40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 PSL Not logged in
Message ID: 2191     Entry time: Fri May 25 14:20:55 2018
 Author: shruti Type: DailyProgress Category: TempCtrl Subject: Simulation and measurement of thermal conductivity time constant - Vacuum Can

A model of vacuum can was constructed taking into account the heat conduction across the foam, neglecting the geometry of the foam and approximating an effective cross-sectional area and thickness.

The analytically calculated time for the decay of temperature to 1/e of the initial value  (time constant) = d*m*C/k/A = 2.99 hours, with constant ambient temperature and no heating. The parameters used in this calculation :

Mass of assembly Specific heat of steel can m 15.76 kg C 505 J/kg-K A 1.3 m^2 d 5.08e-2 m k 1.136*25.4e-3 W/m-K

'A' is not known very accurately and could even be as low as 0.48 m^2, and since the time constant is very sensitive to A a better estimate is required for a more accurate model. The units for 'k' in the spec sheet was confusingly W/m^2-K, nonetheless an approximation was made assuming it scales by thickness. An experiment to measure the time constant is now underway. This will give us a better idea of the values.

In order to study the evolution of temperature, scipy.odeint was used to perform numerical integration of the following equation:

$\frac{\text{d}T_{can}}{\text{d}t} = -\frac{kA}{mC}\frac{(T_{can}-T_{amb})}{d} + \frac{H}{mC}$,

where 'H' is the heating power.

This can be done even in the presence of fluctuating ambient temperatures and variable heating power (taken as a lists, piecewise functions).

In the two trial plots shown, the ambient temperature was stepped up from 300K to 315K at 10000 s (~2.77hours). One plot shows the evolution without heating and the other with a heating power of 18.46 W.

 Attachment 1: Temp_18W_StepTempAmbient.pdf  50 kB  Uploaded Fri May 25 15:21:55 2018
 Attachment 2: Temp_NoHeat_StepTempAmbient.pdf  63 kB  Uploaded Fri May 25 15:22:11 2018
ELOG V3.1.3-