An improved fourier transform method for measuring thermal boundary layer temperature field using fringe extrapolation

Abstract

Using Gerchberg fringe extrapolation as the interferogram preprocessing, we improve the spatial carrier Fourier transform method (FTM) for measuring temperature field of the thermal boundary layer. Since the fringes abruptly disappear on the solid boundary, large ripples may occur in the retrieved phase/temperature if the original interferogram is directly analyzed by the FTM. Using the extrapolated interferogram, the edge effect can be shifted to the region near the virtual extrapolated boundary, so the ripples are significantly reduced near the physical solid boundary. In our interference experiment, the spatial resolution of the interferogram is 5.47 μm. Through adjusting the fringe density, a large enough spatial carrier frequency can be obtained to void frequency aliasing for high temperature gradient measurement. We first validate the proposed FTM through the measurement of a stagnant air layer between a hot upper plate and a cold lower plate. In comparison with temperatures measured by the thermocouple, the maximum difference is less than 0.3 °C for temperature measurement and 2% for local temperature gradient measurement. We then study the free convection of a hot vertical plate. Through the temperature field measurement, we obtain the local heat transfer coefficient and the Nusselt number. Compared to the similarity solution, the deviation of the local Nusselt number is 2%–6%, except the upper and lower edge regions. The proposed method can also be used to capture the transient temperature field for further studying the convection formation and evolution.