Appendix E - Power
EPower
E.1.1- Justin Tucker
This MATLAB code was used to do the analysis on the use of solar power. It shows the array sizing for the power required for this mission.
%%POWER_solar_array_sizing
%AAE 450 - Spring 2004
%Author/s: Justin Tucker
%Date Created: 2/2/04
%Last Modified: 4/3/04
%**********************************************************************************
%DESCRIPTION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This code was created to estimate the sizing of solar %
% arrays based on the power requirement and solar dista- %
% nce. %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Outputs from Command Window %%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The Solar Array Area = 2618.63 m^2 %
% The Solar Array Mass = 8143.14 kg %
% > %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%METHODS OF CALCULATION
% The solar array sizing is calculated by adjusting the power production
% equation used in Larson and Pranke (see Reference section). We are able
% to solve the equation for the solar array area (A) from knowing the power
% requirement, solar flux, conversion efficiency, packing fraction, and
% angle (theta) normal to the Sun. We assume that theta is adjusted so that
% it is always facing the Sun, making theta equal to zero. The temperature
% was estimated to be zero Kelvin due to space conditions. Although the
% temperatures differ, this was only an estimated calculation to show the
% feasibility of using solar power for our mission. Some of the other
% assumed values are taken from tables shown in Larson and Pranke.
%VARIABLES
% d = Astronomical Distance from the Sun [AUs]
% phi_Sun = Solar Flux [W/m^2]
% T0 = Standard Temperature [deg-K]
% T = Operating Temperature [K]
% Tc = Normalized Temperature Coefficient for Silicon Cell [K]
% nu0 = Standard Efficiency for Silicon Cell [%/100]
% nu = Conversion Efficiency [%/100]
% P = Power Required for Mission [W]
% Fp = Packing Fraction []
% theta = Array Angle Normal to Sun [deg]
% A = Solar Array Area [m^2]
% marray = Solar Array Blanket Mass [kg]
% mdrive = Solar Array Drive Mass [kg]
% marrtot = Solar Array Total Mass [kg]
%**********************************************************************************
%CODE
clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Astronomical Distance from the Sun [AUs] %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
d = 1.523;
%%%%%%%%%%%%%%%%%%%%%%
% Solar Flux [W/m^2] %
%%%%%%%%%%%%%%%%%%%%%%
phi_Sun = (1368/d^2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Conversion Efficiency Calculation %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Standard Temperature [deg-K] %
T0 = 25 + 273.15;
% Operating Temperature [K] %
% (estimated temperature of space close to 0 K) %
T = 0;
% Normalized Temperature Coefficient for Silicon Cell [K] %
Tc = -4.5e-3*T;
% Standard Efficiency for Silicon Cell %
nu0 = .148;
% Conversion Efficiency %
nu = nu0*(1 + Tc*(T - T0));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Solar Array Area Calculation from Conversion Efficiency and Power Requirement %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Power Required for Mission [W] %
P = 200000;
% Packing Fraction %
Fp = .875;
% Array Angle Normal to Sun [deg]%
% (assume we adjust to keep the %
% arrays facing the sun at all %
% times. %
theta = 0;
% Solar Array Area [m^2] %
A = P/(phi_Sun.*nu*Fp*cos(theta));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The solar array total mass is based on its blanket mass %
% and its drive mass. The drive mass includes structure %
% mass, orientation motors, and/or deployment packaging. %
% Typical blanket mass for a silicon array is 1.7 kg/m^2. %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Solar Array Blanket Mass [kg] %
marray = 1.7*A;
% Solar Array Drive Mass [kg] %
mdrive = (0.014*marray + 20.6)*marray/100;
% Solar Array Total Mass [kg] %
marrtot = marray + mdrive;
% Results of Analysis %
fprintf('The Solar Array Area = %4.2f m^2',A)
fprintf('\nThe Solar Array Mass = %4.2f kg',marrtot)
AAE 450 Senior Spacecraft Design Spring 2004
1
Appendix E - Power
E.1.1.1Power Losses - Reuben Schuff
We studied the power loss effects for silver, copper, gold, aluminum, and iron. Data for wire diameters of 0.5, 1, 3, and 5 cm are presented in Figs. 1-4.
AAE 450 Senior Spacecraft Design Spring 2004
1
Appendix E - Power
E.1.1.2Justin Tucker
These equations were used to calculate the power budget for our mission. They were found in Brown, Charles D. Elements of Spacecraft Design. By knowing the total power required Pt , we could work the equations backwards to find out the amount of power available to the subsystems. Taking an estimated break down from Brown, we were able to get an approximate value for the subsystem power requirement and how much each subsystem would require. Using these equations and the excel file below, we were able to place the power percentage breakdown for each subsystem’s power requirement.
Estimated Spacecraft Power Allocation
•Pt = 332.93*ln(Ppl)-1047
Total Power Available to Subsystems
•P subsystems = Pt – P pl
Subsystem Percent Allocation
•Subsystem Requirement (kWe) / P subsystems* 100
This excel files shows the power budget for all the subsystems on the spacecraft
Power Budget Based on 200kWe Available for Subsystems200
Subsystems / Power Allotted (kWe) / Percentage of Total Power (%)
Human Factors / 23.0 / 11.5%
Thermal / 20.0 / 10.0%
Dynamics and Controls / 120.0 / 60.0%
Power / 11.0 / 5.5%
Communications / 20.0 / 10.0%
Propulsion / 0.8 / 0.4%
Structures / 1.5 / 0.8%
Aerodynamics / 0.0 / 0.0%
Excess/Peak Power / 4.0 / 2.0%
Total / 200 / 100%
E.1.1.3 - Justin Tucker
These equations were used to analyze the type of wiring required for our spacecraft. By calculating the power loss across the wire as a certain current runs through it, we can find the resulting heat flux. This heat flux then tells us whether or not our wire material and insulation can handle the amount of current we have running through it. It is a critical part to our mission design. If wiring becomes faulty, it would result in a fire, which could be a mission and life threatening event.
Power loss across a wire
Heat flux
This excel file calculates the power loss and heat flux generated by power being transferred across the different types of wires that will be used on this mission.
Heat Flux Across Wire TypesWire Material / Copper
Density(kg/m^2) / 8920
Wire Diameters(m)
14 Gauge / 0.0016
12 Gauge / 0.002
10 Gauge / 0.0026
8 gauge / 0.0033
Wire Cross Sectional Area(m^2)
14 Gauge / 2.01E-06
12 Gauge / 3.14E-06
10 Gauge / 5.31E-06
8 gauge / 8.55E-06
Wire Bundle Cross Sectional Area(m^2)
14-3 AWG / 1.81E-05
12-3 AWG / 2.83E-05
10-3 AWG / 4.78E-05
8-3 AWG / 7.70E-05
Wire Bundle Surface Area(m^2)
14-3 AWG / 0.158
12-3 AWG / 0.198
10-3 AWG / 0.257
8-3 AWG / 0.326
Hab Module Length(m) / 10.5
Hab Module Circumference(m) / 31.416
(2*π*r)
Total Wire Length(m) / 10.479
Current(A) / 30
Copper Resistivity at 25°C(Ω-m) / 1.68E-08
Power Loss(kWe)
14 Gauge
/ 0.079
12 Gauge / 0.050
10 Gauge / 0.030
8 gauge / 0.019
Heat Flux(kWe/m^2)
14 Gauge
/ 0.499
12 Gauge / 0.255
10 Gauge / 0.116
8 gauge / 0.057
E.1.1.4 - Justin Tucker
This excel file calculates the total mass occupied by the power subsystem. It includes all the components, the tether cable, the winch being used to wind up the tether and all the fuel cell masses for the secondary power. By finding the volumes and densities of the different wire types we are able to calculate the mass occupied by the wiring and other components of the spacecraft. The wiring and internal components of the spacecraft occupy a little over 40% of the total power mass.
Power Mass Budget by ComponentTether Cabling / kg
Wire / 112.3
Insulation / 19.9
Magnetic Shielding / 51.5
TOTAL CABLE / 183.7
Winch / 6815
Components / 11.4 / kg/kWe
Plasma Contactors(Ground) / 159.21
Transformers
Large / 670
Small Scale / < 0.5
Regulators, Convertors, charge controllers / 1607.5
TOTAL COMPONENTS / 2277.5
Wiring
10-3 AWG / Dryer / 0.1
12-3 AWG / Dishwasher / 0.2
14-3 AWG / Other component wiring / 3460.5
25% of Total Wiring and Component Mass / 3745.488
HAB Length / 10 / m
HAB Circum. / 31.416 / m
Copper Dens. / 8920 / kg/m^3
Total Possible Length of All Wires / 41.416 / m
Probable Length of 14-3 / 41.416 / m
Probable Length of 12-3 / 5 / m
Probable Length of 10-3 / 2 / m
Diameter of 14-3 / 4.88E-03 / m
Diameter of 12-3 / 6.16E-03 / m
Diameter of 10-3 / 7.76E-03 / m
Volume of 14-3 / 3.88E-01
Volume of 12-3 / 1.49E-04
Volume of 10-3 / 9.47E-05
TOTAL WIRING / 3460.5
Fuel Cell
LOX / 893
LH2 / 112
TOTAL FUEL / 1005
LOX Tank / 229
LH2 Tank / 262
Fuel Cells / 590
TOTAL HARDWARE / 1081
TOTAL / 2086
TOTAL POWER MASS / 14982.0
AAE 450 Senior Spacecraft Design Spring 2004
1
Appendix E - Power
E.1.1.5–Magnetic Fields - Reuben Schuff
The magnetic force caused by parallel currents is found by Eq (E–1). From this Eq, Fig.A6 is created. The magnetic field caused by coiling the primary power cable is calculated from Eq (E–2). Fig. A6 shows the magnetic force due to the current in the primary power cable. The material properties of the tether show no risk of failure due to these forces.
The magnetic field generated by a coil was also investigated. If power is transferred through the primary power cable while it is wound on the winch, a solenoid is created. As a frame of reference, the nominal magnetic field from the earth experienced at PurdueUniversity (40.4 N. Lat. 86.9 E Long) is .0.548 E-04 Tesla.[1]
Equation E–2 calculates the magnetic field generated from an ideal solenoid. This assumes there is no magnetic field outside of the coil. However, in the tether deployment and retraction system, this assumption is not sufficient. The effects of the finite coil produce nearly as powerful of a magnetic field as at the center of the coil. The ideal model predicts the strength of the magnetic field at the center of the coil. This analysis and a discussion with Dr. Hrbud[2] concluded that this magnetic field would have devastating effects on electronic systems on the spaceship. It was also concluded that it would not be feasible to shield against these magnetic effects.
/ E–1/ E–2
AAE 450 Senior Spacecraft Design Spring 2004
1
Appendix E - Power
E.2Study of SAFE-400 Nuclear Reactor – Reuben Schuff
At the onset of this project, the choice of a primary power source was not clear. Early in the design, we concluded the only viable option for a primary power source was nuclear power. Our investigation included nuclear reactors which are currently being developed for space applications or had previously flown on space missions. Both Russian and United States reactors were studied. Data was compiled from the Uranium Information Centre,[3] Landis, Mckissock, and Bailey,[4] and Poston, and Guffee.[5]By the second week of the project, our efforts concentrated on the SAFE-400 nuclear reactor – Reuben Schuff
The reactor core is composed of 127 identical heatpipes. Each heatpipe is its own impendent cooling loop. The design of the heatpipes does not require any pumps. A Brayton cycle has been proposed for the power conversion systems; however this system is still in development.[6]Work at Los Alamos National Labs has produced three highly successful proof of concept tests in the last four years. Fig. A9 shows the basic dimensions for the SAFE-400. Table A.3 and Table A.2 list the mass breakdown and power outputs, respectively.
.
E.3Failure of SAFE-400 – Reuben Schuff
Poston, Kapernick, and Guffee,1 have shown the reactor core will remain subcritical even in the worst case water immersion accident, such as a launch failure scenario. This means there is no radioactive exposure for this failure. The core is kept subcritical until it is activated for operations in space.
The most catastrophic failure of a nuclear reactor is a core meltdown. In this case, the heat transfer system fails to remove sufficient heat from the core. The core then overheats and the structure melts, causes the release of the radioactive fuel. This the worst case loss of life failure possible. A 3D finite-difference thermal/structural code was written by Los Alamos Labs to model the heat transfer.[7] This model shows that a single heatpipe failure would not lead to meltdown nor would it cause cascade failure across the core. We performed a simple analysis modeling the heat transfer in anelement of the reactor core.Our model predicts the number of heatpipes that can fail before we reach a danger of meltdown.
Our model is a one dimensional steady state conduction-convection heat transfer model. It shows the maximum number of heatpipes that can fail before temperatures in the core rise above the melting point of the teicusp, which separates the fuel pellets and the heatpipes. Required data taken from Ref (5) for the analysis is compiled in Table A.4. The assumptions directly drawn from this data are: power to heatpipes is constant, heatpipe temperature is constant, clad temperature is constant.
Fig. A10 shows the conduction temperature gradient modeled across an element of the reactor core. Our model required further simplifying assumptions. The temperature distributionin the core is assumed uniform. The distance between the fuel pellet and the heatpipe was approximated, from Fig. A8, to be 0.4 cm. An average value of thermal conductivity across clad, tricusp, and heatpipe was used. We only modeled conduction heat transfer between fuel, clad, tricusp, and heatpipe, and we only modeled convective heat transfer between heatpipe wall and heatpipe. For our analysis Twc is the temperature between fuel and clad, Twg is the temperature of inner wall of heatpipe, and Taw is the adiabatic temperature of sodium in heatpipe.
Equations for the model are taken from Huzel, and Huang.[8]First, physical and thermodynamic constants are determined from the nominal data in Table A.4. Thermo conductivity is calculated from Eq (E–3).
/ E–3k = (4600*0.4)/(1200-1247) = -39.149 [J/(cm*s*K)]
We calculate the area of heatpipe Eq (E–4).
/ E–4A = (398.7kW)/[(4.6kW/cm2)*127] = 0.6825 cm^2
To validate our calculations we compared our calculated data from our model to the data given in Table A.4. N is the number of failed heatpipes; for the data in Table A.4, the failure mode is N = 1. There are 127 total heatpipes in the core, so the number of non failed heatpipes is 127-N. Our calculations gives
This compares to 4.7kW/cm 2 and 1250K, respectively, from Table A.4. By increasing N(the number of failed heatpipes) using the method outlined, Fig. A11 is generated.
The critical value of temperature is 2896K. This the melting point of the teicusp, which separates the fuel pellets and the heatpipes. Clearly from this analysis, the assumptions need to be constrained further. However, this shows that the best case seneario for this failure mode leaves a large margin of leeway. Nearly all the heatpipes would have to fail before a core meltdown occurs.
The probability of reactor failure was also investigated based on previous reactors in space and nuclear reactors operating in the United States. There have been one United States and two Russian reactors flown in space; all three have been successful. 103 nuclear reactors currently are operating in the United States. Of these, there were 0.03 unplanned shutdown events per reactor per year.[9]
AAE 450 Senior Spacecraft Design Spring 2004
1
Appendix E - Power
E.4Fuel Cell Power System Sizing - Ryan Spalding
This is the Matlab code that sizes the fuel cell system for the secondary and emergency power supply. The basic inputs for this code are the total power requirements for (and the duration of) each situation that requires fuel cell power. The outputs of this code are the mass and volume numbers for each part of the fuel cell power system. This code generated the mass and volume numbers as seen in section 3.8.3 of the report.
%%File: fuel_mass_calc.m
%
%AAE 450 - Spring 2004
%Author: Ryan Spalding
%Date Created: 2/23/04
%Last Modified: 4/6/04
%
%****************************************************************************
%DESCRIPTION
%This code calculates the mass and volume of each part of the fuel cell %system (fuel cells, fuel, and tanks) based on initial variable definitions %for power requirements and duration of use for the secondary and emergency %situations. The specific outputs of the code are: LOX_mass, LOX_volume, %H2_mass, H2_volume, LOX_tank_mass, LOX_tank_volume, H2_tank_mass, %H2_tank_volume, Fuel_cell_mass, Fuel_cell_volume, Total_fuel_mass, %Total_system_mass, Total_mass, Total_volume
%
%METHODS OF CALCULATION
%This code calculates all of the necessary information by scaling our %mission’s requirements from those of the Space Shuttle. The fuel cells %themselves are identical to the ones aboard the Shuttle, and the fuels used %(liquid hydrogen and liquid oxygen) are the same. Our mission requires a %different amount of total fuel than is typically seen for a Shuttle mission, %so the tank masses are scaled to incorporate this difference. Additionally, %all necessary cryogenic and flow distribution components are scaled as well, %and are included in the tank mass and volume numbers.
%
%VARIABLES
%Backup_power: The total power needed by all systems in the habitat module %when the nuclear reactor is not supplying power
%Winch_power: The power required to operate the winch
%Secondary_power: The power required during tether retraction/deployment
%Number_deployments: The number of tether deployments/retractions
%Deployment_time: The worst case scenario time for tether deployment or %retraction
%Aerocapture_time: The time during the aerocapture procedure during which %fuel cells will be used
%Burn_time: The total time the main engines will use all nuclear power for %propulsive means and fuel cells will be used to provide power requirements
%Secondary_time: The total time that secondary power will be needed
%Emergency_power: The total power needed by all systems in the habitat module %during an emergency situation (tether breakage/power cable malfunction)
%Emergency_time: The total time budgeted for the emergency situation
%Mass_margin: Fuel margin to account for fuel losses during the mission
%LOX_mass_rate: Rate of liquid oxygen consumption by the fuel cells to %produce one kW of power for one day
%LOX_mass_secondary: Mass of liquid oxygen needed for secondary power %concerns
%LOX_mass_emergency: Mass of liquid oxygen needed for the emergency situation
%LOX_mass: Total mass of liquid oxygen required
%LOX_density: Density of liquid oxygen
%LOX_volume: Total volume of liquid oxygen required
%H2_mass_rate: Rate of liquid hydrogen consumption by the fuel cells to %produce one kW of power for one day
%H2_mass_secondary: Mass of liquid hydrogen needed for secondary power %concerns
%H2_mass_emergency: Mass of liquid hydrogen needed for the emergency %situation
%H2_mass: Total mass of liquid hydrogen required
%H2_density: Density of liquid hydrogen
%H2_volume: Total volume of liquid hydrogen required
%Shuttle_LOX_mass: The mass of liquid oxygen in one tank on the Space Shuttle
%Shuttle_LOX_tank_mass: The mass of one liquid oxygen tank on the Space %Shuttle
%Shuttle_LOX_tank_volume: The volume of one liquid oxygen tank on the Space %Shuttle
%Scaling_factor_LOX: The scaling factor between our liquid oxygen needs and %those of the Space Shuttle
%LOX_tank_mass: The mass of the liquid oxygen tanks for this mission
%LOX_tank_volume: The volume of the liquid oxygen tanks for this mission
%Shuttle_H2_mass: The mass of liquid hydrogen in one tank on the Space %Shuttle
%Shuttle_H2_tank_mass: The mass of one liquid hydrogen tank on the Space %Shuttle
%Shuttle_H2_tank_volume: The volume of one liquid hydrogen tank on the Space %Shuttle
%Scaling_factor_H2: The scaling factor between our liquid hydrogen needs and %those of the Space Shuttle