Content of Presentation• Low temperature data for magnet-materials (Cu, NbTi,Insulation)

Specific heat, thermal conductivity, resistivity …….

• 4.5K Thermosyphon and 1.9K conduction

• HEPAC Old DOs program calculates: helium properties at different temp and pressures• \\Srv2_div\cryo\TOOLS\CRYODATA\HEPAK3.4

• Computational Fluid Dynamics. https://edms.cern.ch/document/624664/1 .

– MQY study. Heat Conduction through coil with a simple annular heating. (study completed)

– MQY study. Convection of helium through MQY structure. (study in progress)

G.A.Kirby

0

500

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3000

3500

0 50 100 150 200 250 300K

kJ/m3

0

20

40

60

80

%

[LEN97] (4-300K) [COL83] (4-20K)

[ELR82] (4-16K) [COL86] (4-18K)

[IWA90] (4-20K) [LAC98] (4-300K)

[HAN77] 0,38Nb+0,62Ti (10-300K) [AND83] (4-300K)

[DUC98] (4-300K) [STA81] (4-300K)

[TIX98] (4-300K) Cp NbTi i (minimum)

Cp NbTi a (maximum) (Cp NbTi a - Cp NbTi i) / Cp NbTi i (%)

Cp NbTi (kJ/m3.K)

Cp NbTi (B,T) in J/m3.K

T < 20 K TcB= 9.2 * (1 - B / 14.5) ^ 0.59 If T < TcB Then Cp = 49.1 * T ^ 3 + 64 * B * T Else Cp= 16.4 * T ^ 3 + 928 * T

T < 50 K Cp = -0.217724 * T ^ 4 + 11.983792 * T ^ 3 + 553.712993 * T ^ 2 - 7846.120813 * T + 41382.928569

T < 175 K Cp = -0.00000000482 * T ^ 4 + 0.00000297583 * T ^ 3 - 0.00071625148 * T ^ 2 + 0.08302230116 * T - 1.53178 * 10^6

T < 500 K Cp = -0.0000000000629 * T ^ 4 + 0.0000000929657 * T ^ 3 - 0.0000516653121 * T ^ 2 + 0.0137062419692 * T + 1.23554 * 10^6

T < 1000 K Cp = -0.000000257 * T ^ 2 + 0.000955466 * T + 2.450087571 * 10^6

** Hunt for data **Materials

NbTi

Cupper

Kapton

Epoxy

Stainless Steel

Iron

Cryogenic Material Properties

Cp

Resistivity

Conductivity

……..

HeliumTCpMQ ..HeliumTCp

QM

.

gVBuoyancy KK .. 5.48.4

22

hh A

M

D

fP

0.01

0.10

1.00

1.E+02 1.E+03 1.E+04 1.E+05Reynolds number Re

Fric

tion

fact

or

f He 300KwaterHe 40 - 70KHe 4.5KSimonsonHoenigKraftFit

716.04.08.0 PrRe259.0

b

wNu

h

h

D

A

MRe

Cp of Helium at 1.67 and 1.0 Bar

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0 1 2 3 4 5 6

Tem p [K]

Cp

[J/

kg-K

]

Cp He 1.67 Bar

Cp He 1 Bar

f

PDAM hh 2

1200

3LqT

Heat Extraction through Pipe with fixed 0.1K dT 1.85 to 1.95K Helium

0.05.0

10.015.020.025.030.035.040.0

0 0.1 0.2 0.3 0.4 0.5 0.6

Pipe Diameter (m)

Pip

e M

ax L

eng

th (

m)

L(m) 500W

L(m) 1kW

Van Sciver, “Helium Cryogenics”, pp. 143 - 144

>10^5 its turbulent

4.5K thermosyphon and 1.9K conduction

HePAC

Old Dos Program that give Helium many properties.

BUT needed updating to new system before Dos disappears or changes !

\\Srv2_div\cryo\TOOLS\CRYODATA\HEPAK3.4

HEPAK is a computer program for calculating the thermophysical properties of helium from fundamental state equations. The state equations are valid from 0.8 Kelvin or the melting line to 1500 Kelvin, including the superfluid range, the lambda line, and liquid vapor mixtures; as a function of pressure they are valid up to 1000 bars, except between 80 and 300 Kelvin where they are valid to 20,000 bars. HEPAK also includes thermal transport properties in both normal and superfluid, the dielectric constant, refractive index, and fluid surface tension. The user of HEPAK and this manual should be familiar with thermophysical concepts as applied to fluid properties

Cp of Helium at 1.67 and 1.0 Bar

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0 1 2 3 4 5 6

Temp [K]

Cp

[J/

kg-K

]

Cp He 1.67 Bar

Cp He 1 Bar

Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) is an analysis of fluid flow, heat transfer and associated phenomena in physical systems using numerical methods.

The basis of computational fluid dynamics is the reduction of the continuum differential equations describing the dynamics of the fluid (Navier-Stokes + mass and energy conservation equations) into a system of algebraic equations at a finite number of "grid" points, and the solving of the equations at these limited number of points only.

TS/CV/Detector Cooling - CFD Team

A wide range of application fieldsAerospace

Automotive

Biomedical

Buildings

Chemical

Environment

Marine

Power gen.

Turbo-machinery

MQY study. Heat Conduction through coil with a simple annular heating at

inner radii.

Steel

NbTi

Kapton

Fiberglass Epoxy

Cu

4.2 K

Heat source

Conduction heat distribution results

Heating 50 mW/mm^3 Into 2mm annulus

Heating 100 mW/cm^3 Into 2mm annulus

6.9 K5.7 K

Heat load

Convection heat transfer through MQY at 4.5K

Future tests

Quench heaters

The end