Astr512, Spring 2008: Group Beaton/Fields/Privon/Whelan Lab 3


Astr512, Spring 2008: Group Beaton/Fields/Privon/Whelan
Lab 3 Triple Spec Modeling

a work in progress ...

The Data

(postscript files)


The Project

Our objective is to create a model to predict the temperature in the Hawaii2 array based on the heating sources within TripleSpec. As shown in the sketch above, the Hawaii2 array is connected to a number of heating and cooling sources. The challenge for trying to understand the heat flow through this system centers on being able to disentangle and isolate the contributions from various heating and/or cooling sources at various points in their own evolution.

Sources of Heating and/or Cooling

  1. Weak Thermal Path from Main Cyrogen Tank
  2. Strong Thermal Path from the Aux Cyrogen Tank
  3. Uncharacterized Thermal Path through Cu Wires connected to 300K
  4. Internal Heater
In theory, each of these paths operate the same way. There is a heat source/sink that travels to the Hawaii2 detector through a thermal path. For some of the components, like the internal heater, this flow is nearly instantaneous. For others, the weak thermal path, the result on the Hawaii2 detector is much weaker. We can qualitatively expect that the terms for the more closely linked heat source/sinks will have much stronger dependencies on time and thereby much steeper slopes.

Weak Thermal Path

A weak thermal path connects the Main Cyrogen tank with both the Hawaii2 detector and the Aux Cyrogen Tank. We set the time that cyrogen is added to the tank to be time = 0. If we ignore the effect of the fill tube to the Aux Cyrogen Tank, then we can fit the temperature response of the Aux Cryogen Tank to the weak thermal path in order to characterize the the effect of the weak thermal path on the Hawaii2 detector. This covers the time range of approximately 54.5 to 55.5 days.
To fit the Aux Cyrogen Tank response to the weak thermal path we first smoothed the voltage data by a running average over 30 data points. This smoothing was determined in order to mitigate the effects of a significant discontinuity in the Aux Cyrogen Tank data. After smoothing, the data were shifted to set the inital introduction of liquid nitrogen as time 0 and the temperature in the Main Cyrogen Tank was set as temperature 0. We then fit two functions to our data, an exponential and a powerlaw of index n=-1.
Two Functional Fits to the Aux Tank (postscript)

We found that the radical fit the response of the Aux Cyro tank better than the exponential. We adopted the following relation for the Weak Thermal Path:
AuxT(t) = 1./(a*t+b) where a = 0.00805915 b = 0.00490098


Mysterious Thermal Path to Hawaii2 Detector

Having fit the Weak Thermal Path for the time range [54.5, 55.5], we can then subtract this effect from the temperature profile of the Hawaii2 array. Now we should only be left with the contribution of the Cu wires to 300K. Indeed, subtracting our fit for the Weak Thermal Path leaves us with a logarithmic like "heating" profile.

Residual Temperature in the Hawaii2 Detector with Model Fit (postscript)

Haw2H(t) = a*(1-exp(b*t)) + c where a = 56.9133 b = -3.44289 c = 8.37424

With this fit, we can characterize the temperature profile in the Hawaii2 Detector completely in the time range [54.5,55.5] (e.g. before cyrogen is added to the Aux Tank).
Hawaii2 Temperature Profile (postscript)

Haw2_T(t) = Haw2H(t) + AuxT(t) for t in [55.4, 55.5] days

Strong Thermal Path with Aux Cyrogen Tank

Applied Heat with Heater (as a Function of Watts)

Temperture Profile with Heated Watts with Fits (postscript)

We fit the portion of the cooling where 0W were applied with a falling exponential to determine the cooling only from the Aux Cooling tank and the weak thermal path. We subtracted this fit from the 2W and 1W data in an effort to isolate the heating from both the detector wires and the heater. As the figure below demonstates, the fit subtracted data points doesn't show clear evidence that we've isolated the heating to the array.

Data with 0W Fit Subtracted