A 3D Finite-Volume Integral Boundary Layer method for icing applications

Abstract

A three-dimensional integral boundary layer code was developed to allow fast computations of boundary layer flows for the purpose of ice accretion modelling. The model is derived in this paper. It is based on a surface Finite-Volume approach. The unsteady equations of momentum deficit and kinetic energy deficit are solved until convergence is reached, preventing from specifying explicitly the stagnation point or separation line. A validation of the code is also presented in the present article. First, the 3D solver is cross-checked against a 2D solver on test cases of self-similar flows and on a NACA0012 configuration. The modelling of the effects of three-dimensionality is also assessed on a self-similar flow test-case. Moreover, the use of unstructured grids is also validated. Finally, an example of the use of the code for the computation of ice accretion is presented.

Theory and validation of a 2D Finite-Volume integral boundary layer method intended for icing applications

“…This allows to perform calculations over airfoils with ice shapes which are often complex geometries. Finally, the model formulation and the discretization method have been chosen to ensure the possible extension of the method to the three dimensional case [23]. Many validation test cases have been performed, both on academic and more realistic configurations.…”

“…The ultimate goal of this work is to implement the IBL method in a 3D icing suite. To that end, the extension of the method to 3D is on-going [23,24,34]. Besides, the solver must be able to calculate the friction coefficient and the heat transfer coefficient over an ice shape.…”

“…However, the method presented here is also intended to be used for 3D and thermal boundary layer [23,24]. Thus, closure relations employed here are based on assumed velocity profiles because they will be easier to implement for the additional equations.…”

Analytical wall function including roughness corrections

“…For instance, in the framework of the development of ONERA's icing suites IGLOO2D [7,8] and IGLOO3D [9], which involve a large number of cycles of a flow solver, different solutions are currently being studied to avoid having resource to the use of wall-refined meshes. The first option consists in coupling a boundary layer code [10,11] to an Euler solver; the second being the development of a wall function approach in a Navier-Stokes environment.…”

“…complementary correction acting in all cells above, otherwise heat transfers would be badly captured. For this reason, Aupoix's correction(11) is acti-vated in all the following computations. AWF models are active in wall cells whereas Aupoix's thermal correction is only activated in the other cells.…”