1. 1 Calorimeter Thermal Analysis with Increased Heat Loads September 28, 2009

2. 2 Coupling Between the Thermal and Convective Flow Solutions The temperature distribution at the ID of the outer 12 mm Argon blanket reduces the net heat transfer by 10% –The lower half of the collimator OD is warmer because the internal argon gap is thinner there –Convection coefficients in the thermal analysis cases are reduced to 90% of the values obtained from the CFD. The circumferential variation in heat removal rates determined from the CFD result, decreases the maximum calorimeter temperature rise by 4% at nominal heating rates (less at anticipated higher heating rates). –This effect is neglected These issues are discussed on slides 3-7 Slide 8 explains why a coupled analysis was not performed.

3. 3 Interaction Between Conduction and Convection Solutions Convection Calculations (CFD) –Most convection models were run with uniform temperatures on the inner and outer walls enclosing the 12 mm argon layer. –One convection case used a representative circumferential temperature distribution on the ID and gave 90% of the uniform temperature heat transport. Thermal solutions use an OD convection coefficient that increases with increasing temperature. This is derived from uniform wall temperature results. –The following slides show that, for uniform temperature walls, heat is removed faster from the bottom of the OD of the calorimeter and deposited further up on the heat sink’s ID (for ΔT < 2°K). –The use of the temperature dependent convection coefficient has the effect of increasing heat flow from the bottom of the OD of the calorimeter because that region is warmer. I reduced convection coefficients to 90% of the value obtained for uniform wall temperatures to account for the reduction in film coefficient obtained from the realistic temperature distribution. I think this ensures that the thermal results are conservative. The temperature dependent convection coefficient is needed to accommodate the axial temperature variation seen on the OD of the calorimeter. It also gives a bit more heat removal at the bottom compared to the top but doesn’t bias heat flux as heavily to the lower, warmer, areas at nominal heat loads as the CFD solution.

4. 4 Interaction Between Conduction and Convection Solutions, Cont. The plot below gives the nodal heat flux for a 2D case with uniform convection coefficient and with a convection coefficient that varies from bottom to top approximating the 2D CFD solution for heat removal on the next slide. The maximum temperature with the varying convection coefficient was 4% less than for the uniform convection coefficient. A model that simultaneously solved the thermal and convective flow equations would be expected to yield a 4% lower maximum temperature at the lowest heat load cases being considered. The effect will be less at higher heat loads since the minimum convection is a larger fraction of the maximum convection for those cases.

5. 5 Heat Flux at 0.5°K Differential (Turbulent Option Off) The variation in heat removal on the inner cylinder is more pronounced when the turbulent option is turned off. Laminar flow probably persists at an 0.5°K differential

6. 6 Heat Flux at 0.5°K Differential (Turbulent Option On) While laminar flow probably persists at an 0.5°K differential, the effect of turbulence would be to increase the heat transfer from the inner cylinder from about -70 to +70 degrees (angular).

7. 7 Heat Flux at 2°K Differential At a 2°K differential the flow might be turbulent (Re=1822)and Heat transfer from the inner cylinder is slightly enhanced at the bottom and depressed near +70°

8. 8 Simultaneous Convection and Heat Conduction Solution Time constants: –Convective flow:~ 2 sec (time steps are 0.1 to 1 sec) –Thermal transient:~940 sec (see below) A combined run was not attempted because the run time (~6 hrs) for the CFD model limits the transient duration to about 300 seconds Temperature response of a point on the ID to a 1° step change in temperature of 1/8 of the OD. Temperatures at 752 sec

9. 9 Flow Patterns at the Top and Bottom At the top, convective cells form as would be expected for a fluid layer heated from below. At the bottom, convective cells are not apparent but the fluid is stirred by the cool argon flowing down the OD. The images on slides 10-12 showing these patterns were requested.

10. 10 Flow Pattern at the Top, 0.5 and 2° K Differential 2°K Differential 0.5°K Differential

11. 11 Flow Pattern at the Bottom, 0.5 and 2° K Differential 0.5°K Differential Laminar Flow (contour values are not the same as below) 0.5°K Differential Turbulent Flow is turned on, results are similar to those above

12. 12 Flow Pattern at the Bottom, 2 deg K Differential 2°K Differential, Turbulent Flow is turned on

13. 13 Reynold’s Number The effective channel depth for flow is half the thickness of the fluid layer (full thickness flows are possible but have not been observed) R = 2*p*V*h/mu for full thickness flow (the hydraulic diameter is 2*h) Transitional flow for 2000 < R < 4000 Turbulent flow if V>0.062 m/sec

14. 14 Laminar vs Turbulent Solution Options For all the higher heating rates, the laminar solution gives a Reynold’s number, Re, in the transitional or turbulent region but when the turbulent flow option is activated, the flow velocity drops and Re becomes characteristic of laminar flow. –Maximum velocity is used to compute Re so turbulent effects do not occur everywhere –The true solution is likely to be in the transitional region with convective heat transport rates that are higher than laminar and lower than turbulent rates. All results have used laminar convection to be conservative (H is 42% greater when turbulence is switched on)

15. 15 Three Dimensional Flow Results I ran the 3D model to see if convective cells consisting of near through thickness flows would develop. The 3D results hint at slightly increased heat flow compared to 2D results but these coarser mesh models predict about 40% of the heat flux of the fine mesh 2D model. –The 3D results were compared to comparably meshed 2D results to estimate the effect of 3D vs 2D flows. –3D models (and the comparably meshed 2D models) may not have been run long enough to establish a quasi-steady state heat flow (net heat flow tends to increase slowly with time from the intial conditions of zero velocity and linear thermal gradients).

16. 16 Circulation Pattern, Inside and Outside Views at the Same Time Inside View Surface is ¼ thickness Outside View Surface is 3/4 thickness 2°K differential, 4 element layers in model, the inner two layers are shown See the movie files “D3-velocities.avi” and “D3-flux.avi” (use Windows media player)

17. 17 Circulation at an Earlier Time (Eddy’s are not Stable) Inside View Surface is ¼ thickness Outside View Surface is 3/4 thickness

18. 18 Increased Heat Loads The following models all have: –10 W/m 2 heat leak at the ID (unless otherwise noted) –Ohmic heating of 4.95 W/m 3 –Temperature dependent Convection at the OD Laminar flow results used Convection coefficient reduced 10% based on evaluating convection with a representative temperature profile on the id. The convection coefficient at each location was assigned based on the temperature at that location. –Several iterations were required to converge on stable temperatures.

19. 19 Convection Results The equation fits the laminar results and was used in the runs reported on subsequent slides. Reynold’s numbers for laminar flow indicate that the turbulent solution might be appropriate for ΔT > 0.5°K (Re=2000) and certainly for ΔT > 2°K (Re=4000). The problem is that when turbulence is turned on the velocity drops making Re<2000 up to a ΔT of 8°K. I assumed that turbulence was appropriate in local regions (Re was computed for the maximum velocity) so results would be somewhat conservative if the laminar H was used.

20. 20 Summary of Results See above for more information about run parameters The maximum temperature listed is the increase over the outer wall in contact with the 12 mm thick argon layer. This surface was fixed at 90°K. The “OD Annulus Inner T” gives the minimum and maximum temperatures on the aluminum tube that forms the inner wall of the 12 mm outer argon jacket.

21. 21 Nominal Heat Load + Ohmic Heating and 10 W/m 2 ID Heat Leak

22. 22 Temperature Dependent Convection Coefficient, Nominal Loading Temperatures applied to the equation H=0.9*(47.6+7.51ln(ΔT)) W/m 2 /°K give the convective coefficients shown below in W/mm 2 /°K

23. 23 6xNominal Heat Load + Ohmic Heating and 10 W/m 2 ID Heat Leak

24. 24 10xNominal Heat Load + Ohmic Heating and 10 W/m 2 ID Heat Leak

25. 25 20xNominal Heat Load + Ohmic Heating and 10 W/m 2 ID Heat Leak

26. 26 10xNominal Heat Load + Ohmic Heating and 20 W/m 2 ID Heat Leak