1 - Purdue University College of Engineering



Thermal Control

Nomenclature

Radiators

α = insulation angle of the radiator

Ts = effective sink temperature

Tb = fin base temperature

Q = heat rejection capacity (Q = Aε*η* σ *Tb4)

L = distance between coolant tubes divided by 2

ε1, ε2 = radiator emmittance of side 1 and side 2

k = fin conductivity

t = fin thickness

η = radiator fin effectiveness

σ = Stefan-Boltzmann constant

mpanel = radiator panel mass (not including deployment structure)

A = radiator area

Aeroshell

d = diameter (cm) of particle

ρ b = density (g/cm3) of bumper (top) layer

ρ p = density (g/cm3) of particle

ρ t = density (g/cm3) of wall (bottom) layer

ρ ∞ = density of free-stream

rcyl = radius of aeroshell

S = separation distance from top and bottom layers

σ = yield strength

tb = thickness (cm) of bumper

tw = thickness (cm) of back wall

V = velocity of particle

V∞ = velocity of freestream

1 Crew Module Active Thermal Control System - Alessandro Ianniello

Matlab Code (Initial Flash Evaporator Analysis, later found out to be unnecessary since the Flash Evaporator is found out to be a continuously operating heat rejection system as long as the fuel cells generate water)

% Author: Alessandro Ianniello

% Class: AAE 450 Senior Design

% Semester: Spring 2004

% Team: Thermal Control

% Code Title: "Atmospheric Flight Heat Rejection System"

clear all

clc

%Mars Mission Requirements:

Q = input('Specify Amount of Heat Rejection needed by Flash Evaporator in kW: ');

%FLASH EVAPORATOR DESIGN

%Space Shuttle Flash Evaporator Performance:

%Typical Heat Rejection: 8.5 kW

Heat_rej = 0.646; %Heat Rejection water consumption: 0.646 kJ for 1 second requires kg of H20

%Shuttle water tank dry mass: 18.1 kg

%Shuttle water mass for each tank: 74.8 kg

perc = .242; % percentage of tank mass that is dry mass

n = 4 ; %Number of spache shuttle water tank

P_flash = 0.2 ; %Shuttle Flash Evaporator Power consumption in kW

m_flash = 44 ; %Shuttle Flash Evaporator mass

v_flash = 0.364 ; %Shuttle Flash Evaporator volume in m^3

D_tank = .4 ; %Shuttle water tank diameter

%FLASH EVAPORATOR SYSTEM MISSION OPERATING TIME AND WATER CONSUMPTION

t = input('Specify Mission Required Time for Flash Evaporator Operation in minutes: ');

m_water = Qtotal / Q_lb; %mass of water needed for time t

m_dry = m_water*perc; % dry mass of water tanks assuming same design as space shuttle water tanks

v_water = m_water/1000; % assume density of water as 1000 kg/m^3, this give volume of tanks

n_tank = 4; %number of water tanks

v_water_tank = v_water/n_tank; % volume of water per tank

%Water Tank totals

m_tank = m_dry + m_water;

%H = V/A = 4*V/pi*D^2

H = 4*v_water_tank/pi*D_tank^2; %heigh of cyclindrical tank based on given diameter D_tank

%FLASH EVAPORATOR SYSTEM MASS, VOLUME, POWER BUDGET RESULTS

flash_mass = (m_mars + m_tank)*4; %Total Flash Evaporator System Mass

flash_vol = (v_mars + v_water)*4; %Total Flash Evaporator System Volume

flash_power = P_mars*4; %Total Flash Evaporator System Power Requirement

fprintf('\n\n =============== FLASH EVAPORATOR ANALYSIS ===============\n\n')

fprintf('\n\nFor a Flash Evaporator Rejecting %.f kW of heat for %.f mintues for entire mission\n\n', Q,t)

fprintf('Flash Evaporator Mass: %.4f\n', m_mars)

fprintf('Flash Evaporator Volume: %.3f\n', v_mars)

fprintf('Flash Evaporator Power Consumnption: %.3f\n', P_mars)

fprintf('Total Water Tank Mass (dry mass plus water mass): %.3f\n', m_tank)

fprintf('Total Water Tank Volume: %.4f\n', v_water)

fprintf('Total Water Tank Power: %.f\n', 0)

fprintf('Number of Water Tanks: %.f\n', n_tank)

fprintf('Water Tank Height: %.4f\n', H)

fprintf('Water Tank Diameter: %.1f\n\n', D_tank)

fprintf('___________________________________\n\n')

fprintf('Total Crew and Nuclear Flash Evaporator System Totals with double redundancy (2 main, 2 backup Flash Evaporators)\n\n')

fprintf('Total Flash Evaporator System Mass: %.1f\n', flash_mass)

fprintf('Total Flash Evaporator System Volume: %.2f\n', flash_vol)

fprintf('Total Flash Evaporator System Power Requirement : %.2f\n\n', flash_power)

%PLOTS

%Mass of water vs. Heat Rejection Time for varous heat rejection rates

Q=0:20:160

t=0:180:1440

m_water = Q./Heat_rej_mars

Fig.(1)

plot3(t,m_water,Q)

grid on

2 Flash Evaporator Malfunction History

STS 1,2,3 – FES slight malfunction, higher than normal inlet temperatures

STS 2 – FES erratic operation of fuel cell 3

STS 4 – FES cooling malfunction ,outlet temperature higher than normal

STS 41-C/10 – FES temporary malfunction, water dump failure due to line freezing

STS 41-D/11 – water dump malfunction

STS 67 – FES feedline heater malfunction

STS 33 – FES un-commanded shut down

STS 34 – FES Controller A failure, controller B successful operation

STS 48 – FES Primary controller A failure, controller B successful operation

STS 55 – water tank de-pressurization due to tank leak

STS 56 – controller A shutdown, manual restart of controller A

STS 65 – waster water dump nozzle ice up, flash evaporator used to consume water

STS 66 – contoller B erratic operation, outlet temperature fluctuation, no problem during re-entry

STS 68 – FES feedline heater system 1 failure, system 2 functioned well for remainder of mission

STS 72 – FES un-commanded shutdowns, stable FES outlet temperature

STS 78 – feedline heater malfunction

STS 111 – Controller B failure

The following are extracts from

The water membrane evaporator is being considered as a replacement for the orbiter's flash evaporator system, which cools the orbiter during ascent and reentry and also provides supplemental cooling in orbit. The flash evaporator is experiencing corrosion, which creates a risk of freon leaks. The water membrane evaporator takes advantage of the hydrophobic, or water-repelling, nature of microporous Teflon to evaporate water while maintaining excess liquid water in a hydrophilic layer behind the hydrophobic layer.

Erratic operations of Fuel Cell 3 and the Flash Evaporator System continued throughout the mission, but the crew were able to demonstrate the usefulness of man in space by changing out a failed CRT on the flight deck with an unused unit from a Mission Specialist station on the aft control console.

Supply water tank C remained in the 99.8-percent quantity position for 4 hours after launch. Analysis showed that the tank C bellows were stuck, and the bellows were freed using the flash evaporator system (FES) B for a short time to increase the differential pressure across the bellows. Once freed, tank C and D quantities equalized and the bellows performed normally for the remainder of the mission. (STS-31)

The flash evaporator system (FES) feedline heaters are normally conFig.d to heater string 2 during prelaunch operations. During the countdown, the FES accumulator B feedline temperature began to decrease from 75 deg F shortly after cryogenics loading began. The temperature reached 56.6 deg F before the heater was reconFig.d to string 1. The LCC limit is 56 deg F. After the heater reconfiguration, the temperature began to increase; however, the final countdown to launch that begins at T-9 minutes was delayed 1 minute 13 seconds until a positive indication of the temperature increase from the string 1 heater was observed.(STS-67)

Also, the flash evaporator system (FES) shut down when the FES was reconFig.d for entry. A successful restart was made, and the FES worked properly for the rest of the mission. (STS 33)

At 117:02:24 G.m.t. (00:11:34 MET), about three hours into a flash evaporator system (FES) water dump, the gaseous nitrogen regulator pressure in the common manifold for the supply and waste water tanks dropped to 6 psig. The FES water dump was terminated 11 minutes later to prevent any anomalous FES operation. Troubleshooting and malfunction-procedure workarounds pinpointed a probable leak in the nitrogen system that pressurizes the water tanks. The water alternate pressure valve was opened and all water tanks were pressurized with cabin air. A FES supply water dump was subsequently completed successfully.

At approximately 118:02:12 G.m.t. (01:11:22 MET), the crew reported that a puncture was found in the wall of the waste water tank. Subsequent video was downlinked showing the puncture and deformation of the waste water tank wall. The crew reported no signs of liquid leakage, therefore indicating that the tank bellows was still intact. The postflight investigation showed that an existing dent in the tank wall jammed one side of the bellows, eventually forcing a rulon tab, which is connected to the bellows, to puncture the tank wall. As a result of the gaseous nitrogen leak, the contingency water container (CUC) was placed in use for holding the waste water. Waste water dumps from the CWC were successfully performed throughout the flight. An in-flight maintenance (IFM) procedure to isolate the GN2 leak from the water tank pressurization system was completed successfully at 118:23:34 G.m.t. (02:08:44 MET), and all supply water tanks were repressurized to 16 psig. (STS 55)

During ascent, about 1.5 minutes after lift-off, the unexplained cooling of the Freon coolant loops between the ammonia boiler inlet and the flash evaporator outlet occurred. This cooling also occurred during the STS-1 and STS-2 missions and is possibly due to the evaporation of condensation in the flash evaporator cores. Flight data indicates that the high load flash evaporator was inhihited too early during initial radiator activation. At the time it was inhibited, the evaporator inlet temperature was about 74° F, higher than the 60° F maximum inlet temperature for topping evaporator operation with the high load evaporator inhibited. no over-temperature shutdown of the evaporator occurred as a result of this error. However, the evaporator did lose control for about 100 seconds, during which time the evaporator outlet temperature peaked at 48° F. About 2.8 hours after launch, upon positioning the flow proportioning modules to the payload position, fault messages were triggered because the interchanger flowrates dropped below the 1950 lb/hr lower limit that is applicable while in the interchanger position and during the transition from the interchanger to the payload position. (STS 1,2 and 3)

During ascent, unexplained cooling of the Freon coolant loops occurred momentarily, as seen on all previous flights. The flash evaporator outlet temperature on Freon coolant loop 1 exceeded 100° F during the ascent no-cooling transient, triggering a caution and warning alarm (Loop 2 temperature was lagging slightly and did not exceed 100° F). The topping flash evaporator steam duct starboard nozzle temperature fell to 23° F, triggering a fault message. This low,temperature was caused by freezing of rain water in the nozzle during ascent. The ice later cleared by sublimation causing no problem with flash evaporator operation. (STS 4)

STS 6, no unexplained FES cooling experienced as in STS 1 through 5

Supply Water Dump Valve Failed To Open - At approximately 039:08:35 G.m.t., the supply water dump valve failed to open when commanded. The excess water was disposed of by operating the flash evaporator system. Later, during thermal conditioning using the dump nozzle heaters and after one revolution of Orbiter side sun, the valve was opened at 40:05:39 G.m.t. The supply water continued to fail to dump, thus indicating line freeze up. Postflight, the water line was found ruptured upstream of the dump valve. Discoloration of the TPS indicated ice formation on both potable and waste water nozzles. (STS 10)

STS 41-D ---Due to the ice formation, all subsequent supply water dumps were deleted from the STS 41-D mission timeline and the flash evaporator system was used to manage that water. A waste water dump was required and attemped on flight day 4 during live RMS CCTV coverage. The waste water dump was discontinued after expelling about 5 - 7 percent because of rapid ice buildup on the waste water nozzle. During the remainder of the mission, the crew used available bags for urine collection. Adequate waste water tank capacity existed for condensate col1ection.

A procedure was developed and successfully implemented to remove the ice from the supply water nozzle using the RMS to impact and dislodge the ice formation. Due to the proximity of the waste water nozzle to the wing, the waste water ice removal with the RMS was not attempted. Positioning the vehicle for side sun and repeated heater cycling resulted in the waste water ice being almost completely removed by flight day

The formation of ice during the third supply water dump resulted from ice particles being trapped by the AFRSI/nozzle configuration and a large system pressure drop which caused the water dump spray pattern to widen and come in contact with the ice particles. Ice growth eminated from the ice particles back to the supply water nozzle completely covering the nozzle.

Waste and Supply Water Dumps (DTO 0325) - Thirteen water dumps were performed (10 supply, 2 waste and 1 simultaneous). All were accomplished without incident. The RMS television was used to observe five dumps: the first use of the reconFig.d waste nozzle, the first supply and waste dumps at 10.2-psia cabin pressure, the simultaneous dump (the first simultaneous dump with the redesigned nozzles), and a supply dump with the radiator in high-set point to force flash evaporator system (FES) operation. All dumps were useful in the evaluation of the new nozzles, but only the supply dump with the FES activated actually cleared a test condition of the DTO. (STS-61-B , flight 23)

STS-34

Following main engine cutoff (MECO), the high-load inboard duct heater temperature in the flash evaporator (FES) started dropping, indicating water carry-over into the duct. The FES shut down and the secondary FES controller operated satisfactorily. The FES duct heaters were activated in an attempt to thaw any ice that may have been present in the FES core or ducts. A test of the FES was conducted of the topping evaporator with the primary B controller, and the FES operated properly. The FES was operated satisfactorily for the remainder of the mission.

The launch of the STS-48 vehicle occurred at 255:23:11:04.005 G.m.t. (7:11:04 p.m. e.d.t. on September 12, 1991) from launch pad A at KSC. Orbiter performance was satisfactory during ascent; however, the flash evaporator system (FES) primary A controller experienced an automatic shutdown. The FES was restarted with primary B controller and operated normally. After orbit was reached, the FES A controller was reactivated and operated nominally. (STS 48)

All subsystems performed satisfactorily throughout the ascent phase except the flash evaporator system (FES) which shut down at 98:05:33:16 G.m.t. (00:04:16 MET) while operating on the A controller. The crew manually restarted the FES on the primary A controller, and it operated satisfactorily thereafter. (STS 56)

A supply water dump was initiated at 192:07:27:20 G.m.t. (02:14:44:20 MET). At 192:07:59:02 G.m.t. (02:15:16:02 MET) (32 minutes later), the dump was prematurely terminated because of excessively low dump-nozzle temperatures. Data analysis concluded that the supply water dump nozzle had accumulated an unknown amount of ice that may also have obstructed the waste water dump nozzle. The supply and waste water dump nozzle heaters were cycled to eliminate the ice from the nozzle area. After the supply and waste water dump nozzle temperatures indicated ice was no longer present, a successful waste water dump was initiated at 193: 16:49 G.m.t. (04:00:06 MET). The dump was completed 56 minutes later with good nozzle temperatures and no signs of ice. Supply water dumps were performed using the flash evaporator system (FES) for the remainder of the flight. (STS 65)

After the flash evaporator system (FES) feedline heater reconfiguration to heater system 2 at 278:15:15 G.m.t. (05:04:00 MET), the FES feedline A high-load line temperature went off-scale high (>250 øF) for nearly eight hours. The crew switched back to heater system 1 at 280:04:14 G.m.t (06:16:59 MET) and all temperature conditions became nominal. (STS 68)

At 318:10:05 G.m.t. (10:17:05 MET), the flash evaporator system (FES) B controller experienced an under-temperature shutdown. The primary B controller power was cycled and the FES operated normally until radiator bypass was selected. Following radiator bypass/FES checkout, several large transients occurred on the primary B controller. The evaporator outlet temperature oscillated between 34 øF and 47 øF (limits are 39 deg F + 2 deg F) and the primary A controllerwas selected at 318:12:04 G.m.t. (10:19:04 MET). The FES operated nominally during entry. (STS 66)

At 011 :11 :07 G.m.t. (00:01 :26 MET), while on the primary A controller, the flash evaporator system (FES) shut down as the high-load evaporator transitioned to standby. The high-load transition to standby occurred as the heat load to the FES decreased because of radiator flow initiation just prior to payload bay door opening.

The FES subsequently failed to come out of standby twice during the first day of flight. The FES was successfully restarted on the primary A controller in both cases. On flight day 4, the FES experienced four shutdowns. At approximately 015:03:03 G.m.t. (03:17:22 MET), while still operating on the primary A controller, the FES shut down. At the time of the shutdown, the cabin pressure was at 10.2 psia in preparation for EVA 1 and a FES water dump was being performed. The FES was successfully restarted on the A controller about 10 minutes after the shutdown. Twenty minutes later, the FES shut down again. Twenty-four minutes later, the FES was started on the primary B controller. Prior to the FES outlet temperature reaching the control temperature, the FES once again shut down. FES operation on the primary B controller was attempted again approximately 4 hours later. The FES outlet temperature came into range, but the FES shut down again after approximately 11 minutes. It was suspected that ice had formed in the FES topper core, and the FES core-flush procedure was performed; however, the FES core-flush was terminated prematurely because of low duct temperatures (0 deg F). A second FES core-flush procedure was initiated at 017:13:07 G.m.t. (06:03:26 MET), and no evidence of ice was noted during this procedure. Nominal FES operation with radiators at the high set point was demonstrated using the primary B controller for 20 minutes following the flush procedure. The FES primary B controller was deactivated at 017:13:52 G.m.t. (06:04:11 MET) and remained off with the radiators conFig.d to the normal set point throughout the subsequent crew sleep period. After crew awakening, the FES was enabled on the primary B controller and it performed nominally in both the topping and water-dump modes for the remainder of the mission. (STS 72)

During ascent, the flash evaporator system (FES) high-load duct temperatures were erratic and lower than normal (Flight Problem STS-78-V-02). The inboard duct temperature dropped to approximately 119 degrees F (normally remains above 190 degrees F) by 172:15:02 G.m.t. (13 minutes MET). The heaters were reconFig.d from system-A-only to systems A and B at approximately 13.5 minutes MET, and the temperatures eventually recovered. Throughout the occurrence, the evaporator outlet temperatures were stable. No further problems with the FES were noted during ascent. To verify the performance of the high-load-duct system A heater, the heater was powered up at 173:16:14 G.m.t. (01:01:25 MET), and temperatures were monitored for approximately 2 hours and 45 minutes. A nominal temperature signature was observed. (STS 78)

2 Radiator Panel Design Method

Procedure

The radiator panels are designed based on the method described in the Spacecraft Thermal Control Handbook Handbook Vol 1, 2nd ed. by David Gilmore, pp 207-222.

Step 1: Determining Ts

The effective sink temperature Ts is essentially the temperature that radiators are radiating to. It takes into account the panel’s exposure to the Sun. Values for the sink temperature at various locations and inclinations are found on p. 9 of NASA/TM-2001-210063. For this analysis, we selected an inclination angle of 45o and a distance of 1 AU from the Sun. At this location, Ts = 212.9 K.

Step 2: Calculating fin effectiveness (η)

Eq. I–1 and I–2 give the fin effectiveness for a fin of uniform thickness.

|[pic][pic][pic] |I–1 |

|[pic][pic][pic] |I–2 |

The variables δ and θ* are given by Eq. I–3 and I–4 below.

|[pic][pic] |I–3 |

|[pic][pic] |I–4 |

In Eq. I–3 and Eq. I–4, the parameters L, Tb, ε1, ε2, k, and t are all variables specified by the user. The goal is to choose these values to minimize panel mass and area by selecting a fin material with a high conductivity and low density such as aluminum, beryllium, or a composite, choosing a coating with a high emissivity, maximizing Tb within reason, and optimizing L and t for the best solution.

Step 3: Calculating radiator area (A)

|[pic] |I–5 |

Eq. I–5 can be used to calculate the required radiator area. Q is a predetermined value, and ε is taken to be the average of ε1 and ε2.

Step 4: Calculating radiator panel mass (mpanel)

The mass of the panel is approximated by assuming the fin to be a sheet of the selected fin material with the uniform specified thickness t and the previously calculated area A. From these values the volume of material can be calculated. The fin mass is then calculated using the density of the fin material. The mass of the heat pipes is calculated using the distance between heat pipes, the total area A, and an assumed specific mass for the pipes of 0.11 kg/linear meter.

Step 5: Iteration and optimization

The above steps are repeated for various fin materials, coatings, and values of t and L and Tb. Plots of these evaluations are shown below in Fig. I.1, Fig. I.2, Fig. I.3, and Fig. I.4.

[pic][pic]

[pic][pic]

3 Matlab Code

The code shown here is used to produce the plots of radiator mass and area for variations in distance between heat pipes and fin thickness shown on the previous page. A more detailed description of the function of the code, methods of calculation, and assumptions is given within the heading below.

% RADIATOR PARAMETER COMPARISON - THERM_L_t_comp.m

%

% AAE 450 - Spring 2004

% Author: Melanie Silosky

% Date Created: 2/9/04

% Last Modified: 3/4/04

%

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

%

% DESCRIPTION

% Plots the variation of radiator mass and area with changes in heat

% pipe separation length and fin thickness

%

% METHODS OF CALCULATION

% Utilizes the method described on pages 218, 219 of the Spacecraft Thermal Control

% Handbook to size a radiator

% Assumptions:

% - emissivity is the same for side 1 and side 2 = .92 (Z-93)

% - The fin base temperature is 130.8 deg C

% - The effective sink temperature is the temp at 1 AU with an inclination

% of 45 degrees

% - The conductivity is equal to that for Be = 220 W/m K

% CALLED FUNCTIONS

% sinktemp.m

%

% VARIABLES

% ang = insolation angle of the radiator

% Ts = effective sink temperature

% Tb = fin base temperature

% Q = heat rejection capacity (Q = Ae*eta*sigma*Tb^4)

% L = distance between coolant tubes divided by 2

% e1, e2 = radiator emmittance of side 1 and side 2

% k = fin conductivity

% t = fin thickness

% eta = radiator fin effectiveness

% sigma = Stefan-Boltzmann constant

% m_panel = radiator panel mass (not including deployment structure)

% A = radiator area

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

clear all

close all

%Variables

ang = [45];

Ts = sinktemp(ang);

Tb = 130.78 + 273.15; %[K]

Tb = 25.625 + 273.15;

Tb = (4.4 + 83)/2 + 273.15; % for HAB radiator sizing

Q = [1000]; %:1000:300000]; %[W]

sigma = 5.67e-8; %[W/(m^2*K^4)]

e1 = 0.92;

e2 = 0.92;

k = 220; %[W/m K]

% Calculation of delta parameter

t_counter = 1;

for t = [0.18 0.28 0.38 0.48 0.58 1 1.5 2]./1000

L_counter = 1;

for L = [5:5:50]./100

delta(L_counter) = sigma.*L.^2*Tb^3*(e1 + e2) ./ (k.*t);

L_counter = L_counter + 1;

end

delta_array(t_counter,:) = delta;

t_counter = t_counter + 1;

end

[m,n] = size(delta_array);

% Calculation of fin effectiveness (eta)

theta_star = Ts ./ Tb;

for i = 1:m

for j = 1:n

d = delta_array(i,j);

if d >0.01 & d 0.2 & d maximum temperature seen is 116.3989391305419 [deg. K]

plot(P_loss(1:maxplossindex), Temp1(maxplossindex,1)*ones(1,maxplossindex), ':r')

plot(P_loss(maxplossindex), Temp1(maxplossindex,1), '*r')

plot(P_loss(maxplossindex)*ones(1,maxplossindex), Temp1(1:maxplossindex), ':r')

text(P_loss(maxplossindex)*.1, Temp1(maxplossindex,1)*1.02, 'Maximum Temperature = 116 degrees Kelvin')

text(P_loss(maxplossindex)*.57, Temp1(maxplossindex,1)*.7, 'Total Power_l_o_s_s = 584 W')

%Near Mars:

%plot(P_loss, Temp1(1:length(P_loss),100), 'r')

function output = T2(P_loss, r_w, L_w, sigma, epsilon_coat, Re, Rm, solar_e, solar_m, IR_e, IR_m, albedo_e, albedo_m, E_alt, M_alt, S_dist)

output = ((P_loss/(2*pi*r_w*L_w) + (1367/(S_dist^2))*(1+ albedo_e/100 + albedo_m/100) + IR_e*Re/((E_alt + Re)^2) + IR_m*Rm/((M_alt + Rm)^2))/sigma/epsilon_coat)^(1/4);

function output = T1b(P_loss, r_w, L_w, sigma, epsilon_coat, Re, Rm, solar_e, solar_m, IR_e, IR_m, albedo_e, albedo_m, E_alt, M_alt, S_dist, Temp2, w_ins, k_ins)

output = Temp2 - (-P_loss/(2*pi*r_w*L_w) - sigma*epsilon_coat*Temp2^4 + (1367/(S_dist^2))*(1+ albedo_e/100 + albedo_m/100) + IR_e*Re/((E_alt + Re)^2) + IR_m*Rm/((M_alt + Rm)^2))*w_ins/k_ins;

2 Heat Shields – Matthew Branson

To help aid in the endeavor of heat shield design, the Sandia One-Dimensional Direct and Inverse Thermal (SODDIT) computer code designed by Sandia National Laboratories in 1972. SODDIT was created to calculate the ablation of different bodies entering the atmosphere. As further development of the code occurred, SODDIT had the ability to do inverse heat conduction problem and time integrated heat flux problems. Integrated heat flux is the option used in SODDIT to calculate temperature histories along a depth of thermal protection system (TPS) using only a given a heat flux and the material properties of the TPS. Proving the heat shield will hold up against the harsh conditions can be done using the temperature distributions of the material.

The first step in heat shield design is material selection. A Matlab code is created using thermal networks to determine approximated layer thickness. The following equation is used for the thermal networks of the heat shield2:

|[pic] |I–6 |

SODDIT uses an .inp file to run. An output file will be produced after an input file utilizes 10 blocks of properly formatted information as outlined in the SODDIT manual to run SODDIT. [pic]

An example of one of the input files we used is shown below

Code 1: Example Input file for SODDIT

**block 1 control flags

c23456789 123456789 123456789 123456789 123456789 123456789 123456789 123456789

03001000000000010000000000000000000000000000000000000000000000000000000000000000

RCC, AETB, RCC, Honeycomb,

0.002000, 0.020000, 0.002000, 0.060000,

Heating with known time dependant flux

**block 3 print times and print intervals, maximum of 20 and 19 resp

0.0 3000 6

**block 4 general problem constants

dtmin dtmax theta dtempm sigma radius expn fract1 fract2

0.000001 0.5 1.0 10. 5.66961e-8 0.0 0.0

**block 5**********material property data

**rho dhf treff qstar tabl matnam (start past col 41)

1560 0.0 2060 C-C Reinforced

**temp cp cond emit absrp

144.44 502.80 2.338 0.60

366.67 879.90 5.144 0.80

533.33 1089.41 6.356 0.83

811.11 1298.91 7.361 0.87

1088.89 1424.61 7.655 0.90

1366.67 1550.31 7.749 0.89

-1 1944.44 1843.61 7.500 0.54

**rho dhf treff qstar tabl matnam (start past col 41)

128 0.0 1850 AETB

**temp cp cond emit absrp

255.56 628.50 0.064 0.85

366.67 988.84 0.077 0.85

588.89 1051.70 0.107 0.85

811.11 1118.74 0.150 0.85

1033.33 1185.78 0.211 0.85

1366.67 1269.58 0.354 0.85

1644.44 1269.58 0.535 0.85

-1 1755.56 1269.58 0.626 0.85

**rho dhf treff qstar tabl matnam (start past col 41)

1560 0.0 2060 C-C Reinforced

**temp cp cond emit absrp

144.44 502.80 2.338 0.60

366.67 879.90 5.144 0.80

533.33 1089.41 6.356 0.83

811.11 1298.91 7.361 0.87

1088.89 1424.61 7.655 0.90

1366.67 1550.31 7.749 0.89

-1 1944.44 1843.61 7.500 0.54

**rho dhf treff qstar tabl matnam (start past col 41)

129 0.0 533 Honeycomb

**temp cp cond emit absrp

297 878 0.0751

-1 477.5 1005.6 0.1389

/end of block 5 material property tables

**block 6 user defined node generation data

**initial temperature

** 200 290

**(node no) (mat) (dxi) (Temperature) (Area) (Vol) )(NGAP)

1 1 0.00013333 200.00 1.00000000 0.00013333 0

2 1 0.00013333 200.14 1.00000000 0.00013333 0

3 1 0.00013333 200.29 1.00000000 0.00013333 0 …

61 4 0.00400000 290.00 1.00000000 0.00400000 0

/end of Block 6 Node generation

**block 7 front face boundary condition data

**ibcty1 ifmt1 trad1

1 0 20

**time rec enthapy rad input C sub h P

** sec J/Kg W/m^2 Kg/m^2-s atm

0 0 7.2766E+002 0

2 0 8.4184E+002 0 …

598 0 6.0851E+002 0

600 0 6.0784E+002 0

601 0 0.0000E+000 0

3000 0 0.0000E+000 0

/end of block 7 aero heating boundary conditions

**block 8 back face boundary condition data

**ibctyn ifmtn tradn (perfectly insulated back face boundary condition)

0 1.0E-03 1.0E-9 1000. -1720.44 MARS NO ABLATE

1.0E-03 1.0E-9 300. -1929.71 MARS NO ABLATE 1

1.0E+01 1.0E-9 1000. -1720.44 MARS NO ABLATE

1.0E+01 1.0E-9 300. -1922.91 MARS NO ABLATE 3

The output file is very large so a perl script is written to find the important information and place that into a separate file for each case ran and then deletes the output file to save computer memory for important information. The following is an example of the output file created.

Code 2: Output File from Perl Code

C1_out.out: 6.477841E+02 6.467295E+02 3.183484E+02 3.182669E+02 2.900000E+02

C2_out.out: 8.490033E+02 8.474768E+02 3.529327E+02 3.528010E+02 3.001505E+02

C3_out.out: 9.638606E+02 9.618139E+02 3.521541E+02 3.520377E+02 3.038407E+02

C4_out.out: 1.033539E+03 1.031424E+03 3.632496E+02 3.631168E+02 3.093869E+02

C5_out.out: 1.072052E+03 1.069245E+03 3.508359E+02 3.507318E+02 3.068508E+02

C6_out.out: 1.084357E+03 1.081585E+03 3.525426E+02 3.524363E+02 3.077758E+02

S1_out.out: 6.683623E+02 6.673241E+02 3.218976E+02 3.218125E+02 2.900000E+02

S2_out.out: 8.723183E+02 8.708512E+02 3.571622E+02 3.570255E+02 3.021030E+02

S3_out.out: 9.889504E+02 9.866944E+02 3.560138E+02 3.558921E+02 3.057743E+02

S4_out.out: 1.059012E+03 1.056167E+03 3.674710E+02 3.673316E+02 3.114866E+02

S5_out.out: 1.097697E+03 1.094955E+03 3.544571E+02 3.543485E+02 3.088127E+02

S6_out.out: 1.109807E+03 1.107094E+03 3.562438E+02 3.561328E+02 3.097798E+02

Table I.2 shows the flow of the computer codes.

[pic]

This coding was run numerous times to verify that the thicknesses of the material would hold up against the harsh conditions of the Mars atmosphere.

Code 3: Matlab Code converting.m

function converting(filenameM,z1)

% Program to make multiple input files at one time

% By Matthew Branson AAE 450 Senior Design Project

% March 18, 2004

%

% Input filenames into a matrix and panel location, if no panel location

% then make z >6

%

% This is for a four layer insulator with the following layers.

% Material 1 C-C composite matrix (Front Facesheet)

% Material 2 AETB

% Material 3 C-C Composite matrix (Backside Facesheet)

% Material 4 Honeycomb

% Filename inputs should be in the following format ['1','2','3','etc']

% This insures proper placement throughout program

% Example of function input file

% converting(['1_CLD1'; '2_CLD2'; '3_CLD3';], [1;2;3])

%filenameM=['1_CLD5'; '1_CLD4'; '1_CLD3'];

%z1=[1;2;3;]; If z>6 then it will ask for your input

%Find all the areas/thickness

ang=(1.3090-1.0472)/(pi/2);

r=5.2;

%Area numbers are different panels throughout the shield

A1=r*(1/6)*40;

A2=r*(1/6)*40;

A3=r*(1/6)*40;

A4=r*(1/6)*40;

A5=r*(1/6)*40;

A6=r*(1/6)*40;

%Sphere surface areas

A7=(1/6)*4*pi*r^2/2;

A8=(1/6)*4*pi*r^2/2;

A9=(1/6)*4*pi*r^2/2;

A10=(1/6)*4*pi*r^2/2;

A11=(1/6)*4*pi*r^2/2;

A12=(1/6)*4*pi*r^2/2;

%A=A1+A2+A3+A4+A5+A6+A7+A8+A8+A9+A10+A11+A12

rho1=1560; % Density of the C-C

rho2=128; %Density of the AETB

rho3=1560; % Density of the C-C

rho4=129; % Density of Honeycomb

%Find the total size of all the input files

b=size(filenameM);

i=b(:,1);

v=b(:,2);

masses=[];

As=[];

Vs=[];

for j=1:1:i

z=z1(j);

% Find different Thickness

%Develop thickness for this heat Shield

if z==1

thick1=0.002;

thick2=0.02;

thick3=0.002;

thick4=0.06;

A=A1;

elseif z==2

thick1=0.002;

thick2=0.02;

thick3=0.002;

thick4=0.06;

A=A2;

elseif z==3

thick1=0.002;

thick2=0.025;

thick3=0.002;

thick4=0.06;

A=A3;

elseif z==4

thick1=0.002;

thick2=0.025;

thick3=0.002;

thick4=0.06;

A=A4;

elseif z==5

thick1=0.002;

thick2=0.03;

thick3=0.002;

thick4=0.06;

A=A5;

elseif z==6

thick1=0.002;

thick2=0.03;

thick3=0.002;

thick4=0.06;

A=A6;

elseif z==7

thick1=0.002;

thick2=0.02;

thick3=0.002;

thick4=0.06;

A=A7;

elseif z==8

thick1=0.002;

thick2=0.02;

thick3=0.002;

thick4=0.06;

A=A8;

elseif z==9

thick1=0.002;

thick2=0.025;

thick3=0.002;

thick4=0.06;

A=A9;

elseif z==10

thick1=0.002;

thick2=0.025;

thick3=0.002;

thick4=0.06;

A=A10;

elseif z==11

thick1=0.002;

thick2=0.03;

thick3=0.002;

thick4=0.06;

A=A11;

elseif z==12

thick1=0.002;

thick2=0.03;

thick3=0.002;

thick4=0.06;

A=A12;

else

fprintf('For %s\n',filenameM(j,:))

thick=input('Input thickness from outside to inside of spacecraft in meters (place in matrix)');

thick1=thick(:,1);

thick2=thick(:,2);

thick3=thick(:,3);

thick4=thick(:,4);

A=input('Input area of this section')

end

fprintf('Running file %s\n',filenameM(j,:))

filename=filenameM(j,:);

soddit2({'RCC','AETB','RCC','Honeycomb'},[thick1 thick2 thick3 thick4],[1:2],filename,1,'materialsaerobraking');

clear filename

%protect against micro-metorites

%thick2=thick2*2;

%thick1=thick1*2;

mass=(rho1*thick1+rho2*thick2+2*rho3*thick3+2*rho4*thick4)*A;

As=[As A];

masses=[masses mass];

V=(thick1+thick2+2*thick3+2*thick4)*A;

Vs=[Vs V];

end

masses

totalmass=sum(masses)

totalarea=sum(As);

totalV=sum(Vs)

density=totalmass/totalV

Soddit2.m matlab code, used to develop the .inp files

Code 4: Soddit2.m

function [density, masses, Tmaxwall,heatout]=soddit2(mat,thick,tpsmat,filename,hindex,type)

% Matlab code orginally written by Damon Landau

% Modfied 2-23-2004 By Matthew Branson

%soddit2({'Graphite Ablator','RCC','Carbon Insulator','RCC','Honeycomb'},[1e-3 2e-2 4e-2 1e-3 4e-2],[1:2],'6',1);

comp=1;%are we using UNIX (1), or DOS (2)

%If top layer is an ablator, then "Ablator" must be part of its name to model ablation

%Problem constants

%dims=[ 10 4.5 4 45 .05 ];% cylinder length, nose radius, leading edge length, sweep, LE radius (fin),

linrho=[7.1768 0 4.4853 3.2038 .1922 .1922 .7352 0 0]; %linear density of TPS kg/m for hindex values

n=15;%number of elements per material

timemax=3000;%10000;%Maximum time of simulation

n_output=500;%number of output time values

%geometry

nmat=length(thick);%number of layers modelled

node=nmat*n+1;%total number of "nodes"

chunk=sum(thick);%total thickness

dx=thick/n;%thickness of element per material

%Form vector of temperature distribution across thickness

tinit=[200 290];%0 & thickness initial temp, linearized across length

delT=thick/chunk*(tinit(1)-tinit(2));%Change in temperature across each individual layer

Tn=tinit(1)-cumsum(delT);%Temperature at the bottom of each layer

Tn=[tinit(1) Tn(1:nmat-1)];%Temperature at the top of each layer

Tdist=tinit(1);%initialive Temperature distribution vector

for mc=1:nmat

Tdist_mc=Tn(mc)-delT(mc)/n*[1:n];%Find temperature at each node for a given layer

Tdist=[Tdist Tdist_mc];%append to the vector for use in Block six

end

disp('Creating input file');

inputfname=[filename '.inp'];

infile=fopen(inputfname,'w');

%set flags

prt=1;%1 to write to print file, 0 not to

%if top layer is an ablator, specify the proper flag, and create FRACT for use in block 4

if findstr('Ablator',mat{1});abl=3;else;abl=0;end

if abl==3;fract=[.001 0.05];else;fract=[];end

flags=zeros(1,80);%all other flags are zero

flags(4)=abl;flags(5)=prt;flags(16)=1;flags(2)=3;

%get heating data

heat=load([filename '.qw']);%load heating data from file

heat=[heat(:,1) zeros(size(heat,1),1) heat(:,1+hindex) zeros(size(heat,1),1)];%format for use in SODDIT

heatout(1)=max(heat(:,3));

heatout(2)=trapz(heat(:,1),heat(:,3));

%condense heating data by removing long series of zeros (SODDIT wil interpolate)

i=2;%initialize

while i< length(heat)-1

%if the heating value is zero for three successive points then remove the middle one.

%this leaves the beginning and end of long stretches of zeros

if heat(i-1,3)==0 & heat(i,3)==0 & heat(i+1,3)==0;

heat(i,:)=[];i=i-1;

end

i=i+1;

end

if heat(end,1)>timemax

timemax=heat(end,1);;%run for longer of user specified and file specified time values

else

%add q=0 at end to allow for equilibrium

heat=[heat;heat(end,1)+1 0 0 0;timemax 0 0 0];%append

end

mp=fopen('matprop');%material property file

%write to input file

%block 1

fprintf(infile,'%s \n',...

'**block 1 control flags',...

'c23456789 123456789 123456789 123456789 123456789 123456789 123456789 123456789',...

sprintf('%1i',flags));

%block2

%write material names and thicknesses

fprintf(infile,' %s, ',mat{:});fprintf(infile,'\n');

fprintf(infile,' %f, ',thick);

fprintf(infile,'\n Heating with known time dependant flux\n');

%block3

fprintf(infile,'%s \n',...

'**block 3 print times and print intervals, maximum of 20 and 19 resp',...

[' 0.0 ' num2str(timemax) ],...

[' ' num2str(ceil(timemax/n_output))] );

%keep number of time steps to under 300

%block4

fprintf(infile,'%s \n',...

'**block 4 general problem constants',...

' dtmin dtmax theta dtempm sigma radius expn fract1 fract2',...

[' 0.000001 0.5 1.0 10. 5.66961e-8 0.0 0.0 ' num2str(fract)]);

% % %block5

fprintf(infile,'%s\n','**block 5**********material property data ');

% for matc=1:length(mat)

materialsaerobraking

fprintf(infile,'%s \n','/end of block 5 material property tables');

%block6

fprintf(infile,'%s \n',...

'**block 6 user defined node generation data',...

'**initial temperature',['** ' num2str(tinit)],...

'**(node no) (mat) (dxi) (Temperature) (Area) (Vol) )(NGAP)');

mat_dist=ceil([1:node]/n);mat_dist(end)=mat_dist(end)-1;%Find which material correponds to each node

thick_dist=thick(mat_dist)/n;%thickness of each element

A_dist=ones(n*nmat+1,1)';%Relative area of each element, (can change for different geometries)

V_dist=thick_dist.*A_dist;%Relative volume of each element, (can change for different geometries)

nodedat=[ [1:n*nmat+1]' mat_dist' thick_dist' Tdist' A_dist' V_dist' zeros(n*nmat+1,1)];%make matrix

fprintf(infile,'%i %4i %10.8f %10.2f %10.8f %10.8f %5i \n',nodedat');%format & write

fprintf(infile,'/end of Block 6 Node generation\n');

%block 7

fprintf(infile,'%s \n',...

'**block 7 front face boundary condition data',...

'**ibcty1 ifmt1 trad1',...

[' ' num2str([1 0 20])],...

'**time rec enthapy rad input C sub h P',...

'** sec J/Kg W/m^2 Kg/m^2-s atm');

%write qdot data to input file

fprintf(infile,' %i %i %.4E %i \n',heat');

fprintf(infile,'%s \n',...

'/end of block 7 aero heating boundary conditions',...

'**block 8 back face boundary condition data',...

'**ibctyn ifmtn tradn (perfectly insulated back face boundary condition)',num2str(0));

%block 9 pseudo atmosphere data (not used but necessary to fool SODDIT, hahaha)

fprintf(infile,'%s\n',...

' 1.0E-03 1.0E-9 1000. -1720.44 MARS NO ABLATE ',...

' 1.0E-03 1.0E-9 300. -1929.71 MARS NO ABLATE 1 ',...

' 1.0E+01 1.0E-9 1000. -1720.44 MARS NO ABLATE ',...

' 1.0E+01 1.0E-9 300. -1922.91 MARS NO ABLATE 3 ');

disp(['Created ' inputfname]);

ext=findstr('.inp',inputfname);%find index of .inp extension

Mass properties .dat file used in Soddit2 to find best suitable materials for heat shield is shown below

Code 5: materials.dat

TPS material properties (SI units)

first line is density, maximum temp, and heat of ablation (For ablators only)

following lines are

temp(k) Cp(J/kg/k) K(W/m/k) emmisivity (For surface materials only)

*note: Precision is not specified and is not to be assumed through significant digits.

charts

Alumina Enhanced Thermal Barrier-8

AETB

128.15 1850

255.56 628.50 0.064 0.85

366.67 988.84 0.077 0.85

588.89 1051.70 0.107 0.85

811.11 1118.74 0.150 0.85

1033.33 1185.78 0.211 0.85

1366.67 1269.58 0.354 0.85

1644.44 1269.58 0.535 0.85

1755.56 1269.58 0.626 0.85

Advanced Flexible Reusable Surface Insulation

AFRSI

144.16 1644.4

255.56 628.50 0.043 0.87

477.78 817.05 0.072 0.82

700.00 1005.60 0.114 0.72

811.11 1089.41 0.137 0.66

1033.33 1257.01 0.187 0.56

Aluminum

2707 933.3

200.00 791.91 237.000

500.00 925.99 237.000

700.00 997.22 226.000

900.00 1086.47 213.000

Graphite/Epoxy, (IM-6/3501-6), Fiber Volume = 63.5%

Composite

1440 450

298 857.2 5.3229

300 857.2 5.3229

Graphite Ablator

1730 3500 67.22e6

200.00 838.00 120.00 0.85

500.00 1131.30 106.00 0.85

1000.00 1738.85 64.000 0.83

1500.00 1843.60 47.500 0.82

2000.00 2053.10 40.000 0.82

2500.00 2136.90 35.500 0.82

3000.00 2136.90 31.000 0.80

3500.00 2304.50 22.000 0.80

Carbon Insulator

228.9 3500

277.78 544.70 0.087 0.90

555.56 1319.85 0.100 0.90

833.33 1613.15 0.117 0.90

1111.11 1801.70 0.137 0.90

1388.89 1927.40 0.168 0.90

1666.67 2011.20 0.212 0.90

1944.44 2082.43 0.274 0.90

2222.22 2136.90 0.374 0.90

2500.00 2168.32 0.549 0.90

2777.78 2199.75 0.860 0.90

3055.56 2220.70 1.434 0.90

3333.33 2220.70 2.494 0.90

3611.11 2220.70 4.614 0.90

3888.89 2220.70 8.480 0.90

HEXCEL HRH - 327 Glass Rinforced Polymide

Honeycomb

129 533

297 878 0.0751

477.5 1005.6 0.13893

LI-2200

Shuttle Tile

352.9 1811

255.56 628.50 0.074 0.90

533.33 1055.89 0.113 0.77

811.11 1206.73 0.152 0.61

1088.89 1257.01 0.206 0.46

1366.67 1269.58 0.277 0.37

1644.44 1269.58 0.367 0.30

1783.33 1269.58 0.423 0.28

Steel

7625 2700

300 460.9 30

300 460.9 30

Reinforced Carbon-Carbon

RCC

1560 2060

144.44 502.80 2.338 0.60

366.67 879.90 5.144 0.80

533.33 1089.41 6.356 0.83

811.11 1298.91 7.361 0.87

1088.89 1424.61 7.655 0.90

1366.67 1550.31 7.749 0.89

1944.44 1843.61 7.500 0.54

Titanium

4510 873

200.00 460.90 24.500

500.00 628.50 19.700

1000.00 754.20 20.700

1500.00 670.40 24.500

2000.00 670.40 28.000

Teflon Ablator

2194.47 822. 2.19e6

277.78 879.27 2.492 0.5

333.33 963.01 2.928 0.5

388.89 1055.12 3.115 0.5

444.44 1130.49 3.190 0.5

500.00 1201.67 3.115 0.5

572.22 1381.71 2.772 0.5

ZrB2+SiC

UHTC

5520 2858

370.00 712.30 98.884 0.70

770.00 712.30 84.638 0.70

1270.00 717.33 89.247 0.70

1770.00 763.42 75.420 0.70

2270.00 807.00 68.297 0.70

A matlab file was written to be used in the matlab codes

Code 6: Matlab Material File

fprintf(infile,'%s \n',...

'**rho dhf treff qstar tabl matnam (start past col 41) ',...

' 1560 0.0 2060 C-C Reinforced ',...

'**temp cp cond emit absrp ',...

' 144.44 502.80 2.338 0.60',...

' 366.67 879.90 5.144 0.80',...

' 533.33 1089.41 6.356 0.83',...

' 811.11 1298.91 7.361 0.87',...

' 1088.89 1424.61 7.655 0.90',...

' 1366.67 1550.31 7.749 0.89',...

'-1 1944.44 1843.61 7.500 0.54',...

'**rho dhf treff qstar tabl matnam (start past col 41) ',...

' 128 0.0 1850 AETB',...

'**temp cp cond emit absrp ',...

' 255.56 628.50 0.064 0.85',...

' 366.67 988.84 0.077 0.85',...

' 588.89 1051.70 0.107 0.85',...

' 811.11 1118.74 0.150 0.85',...

' 1033.33 1185.78 0.211 0.85',...

' 1366.67 1269.58 0.354 0.85',...

' 1644.44 1269.58 0.535 0.85',...

'-1 1755.56 1269.58 0.626 0.85',...

'**rho dhf treff qstar tabl matnam (start past col 41) ',...

' 1560 0.0 2060 C-C Reinforced ',...

'**temp cp cond emit absrp ',...

' 144.44 502.80 2.338 0.60',...

' 366.67 879.90 5.144 0.80',...

' 533.33 1089.41 6.356 0.83',...

' 811.11 1298.91 7.361 0.87',...

' 1088.89 1424.61 7.655 0.90',...

' 1366.67 1550.31 7.749 0.89',...

'-1 1944.44 1843.61 7.500 0.54',...

'**rho dhf treff qstar tabl matnam (start past col 41) ',...

' 129 0.0 533 Honeycomb',...

'**temp cp cond emit absrp ',...

' 297 878 0.0751',...

'-1 477.5 1005.6 0.1389');

This is only a preliminary analysis. There are some faults with this analysis since SODDIT is being used as a one-dimensional heat flux. Even with these faults we feel this is accurate enough program to do analysis of this problem since no ablation was used.

1 Aeroshell heat flux prediction and design – Robert Manning

A large surface of the vehicle is covered by the aeroshell, over 700 square meters. Any reduction in TPS thickness or density could reduce the dry mass by several thousand kilograms and ultimately reduce cost. However, reducing aeroshell mass diminished the probability of mission success for two reasons. The Martian atmosphere varies greatly in density and could result in large temperature variances on the heat shield, eventually causing failure. Secondly, the TPS materials would be subject to the hostile space environment, in particular meteoroids, for long periods of time. Meteoroid impacts would expose damage the outer TPS materials and cause thermal failure during the aerocapture maneuver.

In order to design a proper TPS, we found heating rates for all locations on the surface. First, the Knudsen number was calculated to be about 0.01 for the portions of higher heating fluxes. This ensured that a continuous flow existed; otherwise modeling the flow would be more difficult. Also laminar flow is assumed. On top of these assumptions, the aeroshell is treated as a yawed infinite cylinder.[i] Using this assumption, Eq. I-7 provides the stagnation heat fluxes. We apply a cosine distribution for the heat fluxes away from the stagnation point.

|[pic] |I–7 |

As stated before, the density on Mars varies greatly. We found a Martian general climatic model that predicts density and density standard deviations for different times, storm conditions, seasons, location, and altitude.[ii] By varying the several aerodynamic properties (discussed in previous sections) and density profiles, a variety of heating profiles is determined, see Fig. I.5. From this the aeroshell materials and thicknesses is picked.

[pic]

[pic]

In addition to designing for thermal heating, the aeroshell must survive meteorite impacts for trans-Mars portion of the mission. In order to design a protection scheme, we assumed that the heating rates would not be altered due to small irregularities from these impacts. This allowed us to simply add additional layers on top of the original TPS. Two outer sacrificial layers were added to absorb these impacts. The thickness (tb) of the bumper, the outer most layer, was determined by equation 8. The separation (S) was provided by the low density AETB foam. The back wall, which absorbs the remaining particles and gases from the impact, is much thicker (tw).[iii] The most damage will be sustained by the foam

|[pic] |I–8 |

2 Micrometeorite damage assessment – Robert Manning

In order to do a preliminary risk assessment, we needed to find the probability of aeroshell damage to due micrometeorites. The amount of material needed to protected against a hit is proportional to the cube root of the kinetic energy of the particle, referred to as quasi-energy in this paper (dV2/3).

By combining a diameter (d) and velocity (V) distributions, a distribution of the kinetic quasi-energy of the micrometeorites is obtained. First we calculate the probability of a particle of a certain mass hitting the aeroshell area over a period of one year.[iv] The diameter is exacted by assuming a density of 2.7 g/cm3. The velocity distribution (Fig. I.7) describes the relative velocity of these particles in respect to Earth.[v] We assume the identical velocity distribution for the spacecraft. By assuming that the velocity and diameters are independent of one another, the quais-energy distribution is found, see Fig. I.8.

The aeroshell is designed to protected against meteoroid with less than 0.8 cm-(km/s)2/3. This means that the impact will not affect the aeroshell’s thermal performance. From Fig. I.9, we have a probability of being hit from leaving earth to arrive at Mars, about 11%

[pic]

[pic]

[pic]

% LoadMarsDensity.m

%AAE 450 - Spring 2004

%Author/s: Robert Manning

%Date Created: 3/6/04

%Last Modified: 3/6/04

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

%DESCRIPTION

%Loads the density (kg/m^3) and standard deviation of atmosphere for Mars

%based on time of day, dust conditions, and season.

% MUST BE CALLED: [RhoData,RhoDev]=LoadMarsDensity(0,90,'High','./');

%METHODS OF CALCULATION

% Data analyzed and collected from

%CALLED FUNCTIONS

% Rho_High_LS120_0.mat* Rho_Low_LS120_0.mat* Rho_Mod_LS120_0.mat*

% Rho_High_LS120_12.mat* Rho_Low_LS120_12.mat* Rho_Mod_LS120_12.mat*

% Rho_High_LS120_16.mat* Rho_Low_LS120_16.mat* Rho_Mod_LS120_16.mat*

% Rho_High_LS120_20.mat* Rho_Low_LS120_20.mat* Rho_Mod_LS120_20.mat*

% Rho_High_LS120_4.mat* Rho_Low_LS120_4.mat* Rho_Mod_LS120_4.mat*

% Rho_High_LS120_8.mat* Rho_Low_LS120_8.mat* Rho_Mod_LS120_8.mat*

% Rho_High_LS120_Dev.mat* Rho_Low_LS120_Dev.mat* Rho_Mod_LS120_Dev.mat*

% Rho_High_LS90_0.mat* Rho_Low_LS90_0.mat* Rho_Mod_LS90_0.mat*

% Rho_High_LS90_12.mat* Rho_Low_LS90_12.mat* Rho_Mod_LS90_12.mat*

% Rho_High_LS90_16.mat* Rho_Low_LS90_16.mat* Rho_Mod_LS90_16.mat*

% Rho_High_LS90_20.mat* Rho_Low_LS90_20.mat* Rho_Mod_LS90_20.mat*

% Rho_High_LS90_4.mat* Rho_Low_LS90_4.mat* Rho_Mod_LS90_4.mat*

% Rho_High_LS90_8.mat* Rho_Low_LS90_8.mat* Rho_Mod_LS90_8.mat*

% Rho_High_LS90_Dev.mat* Rho_Low_LS90_Dev.mat* Rho_Mod_LS90_Dev.mat*

%VARIABLES

%Time: Time (hr) on 0"W on Mars (0,4,8,12,16,20)

%Season: Season on Mars (90,120)

%Dust: Amount of Dust on Mars: (Low, Mod, High)

%Expect_Rho: Mean density at point (kg/m^3)

%SD_Rho: Standard deviation at point (km/m^3)

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

function [RhoData,RhoDev] = LoadMarsDensity(Time,Season,Dust,Path);

load([Path, 'Rho_' Dust, '_LS', Num2Str(Season), '_', Num2Str(Time), '.mat']);

load([Path, 'Rho_', Dust, '_LS', Num2Str(Season), '_Dev.mat']);

% GetMarsDensity.m

%AAE 450 - Spring 2004

%Author/s: Robert Manning

%Date Created: 3/6/04

%Last Modified: 3/6/04

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

%DESCRIPTION

%Returns the density (kg/m^3) and standard deviation of atmosphere for

%certain latitude, longitude, altitude, time of day, dust conditions, and

%season.

%METHODS OF CALCULATION

% Data analyzed and collected from

%CALLED FUNCTIONS

% LoadMarsDensity.m must be called first.

%VARIABLES

%Lat: Latitude (deg) - East is positive

%Long: Longitude (deg) - North is positive

%Alt: Altitude (m)

%RhoData: When called should be RhoData

%RhoDev: When called should be RhoDev

%Expect_Rho: Mean density at point (kg/m^3)

%SD_Rho: Standard deviation at point (km/m^3)

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

function [Expect_Rho,SD_Rho] = GetMarsDensity(Lat,Long,Alt,RhoData,RhoDev);

% Assume E is positive (deg)

LongNum = interp1([-180:15:180],[1:25],Long,'spline');

% Assume N is positive (deg)

if (abs(Lat) < 87.5)

LatNum = interp1([87.5:-5:-87.5],[1:36],Lat,'spline');

elseif (Lat >= 87.5)

LatNum = 1;

else

LatNum = 36;

end

%Altitude above surface (meters)

if (Alt < 5)

AltNum = 1;

Expect_Rho = interp3(RhoData,LongNum,LatNum,AltNum,'linear');

SD_Rho = interp3(RhoDev,LongNum,LatNum,AltNum,'linear');

elseif (Alt > 120000)

Expect_Rho = 0;

SD_Rho = 0;

else

AltNum = interp1([5,20,50,115,240,490,980,1800,3400,7000,9600,14200,19500,25000,31000,37000,43000,48000,54000,60000,65000,71000,77000,82000,87000,92000,97000,101000,106000,110000,114000,120000],[1:32],Alt,'spline');

Expect_Rho = interp3(RhoData,LongNum,LatNum,AltNum,'linear');

SD_Rho = interp3(RhoDev,LongNum,LatNum,AltNum,'linear');

end

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] Tauber, Michael E. “A Review of High-Speed, Convective, Heat-Transfer Computation Methods.” NASA TP-2914, July 1989.

[ii] “Martian Server home page (LMD/AOPP).”

[iii] Eric L. Christiansen. “METEOROID/DEBRIS SHIELDING.” TP.2003-210788, August 2003.

[iv] “Meteoroid Environment Model – 1970 [Interplanetary and planetary].” NASA SP-8038, October 1970.

[v] “Background: Meteoroid and debris models.” 23 April 2003.

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

Mass (kg)

[pic]

Fig. I.3 Radiator mass and area vs. thickness, L = 0.1 m

[pic]

Fig. I.2 Radiator panel mass vs. heat pipe separation for various fin thicknesses

[pic]

Fig. I.1 Radiator area vs. heat pipe separation for various fin thicknesses

Area (m2)

[pic]

Fig. I.4 Radiator mass and area vs. thickness, L = 0.2 m

Mass (kg)

Area (m2)

Table I.1 SODDIT formatting information

|Block |Formatted Information |

|1 |Control Flags |

|2 |Title of heading characters |

|3 |Print intervals, print times for results |

|4 |General problem constraints |

|5 |Material property data |

|6 |Initial temperature distribution, node and element data |

|7 |Boundary condition for front face |

|8 |Boundary condition for back face |

|9 |Enthalpy of boundary layer gas |

|10 |Energy generation rate constants |

Table I.2 Computer code flow

|Function |Program |

|Location of Possible Entry Coridor |Aero_capt_fail.m, Aero_de.mi |

|Density Outputs for Mars |LoadMarsDensity.mii |

|Finding Heating of Spacecraft throughout Aero-braking |Aerocapture_heat.m, cylinder_stag_heat.mii |

|Distriubuting the thickness to proper locations |Converting.m |

|Creating Material Property file |Materials.m, matprop.dat |

|Creating .inp file for SODDIT |Soddit2.miii |

|Runs SODDIT a set number of times |Masterrun.plii |

|Finding temperature distribution |SODDITiv |

|Formating the output file for ease of analysis |Rencase.pl, findmax.pl, makesmall.plii |

i Matlab codes written by Ryan Whitley

ii Computer codes written by Robert Manning

iii Sandia One-Dimensional Direct and Inverse Thermal Code (SODDIT), Sandia National Laboratories, Albuquerque, New Mexico, 1990

iv Soddit Matlab code written by Damon Landau and modified by Matthew Branson

[pic]

Fig. I.5 Monte Carlo simulation of maximum heating rates

[pic]

Fig. I.6 Damage on aeroshell - small holes (red), extensive damage (green), damage but no penetration (blue)

[pic]

Fig. I.7 Probability of certain diameter cometary meteoroid hitting spacecraft

[pic]

Fig. I.8 Relative velocity distribution of cometary meteoroids

[pic]

Fig. I.9 Probability of aeroshell damage for a shield protected against meteoroids of certain quasi-energy

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