small liquid propellant rocket engine - técnico lisboa - … · small liquid propellant rocket...

Small Liquid Propellant RocketEngine

Design, Build and Test

Mariana Peralta Páscoa Martinho Marques

DEM, MEA, Instituto Superior Técnico, Universidade de Lisboa, [email protected]

December 2016

Abstract

The present document reflects the work developed in the S-SHE project, at Omnidea Lda. It was intendedto design, build and test a small liquid rocket engine. The prototype should be able to produce 25N ofthrust. This project aims to study the stability of the liquid engine with regenerative cooling and externalpressurization, and the feasibility of the self-pressurized system. Therefore, the system should be flexibleenough to allow two operation modes: external and auto pressurization. It is intended to have a low cost teststand and as simple as possible. Further objectives of this project are having a repeatable ignition, injectionin gaseous phase and building a simple injector.Keywords: Small liquid rocket engine, Self-pressurization, Regenerative cooling, gaseous injection,Repeatable ignition.

I. Introduction

There is a constant need to make launcher sys-tems lighter and less complicated. Traditionalfeed systems are complex and heavy, and theyconsist mainly two types: turbopumps and gas-pressurized. The interest of revisiting the self-pressurization concept comes from the beliefthat it can simplify the pressurization mecha-nism and produce lighter systems.

There are currently five main organizationsleading the space exploration [1]: NASA fromthe United States of America, ROSCOSMOSfrom Russia, ESA from Europe, JAXA fromJapan and CNSA from China. The number oflaunchers in use is very high. Through themost successful launchers of the present-daysit is possible to understand the technology inuse. For example, one of the most recent en-gines is the Merlin, the upper stage enginefrom Falcon 9. This engine has as its propel-lants liquid oxygen and Kerosene. One of its

characteristics is that it allows operation withdifferent OF ratios due to the flow trimming.Similar to what is proposed in this project, itscooling is done by regenerative cooling. Theengine characteristics give the five main param-eters to define in this work: propellants in use,properties of the burn (OF, flame temperature,specific impulse, etc.), sizing, material and heattransfer analysis.

As one of the objectives of this study isto evaluate the feasibility of building a self-pressurized system, all the design shouldtake it into account. The concept of self-pressurization through regenerative cooling re-lies on the pressurization of the tank using heatfrom the combustion chamber. Which meansthat the cooling, in this case, would not onlyserve to keep the system integrity, but alsokeep the pressure in the fuel tank. The sys-tem stability should be assured by its capacityto correct deviations. Figure 1 shows that for

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Small Liquid Rocket Engine • Design, Build and Test

a range of OF between 0.5 and 1.5 (which isthe ideal range of operation), the decrease ofthis ratio should trigger the same change intemperature.

Figure 1: Flame temperature evolution with the OF.

Therefore, if the pressure in the fuel tankdecreases, the OF will increase, which leadsto a higher flame temperature, that increasesheat transfer and, therefore, the pressure in thetank.

II. Background

There are three types of rockets motors: solid,liquid and hybrid. Their designations arebased in the physical state of the propellantsinvolved. There are also mono-propellants andbi-propellants engines. The first ones are madeof a single substance and their use relies ontheir exothermal decomposition by a catalyst -for example, hydrogen peroxide or hydrazine.In the second case, there are two reactants thatare stored apart. In this particular project weare dealing with a bi-propellant liquid rocketengine. The liquid propellant engines are usu-ally more efficient in terms of specific impulse -Isp, can be shut down and may be throttleableand re-startable it if necessary [2]. The systemof a liquid engine can be divided into six mainparts: thrust chamber - which contains thenozzle, injector and the combustion chamber;tanks - for the reactants; feed mechanism - ei-ther using pumps or pressurant gases - in somecases both mechanisms are combined; powersource to electrical modules; piping; controlsystems. The combustion chamber is the main

part, where the reaction occurs. Its design mustconsider the sizing so there is enough spaceto allow an effective reaction, atomization andmixture of the reactants. The gases producedare accelerated and ejected through the nozzleat high speed. A cylindrical chamber is fareasier to manufacture, which decreases enginecosts, and it is the most widely used, as it of-fers a fair length for the reaction to develop.Usually, the characteristic chamber length cor-responds to the length that the chamber wouldhave if it were a straight tube with the samevolume and the values vary between 0.8 and3 meters in the engines described in the lit-erature. The nozzle is the component wheregases are expanded to match the outer pressure.There are several types of nozzle shapes: conic,bell and spike. The divergent part of the noz-zle is crucial to rocket performance, since onlyconvergent-divergent nozzles allow expansionto supersonic velocities. The expansion ratio- ratio between exit and throat area - is an en-gine parameter that depends on the chambergeometry. Its optimal value depends on engineparameters such as the chamber pressure, re-actants, etc. Knowing the throat area, the exitarea can be estimated. For the nozzle sizing itis current practice to apply isentropic expan-sion relations. The exit area - Ae - is given bythe relation between the exit and the throatarea - At.

Ae

At=

1Mae

(1 + γ−1

2 Ma2e

(γ + 1)/2

) γ+12(γ−1)

(1)

Where Mae corresponds to the Mach numberat the exit and γ is the heat capacity ratio. Thethroat area is computed using the sonic throatassumption. The following equation can bemanipulated in order to solve it for the maxi-mum accepted area to have sonic conditions,given by A∗, from the drag coefficient - Cd -,mass flow rate - m -, density - ρt and pressure -Pt.

m = Cd A∗

√√√√2ρtPt

(2

γ + 1

) γ+1γ−1

(2)

The material should also be carefully analysed.Some materials are not compatible with somepropellants, for example, ammonia deteriorates

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copper. It is also desirable to have a materialwith strong mechanical properties to ensurethat the chamber is capable of withstandingboth pressure and temperature conditions. Thetemperatures in the chamber during the com-bustion are higher than the service temper-ature of most of the materials, whereby theneed for chamber cooling must be consideredduring the design to avoid damage. This isdeterminant for calculating wall thickness andthe choice of the material.

The heat transfer is a crucial part of the de-sign. Chamber heat is mostly transferred byconvection from the hot gases to the wall, andthen conducted through the wall. There is asignificant increase of the heat transfer in thethroat, which means that the cooling must beexceptionally effective in this area to avoid sig-nificant damage. Cooling can be done mainlyby a combination of five different methods:

• Regenerative cooling - It is the most usedmethod. One or both propellants passtrough conduits in the chamber’s outerwall in order to cool it, before being in-jected.• Film cooling - In this case, as its name in-

dicates, the wall surface is protected fromexcessive heat by a thin film of a coolant orpropellant, that is introduced in the cham-ber around the injector or through orificesin the chamber wall. It can be used incombination with regenerative cooling.• Transpiration cooling - It is similar to film

cooling. In this case the walls in the cham-ber are porous. A coolant is introducedthrough them at a rate that allow the de-sired temperature to be maintained.• Ablative cooling - This method was mainly

used in solid motors, although it is alsosuitable to liquid engines of short dura-tion and low chamber pressure. For thismethod the wall material is a thermal insu-lator, resulting in a poor heat transmissionto the outside. In the inner chamber wallthe material suffers melting, vaporization,and chemical changes to dissipate heat.• Radiation cooling - The heat is radiated

from the surface to the outer wall of the

chamber. This type of cooling is prefer-able in regions with low heat flux as, forexample, nozzle extensions.

The most relevant performance parameter isthe specific impulse - Isp - which SI unit is N·s

kg .It depends on a wide range of factors such aschamber pressure and propellants ratio. It isgiven by the ratio between the engine’s thrust -F - and the total mass flow rate - m, which isdefined by [3]:

Isp =Fm

(3)

This parameter depends on the burn and ex-pansion efficiency. I varies with OF 1, as hav-ing a lean or rich mixture is determinant tothe combustion efficiency. This ratio can becalculated from the stoichiometric combinationof the fuel and the oxidizer.

To predict the engine performance and thecombustion characteristics software is availablefrom NASA - CEA [4] [6] - that is capableto compute these parameters. This software,called Chemical Equilibrium with Applications,was developed to calculate chemical equilib-rium and properties of complex mixtures. Ithas specific functionalities for rocket problems,and was used during this project.

The injector is the component responsible byintroducing the reactants into the combustionchamber. Usually the propellants are in liq-uid state when injected. Therefore the injectormust be capable of breaking down the streaminto small droplets and maximize the mixingin order to achieve an effective burn. There isa drop of pressure in the injector that must beconsidered when designing the system. It canbe estimated by the non saturated throat equa-tion, that comes from the mass conservationequation.

m = Cd Ainj

√√√√2ρP(

γ

γ− 1

)((Pc

P

) 2γ

−(

Pc

P

) γ+1γ

)(4)

There is a lot of research about injectors andtheir influence in the engine behaviour, regard-ing the orifice pattern, angles on injection, etc.Although it is a field with a considerable com-plexity, the goal of this project was to design a

1Ratio between oxidizer an fuel.

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simple injector. Having a good mixture is thekey to achieve an efficiency near the expected.

III. Mathematical model

The mathematical model in this project servesto determine if the auto pressurization conceptis stable. The model in use is iterative. Theobjective is to determine the pressure evolutionin the tank when the heat transfer is responsi-ble for increasing the remaining fuel’s pressure.The layout considered is in figure 2.

Figure 2: Theoretical layout.

The mass on the tank is estimated through amass balance within the tank, in equation 11,where mF if the fuel mass flow, m is the fuelmass and m0 is the initial fuel mass.

dmdt

= −mF ⇒ m = m0 −∫ ∆t

0mFdt (5)

In order to calculate the fuel’s mass flow rate -equation 6 - it is necessary to know the veloc-ity, which can be calculated with equation 7,which is a manipulated form of the Bernoulliequation. Notice that, in this equation, k rep-resents the pressure losses in each section thepiping lines. In the mentioned equation theterm f represents the Darcy friction factor inthe system. Both the presented terms can beestimated using available reference and [7].

mF =AVνg

(6)

Where A is the area of the piping, V is thevelocity and νg is the specific volume.

From the Bernoulli equation in 7 in is possi-ble to estimate the velocity, in 8.

P− ∆hloss = P0 ⇒ ∆hloss =V2

2νg

(f LD

+ Σk)

(7)

V =

√√√√2νg (P− P0)

Σk + f LD

(8)

Applying an energy balance in the tank wehave equation 9, where u and m are defined byequations 10 and 11, respectively.

Q =ddt

(mu) + mFhg (9)

u = ul + x(ug − ul

)(10)

m =VolV

=Vol

νl + x(νg − νl

) (11)

The x value is the gas fraction, that can beestimated through equation 14. The heat rateis given by equation 12. As it is an iterativemodel, it is possible to compute the evolutionof the properties in each step, as for examplethe temperature of the fluid in the tank.

Q = AU∆T (12)

The variable A is the area, ∆T is the tempera-ture difference and the U is explained in equa-tion 12.

U =1

12πrhi

+ 12πk ln

(x+l

r

)+ 1

2π(x+l)h′e

(13)

Where h are the convection coefficients for theconvection in the chamber and at the vaporizer.

x(t) =mg

m=

∫ ∆t0 Q/h f gdt

m0 −∫ ∆t

0 mFdt(14)

To close the problem it is necessary to includean extra equation. When using the sonic throatassumption it is possible to write the equationin order to the pressure value, so it can beestimated.

mt = mF + mox =0.6847p0 A∗

(RT0)1/2 (15)

When applying equation 15 it is consideredthat the throat is sonic, which is true as longas the chamber pressure is about twice as theatmospheric pressure [7].

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MethodGiven the initial pressure of the tank - set as

20bar - the burning process starts. The flametemperature depends on the oxidizer fuel ra-tio. The polynomial that describes the relationis obtained using CEA software, by varyingthe OF value and registering the given flametemperature. This temperature is crucial to es-timate the heat transfer, as it will depend on it.The heat is absorbed by the fuel in the vapor-izer, and its properties will change. Throughthe energy balance it is possible to determinethe new pressure value. This new state, withthe updated properties, will result in a differ-ent fuel mass flow and, therefore, in a differentOF, which will lead to new temperatures in thechamber and therefore, new values of heat rate.This creates a cycle during the burn, where thenew properties in the tank are calculated ateach step.

It is important to refer that this is a simplifiedmathematical model that does not contemplatesome losses during the process. Some of theconsulted literature [8], [9] and [10] provide amathematical model to incorporate this lossesby friction and heat transfer. However it wasdecided to make a simpler model relying onthe assumption that the system is isentropicwith heat transfer. In fact,the second principleof thermodynamics (equation 16), does not dis-card this possibility for dQ < 0, since dσ > 0[5].

dQT

+ dσ = dS (16)

The thermodynamic properties of the satu-rated fluid were found on NIST 2. The poly-nomials that correlate pressure with internalenergy, enthalpy, etc. were computed fromthe mentioned saturated property tables, usingMatlab.

IV. Experimental Work

The departure characteristics for this engineare in table 1.

2National Institute of Standards and Technology

Table 1: Baseline characteristics.

Pressure Oxidizer Fuel Thrust15bar Gaseous Oxygen To define 25N

As it was previously mentioned, the layoutshould be flexible enough to enable the op-eration with external and auto pressurization.Figure 3 shows the layout used. The dottedline between the vaporizer and the tank can beopened to allow gases from the vaporizer topressurize the tank. When this line is closed anitrogen bottle, connected to the the fuel’s tankis responsible for the pressurization.

Figure 3: Layout in use.

To build the small liquid rocket engine asignificant part of the work has to do withsizing. It was an iterative process due to thedifferent options in each step. Nevertheless,as found on literature [3], a sequence ofcomputation was followed: propellant choice,OF calculation, total flow rate computation,nozzle sizing, combustion chamber, chamberwall thickness and cooling.

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The fuel must fulfil the requirements of thisproject, there were several parameters analysed:critical pressure and temperature, enthalpy ofvaporization and specific impulse when com-bined with oxygen. From the three candidates- Ammonia, Ethanol and Propane - Ammoniawas chosen. It has good cooling capabilitiesand can achieve high pressures with relativelylow temperatures. Part of these estimationswere done using CEA software and the otherinformation was obtained from NIST.

The heat transfer analysis shows that it ispossible to have a proper cooling with the en-gine characteristics.

The injector used, in figure 4, has swirl tocause a recirculation bubble which will anchorthe flame and prevent undesired instabilities.

Figure 4: Swirl injector.

The final design can be consulted in table 2.

Table 2: Engine and propellant properties

Item Unit Value

ENGINE

OF 1.4Total mass flow kg/s 0,00999

Isp m/s 2501,6Power kW 31.3

Chamber diameter mm 30Throat diameter mm 3

Area ratio 3.2Chamber pressure bar 15Chamber material Stainless Steel 304

Burn time s

OXIDIZEROxygenPressure bar 40

Temperature K 293

FUELAmmonia 20Pressure bar 40

Temperature K ∼300

V. Tests

Figure 5 shows the test stand that was usedduring the test campaign. In order to get use

to the operation of the test stand, the first testswere performed with ethanol, which is saferand easier to handle than ammonia.

Figure 5: Test stand used.

The instrumentation in the test stand allowto measure the pressure, temperature and thethrust. The first tests were external pressur-ized.

Figure 6: Temperature evolution during the test.

From the temperature plot, in figure 6, itis possible to understand that the flame wascloser to the thermocouple than in previoustests, once the chamber’s temperature reachedalmost 400 deg C. The temperature in the va-porizer, even in this test, where it was alreadyabove the ambient temperature, did not reachthe high temperatures that were observed inthe ethanol case. This allowed to operate the

6


test stand for longer tests, what was not possi-ble with ethanol.

Figure 7: Pressure evolution during the test.

In the pressure chart, in figure 7, the twolines are very different from the previous test.There is a hard start at the beginning of theburn. The chamber pressure starts to decayaround 7 seconds after the beginning. Thishappens because the ammonia ends. As it wasexplained before, this test was performed afteran self-pressurized test, which means that partof the ammonia available was spent in that test.The vaporizer’s pressure, represented by theblue line, has three different stages.

Figure 8: Thrust evolution during the test.

The thrust, which can be seen in figure8, achieved during the test was satisfactory,around 23N - for a projected value of 25N. Itstarts to drop when the fuel tank runs out ofammonia. It is possible that the stoichiometry

was not the desired, specially when ammoniastarts to evaporate. Although, with the lackof instrumentation to actively control the fuelmass flow rate, the results are satisfying.

The plume obtained during the test can beseen in figure 9.

Figure 9: Plume during the test.

For the self-pressurized test two types oftest were made: low OF and high OF. It wasdecided to predict the engine’s behaviour whenoperating in different regions on the curvesshowed in figure 1.

The first test was made with higher OF. Fromthe pressure plot it is possible to understandthat the vaporizer line has the same tendencypredicted from the mathematical model. Thefirst depression in the vaporizer pressure lineis the point where nitrogen in the fuel’s linestops being responsible for the pressurization.It is possible to see a small decrease in the va-porizer’s pressure, followed by its increasingdue to the regenerative cooling, from whereit behaves as it was predicted. Although, inthe case of the chamber pressure, the pressurestarts to increase, as was expected, and then itdecays. There is a small increase of the pres-sure and its decay, until the valves are closedaround 14 seconds.

During the test the sound denoted the thatthe engine’s behaviour was fickle, what canbe translated by the chamber’s pressure plot,where it is possible to understand that the pres-sure was constantly trying to rise, but it de-cayed few moments after, ending by decay-ing consistently until the valves were closed.The behaviour of the pressure in the vaporizeris close to the predicted by the mathematicalmodel for this case.

In the second case, with low OF, the oxygen

7



bottle was regulated to 20bar and the fuel’s linewas initially pressurized with 18bar. The flowcontrol valves were also adjusted with the sameheight. The pressure in the chamber resemblesmore to a step than in the previous case. Thepressure in the vaporizer shows an increase,although it is notorious that there are someoscillations in the pressure growing. Figure 11shows the pressure evolution during the test.


The discrepancy between experimental andtheoretical results has to do with the settledpressure in test stand, which was lower thanthe theoretical. However, the tendency is simi-lar.

VI. Conclusions

This master thesis marks the beginning of acompany’s project to build a successful engine.

It was a work based on research and develop-ment that, as it was expected, had successfuland unsuccessful points. After all it was im-portant to understand the system behaviour.

In this project it was possible to accomplishthe objectives that were proposed at the begin-ning. To simplify, it is possible to divide theproject in two main parts: work with externalpressurization and with self-pressurization.

The external pressurized system was stableand behaved as expected. It was possible tobuild a simple and low cost engine, properlysized and in which the heat transfer was wellestimated. The heat transfer analysis was animportant point of the work, which assuredmaterial safety and, therefore, the success ofthe test campaign. The data collected leads tothe conclusion that, with ammonia, the objec-tive of having gaseous injection was achieved.

The second part of the work, that had to dowith the study of the self-pressurized system,allowed to prove that the concept is feasibleand it is worth studying and investing in. Theresults obtained with this type of pressuriza-tion were different from those previously ob-tained, which were closer to the predictions.However, the fact that there is an explanationto this discrepancies proves that there is moreto study about the concept. The fact that thesystem was able to sustain an effective burnduring a brief time was a success.

In the beginning of this document there isan explanation about how the system wouldbe able to correct itself through the change ofthe flame temperature with the OF. Experienceand the model showed that there are actuallydifferences when operating with low and highOF.

i. Future Work

The company intends to increase the engine’scapacity. Therefore, using the same methodas before, the chamber was resized in order toachieve a thrust of 300N, using the same teststand. The objective is to change the minimumpossible.

To increase thrust is necessary to increase

8


pressure, in order to achieve reasonable dimen-sions and a sonic throat. The security valvesinstalled can go up to 70bar, so the chamber’spressure is fixed at 50bar.

It would be important if a flow meter was in-stalled in the test stand, allowing the operatorsto know the actual fuel flow rate and, therefore,the OF.

The flame’s temperature is also unknown.The thermocouple that was meant to be usedto measure the temperature in the plume wasdamaged. Acquiring a new one should also beconsidered.

VII. Acknowledgments

I would like to thank Omnidea Lda. for offer-ing me this fellowship to develop my masterthesis. All the experimental work was devel-oped in Omnidea facilities and the companysupported all the costs involved. A specialword for Horácio Moreira, my supervisor atthe company. Thank you for the patience andfor teaching me so much. A heartfelt thanks toTiago Pardal, the owner of Omnidea Lda andthe inventor of this concept, for giving me thisopportunity.

References

[1] Space exploration http://www.spacelaunchreport.com/library.html#lvdata

[2] Sutton, Gp and Biblarz, O Rocket PropulsionElements 2001

[3] Krzycki, Leroy J How to Design, Build andTest Small Liquid-Fuel Rocket Engines 1967

[4] McBride, Bonnie J. and Gordon, SanfordComputer Program for Calculation of ComplexChemical Equilibrium Compositions and Ap-plications: II-User Manual and Program De-scription 1996: NASA Reference Publication1311.

[5] M. J. Moran and H. N. Shapiro Fundamen-tals of Engineering Thermodynamics John Wi-ley & Sons Inc., West Sussex, 5th Edition,2006.

[6] Gordon, Sanford and McBride, Bonnie J.CEA Analysis 1994: NASA RP-1311

[7] White, Frank Fluid Mechanics 2010:McGraw-Hill,New York

[8] Beri, J. N. Flow Heat Transfer 1960: DefenceScience Organization, New Delhi.

[9] Bandyopadhyay, Alak Nozzle Flow with HeatTransfer and Friction 1995.

[10] Bandyopadhyay, Alak Modeling of Com-pressible Flow with Friction and Heat Transferusing the Generalized Fluid System SimulationProgram (GFSSP) 2007.

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