5_4_2 100g payload propulsion analysis_design

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					100 g Payload – Lunar Descent – appendix A                                                                          Section 5.4.2, Page X

Propulsion System Design

                                             Propellant and Propulsion System Selection
Selection of the Lunar Lander Propulsion system began with a preliminary
propellant/propulsion system type vs. required propellant mass study to determine the
relative masses between the available choices. Using the ideal rocket equation as a
starting point, and assuming a vehicle inert mass fraction, finert, along with a mission ∆V
and payload mass, mpay it is possible to derive an equation that computes the required
propellant mass for a given propulsion systems specific impulse, Isp.Humble


Assuming a payload mass of 85 kg, minimum and maximum finert values of 0.1 and 0.25
based off of historical data and a ∆V of 1950 m/s, Eq. (5.4.2-1) was used to compute the
two dashed lines of propellant mass vs. Isp for the two inert mass fractions shown in
Figure (5.4.2-1).





                               160           Mono-Prop
        Propellant mass [kg]





                               60                                                             Bi-Prop


                                150    200         250            300   350             400             450   500       550     600
                                                                              Isp [s]

                                      Fig. (5.4.2-1) Propellant mass required vs. propulsion system Isp
                                                            (Thaddaeus Halsmer)

                                                            Author: Thaddaeus Halsmer
100 g Payload – Lunar Descent – appendix A                           Section 5.4.2, Page X

Because the inert mass fractions were chosen as historical limits, when data points were
plotted for various propulsion systems empirical Isp values, they fall within this
envelope.    The result of propellant mass vs. Isp study shows that an exponential
propellant mass penalty is paid for choosing a propulsion system with a lower Isp.

Assuming that lunar descent should conclude with a fully controlled soft landing leads to
the requirement of an engine with variable thrust. Varying the thrust of a rocket engine is
done by changing the mass flow rate of propellants as seen in the vacuum thrust equation

where Isp is assumed constant,        is the propellant mass flow rate and go is the Earth
gravity acceleration constant.      Mono-propellant, bi-propellant and hybrid propulsion
systems were all initially considered because they fulfill this requirement by varying the
propellant mass flow rates using flow control devises in the propellant feed systems.
Both mono-propellant and hybrid propulsions systems have the added advantage of being
throttled by controlling only a single fluid mass flow rate where in a bi-propellant engine
both oxidizer and fuel flow rates must be controlled simultaneously to maintain the
correct oxidizer to fuel ratio.

An additional constraint on the propulsion system selection was that there are currently
no commercially available rocket engines sold that meet the variable thrust requirement
and scale needed for this mission. This made the cost of development of the chosen
propulsion system another significant factor. Because of the complexity of bi-propellant
rocket engines and their associated feed systems it is not realistic to suggest that such a
system could be developed with sufficient reliability within the time and cost constraints
in this project, therefore the bi-propellant option was eliminated as a possibility on this

Based on expert advice it was determined that an H2O2 / Polyethylene Radial Flow
Hybrid propulsion system of appropriate scale could be developed within one year and

                                  Author: Thaddaeus Halsmer
100 g Payload – Lunar Descent – appendix A                                     Section 5.4.2, Page X

for less than $250000.              Using CEAGordon we determined that this system could
easily achieve a vacuum Isp >300 seconds. Using this information and the associated
propellant masses shown in Fig. (5.4.2-1) the H2O2 / Polyethylene hybrid propulsion
system was selected over the mono-propellant system because of its significant propellant
mass savings and low cost of development.

                     Radial Flow Hybrid Rocket Engine Overview
Traditional hybrid rocket engines contain a solid fuel grain in the combustion chamber
and liquid oxidizer is injected into axial ports in the fuel grain, however, this
configuration leads to engines that have a high Length/Diameter and are not well suited
to our compact landing vehicle. Because of the dimension constraints an experimentally
proven radial flow configuration was chosen that allows the combustion chamber to have
a much larger diameter and shorter length.Heister

                      Fig. (5.4.2-2) Radial Flow Hybrid engine configuration
                                       (Thaddaeus Halsmer)

Figure (5.4.2-2) presents the architecture of a radial flow hybrid rocket engine. It also
shows how the oxidizer is injected around the combustion chamber perimeter between
the two Polyethylene fuel plates, with the combustion gasses exiting through the hole in
the lower fuel grain plate and into the nozzle.

                      Chamber Pressure & Feed System Selection
Space engines enjoy the benefit of being able to achieve high efficiency at relatively low
chamber pressures and one of the benefits of this is that the entire oxidizer feed system
mass can be reduced because of the low operating pressure. CEA was initially used to do
a preliminary Isp sensitivity study to reductions in chamber pressure and it was found that

                                   Author: Thaddaeus Halsmer
100 g Payload – Lunar Descent – appendix A                           Section 5.4.2, Page X

benefits of reducing the chamber pressure far outweighed the minimal change in Isp. A
key assumption that was made in determining the chamber pressure operating range was
that the engine would be designed for a 10:1 throttle ratio which has been experimentally
proven to be possible without extraordinary difficulty.Sutton       Because the chamber
pressure of the engine changes by almost exactly the same factor that the thrust is
throttled, we assumed that the change in chamber pressure would be 10:1 for an engine
with 10:1 throttle ratio. Based on this the maximum combustion chamber pressure, at
maximum thrust, will be 10 times the minimum possible chamber pressure at which
steady combustion can be maintained. While the exact minimum chamber pressure will
need to be experimentally determined for this particular design hybrid engines using the
same propellants have demonstrated steady operation at chamber pressures as low as 0.21
MPa therefore that will be the assumed minimum chamber pressure for this design
making the maximum steady state chamber pressure 2.1 MPa. Based on these pressures
the optimum feed system architecture is a gas-pressurized propellant feed system. This is
because of its ability to supply the required oxidizer injection pressures without the added
complexity of pumps.

                      Mean Isp and Combustion Chamber Sizing
Sizing of the combustion chamber for the Radial Flow Hybrid is based on the dimensions
of the fuel grains shown in Fig. (5.4.2-2) and these are dictated by the fuel grain
regression rate, the desired oxidizer to fuel ratio and thrust.       Hybrid engine fuel
regression rates can be modeled using Equation (5.4.2-2)


where r is the fuel regression rate in m/s, Go is the total oxidizer mass flux in kg/m2-s,
and a and n are empirically derived constants. By taking Eq. (5.4.2-2) and multiplying it
by the fuel grain density ρf and the burn area Ab, the equation for the fuel mass flow rate
is given as Equation (5.4.2-3).


                                  Author: Thaddaeus Halsmer
100 g Payload – Lunar Descent – appendix A                                 Section 5.4.2, Page X

                         Fig. (5.4.2-3) Fuel grain dimension definitions
                                       (Thaddaeus Halsmer)

Using the variable definitions in Fig. (5.4.2-3) along with the definition of Go and
substituting them into Eq. (5.4.2-3) yields an expression for the fuel mass flow rate as a
function of the fuel grain/combustion chamber geometry


Assuming that all terms in (5.4.2-4) are constant except h, which is changing at a rate
proportional to the fuel regression rate r, taking its inverse, lumping all constant terms in
to a single term k, and multiplying by the oxidizer mass flow rate gives Eq. (5.4.2-5)


which is an expression for how the engines oxidizer to fuel ratio changes as the fuel
grains regress. In Eq. (5.4.2-5), n is a constant that has been empirically proven to be
approximately 0.8. From Eq. (5.4.2-5) we can see that the O/F ratio will change as the
engine burns and this directly affects the engines efficiency or Isp. Because h is an
increasing function of time the O/F ratio will be increasing and because maximum Isp
occurs near the stoichiometric O/F ratio it is necessary to size the fuel plates so that
initially the engine is fuel rich and as the oxidizer fraction increases through the burn
time the mean Isp is maximized.

                               Author: Thaddaeus Halsmer
100 g Payload – Lunar Descent – appendix A                                                Section 5.4.2, Page X

Using CEA integrated into a Matlab script along with an empirical fuel regression rate of
0.000559 m/s                      and Eq. (5.4.2-5) it was possible to iteratively find an initial O/F
ratio that maximized the mean Isp over the burn time. Figure (5.4.2-4) is an example of
the program output, over a 200 s burn time, and it demonstrates the significant O/F shift
along with the corresponding changes in Isp.




              Isp [s]





                              0    2      4      6     8      10       12   14    16      18   20
                                                           O/F ratio

                                   Fig. (5.4.2-4) Isp vs. O/F ratio for 200 s burn time
                                                  (Thaddaeus Halsmer)

Through the previously discussed analysis an initial O/F ratio was found. Using Eq.
(5.4.2-3) along with the initial O/F ratio, Isp, and thrust the initial dimensions of the fuel
grains are determined and from these the dimensions of the combustion chamber

                                               Nozzle Sizing Analysis
For rocket engines operating in space, as the nozzle area ratio Aexit/Athroat is increased,
their Isp also increases. However, the cost of increasing the Isp with a increase in nozzle
area ratio is the added mass and size of the physically larger nozzle. Because an increase
in Isp reduces the required propellant mass there exists theoretically a optimum nozzle
mass and corresponding area ratio. To make a preliminary examination of tradeoff
between the nozzle area ratio and the propellant mass required for lunar descent a Matlab
script was written that used CEA to compute the Isp of the engine for a given area ratio
along with the corresponding nozzle mass and propellant mass. Thrust and burn time
were kept constant during this analysis and only the nozzle area ratio was varied. The
                                              Author: Thaddaeus Halsmer
100 g Payload – Lunar Descent – appendix A                                                          Section 5.4.2, Page X

mass of the nozzle was determined using an empirically derived equation that estimates
the mass of a carbon phenolic hybrid engine nozzle.Humble Inputs for this equation are the
nozzle area ratio , and total burned propellant mass mprop.
       Nozzle + Prop mass [kg]

                                                                          Pc = 1.72 MPa, 2000N thrust



                                     50                 100                      150                      200
                                                          nozzle area ratio 
                                          Fig. (5.4.2-5) Mass penalty vs. nozzle area ratio trade
                                                          (Thaddaeus Halsmer)

Figure (5.4.2-5) is an example of the output generated by the script. It shows that the
minimum combined mass of the nozzle and propellant occurs at an area ratio of
approximately 150. Based on this analysis an area ratio of 100 was chosen because there
is only a approximately 0.5 kg mass increase by using the smaller nozzle area ratio and
its dimensions were near the maximum that could be integrated into the vehicle.

The throat area of the nozzle is computed as a function of the engine thrust F, coefficient
of thrust Cf, and the chamber pressure Po using Equation (5.4.2-6)


                                                    Author: Thaddaeus Halsmer
100 g Payload – Lunar Descent – appendix A                            Section 5.4.2, Page X

where Cf is computed using CEA and the thrust correction factory        was assumed to be
0.96. Sutton   Once the nozzle area ratio is known and along with the throat diameter the
exit diameter is easily computed and the length of the nozzle estimated using Eq. (5.4.2-
7) which was derived from empirical data for 80% bell contour nozzles


where Dt is the throat diameter of the nozzle derived from Equation (5.4.2-6).Sutton

                                Author: Thaddaeus Halsmer