A novel 3-D unsteady model of in-flight electrothermal deicing process is presented in this paper to simulate the conjugate mass and heat transfer phenomena of water film runback, phase change, and solid heat conduction. Mathematical models of water film runback and phase change are established and solved by means of a loosely coupled method. At the current time step, solid heat conduction, water film runback, and phase change are iteratively solved until the heat boundary condition reaches convergence, then the temperature distribution and ice shape at the moment are obtained, and the calculation of the next time step begins subsequently. A deicing process is numerically simulated using the present model following an icing tunnel experiment, and the results match well with those in the literatures, which validate the present model. Then, an in-flight deicing process is numerically studied to analyze the effect of heating sequence.

The water droplet in clouds may remain in a liquid state even if the temperature is below freezing point due to the surface tension and a lack of condensation nucleus. Supercooled water droplet would solidify when impinging on windward surfaces of aircraft, which would cause the deterioration in the aerodynamic performance due to the change of aerodynamic configuration [

In view of the serious threats that ice accretion would impose on flight safety, ice protection methods must be applied to prevent or control the ice accretion. Hot air anti-icing method is widely applied in commercial jets. The bleed air from engine compressor impinges on the structure to heat the surface, so that the water evaporates or stays in a liquid state rather than freezes. Electrothermal ice protection method uses heating pads, which are incorporated in the multilayer structure, to heat the surfaces. Electrothermal pads are available in both anti-icing mode with a constant power density and deicing mode with a periodic power density. Besides, some other deicing methods have been developed, such as the thermomechanical expulsion deicing method [

Since the icing tunnel experiments and the flight experiments are complex, expensive, and not able to cover all environment conditions, the investigation of a deicing process by an experimental method is quite limited and seldom reported to date. The numerical simulation method, which is time-efficient and cost-effective, becomes an important tool for the design of the ice protection system. The in-flight deicing process is a conjugate mass and heat transfer phenomenon, which is very complex and consists of a variety of coupled processes such as the air-droplet flow, water film runback and phase transition, and multilayer solid heat conduction. The phase state varies with both spatial locations and time. Due to the periodic power density, spatial distribution of heaters, and sustained droplet impingement, phase transition phenomena, such as evaporation, solidification, liquefaction, and sublimation, may coexist on the surface of the protection area, which makes it complex and typically unsteady.

The early study of electrothermal deicing concentrated on the solution of multilayer structure heat conduction. Stallabrass [

Wright et al. [

As electrothermal deicing method is increasingly employed in the new generation of aircraft, the study on the mechanism and simulation methods is urgently needed. While most current studies on the deicing process concentrated on the multilayer structure heat conduction and ice melting process, studies available on the in-flight deicing were quite rare.

This paper focuses on the conjugate heat transfer mechanism of the in-flight electrothermal deicing. A novel 3-D unsteady model is established based on the water film runback dynamic mechanism and phase transition thermodynamic model and solved by a loosely coupled method. Using the present model, the deicing process is numerically investigated, which contributes to a better understanding of electrothermal deicing so as to guide the design and optimization of an aircraft ice protection system.

The in-flight deicing process is a conjugate mass and heat transfer process, which involves air-droplet flow, solid heat conduction, water film runback, and the phase transition. The mass and energy balance, as is briefly shown in Figure

Mass and energy balance of deicing process.

Since the volume fraction of droplet is very small, typically under 10^{−6} for icing conditions, the air-droplet flow can be solved by a one-way coupled method [

The continuity and momentum equations of droplet flow are expressed as [

The differential form of continuity equation for runback water film on the surface of ice protection area is expressed as

The mass flux of droplet impingement is determined by local collection efficiency

The evaporation rate is determined by the Chilton-Colburn analogy theory where the convective mass transfer coefficient

The momentum equation of water film runback is given by incompressible Navier–Stokes equation as

The air-film boundary condition is defined as

The solid-film boundary is depicted under the nonslip boundary condition.

Previous studies suggest that the effects of pressure gradient should only be considered for water film with a large thickness [

The velocity distribution normal to the surface is derived as

The average velocity

The energy balance of water film is described by the following differential equation:

Integrating the above equation, the energy balance in a control volume is expressed as

The latent heat of solidification

If

If

If 0 <

If

The unsteady heat conduction through the multilayer materials is expressed as

The Dirichlet heat boundary condition of heat conduction is provided by the solution of water film runback and phase transition during the coupled solution. In return, the deicing heat flux is calculated and sent to the calculation of water film. The deicing heat flux is obtained at the boundary of a solid structure as shown in

During the solution of the above unsteady conjugate heat transfer model, the water film runback and phase transition are coupled with the solid heat conduction, due to the fact that the solution of the solid heat conduction provides the interface heat flux which is needed in the water film energy balance equation; on the other hand, the boundary condition of the solid heat conduction is provided by the solution of the film runback and phase transition. A loosely coupled method is applied to solve the present model, in which both the water film runback and the heat conduction are iteratively calculated until the heat boundary condition reaches convergence, and during each iteration, the surface temperature

Diagram of coupling solution method.

Considering that the ice thickness during deicing process is typically controlled at a very small value, the effect of the ice shape on air-droplet flow is slight. As a result, the steady airflow solution is computed as an initial condition and is assumed unchanged during the simulation. Besides, it is accurate as long as the ice thickness does not exceed a certain limit due to a protection failure. The RANS equations of airflow are discretized, using a finite volume method in a second order upwind scheme. To simulate the turbulent flow, the transition SST model, which is shown to obtain good results for wall-bounded flows, such as the airfoil, is utilized. A CFD solver FLUENT is used to solve the governing equations. The governing equations of droplet flow field are solved by the finite volume method using the User-Defined Scalar (UDS) transport equation. The droplet volume fraction and velocity components are set as the UDS, and the convective terms, diffusion terms, and source terms are defined by codes which are programmed using the User-Defined Functions (UDF). The solution of air-droplet flow is the initial condition of water film runback and solid heat conduction, and the data exchange is achieved by interpolation due to the difference between flow field mesh and solid mesh.

A loosely coupled method is applied to solve the deicing model. At the current time step, both the solid heat conduction and the water film runback are iteratively calculated until convergence. During each iteration, the surface temperature and heat flux are exchanged, and the boundary conditions are updated. The ice shape is obtained by the icing rate or melting rate, and the calculation of the next time step then begins. The flowchart is shown in Figure

Solve the air-droplet flow and transfer the data by interpolation;

Loop all the surface control volumes and check them. If the input water mass is already known, assume an initial temperature, solve the mass and energy balance equations, update the value of temperature and phase state, and provide input conditions for adjacent volumes. Keep the calculation of water film runback and phase transition until the calculations of all control volumes are done; the temperature distribution at boundary surface is obtained;

Set Dirichlet boundary condition for solid heat conduction using the temperature distribution of step (2) and solve the heat conduction; calculate the deicing heat flux at boundary.

Update the deicing heat flux of water film energy equation using the data of step (3).

Repeat steps (2)–(4) until convergence, calculate ice accretion at the moment, and advance to the next time step.

Flowchart of solution procedure.

Validations of the present model are conducted, and the results are compared with the experimental data. Then, a simulation of in-flight deicing process is conducted to optimize the heating sequence.

In order to perform the in-flight deicing simulation, a deicing experiment model is selected in the very rare records available in the open literature, which is conducted in the NASA Lewis Icing Research Tunnel (IRT) by Al-Khalil et al. [

The experiment model is a NACA 0012 airfoil with a chord of 0.914 m (36 in), and the environment conditions are listed in Table

Environment conditions of NASA experiment.

Temperature (K) | Velocity (m/s) | LWC (g/m^{3}) |
MVD ( |
AoA |
---|---|---|---|---|

266.48 | 44.7 | 0.78 | 20 | 0 |

Material and structure of ice protection area.

Material properties of NASA experiment.

Material | Density (kg/m^{3}) |
Heat conductivity (W/mK) | Heat capacity (J/kgK) |
---|---|---|---|

Erosion shield | 8025.25 | 16.26 | 502.4 |

Elastomer | 1383.96 | 0.2561 | 1256.0 |

Fiberglass | 1794 | 0.294 | 1570.1 |

Silicone foam | 648.75 | 0.121 | 1130.4 |

Heating sequence of NASA experiment (power in W/m2).

The steady air-droplet flow was solved to obtain parameters such as the convective heat flux, the shear stress, and the local droplet collection efficiency. Then, the data were transferred to solid mesh by interpolation, and the unsteady deicing process was coupled solved. Structured grids were generated for the solution of air-droplet flow. To verify the mesh independence of the solution, three mesh files were applied, and the normal distance of the first layer is 0.01 mm (mesh a), 0.0075 mm (mesh b), and 0.005 mm (mesh c), respectively. The ^{+} at the ice protection area of all three mesh files was controlled around or lower than 1.

The simulated convective heat transfer coefficient curves are shown in Figure

Comparison of convective heat transfer coefficient.

Comparison of droplet collection efficiency.

The simulated temperature of heater 3 is shown in Figure

Comparison of temperature of heater 3.

Simulated ice shape following NASA experiment.

At the first stage (0–100 s), only the heat blade is activated. Due to the solid conduction and the runback liquid water, the temperature of heater 3 rises. Figure

The simulated temperature of heater 3 is slightly higher than that of the experimental data. When heater 3 is off, the experimental temperature is around 270 K, and it is about 3 K lower than the simulated results. At this period, the surface is under a runback icing condition, which means a water-ice mixed state, and the temperature of such condition is set at 273.15 K (the freezing point) in the thermodynamic model during simulation. The possible reasons for the temperature difference between experiment and simulation are as follows: (1) The supercooled water film runback phenomenon, which is observed in the experiments [

The above simulations validate the present model and the solution method. In this section, another deicing simulation is conducted under in-flight environment conditions to analyze the deicing performance of different heating sequences. The environment conditions are listed in Table

Environment conditions of in-flight case.

Temperature (K) | Velocity (m/s) | LWC (g/m^{3}) |
MVD ( |
AoA |
---|---|---|---|---|

263 | 97.6 | 1 | 20 | 0 |

The heating sequence is shown in Figure

Initial heating sequence of in-flight case (power in W/m2).

The convective heat transfer coefficient distribution is shown in Figure

Contour of convective heat transfer and droplet impingement.

Convective heat transfer coefficient (W/m^{2}K)

Local collection efficiency

Figures

Temperature distribution at cross section (K).

Simulated ice shape of in-flight case.

At the end of the second heating stage (

Altered heating sequence.

Simulated ice shape under altered heating sequence.

Based on the water film runback dynamics and energy balance theory, an unsteady conjugate heat transfer model for electrothermal deicing is established, and a loosely coupled solution method is developed. The model is applied in the simulation of deicing process, and the conclusions are as follows:

In-flight deicing process is very complex due to factors such as droplet impingement and water film runback. The present model is capable of simulating the in-flight deicing process. Simulation following an icing tunnel experiment has been conducted to validate the present model, and the results show good agreement.

The environment conditions would strongly affect the solid temperature distribution, the water film runback, and phase transition. A larger velocity or liquid water content would correspond to a larger runback icing range, and a higher power of longer heating duration is needed to perform the deicing process. Water remains at a liquid state over the heat blade, and ice forms on the surface where the heating power is insufficient.

Heating sequence is a key factor for the deicing performance. A proper heating sequence not only leads to a better deicing performance, but also saves energy. The optimization of heat sequence can be conducted by means of numerical simulation.

However, there are several factors not yet considered, including the ice shedding mechanism, the contact thermal resistance between multilayer materials, and the anisotropy of material properties.

The authors declare that they have no conflicts of interest.

The work was supported by the National Natural Science Foundation of China (Grant no. 51206008).