1 - Purdue University



Propulsion

Nomenclature

mf = final vehicle mass [kg]

mi = initial vehicle mass [kg]

c = exit or exhaust velocity of propellant [m/s]

ΔV = change in velocity [m/s]

Isp = specific impulse (engine efficiency) [sec]

go = earth gravity [m/s2]

mprop = mass of propellant [kg]

1 Launch Vehicle

1 Configuration Selection – Chris Ulrich

From past designs, we are choosing a reference point for initial sizing of our launch vehicle. Therefore, the launch vehicle is better tailored to our mission. Lifting the huge mass of the habitat module and its nuclear propulsion system a heavy-lift launch vehicle is needed. Three reference launch vehicles were considered; the Saturn V, Space Shuttle, and Energia. The Space Shuttle and Energia are initially ruled out due to their low payload capabilities. Further investigation of the Saturn V lead to Boeing concepts[i] of the Saturn V used for the Apollo missions. The Boeing concepts of the Saturn V allow for greater payload capabilities. The Saturn V concepts prove a good reference, but to design for our specific mission a new launch vehicle needs to be designed.

To design our launch vehicle a number of variables were addressed. The first variables addressed deal specifically with sizing the launch vehicle. To size the launch vehicle the total launch vehicle weight must be determined. The total weight is determined from the basic rocket equation[ii] shown in equation ‎F–1.

|[pic] |‎F–1 |

In equation ‎F–1 above, ΔV is the change in velocity imparted by the vehicle, Isp is a performance parameter of the specific rocket engine being used, go is the gravitational constant of the earth, minitial is the total initial mass of the rocket and mfinal is the total final mass of the rocket.

The first variable in the rocket equation, change in velocity, is determined using empirical data2. The empirical data accounted for many of the losses by adding ΔV, but only for a 185km orbit. A Hohmann transfer was used to give the additional ΔV for a 500km Earth orbit. A margin was also added to account for the effect of a different launch vehicle and therefore different drag effects as well as to give additional ΔV for the launch orbit maneuver other than a Holman transfer. The resulting ΔV we chose is 10.25 km/s.

The engines are needed to determine the engine performance parameter used in the rocket equation. From research we conducted, we choose the F1 produced by Boeing Rocketdyne and the RD-180 from Pratt & Whitney/ NPO Energomash. Both of these engines are excellent first stage engines because of their low expansion ratio, high thrust and proven reliability. We are considering both for the final concept to give good comparison and ensure the best design.

The ratio of the final mass to the initial mass, also considered the mass ratio, is determined using the intermediate inert mass ratio. Employing the inert mass ratio, we focus on the mass of the tanks and propulsion system as oppose to including the payload as a factor. Therefore with the set payload we can focus on clarifying the components of the launch system specific to propulsion. We defined the inert mass ratio as [pic]. The inert mass ratio was approximated using empirical data of the reference launch vehicles discussed earlier. Inert mass ratio results in a method of relating the final mass to the total initial mass of the launch vehicle used for sizing our launch vehicle.

Initially, we considered a single stage to orbit launch vehicle. Using the rocket equation (eq. ‎F–1) we can find the total launch vehicle mass from the known or empirically approximated values. Due to the enormous initial weight of the launch vehicle a single stage was deemed unacceptable. Fig. F.1 graphically displays the huge advantage of staging. The change in velocity for our mission is 10.25 km/s, as discussed earlier. A multi-stage vehicle provides a great advantage in gross lift-off weight for a change in velocity of 10.25 km/s. The cost of weight savings must also be compared to the complexity and safety of the launch vehicle. The greater risk is simply out weighted, literally, by staging our vehicle. The single stage analysis was quickly converted to a two stage vehicle using strap-on boosters for comparison. The two stage vehicle still resulted in initial launch vehicle masses much greater compared to our reference designs. Therefore we moved to an even more complex three stage launch vehicle. [pic]

Selecting a three stage vehicle a new variable is introduced, the configuration, we addressed this variable next. To select the best configuration for the launch vehicle we looked at 150 different configurations. We generated the different configurations from three variables: the number of boosters, main core engines and third stage engines.

Table ‎F.1 Configuration Number assigned Variables

|Configuration Number |Number of |

| |Core |

| |Engines |

| |(1st & 2nd |

| |Stages) |

This equation is beyond the scope of our analysis; therefore we approximated the center of pressure for each cylinder to be at its midpoint. Center of mass is calculated from the summation in equation ‎F–3 below.

|[pic] |‎F–3 |

Comparing the center of pressure location to the center of mass resulted in a center of pressure well above the center of mass. Therefore our launch vehicle is innately unstable. Fins can be added to the bottom of the launch vehicle to move the center of pressure, but since the effect of the engines gimbal motion is not known fins were not explored further.

Launch vehicles today seem to get around the vehicle having inert stability by applying a gimbaled control system. For a simple analysis of the engine gimbals’ effect, the equation ‎F–4 below was integrated. This analysis method was provided by Dr. S. Heister.

|[pic] |‎F–4 |

In equation ‎F–4 the [pic] is torque, I is the moment of inertia and [pic] is the yaw angle acceleration or angle the rocket rotates horizontally if pointing vertically per second squared. Equation ‎F–4 can be integrated to provide the yaw angle as a function of time as shown in equations ‎F–6 and ‎F–7.

|[pic] |‎F–5 |

|[pic] |‎F–6 |

This is done assuming the initial conditions are zero. The torque of the rocket is know with a given gimbal angle of rocket nozzle. This is determined from the simple equation in equation ‎F–7.

|[pic] |‎F–7 |

In equation ‎F–7, θ is the gimbal angle, F is the thrust of the engines and xm in the distance to the center of mass. The torque is approximately 1.8e8 N-m with an 8o gimbal.

The moment of inertia was approximated as a simple cylinder with evenly distributed mass. This simple analysis gives the general magnitude of the yaw angle achieved in one second; the yaw angle was calculated to be much less than a thousandth of a degree. A more in-depth analysis is needed, but an initial look proves major stability problems for our current launch vehicle design. The stability problem can be alleviated by separating the launches to reduce the payload length and mass (as with current launch vehicles) and therefore reduce the overall launch vehicle mass. Another solution is to add fins to provide the launch vehicle with more of an inert stability.

2 Engine Selection – Chris Krukowski

The engine selection process began with examining different engines that are currently used on launch vehicles. We compiled a list of some of the more common engine types and then made a selection based on certain criteria. This list can be seen in .

Table ‎F.2 Initial Engine Comparison

|Engine |Thrust(kN) (SL) |Isp (s) (SL) |EngineMass (kg) |Propellants |

|SSME |1,668 |363 |3,177 |LOX/H2 |

|SRM |14,679 |237 |86,183(empty) |Solid |

|RD-170 |7,246 |309 |9,750 |LOX/Kerosene |

|RD-180 |3,826 |311 |5,393 |LOX/Kerosene |

|F-1A |6,672 |270 |8,098 |LOX/Kerosene |

From these engines the RD-170 was eliminated because it was a Russian build engine. Eventually the RD-180 and the F-1A were chosen as the two primary engines types to consider for the main core engine. The SSME was also considered for a time but due to the problem with storing large amounts of liquid hydrogen it did not last long as a viable option for the main engine. Instead it was used in as the third stage engine when it became clear that a separate third stage would be needed.

After the selecting the RD-180 and the F-1A, a trade study was conducted to compare the two engines. Chris Ulrich worked more on the F-1A and more information about what was done there can be found in his appendix. As for the RD-180, what was originally envisioned was a central core similar to that of a Saturn V rocket with some SRM engines strapped on.

3 Tank Sizing – Chris Ulrich

The tanks for the launch vehicle were sized using the same method developed my Marina Mazur. Details of Marina’s method are discussed later in appendix F. The difference in the analysis for the launch vehicle was the much larger load on the tanks and the different propellants used with the engines. The different propellant kerosene allowed for a lighter tank to be used. The lighter tank was Aluminum instead of the stainless steel used by the rest of the tanks.

2 Transport Vehicle

1 MITEE-B Engine – Marina Mazur

MITEE-B has basic radial flow geometry with each fuel element located inside its own pressure tube. This configuration simplifies engine construction while reducing engine weight. In addition, since it is possible to be able to test a single pressure tube/fuel element assembly, the nuclear test program can be simplified and cost and time greatly reduced.

Unlike the PBR, this engine has a multi-layer assembly of perforated tungsten-UO2 cermet fuel sheets. This allows the engine to operate with hydrogen at 3000 K for many hours. Furthermore, the local voidage and propellant flow geometry is controlled more precisely then in PBR, which reduces hot channel factors, variation in voidage, and eliminates the chance of mechanical distortion due to shifts in particle position. Also, due to the fact that the fuel/pressure elements are housed in individual compartments it is possible to operate the engine even if one of the elements failed.

In order to produce electric power the heat from the tungsten-UO2 fuel sheets is transfered to the closed cycle coolant, helium, through the cold frit and its beryllium tubes by thermal radiation and conduction. The thermal energy is then transported to an external electric power generation system by the flowing coolant. During this phase, there is no hydrogen propellant flow through the fuel region.1

2 Main Engine Tanks – Marina Mazur

It was assumed that the stainless steel part of the tank wall will be carrying all of the loading transferred through the tank wall structure, and that the rest of the tank wall materials acted as the heat shield materials only. Therefore, the only material thickness that needed to be adjusted for the current mission was the stainless steel wall thickness. Equation 3-1 was used to calculate the necessary thickness of stainless steel wall.

The calculations were done using Matlab software, and tank_thickness.m code. The code can be viewed below. The length of the liquid hydrogen tanks were found using tank_vol.m, and the total fuel mass was calculated using aae450mrop1.m.

3 MITEE-B Engine Code

%**********************************************************************

%% aae450mrop1.m

%AAE 450 - Spring 2004

%Author/s: Marina Mazur

%Date Created: 2/5/04

%Last Modified: 3/26/04

%**********************************************************************

%DESCRIPTION

%calculates the fuel mass for the MITEE-B

%METHODS OF CALCULATION

%using basic rocket equations

%VARIABLES

%fr-reservoir propellant as a fraction of the total necessary propellant mass

%ft-mass of the propellant tanks, as a proportionality to total propellant mass

%mdot – mass flow rate

%MR – mass ratio

%mprop - propellant mass before the addition of reservoir fuel

%time-burn time

%engine_mass – mass of engine

%mass_tot – total fuel mass

%mprop_plus_res – reservoir fuel mass

%mdry – dry mass of spacecraft

%delv – delta v that needs to be performed

%c – effective exhaust velocity

%g - gravity

%**********************************************************************

clear all

%fr and ft are taken from AIAA-2002-3787 Brice N. Cassenti, 'Trajectory

%options for Manned mars missions

fr=0.02; %reservoir propellent as a fraction of the total necessary propellent mass

ft=0.03; %mass of the propellent tanks, as a propertionality to total propellant mass

Isp=1300; %sec

delv=input('What is your delta v? ');

%delv=3+delv+.75

%mdry=input('What is your dry mass? ');

mdry=184000;

num_engines=input('How many engines? ');

%F=input('What is your thrust? ');

F=20000;

g=9.81; %gravity

c=Isp*g; %effective exhaust velocity

delv=delv*1e3;

MR=exp(delv/(g*Isp)); %mass ratio

mprop=(MR-1)*mdry/(1-ft*(MR-1));

mprop_plus_res=13825; %enough fuel for 6 engines to start.

mdot=F*num_engines/c; ; %mass flow rate

time=mprop/mdot/3600; %time of burn in hours

engine_mass=680*num_engines;

mass_tot=engine_mass+mprop_plus_res+mprop;

fprintf('\n\nThe necessary mass of fuel is %f\n',mprop)

fprintf('The mass of fuel w/ contigency is %f\n',mprop_plus_res)

fprintf('The time of burn is %6.2f hours\n',time)

fprintf('The engine weight is %6.2f kg\n',engine_mass)

fprintf('Total mass of system is %6.2f kg\n\n',mass_tot)

4 Main Engine Tank Codes – Marina Mazur

%**********************************************************************

%%tank_vol.m

%AAE 450 - Spring 2004

%Author/s: Marina Mazur

%Date Created: 2/10/04

%Last Modified: 3/26/04

%**********************************************************************

%DESCRIPTION

%calculates the height of the fuel tanks

%METHODS OF CALCULATION

%given the density of liquid hydrogen, the fuel weight, and the shape of the tanks, the

%height can be found.

%VARIABLES

%d – diameter of tank

%A – area of tank cross-section

%d – diameter of tank

%min_mass_in_vol – the minimum fuel mass that must be accommodated

%mass – mass of whatever burn is being performed

%hight# - height of whatever tank is being looked at

%hight_tot – total height of the two tanks

%**********************************************************************

clc

d=10-.1*2 % m diameter

A=pi*d^2/4; %area

min_mass_in_vol=179600+7000

%%%%%% first burn %%%%%

mass=78856; %kg

rad=asin(1/5)

frac=rad/2/pi

a_lost=A*frac

A=A-a_lost

hight1=mass/70/A %m

%%%%%second burn and third tank and Nicks fuel and extra fuel%%%%

mass=63551+7000+13825;

hight2=mass/70/A %m

hight_tot=hight1+hight2

%**********************************************************************

%AAE 450 - Spring 2004

%Author/s: Marina Mazur

%Date Created: 3/01/04

%Last Modified: 3/26/04

%**********************************************************************

%DESCRIPTION

%calculates the necessary thickness of stainless steel wall layer

%METHODS OF CALCULATION

%the calculation is done using the critical buckling load of the material as the load the

system will see. The factor of safety is included in the maximum force the system is

under. Factor of safety is 1.5.

%VARIABLES

%Fy – yielding load of system

%Fu – ulimate load of system

%sw and sw1 are used to determine wether Fy or Fu should be looked at for the max.

%load the system is can withstand

%d – diameter of tank

%A2 – area of tank crossection

%min_load – actual the minimum load on the system

%a_lost - area off tank that is not circular and can not be used for fuel storage

%lc – length of tank

%tc – wall thickness of stainless steel

%r – radius of tank

%E – modulus of elasticity

%Sc – critical buckling load

%A – inside cross-sectional area of tank in ft^2

%A2 - outside cross-sectional area of tank in ft^2

%A_tot – total area of stainless steel

%vol – volume of stainless steel on the tank

%density – density of stainless steel

%mass_skin – mass of stainless steel layer

%**********************************************************************

clc

Fy=200000;%psi

Fu=220000;%psi

sw=Fy/1.33;

sw1=Fu/1.65;

if sw11

dV_a(count+1)=dV_a(count)+a(count);

else

dV_a(count+1)=a(count);

end

count=count+1;

end

Fig.(1);

plot(time,a);

title('Acceleration vs. Time');

xlabel('Time');

ylabel('Acceleration [m/s^2]');

Fig.(2);

plot(time,dV_a(2:length(dV_a)));

title('Delta V attained vs. Time');

Fig.(3);

plot(time,m_propellant);

title('Mass of Propellant vs. Time');

Fig.(4);

plot(time,m_total);

title('Total Mass vs. Time');

m_fuel=m_propellant(length(m_propellant))/2.6; %[kg]

V_fuel=m_fuel/880; %[m^3]

D_fueltank=2*(V_fuel*(3/4)*(1/pi))^(1/3); %[m]

m_oxidizer=m_fuel*1.6;

V_oxidizer=m_oxidizer/1450;

D_oxtank=2*(V_oxidizer*(3/4)*(1/pi))^(1/3); %[m]

fprintf('The mass of fuel is %f\n',m_fuel);

fprintf('The volume of fuel is %f\n',V_fuel);

fprintf('The volume of the fuel in ci is %f\n',V_fuel*61023);

fprintf('The diameter of the fuel tank is %f\n',D_fueltank);

fprintf('The mass of oxidizer is %f\n',m_oxidizer);

fprintf('The volume of oxidizer is %f\n',V_oxidizer);

fprintf('The volume of the oxidizer in ci is %f\n',V_oxidizer*61023);

fprintf('The diameter of the oxidizer tank is %f\n',D_oxtank);

This extra blank page must be here because of the “Section Break”. It is important that the section break be here so that each section can be combined for the final document.

-----------------------

[i] Wade, Mark. “Saturn V.” 9 Sept. 2003 < >

[ii] Sutton, G. P., Bivlarz, O. Fundamentals of Rocket Propulsion, 7th ed., Wiley-Interscience, New York, 2001, 426.

[iii]Shelton, B. W., T. Murphy . "The Saturn V F-1 Engine Revisited." AIAA 92-1547. Huntsville, Alabama. 24-27 March 1992. < >

-----------------------

[pic]

Fig.

F.1 Gross Liftoff Weight vs. Change in Velocity

[pic]

Fig.

F.2 All 150 Configurations

[pic]

Fig.

F.4 Configur‎F.1 Gross Liftoff Weight vs. Change in Velocity

[pic]

Fig. ‎F.2 All 150 Configurations

[pic]

Fig. ‎F.4 Configurations 26-50

[pic]

Fig. ‎F.3 Configurations 1-25

[pic]

Fig. ‎F.5 Configurations 51-75

[pic]

Fig. ‎F.6 Configurations 76-100

[pic]

Fig. ‎F.7 Configurations 76-100 (opposite side view)

[pic]

Fig. ‎F.8 Configurations 101-125

[pic]

Fig. ‎F.9 Configurations 126-150

[pic]

Fig. ‎F.14 A plot of Eq. ‎F–12. This is the mass of propellant versus the engine efficiency.

[pic]

Fig. ‎F.15 Total propellant mass of a three-stage system as a function of different ΔV breakups, which are referenced by a generic number (Combination Number).

[pic]

Fig. ‎F.16 Total propellant mass of a two-stage system as a function of different ΔV breakups, which are referenced by a generic number (Combination Number).

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download