Large-eddy simulations of complex aerodynamic flows over multi-element iced airfoils
Introduction
The supercooled water droplets available in clouds can result in ice accretion on the surfaces of aircrafts and engines when an aircraft flies at subfreezing temperatures. The ice accretion shapes are affected by atmospheric temperature, liquid–water content (LWC), median volume diameter (MVD) of droplet, flight speed, and phase of flight, and the accreted ice leads to a severe reduction in lift, increased drag, and aircraft instability [1], [2], [3], [4]. Furthermore, the droplet diameter is known to have strong influence on the amount, location, and shape of the ice accretion [5], [6], [7]. In the aviation community, the droplet diameter in the range of 40 μm or less has been considered for certification (FAA Appendix C). However, in some atmospheric conditions the droplet size may reach 40 μm to 400 μm, which is known as a supercooled large droplet (SLD). Hence, in 2014, a new certification regulation is added (Appendix O) along with the present regulations (Appendix C) to address the effect of SLD icing conditions. Because an investigation of ice shapes generated under various conditions along with aerodynamic performance is essential for the certification process and ice protection system design, it is valuable to study the effects of icing on the aerodynamics around various iced airfoils.
For several decades, much effort has been devoted to the study of flows around single-element iced airfoils [1], [8], [9], [10], [11]. However, since modern aircraft usually use multi-element wings to attain high lift at a high angle of attack (AOA) and low speeds [12], recent studies have examined the effects of ice accretion on multi-element airfoils with a supercooled large droplet (SLD) greater than 40 μm and/or a non-SLD smaller than 40 μm. In the NASA Lewis Icing Research Tunnel (IRT), Shin et al. [13] analyzed the effects of droplet size on a multi-element airfoil under a non-SLD condition. They employed two median volume diameters (MVDs) of 20 and 25 μm and showed that the icing limits generated with a larger MVD move further downstream on both the upper and lower surfaces despite a slight spread. Miller et al. [14] investigated the influence of the flap gap distance on ice accretion with a 20-μm MVD using three flap-gap sizes (1.52%, 1.75%, and 2.02% chord). They reported that changing the flap gap has a small effect on ice accretion over a multi-element iced airfoil compared to that of the AOA. Under a SLD condition, Zhang et al. [15] simulated flows around multi-element airfoils using three large droplet sizes (, 200, and 400 μm) to investigate the aerodynamic features. They found that the lift loss with a higher MVD is significantly greater for all elements (i.e., slat, main, and flap elements), similar to earlier observations for single-element iced airfoils [16], [17]. Recently, Raj et al. [18] conducted numerical simulations of flows over multi-element iced airfoils under both SLD ( and 154 μm) and non-SLD ( μm) conditions. The variation of the lift and drag coefficients showed a higher aerodynamic degradation under a non-SLD condition than under a SLD icing condition because the horn-shaped ice on the main element under the non-SLD condition significantly decreased the aerodynamic performance of the main element. This result is contrary to earlier observations for single- and multi-element iced airfoils [15], [16], [17].
Many previous numerical studies have been performed to investigate unsteady flows over iced airfoils using the Reynolds-averaged Navier–Stokes (RANS) method [19], [20], [21]. However, this method overestimates the pressure coefficient on the upper surface and underestimates the stall angle and lift coefficient because it cannot correctly resolve the separation bubbles (SBs), which are an important phenomenon that determines the aerodynamic performance on an iced airfoil [1]. As a remedy, Brown et al. [9] showed that an implicit LES method provides a better prediction of the lift coefficient as a function of the AOA than that of the RANS simulations. Pan and Loth [19] reported that the detached-eddy simulation (DES) method provides a more accurate prediction of the maximum lift coefficient and stall angle than the RANS method, similar to previous observations [22], [23]. However, the prediction of the DES method is poor on the Kelvin–Helmholtz (K-H) instability for a mixing shear layer, although the prediction of K-H instability is a key issue for the accurate prediction of SBs over iced airfoils [11]. Furthermore, the zonal detached-eddy simulations (ZDES) have been applied to prediction of flows over iced airfoils [10], [24], [25]. Zhang et al. [10] showed that the ZDES provides a better prediction on pressure distribution and lift than the RANS approach, although a small difference was observed in the surface pressure between the ZDES and experimental data. Recently, Deck and Renard [26] proposed a new ZDES method to ensure a RANS mode in attached boundary layers for any mesh size without an excessive delay in the resolved LES content and formation of instabilities. The profiles of skin friction, eddy viscosity and mean velocity from the proposed method in a flat-plate turbulent boundary layer flow under an infinitely fine mesh demonstrated that an improved shielding function of the proposed method leads to a better prediction performance than that of the original delayed detached-eddy simulation (DDES) [27] and ZDES [28].
Although the flows over single-element iced airfoils with a wide range of droplet sizes are understood, a detailed analysis of the flow fields around multi-element iced airfoils is lacking because of the wide range of geometrical parameters and complicated flow features [15], [18]. Furthermore, although unsteady turbulent motions are closely related to the aerodynamic features [29], [30], most previous studies have focused on the analysis of only the mean (steady) properties of multi-element iced airfoils [13], [14], [18], [31]. Thus, it is necessary step to study flow fields around a multi-element iced airfoil with slat and flap elements to gain a better understanding of their aerodynamic characteristics. In this study, the accurate prediction of unsteady complex flows around multi-element iced airfoils using LES is performed to provide valuable insight on their aerodynamics. Iced airfoils under SLD and non-SLD conditions are taken into account, and results are compared with those of a clean airfoil to identify unique aerodynamic characteristics. In addition to LES, we have performed unsteady RANS (URANS) simulations to highlight the differences between the LES and URANS data. In the following, the flow characteristics under the influences of ice shapes and AOA are investigated by considering the lift coefficient, ratio of lift to drag, pressure coefficient, mean velocity, streamlines, and Reynolds stresses. In addition, instantaneous flow fields using velocity magnitude and time-evolving spanwise vorticity are analyzed to scrutinize complex flow interactions. Finally, a spectral analysis of pressure fluctuations is performed in highly unsteady regions to identify the dominant frequencies of unsteady flows.
Section snippets
Numerical method
ANSYS Fluent 17.1 (Ansys Inc., PA, USA) is utilized for all simulations in this study. The good prediction performances of LESs for turbulent flows based on the ANSYS Fluent code have been validated by previous studies [32], [33]. For a compressible flow, a density-based solver is used for three-dimensional and unsteady conditions. The computational domain is discretized through the finite volume method (FVM). The filtered Navier–Stokes (NS) equations are solved by the second-order upwind
Mean properties
In this section, turbulent statistics such as lift coefficient, ratio of lift to drag, surface pressure coefficient, mean velocity with streamlines, and Reynolds stresses are examined with varying AOAs. The LES results are compared with independently simulated URANS data to show the prediction improvement of our LES data for multi-element airfoils. For the two-dimensional URANS simulations, the total number of grids used are 0.16 million, 0.19 million, and 0.14 million for the clean, SLD and
Summary and conclusion
In the present study, we performed LESs around three element iced airfoils under SLD and non-SLD conditions to examine the unique flow characteristics. Direct comparison of our LES data and independently simulated URANS data with previous experimental data showed that the LES provides a good prediction of the aerodynamics of the clean and iced airfoils. However, the URANS data overestimated the suction peaks on the slat and main elements at an AOA ≥ 4° for the clean and iced airfoils because
Declaration of Competing Interest
The authors declare that the article has no financial and personal relationships with other people or organization. No conflict of interest exists and the manuscript is approved by all authors for publication.
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Ministry of Science, ICT and Future Planning (NRF-2017R1A5A1015311).
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