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Aljure 2007
1. CONSTRUCTION OF A MODEL LIQUID FUELED ROCKET ENGINE
ALEJANDRO ALJURE OSORIO
UNIVERSIDAD DE LOS ANDES
FACULTY OF ENGINEERING
DEPARTMENT OF MECHANIC AL ENGINEERING
BOGOTA D.C., JANU ARY 2007
2. CONSTRUCTION OF A MODEL LIQUID FUELED ROCKET ENGINE
ALEJANDRO ALJURE OSORIO
Cod. 200125087
Thesis project presented to obtain the Bachelor of Science in Mechanical
Engineering
Ad visor
FABIO A. ROJAS
Dr. Eng.Mec.
UNIVERSIDAD DE LOS ANDES
FACULTY OF ENGINEERING
DEPARTMENT OF MECHANIC AL ENGINEERING
BOGOTA D.C., JANU ARY 2007
3. ACKNOWLEDGEMENTS
I wish to thank Fabio Rojas, who as a professor and advisor guided me through a
great part of my undergraduate studies. Also for the great interest he showed in the
rocketry area and the will to work on it.
I would also like to thank Mateo, Ramiro, Jorge and the rest of the staff of the
Mechanics Lab, for their patience and help in the construction of the rocket engine.
4. Dedicated to my parents Eduardo and Gloria
for everything they have gi ven me and
the faith they had in me.
To my brothers, my grandparents
And all my family, especially
my family in Bogotá, for helping me
getting settled in the city
and being there when I needed help
5. IM-2006-II-01
v
TABLE OF CONTENTS
INTRODUCTION.......................................................................................................................7
PROPERTIES OF LIQ UID PROPELLANTS.............................................................................. 10
P HYSICAL PROPERTIES.............................................................................................................. 10
C OMBUSTION PROPERTIES......................................................................................................... 11
S TART AND IGNITION............................................................................................................... 11
DESIGN EQ UATIONS.............................................................................................................. 13
NOZZLE ................................................................................................................................ 14
C OMBUSTION CHAMBER ........................................................................................................... 15
INJECTORS ............................................................................................................................. 16
P ROPELLANTS ........................................................................................................................ 17
ROCKET ENGINE DESIGN..................................................................................................... 20
CONSTRUCTION.................................................................................................................... 25
T HRUST CHAMBER................................................................................................................... 25
INJECTORS ............................................................................................................................. 26
INJECTOR COVER ..................................................................................................................... 28
INJECTOR TUBE CONECTION PIECE............................................................................................... 28
C OOLING JACKET .................................................................................................................... 29
C OOLING JACKET TUBE FITTINGS ................................................................................................ 30
C LOSING SUPPORTS ................................................................................................................. 30
S EALS................................................................................................................................... 31
F UEL TANK ............................................................................................................................ 32
GAS TANKS ............................................................................................................................ 33
S UPPORTING STRUCTURE .......................................................................................................... 33
P LUMBING............................................................................................................................. 34
IGNITOR ................................................................................................................................ 37
ASSEMBLY.......................................................................................................................... 38
EXPERIMENTAL PROCEDURE .............................................................................................. 44
OPERATING PROCEDURE ........................................................................................................... 44
T HRUST................................................................................................................................. 45
C HAMBER TEMPERATURE.......................................................................................................... 49
P RESSURE .............................................................................................................................. 50
SUPPLIERS AND COSTS ......................................................................................................... 51
C OST .................................................................................................................................... 51
S UPPLIERS ............................................................................................................................. 52
CONCLUSIONS AND RECOMMENDATIONS .......................................................................... 54
BIBLIOGRAPHY..................................................................................................................... 55
ANNEX: BLUEPRINTS ............................................................................................................ 56
6. IM-2006-II-01
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TABLE OF FIGURES
Figure 1. Flow of the project...............................................................................................8
Figure 2. Schematic of the combustion chamber and nozzle [3]. ..............................15
Figure 3. Types of injection systems [3].........................................................................17
Figure 4. Performance of some liquid propellants [3]. .................................................18
Figure 5. Variation of flame temperature with O/F ratio [3]. ........................................18
Figure 6. Specific impulse as a function of chamber pressure [3]. ............................19
Figure 7. Nozzle parameter for various chamber pressures [3].................................21
Figure 8. Inside of the thrust chamber............................................................................25
Figure 9. Nozzle. ................................................................................................................26
Figure 10. Fuel inlet in injector piece..............................................................................27
Figure 11. Injector holes...................................................................................................27
Figure 12. Angle of injector holes....................................................................................28
Figure 13. Inside of cooling jacket...................................................................................29
Figure 14. Weld of injector cover.....................................................................................31
Figure 15. Weld of cooling jacket....................................................................................31
Figure 16. Dry seals. .........................................................................................................32
Figure 17. Fuel tank...........................................................................................................33
Figure 18. Support structure. ...........................................................................................34
Figure 19. L-shaped fitting................................................................................................35
Figure 20. Engine support, feeding hoses and valves.................................................35
Figure 21. Bottom part of tank with an L-shaped fitting...............................................36
Figure 22. Schematic of hydraulic system [3]................................................................37
Figure 23. Schematic of ignition system [3]...................................................................38
Figure 24. Coupling of o-ring............................................................................................38
Figure 25. Coupling of small dry seal.............................................................................39
Figure 26. Assembly of injector and injector cover.......................................................39
Figure 27. Coupling of thrust chamber and cooling jacket..........................................40
Figure 28. Coupling of 35 mm-hole dry seal..................................................................40
Figure 29. Coupling of 30.2 mm-hole dry seal..............................................................41
Figure 30. Coupling of injector assembly and thrust chamber assembly. ................41
Figure 31. Coupling of bolts.............................................................................................42
Figure 32. Coupling of engine with support bar............................................................42
Figure 33. Coupling of tube fittings.................................................................................43
Figure 34. Connection of hoses to engine.....................................................................43
Figure 35. Schematic of thrust force in the support bar...............................................45
Figure 36. Schematic of signal conditioning circuit. .....................................................47
7. INTRODUCTION
Rockets are nowadays a way of reaching high altitudes, whether it is to deliver
satellites to a low or high earth orbit, meteorological devices to the upper
atmosphere or other experimental equipment.
There are solid and liquid fuel
rockets: the solid fuel rockets were used in the early studies and the first rockets
built, but very quickly the liquid fuel rockets were introduced, due to their ability to
control the velocity and their precision. However, because of their increased
complexity, little work has been done on them in Colombia, as said in [5].
The purpose of this work, then, is to provide a basic practical work on liquid fuel
rocket engines, so that this becomes a first step in developing liquid fuel rockets,
parallel to the practical work on solid fuel rockets that is being developed by [1], [2]
and [5]. The idea is also to demonstrate that the liquid fuel rocket engines can also
be built in Colombia, just like the solid ones, using materials readily available to
any civilian.
The objectives of this project are to search (and modify if necessary) an existing
design on a liquid fuel rocket engine, build this design with commonly available
materials and with a low cost (if possible), to test this engine and to lay a
background with the knowledge obtained on liquid fuel rocket engines,for future
reference.
The advantage of the liquid fuel rocket over the solid fuel rocket is that, since the
liquid fuel rocket has better control and more accuracy, and it has a smoother
acceleration (due to the greater mass of fuel that it uses and of its components), it
is preferred for the big aerospace projects (including the manned missions). Since
the liquid fuel engine weighs up to 30% of the total empty weight, then the idea is
to load the rocket with the most fuel possible, and this limits its acceleration. That is
why the rocket ends up with a smoother acceleration but a greater range, which is
ideal to launch precision instruments. Besides, the simplicity of a solid fuel rocket is
8. IM-2006-II-01
8
lost in the fuel, which is a complex mixture with a special formulation and special
burning conditions. Also, since the pressure and acceleration are greater in a solid
fuel rocket, the casing must be thicker, thus increasing the empty weight. [7]
In this project, therefore, the basic equations for developing the different parts of
the engine will be presented and used to validate an engine design, which will be
built to show the feasibility and performance. This process is illustrated in the
following figure.
Figure 1. Flow of the project.
The project is the grey box that transforms the equations and parameters into an
engine that works according to the theory.
The restrictions associated with the finished product (the engine in this case) are
primarily ease of construction (including availability of materials and costs), weight
of the overall engine (which must be the lightest possible) and portability (or selfstanding, meaning that the overall construction is not restricted to work on a given
area but can be moved to any location with ease).
Some other criteria associated with this project is esthetics (overall aspect of the
finished product, which in this case is not so important), amount to be produced
(since this is not a finished product, it is not to be mass produced yet; just one or
maximum two units are to be produced) and safety (it must be high).
These elements are to be given a relative value, according to their importance to
the project.
9. IM-2006-II-01
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Restriction / Criterion Relative value
Availability of materials
0.2
Cost
0.2
Weight
0.1
Portability
0.1
Aesthetics
0.05
Production
0.05
Safety
0.3
The highest criterion is safety, as always, because safety will allow the repetition
and reproduction of any results and procedures made here. The next criteria are
availability of materials and cost, because one of the objectives of this project is to
build a real engine. The next criteria are weight and portability, which are also
important but not so much as the latter. If a lightweight and portable engine is not
found, then a heavier one will still work (although it is not the preferred option). And
the last two criteria are aesthetics and production. It is not a requirement for the
engine to be beautiful, but it can not be very ugly, because after all it must interest
other people to continue working on it. Production is not an important factor for
now, because mass production is not yet in sight, but eventually it will be.
The best solution is to build a rocket engine alone, not the whole rocket, and its
test stand. This way, the weight and portability are not important. Also, the project
becomes more accessible, because there is no need to build the rocket body and
launching equipment.
10. PROPERTIES OF LIQUID PROPELLANTS [6]
What is desired with the liquid propellants is that they have a high chemical energy
content and that the combustion gases have a low molecular weight. Due to this,
the best fuel / oxidizer mixture is not the stoichiometric one, but a mixture rich in
fuel which generate low molecular weight combustion products, such as H 2.
Besides this, the addition of metallic particles in suspension (such as beryllium or
aluminum) increases the specific impulse between 9 and 18%. However, these
particles can be toxic. Based on the information above, different experimental
analyses have determined that the best fuel and oxidizer mixture is hydrogen and
liquid fluorine respectively, with beryllium particles in suspension. The specific
impulse is 480 seconds with a chamber pressure of 1000 psi at sea level, and 565
seconds in vacuum, with an expansion ratio of 50 (relation between the exhaust
area and the throat area).
Physical properties
The desired physical properties in liquid propellants are the following:
•
Low freezing point: Desired property for operation at low temperatures, such
as in space.
•
High specific gravity: Is desired because it will allow the propellant to be
stored in a reduced space, reducing the total weight of the vehicle and
improving its aerodynamics.
•
Stability: It is convenient that the propellant does not decay or decompose
while it is in the storage tank or in the feeding pipes.
•
Heat transfer properties: It is desired to have a high specific heat, high
thermal conductivity and high boiling point, when they are used to cool the
nozzle and combustion chamber.
•
Pumping properties: A low vapor pressure is desired to reduce the risk of
cavitation in the turbomachinery (in case the propulsion system uses
11. IM-2006-II-01
11
turbomachinery). Besides, the propellant should have low viscosity so that
the system calibration is easier.
•
Temperature variation: The physical properties should vary little with
temperature variations, so that the calibration obtained is more precise.
The properties should not vary from time to time or between manufacturers. This is
why the propellant components and properties should be fully specified, so as to
guarantee uniformity in the properties. If these properties are to change, additives
can be added to the propellant.
Combustion properties
All propellants should start the combustion process readily to reduce the risks of
explosion and to make it more stable. Some propellants can start combustion when
they come in contact with each other. These are known as hypergolic propellants.
The use of these type of propellants greatly simplifies the combustion process,
because it eliminates the need for an ignition system.
If the propellants are not hypergolic they must be able to start the combustion with
a low energy level, so a low power ignition system will suffice. Smoke should not
appear in the combustion products.
Start And Ignition [6]
Initially the propellant flow is less than the operation flow and the mixture is
different than that during the operation. This period is known as the preliminary
stage. The low flow prevents the accumulation of unburned propellant inside the
combustion chamber, which can cause an explosion. The flow should not be the
full operational flow until the combustion has not been completely initialized.
The chamber conditions in this preliminary stage include a low injection velocity,
the vaporization, atomization and mixture of the propellants is incomplete. The
12. IM-2006-II-01
12
equivalence ratios close to the stoichiometric deliver a high heat generation ratio
and allow the chamber to reach to the operating conditions faster.
The start time for combustion in the chamber is affected by the following
parameters:
• The time required to open the valves. It can go from 0.002 to 1 second
depending on the valve type.
• The time required for the propellant to fill all cavities, pipes and injectors.
• The time needed to form jets of propellant and its atomization and mixture.
• The time required for the droplets to evaporate and burn. This time is
between 0.02 and 0.05 seconds. Once there is combustion in a particular
place, it takes certain amount of time for the flame to propagate and raise
the chamber temperature.
• The time needed to raise the pressure to a point where combustion can be
self sustained and then to the operating point.
The start time increases with an increase in engine size. Small engines usually
require several milliseconds, while bigger engines might require 1 second or more.
For a more reliable start, one of the propellants must arrive before the other to the
combustion chamber. For example, if a rich mixture is desired to start the engine,
the fuel must be injected first, and then the oxidizer.
13. DESIGN EQUATIONS
The momentum equation is mass times velocity. The change of momentum is the
one that produces force.
P = M •V
dP dm
dv
=
V +M
=F
dt
dt
dt
The first term in this equation corresponds to the change of momentum of the
escape gases coming out of the nozzle. The second term corresponds to the force
that the gases make in the exit area of the nozzle. The equation can be rewritten
like this:
&
F = mV + ( pe − pa ) Ae [1]
The thust (pushing force) is related to the pressure of the exhaust gases coming
out of the nozzle and the atmospheric pressure, since this net pressure applied in
the exhaust area of the nozzle adds to the overall thrust. Maximizing this
expression shows that the maximum thrust is achieved when the gases are
expanded to match the atmospheric pressure. An equivalent exhaust velocity can
be thus defined like this:
⎛ p − pa ⎞
&
u eq = u e + ⎜ e
⎟ Ae , so that the effective thrust is: F = m ueq .[1]
&
⎝ m ⎠
To characterize the rocket engines, the most important parameter is the specific
impulse. The impulse is the area under the curve of Thrust vs. time; it is the total
momentum transferred to the vehicle by the engine. It is a force multiplied by a
time (I = F * t = M * ueq ). The impulse per unit mass flow would be equivalent to ueq
or to
F
. The specific impulse is:
m
&
I sp =
u eq
.[1]
g
14. 14
IM-2006-II-01
This value is equivalent to the thrust generated by unit mass flow of fuel. In any
system of units this value is measured in seconds. It is also expressed by the
following expression:
I sp =
F
[5].
mg
&
The greater the specific impulse of the engine, the greater is efficiency in producing
thrust. Since the specific impulse depends directly of the exhaust velocity of the
gases, the less their molecular weight, the greater the specific impulse will be.[7]
Nozzle
For the operation of the nozzle, the flow must be assumed as isentropic,
compressible and unidimensional. Therefore, the following relations between the
properties of the gas and the stagnation properties can be obtained:[1]
To
γ − 1⎞ 2
=1 +⎛
⎜
⎟M
T
⎝ 2 ⎠
γ
p o ⎡ ⎛ γ − 1 ⎞ 2 ⎤ γ −1
= 1+ ⎜
⎟M ⎥
p ⎢ ⎝ 2 ⎠
⎣
⎦
1
ρ o ⎡ ⎛ γ − 1 ⎞ 2 ⎤ γ −1
= 1+ ⎜
⎟M
ρ ⎢ ⎝ 2 ⎠ ⎥
⎦
⎣
A
1 ⎛ 1
2
γ
= 2⎜
⎜ γ + 1 2 + { − 1}M
A* M ⎝
[
γ +1
⎞ 2 (γ −1 )
⎟
⎟
⎠
]
The stagnation properties (To, po and ρo) are the ones that are present in the
combustion chamber, since the speed of the gases is very small and can be
neglected. The other properties (T, p and ρ) are present where a given Mach
number is present. When the Mach number is one, the properties are those of the
throat (T*, p* and ρ*). The same happens for the throat and exhaust areas.
The nozzle has a convergent – divergent geometry, because when the flow is
subsonic the flow accelerates by reducing the area; when the flow is supersonic it
is accelerated by increasing the area. The narrowest section, called the throat, is
15. 15
IM-2006-II-01
where the flow has sonic velocity (Mach = 1). The following graph shows a
schematic nozzle and combustion chamber.[3]
Figure 2. Schematic of the combustion chamber and nozzle [3].
The throat area (A*) can be determined by the following equation:[3]
At =
m RT *
&
p* γ g
where m · is the mass flow, p* is the pressure at the throat, T* is the temperature at
the throat, R is the gas constant (R = Ru/Mw, Mw=molecular weight of the gas), γ is
the specific heat ratio and g is the acceleration of gravity.
Combustion chamber
The defining parameter of the combustion chamber is the characteristic length (L*),
which is defined as:[3]
L* =
Vc
At
where Vc is the volume of the combustion chamber and At is the area of the throat.
The combustion chamber cross-sectional area (Ac) should be at least three times
the nozzle throat area, so that the chamber is big enough compared to the throat,
and so the flow velocity in the chamber is low.
The volume of the chamber is given by:
16. IM-2006-II-01
16
Vc = Ac Lc + convergent volume
where the convergent volume is the convergent part of the nozzle. For small
nozzles, it can be reduced to:
Vc = 1.1 Ac Lc
considering that the convergent volume of the nozzle is about 1/10 of the chamber
volume. The chamber diameter should be, therefore, three to five times the
diameter of the throat.[3]
The combustion chamber thickness should be calculated to withstand the stresses
generated by the pressure inside. The expression used is:
σ=
pD
2t w
where σ is the stress applied to the chamber material, p is the inside pressure, D is
the chamber diameter and tw is the wall thickness. The stress applied must be way
less than the resistance of the material used to make the combustion chamber, to
take into consideration defects of the material and stress concentrations.[3]
Injectors
The injectors are in charge of introducing the fuel and oxidizer into the combustion
chamber in a liquid fuel rocket engine. They must atomize the propellants and
make sure that the fuel and oxidizer mix thoroughly in the combustion chamber.
One type of injector is the impinging stream, which is a hole through which the
propellants are introduced into the combustion chamber. The other type is the
spray nozzle, which is originally design for home oil burners. The following figure
shows both types of injectors.[3]
17. 17
IM-2006-II-01
Figure 3. Types of inj ection systems [3].
The mass flow of propellant can be determined by the following expression:[3]
&
m = C d A 2 gρ ∆p
where Cd is the orifice discharge coefficient (typically between 0.5 and 0.7), A is the
area of the orifice, g is the acceleration of gravity, ρ is the density of the propellant
and ∆p is the pressure drop across the orifice. The injection velocity is given by the
expression:
v = Cd 2g
∆p
ρ
Propellants
There are several combinations of fuels and oxidizers that can be used in a liquid
fuel rocket engine. However, [3] recommends the use of gaseous oxygen and a
hydrocarbon fuel as the best combination; it is readily available, reasonably safe,
easy to handle and inexpensive. The following table lists some liquid propellants.
18. 18
IM-2006-II-01
Figure 4. Performance of some liquid propellants [3].
The mixture ratio is defined as the flow of oxygen divided by the flow of fuel (O/F).
The highest temperature is achieved at the stoichiometric ratio of oxygen to fuel, as
it is shown in the following graph at 300 psi chamber pressure.[3]
Figure 5. Variation of flame temperature with O/F ratio [3].
19. 19
IM-2006-II-01
Because of this, it is recommended that the mixture be a little rich, so that the
flame temperature is as low as possible without losing performance.
The following graph relates the chamber pressure to the specific impulse for two
different propellants.[3]
Figure 6. Specific impulse as a function of chamber pressure [3].
With the help of this graph the specific impulse can be determined, by defining the
chamber pressure and the type of propellant to be used. Knowing this and the
required thrust for the desired engine lead to determine the total propellant flow
required for the desired operation. The fuel and oxidizer flow can also be
determined.[3]
m=
&
F
I sp g
r
r +1
&
m
&
mf =
r +1
& = mo + m f
&
&
m
&
&
mo = m
Where m is the total mass flow, m o is the oxidizer mass flow, m f is the fuel mass
flow and r is the oxygen-fuel ratio.
20. ROCKET ENGINE DESIGN [3]
The proposed design for a rocket engine has a combustion chamber pressure of
300 psi (2068 kPa) and a thrust of 20 pounds (9.07 kg = 88.9 N), using gaseous
oxygen and gasoline. It is assumed that the exhaust gases have a specific heat
ratio (k) of 1.2.
From figure 6 the specific impulse and oxygen to fuel ratio can be determined. The
specific impulse for this case is about 260 seconds, and the O/F ratio is 2.5.
Therefore, the mass flow rate is:
m=
&
20
F
=
= 0.077 lb / sec = 0.035 kg / s = 35 g / s
I sp 260
The fuel and oxygen flow rate are:
&
0.077
m
=
= 0.022 lb / sec = 10 g / s
O /F +1
3.5
m(O / F ) 0.077 * 3.5
&
&
mo =
=
= 0.055 lb / sec = 25 g / s
O /F +1
3.5
mf =
&
From [3] the chamber temperature is 5742°F (3172°C), or 6202 R (3445 K). The
temperature and pressure at the nozzle are:
T * = 0.909To = 0.909 * 6202 = 5650 R = 3132 K
p* = 0.564 Po = 0.564 * 300 = 169 psi = 1165 kPa
The nozzle throat area and diameter can now be determined. (Ru=1545.32 ft lb/(lb
2
R), Mm=24, R=65 ft lb/(lb R), gc=32.2 ft/s .
A* =
d* =
m RT * 0.077 65 * 5650
&
=
= 0.0444 in 2 = 0.286 cm 2
p * kg c
169 1.2 * 32.2
4A *
π
=
4 * 0.0444
π
= 0.238 in = 0.605 cm
21. IM-2006-II-01
21
From the following table the exhaust velocity, area (therefore diameter too) and
temperature can be determined [3].
Figure 7. Nozzle parameter for various chamber pressures [3].
ve = M e Ce = M e kR
Te
Tc = 2.55 1.2 * 65 * 0.606 * 6202 = 7835 ft / s = 2376 m / s
Tc
Ae
A* = 3.65 * 0.0444 = 0.162 in 2 = 1.045 cm 2
A*
4 Ae
4 * 0.162
de =
=
= 0.4542 in = 1.154 cm
Ae =
π
Te =
π
Te
T * = 0.606 * 6202 = 3758 R = 2088 K
T*
For the combustion chamber, L*=60 in (152.4 cm) is used. Therefore, the chamber
volume is:
Vc = L * A* = 60 * 0.0444 = 2.67 in 3 = 43.75 cm 3
It is also assumed that the chamber diameter dc is 5 times that of the throat. Now
the chamber length can be determined.
d c = 5d * = 5 * 0.238 = 1.19 in = 3.02 cm
Ac =
π
4
d c = 1.11 in 2 = 7.16 cm 2
2
Vc = 1.1Ac Lc → Lc =
Vc
2.67
=
= 2.18 in = 5.54 cm
1.1Ac 1.1 *1.11
22. IM-2006-II-01
22
The combustion chamber and nozzle will be made of copper. The thickness of the
wall can be calculated as follows, knowing the pressure and diameter of the
chamber, and assuming a resistance of copper (σ) of 8000 psi (55.14 MPa).
σ=
pd
pd 300 * 1.19
→t=
=
= 0.0223 in = 0.0566 cm
2t
2σ
2 * 8000
However, for safety factors, the thickness will be set at 3/32, or 0.09375 in (0.24
cm).
The average heat transfer from inside the combustion and chamber and nozzle
2
2
can be assumed to be 3 Btu/(in sec) (490.58 W/cm ), through the outer surface
area of the chamber and nozzle. The area is calculated as follows:
A = π (d c + 2t )Lc + area of nozzle cone
The area of the nozzle cone can be estimated as 10% of the total area. Therefore,
A = 1.1π (d c + 2t )Lc = 1.1π (1.19 + 2 * 0.09375) * 2.18 = 10.37 in 2 = 66.90 cm 2
The total heat transfer out of the combustion chamber and nozzle is:
& &
Q = qA = 3 *10.37 = 31 Btu / sec = 32.705 kW
Re =
Pr =
4m
&
4 * 0.035
=
π Dµ π * 0.0302 * µ
µcp
κ
hg = 0.026 Re 0.8 Pr 0.4
κ
D
To cool the engine with water, a temperature increase of 40 °F (4.44°C) is going to
be used. The required flow of water can be calculated:
& &
&
Q = mC p ∆T → m =
&
Q
31
=
= 0.775 lb / s = 0.352 kg / s
C p ∆T 1* 40
The velocity of the water is set to be 30 ft/s, so the annular flow passage must be
calculated as follows.
23. IM-2006-II-01
23
&
m = ρAv
A=
π
(
d − d1
4 2
d1 = d c + 2t
d2 =
2
2
)
4m
4 * 0.775
&
+ d 12 =
+ (1.19 + 2 * 0.09375 )2 = 1.475 in = 3.747 cm
πρv
π * 62 * 30
That makes the water flow gap to be (d2-d1)/2=0.0425 in (0.108 cm).
Hydraulic diameter:
(
[
4 * Area
4 * 0.25π Lc d 1 + d 2
=
Dh =
Wet perimeter
π Lc [d1 + d 2 ]
=
2
2
]) = d
+ d2 2
d1 + d 2
2
1
1.3775 2 + 1.475 2
= 1.428 in = 3.63 cm
1.3775 + 1.475
&
4m
4 * 0.352
=
= 12346
π Dµ π * 0.0363 * 0.001
µ c p 0.001 * 4.182
=
= 0.00747
Pr =
k
0.56
Re =
hl = 0.023 c p
m −0 .2 − 2 3
0.352
&
−2
−
Re Pr
= 0.023 * 4.182 *
*12346 0 .2 * 0.00747 3
A
0.25π 1.475 2 − 1.3775 2
(
)
= 0.6163
The fuel injector is going to be a commercial spray nozzle with a 75° spray angle,
preferably made of brass. The capacity of the spray nozzle is determined by the
fuel flow rate:
&
m = 0.022 lb / s = 1.32 lb / min = 0.22 gal / min
If an impringing jet injector had been used, the hole area would be calculated as
3
follows, assuming a Cd of 0.7, a density of gasoline of 44.5 lb/ft and a pressure
drop of 100 psi.
24. IM-2006-II-01
A=
mf
&
C d 2 gρ ∆p
24
0.022
=
= 0.000706 in 2 = 0.00455 cm 2
0.7 2 * 32.2 * 44.5 *100
If one hole is used, its diameter would be of 0.030 in (0.0762 cm) (use a number 69
drill); if two holes are used, their diameter would be 0.021 in (0.05334 cm) (number
75 drill).
For the oxygen injector, a velocity of about 200 ft/s (60.96 m/s) is desired (not
higher, because it is not desirable for the oxygen to reach sonic velocity).
Assuming a pressure drop of 100 psi (689.29 kPa), the pressure before the oxygen
enters the injector is 400 psi (2757.14 kPa) (adding the chamber pressure). From
[3] the oxygen density can be determined (at 68°F [20°C]).
ρ 2 = ρ 1 ⎛ p 2 p ⎞ = 2.26 3 = 36.27 3
⎜
⎟
⎝
1⎠
ft
m
lb
A=
kg
m
0.055
&
=
= 0.0175 in 2 = 0.1129 cm 2
ρ v 2.26 * 200
This is the area required for the oxygen injection, assuming incompressibility for
the gas flow. If 4 holes are used, then each one has a diameter of 0.0747 in (0.19
cm) (number 48 drill).
The fuel and oxygen jets should be at an angle of 45° with respect to the injector
face and intersecting at about ¼ inch (0.635 cm) from it.
25. CONSTRUCTION
The actual construction of the rocket engine required several things to be slightly
different than what was designed, to adjust to the available tools and supplies. All
hole – shaft assemblies were machined to a tolerance of H7n6, a transition fitting
to provide a tight fitting but allow for easy assembly.
Thrust chamber
The thrust chamber has the combustion chamber and the nozzle in one piece, for
ease of construction. The piece was made from solid bronze, because it is easier
to machine than copper and still has similar mechanical properties, desirable for
the piece.
The starting blank was a bronze cylinder of 1 ¾” (44.45 mm) diameter and 4” long
(100 mm). After the front was faced, the outside was machined to a diameter of 35
mm. A 5.5 mm hole was drilled through the blank. Then, successive holes were
drilled with ¾” and 1” to a depth of 60.4 mm (not counting the cone of the drill bit).
Then the inside was machined to achieve an inner diameter of 30.2 mm.
Figure 8. Inside of the thrust chamber
To machine the other side of the blank, a 30.2 mm cylinder was previously
machined to fit inside the hole, so that the blank could be tightened without
deforming the piece. A ½” drill bit was sharpened to a half angle of about 15°, to
machine the inside of the nozzle. With the blank in place, the front was faced to
26. IM-2006-II-01
26
make the piece have a length of 75.22 mm. Then this drill bit was used to drill a
cone, to a depth of 7 mm, then advancing until the larger diameter of the cone was
11.54 mm. For the outside of the nozzle, just the 13 mm diameter dent was
machined to a depth of 2.4 mm. The outside cone was not machined to leave more
material to use as a heat sink and for ease of manufacture, because the weight
was not an important issue.
Figure 9. Nozzle.
Injectors
The injector block (or combustion chamber lid, as it is named in the blueprints) was
also machined from a cylindrical blank of 1 ¾” (44.45 mm). The propellant manifold
part was machined first. This is the part where the propellants come from the
hoses and then goes to the injectors. After facing the blank, the entire cylinder was
machined to an external diameter of 44 mm. Then material was removed to
produce a cylinder of ¾” outer diameter and a length of 30 mm. A hole of 12 mm
and 30 mm depth (including the drill bit cone) was made. These dimensions
allowed for the tube fitting to be screwed and thicker walls to be used (3.5 mm
instead of 3 mm as shown in the blueprint). This change was made also because
the tube fitting had a diameter of ½”, so the 10 mm hole initially planned did not
work. Finally, a 3 mm wide channel was dug on the outer surface of the cylinder to
a depth of 1.5 mm, to allow an o-ring to be placed.
27. IM-2006-II-01
27
Figure 10. Fuel inlet in inj ector piece.
The other side was machined and faced to produce a piece of 37 mm in length.
Then a 30.2 mm cylinder was machined to a depth of 5.5 mm. This part would fit
inside the combustion chamber, so a tight fit had to be assured. All the flat surfaces
had to be given a flat finished, as shown on the blueprints. These faces would
come in contact with other surfaces to seal the engine, so a good surface finish is
in order. Because of the small thickness of the outer ring, no channel was dug for
an o-ring.
Figure 11. Injector holes.
The fuel injection hole was drilled with a 0.7 mm drill bit, using a mototool. It was
drilled through the center of the injector face. For the oxygen injection holes, a 1.9
mm bit was used. However, these holes were drilled at an angle with respect to the
fuel injection hole, to produce am impringing jet injector. The piece was held tight in
the drill stand, which was tilted at an angle of approximately 30° relative to the fuel
injection hole, so the drilled holes were at the mentioned angle.
28. IM-2006-II-01
28
Figure 12. Angle of injector holes.
Injector cover
Or oxygen chamber cover, as it appears on the blueprints. This piece started also
with a 1 ¾” solid cylindrical blank. First it was faced and then machined to a
diameter of 44 mm. Then it was machined to a diameter of 40 mm for a length of
28.5 mm, making sure the resulting tab was perpendicular. After this, a ¾” hole
was drilled through the center of the blank. The other side was faced and cut to
make the whole piece have a length of 30 mm. Then a 1” hole was drilled to a
depth of 25 mm (including the drill bit cone tip). After this, the inside was machined
to produce an internal diameter of 30 mm and a wall thickness of 5 mm in all faces.
No o-ring channel was made because the thickness of the piece did not allow for a
channel.
On the side, a ½” hole was drilled, as shown in the blueprints, for the incoming line
of oxygen. The a xis of the hole intersects with the axis of the piece. Using a ¾” drill
bit, a hole 2.5 mm deep was drilled, to make a guide for the injector tube fitting.
Injector tube conection piece
Or oxygen connection piece, as it appears in the blueprints. This piece was made
from a ¾” (19.2 mm) solid cylinder. After it was faced, the outside was machined to
a diameter of 19 mm and the inside was drilled with a 12 mm drill bit. It was then
cut to a length of 10 mm. The curve to fit the piece to the cooling jacket was made
using the milling machine with a bit of around 40 mm in diameter.
29. IM-2006-II-01
29
This piece was soldered to the injector cover, over the ½” hole on one side. A silver
weld was used to create a fillet around the piece. Then, the inside cylinder was
threaded to fit the ¼” NPT fittings.
Cooling jacket
Or water jacket piece, as seen in the blueprints. The cooling jacket was made from
a solid cylinder of 1 ¾” (44.45 mm) diameter and 100 mm length. First it was faced
and machined to an external diameter of 42.27 mm. Then a 13 mm hole was drilled
through the center. The other side was cut and faced to make the length of the
whole piece 73.82 mm. Then successive holes were drilled, using ¾”, 1” and 1 ¼”
drill bits, to a depth of 70 mm (counting the bit cone). Then the inside was
machined to achieve an internal diameter of 37 mm and allow for a wall thickness
of 2.4 mm at the flat face. Then, ½” holes were drilled through the side surface, as
shown in the blueprints. However, the holes were slightly off-center to produce
swirling in the incoming cooling water.
Figure 13. Inside of cooling j acket.
This piece could be made from a tube blank to avoid wasting most of the material.
However, for this project it was less costly to use a solid blank, because the
shortest tube sold was 1 m in length. Therefore, to build only one engine it is
30. IM-2006-II-01
30
cheaper to buy the solid blank, but to build several engines it is useful to buy the
tube.
Cooling jacket tube fittings
Or water connection piece, as seen in the blueprints. These pieces were made
from a ¾” (19.2 mm) solid cylinder. After it was faced, the outside was machined to
a diameter of 19 mm and the inside was drilled with a 12 mm drill bit. It was then
cut to a length of 10 mm. The curve to fit the piece to the cooling jacket was made
using the milling machine with a bit of around 40 mm in diameter. This curve was
milled eccentrically to allow fit with the holes of the cooling jacket and allow the
cooling water to swirl inside.
Closing supports
The round closing supports were made from a bronze plate 3” (76.2 mm) wide and
¼” (6.35 mm) thick. Two square plates were cut from this bronze plate. Successive
holes were drilled through the center, using ½”, ¾” and 1” drill bits. Using this hole,
the square plates were machined to become round using the turning machine.
For the combustion chamber cover round support, the inner hole was machined to
a diameter of 40 mm. Then a 44 mm diameter cylinder was machined to a depth of
3 mm. For the water jacket round support the inner hole was made 35 mm in
diameter. Then, a 42.27 mm diameter hole was machined to a depth of 2.6 mm.
In both supports 4 holes of ¼” diameter were drilled in a 66.14 mm diameter circle,
as shown in the blueprints. These holes had to be made a little bit bigger (5/8”) in
order to allow the bolts to pass freely.
The combustion chamber cover closing support was welded to the injector cover,
as shown in the blueprints, using a silver weld.
31. IM-2006-II-01
31
Figure 14. Weld of injector cov er.
The water jacket closing support was welded to the cooling jacket using too the
silver weld.
Figure 15. Weld of cooling j acket.
Seals
One o-ring (15mm diameter x 2 mm thickness) was used in the fuel manifold,
where the channel was dug. The o-ring had to be stretched in order to achieve the
required thickness for a tight fit and easy assembly.
For the other joints, rings of asbestos dry seal were used, to be able to resist high
temperatures. One dry seal was placed between the injector and the injector cover.
This seal had an internal diameter of 30 mm and external diameter of 44 mm.
32. IM-2006-II-01
32
And 2 dry seals were used between the injector assembly and the water jacket
assembly. Both seals had an external diameter of 76 mm; one had an internal
diameter of 35 mm and the other one an internal diameter of 30.2 mm. Both of
these seals had 4 holes of ¼” each, placed in a circle 66.14 mm in diameter and
with the same arrangements as the closing supports.
Figure 16. Dry seals.
Fuel tank
The fuel tank was made using a sch.80 petroleum tube, of 4 ½” inches of diameter
and 300 mm long. The tube had to be cleaned near the ends and a chamfer had to
be cut to allow for welding. The lids cut from a steel plate ¼” thick were 4 ½” in
diameter and had 2 holes of 12 mm in diameter. The holes were threaded to screw
the ¼” NPT tube fittings. These lids were also cleaned to allow for welding. The lids
were welded to the tube using a 7013 electrode.
33. IM-2006-II-01
33
Figure 17. Fuel tank.
Gas tanks
One oxygen tank and one nitrogen tank were needed for the assembly. These
tanks had to supply a pressure of at least 400 psi in order to reach the desired
thrust. The first choice was to use commercial tanks with high pressure regulators.
These tanks have gas stored at a pressure of about 1500 psi and have a capacity
3
of about 6 m . Therefore they could provide a steady 400 psi flow. However, the
high cost of the pressure regulator did not allow this option to be used. Therefore,
the other choice was to use small 3 L tanks with the oxygen and nitrogen at about
500 psi. The flow would not have a steady pressure, it would decrease
monotonically. However, for a few seconds (around 4) the average pressure would
be 400 psi. This set up would only allow one testing for a few seconds, while the
tanks empty, but it is a viable possibility.
Supporting structure
The supporting structure was made of steel angles (5 mm x 5 mm). The support
structure was built as a prism, with a square base of length 750 mm and a height of
1500 mm. In the middle, other steel angles were placed to support the fuel tank
and the engine. 4 long angles (1000 mm), 13 short angles (750 mm), 2 shorter
angles (500 mm) and smaller pieces (diagonal supports) were used. These angles
were joined by screws.
34. IM-2006-II-01
34
For the engine support, a cantilever bar was used. It was cut from an A-36
structural steel plate. Then, the hole-array was drilled to allow the engine to be
attached and the holes to hold the bar to the supporting structure.
Figure 18. Support structure.
Plumbing
The hoses used for the gas lines were ¼” stainless braided Teflon. 3 hose pieces
were needed: one 1000 mm piece and two 500 mm pieces. The hoses used for the
fuel lines were two SAE 100 rated for 190 bar, with a length of 500 mm each. All
hoses were fitted with ¼” NPT female threads. The hoses used for the water
cooling were 3/8” diameter plastic hoses.
The valves used were two stainless steel valves, rated for use with natural gas and
up to 1000 psi.
35. IM-2006-II-01
35
The fittings used were ¼” NPT male threaded. There were 6 straight fittings and 3
L-shaped fittings. There were also 2 hose fittings, to connect the water hoses, and
2 lids to close the filling hole and the drain hole in the fuel tank.
Figure 19. L-shaped fitting.
For the oxygen line, two straight fittings were screwed to each end of the valve.
The 1000 mm stainless braided Teflon hose was screwed to one fitting at one side
of the valve, and one of the 500 mm Teflon hoses was screwed to the other side.
For the nitrogen line, one 500 mm Teflon hose was screwed to a straight fitting,
which in turn was screwed to the top of the fuel tank. For the fuel line, one of the
SAE 100 hoses was screwed to an L-shaped fitting, which in turn was screwed to
the bottom of the tank. The other valve was connected with straight fittings on both
sides. The hose that was connected to the fuel tank was connected to one side of
the valve, and the other SAE 100 hose was connected to the other side of the
valve.
Figure 20. Engine support, feeding hoses and v alves.
36. IM-2006-II-01
36
Figure 21. Bottom part of tank w ith an L-shaped fitting.
The original design [3] required a nitrogen purge line, which is a line that carries
nitrogen directly into the engine to clean it of residual fuel after a burn has been
made. However, this purge line required a check valve to a void fuel from entering
this line. A check valve with the required resistance (about 500 psi) could not be
found, so in this project no purge line was used.
37. IM-2006-II-01
37
Figure 22. Schematic of hydraulic system [3].
Ignitor
The ignition system for the rocket engine was made using wire and cotton. Two
wires were pealed and left with a small gap (1/8”). A piece of cotton is put around
the wire where the gap is. When the engine is going to be started, the cotton is
soaked in fuel and electricity is allowed to pass through the wires. A spark is
created and it ignites the cotton. However, there should be oxygen passing through
the cotton for the ignition to be effective.
38. IM-2006-II-01
38
Figure 23. Schematic of ignition system [3].
ASSEMBLY
The rocket engine assembly procedure was as follows:
1. The structural assembly was joined, as the figure shows. The fuel tank was
placed and the cantilever bar was screwed to the assembly.
2. The o-ring was placed in the cavity of the injector piece.
Figure 24. Coupling of o-ring.
39. IM-2006-II-01
39
3. With the injector cover upside down, the small dry seal was placed in the
center cavity.
Figure 25. Coupling of small dry seal.
4. The injector piece was inserted in the injector cover. The side with the o-ring
was inserted first, until the surface of the injector is in contact with the dry
seal.
Figure 26. Assembly of injector and inj ector cover.
5. The thrust chamber was inserted in the cooling jacket assembly (previously
welded with the closing support).
40. IM-2006-II-01
40
Figure 27. Coupling of thrust chamber and cooling jacket.
6. The dry seal with the inner 35 mm hole was placed on the top of the injector
assembly (with the assembly still upside down).
Figure 28. Coupling of 35 mm-hole dry seal.
7. The dry seal with the inner 30.2 mm hole was placed on top of the cooling
assembly (with the thrust chamber inside).
41. IM-2006-II-01
41
Figure 29. Coupling of 30.2 mm-hole dry seal.
8. The injector assembly was placed on top of the cooling assembly, covering
the thrust chamber with the injector face and matching the holes for the
bolts.
Figure 30. Coupling of inj ector assembly and thrust chamber assembly.
9. Four ¼” bolts were inserted through the holes, from the bottom side.
42. IM-2006-II-01
42
Figure 31. Coupling of bolts.
10. The bolts (with the whole assembly) were inserted through the holes in the
cantilever bar and secured with nuts.
Figure 32. Coupling of engine w ith support bar.
11. The hose fittings were screwed to the cooling jacket connection tubes, one
L-shaped fitting was screwed to the top of the injector assembly and one
straight fitting and another L-shaped fitting were screwed to the side of the
injector assembly.
43. IM-2006-II-01
43
Figure 33. Coupling of tube fittings.
12. The oxygen hose was screwed to the connection on the side of the injector
assembly, the fuel hose was screwed to the fitting on top of the injector and
the water hose was connected to the hose fitting.
Figure 34. Connection of hoses to engine.
44. EXPERIMENTAL PROCEDURE
First, a leak test should be performed to check all joints. For the fuel line and
cooling water line, water can be used to pressurize the line and check for leaks. If
there are leaks in the joints, they must be tightened or Teflon tape must be put to
the thread prior to screwing. For the oxygen line, compressed air can be used to
pressurize the line.
Operating procedure
When the leak test is finish, the engine can be started. The procedure to start the
rocket engine is as follows [3]:
1. The test area must be clear and all personnel secured. A fire extinguisher
must be located in the test area where it can be easily reached.
3
2. The fuel is poured in the fuel tank. No more than 56 cm of fuel should be in
the fuel tank, to limit the time of operation of the engine to 4 seconds.
3. The ignitor is soaked in fuel and placed inside the combustion chamber and
be secured.
4. The cooling water is allowed to flow through the engine.
5. The oxygen line is opened a little bit.
6. The ignitor is energized. At this point there should be sparks coming out of
the engine.
7. The fuel line is opened a little bit. Now there should be flames coming out of
the engine and a low whistling sound.
8. Both oxygen and fuel lines must be rapidly opened completely to avoid
combustion instabilities. The noise produced is loud, but it is an indication of
good operation.
9. The exhaust should be transparent but the mach diamonds visible,
indicating that the mixture is stoichiometric. However, if the exhaust is bright
yellow, it means that the mixture is rich. Therefore, the fuel line should be
45. 45
IM-2006-II-01
closed a little bit. If the e xhaust is bluish, it means that the mixture is poor.
The oxygen line should be closed a little bit.
10. The engine should be allowed to run until the fuel runs out. That way, the
gaseous nitrogen purges the fuel line, and then the oxygen can be shut
down (should there still be oxygen).
11. If the engine has to be shut down before it runs out of fuel, then the fuel line
must be shut down first, then the oxygen line.
12. The cooling water should be left on for a couple of minutes to assure the
engine is effectively cooled down.
If a new test wants to be run, a new ignitor is needed. The tanks should be filled
again and the lines and engine inspected for leaks and possible damage. If any
piece shows any sign of damage it must be replaced with a new one.
Now that the operating procedure for the rocket engine has been established, the
measuring of the thrust can be made.
Thrust
To measure the thrust of the rocket engine an extension gauge is used in a long
bar [8]. The rocket engine on one side pushes the bar with a force that produces
deflection on it. The gauge, on the other end of the bar, measures this deflection.
The thrust force, then, can be inferred.
Figure 35. Schematic of thrust force in the support bar.
σ=
Mc 6 M
= 2 (For a rectangular cross section).
I
bh
46. 46
IM-2006-II-01
σ = Eε
The change in length of the gauge is
proportional to a resistance change, which
is in turn measured with a Wheatstone
bridge.
The gauge takes
the place of one
resistance. Knowing the values of the
resistances of the gauges, their deflection can be calculated, knowing the gage
factor. This factor relates the change in resistance with the deflection and the
nominal resistance of the gauge.
∆R
= fε
R
The voltage between the two nodes of the Wheatstone Bridge is calculated by the
formula:
⎡ R2
R4 ⎤
∆V = V ⎢
−
⎥ , where R1 is the gauge, and is represented as R+∆R. If
⎣ R1 + R 2 R 3 + R 4 ⎦
all the resistances are the same, this expression can be rewritten as : ∆V =
V∆ R
.
4R
The gauge to be used is a Vishay Micro-Measurements Student Gauge (CEA-06240UZ-120), that has a nominal resistance of 120.0 +/- 0.3% and a gage factor of
2.075 +/- 0.5%.
The thrust force measured can be represented by the following equation, which is
a combination of the equations shown before:
F=
bh 2 E 4∆V 4 1 2 −2 −1 1
= b h L f ∆V
6L
f
6
The propagation of error can be determined by the following equation [8]:
47. 47
IM-2006-II-01
UF
⎛U ⎞ ⎛ U ⎞ ⎛ U ⎞ ⎛ U
= ⎜ b ⎟ + ⎜2 h ⎟ + ⎜− 2 L ⎟ + ⎜− f
F
L ⎠ ⎜ f
⎝ b ⎠ ⎝ h ⎠ ⎝
⎝
2
2
2
2
⎞ ⎛ U ∆V ⎞
⎟ +⎜
⎟ ⎝ ∆V ⎟
⎠
⎠
2
And the error of the ∆V term is as follows:
2
2
U ∆V
⎛U ⎞ ⎛U ⎞ ⎛ U ⎞
= ⎜ V ⎟ + ⎜ ∆R ⎟ + ⎜ − R ⎟
∆V
⎝ V ⎠ ⎝ ∆R ⎠ ⎝ R ⎠
2
The following table shows the given values for the different parameters and the
expected values of Thrust force, stress, strain, ∆R and ∆V.
F (N)
L (m)
b (m)
h (m)
E (GPa)
R (ohms)
F
V (V)
R2 (ohms)
R3 (ohms)
R4 (ohms)
88
0,59
0,05
0,00635
200
120
2,075
12
120
120
120
sigma (Mpa)
154,514229
deformation
(micro)
772,5711451
delta R (ohms)
delta V (V)
0,192370215
0,004805404
The voltage obtained is then passed through a low pass filter with a cutoff
frequency of 5 Hz, to eliminate noise and combustion instabilities that are not
desirable for this measure. It is amplified by a factor of 1000 (using 3 consecutive
10-fold amplifiers), so the obtained expected voltage is 4.805 V. This means that
the voltage measured must be multiplied by a factor of 18.3127176, to obtain a
value of 88 N, which is the expected thrust.
Figure 36. Schematic of signal conditioning circuit.
48. 48
IM-2006-II-01
The following table shows the values of the uncertainties (errors) of each
parameter and the resulting uncertainty of the measurement.
Uv
UdeltaR
UR
0,05
0,00057711
0,36
Ub
Uh
UL
Uf
UdeltaV
2,50E-05
2,50E-05
5,00E-04
1,04E-02
2,85754E-05
UF (%)
UF
1,12019629
0,985772735
This shows that the thrust measured will have an uncertainty of 1.12%. If the
expected thrust is of 88 N, then the uncertainty will be of ±0.985 N.
This data is expected to be taken by a data adquisition card, such as a 12-bit
Labjack card. The expected resolution can be obtained as follows [8]:
∆V =
V
, where V is the feeding voltage and n is the number of bits of the card. If
2n
the card is powered with 12 V, then the resolution is of 0.00292 V. When
multiplying this by the factor of 18.3127176, a resolution of 0.0536 N is obtained.
When taking this resolution and the uncertainty, the overall uncertainty of the
measurement is obtained.
U measurement = U F + Re s 2 = 0.987
2
The overall resolution of the adquisition system will therefore be ±0.987 N.
The purpose of this work is to measure the thrust force. However, more
measurements can eventually be made. Such measurements include chamber
temperature and pressure.
49. 49
IM-2006-II-01
Chamber temperature [9]
Since this engine is water cooled, the increase in the
temperature of the water as it comes out of the engine
(Tout-Tin) can be used to infer the inner combustion
chamber temperature (Tc). The heat generated from
the inside of the combustion chamber is transferred
through convection to the chamber wall, then by
conduction through it and then by convection to the
cooling water.
The heat transferred to the water is determined by the equation:
& &
Q = mC p (Tout − Tin )
This heat is transferred through the hot gas and the water by convection and
through the thrust chamber wall by conduction. The following equations illustrate
this.
&
Q = h g A (Tc − Twall ,gas )
& k A
Q = wall (Twall, gas − Twall,liquid
tw
&
Q = hl A(Twall,liquid − Tliquid )
Convection
)
Conduction
Convection
Therefore, by knowing the entrance and outlet temperatures of the cooling water,
and by using an average temperature for the liquid, the temperature of the wall at
the liquid side can be determined. With this temperature, the temperature at the
gas side of the wall can also be determined. And with this, the temperature of the
inside gas can be determined.
The convection coefficients can be calculated for both the liquid and the gas, using
the following correlations. For the gas convection coefficient:
50. 50
IM-2006-II-01
Re =
Pr =
&
4m
π Dµ
µcp
κ
hg = 0.026 Re 0.8 Pr 0.4
κ
D
And for the liquid convection coefficient:
hl = 0 .023 c p
&
m − 0. 2 − 2 3
Re
Pr
A
The following table shows calculations made based on expected values.
T in (K)
Q dot (W)
hl (W/m^2 K)
hg (W/m^2 K)
m dot water
(kg/ s)
Cp water (J/kg
K)
ro (m)
ri (m)
A liquid (m^2)
A gas (m^2)
k wall (W/mK)
L (m)
298
12000
9576,14
731,87
0,352
T out (K)
T liquid (K)
T wall liquid (K)
T wall gas (K)
306,1518195
302,0759097
489,0883049
502,2964239
Tc (K)
3338,177634
4182
0,0175
0,0151
0,0067007
0,00578175
385
0,0554
Therefore, assuming that the temperature of the water at the entrance of the
cooling jacket is 298 K and the exit temperature is 306 K, the chamber temperature
would be expected to be around 3300 K, which is a typical value for these engines.
Pressure
The measuring of pressure involves placing manometers directly on the areas of
interest, such as the gas tanks, fuel tank, engine manifold and combustion
chamber. This last measure requires careful design, because it involves modifying
the combustion chamber and altering the mechanical properties of the materials.
For further projects it is a good performance parameter.
51. SUPPLIERS AND COSTS
One of the purposes of this work is to provide an experience and to leave
knowledge for future projects, a list of suppliers and the costs involved in making
this engine will be shown.
Cost
The following costs are in Colombian Pesos, and may vary with time.
Engine parts:
•
300 mm solid bronze bar, 1 ¾” diameter:
$ 87,200
•
100 mm solid bronze bar, ¾” diameter:
$ 5,400
•
250 mm bronze plate, 3” x ¼” cross section:
$ 25,000
•
1 O-ring, 15mm x 2mm:
$ 1,000
•
3 dry seals:
$ 6,000
•
4 ¼” UNC bolts and 4 nuts:
$ 2,000
•
Silver welding:
$ 22,000
TOTAL:
$ 148,600
Hoses and valves:
•
2 stainless steel valves:
$ 41,800
•
2 m ¼” stainless threaded Teflon hose:
$ 67,100
•
1 m ¼” SAE 100 hose (Hca R-1):
$ 10,800
•
4 Capsules for R-1 hose:
$ 11,200
•
6 Capsules for Teflon hose:
$ 14,200
•
10 Female fittings, ¼” NPT:
$ 31,400
•
3 L-shaped fittings, ¼” NPT:
$ 25,100
•
6 straight fittings, ¼” NPT:
$ 13,600
TOTAL:
$ 215,200
52. IM-2006-II-01
52
Support structure:
•
15 m steel angle:
$ 150,000
•
600 mm A-36 plate, ¼” thick:
$ 11,000
•
Screws and nuts:
$ 4,000
TOTAL:
$ 165,000
Electronics:
•
Protoboard:
$ 13,000
•
Resistances:
$ 1,000
•
1 Operational amplifier:
$ 1,300
•
Wire:
$ 5,000
TOTAL:
$ 20,300
Fuel and Tanks:
•
300 mm Sch.80 tube:
$ 25,000
•
2 ¼” thick steel plates, 4 ½” diameter:
$ 15,000
•
Oxygen tank:
$ 75,000
•
Nitrogen tank:
$ 75,000
•
1 gal of Fuel:
$ 7,000
TOTAL:
$ 197,000
TOTAL COST:
$ 746,200
Suppliers
The following is the list of suppliers used in this project.
Bronze material:
•
Distribronces Seco Ltda. Diagonal 15 # 22-28. Tel: 247 5644. Bogotá D.C.
54. CONCLUSIONS AND RECOMMENDATIONS
This project was made up until the construction of the engine and support
structure. Although the testing could not be done, an important part of the
objectives was reached.
The rocket engine made proves that a liquid fuel rocket engine can be made in
Colombia with materials readily available to any person interested in doing so. This
is one step taken away from the amateur level and one step taken towards a more
serious approach to the liquid rocketry area.
The support structure and testing equipment is already built and ready to use.
Further projects related with this one could take advantage of this apparatus, to
take a second step in the study of liquid fuel rocket engines. Now that there is a
first practical approach to the building of this type of engine, it is more likely to have
more projects extend the reach of this one.
This first approach to liquid fuel rocket engines can also allow for larger scale
models to be built and tested. Engines that produce a thrust of up to 220 N could
be tested in the actual test structure, where the strain gage reaches its maximum
deformation. However, just by changing the cantilever bar that supports the engine,
bigger engines could be tested.
Therefore, it is recommended that further projects be developed to measure the
performance of the rocket engine. After this is done, and the equations are proven
good, larger engines could be built and the construction of flight weight engines
could be considered.
55. BIBLIOGRAPHY
1. DUQUE, Carlos. Modelo y Caracterización de Patrón de Flujo en un
Sistema Propulsivo. Thesis Project for M.S. in Mechanical Engineering,
Universidad de los Andes, 2003.
2. GARZÓN, Diego. Análisis y Diseño de la Cámara de Combustión de un
Pequeño Cohete. Thesis Project for M.S. in Mechanical Engineering,
Universidad de los Andes, 2002.
3. KRZYCKI, Leroy J. How to Design, Build and Test Small Liquid-Fuel Rocket
Engines. Rocketlab, China Lake, California, 1971. Versión electrónica
descargada de http://www.gramlich.net/projects/rocket/.
4. HILL, Philip. Mechanics and Thermodynamics of Propulsion. Addison
Wesley, Reading, Massachussets, 1992.
5. JIMÉNEZ, Ál varo. Diseño y Simulación de un Cohete de Carburante Sólido.
Thesis Project for B.S. in Mechanical Engineering, Universidad de Los
Andes, 2003.
6. SUTTON, George P. Rocket Propulsion Elements. John Wiley & Sons, New
York, 2001.
7. COCKBURN, Sir Robert. La propulsion por cohetes y la investigación
espacial. Taken from: Endeavour (Londres), Vol. 26 No. 97 Enero 1967. p.
21-26.
8. BECKWITH, Thomas G. Mechanical Measurements. Fifth Edition. AddisonWesley Publishing Co., New York, 1995.
9. INCROPERA, Frank P. Fundamentals of Heat and Mass Transfer. Fifth
Edition. John Wiley & Sons, Hobokem NJ, 2002.
56. ANNEX: BLUEPRINTS
The following pages show the blueprints for the different parts of the engine, pipes
and support structure.
