Hall D Cryostat Heat load and Flow calculations

• What are we doing ?1. Measuring the heat leak into the magnet for all the 4 coils 2. Determining of number of super insulation layers to reduce radiation3. Determining the equivalent diameter for the panels and the plumbing4. Evaluating the head loss in the plumbing due to friction5. Also considered the effects of two phase flow in the panel

6. Mass flow rate of LN2 in the heat shields

• Why are we doing ?1. To determine the relation between flow rate and heat input2. To address whether the coolant pipes are large enough to carry

away the heat leakage with out excessive temperature rise in the heat shields

Ravi AnumagallaJefferson LabGlueX collaboration meetingMay 20th

Cake Pan

Vacuum Tank Cover

Helium Vessel

Inner Panel

Outer Panel

Intermediate Panel

Support & Side Panels

73 Dia

77.5 Dia

114 Dia

Cross section of coil 2,3,4 All Dimension Are In Inches

Support Link

Heat leak into

coils

Conduction70%

Radiation30%

AtmosphereSupportLinks

Convection ? Is reduced by evacuating the coil to 10 -5 torr

The total heat load on each coils are as follows

22736Coil4

9412Coil2/coil3

Total heat load

(Watts)

# of Support links

Coil

Hall D thermo-siphon

Determination of equivalent Diameter

• Verification of Equivalent diameter:– Methods

• Analytical calculations

• CAD geometry verification

• Experimental calculations

• Governing Equations for Analytical Calculations– These Equations have been derived from Darcy Weibach’s equation and Blasius

Equations

75.4/175.475.4

25.0

2

2

5

5

NdD

d

Q

Q

D

f

f

f

f

Q

Q

d

D

sl

s

s

l

l

s

l

s

l

s

l

l

l Where

Dl = Equivalent diameter for N number of passages

ds= Equivalent diameter for a single passage

N = number of passages

f = friction factor in a single passage

Equivalent Diameter

Section A-A

Section A-A

Flow cross-sectional area & thickness of the panelActual flow cross-sectional view

Experimental setup at ODU

Results

Equivalent Diameter (INCHES)Method

0.28015Experimental

0.2708Analytical

0.2653CAD verification

Flow Calculations

• Calculations are based on homogenous model

• The governing equations are

DPliqDPmixxDPcorrDPtot )()(

totgrav

xliqgrav

DPDP

ghDP )(

DPtot = Total pressure drop (gm/cm2)

DPcorr = Two phase pressure drop correction factor

DPmix = Pressure drop in two-phase flow piping (Panels/Returns) (gm/cm2)

DPliq = Pressure drop in single phase supply line (gm/cm2)

DPgrav = Differential density induced driving pressure (gm/cm2)

Hall-D LN2 thermo-Siphon Flowrate

0

20

40

60

80

100

120

140

160

0 200 400 600 800

Heat Load(W)

Ma

ss

flo

w r

ate

(g

m/s

ec

)

MflowrateC

OIL

2 /

CO

IL 3

CO

IL 4

94 227

Mass Flow Rate VS Heat Load

The cooling is generally considered to adequate if the thermo-siphon flow rate increases under an increased heat load, the safe design load to choose would generally be 6 times or more

Hall-D "X" fraction

0

0.002

0.004

0.006

0.008

0.01

0 50 100 150 200 250

Heat Load (W)

Vo

id F

ract

ion

Void Fraction

Void Fraction VS Heat Load