Determination of three-dimensional temperature fields by holographic interferometry and numerical techniques

• Main Author: Yee, K. H.
• Published: University of Leicester 1982
• Subjects: 530.1; Theoretical physics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.345079

The object of this work is primarily to evaluate three-dimensional temperature field reconstruction by numerical techniques using experimental projection data from holographic interferograms with no degree of symmetry taken in reconstructing the test fields. The interferograms are produced using a pulsed laser, and are recorded by means of a photographic system for digitisation. The 3-D test fields are of two types: (i) the smoothly varying plume from a heated block, and (ii) the convective current set up by a localised heated spot on the floor inside an enclosure having walls, ceiling and floor all kept at a constant temperature. A number of numerical techniques is investigated. Using either the Grid element or Finite element mathematical model, overdetermined but inexact sets of equations are obtained, and then inverted using known iterative algorithms of the ART type, and also a new Least Squares of Residuals Technique (LSRT) which was developed by the author. To test the numerical techniques, particularly as only a limited range of viewing angles is obtainable, a preliminary experiment was performed on the plume, providing a thermocouple traverse and projection data. Simulated projection data computed from thermocouple readings compared favourably with the holographic projection data particularly at high fringe numbers. The numerical techniques were tested using both simulated and real projection data. Using ART inversion, the Grid element model produced better approximation to the thermocouple temperature field than the Finite element model. However, when solving the reconstruction equations using digitised projection data from the enclosure model severe instability was encountered with ART because the temperature field structure is now more complicated. Even with increased resolution the problem still persisted LSRT was subsequently developed to overcome this. In reconstruction with LSRT, the temperature on each pixel is determined by the sum of the squares of each of the residuals and thus does not involve using the projection data directly. Although this technique has given much more stable reconstructions, the restricted viewing angle range from the data still presents a problem in that when a comparision is made with the physics of the enclosure model even the best reconstructions available do not show good results. A form of directional bias appears in all of them. Also on a few, some random errors can be seen. These reconstructions therefore suggest that in practise data from the missing views are required when seeking to reconstruct satisfactorily the numerical values and shape of complicated 3-D temperature fields.