed v th can be calculated using the oxidizer density ρ ox , assuming incompressible, stationary, and isentropic Bernoulli flow (cf. [1]): A diameter of 0.8 mm and a length of 5 mm were chosen for a single injector orifice. The volume floẇ Q in a single circular orifice is decreased compared to its theoretical optimum due to stream tube contraction and pressure losses within the orifices [6]. This relation can be expressed by where the effects can be combined in a single factor C D . This coefficient is measured in every test to iterate the number of injecting orifices. Equation 4 is only applicable to negligible changes of density along the injecting orifice length. Due to the strong temperature and pressure dependency, this is only partially applicable to nitrous oxide injection with a strong pressure gradient from feeding line to combustion chamber present. However, this approach was used in combination with the coefficient C D to approximate the real flow behavior of the nitrous oxide. The total number of injecting orifices n ox can be calculated by The strong temperature and pressure dependency of the N 2 O density ρ ox and its effect on the number of injector orifices is to be handled with special consideration. A good control of the N 2 O parameters during fueling can circumvent off-design engine operation. This is also achieved by varying the number of injector orifices according to N 2 O parameters. An auxiliary function Γ is introduced in Equation 7 [7]. The mean of specific heat ratios γ calculated by CEA in Table 3 are used as input. The characteristic velocity C * and the throat area A t are calculated by Equation 8 using molar mass M, temperature T c of the reaction product in the chamber (cf. Table 3) and universal gas constant R ∞ [7]. Subsequently, the nozzle throat diameter d t is computed in Equation 9.
The momentum thrust coefficient C 0 F can be calculated according to Equation 10 by using the nozzle exit pressure p e [7]. Equation 7 and Equation 10 are combined to the nozzle expansion ratio A e /A t in Equation 11 [7]. A conical nozzle is chosen due to simplicity in manufacturing. The divergence cone half angle is set to 15 • . The length of the divergent nozzle l nozzle is calculated through Equation 12.
The thrust coefficient C F is computed by Equation 13, applying a correction factor to the momentum thrust coefficient C 0 F , correcting for the axial divergence of the exhaust of a conical nozzle [1]. The ambient pressure p a corresponds to static pressure of the environment and is equal to p e at the design point. For following test data, the ambient pressure is measured at the test site. 8 of 19 Note that this corresponds to an optimum C F achievable for conical nozzles. The combustion η c and nozzle expansion efficiency η nozzle of the engine are calculated by Equation 14 and Equation 15 as ratios of experimentally measured parameters to ideal design values. This approach enables a comparison of actual engine performance with design performance. As the parameters might shift in the hot fire test, all experimental values are taken as mean over full burn time. According to [1], the overall engine efficiency is then calculated by Equation 16. All design data of HYDRA 4X engine in its latest iteration after the fourth hot fire test is summarized in Table 4.

Description of engine test bed
All engine tests are performed at the test facility of DLR Trauen, where all safety requirements can be achieved. The engine test bed for HYDRA 4X consists generally of two assemblies, the fluid supply system and the test bench. A schematic of the fluid supply system is presented in Figure 5a. The fluid supply system also includes the test bed electronics. An intermediate tank is used to store liquid N 2 O during the fueling process. Nitrous oxide is fed from cylinders directly into this tank where it can be pressurized to 6 MPa. In contrast to the rocket system, nitrogen is used for pressurizing the N 2 O tank on the test bed due to its better availability. Temperature and pressure within the intermediate tank are measured by three sensors. Strain gauges measure the tank weight during testing to control fueling and to determine oxidizer mass flow rates. After pressurization, the tank weight is set to zero. Thus, only the fueled nitrous oxide mass is measured. During the hot test, the intermediate tank is continuously pressurized by nitrogen. The change of tank weight during the hot test gives the oxidizer mass flow. The continuously added nitrogen mass flow for pressurization introduces a systematic Temperature and pressure shortly in front of the injector are measured as well as the combustion chamber pressure by a sensor connected to a small pipe that leads directly into the engine pre-chamber. Pressure is measured at a sampling rate of 1 kHz. The test bench is a robust steel construction that is modular and can be used for different engines, as is displayed in Figure 5b. The HYDRA 4X is mounted to the test bench using a mounting plate, which accommodates the injector and can easily be exchanged. Four load cells are integrated onto the test bench for thrust measurement. Data logging and valve controlling is realized by National Instruments cRIO-9074 controller [29]. It is located within an electronic box near the fluid supply system and can be controlled remotely from the test control center.

hot fire tests and iteration of design
The results for the first four hot fire tests of HYDRA 4X engine are presented in the following. Design changes have been made to increase engine performance between these tests. The changes of defined design parameters are summarized with the resulting measured values from corresponding hot fire tests in Table 5. The value G ox is computed according to [7] G ox =ṁ ox A p (17) where A p is the free port area of the fuel grain. The mean port area over burn time is considered for determination of the regression rate.  Figure 6. Three general test phases are visible in all four graphs: The first phase describes the condition when the intermediate N 2 O tank is filled and pressurized to a pressure between 4.8 and 5.6 MPa. The combustion phase starts with opening of the main oxidizer valve and the tank pressure reduces slightly as oxidizer flows into the engine. A decrease of tank pressure over time can be noticed. This is a result of an insufficient pressurization of the used fluid supply system, which was originally designed for lower oxidizer mass with about 2 m length between main valve and engine, cf. Figure 5a. Due to this, the engine receives oxidizer for a longer time than desired after main valve closure. To reduce this effect, the main valve is relocated directly in front of the engine for the third and fourth test. The mean thrust of the first two engine tests is about 1.2 kN which is apparently lower than design thrust. Accordingly, the average combustion chamber pressure of 1.8 MPa is low compared to the design value of 2.5 MPa. Analysis of test parameters yields that the target value for oxidizer mass flow was not reached, and the nozzle was manufactured inaccurately. Design changes between HYDRA 4X versions 01 and 02 have been made to increase engine performance: Nozzle manufacturing was improved, post combustion chamber length was increased by 30%, and injector design was changed to improve mass flow through an increase of orifice number and manufacturing quality, and combustion of both propellants by flattening the diverting cone angle. Since there are no remarkable changes between performance results of HYDRA 4X-01 and 4X-02, the consumption of the star-shaped solid propellant grain was examined for the second test in Figure 7b. Two main aspects can be determined. First of all, it is evident that HTPB consumption decreases with combustion chamber length. The mean consumption shows values between 30 mm at the fuel grain front and only 20 mm at the end considering the star peaks. This is also apparent for star indentations where consumption values vary from 7 mm to 0 mm. Latter means no consumption at all. Hence, the consumption of star indentations is significantly lower than that of star peaks. The authors assume, that although the target mean regression rate was reached, the uneven consumption over length and major differences between star peaks and indentations contributed to engine performance, as the overall fuel grain surface in the Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 15 April 2020 doi:10.20944/preprints202004.0229.v1 combustion process was decreased. As a result, the fuel grain geometry was changed for the test of HYDRA 4X-03 as is presented in Figure 7a. The number of star peaks was decreased from 8 to 6 and the geometry was changed so that consumption of star indentations is augmented. The consumption measurements of HYDRA 4X-03 show that the design changes enhanced the HTPB consumption, especially for star indentations, as can be seen in Figure 7c. Additionally, a more even consumption along engine length was demonstrated. Therefore, a higher mean thrust value of about 1.6 kN at a chamber pressure of 2 MPa could be reached, as presented in Figure 6c. These values are still below design parameters, which can be traced back to a low oxidizer mass flow. As a result, the injector was adapted once more between tests 03 and 04 by increasing number of injecting orifices.   Figure 6d. However, the mean oxidizer mass flow exceeded the design value of 0.931 kg/s. This resulted in a mean O/F of 8.4 over full test time, compared to a design O/F of 7. The fuel mass flow of 0.123 kg/s is in good accordance with the design value of 0.133 kg/s. To reach an appropriate oxidizer mass flow, the number of injecting orifices have to be decreased and the directional characteristic of the injector will be changed to supply oxidizer more directly at the star indentations. To achieve this directional behavior, the injector orifices will be aligned with the angular position of the star indentations. HYDRA 4X-04 yielded 86% efficiency of the design I sp . This global efficiency can be divided into 87% combustion efficiency and approximately 99% nozzle efficiency. Although the minimum design thrust was surpassed, it could only be achieved through an excess of injected oxidizer mass flow. As the flight fluid supply system would not be able to sustain this increased oxidizer mass flow for the complete burn time, further work would have to be carried out to achieve design performance at tolerable oxidizer mass flows.  Figure 8 shows the fuel grain regression rates obtained from the four tests compared against data from literature [8,[31][32][33]. The regression rate curves from these data follow the empirical power law [7] r = a · G n ox (18) in which the coefficients a and n are obtained through experimental data. These experiments were conducted for the same combination of propellant and oxidizer at similar combustion chamber pressures and comparable O/F. The main differences are the fuel grain geometry and injector type. Only fuel grains with single circular port geometries were tested in the references presented. The determined regression rates from four HYDRA 4X tests are located between fitting curves of [31], [32] and [8].

Impact of engine casing material on flight apogee
The different designs of two HYDRA engines 3X and 4X have already been discussed. Although there is a clear difference between engine performance data, structural changes have also been made. A comparably heavy steel casing of HYDRA 3X was replaced by a CFRP coating to reduce engine mass. This consequently results in a higher apogee. On the other hand, using CFRP also means higher effort in design, calculation, manufacturing, and costs. Therefore, it is interesting to evaluate the impact of this change on engine mass, total hybrid rocket mass, and on flight apogee. Thus, a parametric analysis for fundamental hybrid rocket pre-design is conducted. This is done by a MATLAB tool that was established during STERN II program. It uses geometric and mass relations for estimating the design of sounding rockets. The tool calculates the engine data, such as propellant mass, mass flow and burn time, based on a requested mean thrust and total impulse. The regression rate is assumed to be constant over burn time. The fuel mass flow is calculated according to a mean fuel grain surface and a constant oxidizer mass flow. The selectable fuel grain geometry is either a monoport or a star shape and a conical nozzle is used. Two pressure tanks made from CFRP for oxidizer and pressure gas are calculated based on engine data. Residual rocket components like electronics or parachutes are estimated by the user. Physical relations for hybrid engines and flight mechanics (described in [1], [7] and [34]) are used to estimate flight performance, using the mean thrust as a constant thrust profile over burn time. The tool analyzes first estimations on rocket design factors like engine performance, geometric dimensions, and flight parameters, such as flight apogee. The analysis is suited for rockets in an impulse range of 10 to 50 kNs and cell diameters of 100 to 180 mm. A parametric study is carried out for a basic rocket design with a constant cell diameter of 150 mm while the total impulse is increased continuously from 10 to 50 kNs. The rocket engine gets larger (as more fuel is required) and longer. The engine structure mass and casing mass rise with increasing total impulse. The total impulse of an engine can be calculated by thrust F and engine burn time t b [1] according to Equation 19. This relation can be used here, since the design tool uses a mean thrust value for calculations, even though the thrust profile is usually not constant for HRE.
The launch acceleration of the rocket shall be about 5 g at a rail length of 9 m. This results in a minimum thrust for an estimated rocket mass and a corresponding burn time. To characterize the relation between fuel and engine structure mass, two mass factors are introduced. Firstly, the relation factor f cm compares engine casing mass m cas to fuel mass m f that can be accommodated by the engine. This factor shows how much casing mass is required for a defined fuel mass to reach a certain total impulse.
A second relation factor f em is defined, which represents a comparison between overall engine mass m e (including fuel mass) and fuel mass. This factor links fuel mass to engine structure mass m str that includes casing and other structural engine components.
Using these engine parameters, a basic rocket design is developed and the results are discussed. They are compared to the design parameters of the engine HYDRA 4X for Faust II rocket that has been presented. Figure 9a shows the defined mass relation factors as a function of total impulse in a range from 10 to 50 kNs. Two main aspects can be derived from Figure 9a. A steel casing is heavier than a CFRP casing but the relations between casing mass and fuel mass ( f cm ) change over the total impulse range. For smaller engines with a low total impulse of about 10 kNs, the weight of a steel casing is seven times higher than the respective fuel mass. This relation decreases with total impulse and shows a factor of about 3.5 for engines with a total impulse of 50 kNs. In comparison to that, f cm for a CFRP casing is nearly constant over the impulse range, where a mass factor of about 1.4 is reached. A second aspect addresses the total engine structure mass. It is derived from the casing (outer structure) and other structural components as presented. As Figure 9a shows for small engines (10 kNs), the mass factor for overall engine mass f em is at 15.7 for steel and 8.8 for CFRP casing material. This shows that the residual engine structure mass (disregarding the casing) cannot be neglected, although the mass factor f em decreases with rising total impulse. The overall engine structure mass with a steel casing is about 4 times higher than the required fuel mass at an impulse of 50 kNs. In contrast, the structure mass with a CFRP casing is about twice as high as the accommodated fuel mass. Thus, the data shows that the engine structure mass is relatively high compared to required fuel mass, especially, for a small impulse class. Less structure mass is needed relative to fuel mass for higher impulses. When using CFRP instead of a steel casing, the engine structure mass can be reduced by about 50 % for the whole impulse range. The mass factor f cm for a steel casing shows a maximum for a small engine class, where the engine structure mass is very high compared to the fuel mass. Both mass factors decrease with increasing impulse. However, an engine with steel casing results in a mass twice as high as an engine with CFRP casing over the whole impulse range. The achieved values for the engine HYDRA 4X (35.5 kNs) are added in blue color. A f cm value of 1.12 is in good accordance with the results of the parametric analysis. The engine mass factor f em of 2.45 is lower than the analysis result of 3.3, which means that less structure mass is needed for this engine than the parametric tool assumes. Figure 9b shows the effect of casing material on flight apogee. Two existing (H3X, H4X) and one theoretical (H5) engine and subsequent rocket designs are presented in two versions: Steel and CFRP, as presented in Table 7, where hybrid engine rockets for a range of impulses and rocket diameters are compared. For these designs, an approximated flight apogee is calculated to evaluate the casing mass impact. The flight trajectory is plotted until apogee where the recovery system would be activated. As Figure 9b shows, an apogee of 5.7 km for Faust with a hybrid engine using a steel casing is reached. This is similar to Faust flown in 2015 with an apogee of roughly 5.4 km. Therefore, the analysis provides reasonable results. An apogee difference for the two casing materials of about 500 m and a mass difference of about 2.2 kg were derived for Faust. A higher impact on apogee difference is observed for Faust II. Using a CFRP casing, Faust II is able to reach an altitude of 15.6 km (compared to 13.7 km when using a steel casing), which represents an apogee increase of about 14%. The fully designed Faust II with a CFRP engine shows a higher mass than the pre-design (+6.7 kg), resulting in a lower apogee altitude of 11.2 km. The trend for an increase of apogee rises for the larger engine HYDRA 5 (cf. Table 7). By using a CFRP engine casing, an increase of 3.1 km (20.3%) is achieved compared to a steel casing. It is evident that a lighter CFRP engine casing is beneficial, especially, for engines with higher total impulse and diameter values.

Conclusion and outlook
The previous and current development activities of hybrid rocket engines at Technische Universität Braunschweig were examined. The design of the rocket engine HYDRA 3X was described, which was launched at the Esrange Space Center in 2015. It is a hybrid engine using nitrous oxide as oxidizer and HTPB as fuel. Based on this, a new engine HYDRA 4X was developed, that is designed for the Faust II rocket. The main design changes compared to HYDRA 3X are a higher total impulse and thrust, and the CFRP casing material. Test bed and first test results of the new HYDRA 4X engine were shown. The design changes to iterate a requested engine performance were explained. In addition, the obtained fuel grain regression rates were compared to literature data. To quantify the impact of different casing materials on rocket mass parameters, a parametric study was performed. First, casing and engine structure masses were compared to the fuel mass. It was shown that the fraction of structure mass to overall engine mass decreases over increasing total impulse, although the impact of casing material on rocket apogee altitude increases. The analysis suits best for rockets with diameters between 100 and 180 mm and impulses between 10 and 50 kNs. A CFRP engine casing material shows a clear advantage over a heavy metal casing when only flight altitude is considered. However, other design, manufacturing, and cost parameters have to be taken into account to quantify the benefit of the material choice. In a next step, the parametric analysis will be extended to a wider range of impulses and the pre-design of other rocket components like recovery and electronics system will be refined.