Model wing inviscid flow-around computation by finite element method of high accuracy in conditions of thin ice formation

Aerodynamics and heat-exchange processes in flying vehicles


Duong D. T.

Moscow Institute of Physics and Technology, 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia



The article presents the model wing inviscid flow-around computation by finite element method of high accuracy in conditions of the thin ice formation. The goal of the article consists in solving the problem of flow-around MS(1)-317 profile and NACA 64A008 wing by non-viscous gas water suspension. The system of equations of water content in the framework of Euler approach is described. The system in itself is not hyperbolic, and regions of “vacuum”, where water content ρ tends to zero, appear. To eliminate the said problem the system regularizing was performed to make the system hyperbolic. The new primary variable r = lg ρ was introduced. The resulting modified water content equation system was solved by Galerkin method with discontinuous basis functions (RMG). Orthogonal polynomials are used as basis functions in RMG. Initial and boundary conditions were formulated. At the initial instant the aqueous dispersion mixture is considered moving together with the gas. Parameters on the solid surface were computed in a special way.

The problem solution is split into two stages. At the first stage, the inviscid dry gas flow-around the wing is computed. Then, the obtained field is used as the basic field, and the finely-dispersed aqueous mixture flow around the wing is calculated. The water suspension droplet, sticking to the wing surface (capture coefficient β), defines the probability of the thin ice appearance.

As an example, calcolations for two typical problems were performed: the flow around the MS(1)-317 profile and the NACA 64A008 wing. The obtained results were compared to the experimental data. It is shown, that in the case of moderate incidence angles, the RMG scheme of the third accuracy order ensures the calculation accuracy of the water droplet capture coefficient on the wing about the 5% order. It is acceptable in practice.


wing, thin ice, water content equations, Galerkin method with discontinuous functions, high accuracy order, capture coefficient


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