The effects of atmospheric icing can be anticipated by Computational Fluid Dynamics (CFD). Past studies show that the convective heat transfer influences the ice accretion and is itself a function of surface roughness. Uncertainty quantification (UQ) could help quantify the impact of surface roughness parameters on the reliability of ice accretion prediction. This paper aims to quantify ice accretion uncertainties and identify the key surface roughness correction parameters contributing the most to the uncertainties in a Reynolds-Averaged Navier-Stokes (RANS) formulation. Ice accretion simulations over a rough flat plate using two thermal correction models are used to construct a RANS database. Non-Intrusive Polynomial Chaos Expansion (NIPCE) metamodels are developed to predict the convective heat transfer and icing characteristics of the RANS database. The metamodels allow for the computation of the 95% confidence intervals of the output probability distribution (PDF) and of the sensitivity indexes of the roughness parameters according to their level of influence on the outputs. For one of the thermal correction models, the most influential parameter is the roughness height, whereas for the second model it is the surface correction coefficient. In addition, the uncertainty on the freestream temperature has a minor impact on the ice accretion sensitivity compared to the uncertainty on the roughness parameters.

The prediction of heat transfers in Reynolds-Averaged Navier–Stokes (RANS) simulations requires corrections for rough surfaces. The turbulence models are adapted to cope with surface roughness impacting the near-wall behaviour compared to a smooth surface. These adjustments in the models correctly predict the skin friction but create a tendency to overpredict the heat transfers compared to experiments. These overpredictions require the use of an additional thermal correction model to lower the heat transfers. Finding the correct numerical parameters to best fit the experimental results is non-trivial, since roughness patterns are often irregular. The objective of this paper is to develop a methodology to calibrate the roughness parameters for a thermal correction model for a rough curved channel test case. First, the design of the experiments allows the generation of metamodels for the prediction of the heat transfer coefficients. The polynomial chaos expansion approach is used to create the metamodels. The metamodels are then successively used with a Bayesian inversion and a genetic algorithm method to estimate the best set of roughness parameters to fit the available experimental results. Both calibrations are compared to assess their strengths and weaknesses. Starting with unknown roughness parameters, this methodology allows calibrating them and obtaining between 4.7% and 10% of average discrepancy between the calibrated RANS heat transfer prediction and the experimental results. The methodology is promising, showing the ability to finely select the roughness parameters to input in the numerical model to fit the experimental heat transfer, without an a priori knowledge of the actual roughness pattern.

Ice shedding represents a threat to aircraft safety since ice blocks can strike rear components or can be ingested by engines. The accuracy of current numerical methods for predicting ice block paths in the design phase of an aircraft still need improvement. For the verification and validation of new trajectory calculation methods, shed blocks can be modelled for simplification as sphere or 6 Degree-Of-Freedom (6 DOF) plates. The objective of this paper is to propose a mathematical model for the dynamic moments of the plates and to use it to numerically simulate ice block paths. The results will be useful for verifying high-fidelity methods. Equations of motion in a Lagrangian frame are presented together with the correlations to be used for the aerodynamic coefficients of the ice blocks. The plate model involves the quaternions and a dynamic moment coefficient function of the angular velocity. After the model is validated with test cases obtained from the literature, the trajectories around the blended wing body will be plotted. The sensitivity of the trajectories and footprints to the chosen dynamic moment model will be highlighted.

<div class="section abstract"><div class="htmlview paragraph">In-flight ice accretion on aircraft is a major weather-related threat. Industries use both experimental investigations in icing conditions and ice accretion solvers based on computational fluid dynamics (CFD) for aircraft development. An ice accretion solver couples airflow over the geometry, water droplets impingement, and phase change to compute the ice accretion. Such a solver usually relies on a two-equation model: a mass balance and an energy balance. Past studies highlighted the importance of the roughness-sensitive convective heat loss for energy balance. Uncertainties persist in the CFD models given the complexity of the ice accretion phenomenon, which usually mixes solid ice with liquid runback water (glaze ice). A major uncertainty is related to the surface roughness pattern, which is difficult to measure in experiments. The calibration of the roughness pattern for a CFD test case was seldom investigated in literature. Among the available calibration tools, the Bayesian calibration constitutes a powerful data-driven approach suitable for roughness pattern estimation. The objective of the paper is to set up a methodology for the roughness pattern calibration on an airfoil in glaze ice conditions. Specifically, this methodology determines the roughness pattern needed to minimize the root mean square error between the numerical and experimental accretions. First, an ice accretion solver implemented in SU2 CFD generates a roughness-sensitive ice shape database. Second, a Polynomial Chaos Expansion (PCE) metamodel replaces the database. Finally, a Bayesian inversion is performed on the metamodel to determine the roughness pattern producing a realistic ice shape. The fidelity of an ice shape prediction is measured with a root mean square (RMS) error on the iced portion of the airfoil. Such methodology produces promising results, giving an accretion with a RMS error of less than 0.4% of the chord length compared to the experimental accretion thickness.</div></div>

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