Rocket Performance Characteristics Using Hybrid Propulsion Systems of Plexiglas and Paraffin with Nitrous Oxide Daniel González-Soriano López

Alexander Lavin

Univ. Politécnica de Madrid, Madrid 28040 Spain

Cornell University, Ithaca, NY 14850 USA

Wilson Carreira Instituto Superior Técnico, Lisbon, Portugal

Supervisor: Professor Alon Gany Technion Israel Institute of Technology, Haifa 32000 Israel

The purpose of this study was to observe and analyze the performance values of the nitrous oxide gas as an oxidizer for a hybrid propulsion system with either Plexiglas or paraffin as the solid fuels. To conduct the tests the Fine Rocket Propulsion Center at the Technion was used. The experimental setup allowed for successive firing tests with variable input parameters. A total of 43 tests were run for 6 different days.

Nomenclature m ˙ r˙ a Aox At

Mass flow rate Regression rate Regression rate coefficient Oxidizer nozzle area Nozzle throat area

c∗ CF D G Isp L m mfuel mm n O/F Pc tb

Characteristic exhaust velocity Coefficient of thrust Port Diameter Mass flux Specific impulse Fuel grain length Length exponent Fuel mass Fuel molecular mass Flux exponent Oxidizer-to-fuel ratio Chamber Pressure Burn time

αcu γ cu x

Copper linear expansion coefficient Copper area expansion coefficient Port length coordinate

Subscripts i Initial f Final e Exit * Critical conditions ox Oxidizer property fuel Fuel property Symbols ∆ Variable difference ηox Oxidizer line efficiency ρ Density go Gravitational constant R Universal Gas Constant γ Oxidizer heat capacity ratio

I. Introduction A. Hybrid introduction Hybrid motors are an attractive option in many rocket propulsion systems over conventional liquid or solid propellants. In comparison, hybrid motors present positive features including ease of handling, throttling, capability, and potential low cost. A vital characteristic in designing a hybrid motor system is the fuel regression rate – it determines mass flux and overall sizing and geometry {2}. Simple boundary layer assumptions cannot be extrapolated to account for the complex physical and chemical interactions present, especially when considering combustion stability and throttling capabilities. Additionally, specific impulse and characteristic velocity are important performance measures to study in comparison to liquid or solid systems. For specific impulse one must also take masses of engines turbomachinery and oxidizer tank into consideration. B. Hybrid model Studying the basic hybrid model is largely concerned with regression rate analysis as this is the factor sought to optimize overall performance. Regression rate is defined as the rate at which fuel in the solid phase is converted to gas and is strongly manipulated by reactant pyrolyses and flow conditions {2}. Standard solid rocket motor assumptions are not transferrable including uniform burning rate which is very sensitive to the flow field in the combustion chamber. And as aforementioned, one cannot model the flow in the chamber by extrapolating from well-developed laminar flow theory {4}. Hybrid combustion is not controlled by surface reaction rates, rather it is controlled by the rate at which heat is delivered to the fuel surface {3}. Assuming combustion occurs in the turbulent boundary layer leads to the regression rate equation, but with two important factors: position of the flame in the boundary layer and the effective heat of gasification. Flame position is defined as the point in the boundary layer at which oxidizer mass flux and fuel mass flux meet in the required proportion for combustion to occur. For a Plexiglas-O2 system it has been found that the flame height above the fuel surface is approximately 10 to 20 percent of the total boundary layer thickness. The flame position divides two zones of the boundary layer which together form the boundary layer for momentum transfer. Above the flame the temperature and velocity gradients are in opposite directions. Below the flame the gradients progress in the same direction and serve as the effective boundary layer for heat transfer with the solid fuel wall. For optimal hybrid performance combustion is usually not at the stoichiometric ratio, rather it is observed to be fuel rich. This is because the boundary layer diffusion process restricts the transport of the oxidizer to the flame from the main stream, and due to the close proximity of the flame and the fuel surface. Also having a direct effect on hybrid performance is the fact that oxidizer is not depleted at a given location horizontally along the chamber until the boundary layer fills the entire port. At this condition turbulent flow is fully developed and the flame forms a conical apex at the center of the port; this has been found to be achieved in approximately 40 to 100 diameters from the combustion chamber. Hybrid rocket studies and innovations must progress to concepts that increase physical interactions thus increasing heat flux to fuel surface and in turn improving regression rate {2}. A potential model variation which addresses these points is tangential oxidizer injection in the combustion chamber leading to multiaxial flow fields. Also fuels that form a thin liquid melt layer on the surface may aid regression rate.

C. Nitrous oxide Nitrous oxide (N2O) was chosen to study because there is very little published material covering the use of the oxidizer in hybrid rocket propellants especially considering its prevalent use in the field and potential for space flight propulsion systems. The relative ease of use and safety of nitrous oxide were also considered. Nitrous oxide is safe because it is non-toxic and stable at room temperature. The facts that it is self-pressurizing and relatively inexpensive contribute to its ease of use in the laboratory. It is a health issue only with intense or continued exposure. Although very minimal there is a blow back hazard in rocket systems: The decomposition of N2O occurs exothermically so hot gases are released during the reaction in the combustion chamber. If the pressure drop is insufficient which can occur during unstable combustion flame may propagate back through the injector in the following situations: 1. The heat of burning is greater than the heat at the nozzle and burn pressure is decreasing. This means the pressure at the nozzle will also decrease leading to extinction. 2. The heat of burning is less than the heat at the nozzle and burn pressure is increasing. This means the pressure at the nozzle will also increase leading to explosion. Granted unstable combustion is quite unlikely and merely a side note in safety considerations.

II.

Test Facility

The use of a small scale test facility promotes safety and multiple trials with relative ease. The facility consists of a firing bay with garage door to the outside and an indoor control center with multiple viewing windows to the firing bay. The firing bay contains the test stand measurement devices and gas piping and tanks. Adjusting the gas tank nozzles varies the O/F ratio as the experiment calls for it. Figure 1 below shows a photo of the firing bay. The control center contains all computational equipment and hand measuring devices. This includes the test computer with LabVIEW virtual interface and gas valve controls.

(a) Test stand

(b) Control center & data acquisition system Figure 1 . Test facility

A. Test stand The test stand is specifically designed for small scale hybrid propellant testing. In figure 2 below one can see an interlocking chain allowing for simple fuel grain interchange. This system also has the capability of fitting a wide range of fuel grain sizes. At the back end is a converging or choked nozzle. In the field a convergentdivergent nozzle is used. For testing however the convergent nozzle was implemented because it allows for a more functional experimental setup when varying other parameters. In the first two sets of trials (12 fire tests)

nozzle diameter was 4.2mm giving an area of 13.85mm2. In the subsequent trials (fire tests) nozzle diameter was widened to 5.15 mm. At the front end is the pre-combustion chamber with the igniter and the injector. In front of this the load cell measures the force of the thrust.

Figure 2. lgniter Design

B. Plumbing system The feed system shown in figure 3 consists of feed lines for the nitrous oxide ethylene gas and nitrogen gas. The nitrous oxide nozzle diameter was adjusted throughout the trials to vary the oxidizer flow rate. This allowed us to manipulate the O/F as an independent variable for each trial. The setup includes two oxidizer inlet nozzles to aid in initial combustion. The ethylene (C2H4) gas is used with the spark plug to initially ignite the precombustion chamber. The nitrogen gas is flushed through the system after each firing test to clean out any remaining oxidizer or residue.

Figure 3. Feed System Design

C. Measuring devices Measurement devices in the firing bay include pressure gauges to measure combustion and oxidizer stagnation pressures and a load cell to measure the force of the thrust. These instruments output a voltage which must then be converted to the relative units. For the combustion and oxidizer pressures the following formulas were used:

For the load cell a pre-test calibration was done. With a pulley system known forces were applied to the load cell. This yielded a linear regression between load in Newtons and output in volts. D. Data collection The data acquisition system was executed via a LabVIEW virtual interface. Shown in the Appendix the VI simultaneously records entrance and exit oxidizer pressure chamber pressure and thrust measurements. Burn time was calculated from the chamber pressure and is from 50% of the ignition climb to 50% of the shutdown drop in agreement with international standards. The LabVIEW outputs an Excel file of all the data. All experimental values once converted into its corresponding units have been recalculated in order to delete offsets. For this purpose first 15 values of each measure have been averaged and furtherly eliminated from its referred magnitude. Due to testing stand is initially at atmospheric conditions Pa must be added to both Pox and Pc . E. Firing procedure To run a firing test from the control station the following procedure was used. First the LabVIEW was initiated. Upon 'all clear' confirmed from the firing bay the main control box master switch was activated. To ignite the system the small oxidizer valve was opened followed by the spark plug and ethylene. The large oxidizer valve was then opened. Once combustion was witnessed from the firing bay viewing window the ethylene was shut off. After an appropriate burn time had elapsed the oxidizer valves were closed to initiate shutdown. The nitrogen valve was then opened to quickly clean out all remaining nitrous oxide in the pre-combustion chamber and throughout the fuel grain. To finish the VI was stopped and master switch turned off.

III. Fuel Characteristics and Simulation A. Propellant properties Oxidizer

Fuels

Nitrous Oxide (N2O)

Plexiglas(C5H8O2)

γ = 1.275 mm = 0.4399kg Tox=298K

1180kg/m3

ρ= L1 = 01896 m L2 = 0137 m

Parafin ρ =850 kg/m3 L = 01896 m

B. Testing All fuel grains were dimensionally measured before testing and masses were taken prior to and after individual test trials. The comparison of these values along with in-test measurements enabled us to conduct the post test

calculations to determine the desired thrust coefficient characteristic velocity and specific impulse values. The in-test data can be found in the Appendix and can be cross-referenced with figures __ based on fire test number. The duration of each firing test was about 7 seconds to ensure a thorough burn. Due to the uneven latitudinal regression of the Plexiglas the fuel grain direction was flipped after three burns to even out. Oxidizer pressure was varied from trial to trial in order to adjust the O/F ratio. Subsequent trials were run with decreasing O/F allowing for a lower oxygen pressure with greater fuel grain diameter thus enhancing the decrease in O/F. C. Computation and analysis The experimental specific impulse is found with equation 1 below. The theoretical Isp is found with equation 2 below where the characteristic velocity (c*) is given with the ProPEP simulation program. The gravitational constant is 9.807m/s2.

(1) (2) The thrust coefficient is obtained from Equation 3. Mentioned earlier, it is easier to use a converging or choked nozzle in the experimental setup when varying several parameters. To account for this (3) must be solved considering Ae=At and Pe=Pt .

(3) Of the desired rocket performance characteristics, theoretical Isp is the only value that varies with CF. Thus the above theoretical CF is used to calculate the theoretical Isp values in the pretest simulations. The real CF value is found with equation 4 using FT and Pc from the trial data. (4) The combustion pressure needs to be averaged over the burn time. The burn time begins at 50% of the pressure climb from ignition and ends at 50% of the pressure decrease following shutdown. The Pc used in calculations for a given trial is then the mean of the values over tb. (5) Characteristic velocity is a function of . The mass flow rate through a tube is a constant by the conservation of mass. It is the sum of the oxidizer mass flow – the main independent variable from trial to trial – and fuel mass flow. mox is calculated in the oxidizer nozzle before combustion in order to obtain the maximum mox posible. It is considered that M=1 is reached in this nozzle. (6)

The pressure (P) in equation 6 is static pressure but the measured pressure from experimental trials is stagnation or total pressure. The same applies to the temperature (T). Thus the isentropic relations in equations 7 and 8 allow converting to the desired static pressure and temperature values respectively.

(7)

(8) Equation 6 now becomes: (9)

The oxidizer nozzle area is a summation of the two oxidizer nozzle areas aforementioned in the experimental setup discussion. Adjusting the nozzle diameters was done in conjunction with varying the oxidizer pressure in order to manipulate oxidizer flow rate. For corresponding calculations, the equivalent nozzle diameter was used. Alternatively the oxidizer mass flow may be calculated using equation 10 as a gas flow relation: (10) In this case c* is calculated from the cold gas equation: (11) The difference in the results between these methods is negligible. The mass flow rate of the fuel is much simpler to calculate as shown in equation 12. The initial and final fuel grain masses (mfuel initial and mfuel final respectively) are found by removing, massing, and replacing the fuel grain between firing trials. (12) The sum of and yields and the ratio of the two gives O/F. The desired rocket performance characteristics c* and Isp are subsequently found with equations 5 and 1 respectively. (13) The final rocket performance characteristics desired for comparison are regression rate and oxidizer mass flux. Equation 14 is the classic hybrid regression rate formula. (14) The time derivative of fuel grain port radius – – is a function of Gox, the horizontal location (x), and three ballistic coefficients (a, n, and m). Due to the burn inconsistencies throughout the fuel grain, as is the nature of hybrid rocket propulsión, it is more reliable to apply space and time averaging methods in calculating .

Variation of the regression rate in the radial direction for a given location x is minimal allowing for a simple space-average value. Thus in equation 14 the exponent m=0. From experiment trial data the space-averaged and Gox values are calculated with equations 15 and 16 respectively. (15) (16) Equation 17 employs diameter averaging to minimize space-averaging induced error. The initial diameter for the first trial is easily measured by hand. The final diameter must be space-averaged because it varies erratically over the length of the fuel grain. The most accurate method in doing so is to use the fuel grain density (ρ) and change in mass with the initial diameter to determine Df using equation 18. The Df of a given trial is the Di for the subsequent trial. (17) From the calculated data regression rate analysis is employed to determine the regression rate power law relationship in equation 14. The space and time averaged regression rate is plotted against Gox. A power regression is then used as nonlinear analysis to determine the ballistic coefficient and exponents a and n respectively. Plotted values from multiple firing test trials conducted over a range of O/F values are shown in the results section. D. CEA & PROPEP simulations The NASA thermochemical program CEA (Chemical Equilibrium with Applications) was originally used to model the Plexiglas and nitrous oxide propellant system. The simulated values of specific impulse and characteristic velocity as functions of O/F were found to be inaccurate. For more reliable simulation data the program ProPEP (Propellant Performance Evaluation Program) was implemented in replacement. This program is specifically designed to model rocket combustion and yielded expected values in line with theory. The simulation results are shown in the results plots alongside the experimental data. The simulations yielded two sets of results: frozen and shifting. Shifting accounts for mixing and combustion in the rocket nozzle thus projecting the maximum performance. Frozen is more realistic because after the throat the velocity increases from mach one to approximately mach three at which there is insufficient time for more reaction to occur. This is magnified in the case of a short nozzle. The frozen model was chosen in order to compare test results with the maximum possible performance of the system. During this study ProPEP has been useful in two different situations: To obtain the ideal and lines versus O/F for a given Pc and to determine and efficiency. However due to ProPEP calculates and for an input Pc Pe and O/F in the case of a de Laval nozzle in order to obtain results for the converging part the next procedure has been followed: Run ProPEP for given Pc O/F and Pa=Pt = P* to obtain (18)

:

2

Calculate theoretical Cf as shown in (3).

3

Calculate

via (2)

To obtain the efficiency of a given test another (named ) should be calculated via the previous procedure. In this case ProPEP should be runner with the chamber pressure measured in the test. and efficiency will be defined as : (21)

(22)

IV. Results - Plexiglas A total of 32 hot fire tests with Plexiglas and nitrous oxide were conducted in the test facility during 6 different days within the months of August and July. Sequence of trials was: 6-6-6-7-7. First two sets of tests (12 in total) are considered as preliminary test. Tests were conducted in the following days: 04/07/2011, 19/07/2011, 10/08/2011, 18/08/2011 and 23/08/2011. A. Preliminary tests Results of the 2 first days showed an extremely poor performance. Analyzed results showed that M=1 was not reached in the oxidizer nozzle throat. All results from these tests were directly eliminated from this study and the test facility was modified in order chock the oxidizer nozzle. The choked state of a nozzle depends on γ of the incoming flow. Regarding (7) a relationship between Pc and Pox can be developed in order to ensure that oxidizer nozzle is choked:

(23)

None of the first 12 tests achieved this condition: This sufficiently explains the poor performance of the system. Specific impulse and characteristic exhaust velocity are both inversely proportional to the mass flow rate. For subsequent trials

was increased to a value over 1.818. In order to archive this condition

to have a lower value which may be obtained increasing the exit nozzle increased guaranteeing its choked state. (24)

was required

. However it should be

These preliminary tests are not taken into account for the subsequent results and conclusions. All data from these 12 tests may be found in Appendix A. B. Behavior within time Figure 7 shows a typical LABVIEW test result after unit conversion. Chamber pressure increases in a linear fashion after ignition, then a quasi-constant value until shutdown. Similar behavior is observed in FT. Despite oxidizer pressure should maintain constant from ignition star until shutdown start it is observed that when Pc reaches its maximum value Pox drops suddenly. This phenomenon is due to the opening of the second oxidizer nozzle which increases

but lowers

. Despite this pressure drop

guaranteeing

the chocked state of the oxidizer nozzle.

46 41

36 31 26 21 16 11 6 1 0

5 Pc (atm)

10 Thrust (N)

15 Pox (atm)

Figure 4. Test #10 measurements vs. time (s).

C. Performance analysis The data sets from the valid firing tests are shown Figures 5, 6, and 7 show characteristic exhaust velocity and specific impulse values for all valid tests. The green solid line determines the ideal values for a Pc of 10 atm, and thinner green lines represent a 10% less efficiency in the ideal line (90% 80% 70%...). Experimental values have been corrected for the same chamber pressure in order to plot them all together in Figures 5 and 6. Table 1 shows the experimental data obtained for each test. Table 2 the corresponding results of performance calculations described in previous points of this study. According to (21) and (22):

A wide range of O/F values has been obtained:

In order to archive it was decreased from test to test in order to increase lowering and . Fuel grain length was also modified during trials in order to archive higher O/F. For tests #1 to #13, L 1 was used. L2 (2/3·L1 approx.) was used in tests #14 to #20. Due to the high dispersion of Test #1 results comparing to the averaged values of the other tests, results from #1 should not be taken into account for any further analysis.

C* vs O/F

1600 1400 1200 1000 800 600 400 200 0 0

2

4 10-Aug

6 18-Aug

8 23-Aug

10

Figure 5 . Characteristic velocity vs. O/F

12 IDEAL

14

Isp vs O/F

200 180 160 140 120 100 80 60 40 20 0 0

2

4

6 18-Aug

10-Aug

8 23-Aug

10

12

14

IDEAL

Figure 6 . Specific Impulse vs. O/F

1.2

Cf vs Pc 1 0.8 0.6 0.4 0.2 0 0

2

4

6 10-Aug

8

10 18-Aug

12

14 23-Aug

Figure 7 . Thrust Coefficient vs. Chamber Pressure

16

18

Table 1: Test conditions & averaged measurements Test 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(s) 7.203 6.701 8.000 8.098 8.202 8.601 7.799 6.797 6.701 7.501 6.200 6.107 7.903 9.486 7.596 7.802 8.303 8.201 7.700 8.703

mfueli (Kg)

mfuelf (Kg)

Di(m)

Pc (atm)

FT (N)

Pox (atm)

Pox,, input (atm)

1.023 1.011 0.994 0.974 0.956 0.939 1.026 0.990 0.960 0.933 0.902 0.876 0.843 0.769 0.731 0.706 0.682 0.658 0.634 0.612

1.011 0.994 0.974 0.956 0.939 0.925 0.990 0.960 0.933 0.902 0.876 0.852 0.811 0.731 0.706 0.682 0.658 0.634 0.612 0.586

0.023 0.024 0.026 0.028 0.030 0.032 0.023 0.027 0.030 0.032 0.035 0.037 0.039 0.020 0.025 0.029 0.032 0.035 0.037 0.039

11.811 8.719 8.203 6.795 5.036 4.134 15.404 15.283 13.687 12.739 10.969 10.124 7.827 14.938 14.419 12.844 10.848 9.673 8.925 7.508

27.672 20.248 18.443 14.449 10.943 8.126 36.885 36.623 33.036 30.625 25.996 23.182 17.425 32.423 30.972 27.624 22.082 20.552 18.401 15.532

26.081 20.024 18.605 14.853 11.825 9.389 32.883 32.892 29.952 28.159 23.968 22.122 16.816 32.886 32.080 28.741 24.797 22.165 20.214 16.966

45 40 35 30 25 20 60 60 55 50 45 40 30 60 55 50 45 40 35 30

Table 2: Test results Test 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

(g/s) 1.666 2.537 2.500 2.223 2.073 1.628 4.616 4.414 4.030 4.133 4.194 3.930 4.049 4.006 3.291 3.076 2.891

(g/s) 18.966 14.561 13.529 10.801 8.599 6.827 23.912 23.918 21.780 20.476 17.428 16.086 12.228 23.914 23.328 20.899 18.031

O/F 11.384 5.739 5.411 4.859 4.149 4.194 5.180 5.419 5.405 4.954 4.156 4.093 3.020 5.970 7.087 6.794 6.238

(mm/s) 0.170 0.188 0.169 0.138 0.121 0.090 0.355 0.287 0.235 0.220 0.207 0.183 0.178 0.341 0.313 0.254 0.214

(gr/cm2s) 4.399 2.938 2.340 1.628 1.159 0.842 4.890 3.748 2.843 2.287 1.703 1.417 0.970 6.062 4.174 2.938 2.095

CF

c* (m/s)

Isp (s)

1.048 1.039 1.006 0.951 0.972 0.879 1.071 1.072 1.080 1.075 1.060 1.024 0.996 0.971 0.961 0.962 0.911

1279.696 1139.951 1143.998 1166.322 1054.937 1092.866 1207.036 1205.815 1185.472 1157.141 1134.046 1130.680 1074.930 1196.044 1210.920 1197.572 1159.030

136.720 120.716 117.293 113.095 104.527 97.976 131.800 131.769 130.477 126.856 122.555 118.055 109.122 118.380 118.608 117.451 107.591

18 19 20

2.927 2.857 2.987

16.117 14.699 12.337

5.507 5.144 4.130

0.199 0.180 0.177

1.596 1.275 0.948

0.950 0.922 0.926

1135.400 1136.423 1095.137

110.007 106.847 103.319

C. Regression rate Due to the wide range obtained, the regression rate for the tested fuel could be easily obtained. Regarding (14), formula to be obtained will be: (25) Coefficients a and n could be calculated through a statistic power regression. First (26) and (27) are defined: (26)

;

(27)

To finally obtain the regression coefficients: (28) (29) For the obtained Gox and r values, the regression rate is: (30)

r vs Gox

0.3

0.25

0.2

0.15

0.1

0.05

0 0

1

2

3 10-Aug

18-Aug

4 23-Aug

5

6

7

Figure 8 . Regression rate vs. Gox

E. Conclusions Nitrous oxide has demonstrated that could be used as propellant despite showing a weak and poor performance. A notable difference between and has been appreciated. One of the reasons that may explain the low performance of this rocket is the copper nozzle used in the experiments. Copper expands and nozzle throat increases while heated flux goes through it. According to a linear thermal regression model based on the area, the nozzle expansion could be calculated. (31) (32) could be calculated (18) and (33): (33) is defined as the molecular mass of the burned flow (calculated through ProPEP) divided into the universal gas constant. Finally, the nozzle expansion can be calculated:

Another issue involving the nozzle is the unavailability to determine its real diameter. Nozzle diameter was initially 5.00mm however, after several tests it has an eccentric shape of 5.15mm (value used in the calculations). Considering the thermal expansion, a 5.30mm nozzle has been considered at the time of doing all calculations. It has also been observed that O/F values obtained are situated around the estequiometric O/F: (33) (34)

Showed a good performance between trials:

Final results show a good correlation between expected and obtained results. However, the poor performance of the nozzle has a clear effect on and . Further research may try to solve this issue in order to obtain more accurate results. Engine parameters such as the nozzle or the mixing chamber length may be modified to improve results and to obtain new conclusions. Effects of nitrous oxide may be observed in comparison with other oxidizers such as Oxygen, for which the efficiency is much higher.

V. Results – Paraffin The performance of nitrous oxide was also evaluated using paraffin as the solid fuel. As it is known, paraffin burns at rates much higher than conventional hybrid fuels. In fact, these kind of engines take on the liquefying fuel properties, and hence the formation of a thin and hydrodynamically unstable layer of liquid on the fuel solid grain. The entrainment of droplets from the liquid-gas interface increases significantly the rate of fuel mass transfer and therefore the fuel regression rate as well. In all of the following paraffin 704 was used, being referred simply as paraffin. A. Testing conditions Apart from the engines themselves, all the testing facility and instrumentation set up were kept the same for the paraffin testing. From previous tests carried on [1] with paraffin with oxygen, it was know that the chamber pressure typical values would range from about 12 atm up to around 20 atm. Based on this, it was considered to use the same 5.024 mm diameter nozzle of the previous tests with Plexiglas and nitrous oxide, provided it would keep the same chocked state as before. The regression rate has shown to be lower than when using oxygen, and hence providing higher burning times for each engine. Facing this fact, it was chosen to burn the first engine a second time, since it hadn’t burn totally on the first test and another test could be carried out. Therefore, a total of seven tests out of 6 engines were run. Unfortunately, due to a malfunction in shutting off the oxidizer fed into the engine during test #7, the combustion kept on going consuming all the paraffin until Plexiglas started to be burned. As the combustion continued and the Plexiglas regressed thinner, the chamber pressure got to be enough to burst out the engine, obviously resulting in the test failure. No more tests could have been run since, given that the malfunction reasons had to be determined and be taken care of.

B. Performance analysis The test results are as summarized in the table and charts below. The data shown is converted for the average chamber pressure of 8.014 atm. The data from the 7th test is not included.

1200

C* vs O/F 1000 800 600 400 200 0 0

1

2

3

4

5

6

7

14-Set Figure 9 . Characteristic velocity vs. O/F

140

Isp vs O/F

120 100 80 60 40 20 0 0

1

2

3

4

5

14-Set Figure 1 0 . Specific Impulse vs. O/F

6

7

1.2

Cf vs Pc

1 0.8 0.6 0.4 0.2 0 0

2

4

6

8

10

12

14

14-Set Figure 1 1 . Thrust Coefficient vs. Chamber Pressure

All the calculations here presented are made on the same way as the ones for Plexiglas testing. To obtain the ideal curves from PROPEP, paraffinic oil (code 755) was used to model the paraffin 704. As it can be seen the nozzle kept its chocked state, validating the calculations and confirming the initial assumption.

Table 3: Test conditions & averaged measurements Test 1 2 3 4 5 6

(s) 5.704 7.194 9.360 8.535 8.400 8.805

mfueli (Kg)

mfuelf (Kg)

Di(m)

Pc (atm)

FT (N)

Pox (atm)

Pox,, input (atm)

0.964 0.922 0.965 0.960 0.950 0.931

0.929 0.882 0.933 0.925 0.863 0.806

0.020 0.026 0.020 0.020 0.020 0.020

4.819 4.852 6.589 8.227 10.410 13.186

8.117 9.104 13.372 17.051 21.785 27.954

11.975 12.492 16.037 18.741 22.488 27.514

25 25 30 35 40 45

Table 4: Paraffin test results Test 1 2 3 4 5 6

(g/s) 6.136 5.560 3.953 4.101 10.358 14.197

(g/s) 8.708 9.084 11.661 13.628 16.353 20.007

O/F 1.419 1.634 2.950 3.323 1.579 1.409

(mm/s) 0.525 0.381 0.336 0.351 0.770 0.977

(gr/cm2s) 2.079 1.392 2.748 3.254 2.950 3.092

CF

c* (m/s)

Isp (s)

0.839 0.934 1.010 1.032 1.042 1.055

652.114 665.498 847.624 932.083 782.880 774.333

55.745 63.374 87.302 98.038 83.139 83.310

1.2

r vs Gox

1 0.8 0.6 0.4

y = 0,3411x0,443 0.2 0 0

0.5

1

1.5

2

2.5

3

3.5

Figure 1 2 . Regression rate vs. Gox

According to the empirical law (25) we can then obtain:

As it can be seen, the data scatter for the regression rate as a function of Gox is very sparse. In fact for the 3rd and 4th tests, the amount of burned paraffin was very low in comparison with the other tests, and hence the lower regression rates obtained for these two tests. A study on the efficiency of the runs, when compared with the PROPEP results, provided the following values:

#Run 1 2 3 4 5 6 Average

0.72 0.73 0.87 0.95 0.85 0.86 0.83

0.58 0.65 0.80 0.86 0.77 0.77 0.74

As expected from previous tests [1], the specific impulse efficiencies are smaller than the ones for the characteristic velocity, with an average difference of 9%, which is in agreement with the past experience with tests using oxygen. [1] C. Conclusions Follows a comparison between the results obtained from combustions of Plexiglas with nitrous oxide, paraffin with nitrous oxide, and paraffin with oxygen. The regression rates for each case are presented as well as the specific impulse and characteristic velocities.

2.000 1.800 1.600 y = 0.8831x0.3998

1.400 1.200 1.000 0.800 0.600

y = 0.3411x0.443

0.400 0.200 y = 0.1127x0.4775

0.000 0.000

1.000

2.000 Paraffin/N2O

3.000

4.000

Plexiglass/N2O

5.000

6.000

7.000

Paraffin/O2

Figure 1 3 . Regression rate vs Gox for different sets of propellants.

Despite the low amount of data from paraffin burned with N2O it is possible to notice different trends for each of the three propellant sets. As expected, paraffin burns faster than Plexiglas, in the case where both are burned with nitrous oxide. On the other hand, the observed regression rates of the combustion between paraffin and oxygen are higher than with nitrous oxide, as it should be expected.

100 90 80 70 60 50

Isp

40

C*

30 20 10 0 Plexiglas/N20

Paraffin/N20

Paraffin/O2

Figure 1 4 . Performance efficiencies (%) obtained for different sets of propellants.

In the same fashion, the performance efficiencies follow the same tendency. In the chart above it can be noticed the higher combustion efficiency of oxygen in comparison to nitrous oxide, as stated before. In order to attain better conclusions, a higher number of runs would be needed. Nevertheless the amount of points taken is enough to perceive the different behavior of the combustion between paraffin and nitrous oxide in comparison to other sets of propellants. The data obtained should be considered as starting point on further research with these propellants and shall provide an idea on future performance results and behavior of characteristic curves.

VI. References 1. Lohner, K., Dyer, J., Doran, E., Dunn, Z., Zilliac, G., "Fuel Regression Rate Characterization Using a Laboratory Scale Nitrous Oxide Hybrid Propulsion System," 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Sacramento, California, July 2006. 2. Chiaverini, M. J., Kuo, K.K., "Fundamentals of Hybrid Rocket Combustion and Propulsion," Progress in Astronautics and Aeronautics, vol. 218, pp. 207-242 and 323-345, 2007. 3. Marxman, G., Gilbert, M., "Turbulent Boundary Layer Combustion in the Hybrid Rocket," Ninth International Symposium on Combustion, Cornell University, Ithaca, New York, August-September 1962. 4. Marxman, G., "Boundary-Layer Combustion in Propulsion," Eleventh International Symposium on Combustion, University of California, Berkeley, California, August 1966.

Appendix A. Preliminary Tests Results

1800 1600

C*

1400 1200

19-jun

1000 800

04-jun

600 400 200 0 0

1

2

3

4

5

6

7

Figure A 1 - 1 . Characteristic exhaust velocity vs. O/F (Preliminary tests)

250

Isp

200

150

19-jun 04-jun

100

50

0 0

1

2

3

4

5

6

7

Figure A 1 - 2 . Specific Impulse vs. O/F (Preliminary tests)

Table A 1 - 1. Test conditions & averaged measurements (Preliminary tests)

Test

(s)

1P 2P 3P 4P 5P 6P 7P 8P 9P 10P 11P 12P

10.500 10.605 10.100 9.998 10.401 7.997 9.001 7.406 7.400 6.602 6.801 7.997

mfueli (Kg)

mfuelf (Kg)

Di(m)

Pc (atm)

FT (N)

Pox (atm)

1.030 1.001 0.965 0.919 0.867 0.807 1.030 1.005 0.984 0.958 0.930 0.899

1.001 0.965 0.919 0.867 0.807 0.756 1.005 0.984 0.958 0.930 0.899 0.855

0.023 0.026 0.030 0.034 0.038 0.042 0.023 0.026 0.028 0.031 0.033 0.036

8.356 10.444 12.539 14.332 16.327 13.731 9.352 11.092 12.869 14.773 16.248 18.990

13.023 16.517 19.888 22.724 26.298 22.811 15.105 17.430 21.579 24.458 27.855 32.510

13.569 16.466 18.934 21.192 23.454 28.332 13.218 15.434 17.599 19.686 21.987 25.607

Table A 1 - 2. Test results (Preliminary tests)

Test 1P 2P 3P 4P 5P 6P 7P 8P 9P 10P 11P 12P

(g/s) 2.722 3.419 4.578 5.178 5.742 6.468 2.777 2.836 3.514 4.241 4.558 5.502

(g/s) 9.867 11.973 13.768 15.410 17.055 20.602 9.612 11.223 12.797 14.315 15.988 18.621

O/F

CF

c* (m/s)

Isp (s)

3.625 3.502 3.008 2.976 2.970 3.185 3.461 3.958 3.642 3.375 3.508 3.384

1.132 1.156 1.172 1.182 1.191 1.179 1.145 1.162 1.174 1.184 1.19 1.199

934.907 955.595 962.601 980.473 1008.689 714.41 1063.174 1111.217 1111.253 1121.265 1113.774 1108.719

107.904 112.621 115.017 118.15 122.426 85.866 124.088 131.596 133.01 135.353 135.146 135.537