Studies on the Electro-Impulse De-Icing System of Aircraft

Article Studies on the Electro-Impulse De-Icing System of Aircraft

Xingliang Jiang * and Yangyang Wang * State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China * Correspondence: [email protected] (X.J.); [email protected] (Y.W.)

Received: 18 March 2019; Accepted: 28 May 2019; Published: 5 June 2019

Abstract: In order to solve the accidents caused by aircraft icing, electro-impulse de-icing technology was studied through numerical simulation and experimental verification. In addition, this paper analyzed in detail the influence of the number, placement arrangement, and starting time of pulse coils on the de-icing effect, which plays a guidance role in the design and installation of the subsequent electro-impulse de-icing system. In an artificial climate chamber, the new de-icing criteria were obtained by tensile test, and the platform for the electro-impulse de-icing system was built. Replacing the skin with an aluminum plate, an electro-impulse de-icing system with a single coil was used. A three-dimensional skin-ice layer model was established by using Solidworks software. The finite element method was adapted. Through comparison between the de-icing prediction results and the test results in the natural environment, it was proven that the calculation process of de-icing prediction was correct, which laid a theoretical foundation for the selection of the number, placement arrangement, and starting time of the pulse coils. Finally, in this paper, by choosing the leading edge of NACA0012 wing as the research object, the influence of the number, placement arrangement, and starting time of pulse coils on the de-icing effect was analyzed. The results show that to get a better de-icing effect, the electro-impulse de-icing system with two impulse coils should be selected. The two coils were installed in the central position of the top and bottom surfaces of the leading edge, respectively. In addition, one of the impulse coils started working 1200 µs later than the other one.

Keywords: aircraft; wing; system; ice; icing; deicing; ice mechanics; electro-impulse; coils; structural dynamics

1. Introduction Since the earliest days of aeronautics, icing was found to be a crucial problem for aircraft flight. In-flight ice accretion occurs on the leading edge of an aircraft wing and usually covers only 2% of the wing chord, with the thickness of the ice layer being about a few centimeters. However, even an ice layer of a few centimeters thickness at the key parts of the aircraft is enough to cause flow separation and destroy lift, increase drag and reduce the maximum lifting capability, affect the control surface effectiveness, and in some cases decrease engine performance and stability [1–3]. Therefore, people have been working on aircraft anti-icing methods for many years [4–6]. The present ice protection methods are hot bleed air, freezing point depressants, and electro-thermal resistance heating. However, they all have potential limitations, for example, pneumatic boots bonded to the ice prone surface are subject to corrosion and damage by external objects, therefore, they need to be replaced every two or three years. The freezing-point depressant systems achieve the purpose of aircraft anti-icing by releasing ethylene glycol through many orifices in the leading edge of an aircraft. There are two main hazards: on the one hand, it increases the weight of the aircraft; on the other hand, since ethylene glycol is a toxic

Aerospace 2019, 6, 67; doi:10.3390/aerospace6060067 www.mdpi.com/journal/aerospace Aerospace 2019, 6, 67 2 of 15 Aerospace 2019, 6, x FOR PEER REVIEW 2 of 15 environmentalsubstance, release pollution. of this substanceThe principle into of the electro-th air can causeermal environmental systems is to use pollution. resistance The pads principle to heat of theelectro-thermal aircraft to above systems the ismelting to use resistancetemperature pads of toice, heat and the in aircraftgeneral toit aboverequires the dedicated melting temperature generators, whichof ice, andresults in generalin significant it requires cost. dedicated generators, which results in significant cost. The aforementioned methods cannot cannot meet meet the the performance performance requirements requirements for for new new aircraft. aircraft. Therefore, it it is is imperative imperative to todevelop develop a safe a safe and andreliable reliable de-icing de-icing system. system. A new Amethod new methodfor electro- for impulseelectro-impulse de-icing de-icing has emerged. has emerged. Electro-impulse de-icingde-icing (EIDI) (EIDI) is is one one of of the the mechanical mechanical de-icing de-icing systems, systems, and itand assures it assures the safety the safetyof aircrafts of aircrafts in an icing in an condition. icing condition. It has major It has advantages, major advantages, such as low such energy, as minimallow energy, maintenance, minimal maintenance,great reliability, great and reliability, low cost and and weight low cost [7 ,and8]. weight [7,8]. The basic circuit of thethe electro-impulseelectro-impulse de-icingde-icing systemsystem isis shownshown inin FigureFigure1 .1. TheThe workingworking principle is the pulse coils are connected to a high voltage voltage capacitor capacitor by low low resistance, resistance, low inductance inductance cables. When the switch is turned on,on, thethe dischargedischarge ofof thethe capacitorcapacitor through through the the impulse impulse coils coils creates creates a arapidly rapidly forming forming and and collapsing collapsing electro-magnetic electro-magnetic field. field. According According to Maxwell’sto Maxwell’s law, law, we we know know that that the thetime-dependent time-dependent magnetic magnetic field inducesfield induces eddy currents eddy incurrents the metal in skin.the Therefore,metal skin. the Therefore, instantaneous the instantaneousimpulse force ofimpulse several force hundred of several pounds hundred magnitude pounds is obtained magnitude by the is obtained Lorentz force by the formula, Lorentz but force the formula,duration but is only the aduration few hundred is only microseconds. a few hundred A microseconds. small amplitude, A small high accelerationamplitude, high movement acceleration of the movementskin acts to of shatter, the skin de-bond, acts to andshatter, expel de-bond, the ice. and expel the ice.

Figure 1. Electro-impulse system basic circuit. Figure 1. Electro-impulse system basic circuit. Researchers [9–11] have studied the phenomenon of ice layer peeling on the surface of the skin underResearchers the action [9–11] of a single have coilstudied system. the phenomenon The number of coilsice layer is greater peeling than on the one surface when aof real the EIDIskin undersystem the is installed action of on a thesingle aircraft coil [system.12–14], soThe the number position of arrangement coils is greater and start-upthan one time when of thea real multiple EIDI systemcoils may is ainstalledffect the vibrationon the aircraft condition [12–14], to the so etheffect position of the ice arrangement removing e ffandect. start-up The de-icing time criteriaof the multipleused in previous coils may studies affect [the15– vibration17] are from condition the literature to the effect [18]. Theof the adhesion ice removing between effect. the iceThe layer de-icing and criteriathe skin used is diff inerent previous under studies different [15–17] icing conditions. are from the Therefore, literature the [18]. conclusions The adhesion of [18 ]between are not suitable the ice layerfor all and icing the environments. skin is different Ice under tensile different strength icing and ice conditions./aluminum Therefore, adhesive shearthe conclusions strength used of [18] in [are19] notare 1.5suitable Mpa for and all 0.5 icing Mpa, environments. respectively. Ice However, tensile strength this does and not ice/aluminum explain how theadhesive values shear are obtained. strength usedTherefore, in [19] the are study 1.5 Mpa of de-icing and 0.5 criteria Mpa, respectively. is very important However, for the this electro-impulse does not explain de-icing how system.the values are obtained.All the experiments Therefore, inthe this study paper of were de-icing obtained criteria in anis artificialvery important climate chamber.for the electro-impulse Replacing the skinde- withicing ansystem. aluminum plate, the electro-impulse de-icing system with a single coil was used. The de-icing rangeAll obtained the experiments by experiments in this afterpaper each were pulse obtained was compared in an artificial with theclimate calculated chamber. result, Replacing and it wasthe skinproven with that an the aluminum calculation plate, process the electro-impulse for de-icing prediction de-icing was system correct. with In a addition, single coil in was the sameused. icing The de-icingenvironment, range the obtained adhesion by betweenexperiments the ice after layer each and pulse the skin was was compared measured with by the a tensile calculated test, and result, the andnew it de-icing was proven criteria that was the obtained.calculation Finally, process a for three-dimensional de-icing prediction NACA0012 was correct. wing-ice In addition, layer modelin the wassame established; icing environment, the effect the of theadhesion number, between placement the ice arrangement, layer and the and skin the was start-up measured time of by pulse a tensile coils test,on the and de-icing the new ratio de-icing was analyzed, criteria was which obtained. provided Finally, a reference a three-dimensio for the designnal andNACA0012 installation wing-ice of the layersubsequent model electro-impulsewas established; de-icing the effect system. of the number, placement arrangement, and the start-up time of pulse coils on the de-icing ratio was analyzed, which provided a reference for the design and installation of the subsequent electro-impulse de-icing system.

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2. System Composition and Structural Dynamic Studies The structural dynamics equation is expressed as [20]

.. . [M]U + [C]U + [K]U = F, (1) where [M] is the overall quality matrix, [C] is the overall damping matrix, [K] is the overall stiﬀness .. . matrix, F is the impulse force, and U is the node displacement, U is the node accelerated velocity, U is the node velocity. In the continuous linear elastic body vibration, the relationship between normal stress, shear stress and displacement and external force is described. The expression for the stress can be written as

[σ] = [D][B] U e. (2) { }

Substituting the node displacement into Equation (2), σx, σy, σz, τxy, τyz, τxz for each node can be obtained. The characteristic equation for the stress state is solved by the theory of one-dimensional cubic equation. Therefore, the practical calculation formulae for the principal stress can be written as r I p θ σ = 1 + 2 − cos , 1 3 3 3 r I p θ θ σ = 1 − cos √3sin , 2 3 − 3 3 − 3 r I p θ θ σ = 1 − cos + √3sin , 3 3 − 3 3 3

 1  3I I2 9I I 2I3 27I 3 2 2 1 1 2 1 3  q p −  where P = − ; q = − − ; θ = arccos (0 < θ < π). 3 27 − 2 − 27  From the formulae above, σ1, σ2, σ3 can be obtained. Substituting σ1, σ2, σ3 into Equation (3), the equivalent stress can be written as r 1 2 σ = [(σ σ )2 + (σ σ )2 + (σ σ )2] . (3) 2 1 − 2 2 − 3 3 − 1

3. Calculation Method Veriﬁcation

3.1. Geometric Model In this paper, an aluminum plate was used as the research object, and the material was the same as the wing skin. The research of electro-impulse de-icing systems mainly includes three parts: electrodynamics research, structural dynamics research, and de-icing prediction. The electro-dynamics studies of this EIDI included the calculation of impulse current, the study of the magnetic field behavior, and the calculation of the impulse force of each grid point on the surface of the aluminum plate, which provided the basis for structural dynamic research. Structural dynamics studies include stress calculations, which provide the basis for de-icing prediction. The model was established by using Solidworks, with a length of 420 mm, width of 420 mm, and thickness of 1.5 mm. The pulse coil was located on the lower surface of the aluminum plate, and the gap between the impulse coil and the skin was 1 mm. It had an inner diameter of 20 mm and an outer diameter of 128 mm. The material characteristics are shown in Table1. The structural dynamics associated with electro-impulse de-icing have proven to be a difficult and challenging problem. The structural dynamics study is mainly to calculate the equivalent stress between the ice layer and aluminum plate under the action of pulse force. If the total pulse force is Aerospace 2019, 6, 67 4 of 15 applied to the aluminum plate, the calculation accuracy will be affected. Therefore, the aluminum plate was divided into different regions in the radial direction. Then, the impulse pressure at different radial points and different times was placed on the corresponding regions on the surface of the aluminum plate. This greatly improved the accuracy of the de-icing prediction. It is assumed that the ice layer with 4 mm thickness was evenly covered on the aluminum plate with 2.0 mm thickness. The material properties are shown in Table2.

Table 1. Material characteristics.

Material Relative Permeability Conductivity (S/m) Density (Kg/m3) Aluminum plate 1.000021 1.74 107 2780 × Impulse coil 0.999991 5.8 107 8933 ×

Table 2. Material properties.

Material E/GPa v ρ/(kg m3) · Aluminum 7.1 0.33 2700 Ice 5.5 0.3 897

The size of the meshing affects the calculation results of structural dynamics. In this paper, the modal analysis of the aluminum plate was calculated by the finite element method. The calculated result of first-order natural frequency was 46.5 Hz. Considering the boundary conditions and bending vibration of the aluminum plate, the aluminum plate was regarded as a free Bernoulli–Euer beam model at both ends, and its natural frequency theoretical calculation formula [17,18] is as follows: s π 1 2 EI fn = (n + ) , n = 1, 2, , (4) 2 2 ρAl4 ··· where l is the length of the aluminum plate, A is the cross-sectional area, ρ is the density, I is the moment of inertia of the section, and E is the elasticity modulus. The first-order natural frequency obtained by the finite element method was 46.5 Hz, and the theoretical calculation was 44.5 Hz. The relative error between the two was very small, only 4.3%. It indicates that the meshing sizes above were feasible, which provided a basis for the correct structural dynamics calculation.

3.2. De-Icing Criteria The key factor of de-icing prediction research is the de-icing criteria. According to [9], there are two main de-icing criteria. One is to consider only a single strength factor at the ice-skin interface, and the other is to consider the tensile and shear stresses at the ice-skin interface. However, no matter which kind of the de-icing criteria is used, the equivalent stress and the shear stress are both determined values (σU = 1.44 MPa, τU = 0.4 MPa). This is contrary to the fact that the equivalent stress and the shear stress between the ice layer and aluminum plate is different under different icing environments. In this paper, the equivalent stress and the shear stress between the ice and aluminum plate was measured by a tensile test. Figures2 and3 show the icing box and tension test device, respectively. The icing test was carried out in an artificial climate chamber. As shown in Figure4, the height and the diameter of the artificial climate chamber were 11.6 m and 7.8 m, respectively. The wind speed in the built-in wind tunnel can be up to 10 m/s. The sprinkler system consisted of 14 high-pressure water mist nozzles. Aerospace 2019, 6, x FOR PEER REVIEW 5 of 15 Aerospace 2019, 6, x FOR PEER REVIEW 5 of 15 Aerospace 2019, 6, x FOR PEER REVIEW 5 of 15 outer surface of the icing box, resulting in inaccurate measurements. Therefore, a better option is to outer surface of the icing box, resulting in inaccurate measurements. Therefore, a better option is to pour a little water into the icing box at first until the water in the icing box freezes completely, and pourouter a surface little water of the into icing the box, icing resulting box at first in inaccura until thete watermeasurements. in the icing Therefore, box freezes a better completely, option andis to repeat this procedure until the icing box is full of ice. In the natural icing environment, the outer repeatpour a thislittle procedure water into until the icingthe icing box atbox first is fulluntil of the ice. water In the in naturalthe icing icing box environment,freezes completely, the outer and surface of the icing box can also freeze. Before the tensile test, the icing around the icing box should surfacerepeat thisof the procedure icing box until can alsothe icingfreeze. box Before is full the of tensile ice. In test, the thenatural icing icingaround environment, the icing box the should outer be carefully removed so that the measurement result is accurate. Aerospacebesurface carefully 2019of the, 6removed, 67icing box so canthat also the measurementfreeze. Before resultthe tensile is accurate. test, the icing around the icing box should5 of 15 be carefully removed so that the measurement result is accurate.

Figure 2. Icing box. Figure 2. Icing box. FigureFigure 2. 2.Icing Icing box.box.

Figure 3. Tension sensor. Figure 3. TensionTension sensor. Figure 3. Tension sensor.

Figure 4. ArtificialArtificial icing test. Figure 4. Artificial icing test. Figure 4. Artificial icing test. TheIn addition, temperature to improve curve during measurement whole test accuracy, was 20 degrees.the aluminum Note that plate if ashould large amount be polished of water with is In addition, to improve measurement accuracy,− the aluminum plate should be polished with togauze be poured to remove into thethe icing oxide box film at first, and therust water on it easilys surface. overflows. During This the causes measurement icing around process, the outer the gauzeIn to addition, remove tothe improve oxide filmmeasurement and rust accuracy,on its surface. the aluminum During the plate measurement should be polished process, withthe surfaceoperating of thespeed icing was box, controlled resulting so in inaccuratethat it accurate measurements.ly read the Therefore,sensor readings. a better The option results is to for pour the a operatinggauze to removespeed was the controlled oxide film so and that rust it accurate on its lysurface. read the During sensor the readings. measurement The results process, for thethe littleadhesion water between into the the icing ice box and at the first alum untilinum the waterplate are in the shown icing in box Table freezes 3. completely, and repeat this adhesionoperating between speed was the icecontrolled and the soalum thatinum it accurate plate arely shownread the in Tablesensor 3. readings. The results for the procedure adhesion between until the the icing ice boxand isthe full alum of ice.inum In plate the natural are shown icing in environment, Table 3. the outer surface of the icing box can also freeze. Before the tensile test, the icing around the icing box should be carefully removed so that the measurement result is accurate. In addition, to improve measurement accuracy, the aluminum plate should be polished with gauze to remove the oxide film and rust on its surface. During the measurement process, the operating speed was controlled so that it accurately read the sensor readings. The results for the adhesion between the ice and the aluminum plate are shown in Table3. The tangential force is produced by electro-impulse de-icing system is small, therefore, this paper only needed to consider that the ice layer falls off when the tensile stress between the ice and aluminum

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plate is greater thanTable the 3. maximumThe adhesion tensile between stress. the As shownice and in the Table aluminum3, the maximum plate. tensile stress σmax between the ice and aluminum plate is Test Object Equivalent Stress (kN) F (1) σ = zave = 0.150.323 MPa, max S (2) 0.325 2 where Fzave is the average value of(3) the adhesion and S is0.274 the area of the ice box, 20.25 cm .

Table 3. The(4) adhesion between the ice0.299 and the aluminum plate. (5) 0.289 Test Object Equivalent Stress (kN) (6) 0.252 (1) 0.323 (7) 0.310 (2) 0.325 (3) 0.274 The tangential force is produced by electro-impulse de-icing system is small, therefore, this (4) 0.299 paper only needed to consider that the ice layer falls off when the tensile stress between the ice and (5) 0.289 aluminum plate is greater than the maximum(6) tensile 0.252stress. As shown in Table 3, the maximum 𝜎 tensile stress between the ice and(7) aluminum plate 0.310 is F σ = = 0.15MPa, The maximum stress σmax between theS ice and aluminum plate obtained in this paper and the result obtained by [21] are not much diﬀerent. Therefore, it is indicative that the maximum stress σmax where F is the average value of the adhesion and S is the area of the ice box, 20.25 cm . measured by tensile test is correct. The maximum stress 𝜎 between the ice and aluminum plate obtained in this paper and the result obtained3.3. Result by Analysis [21] are not much different. Therefore, it is indicative that the maximum stress 𝜎 measured by tensile test is correct. 3.3.1. Analysis of Experimental Results

3.3. Result AnalysisThe icing test was carried out in natural icing station. The icing results of aluminum plates are shown in Figure5. Icing thickness was 4 mm, as shown in Figure6. The circuit parameters are: voltage: U0 = 780 V; charging capacitor: C = 990 µf; inductance: 3.3.1. Analysis of Experimental Results L = 19 µH, Lw = 5 µH. The de-icing results of skin are shown in Figure7. The icingIt cantest be was seen carried from Figure out7 thatin natural the de-icing icing rate st reachedation. The 73.6% icing after three-pulse.results of aluminum It is indicative plates are that the electro-impulse de-icing system was feasible. shown in Figure 5. Icing thickness was 4 mm, as shown in Figure 6.

Figure 5. Icing results of the aluminum plate. Figure 5. Icing results of the aluminum plate.

Figure 6. Icing thickness.

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Table 3. The adhesion between the ice and the aluminum plate.

Test Object Equivalent Stress (kN) (1) 0.323 (2) 0.325 (3) 0.274 (4) 0.299 (5) 0.289 (6) 0.252 (7) 0.310

The tangential force is produced by electro-impulse de-icing system is small, therefore, this paper only needed to consider that the ice layer falls off when the tensile stress between the ice and aluminum plate is greater than the maximum tensile stress. As shown in Table 3, the maximum tensile stress 𝜎 between the ice and aluminum plate is F σ = = 0.15MPa, S where F is the average value of the adhesion and S is the area of the ice box, 20.25 cm . The maximum stress 𝜎 between the ice and aluminum plate obtained in this paper and the result obtained by [21] are not much different. Therefore, it is indicative that the maximum stress

𝜎 measured by tensile test is correct.

3.3. Result Analysis

3.3.1. Analysis of Experimental Results The icing test was carried out in natural icing station. The icing results of aluminum plates are shown in Figure 5. Icing thickness was 4 mm, as shown in Figure 6.

Aerospace 2019, 6, 67 7 of 15 Figure 5. Icing results of the aluminum plate.

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The circuit parameters are: voltage: U0 = 780 V; charging capacitor: C = 990 f; inductance: L = 19Aerospace H, 2019L =, 6,5 x FORH. The PEER de REVIEW-icing results of skin are shown in Figure 7. 7 of 15 μ w μ The circuitμ parameters are: voltage: U0 = 780 V; charging capacitor: C = 990 μf; inductance: L = Figure 6.6. Icing thickness. 19 μH, L =5 μH. The de-icing results of skin are shown in Figure 7.

Figure 7. Ice layer shedding process.

It can be seen from Figure 7 that the de-icing rate reached 73.6% after three-pulse. It is indicative that the electro-impulse de-icing systemFigure 7.was Ice feasiblelayer shedding . process.

3.3.2.It Analysis can be seen of Calculation from Figure Results 7 that the de-icing rate reached 73.6% after three-pulse. It is indicative that the electro-impulse de-icing system was feasible. A threeA three-dimensional-dimensional impulse impulse coil coil-aluminum-aluminum plate plate model model was was es establishedtablished by by using using Solidworks software. The i importingmporting of the model into the Maxwell software is shown in Figure8 8a.a. AnAn externalexternal 3.3.2. Analysis of Calculation Results circuit shown in Figure8 8bb waswas appliedapplied at at the the cross cross section section of of the the impulse impulse coil. coil. A three-dimensional impulse coil-aluminum plate model was established by using Solidworks software. The importing of the model into the Maxwell software is shown in Figure 8a. An external circuit shown in Figure 8b was applied at the cross section of the impulse coil.

(a) 3D impulse coil-aluminum plate model. (b) An external circuit.

Figure 8. ElectroElectro-dynamic-dynamic simulation model model..

Under thethe actionaction ofof the the instantaneous instantaneous impulse impulse force force F, theF, the equivalent equivalent stress stress between between the skinthe skin and (a) 3D impulse coil-aluminum plate model. (b) An external circuit. andthe icethe layer ice layer can becan obtained be obtained by Equations by Equations (1)–(3). (1) The–(3). de-icing The de- rangeicing range on the on surface the surface of skin of was skin found was foundby using by theusing new the de-icing new de- criteria.icingFigure criteria. In8. Electro-dynamic order In order to improve to improvesimulation the calculation the model. calculation result result accuracy accuracy of de-icing of de- prediction,icing predictio then, structural the structural dynamic dynamic response response was obtained was obtained by using by the u finitesing the element finite method. element Themethod force. Theat di ffforceUndererent at timesthe different action in diff oferenttime thes positions instantaneousin different of the positions skinimpulse was offo applied rcethe F,skin tothe the wasequivalent corresponding applied stress to theposition, between corresponding as the shown skin positioninand Figure the ice, 9as. Thelayershown tangential can in be Figure obtained magnetic 9. The by tangential fieldEquationsBr and magnetic (1)–(3). the eddy The field current de-icing B and density range the eddy onJeddy the currentat surface different density of positionsskin Jwas found by using the new de-icing criteria. In order to improve the calculation result accuracy of de- atand different at different positions times of and the at aluminum different plate times were of obtainedthe aluminum by simulating.r plate were Therefore, obtained the by instantaneous simulating.eddy Therefore,impulseicing prediction, force the caninstantaneous the be structural obtained impulse by dynamic Equation force response (5),can asbe shownwasobtained obtained in Figureby Equation by 10 using. (5), the as finite shown element in Figure method. 10. The force at different times in different positions of the skin was applied to the corresponding Z F= Jeddy × Bdv , position, as shown in Figure 9. The tangential→ ∫ magnetic→ →field B and the eddy current density J F =V J eddy Bdv,(5 (5)) at different positions and at different times of the aluminum× plate were obtained by simulating. V Therefore, the instantaneous impulse force can be obtained by Equation (5), as shown in Figure 10. where F is the impulse force, J is the eddy current  density, and B is the magnetic field. FJ=× Bdv, eddy  eddy V (5)

where F is the impulse force, J is the eddy current density, and B is the magnetic field.

Aerospace 2019, 6, x FOR PEER REVIEW 8 of 15 Aerospace 2019, 6, 67 8 of 15

where F is the impulse force, J is the eddy current density, and B is the magnetic ﬁeld. Aerospace 2019, 6, x FOR PEER REVIEWeddy 8 of 15

Figure 9. Excitation and loading area.

As shown in Figure 10, the distribution of force increased first and then decreased along the radial distance. The time required to reach the peak pressure was 100 μs, which meets the Figure 9. Excitation and loading area. requirements of narrow pulse width.Figure 9. Excitation and loading area.

FigureFigure 10. 10.RelationshipRelationship between between force force and and time. time.

AccordingAs shown to inthe Figure process 10, of the calculation, distribution the of eq forceuivalent increased stress first was and obtained then decreased by the finite along element the radial method,distance. as shown The time in Figures required 11 to and reach 12. the peak pressure was 100 µs, which meets the requirements of narrow pulse width. Figure 10. Relationship between force and time. According to the process of calculation, the equivalent stress was obtained by the finite element method,According as shown to the in Figures process 11 of and calculation, 12. the equivalent stress was obtained by the finite element method,The as de-icing shown ratio in Figures obtained 11 byand the 12. experiment was 73.6% after three pulses, and the de-icing ratio obtained by calculation reached 72.1% after three pulses. Although the de-icing ratio was very close, there was a difference in the de-icing range. The experimental results show that the lower and left side of the ice layer on the surface of the aluminum plate were completely detached, and the calculation results did not fall off. This was due to the effect of the external factors, such as wind speed. During the experiment, the ice on the top of the skin was easily able to fall off under the action of external wind speed. This factor was not considered in the calculation process of de-icing prediction. In summary, the de-icing ratio obtained by the experiment was 73.6% after three pulses, and the de-icing ratio obtained by calculation reached 72.1% of the de-icing prediction after three pulses. In the range of errors permitted, the comparison between the experimental results and the predicted results indicated that the calculation process of de-icing prediction was correct. Figure 11. Equivalent stress.

Figure 11. Equivalent stress.

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Figure 9. Excitation and loading area.

Figure 10. Relationship between force and time.

AerospaceAccording2019, 6, 67 to the process of calculation, the equivalent stress was obtained by the finite element9 of 15 method, as shown in Figures 11 and 12.

Aerospace 2019, 6, x FOR PEER REVIEW 9 of 15 Figure 11. Equivalent stress. Figure 11. Equivalent stress.

Figure 12. De-icing prediction results. Figure 12. De-icing prediction results. 3.3.3. The Effect of Ice Thickness on the De-Icing Ratio The de-icing ratio obtained by the experiment was 73.6% after three pulses, and the de-icing To study the changes of de-icing ratio with ice thickness while maintaining all other parameters ratio obtained by calculation reached 72.1% after three pulses. Although the de-icing ratio was very unchanged, we assumed that the thicknesses of ice is 1 mm, 6 mm, 8 mm, and 10 mm, respectively. close, there was a difference in the de-icing range. The experimental results show that the lower and The de-icing ratios obtained by calculation are shown in Table4. left side of the ice layer on the surface of the aluminum plate were completely detached, and the calculation results did not fall off. This was due to the effect of the external factors, such as wind Table 4. Effect of ice thickness on de-icing ratio. speed. During the experiment, the ice on the top of the skin was easily able to fall off under the action of external wind speed.Ice ThicknessThis factor (mm) was not 1considered 6 in the 8 calculation 10 process of de-icing prediction. De-icing ratio 80.7% 71.04% 53.44% 10.42% In summary, the de-icing ratio obtained by the experiment was 73.6% after three pulses, and the de-icing ratio obtained by calculation reached 72.1% of the de-icing prediction after three pulses. In It can be seen from Table4 that the thicker the ice is, the smaller the de-icing ratio will be while the range of errors permitted, the comparison between the experimental results and the predicted maintaining all other parameters unchanged. results indicated that the calculation process of de-icing prediction was correct. 4. Example 3.3.3. The Effect of Ice Thickness on the De-Icing Ratio The number of pulse coils was greater than one when a real EIDI system was installed on the aircraft,To study so the the number, changes position of de-icing arrangement, ratio with and ice start-up thickness time while of the maintaining multiple coils all mayother have parameters affected unchanged,the vibration we condition assumed to that the the eff ectthicknesses of the ice of removing ice is 1 mm, effect. 6 mm, The 8 NACA0012mm, and 10 wing mm, withrespectively. a chord Thelength de-icing of 1000 ratios mm obtained was taken by as calculation the research are object shown in in this Table paper. 4. Since the wing was covered with ice mostly in the leading edge part [22–24], it was only necessary to analyze the de-icing ratio of the Table 4. Effect of ice thickness on de-icing ratio. leading edge of the wing. A three-dimensional wing leading edge-ice layer model was established by using Solidworks, as shownIce Thickness in Figure (mm) 13. Its length 1 along 6 the chord 8 was 300 10 mm, the length along the De-icing ratio 80.7% 71.04% 53.44% 10.42%

It can be seen from Table 4 that the thicker the ice is, the smaller the de-icing ratio will be while maintaining all other parameters unchanged.

4. Example The number of pulse coils was greater than one when a real EIDI system was installed on the aircraft, so the number, position arrangement, and start-up time of the multiple coils may have affected the vibration condition to the effect of the ice removing effect. The NACA0012 wing with a chord length of 1000 mm was taken as the research object in this paper. Since the wing was covered with ice mostly in the leading edge part [22–24], it was only necessary to analyze the de-icing ratio of the leading edge of the wing. A three-dimensional wing leading edge-ice layer model was established by using Solidworks, as shown in Figure 13. Its length along the chord was 300 mm, the length along the exhibition was 600 mm, and the span of one bay of the leading edge was 300 mm. The thickness of the leading edge was 1.5 mm and the thickness of the ice layer was 1.0 mm.

Aerospace 2019, 6, 67 10 of 15

exhibition was 600 mm, and the span of one bay of the leading edge was 300 mm. The thickness of the

AerospaceleadingAerospace 2019 edge2019, 6, ,6 wasx, xFOR FOR 1.5 PEER PEER mm REVIEW REVIEW and the thickness of the ice layer was 1.0 mm. 1010 of of 15 15

(a()a )Electro Electro-impulse-impulse de de-icing-icing system system with with four four coils. coils. (b (b) )Electro Electro-impulse-impulse de de-icing-icing system system with with two two coils. coils.

FigureFigureFigure 13. 13.13. Position PositionPosition arrangement arrangementarrangement of ofof multiple multiplemultiple p pulsepulseulse coils. coils.coils.

4.1.4.1.4.1. P PositionPositionosition A ArrangementArrangementrrangement of ofof the thethe M MultipleMultipleultiple C CoilsCoilsoils InInIn order orderorder to toto study studystudy the thethe influence inﬂuenceinfluence of ofof multiple multiplemultiple coils coilscoils on onon t thehethe de de-icingde-icing-icing ratio ratio,ratio,, the thethe single singlesingle coil coilcoil simulation simulationsimulation methodmethodmethod was waswas extended extended to to a a multiplemulti multipleple coilcoil coil simulation.simulation. simulation Regarding.Regarding Regarding the the the possibilities possibilities possibilities for for for weight weight weight reduction reduction reduction of ofEIDIof EIDI EIDI systems, systems, systems, it it wasit was was also also also important important important to to to determine determine determine thethe the minimumminimum minimum numbernumber number of of coils,coil coils,s, t that hatthat is, is, wwhether whetherhether it itit isisis necessary necessarynecessary to toto place placeplace a aa co coilcoilil in inin every every bay bay of of the the leadingleading leading edge.edge. edge. Because BecauseBecause t thehethe established establishedestablished model modelmodel was waswas symmetricalsymmetrical,symmetrical,, it itit only onlyonly need neededneededed to toto select selectselect two twotwo or oror four fourfour pulse pulsepulse coils. coils.coils. T TheThehe position positionposition arrangements arrangementsarrangements of ofof the thethe four fourfour andandand two twotwo pulse pulsepulse coils coils are are as as shown shown shown in in in Figure Figure Figure 13a 13a,b, 13,ba,b,, respectively. re respectively.spectively. T Thehe The structure structure structure dynami dynamics dynamicscs simulation simu simulationlation of of theofthe thefour four four coil coil coil system system system was was was carried carried carried out. out. out. If If only If only only two two two of of offour four four coils coils coils were were were used, used, it it was was divided divideddivided into intointo three threethree kindkindskindss of ofof modes modes,modes,, which whichwhich are areare respectively respectivelyrespectively Mode ModeMode 1, 1,1, Mode ModeMode 2 22 and andand Mode ModeMode 3 3,3,, a asass shown shownshown in inin Table TableTable 55. .5. Mode Mode 4 4 is is thethethe two twotwo coil coilcoil system. system.system.

TableTableTable 5. 5. 5. FourFour Four k kindskindsinds of ofof two twotwo coils coils.coils..

ModeMModeode (1)(1 (1)) (2)(2 (2)) (3)(3 (3)) (4 (4)) PositionPositionPosition arrangement arrangement arrangement 1,1 1,, 22 2 oror or 3, 3 3,, 4 4 4 1,1 1,, 3 3 or3 or or 2, 2 42,, 4 4 1,1 4 1,, or4 4 or 2,or 32 2,, 3 3 5 5,, 6 66

TheTheThe de de-icingde-icing-icing results resultsresults of ofof simultaneous simultaneoussimultaneous vibration vibrationvibration of ofof the thethe four fourfour coils coilscoils are areare shown shownshown in inin F FigureFigureigure 1414 14... For ForFor the thethe electroelectro-impulseelectro-impulse-impulse de de-icing de-icing-icing systemsystem system ofof of thethe thefour four four coils, coils, coils, the t hethe de-icing de de-icing-icing results results results of of theof the the simultaneous simultaneous simultaneous vibration vibration vibration are areshownare shown shown in Figures in in Figure Figures 15–17s 15 ,15–17, in–17 which, in in onlywhichwhich two only only of four two two coils of of four werefour coils used.coils were were The de-icingused used.. The The results de de-icing-icing of simultaneous results results of of simultaneousvibrationsimultaneous of the vibration vibration two coils of of arethe the showntwo two coils coils in Figureare are shown shown 18. in in F Figureigure 18 18..

(a) Equivalent stress (ice layer). (b) De-icing prediction (ice layer).

(a) Equivalent FigurestressFigure (ice14. 14. E Electro-impulselayer).lectro-impulse d de-icinge-icing(b) De-icing s systemystem of ofprediction f fourour c coils.oils. (ice layer). Figure 14. Electro-impulse de-icing system of four coils.

Aerospace 2019, 6, x FOR PEER REVIEW 11 of 15 Aerospace 2019, 6, x FOR PEER REVIEW 11 of 15 AerospaceAerospace 20192019, ,66, ,x 67 FOR PEER REVIEW 1111 of of 15 15 Aerospace 2019, 6, x FOR PEER REVIEW 11 of 15

Figure 15. 1, 2 or 3, 4 of four coils are used (Mode 1). Figure 15. 1, 2 or 3, 4 of four coils are used (Mode 1). Figure 15. 1, 2 or 3, 4 of four coils are used (Mode 1). Figure 15. 1,1, 2 2 or or 3, 3, 4 of four coils are used (Mode 1).

Figure 16. 1, 3 or 2, 4 of four coils are used (Mode 2).

Figure 16. 1, 3 or 2, 4 of four coils are used (Mode 2). FigureFigure 16. 16. 1,1, 3 3or or 2, 2, 4 4of of four four coils coils are are used used (Mode (Mode 2). 2). Figure 16. 1, 3 or 2, 4 of four coils are used (Mode 2).

Figure 17. 1, 4 or 2, 3 of four coils are used (Mode 3). Figure 17. 1, 4 or 2, 3 of four coils are used (Mode 3). Figure 17. 1, 4 or 2, 3 of four coils are used (Mode 3). Figure 17. 1, 4 or 2, 3 of four coils are used (Mode 3).

Figure 18.18. Electro-impulse de-icing (EIDI) system ofof twotwo coilscoils (Mode(Mode 4).4). Figure 18. Electro-impulse de-icing (EIDI) system of two coils (Mode 4). It can be seenFigure from 18. Figures Electro-impulse 14–18 that de-icing the de-icing (EIDI) system ratios variedof two coils with (Mode the number 4). or the position It can be seenFigure from 18.Figures Electro-impulse 14–18 that de-icing the de-icin (EIDI)g ratiossystem varied of two withcoils (Modethe number 4). or the position arrangementarrangementIt can be ofofseen pulsepulse from coils.coils. Figures In addition, 14–18 that the the ice de-icin layer fellg ratios ooffff within varied a certainwith the distance number from or the thethe position central It can be seen from Figures 14–18 that the de-icing ratios varied with the number or the position positionarrangementpositionIt can ofof be thethe ofseen pulsepulse pulse from coil.coil. coils. Figures This In wasaddition, 14–18 because that the the ice de-icin magneticmagnetlayer fellgic ratios off fieldfield within wasvaried stronger a certainwith the inin distance thisthisnumber range. from or Thethe the positionstronger central arrangement of pulse coils. In addition, the ice layer fell off within a certain distance from the central arrangementthepositionthe magneticmagnetic of the of field,field, pulse pulse thethe coil. coils. biggerbigger This In wasaddition, itsits magneticmagnetic because the the force,force,ice magnetlayer thus,thus, fellic thethe offfield iceicewithin was layerlayer stronger a waswascertain easyeasy in distance this toto fallfall range. ooff.fromff. TheThe the stronger de-icingde-icing central position of the pulse coil. This was because the magnetic field was stronger in this range. The stronger positionratiostheratios magnetic ofof of thethe the severalseveral field, pulse the modelsmodelscoil. bigger This aboveab wasitsove magnetic becauseofof thethe electro-impulseelectro-impulse theforce, magnet thus,ic the field de-icingde-icing ice was layer stronger systemsystem was easy areare in shownthisshownto fall range. off. inin Table TableTheThe 6strongerde-icing .6. the magnetic field, the bigger its magnetic force, thus, the ice layer was easy to fall off. The de-icing theratios magneticIt of can the be several field, seen the frommodels bigger Table ab itsove6 that magnetic of the for electro-impulse the force, electro-impulse thus, the de-icing ice de-icinglayer system was system easy are shownto with fall off. twoin Table The pulse de-icing 6. coils, ratios of the several models above of the electro-impulse de-icing system are shown in Table 6. ratiosthe de-icing of the ratioseveral of Modesmodels 1, ab 2,ove and of 3 werethe electro-impulse only 36.19%, 38.35%, de-icing and system 41.43%, are respectively. shown in Table The de-icing6. ratio of Mode 4 was 47.22%, which was the maximum. The de-icing ratio of the electro-impulse

de-icing system with four coils was 69.83%. According to the experimental results, the ice layer at the

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Table 6. De-icing ratio comparison. Aerospace 2019, 6, 67 12 of 15 Electro-Impulse De-Icing Electro-Impulse De-Icing System with Two Coils

System with Four Coils Mode1 Mode 2 Mode 3 Mode 4 boundaryDe-icing of ratio the skin would also69.83% fall o ff under the influence36.19% of external38.35% factors. 41.43% Therefore, 47.22% from the perspective of not affecting aircraft flight and low energy consumption, the position arrangement of ModeIt 4can is optimalbe seen forfrom the Table research 6 that objects for the mentioned electro-impulse above. de-icing system with two pulse coils, the de-icing ratio of Modes 1, 2, and 3 were only 36.19%, 38.35%, and 41.43%, respectively. The de-icing Table 6. De-icing ratio comparison. ratio of Mode 4 was 47.22%, which was the maximum. The de-icing ratio of the electro-impulse de- icing system with fourElectro-Impulse coils was 69.83%. De-Icing AccordingElectro-Impulse to the experimental De-Icing Systemresults, with the Twoice layer Coils at the boundary of the skinSystem would with also Four fall off Coils under theMode influence 1 of Mode external 2 factors. Mode Ther 3efore, Mode from 4 the perspective of not affecting aircraft flight and low energy consumption, the position arrangement of De-icing ratio 69.83% 36.19% 38.35% 41.43% 47.22% Mode 4 is optimal for the research objects mentioned above.

4.2. The Effect Effect of Start Start-Up-Up Time of Pulse Coil In thethe casecase ofof Mode Mode 4, 4, the the starting starting times times of of the the pulse pulse coils coils 5 and 5 and 6 were 6 were diff erent,different, and theand de-icingthe de- ratiosicing rat obtainedios obtained by the by calculation the calculation were diwerefferent. different. Take asTake an exampleas an example the system the system with two with pulses, two pulses coil, pulse 5 started coil 5 started to work to atwork 0 µ s,at and0 μs pulse, and pulse coil 6 coil started 6 started to vibrate to vibrate from from 0 µs, 0 100μs, 100µs, μs 600, 600µs, andμs, and 1200 1200µs, μs respectively., respectively The. The vibration vibration de-icing de-icing result result at at 0 0µ μss was was thethe samesame asas thatthat of Mode 4. 4. TheThe result resultss of of the the ice ice layer layer detachment detachment of pulse of pulse coil coil 6 start 6 startinging to work to work from from100 μs 100 is shownµs is shown in Figure in Figure19b. Figure 19b. Figure19c shows 19c showsthe pressure the pressure waveform waveform at the coil at the radial coil radialdirection direction r = 30 rmm= 30. T mm.he result Thes results of the ofice thelayer ice detachment layer detachment of pulse ofcoil pulse 6 start coiling 6 to starting work from to work 600 μs from and 6001200usµs andare shown 1200 µ ins areFigure showns 20 inand Figures 21, respectively 20 and 21., respectively.

(a) Equivalent stress (ice layer). (b) De-icing prediction (ice layer).

(c) The pressure waveform of pulse coil 5 and 6. Aerospace 2019, 6, x FOR PEER REVIEW 13 of 15 Figure 19. DDe-icinge-icing r resultsesults of p pulseulse c coiloil 6 startingstarting 100 µμss later than coil 5.5.

(a) De-icing prediction (ice layer). (b) The pressure waveform of pulse coil 5 and 6.

FigureFigure 20. 20. DDe-icinge-icing results results of of p pulseulse c coiloil 6 6start startinging 6 60000 μsµs later later than than coil coil 5. 5.

(a) De-icing prediction (ice layer). (b) The pressure waveform of pulse coil 5 and 6.

Figure 21. De-icing results of pulse coil 6 starting 1200 μs later than coil 5.

It can be seen from Figures 19–21 that the de-icing ratios obtained by calculation were different under the different starting times of pulse coil 6. De-icing prediction results are shown in Table 7.

Table 7. De-icing ratios.

Start Time Delay of Coil 6 with Respect of 0 μs 100 μs 600 μs 1200 μs Start Time of Coil 5 De-icing ratio 47.22% 51.38% 45.42% 54.03%

It can be seen from Table 7 that if pulse coil 6 started working at the same time as coil 5, or 600 μs later, the de-icing ratios obtained by calculation were almost the same. This was because the interval between the continuous applied force at the same position of the wing was the same. However, if pulse coil 6 started working 1200 μs later than coil 5, the de-icing ratio was the largest, which served as a guiding function for the subsequent pulse coil vibration control.

5. Conclusions (1) In an artificial climate chamber, the maximum adhesion between ice layer and aluminum plate was 0.15 Mpa obtained by the tensile test. Since the tangential force generated by the electro- impulse de-icing system was very small, as long as the equivalent stress between the ice layer and the aluminum plate was greater than 0.15 Mpa, the ice layer fell off, which laid a foundation for the simulation calculation of the subsequent electro-impulse de-icing system. (2) We replaced the skin with an aluminum plate and built a platform of the electro-impulse de- icing system in an artificial climate chamber. The range of de-icing of the skin surface obtained by the experiments was recorded under different pulse times. A three-dimensional aluminum plate-ice layer model was established by using Solidworks. The results obtained by the three- step calculation of electrodynamics, structural dynamics, and de-icing prediction were compared with the experiment results of the electro-impulse de-icing system. It was indicative that the calculation process of de-icing prediction obtained by this paper was correct. (3) Taking the leading edge of the NACA0012 wing with a chord length of 1 m as the research object, its length along the chord was 300 mm, the length along the exhibition was 600 mm, and the span of one bay of the leading edge was 300 mm. The leading edge had a thickness of 2.0 mm and the ice thickness was 4.0 mm. The de-icing ratio of the four pulse coil system was 69.83%.

Aerospace 2019, 6, x FOR PEER REVIEW 13 of 15

(a) De-icing prediction (ice layer). (b) The pressure waveform of pulse coil 5 and 6. Aerospace 2019, 6, 67 13 of 15 Figure 20. De-icing results of pulse coil 6 starting 600 μs later than coil 5.

(a) De-icing prediction (ice layer). (b) The pressure waveform of pulse coil 5 and 6.

FigureFigure 21. 21. DDe-icinge-icing r resultsesults of of p pulseulse c coiloil 6 6 start startinging 1 1200200 μsµs later later than than coil coil 5 5..

ItIt can can be seen from FigureFigure s19 19 that–21 thethat de-icing the de-icing ratios rat obtainedios obtained by calculation by calculation were diwereﬀerent different under underthe diﬀ theerent different starting starting times oftime pulses of coilpulse 6. De-icingcoil 6. De prediction-icing prediction results results are shown are shown in Table in7 .Table 7.

TableTable 7. DeDe-icing-icing ratio ratios.s.

Start TimeStart Delay Time of Delay Coil 6 of with Coil Respect 6 with of 0 µs0 μs 100 µs100 μs 600 µs600 μs 1200 µs 1200 μs RespectStart Tim of Starte of TimeCoil of5 Coil 5 De-De-icingicing ratio ratio 47.22%47.22% 51.38%51.38% 45.42% 45.42% 54.03% 54.03%

ItIt can can be seen from TableTable7 7that that if if pulse pulse coil coil 6 started6 started working working at at the the same same time time as coilas coil 5, or5, 600or 600µs μslater, later, the the de-icing de-icing ratios rat obtainedios obtained by calculation by calculation were almostwere almost the same. the Thissame. was This because was because the interval the intervalbetween between the continuous the continuous applied force applied at the sameforce positionat the same of the position wing was of the the same. wing However, was the ifsame. pulse However,coil 6 started if pulse working coil 6 1200 startedµs later working than 1200 coil 5, μs the later de-icing than coil ratio 5, wasthe de the-icing largest, ratio which was the served largest as a, whichguiding served function as a forguiding the subsequent function for pulse the coilsubsequent vibration pulse control. coil vibration control.

5.5. Conclusion Conclusionss (1)(1) InIn an an artificial artificial climateclimate chamber,chamber, the the maximum maximum adhesion adhesion between between ice ice layer layer and and aluminum aluminum plate plate was was0.15 0.15 Mpa Mpa obtained obtained by the by tensile the tensile test. Sincetest. Since the tangential the tangential forcegenerated force generated by the electro-impulseby the electro- impulsede-icing de system-icing wassystem very was small, very as small, long as thelong equivalent as the equivalent stress between stress between the ice layerthe ice and layer the andaluminum the aluminum plate was plate greater was greater than 0.15 than Mpa, 0.15 the Mpa, ice layerthe ice fell layer off, fell which off, laidwhich a foundation laid a foundati for theon forsimulation the simulation calculation calculation of the subsequentof the subsequent electro-impulse electro-impulse de-icing de system.-icing system. (2)(2) WeWe r replacedeplaced the skinskin withwith an an aluminum aluminum plate plate and and built buil at platform a platform of theof the electro-impulse electro-impulse de-icing de- icingsystem system in an in artificial an artificial climate climate chamber. chamber. The The range range of de-icing of de-icing of theof the skin skin surface surface obtained obtained by bythe the experiments experiment wass was recorded recorded under under di differentfferent pulse pulse times. times. AA three-dimensionalthree-dimensional aluminum plateplate-ice-ice layer layer model waswas establishedestablished by by using using Solidworks. Solidworks. The The results results obtained obtained by by the the three-step three- stepcalculation calculation of electrodynamics, of electrodynamics, structural structural dynamics, dynamic and de-icings, and predictionde-icing prediction were compared were comparedwith the experiment with the experiment results of results the electro-impulse of the electro- de-icingimpulse system.de-icing Itsystem. was indicative It was indicat thative the thatcalculation the calculation process process of de-icing of de prediction-icing prediction obtained obtained by this paperby this was paper correct. was correct. (3)(3) TakingTaking the the leading leading edge edge of of the the NACA0012 NACA0012 wing wing with with a a chord chord length length of of 1 1 m m as as the the research research object, object, itsits length length along thethe chordchord was was 300 300 mm, mm the, the length length along along the the exhibition exhibition was was 600 mm,600 mm and, theand span the spanof one of bayoneof bay the of leading the leading edge wasedge 300 was mm. 300 The mm. leading The leading edge had edge a thicknesshad a thickness of 2.0 mm of 2.0 and mm the andice thicknessthe ice thickness was 4.0 mm.was 4.0 The mm. de-icing The ratiode-icing of the ratio four of pulsethe four coil pulse system coil was system 69.83%. was Under 69.83%. the action of the two pulse coil system, the de-icing ratio of Mode 1, 2, and 3 was lower, and the de-icing ratio of Mode 4 reached 47.22%. From the perspective of low energy consumption and without affecting the safe flight of the aircraft, the aforementioned structure was best to select the electro-impulse de-icing system with two pulse coils. (4) With regard to the electro-impulse de-icing system with two-pulse coils, the starting time of the pulse coil was different, and the de-icing effect was different. If pulse coil 6 started working at the same time as coil 5 or 600 µs later, the de-icing ratio was almost the same. This was because the interval between the continuous applied pressure at the same position of the wing was the Aerospace 2019, 6, 67 14 of 15

same. However, if pulse coil 6 started working 1200 µs later than coil 5, the de-icing ratio was the largest, which served as a guiding function for the subsequent pulse coil vibration control.

Author Contributions: Conceptualization, X.J. and Y.W.; methodology, Y.W.; software, Y.W.; writing—original draft preparation, Y.W.; writing—review and editing, X.J. and Y.W. Funding: (1) This research was funded by the National Natural Science Foundation of China, grant number 51637002. (2) This research was funded by State Grid Science and Technology Project: Research on numerical prediction technology of grid icing in micro-topography and micro-meteorological areas, grant number 521999180006. (3) This research was funded by the Fundamental Research Funds for the Central Universities, grant number 2019CDXYDQ0010. Acknowledgments: The presented work is part of the electro-impulse de-icing system for aircraft, which is funded by State Grid Corporation of China. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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