Multidimensional Heat Flux Prediction From Surface Heating Rate Data with DFT Error Analysis

Paper number

IAC-05-C2.6.06

Author

Dr. J.I. Frankel, University of Tennessee, United States

Year

2005

Abstract

In aerospace applications, transient surface heat fluxes are often interpreted from surface temperature measurements. Unfortunately, inherent time differentiation of the surface temperature data is required to in order to reconstruct the heat flux. This is evident in one-dimensional, half-space, heat conduction studies where an Abel equation and its inversion provide a clear interpretation to this issue.  In the presence of temperature data, increasing the sample density exacerbates the problem even further. It has been previously described by the author that the appropriate data form in these cases should involve the heating/cooling rate, i.e., the instantaneous time derivative of temperature. This paper presents three important new findings applicable to hypersonics, arcjets and re-rentry investigations. 

medskip
First, the two-dimensional half-space heat conduction problem involving a surface mounted sensor network is analyzed indicating that the stable form of data collection for estimating the surface heat flux involves heating/cooling rate sensors. The resulting multidimensional Volterra-Fredholm equation is derived and numerically resolved. The placement of the sensor network is also discussed. As an aside, some remarks on proper temperature filtering using a newly designed Gaussian, low-pass filter is related containing an embedded cutoff frequency parameter based on discrete Fourier transforms (DFT) of signals. The cut-off frequency occurs when the noise begins to dominate over the signal. Second, a new discrete Fourier transform (DFT) error analysis method is briefly described illustrating that the root mean-square error of the surface heat flux can be predicted a priori as a function of sample density. Finally, the development of heating/cooling rate sensors at the University of Tennessee will be reviewed and their state will be discussed.

  

Abstract document

IAC-05-C2.6.06.pdf

Manuscript document

IAC-05-C2.6.06.pdf (🔒 authorized access only).

To get the manuscript, please contact IAF Secretariat.