40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 ATF eLog Not logged in
 Thu Aug 5 11:53:26 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Wed Aug 11 14:58:47 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Wed Aug 11 18:00:19 2021, Koji, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Fri Aug 13 15:14:14 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Fri Aug 13 21:01:42 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Thu Aug 19 14:34:10 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Fri Aug 20 13:44:58 2021, rana, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Fri Aug 20 14:05:45 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS
Message ID: 2641     Entry time: Wed Aug 11 14:58:47 2021     In reply to: 2636     Reply to this: 2642
 Author: Radhika Type: DailyProgress Category: Cryo vacuum chamber Subject: Cooldown model fitting for MS

I've made simplifications to the testmass cooling model. Assuming 2 possible cooling mechanisms, radiative and conductive, the ODE must be a function of only $(T_{coldplate}^4 - T_{testmass}^4)$ and $(T_{coldplate} - T_{testmass})$. If conductive cooling/heating of the testmass is treated as negligible, as we previously assumed, then:

$\ddot{Q}_{testmass} \approx {\color{Blue} a} \sigma (T_{coldplate}^4 - T_{testmass}^4)$, where a is the fit parameter. I include $\sigma$ in the equation because it would appear as a constant in any radiative transfer model. I use the measured coldplate/inner shield temperature data for $T_{coldplate}$. Note that $\frac{dT}{dt} = \frac{\ddot{Q}}{Cp*m}$, and here and throughout I use a temperature-dependent $Cp_{Si}(T)$.

The best fit parameter is a = 0.014, and the result of this fit can be seen in Attachment 1. The disagreement between the best-fit model and data suggest that cooling is not only dependent on $(T_{coldplate}^4 - T_{testmass}^4)$, i.e. it cannot be radiative alone. I added back a conductive heating/cooling component:

$\ddot{Q}_{testmass} = {\color{Red} a} \sigma (T_{coldplate}^4 - T_{testmass}^4) + {\color{Red} b}(T_{coldplate} - T_{testmass})$, where a and b are the parameters of the fit.

The result of the fit can be seen in Attachment 2. The best fit parameters [a, b] = [0.022, -0.0042]. This model matches the data much better than the purely radiative model, but the negative sign on b is non-physical (I think) since $(T_{coldplate} - T_{testmass})$ should always be < 0, so the sign of the conductive term should also be < 0. I'm not sure how to interpret this result, but it almost seems like there is conductive heating to the test mass even though physically this shouldn't be the case.