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SUMMARYThe present paper is the second article in a three-part series on anisotropic mesh adaptation and its application to (2-D) structured and unstructured meshes. In the ÿrst article, the theory was presented, the methodology detailed and brief examples given of the application of the method to both types of grids. The second part details the application of the mesh adaptation method to structured grids. The adaptation operations are restricted to mesh movement in order to avoid the creation of hanging nodes. Being based on a spring analogy with no restrictive orthogonality constraint, a wide grid motion is allowed. The adaptation process is ÿrst validated on analytical test cases and its high e ciency is shown on relevant transonic and supersonic benchmarks. These latter test cases are also solved on adapted unstructured grids to provide a reference for comparison studies. The third part of the series will demonstrate the capability of the methodology on 2-D unstructured test cases.

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In-flight ice accretion, even though driven by a steady flow airstream, is an inherently unsteady phenomenon. It is, however, completely ignored in icing simulation codes (one-shot) or, at best approximated via quasi-steady modeling (multishot). The final ice shapes thus depend on the length of the total accretion time (one-shot), or of the arbitrarily prescribed time intervals (multishot), during which the impact of ice growth on both airflow and water impingement is ignored. Such a longstanding heuristic approximation is removed in this paper by coupling in time the dilute two-phase flow (air and water droplets flow) with ice accretion, and is implemented in a new code, FENSAP-ICE-Unsteady. The two-phase flow is solved using the coupled Navier-Stokes and water concentration equations, and the water film characteristics and ice shapes are obtained from laws of conservation of mass and energy within the thin film layer. To continually update the geometry of the iced surface in time, arbitrary Lagrangian-Eulerian terms are added to all governing equations to account for mesh movement in the case of stationary components. In the case of rotating/stationary interacting components, a dynamically stitched grid is used. The numerical results clearly show that unsteady modeling improves the accuracy of both rime and glaze ice shape prediction, compared with the traditional quasi-steady approach with frozen solutions. The unsteady model is shown to open the door for a unified approach to icing on fixed wings, on helicopters with blades/rotors/fuselage systems. Problems of current concern in the icing community such as the ingestion of ice crystals at high altitude become tractable with the new formulation.

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