Local Solution to the Unsteady Stefan Problem for In-Flight Ice Accretion Modeling

Abstract

A new model for in-flight ice accretion is presented for both rime and glaze conditions. The model is based on the\ud local, exact solution of the unsteady Stefan problem for the temperature profiles within the ice layer in glaze\ud conditions. The new model moves from Myers’s formulation, and it includes an unsteady description of the heat\ud diffusion problem within the ice layer. Moreover, the local value of the air temperature outside the boundary layer is\ud used to compute convective heat fluxes, in place of the constant freestream temperature value considered in Myers’s\ud model. A source term is introduced to take into account mass transfer at the boundary separating rime and glaze\ud regions. The model was implemented in the ice accretion software PoliMIce to perform numerical simulations of inflight\ud ice accretion over two-dimensional airfoils in both rime and glaze ice regimes. The open-source computational\ud fluid dynamics software OpenFOAM was used to compute the aerodynamic flowfield and to reconstruct water\ud droplet trajectories. Numerical results suggest that the modifications introduced with respect to the original Myers\ud model improve significantly the accuracy of the predicted ice shapes for the considered test cases. The introduction of\ud the local value of air temperature was found to be essential for the formation of the well-known two-horn ice shape,\ud due to the occurrence of a local glaze to rime transition. The diverse contributions to the heat fluxes are discussed for\ud both the proposed and the Myers models

Modeling In-Flight Ice Accretion Under Uncertain Conditions

“…Within each sub-domain, a one-dimensional phase-transition problem is solved (in the direction of the local surface normal). [6]. According to this reference, the 𝑄 bottom contribution, depending on the unsteady heat diffusion problem within the ice layer, can be expressed by means of a similarity variable…”

“…The reader is referred to the nomenclature section for the definition of each entry included in the aforementioned equations and to Ref. [6] for a comprehensive analysis of the accretion model.…”

“…Practically, the icing modeling activity resulted into the development of a wide variety of mathematical models which are implemented in several numerical codes, see e.g. [3][4][5][6][7][8][9][10][11][12][13][14]. Computational models help investigating ice build-up, providing a mean to predict ice formation at critical locations over the aircraft fuselage and wings.…”

Acoustic Characterization of Glaze and Rime Ice Structures on an Oscillating Airfoil via Fully Unsteady Simulations

“…The model used in this work to capture the complex experimental ice shapes is the local exact solution of the unsteady Stefan problem for the temperature profiles within the ice layer in glaze conditions (Ref. 34). This model moves from Myers' formulation and includes an unsteady description of the heat diffusion problem within the ice layer and uses local values of the air temperature outside the boundary layer to compute the convective heat fluxes.…”

Efficient radial basis function mesh deformation methods for aircraft icing

“…The PoliMIce software library provides state-of-the-art ice formation models [16]. The model used in this work to capture the complex experimental ice shapes is the local exact solution of the unsteady Stefan problem for the temperature profiles within the ice layer in glaze conditions [19]. Multi-step ice accretion simulations are performed at 5 second intervals to iteratively update the solution and account for unsteady ice accretion.…”