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Keywords = runback ice

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20 pages, 2760 KB  
Article
A Rapid Prediction Model of Three-Dimensional Ice Accretion on Rotorcraft in Hover Flight
by Weibin Li, Fan Liu, Dazhi Zhao, Xingda Cui, Zhongyun Xiao and Kaicheng Li
Aerospace 2025, 12(9), 795; https://doi.org/10.3390/aerospace12090795 - 3 Sep 2025
Viewed by 680
Abstract
Helicopters often operate at altitudes where cloud activity is prevalent, making them susceptible to icing hazards. Accurate and rapid prediction of ice accretion on rotors is crucial for expanding helicopter flight capabilities and enhancing flight safety. In this paper, we first introduce an [...] Read more.
Helicopters often operate at altitudes where cloud activity is prevalent, making them susceptible to icing hazards. Accurate and rapid prediction of ice accretion on rotors is crucial for expanding helicopter flight capabilities and enhancing flight safety. In this paper, we first introduce an improved 3-D ice accretion simulation method that accurately models runback water characteristics by considering factors such as control volume size, runback water speed, and direction. This method precisely calculates the ice accretion mass and runback water distribution. Building upon this foundation, we then present a rapid ice accretion prediction model, designed to overcome the time-consuming nature of traditional CFD frameworks. In the experimental section, our simulation methodology is applied to a hovering UH-1H rotor. A comparative analysis with experimental results reveals that the maximum absolute ice thickness error remains below 3 mm, demonstrating satisfactory computational accuracy of the proposed approach. Moreover, we demonstrate the model’s rapid prediction capabilities (achieving within a computational time of 2.66 s and a maximum ice thickness error of 7.2 mm) and implement multi-parameter predictions. Full article
(This article belongs to the Section Aeronautics)
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16 pages, 2272 KB  
Article
A Rapid Method for Heat Transfer Coefficient Prediction on the Icing Surfaces of Aircraft Wings Based on a Partitioned Boundary Layer Integral Model
by Liu Wang, Dexin Zhang, Zikang Cheng, Jiaxin Feng, Bo Sun, Jianye Chen and Junlong Xie
Aerospace 2025, 12(7), 634; https://doi.org/10.3390/aerospace12070634 - 16 Jul 2025
Viewed by 961
Abstract
Aircraft wing surface icing compromises flight safety, where accurate calculation of heat transfer coefficient on airfoil surfaces serves as a prerequisite for designing thermal anti-icing systems. However, during icing conditions, ice morphology changes wall roughness and transition properties, making it difficult to accurately [...] Read more.
Aircraft wing surface icing compromises flight safety, where accurate calculation of heat transfer coefficient on airfoil surfaces serves as a prerequisite for designing thermal anti-icing systems. However, during icing conditions, ice morphology changes wall roughness and transition properties, making it difficult to accurately determine the heat transfer coefficient. The current study develops a partitioned rough-wall boundary layer integral methodology in order to overcome this issue, extending the conventional boundary layer integral method. The technique generates a convective heat transfer coefficient formulation for aircraft icing surfaces while accounting for roughness differences brought on by water droplet shape. The results show that the partitioned rough-wall boundary layer integral method divides the wing surface into three distinct zones based on water droplet dynamics—a smooth zone, rough zone, and runback zone—each associated with specific roughness values. The NACA0012 airfoil was used for numerical validation, which showed that computational and experimental data concur well. Additionally, the suggested approach predicts transition locations with a high degree of agreement with experimental results. Full article
(This article belongs to the Section Aeronautics)
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28 pages, 8090 KB  
Article
Prediction of Airfoil Icing and Evaluation of Hot Air Anti-Icing System Effectiveness Using Computational Fluid Dynamics Simulations
by Yifan Niu, Zhiqiang Wang, Jieyao Su, Jiawei Yao and Hainan Wang
Aerospace 2025, 12(6), 492; https://doi.org/10.3390/aerospace12060492 - 30 May 2025
Cited by 3 | Viewed by 1731
Abstract
Icing poses a serious threat to flight safety, and ice accretion simulations are essential for addressing aircraft icing problems. In ice accretion prediction, systematic research covering all icing conditions based on actual flight phases is lacking, and the performance of anti-icing systems has [...] Read more.
Icing poses a serious threat to flight safety, and ice accretion simulations are essential for addressing aircraft icing problems. In ice accretion prediction, systematic research covering all icing conditions based on actual flight phases is lacking, and the performance of anti-icing systems has not been investigated. In this study, maximum ice thickness prediction models for airfoils considering all flight phases were developed, and the performance of hot air anti-icing systems was analyzed. A hot air anti-icing system model was established, and the anti-icing effectiveness of the system under severe icing conditions was evaluated via conjugate heat transfer (CHT) calculations. The calculation results showed that during climbing above 10,000 ft under glaze ice conditions, the maximum ice thickness reached 13.47 mm at −6 °C, with a median volumetric diameter (MVD) of 20 μm. Under rime ice conditions, the maximum thickness exhibited linear relationships with the icing parameters, remaining below 5 mm. The calculation results revealed nonlinear relationships between maximum ice thickness on the airfoil leading edge and the icing conditions. Ice thickness models were established via polynomial regression. The maximum ice thickness data were classified, and 15 regression models were obtained. The relative errors between the predicted and calculated values remained below 3%, demonstrating high predictive accuracy. These models were employed to estimate the effectiveness of piccolo tube hot air anti-icing systems under the most severe icing conditions. The results indicated that 100% anti-icing efficiency was achieved at high ambient temperatures (above −10 °C). During takeoff, holding, and climbing phases with a high speed of 154.3 m/s, the system may face challenges in maintaining anti-icing protection, resulting in runback ice with a maximum thickness exceeding 5 mm. Full article
(This article belongs to the Section Aeronautics)
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26 pages, 7657 KB  
Article
UAV Icing: Aerodynamic Degradation Caused by Intercycle and Runback Ice Shapes on an RG-15 Airfoil
by Joachim Wallisch, Markus Lindner, Øyvind Wiig Petersen, Ingrid Neunaber, Tania Bracchi, R. Jason Hearst and Richard Hann
Drones 2024, 8(12), 775; https://doi.org/10.3390/drones8120775 - 20 Dec 2024
Cited by 4 | Viewed by 2951
Abstract
Electrothermal de-icing systems are a popular approach to protect unmanned aerial vehicles (UAVs) from the performance degradation caused by in-cloud icing. However, their power and energy requirements must be minimized to make these systems viable for small and medium-sized fixed-wing UAVs. Thermal de-icing [...] Read more.
Electrothermal de-icing systems are a popular approach to protect unmanned aerial vehicles (UAVs) from the performance degradation caused by in-cloud icing. However, their power and energy requirements must be minimized to make these systems viable for small and medium-sized fixed-wing UAVs. Thermal de-icing systems allow intercycle ice accretions and can result in runback icing. Intercycle and runback ice increase the aircraft’s drag, requiring more engine thrust and energy. This study investigates the aerodynamic influence of intercycle and runback ice on a typical UAV wing. Lift and drag coefficients from a wind tunnel campaign and Ansys FENSAP-ICE simulations are compared. Intercycle ice shapes result in a drag increase of approx. 50% for a realistic cruise angle of attack. While dispersed runback ice increases the drag by 30% compared to the clean wing, a spanwise ice ridge can increase the drag by more than 170%. The results highlight that runback ice can significantly influence the drag coefficient. Therefore, it is important to design the de-icing system and its operation sequence to minimize runback ice. Understanding the need to minimize runback ice helps in designing viable de-icing systems for UAVs. Full article
(This article belongs to the Special Issue Recent Development in Drones Icing)
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15 pages, 7218 KB  
Article
Experimental Investigation of Runback Water Flow Behavior on Aero-Engine Rotating Spinners with Different Wettabilities
by Kuiyuan Ma, Guiping Lin, Haichuan Jin, Xiaobin Shen and Xueqin Bu
Aerospace 2024, 11(7), 591; https://doi.org/10.3390/aerospace11070591 - 20 Jul 2024
Cited by 1 | Viewed by 1515
Abstract
The accumulation of ice on the aero-engine inlet compromises engine safety. Traditional hot air anti-icing systems, which utilize bleed air, require substantial energy, decreasing engine performance and increasing emissions. Superhydrophobic materials have shown potential in reducing energy consumption when combined with these systems. [...] Read more.
The accumulation of ice on the aero-engine inlet compromises engine safety. Traditional hot air anti-icing systems, which utilize bleed air, require substantial energy, decreasing engine performance and increasing emissions. Superhydrophobic materials have shown potential in reducing energy consumption when combined with these systems. Research indicates that superhydrophobic surfaces on stationary components significantly reduce anti-icing energy consumption by altering runback water flow behavior. However, for rotating aero-engine components, the effectiveness of superhydrophobic surfaces and the influence of surface wettability on runback water flow remain unclear due to centrifugal and Coriolis forces. This study investigates the runback water flow behavior on aero-engine rotating spinner surfaces with varying wettabilities in a straight-flow spray wind tunnel. The results demonstrated that centrifugal force reduces the amount of runback water on the rotating spinner compared to the stationary surface, forming rivulet flows deflected opposite to the direction of rotation. Furthermore, wettability significantly affects the flow characteristics of runback water on rotating surfaces. As the contact angle increases, the liquid water on the rotating spinner transitions from continuous film flow to rivulet and bead-like flows. Notably, the superhydrophobic surface prevents water adhesion, indicating its potential for anti-icing on rotating components. In addition, the interaction between rotational speed and surface wettability enhances the effects, with both increased rotational speed and larger contact angles contributing to higher liquid water flow velocities, promoting the rapid formation and detachment of rivulet and bead-like flows. Full article
(This article belongs to the Special Issue Deicing and Anti-Icing of Aircraft (Volume III))
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17 pages, 22285 KB  
Article
Effects of Wind Speed and Heat Flux on De-Icing Characteristics of Wind Turbine Blade Airfoil Surface
by Ting Zhang, Yangyang Lian, Zhi Xu and Yan Li
Coatings 2024, 14(7), 852; https://doi.org/10.3390/coatings14070852 - 7 Jul 2024
Cited by 5 | Viewed by 2576
Abstract
The icing on wind turbines reduces their aerodynamic performance and can cause other safety issues. Accordingly, in this paper, the de-icing characteristics of a wind turbine blade airfoil under different conditions are investigated using numerical simulation. The findings indicate that when the de-icing [...] Read more.
The icing on wind turbines reduces their aerodynamic performance and can cause other safety issues. Accordingly, in this paper, the de-icing characteristics of a wind turbine blade airfoil under different conditions are investigated using numerical simulation. The findings indicate that when the de-icing time is 10 s, the peak ice thickness on the leading edge of the airfoil surface decreases from 0.28 mm to 0.068 mm and from 0.77 mm to 0.45 mm at low (5 m/s) and high (15 m/s) wind speeds, respectively. This is due to the fact that the ice melting rate is much greater than the icing rate at low wind speeds, while the icing rate increases at high wind speeds. When the de-icing time is 20 s, ice accretion on the leading edge of the airfoil is completely melted. At a low heat flux (8000 W/m2) and high heat flux (12,000 W/m2), the peak ice thickness decreases by 31.2% and 64.9%, respectively. With an increase in de-icing time and heat flux, the peak thickness of runback ice increases. This is due to an increase in runback ice as a result of more ice melting on the leading edge of the airfoil. The surface temperature in the ice-free area is significantly higher than that in the ice-melting area, due to high thermal resistance in the ice-free area. This study will provide guidance for the thermal distribution and coating layout of a wind turbine blade airfoil to make the anti-/de-icing technology more efficient and energy-saving. Full article
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20 pages, 10356 KB  
Article
Anti-Icing System Performance Prediction Using POD and PSO-BP Neural Networks
by Handong Mao, Xiaodan Lin, Zhimao Li, Xiaobin Shen and Wenzhao Zhao
Aerospace 2024, 11(6), 430; https://doi.org/10.3390/aerospace11060430 - 26 May 2024
Cited by 8 | Viewed by 1683
Abstract
The anti-icing system is important for ice protection and flight safety. Rapid prediction of the anti-icing system’s performance is critical to reducing the design time and increasing efficiency. The paper proposes a method to quickly predict the anti-icing performance of the hot air [...] Read more.
The anti-icing system is important for ice protection and flight safety. Rapid prediction of the anti-icing system’s performance is critical to reducing the design time and increasing efficiency. The paper proposes a method to quickly predict the anti-icing performance of the hot air anti-icing system. The method is based on Proper Orthogonal Decomposition (POD) and Back Propagation (BP) neural networks improved with the Particle Swarm Optimization (PSO) algorithm to construct the PSO-BP neural network. POD is utilized for data compression and feature extraction for the skin temperature and runback water obtained by numerical calculation. A lower-dimensional approximation is derived from the projection subspace, which consists of a set of basis modes. The PSO-BP neural network establishes the mapping relationship between the flight condition parameters (including flight height, atmospheric temperature, flight speed, median volume diameter, and liquid water content) and the characteristic coefficients. The results show that the average absolute errors of prediction with the PSO-BP neural network model on skin temperature and runback water thickness are 3.87 K and 0.93 μm, respectively. The method can provide an effective tool for iteratively optimizing hot air anti-icing system design. Full article
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18 pages, 8425 KB  
Article
An Experimental Study on Blade Surface De-Icing Characteristics for Wind Turbines in Rime Ice Condition by Electro-Thermal Heating
by Xiaojuan Li, Haodong Chi, Yan Li, Zhi Xu, Wenfeng Guo and Fang Feng
Coatings 2024, 14(1), 94; https://doi.org/10.3390/coatings14010094 - 10 Jan 2024
Cited by 9 | Viewed by 3642
Abstract
Wind turbines in cold and humid regions face significant icing challenges. Heating is considered an efficient strategy to prevent ice accretion over the turbine’s blade surface. An ice protection system is required to minimize freezing of the runback water at the back of [...] Read more.
Wind turbines in cold and humid regions face significant icing challenges. Heating is considered an efficient strategy to prevent ice accretion over the turbine’s blade surface. An ice protection system is required to minimize freezing of the runback water at the back of the blade and the melting state of the ice on the blade; the law of re-freezing of the runback water is necessary for the design of wind turbine de-icing systems. In this paper, a wind tunnel test was conducted to investigate the de-icing process of a static heated blade under various rime icing conditions. Ice shapes of different thicknesses were obtained by spraying water at 5 m/s, 10 m/s, and 15 m/s. The spray system was turned off and different heating fluxes were applied to heat the blade. The de-icing state and total energy consumption were explored. When de-icing occurred in a short freezing time, the ice layer became thin, and runback water flowed out (pattern I). With an increase in freezing time at a low wind speed, the melting ice induced by the dominant action of inertial force moved backward due to the reduction in adhesion between the ice and blade surface (pattern II). As wind speed increased, it exhibited various de-icing states, including refreezing at the trailing edge (pattern III) and ice shedding (pattern IV). The total energy consumption of ice melting decreased as the heat flux increased and the ice melting time shortened. At 5 m/s, when the heat flux was q = 14 kW/m2, the energy consumption at EA at tδ = 1 min, 5 min, and 7 min were 0.33 kJ, 0.55 kJ, and 0.61 kJ, respectively. At 10 m/s, when the heat flux was q = 14 kW/m2, the energy consumption at EA at tδ = 1 min, 3 min, and 5 min were 0.77 kJ, 0.81 kJ, and 0.80 kJ, respectively. Excessive heat flow density increased the risk of the return water freezing; thus, the reference de-icing heat fluxes of 5 m/s and 10 m/s were 10 kW/m2 and 12 kW/m2, respectively. This paper provides an effective reference for wind turbine de-icing. Full article
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14 pages, 1408 KB  
Article
Evaluation of Anti-Icing Performance for an NACA0012 Airfoil with an Asymmetric Heating Surface
by Koji Fukudome, Yuki Tomita, Sho Uranai, Hiroya Mamori and Makoto Yamamoto
Aerospace 2021, 8(10), 294; https://doi.org/10.3390/aerospace8100294 - 12 Oct 2021
Cited by 5 | Viewed by 3935
Abstract
Heating devices on airfoil surfaces are widely used as an anti-icing technology. This study investigated the aerodynamic performance with a static heating surface based on the modified extended Messinger model. The predicted ice shape was validated through a comparison with the experimental results [...] Read more.
Heating devices on airfoil surfaces are widely used as an anti-icing technology. This study investigated the aerodynamic performance with a static heating surface based on the modified extended Messinger model. The predicted ice shape was validated through a comparison with the experimental results for HAARP-II. A reasonable agreement was found for both the icing area and the ice mass on the suction surface. Then, the prediction method was adopted for an NACA0012 airfoil at an attack angle of 4.0 under a glaze ice condition. An asymmetric heating area was imposed on the suction and pressure surfaces considering a temperature of 10C near the leading edge. As a result of heating, the round ice formation when was no longer observed, and the formed ice volume decreased. However, bump-shaped pieces of ice were formed downstream of the heater owing to runback water; these bump-shaped pieces of ice formed on the suction surface significantly increased the flow drag and reduced the lift. The results indicated that extending the heating area on the suction surface can improve the aerodynamic performance. Consequently, the overall aerodynamic performance is deteriorated by adding static heating compared to the case without heating. Full article
(This article belongs to the Special Issue Deicing and Anti-Icing of Aircraft (Volume II))
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19 pages, 8691 KB  
Article
Design and Development of an Experimental Setup of Electrically Powered Spinning Rotor Blades in Icing Wind Tunnel and Preliminary Testing with Surface Coatings as Hybrid Protection Solution
by Eric Villeneuve, Caroline Blackburn and Christophe Volat
Aerospace 2021, 8(4), 98; https://doi.org/10.3390/aerospace8040098 - 2 Apr 2021
Cited by 22 | Viewed by 5411
Abstract
In order to study ice protection systems for rotating blades, a new experimental setup has been developed at the Anti-Icing Materials International Laboratory (AMIL). This system consists of two small-scale rotating blades in a refrigerated icing wind tunnel where atmospheric icing can be [...] Read more.
In order to study ice protection systems for rotating blades, a new experimental setup has been developed at the Anti-Icing Materials International Laboratory (AMIL). This system consists of two small-scale rotating blades in a refrigerated icing wind tunnel where atmospheric icing can be simulated. Power is brought to the blades through a slip ring, through which the signals of the different sensors that are installed on the blades also pass. As demonstrated by the literature review, this new setup will address the need of small-scale wind tunnel testing on electrically powered rotating blades. To test the newly designed apparatus, preliminary experimentation is done on a hybrid ice protection system. Electrothermal protection is combined with different surface coatings to measure the impact of those coatings on the power consumption of the system. In anti-icing mode, the coatings tested did not reduce the power consumption on the system required to prevent ice from accumulating on the leading edge. The coatings however, due to their hydrophobic/superhydrophobic nature, reduced the power required to prevent runback ice accumulation when the leading edge was protected. One of the coatings did not allow any runback accumulation, limiting the power to protect the whole blades to the power required to protect solely the leading edge, resulting in a potential 40% power reduction for the power consumption of the system. In de-icing mode, the results with all the substrates tested showed similar power to achieve ice shedding from the blade. Since the coatings tested have a low icephobicity, it would be interesting to perform additional testing with icephobic coatings. Also, a small unheated zone at the root of the blade prevented complete ice shedding from the blade. A small part of the ice layer was left on the blade after testing, meaning that a cohesive break had to occur within the ice layer, and therefore impacting the results. Improvements to the setup will be done to remedy the situation. Those preliminary testing performed with the newly developed test setup have demonstrated the potential of this new device which will now allow, among other things, to measure heat transfer, force magnitudes, ice nucleation, and thermal equilibrium during ice accretion, with different innovative thermal protection systems (conductive coating, carbon nanotubes, impulse, etc.) as well as mechanical systems. The next step, following the improvements, is to measure forced convection on a thermal ice protection system with and without precipitation and to test mechanical ice protection systems. Full article
(This article belongs to the Special Issue Deicing and Anti-Icing of Aircraft (Volume II))
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19 pages, 4537 KB  
Article
Investigation on the Mechanism of Heat Load Reduction for the Thermal Anti-Icing System
by Rongjia Li, Guangya Zhu and Dalin Zhang
Energies 2020, 13(22), 5911; https://doi.org/10.3390/en13225911 - 12 Nov 2020
Cited by 15 | Viewed by 2738
Abstract
The aircraft ice protection system that can guarantee flight safety consumes a part of the energy of the aircraft, which is necessary to be optimized. A study for the mechanism of the heat load reduction in the thermal anti-icing system under the evaporative [...] Read more.
The aircraft ice protection system that can guarantee flight safety consumes a part of the energy of the aircraft, which is necessary to be optimized. A study for the mechanism of the heat load reduction in the thermal anti-icing system under the evaporative mode was presented. Based on the relationship between the anti-icing heat load and the heating power distribution, an optimization method involved in the genetic algorithm was adopted to optimize the anti-icing heat load and obtain the optimal heating power distribution. An experiment carried out in an icing wind tunnel was conducted to validate the optimized results. The mechanism of the anti-icing heat load reduction was revealed by analyzing the influences of the key factors, such as the heating range, the surface temperature and the convective heat transfer coefficient. The results show that the reduction in the anti-icing heat load is actually the decrease in the convective heat load. In the evaporative mode, decreasing the heating range outside the water droplet impinging limit can reduce the convective heat load. Evaporating the runback water in the high-temperature region can lead to the less convective heat load. For the airfoil, the heating power distribution that has an opposite trend with the convective heat transfer coefficient can reduce the convective heat load. Thus, the optimal heating power distribution has such a trend that is low at the leading edge, high at the water droplet impinging limit and zero at the end of the protected area. Full article
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15 pages, 2112 KB  
Article
Numerical Simulation of the Anti-Icing Performance of Electric Heaters for Icing on the NACA 0012 Airfoil
by Sho Uranai, Koji Fukudome, Hiroya Mamori, Naoya Fukushima and Makoto Yamamoto
Aerospace 2020, 7(9), 123; https://doi.org/10.3390/aerospace7090123 - 27 Aug 2020
Cited by 26 | Viewed by 7116
Abstract
Ice accretion is a phenomenon whereby super-cooled water droplets impinge and accrete on wall surfaces. It is well known that the icing may cause severe accidents via the deformation of airfoil shape and the shedding of the growing adhered ice. To prevent ice [...] Read more.
Ice accretion is a phenomenon whereby super-cooled water droplets impinge and accrete on wall surfaces. It is well known that the icing may cause severe accidents via the deformation of airfoil shape and the shedding of the growing adhered ice. To prevent ice accretion, electro-thermal heaters have recently been implemented as a de- and anti-icing device for aircraft wings. In this study, an icing simulation method for a two-dimensional airfoil with a heating surface was developed by modifying the extended Messinger model. The main modification is the computation of heat transfer from the airfoil wall and the run-back water temperature achieved by the heater. A numerical simulation is conducted based on an Euler–Lagrange method: a flow field around the airfoil is computed by an Eulerian method and droplet trajectories are computed by a Lagrangian method. The wall temperature distribution was validated by experiment. The results of the numerical and practical experiments were in reasonable agreement. The ice shape and aerodynamic performance of a NACA 0012 airfoil with a heater on the leading-edge surface were computed. The heating area changed from 1% to 10% of the chord length with a four-degree angle of attack. The simulation results reveal that the lift coefficient varies significantly with the heating area: when the heating area was 1.0% of the chord length, the lift coefficient was improved by up to 15%, owing to the flow separation instigated by the ice edge; increasing the heating area, the lift coefficient deteriorated, because the suction peak on the suction surface was attenuated by the ice formed. When the heating area exceeded 4.0% of the chord length, the lift coefficient recovered by up to 4%, because the large ice near the heater vanished. In contrast, the drag coefficient gradually decreased as the heating area increased. The present simulation method using the modified extended Messinger model is more suitable for de-icing simulations of both rime and glaze ice conditions, because it reproduces the thin ice layer formed behind the heater due to the runback phenomenon. Full article
(This article belongs to the Special Issue Deicing and Anti-Icing of Aircraft)
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18 pages, 5834 KB  
Article
Study on Loose-Coupling Methods for Aircraft Thermal Anti-Icing System
by Xiaobin Shen, Qi Guo, Guiping Lin, Yu Zeng and Zhongliang Hu
Energies 2020, 13(6), 1463; https://doi.org/10.3390/en13061463 - 20 Mar 2020
Cited by 7 | Viewed by 3495
Abstract
To simulate aircraft thermal anti-icing systems and solve the conjugate heat transfer of air-droplet flow and solid skin, the heat and mass transfer model of the runback water on the anti-icing surface was combined with the heat conduction equation of the skin by [...] Read more.
To simulate aircraft thermal anti-icing systems and solve the conjugate heat transfer of air-droplet flow and solid skin, the heat and mass transfer model of the runback water on the anti-icing surface was combined with the heat conduction equation of the skin by loosely coupled methods. According to the boundary conditions used for the runback water conservation equations, two loose-coupling methods for the heat exchange between the runback water and the solid skin were developed based on surface heat flow and surface temperature, respectively. The anti-icing and ice accretion results of a NACA 0012 electro-thermal anti-icing system were obtained by the two loose-coupling methods. The heat flow-based method directly solves the thermodynamic model of the runback water without any extra assumptions, but the convergence rate is relatively slow. On the other hand, the temperature-based method achieves higher calculation speed, but the freezing point is extended to an artificial temperature range between water and ice phases. When the value of the artificial temperature range is small, the results obtained by the temperature-based method are consistent with those of the heat flow-based method, indicating that the effect of freezing point extension can be ignored for thermal anti-icing simulation. Furthermore, the solutions of the two methods are in acceptable and comparable agreement with the experimental and simulative results in the literature, confirming their feasibility and effectiveness. In addition, it is found that the ice thicknesses and ice shapes rise obviously near the runback water limits as a result of the transverse heat conduction of the solid skin. Full article
(This article belongs to the Special Issue Fluid Flow and Heat Transfer Ⅱ)
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