Level-Set Mass-Conservative Front-Tracking Technique for Multistep Simulations of In-Flight Ice Accretion

Abstract

This paper presents a novel level-set-based approach to model evolving boundary problems for in-flight ice accretion. No partial differential equations are solved as in the standard level-set formulation, but simple geometrical quantities are employed to provide an implicit discretization of the updated boundary. This method avoids mesh entanglements and grid intersections typical of algebraic and mesh deforming techniques, making it suitable for generating a body-fitted discretization of arbitrarily complex geometries as in-flight ice shapes, including the collision of separate ice fronts. Moreover, this paper presents a local ice thickness correction, which accounts for the body’s curvature, to conserve the prescribed iced mass locally. The verification includes ice accretion over an ellipse and a manufactured example to show the proposed strategy’s advantages and robustness compared to standard algebraic methods. Finally, the method is applied to ice accretion problems. A temporal and grid convergence study is presented for automatic multistep in-flight simulations over a NACA0012 airfoil in rime, glaze, and mixed ice conditions.

Ice Shape Convergence in Multi-Step Ice Accretion Simulations over Straight Wings

“…In fact, this process must be robust and automated so that no user intervention is required throughout the process. Following the work proposed in [14], the new ice-air interface is represented as the zero-contour level of a level-set function [33]. Given a 2D, or 3D, domain Ω ⊂ R 2,3 , a curve, or a surface, can be represented by a certain level-set (or isocontour) of the auxiliary function 𝜙(x), with x ∈ Ω.…”

“…In [14], the discrete level-set field was built considering the ice thickness to be accreted at the airfoil boundary and the distance of each grid node from it. This work defines the level-set scalar field with a novel algorithm, which can accurately describe the new ice-air interface even for large displacements.…”

“…The first concerns the choice of the duration of the various time steps, especially when no experimental data is available, and preliminary guesses about the ice shape must heavily rely on the user's experience. The second one regards the formation of the oscillations mentioned above and the importance of highly robust methods based, for instance, on remeshing techiniques [11,12], level-set methods [13,14], or immersed boundary methods [15,16] capable of overcoming mesh entanglement and grid intersections, which typically occur with standard deformation techniques when dealing with these complex ice shapes. Remeshing is also unavoidable to preserve the mesh quality even if no grid intersections occur.…”

Towards blade-resolved ice accretion simulations of flexible blades using mixed-fidelity models

“…Ice accretion is a complex multi-physics problem. Numerical modelling of the problem requires, in general, four steps: (1) the computation of the flow field around the geometry under analysis; in our framework, SU2 is used; (2) the computation of the trajectory of the droplets, to assess the fraction of free-stream water mass collected at a given location over the object's surface, i.e., the collection efficiency β = dA i dA∞ ; we use the in-house developed code PoliDrop [16]; (3) the computation of the ice growth with a thermodynamic module (PoliMIce [17]); and (4), the update and re-meshing of the geometry to restart from step (1), both for 2D and 3D geometries [18]. Indeed, accurate numerical representation of the evolution of the ice shape on a wing requires frequent updates of the geometry using a multi-step approach.…”

“…Indeed, accurate numerical representation of the evolution of the ice shape on a wing requires frequent updates of the geometry using a multi-step approach. Donizetti et al [19] recently showed that there is a strict relationship between the local ice thickness, the surface discretization, and the update frequency, allowing also to automatically set a timevarying optimal time discretization in the multi-step process.…”