Airfoil Surface Research Articles

The effect of leading-edge shape on separation-induced transition on the suction surface of a controlled-diffusion airfoil

To investigate the effect of leading-edge shape on separation-induced transition on suction surface, a large eddy simulation is performed on two compressor controlled-diffusion airfoils: a conventional one with an elliptical leading edge and an optimized one with a curvature-continuous design based on the B-spline description. The Reynolds number based on inflow velocity and chord length is 4.5×105. The critical angle of attack +4°, over which the aerodynamic loss rises sharply, is chosen for simulation. Two transitions are observed on the suction surface, one near the leading edge and the other at 40% chord length. The primary difference between the two airfoils lies in the leading-edge transition, which also leads to the distinction of fluctuating velocity amplitude and energy loss in the subsequent development of boundary layer flow. In order to provide an insight into the transition mechanism, the frequency spectrum analysis is conducted, and the results indicate that the amplification of disturbances during transition is dominated by Kelvin–Helmholtz instability. The mechanisms of energy transport and dissipation are analyzed, and the influence of leading-edge curvature on the initial state of boundary layer flow is elucidated from a dynamic perspective. The results show that continuous and large curvature distributions are more conducive to suppressing the formation of leading-edge separation bubble and delaying the onset of transition.

Large-Eddy Simulation of Low-Reynolds-Number Flow Around Partially Porous Airfoils

This paper uses the large-eddy simulation framework in OpenFOAM to investigate the flow characteristics around two-dimensional partially porous airfoils with symmetrical flat geometries, which were used in a previous experiment. The effects of a porous medium near the trailing edge are investigated at a chord Reynolds number of 350,000. Two porous media are modeled to investigate how the porous medium influences the flow around the airfoil and aerodynamic performance: One is a normal porous medium, defined as a homogeneous and isotropic material with identical properties in all directions. The other medium consists of straight holes perpendicular to the airfoil surface, allowing fluid to pass through unidirectionally. It is observed that drag and lift forces vary, depending on the internal structure of the porous medium. The size of the laminar separation bubbles also varies, depending on the parameters of the porous medium, such as the internal structure, the length of the porous section, and the porosity. It is shown that an airfoil with a low-porosity unidirectional porous medium increases the lift-to-drag ratio at high angles of attack as compared with the nonporous airfoil.

Bio-inspired Surface Texture Fluid Drag Reduction using Large Eddy Simulation

Skin friction drag can be reduced through the application of bio-inspired riblet surfaces. Numerical simulations were performed using Large Eddy Simulation (LES) to investigate the effect of using riblets on reducing skin friction drag. In this study, three different riblet configurations were used; scalloped, sawtooth and a new design, hybrid, riblet. To validate the effect of using the proposed hybrid riblet design compared with other riblets used in the literature; before applying to complex geometries, they were initially applied to a flat plate in parallel arrangement. Results showed skin friction coefficient reduction of 14% using the proposed hybrid riblet. This reduction was 9.2 times and 1.2 times more compared to sawtooth and scalloped configurations, respectively. The hybrid riblet was then applied partially and fully to NACA 0012 airfoil. Skin friction coefficient reduction of 34.5% was obtained when the hybrid riblet fully applied on the airfoil surface. Furthermore, the Convergent-Divergent (C-D) arrangement was studied, where the riblets were placed fully on the NACA 0012 and aligned with a yaw angle with respect to the flow direction. The convergent lines are inspired by the sensory part of the shark skin, whereas the divergent lines or herringbone are found on the bird feather. The two different riblet configurations, sawtooth and hybrid were modeled with the C-D arrangement and the hybrid riblet with C-D arrangement contributed to higher skin friction coefficient reduction, 34.5%, than the sawtooth riblet shape, 26.75%. Moreover, the C-D arrangement was compared to the parallel arrangement and shown that the C-D arrangement increased the lift coefficient (cl) of the airfoil, the flow separation was delayed and the overall performance of the airfoil was enhanced.

Unsteady flow control mechanisms of a bio-inspired flexible flap with the fluid–structure interaction

Recently, the development of bio-inspired aircrafts has broad application prospects. However, the flow separation in the boundary layer of the bio-inspired wing under low Reynolds number becomes a great challenge for the design of a novel bio-inspired aircraft. It is worth noting that birds in nature can easily control flow separation, thanks to the flap-like flexible plumes attached to their wing surfaces. In this paper, the unsteady flow control of the flexible flap is studied by the immersed boundary-lattice Boltzmann-finite element method (IB-LB-FEM). The mechanism of flow separation on the airfoil surface at a bio-inspired large angle of attack (AOA) is suggested. The effects of the flexible flap position and its material properties on the unsteady flow control of the airfoil at large AOA are systematically discussed. The deformation law of the flexible flap with fluid–structure interaction (FSI) is revealed, and its influence on unsteady aerodynamics of the airfoil is discussed. The results show that with the increase in the AOA, the aerodynamic characteristics of the airfoil change with time from “periodic state” to “chaotic state” to “quasi-periodic state,” which is closely related to the unsteady flow separation on the airfoil upper surface. The new induced vortex is formed at the end of the flexible flap because of the FSI, which enhances or weakens the strength of vortices on the airfoil surface, affecting the aerodynamics of the airfoil. The flow control mechanism of the flexible flap proposed in this paper will provide a new design idea for the novel bio-inspired aircraft.

Wind tunnel test of airfoil with erosion and leading edge protection

This paper describes wind tunnel tests of a NACA 633 – 418 airfoil with erosion and leading edge protection. Measurements are carried out at high Reynolds number (Re = 5 million) representing modern wind turbines. Three examples of deviations from the perfect airfoil surface are shown. It is seen how the presence of a roughness mesh degrades the aerodynamics and that the presence of the mesh is more important than the actual topology of the mesh. That is also the case for the stall strips where a small strip influences the performance slightly less than a big stall strip, but the presence of the stall strip alone is influencing the performance significantly. Finally, a simulated leading edge protection (LEP), represented by a sheet of paper, can influence the performance significantly as the paper leads to a backward facing step. Furthermore, the measurements showed that correct mounting of LEP is important to avoid too big losses in aerodynamic performance. Investigating the impact of reduced airfoil performance for the rotor performance showed losses in annual energy production of between 0.3% and 4.0%. All in all the wind tunnel tests reflected that leading edge damages have a significant impact on the aerodynamic performance.

Aerodynamic Exploration for Tandem Wings with Smooth or Corrugated Surfaces at Low Reynolds Number

Skin corrugation and tandem configuration are two distinct features that characterize the flow around dragonfly wings. In contrast to the smooth airfoil and single pair of wings of conventional airplanes, corrugated surfaces and tandem wings influence aerodynamics both locally and globally. In this article, several kinds of doubly- tandem wing configurations were designed, then computational investigations based on wind tunnel experiments were conducted to investigate the aerodynamic characteristics of these models. Computational simulations using in-house codes were carried out with a freestream velocity of 20 m/s at an angle of attack from −4° to 16°. Based on these computational results, the effects of airfoil thickness, surface waviness and hindwing decalage on aerodynamic characteristics were compared and presented quantitatively. Final results demonstrate that a tandem wing configuration could eliminate separation close to the trailing edge at angles of attack 8°~10°, or delay the trailing edge separation at angles of attack greater than 10°. Thus, the aerodynamic efficiency of tandem configurations could provide significant improvement compared to configurations with a single wing. The greatest percentage of aerodynamic efficiency improvement for a tandem thick configuration compared to a single thick configuration is 1376% at angle of attack 0°. Surface waviness will stall at a lower angle of attack, but will gain some aerodynamic benefit from the standing separated flow. Hindwing decalage has obvious lift enhancement for the tandem configuration. Therefore, it is concluded that the tandem configuration is attractive and promising for MAVs with flexible structures in the near future.

Lattice Boltzmann method for heat transfer in transitional flows with unified single-node curved boundary conditions

Laminar separation bubbles in transitional flows of low-Reynolds-number airfoils significantly affect aerodynamic efficiency and heat transfer characteristics, which can be dealt with using the numerical method with boundary treatment of complex geometry. This work proposes the unified single-node curved boundary conditions based on the thermal lattice Boltzmann method, and several benchmarks verify the higher accuracy and parallel scalability over conventional schemes. Multi-GPU simulations for airfoil Eppler 61 and SD8020 are carried out, and the lift coefficients CL are accurately simulated by the parametric combined momentum-exchange method. Furthermore, time-averaged pressure coefficients Cp and local Nussel number Nu of airfoil surfaces are obtained, and the unsteady flow and heat transfer characteristics of laminar separation bubbles are captured. Simulated average Nussel numbers Nu¯ for an Eppler 61 airfoil with different Reynold numbers are equivalent to and modify the Hilpert correlation. The numerical method can quickly and accurately predict transitional flows of low-Reynolds-number airfoils and guide the design and application of heat transfer with blade configuration.

Active control of airfoil turbulent boundary layer noise with trailing-edge blowing

Large Eddy Simulation (LES) and Ffowcs Williams-Hawkings acoustic analogy are performed to study the effect of trailing-edge blowing on airfoil self-noise. Simulations were conducted using a National Advisory Committee for Aeronautics 0012 airfoil at zero angle of attack and a chord-based Reynolds number of 4 × 10 5. The aerodynamic and aeroacoustic characteristics of the baseline airfoil were thoroughly verified by comparison with previous numerical and experimental data. The noise reduction effects of continuous and local blowing with different blowing ratios and blowing momentum coefficients were compared. A maximum noise reduction of 20 dB was achieved via trailing-edge blowing and the noise reduction mechanisms of the two blowing methods were discussed. The LES results show a pair of recirculation bubbles in the airfoil wake which are suppressed by trailing-edge blowing. As the blowing vortices convect into the wake, they stretch and stabilize the shear flows from airfoil surfaces. Instantaneous vorticity and root mean square velocity fluctuations are also weakened. There is a decrease in the spanwise coherence and an increase in the phase difference, which contribute to noise reduction. It is concluded that the suppression of turbulence fluctuations in the near wake is the main mechanism of noise reduction for airfoil trailing-edge blowing.

Sparse sensor reconstruction of vortex-impinged airfoil wake with machine learning

Reconstruction of unsteady vortical flow fields from limited sensor measurements is challenging. We develop machine learning methods to reconstruct flow features from sparse sensor measurements during transient vortex–airfoil wake interaction using only a limited amount of training data. The present machine learning models accurately reconstruct the aerodynamic force coefficients, pressure distributions over airfoil surface, and two-dimensional vorticity field for a variety of untrained cases. Multi-layer perceptron is used for estimating aerodynamic forces and pressure profiles over the surface, establishing a nonlinear model between the pressure sensor measurements and the output variables. A combination of multi-layer perceptron with convolutional neural network is utilized to reconstruct the vortical wake. Furthermore, the use of transfer learning and long short-term memory algorithm combined in the training models greatly improves the reconstruction of transient wakes by embedding the dynamics. The present machine-learning methods are able to estimate the transient flow features while exhibiting robustness against noisy sensor measurements. Finally, appropriate sensor locations over different time periods are assessed for accurately estimating the wakes. The present study offers insights into the dynamics of vortex–airfoil interaction and the development of data-driven flow estimation.Graphic abstract

Analyzing the aerodynamic characteristics of eroded wind turbine blades

The study investigates the influence of erosion over the leading edge of S809 series airfoil and its impact on the aerodynamic performance of wind turbine blades. The research work determines how erosion affects the performance of wind turbine blades at an angle of attack varying from 0° to 45° for the fixed Reynolds number of 2.1 x 105. To analyse the flow characteristics, the average pressure acting around the surface of the airfoil is scanned with the aid of 20 pressure taps. The time series pressure of 10,000 samples at each point has been collected. The roughness is introduced at the leading edge of the airfoil and measures 0.1% of the total chord at the top and bottom surface, respectively. Six different intensities of roughness are introduced and tested. The base airfoil, as well as roughed surface airfoil, is compared and the results are discussed. The aerodynamic parameters like lift, drag, and pressure coefficients are included. The estimated data suggests the erosion that occurs on the wind turbine blade surface alters the flow pattern and the aerodynamic properties of the wind turbine blades. Collectively, the experiment on analysing the eroded surface possibly taking place over the wind turbine blade surface affects the lift parameter with a considerable increment in drag. However, the roughness allows the airflow to remain fixed with the airfoil surface, favouring the concept of extending the stall.

Numerical simulation of ice shedding motion characteristic on airfoil surface

In order to accurately predict the motion trajectory of ice shedding and ensure the safe flight of aircraft, the motion characteristics of ice shedding under two-dimensional (2D) and three-dimensional (3D) conditions are simulated and analyzed. Considering the influence of any possible shape of shedding ice and its rotation and the magnitude and direction of acceleration with time under aerodynamic force, a six degree-of-freedom analysis method is introduced in this paper. This paper proposes a theoretical model, which can be used to calculate the 3D trajectory of ice shedding with arbitrary shape. The dynamic analysis of real 3D shedding ice is carried out, and the motion behavior of shedding ice with different positions and shapes is calculated. The results show that the movement mode of the shedding ice after leaving the aircraft is translation and rotation. The shape of the low-speed region on the leeward side of the shedding ice will first increase, then decrease, and then increase with the rotation of the ice body. The influence of ice shape on ice shedding trajectory is mainly that the shedding ice continues to flip during the downstream movement of the flow field, and the projected area of the effective windward area in the lift and the drag direction changes with time. The average deviation of the shedding ice at position 5 along the spanwise is only 22.9% of that at position 1. Finally, the closer the initial position of ice shedding is to the airfoil root, the greater the probability of ice shedding hitting the aircraft fuselage. In this paper, the probability of ice shedding hitting the aircraft fuselage is 8%, which all occurred in the case with position 1 as the initial position of ice shedding.

A Wind Tunnel Test of the Anti-Icing Properties of MoS2/ZnO Hydrophobic Nano-Coatings for Wind Turbine Blades

Wind turbines operating in cold regions are prone to blade icing, which seriously affects their aerodynamic characteristics and safety performance. Coatings are one of the effective solutions to the icing problem on wind turbine blades. In this study, MoS2/ZnO/PDMS superhydrophobic nano-anti-icing coatings were prepared using the hydrothermal method and the liquid phase method. SEM revealed that the MoS2/ZnO coating was a typical superhydrophobic nanostructure with an ultra-thin sheet-like morphology of clusters and a hilly nano-rough structure, with contact angles (CA) of 152.1° and 4.7° with water droplets and the sliding angle (SA), respectively. The MoS2/ZnO/PDMS coating had an adhesion strength to ice of 78 kPa, which was 60.2% lower than an uncoated surface. The icing effects of the NACA0018 airfoil blade model with or without MoS2/ZnO coatings were studied at different ambient temperatures and wind speeds using the icing wind tunnel test. The results showed that, compared to uncoated blades, the level of icing was lower on the blade airfoil surface that was coated with MoS2/ZnO. At 10 m/s and −10 °C, the icing thickness and icing area of the leading edge of the blade airfoil were 13.7% and 28.3% lower, respectively. This study provides a valuable reference for the development of anti-icing coatings for wind turbine blades.

Comparative study of two combined blowing and suction flow control methods on pitching airfoils

A comparative study of two combined blowing/suction flow control methods was conducted on the pitching airfoil using the unsteady Reynolds-averaged Navier–Stokes (URANS) method. One used leading-edge blowing and trailing-edge suction, which is referred to as a co-flow jet (CFJ), and a conformal slot CFJ (C-CFJ) was adopted. Another used leading-edge suction combined with trailing-edge blowing, which was called reversed CFJ (R-CFJ). The S809 airfoil was used as the baseline as its stall characteristic is suitable for separation flow or stall control research. Aerodynamic coefficients of these two combined blowing/suction methods were compared under no-stall, mild-stall, and deep-stall cases. The net gain of output power was also discussed if CFJ methods were used for wind energy applications. The influence mechanism of these two methods on the flow around the airfoil was revealed. The results showed that the C-CFJ is suitable for the no-stall and mild-stall cases, while the R-CFJ is suitable for the deep-stall case. Leading-edge suction is more stable than leading-edge blowing when suppressing the dynamic stall. The leading-edge jet flow will cause dynamic stalls when it is detached from the airfoil surface, while the detached jet flow can block the development of the separation when it is placed on the trailing edge.

Effect of offset distances for rod-airfoil interaction noise

The noise generated by the interaction between the wake of rods and airfoils is a universal phenomenon in the engineering field. The noise generation mechanism is mainly caused by the violent changes of the pulsating pressure on the airfoil surface, impacted by different vortex scales in the wake of rods. During this process, the energy is radiated outward by sound waves. To capture wakes and the sound generated by the interaction of rod-airfoil with relatively small computing resources is a challenge. In this paper, the sound pressure generated by the rod-airfoil interaction is calculated by solving the Reynolds average N-S equation and non-linear acoustic equations. This numerical method is verified by a rod-airfoil interaction benchmark. This paper focuses on the influence of offset distances between rods and airfoils. The results show that the peak of far-field sound decreases from 89 dB to 80.6 dB as the offset distance from the airfoil to the center of the cylinder increases (the maximum deviation is three times the cylinder diameter). The frequency of peak sound pressure also shifts.

The noise-generating mechanism of rod-airfoil configuration and the effect of spanwise length on noise prediction

The wake-blade interaction in turbo-engines is the primary source of broadband noise. In this work, the noise mechanism of a benchmark rod-airfoil configuration is exhaustively analyzed using compressible Large Eddy Simulation (LES) and Ffowcs Williams-Hawkings (FW-H) methods. The baseline model with a spanwise length shortened by 7d (d is the rod diameter) is simulated under periodic boundary conditions, and the effect of spanwise lengths on noise prediction and correlation is investigated in combination with two other models (3d and 1d). In terms of the baseline model, the noise predicted by different FW-H surfaces is compared first, and the noise radiated from different chordwise and spanwise regions of the airfoil surface reveal the generating mechanism of the main dipolar noise and the effect of periodic boundary conditions on noise prediction, respectively. Additionally, the fluctuating surface pressure characterized at four frequency bands confirms that the wake-airfoil interaction dominates the leading-edge noise at low frequencies. The characteristic frequencies of the noise and transient velocity fields reveal that the primary broadband noise source is the interaction of large-scale vortices with the airfoil surface at the leading-edge region. Finally, the effect of spanwise length on noise prediction and correlation is studied for three models. The differences in the flow structures lead to different features of their coherence coefficients. The results presented in this work provide a comprehensive understanding of the noise-generating mechanism of wake-airfoil interaction in turbomachinery and the practical application of simplified models in the future numerical simulations.

An experimental investigation into the influence of installed passively controlled jet flows on wall-pressure fluctuations

Jet-surface interaction(JSI) represents a significant noise problem in the installation of modern ultra-high bypass ratio turbofan engines. The use of chevron nozzles is known to reduce low-frequency jet mixing noise(JM) by increasing the velocity gradient in the jet shear layer. This effect is expected to influence the jet flow in the vicinity of the wing and to modify the jet-surface interaction noise. To clarify the physics of these two(JSI and JM) noise source mechanisms, an extensive experimental investigation has been conducted in the anechoic chamber of the Doak Laboratory at the University of Southampton. Various measurements were carried out on an isolated subsonic jet and an installed beneath a 2D NACA4415 airfoil using different nozzle shapes and passive vortex generator geometries. The wall-pressure field on the airfoil surface was investigated using a set of wall-pressure transducers flush-mounted in the streamwise and spanwise directions on the pressure side of the airfoil. The unsteady wall-pressure data were analysed in both time and frequency domains to assess changes in: 1) surface trailing edge spanwise correlation length, 2) streamwise convection velocity of the hydrodynamic pressure field, and 3) modification of the hydrodynamic pressure field in the vicinity of the surface trailing edge.

Parameter-Based Design and Analysis of Wind Turbine Airfoils with Conformal Slot Co-Flow Jet

A co-flow jet (CFJ), an active flow control method combining blowing and suction control, can effectively suppress the stall of airfoils. However, the streamwise jet channel along the upper surface of a conventional CFJ airfoil reduces the thickness and camber of the baseline, degrading the aerodynamic performance when the jet is inactive. The conformal slot CFJ airfoil was proposed to address this problem, but the design method is still absent. This paper proposed a general design method based on parameters including the slot angle, transition shape and distance of the injection and suction slot. The mechanism of the best parameter was analyzed. The designed conformal slot CFJ airfoil was checked under different jet intensities, and the turbine power curve was predicted when substituting CFJ airfoils for the baseline. Compared with the conventional CFJ airfoil, the designed conformal slot CFJ airfoil has three advantages: eliminating the performance loss when the jet is off, saving jet energy when suppressing the flow separation, and improving the power generation of wind turbines at low wind speeds.

Experimental study on influence of sharkskin denticles structure on the hydrodynamic performance of airfoil

The hydrodynamics properties of sharkskin have been studied for the past few decades, demonstrating the drag-reducing effect of the sharkskin surface denticle structure. This study explores the influence of the sharkskin denticles structure on the hydrodynamic performance of airfoil and the drag reduction mechanism using time-resolved particle image velocimetry (TR-PIV) by arranging the sharkskin denticles on the National Advisory Committee for Aeronautics (NACA) 0012 airfoil. The change in lift and drag of the airfoil was measured by a six-dimensional force sensor. The effects of angle of attack, sharkskin denticles location, Reynolds number, and arrangement on the hydrodynamic performance of the airfoil were mainly analyzed. The results show that for the single-row sharkskin denticles structure, the closer the bionic structure is arranged to the trailing edge of the airfoil, the better the drag reduction effect is. The maximum drag reduction is up to 25.4% by arranging the bionic denticles at 0.38L of the airfoil, when Re = 1.62 × 105 (U = 0.8 m/s) and α = 0°. For the double-row sharkskin denticles structure, the staggered arrangement is less effective in reducing drag than the aligned arrangement due to the influence of form resistance. The velocity field of the turbulent boundary layer on the airfoil surface was obtained by TR-PIV. The experiment results show that the sharkskin denticles structure can change the boundary layer of the airfoil, and the static flow area formed at the tail can reduce the disturbance of the airfoil by the turbulent flow.

2D Numerical investigation of surface wettability induced liquid water flow on the surface of the NACA0012 airfoil

The accumulation of ice on wind turbine blades is a serious threat to the safety of wind power generation. Anti-icing techniques with low energy consumption, especially when combined with superhydrophobic surfaces, have recently attracted increasing levels of interest. In this work, the anti-icing mechanism of superhydrophobic surfaces was investigated by conducting the two-dimensional numerical analysis of the flow patterns of liquid water on surfaces with different wettability, which was based on the phase field method (PFM) and a dynamic contact angle (DCA) model. It is found that the wettability of surfaces significantly influences the flow, break, and shedding behaviors of liquid water on the surfaces. An increase in contact angle (CA) leads to more frequent break and shedding behaviors, and the flow pattern of liquid water gradually transformed from continuous water film to fragmented droplets because of the vortical flow field. In addition, it is also investigated that when the CA of surfaces exceeded 145°, the broken liquid water completely shed away in 0–0.1 chord length. Moreover, the average chordwise location (x‾/c) and maximum chordwise location (xmax/c) of the liquid water that had traveled the farthest on the surface in 30 ms gradually decreased with increasing contact angle, which is beneficial to superhydrophobic-dry anti-icing. What's important, the wettability characteristics should be responsible for the unique water flow patterns coupled with shear stress, which has been validated again, and previously proposed by our work. The results of this study provide theoretical support for the incorporation of superhydrophobic surfaces in anti-icing technology applied to wind turbine blades, which is promising for solving the icing issue of wind turbine blades with low energy consumption.

Numerical investigation of airfoil ice accumulation: Ice shape and ice crack propagation

For aircraft ice accumulation, this paper analyzed airfoil icing with OpenFOAM software, including the ice shape analysis, ice crack propagation analysis and ice stress intensity analysis. The direction of water overflow is divided along the chordwise and spanwise of the airfoil. And the heat and mass transfer process of icing is investigated by modifying the classical Messinger icing thermodynamic model. Based on the traditional calculation method of 2D surface heat transfer coefficient, an improved 3D airfoil surface heat transfer coefficient calculation method is proposed. And ice accretion is along the direction normal to the surface. The model of airfoil ice shape and crack growth was established by the self-developed C-DEICE program. The flow field of the 2D and 3D ice shape obtained by reverse modeling were calculated by the C-DEICE program. The crack propagation and ice shedding shape were simulated in 2D and 3D. Icing completely changes the pressure distribution on the airfoil surface, and the aerodynamic performance is decreased by 91.6%. The displacement of ice body above the crack increases significantly with the crack propagation, and the displacement increases with the distance from the crack tip, which is consistent with the 2D crack propagation simulation results. Furthermore, the self-developed C-DEICE program can better capture the trend of ice shape and the range of ice covering on the airfoil surface. It is found that the fluid–solid coupling method is reliable for determining the initial crack location. Meanwhile, it also lays a theoretical foundation for the follow-up study of ice shedding trajectory.