Final Project Discussion - University Of...

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Final Project Discussion And Thermal DesignENAE 697 - Space Human Factors and Life Support

U N I V E R S I T Y O FMARYLAND

Final Project Discussion• Final Report Discussion• Thermal Systems Design Overview

Thermal Systems Design• Fundamentals of heat transfer• Radiative equilibrium• Surface properties• Non-ideal effects

– Internal power generation– Environmental temperatures

• Conduction• Thermal system components

Classical Methods of Heat Transfer• Convection

– Heat transferred to cooler surrounding gas, which creates currents to remove hot gas and supply new cool gas

– Don’t (in general) have surrounding gas or gravity for convective currents

• Conduction– Direct heat transfer between touching components– Primary heat flow mechanism internal to vehicle

• Radiation– Heat transferred by infrared radiation– Only mechanism for dumping heat external to vehicle

Thermodynamic Equilibrium• First Law of Thermodynamics

! heat in -heat out = work done internally• Heat in = incident energy absorbed• Heat out = radiated energy• Work done internally = internal power used

(negative work in this sense - adds to total heat in the system)

Q "W =dUdt

Radiative Equilibrium Temperature• Assume a spherical black body of radius r• Heat in due to intercepted solar flux

• Heat out due to radiation (from total surface area)

• For equilibrium, set equal

• 1 AU: Is=1394 W/m2; Teq=280°K

Qin = Is" r2

Qout = 4" r 2#T 4

Is" r2 = 4" r2#T 4 $ Is = 4#T 4

Teq =Is4"#

Effect of Distance on Equilibrium Temp

Mercury

PlutoNeptuneUranus

SaturnJupiter

Asteroids

Shape and Radiative Equilibrium• A shape absorbs energy only via illuminated faces• A shape radiates energy via all surface area• Basic assumption made is that black bodies are

intrinsically isothermal (perfect and instantaneous conduction of heat internally to all faces)

Effect of Shape on Black Body Temps

Incident Radiation on Non-Ideal Kirchkoff’s Law for total incident energy flux on solid

bodies:

! where– ! =absorptance (or absorptivity)– " =reflectance (or reflectivity)– # =transmittance (or transmissivity)

QIncident =Qabsorbed+Qreflected +Qtransmitted

Qabsorbed

QIncident

+Qreflected

QIncident

+Qtransmitted

QIncident

" #Qabsorbed

QIncident

; $ #Qreflected

QIncident

; % #Qtransmitted

QIncident

Non-Ideal Radiative Equilibrium • Assume a spherical black body of radius r• Heat in due to intercepted solar flux

• Heat out due to radiation (from total surface area)

• For equilibrium, set equal

Qin = Is"# r2

Qout = 4" r 2#$T 4

Is"# r2 = 4# r 2$%T4 & Is = 4 $

Teq ="#Is4$

($ = “emissivity” - efficiency of surface at radiating heat)

Effect of Surface Coating on Temperature

$ = emissivity

Non-Ideal Radiative Heat Transfer• Full form of the Stefan-Boltzmann equation

! where Tenv=environmental temperature (=4°K for space)

• Also take into account power used internally

Prad ="#A T 4 $Tenv4( )

Is" As + Pint =#$Arad T4 % Tenv

Example: AERCam/SPRINT• 30 cm diameter sphere• !=0.2; $=0.8• Pint=200W• Tenv=280°K (cargo bay

below; Earth above)• Analysis cases:

– Free space w/o sun– Free space w/sun– Earth orbit w/o sun– Earth orbit w/sun

AERCam/SPRINT Analysis (Free Space)• As=0.0707 m2; Arad=0.2827 m2

• Free space, no sun

Pint = "#AradT4 $ T =

0.8 5.67 %10&8 Wm2°K 4

+ , 0.2827m2( )

) ) ) )

, , , ,

= 354°K

AERCam/SPRINT Analysis (Free Space)• As=0.0707 m2; Arad=0.2827 m2

• Free space with sun

Is" As + Pint = #$AradT4 % T =

Is" As + Pint#$Arad

= 362°K

AERCam/SPRINT Analysis (LEO Cargo Bay)

• Tenv=280°K

• LEO cargo bay, no sun

• LEO cargo bay with sun

Pint ="#Arad T4 $ Tenv

4( )% T =200W

0.8 5.67 &10$8 Wm 2°K 4

+ , 0.2827m2( )

+ (280°K)4

) ) ) ) )

, , , , ,

= 384°K

Is" As + Pint =#$Arad T4 % Tenv

4( )& T =Is" As + Pint#$Arad

+ Tenv4

= 391°K

EVA Thermal Equilibrium• Human metabolic workload = 100 W• Suit electrical systems = 40 W• Total heat load = 140 W

Q = �σAT 4 ⇒ A =Q

�σT 4

A =140

(0.8)(5.67× 10−8)(295)4= 0.41 m2

EVA Thermal Equilibrium with Sun• Human metabolic workload = 100 W• Suit electrical systems = 40 W• Total internal heat load = 140 W

Q + αAIs = �σAT 4 ⇒ A =Q

�σT 4 − αIs

A =140

(0.8)(5.67× 10−8)(295)4 − 0.2(1394)= 2.2 m2

Sublimation• Water heat of sublimation = 46.7 kJ/mole• @ 18 gm/mole = 2594 W-sec/gm• Mass flow for 140 W = 0.54 gm/sec• per hour = 194 gm/hr• 8 hr total EVA time = 1.55 kg of water• @ 2 EVA/day and 180 days = 559 kg of water

Sitting on a Planetary Surface

Radiative Insulation• Thin sheet (mylar/kapton with

surface coatings) used to isolate panel from solar flux

• Panel reaches equilibrium with radiation from sheet and from itself reflected from sheet

• Sheet reaches equilibrium with radiation from sun and panel, and from itself reflected off panel

Tinsulation Twall

Multi-Layer Insulation (MLI)• Multiple insulation

layers to cut down on radiative transfer

• Gets computationally intensive quickly

• Highly effective means of insulation

• Biggest problem is existence of conductive leak paths (physical connections to insulated components)

Emissivity Variation with MLI Layers

Ref: D. G. Gilmore, ed., Spacecraft Thermal Control Handbook AIAA, 2002

MLI Thermal Conductivity

Effect of Ambient Pressure on MLI

1D Conduction• Basic law of one-dimensional heat conduction

(Fourier 1822)

! whereK=thermal conductivity (W/m°K)A=areadT/dx=thermal gradient

Q = "KAdTdx

3D ConductionGeneral differential equation for heat flow in a solid

! whereg(r,t)=internally generated heat"=density (kg/m3)c=specific heat (J/kg°K)K/"c=thermal diffusivity

" 2T ! r ,t( ) +g(! r ,t)

K=#cK$T ! r ,t( )$t

Simple Analytical Conduction Model• Heat flowing from (i-1) into (i)

• Heat flowing from (i) into (i+1)

• Heat remaining in cell

TiTi-1 Ti+1

Qin = "KATi " Ti"1#x

Qout = "KATi+1 "Ti#x

Qout "Qin =#cK

Ti( j +1) " Ti( j)$t

… …

• Time-marching solution

• For solution stability,

Finite Difference Formulation

= thermal di!usivityd =!!t

i + d(Tn

i+1 ! 2Tn

i + Tn

!t <!x2

Heat Pipe Schematic

Shuttle Thermal Control Components

Shuttle Thermal Control System

ISS Radiator Assembly

Final Project Discussion - University Of...

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