1. 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 radiation 3. Determining the equivalent diameter for the panels and the plumbing 4. Evaluating the head loss in the plumbing due to friction 5. Also considered the effects of two phase flow in the panel 6. Mass flow rate of LN 2 in the heat shields Why are we doing ? 1.To determine the relation between flow rate and heat input 2.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 Anumagalla Jefferson Lab GlueX collaboration meeting May 20th

2. 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

3. Heat leak into coils Conduction 70% Radiation 30% AtmosphereSupport Links 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

4. Hall D thermo- siphon

5. 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 Where D l = Equivalent diameter for N number of passages d s = Equivalent diameter for a single passage N = number of passages f = friction factor in a single passage

6. Equivalent Diameter Section A-A Flow cross-sectional area & thickness of the panelActual flow cross-sectional view

8. Experimental setup at ODU

9. Results Equivalent Diameter (INCHES)Method 0.28015Experimental 0.2708Analytical 0.2653CAD verification

10. Flow Calculations Calculations are based on homogenous model The governing equations are DP tot = Total pressure drop (gm/cm2) DP corr = Two phase pressure drop correction factor DP mix = Pressure drop in two-phase flow piping (Panels/Returns) (gm/cm2) DP liq = Pressure drop in single phase supply line (gm/cm2) DP grav = Differential density induced driving pressure (gm/cm2)

11. COIL 2 / COIL 3 COIL 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

12. Void Fraction VS Heat Load