Technique for Heat Flux Determination

1
Technique for Heat Flux Determination

• John Heim
• Vanderbilt University

2
Motivation

• Accurate characterization of heating loads is
  crucial.
• Heat flux can provide meaningful information
  concerning the environment that a full-scale
  structure will experience.
• Temperature does not typically scale well.

3
Standard Techniques

• Heat Flux Gauge
• Uses thermopiles to measure temperature
  differences which can be converted to heat
  fluxes.
• Lagging response times, flow disturbance, and
  Calibration

• Calorimeter
• Lagging response times, flow disturbance.
• Complicated because heat load is not uniform
  across a surface due to lateral heat conduction.

4
Standard Techniques

• Thermochromatic Liquid Crystals
• Layers of crystals in thin films aligning based
  on temperature gradients.
• Calibration, difficult to apply, and difficult to
  measure accurately.

• Inverse Method
• Appropriate data reduction is a balancing act
  between introducing smoothing bias and
  amplification of noise
• Solutions may contain unacceptable errors.

5
New Heat Flux Determination Approach

• Measure a different quantity
• HEATING RATE- the time rate of change of
  temperature for a given location and time.
• Data reduction is inherently more stable.
• Inverse method techniques

6
New Problem

• No method exists to measure heating rate
  directly.
• Describe a technique to measure heating rate.
• Demonstrate a stable method for estimating heat
  flux from a measured heating rate.

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Thermographic Phosphors

• Rare-earth-doped ceramics that fluoresce when
  exposed to light.
• Intensity, frequency line shift, and decay rate
  are all temperature dependent.
• The strong dependence of the decay rate on
  temperature will be leveraged to acquire a
  heating rate.

8
Heating Rate

• Measure the intensity of phosphor emission.
• Temperature is not constant the normalized
  intensity is
• The heating rate can now be found

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Phosphor Activity
Excitation
Intensity
Phosphors Decay
Time
10
Theory

• The infinite series solution for the normalized
  temperature is
• The solution for the heating rate

11
Data Reduction Procedures
Q
q
Yn
QYn
QY
Hd
QHd
H
Hn
QHn
12
Triangular Heat Flux From Surface Temperature
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Triangular Heat Flux From Heating Rate
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Square Heat Flux
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Exact Heat Flux vs. Estimated Heat Flux
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Conclusion

• Improved heat flux estimates by reducing
  instabilities inherent in temperature to heat
  flux data reduction methods.
• By measuring heat rate the integral equation for
  heat flux becomes a Volterra equation of the
  second kind.
• More stable solutions which can accommodate more
  noise then a temperature approach.