Thermal analysis of anti-icing systems in aeronautical velocity sensors and structures

Abstract

This work reviews theoretical–experimental studies undertaken at COPPE/UFRJ on conjugated heat transfer problems associated with the transient thermal behavior of heated aeronautical Pitot tubes and wing sections with anti-icing systems. One of the main objectives is to demonstrate the importance of accounting for the conduction–convection conjugation in more complex models that attempt to predict the thermal behavior of the anti-icing system under adverse atmospheric conditions. The experimental analysis includes flight tests validation of a Pitot tube thermal behavior with the military aircraft A4 Skyhawk (Brazilian Navy) and wind tunnel runs (INMETRO and NIDF/COPPE/UFRJ, both in Brazil), including the measurement of spatial and temporal variations of surface temperatures along the probe through infrared thermography. The theoretical analysis first involves the proposition of an improved lumped-differential model for heat conduction along a Pitot probe, approximating the radial temperature gradients within the metallic and ceramic (electrical insulator) walls. The convective heat transfer problem in the external fluid is solved using the boundary layer equations for compressible flow, applying the Illingsworth variables transformation considering a locally similar flow. The nonlinear partial differential equations are solved using the Generalized Integral Transform Technique in the Mathematica platform. In addition, a fully local differential conjugated problem model was proposed, including both the dynamic and thermal boundary layer equations for laminar, transitional, and turbulent flow, coupled to the heat conduction equation at the sensor or wing section walls. With the aid of a single-domain reformulation of the problem, which is rewritten as one set of equations for the whole spatial domain, through space variable physical properties and coefficients, the GITT is again invoked to provide hybrid numerical–analytical solutions to the velocity and temperature fields within both the fluid and solid regions. Then, a modified Messinger model is adopted to predict ice formation on either wing sections or Pitot tubes, which allows for critical comparisons between the simulation and the actual thermal response of the sensor or structure. Finally, an inverse heat transfer problem is formulated aimed at estimating the heat transfer coefficient at the leading edge of Pitot tubes, in order to detect ice accretion, and estimating the relative air speed in the lack of a reliable dynamic pressure reading. Due to the intrinsic dynamical behavior of the present inverse problem, it is solved within the Bayesian framework by using particle filter.