Equivalent Sand Grain Roughness Correlation for Aircraft Ice Shape Predictions 2019-01-1978

Many uncertainties in an in-flight ice shape prediction are related to convection heat transfer coefficient, which in turn depends on the flow, turbulence and laminar/turbulent transition models. The height of ice roughness element used to calculate the Equivalent Sand Grain Roughness height (ESGR) is a very important input of the turbulence model as it strongly influences the shape of the accreted ice. Unfortunately, for in-flight icing, the ESGR is unknown and generally calculated using semi-empirical models or empirical correlations based on a particular ice shape prediction code. Each ice shape prediction code is unique due to the models and correlations used and the numerical implementation. Ice roughness correlations do not have the same effect in each ice shape prediction code. A new approach to calculate the ESGR correlation taking into consideration the particularities of the ice shape prediction code is developed, calibrated and validated. This new approach derives a correlation based on two dimensionless numbers: the first by re-defining the Stanton number and the second based on the thermodynamic heat balance. A calibration procedure is used based on 14 different 2D experimental ice shapes for a NACA 0012 airfoil of 21 inches chord. The correlation is validated against 41 2D experimental ice shapes obtained on 5 airfoils: the GLC 305; a commercial transport airfoil; NACA 23014; NACA 0015 and NACA 0012. A large range of icing conditions are covered. The results of this validation exercise show 90% of the predicted ice shapes are visually in good to excellent agreement with experiment. The advantage of the proposed ESGR correlation for the calculation of the ice roughness is that the correlation is calibrated with only a few cases for a specific icing simulation suite. This is possible because the correlation depends on two dimensionless numbers related to the in-flight icing physics simulation.