rv rw roz

z=L

0

z=le

Evaporator

Condenser

VAPOR

LIQUID

Capillary Structure

Φg

Heat Pipe PrinciplesUse 2 phase flow, latent heat of vaporization, and capillary action to circulate a working fluid between heated and cooled regions via a wick.

ro = outer radius

rw = inner radius of wick

rv = radius of free space in tube

le = length of evaporation regime

Capacity of Heat Pipe• Increase in heat transfer must be consistent withcapillary driven circulation of the working fluid.

Difference in pressure between the vaporphase, pv (z ) , and the liquid phase pl (z ) , mustbe balanced by the surface tension in thecapillary structure.

pv (z ) − pl (z ) = ∆pv − ∆pl = 2γ cos θ

rc

pushes down pulls up

radius of capillary pore

∆pl = −pl (L ) + pl (0)

Constant

∆pl = −ρlgL sin ϕ −

bηlQeL

2π rw2 − rv

2( )ρlεrc2l

Angle to Frac. ofgravity Wick Vol.Φ=π/2 vertical Occ. by

Density of Φ=0 horizontal LiquidLiquid

Accelerationdue to gravity

Value of Constant 'b'

If pores are not interconnected, then b≈8

If the pores are interconnected, then b≈10-20

Optimum Pore Size (see Ref 10 Book by Silverstein)

Viscosity of liquid

r c =

bηlQeL

4π rw2 − rv

2( )ρlεlγ cos θ

Maximum Heat Transport

Qe =

πrw2 lγ cos θ

3Lερvρl

3bηv ηl

(Reynolds #<<1)

Qe =

4πrw2 l

32ρvρlεγ 2 cos2 θ

π 2 − 4( )bLη

13

(Reynolds #>>1)

Surface_Tension.xls

Surface Tension of Some Heat Pipe Liquids

T-°C Gamma-N/cmMethyl Alcohol 5 0 2.01

Ammonia 1 1 2.35Water 2 0 7.28

Na 816 12.1Li 1204 2 6

Page 1

Key Features of High Temperature Heat Pipes

• Extremely high heat transfer in a simplecontainer

• Allows many heat transfer loops, avoiding a single point failure

• Smaller units avoid bulky pressure vessel (implications for reentry)

• Avoids the use of valves, pumps orcompressors

• Ability to start up 'cold' avoids the need for preheat

• Nearly isothermal temperature transfer andhigh temperatures allows very highefficiency operation

Typical Performance Parameters for SpaceReactor Heat Pipe

Working Fluid LiOp. Temp. ° C 1200Axial Power Density Normal 8 kW/cm2 Contingency 10.5 kW/cm2Max. Radial Power Evaporator 105 W/cm2 Condensor 6.5 W/cm2Reliability 7 y normal 98 % 7 y contingency 96 %

Transport Limitations

• Sonic Limits

- Choked Vapor Flow - Typically occurs when pipe operates near the freezing point where vapor pressures and densities are very low. • Entrainment Limit

- High velocity vapor flow strips and entrains liquid droplets thereby impeding liquid flow to evaporator - Occurs at high loads and near freeze point

• Capillary Pumping

- Hydrodynamic balance between capillary forces and liquid/vapor viscous pressure drops - Usually determines limiting performance

• Boiling Heat Flux

- High local heat fluxes that cause nucleate boiling and interupts liquid flow in evaporator

Radiator Thermal Design

Energy Rejected by Radiator

Direct SolarRadiation

Earth Reflected Solar Radiation

Earth DirectRadiation

InternallyGeneratedHeat Load

F G F A G

F E P /A

T

α α

α

ε σ

s s s r pr s

e e ei

4

α=solar absorptivity= 0-1.0 (direct or reflected from the Earth)Fs=cosine of angle to sun = 0-1.0

Gs=solar constant= 1371 W/m2 at 1 AU

Fr=view factor ≈ 0.1 from low Earth orbit, 0.02 from GEOAp=Earth's albedo ≈ 0.3Fe=view factor of radiation emitted from the Earth to radiator ≈ 0.3

Ee=Earthshine radiation ≈ 240 W/m2