Collision Mechanism and Deposition Characteristics of Particles on the Catenary Insulator Surface

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Article Collision Mechanism and Deposition Characteristics of Particles on the Catenary Insulator Surface

Shanpeng Zhao 1,2,*, Chenrui Zhang 1, Youpeng Zhang 1,3 and Dingchang Zhang 1

1 School of Automation & Electrical Engineering, Lanzhou Jiaotong University, Anning District, Lanzhou 730070, China; [email protected] (C.Z.); [email protected] or [email protected] (Y.Z.); [email protected] (D.Z.) 2 Key Laboratory of Opto-Technology and Intelligent Control Ministry of Education, Lanzhou Jiaotong University, Anning District, Lanzhou 730070, China 3 Rail Transit Electrical Automation Engineering Laboratory of Gansu Province, Lanzhou Jiaotong University, Anning District, Lanzhou 730070, China * Correspondence: [email protected] or [email protected]; Tel.: +86-151-01316773 or +86-0931-4938656

Received: 3 June 2020; Accepted: 17 July 2020; Published: 19 July 2020

Abstract: To solve the problem of contamination flashover of a catenary insulator in an electrified railway, the collision mechanism and deposition characteristics of contamination particles on the insulator surface should be studied to ensure the safe operation of traction power supply systems. This research used horizontal and oblique cantilever insulators as objects, and established the collision model between particles and insulator surface under different arrangements. The deposition conditions of particles on the insulator surface were obtained, and the simulation model of insulator contamination accumulation was established by using the Euler two-phase flow. The difference of contamination deposition characteristics between horizontal and oblique cantilever insulators was analyzed with the volume fraction of contamination particles as the characterization parameter. By comparing the cantilever insulator with the positive feeder insulator, this study analyzed the influence of shed structure on the contamination deposition characteristics. Results show that the installation method of an insulator has an impact on the contamination deposition on the insulator surface. When particle size and wind velocity are fixed, the degree of contamination accumulation on the surface of the oblique cantilever insulator is constantly higher than that of the horizontal cantilever insulator. The insulator shed structure also has a certain effect on the contamination deposition on the insulator surface. For the cantilever insulator, the degree of contamination accumulation of the windward side is higher than that of the leeward side. However, for the positive feeder insulator, the degree of contamination accumulation of the windward side is consistently less than that of the leeward side. Measures to deal with contamination flashover of catenary insulator are proposed.

Keywords: electriﬁed railway; catenary insulator; collision model; Euler two-phase ﬂow; contamination deposition characteristics

1. Introduction An electriﬁed railway catenary is a special high-voltage transmission line installed above rails and transmits electric energy to electric locomotives or motor train units by making contact with pantographs [1]. Catenary insulators are insulation equipment of traction power supply systems that mainly serve as mechanical support and electrical insulation [2]. Insulators are exposed to the atmosphere at all times to enable the easy deposition of contamination particles in the air on the insulator surface with the airﬂow, and the contamination contains a large amount of soluble substances. In humid

Coatings 2020, 10, 697; doi:10.3390/coatings10070697 www.mdpi.com/journal/coatings Coatings 2020, 10, 697 2 of 19 environments such as those affected by rain, snow, and fog, they easily form a high conductivity dielectric layer [3,4]; hence, the increase in the insulator partial leakage current leads to a decline in insulation performance, thereby easily generating arc and even flashover [5–8]. Contamination deposition on the insulator surface is the fundamental factor inducing contamination flashover. Therefore, the collision mechanism and deposition characteristics of particles on the insulator surface should be studied for the insulation design of catenary and the formulation of anti-contamination flashover measures [9,10]. Many studies have been conducted on collision theory and the contamination deposition characteristics of particles on an insulator surface. Li et al. established the collision model between particles and insulator surface, analyzed the collision and adsorption movement of particles on the insulator surface, formulated the adsorption criterion between particles and insulator surface, and considered the corresponding effects of particle size, wind velocity, and humidity. He believed that the smaller the particle size, the higher the humidity, and the higher the wind velocity, the easier the particles are to be adsorbed [11]. Horenstein et al. studied the collision of charged insulator particles through experiments and theories. We obtained the relationship between the influence of wind force on the particle trajectory and the particle size, and proposed a model for quantitative prediction of the DC insulator contamination on transmission lines [12]. Hernandez et al. conducted the contamination test on the surface of the suspension insulator. The study found that the contamination accumulation on the insulator surface is serious when the shed structure is complex and many ribs exist on the lower surface. The structure of the insulator shed with less contamination accumulation on the insulator surface is simple, and the shed surface is smooth [13]. Jiang et al. regarded the insulator surface as an infinitely large flat plate, and established a collision model between the particles and insulator surface. The deposition conditions of the particles are obtained from the perspective of torque balance that consider the rolling of particles on the insulator surface. When the adsorption torque of the particles is higher than the sum of the frictional stress, drag stress, and elastic moment of the particles, the particles will be deposited on the insulator surface. Therefore, particle size is the critical value for deposition when it is 25 µm. If the particle size is below 25 µm, then the particles are deposited on the insulator surface [14]. Lv et al. considered the surface energy of the insulator surface, regarded the insulator as an infinitely large flat plate, and established a collision model between the particle and insulator surface from a three-dimensional perspective. The deposition conditions of particles are obtained according to their force balance. If the kinetic energy of all forces acting on the particles is higher than the energy of the particles before collision on the insulator surface, then the particles are eventually deposited on the insulator surface [15,16]. In the preceding research, the main object was the insulators in the power system environment and the arrangement of the insulators was vertical installation, so the application of the results is limited. To date, there is still a lack of research on the contamination deposition of an insulator in a catenary environment and the collision theory of particles on the insulator surface for the arrangement of the insulator. In summary, the research object of this study was the catenary insulators of an electrified railway, which mainly include cantilever insulators installed horizontally and obliquely and positive feeder insulators. First, the collision model between particles and insulators with different installation methods was established, and the deposition conditions of particles and insulator surface were obtained. Second, fluent fluid software was used to establish a simulation model under a wind environment, the contamination deposition distribution of insulator surface was analyzed, and the differences of the contamination deposition characteristics on the insulator surface of the horizontal and oblique cantilever insulators were studied. Finally, the cantilever and positive feeder insulators with different shed structures were compared to study the effects of shed structure on the contamination deposition characteristics. The research can further improve the existing contamination deposition mechanism of insulators, and the results have certain guiding significance for the design, operation, and maintenance of the external insulation of the catenary [17]. Additionally, the maintenance cycle can be formulated according to the distribution of the contamination on the insulator surface to avoid flashover. CoatingsCoatings2020 2020, 10, 10, 697, x FOR PEER REVIEW 33 ofof 19 19 Coatings 2020, 10, x FOR PEER REVIEW 3 of 19 2. Theory of Particle Collision and Deposition on Insulator Surface 2. Theory2. Theory of Particle of Particle Collision Collision and Deposition and Deposition on Insulator on Insulator Surface Surface Various installation methods are used for catenary insulators including cantilever insulators VariousinstalledVarious installation horizontally installation methods and methods obliquely, are used are and used for positive catenary for catenary feeder insulators insulatorsinsulator including strings including cantileverinstalled cantilever vertically. insulators insulators Figure installedinstalled1 shows horizontally horizontally the site and chart andobliquely, of obliquely, electrified and and positive railway positive feeder catenary feeder insulator insulatorinsulators. strings strings The installed particles installed vertically. vertically.are infinitely Figure Figure small1 1 showsshowsrelative the the siteto site thechart chart insulator, of of electrified electrified and the railway shed catenarycatenary occupies insulators. insulators. most of The theThe particlesinsulator particles are area,are infinitely infinitely so the small insulatorsmall relative is relativetoconsidered the to insulator,the insulator, as an and infinite theand shedflatthe plateshed occupies when occupies most establishing most of the of insulator the the collision insulator area, model. soarea, the As so insulator the the insulator insulator is considered sheds is are consideredasabout an infinite asperpendicular an infinite flat plate flat to whenplate the centralwhen establishing establishing axis of the the collision theinsulator, collision model. in model. the As preceding As the the insulator insulator research, sheds sheds the are insulatorare about aboutperpendiculararranged perpendicular vertically to to the the centralwas central often axis axisconsidered of theof the insulator, insulator, as a inhorizontal the in precedingthe precedinginfinite research, flat research, plate the insulator[18]. the insulatorHowever, arranged the arrangedverticallyinstallation vertically was methods often was considered often of catenary considered as acantilever horizontal as a insulators infinitehorizontal flat are plateinfinite unique, [18 ].flat hence, However, plate the [18]. research the installation However, should methods theconsider installationofthe catenary installation methods cantilever ofmethod catenary insulators of thecantilever insulator. are unique, insulators hence, are the unique, research hence, should the consider research the should installation consider method the installationof the insulator. method of the insulator.

(a) (b) (a) (b) Figure 1. Insulators of the electrified railway catenary: (a) insulator in the working state; (b) catenary FigureFigurestructure 1. Insulators 1. Insulators chart. of the of electrified the electrified railway railway catenary: catenary: (a) insulator (a) insulator in the in working the working state; state; (b) catenary (b) catenary structurestructure chart. chart. This study assumes that the particle shape is spherical. For horizontally installed insulators, the This study assumes that the particle shape is spherical. For horizontally installed insulators, Thissurface study of assumesthe insulator that the sheds particle was shape regarded is spherical. as an infinitelyFor horizontally large plate installed placed insulators, vertically the when the surface of the insulator sheds was regarded as an infinitely large plate placed vertically when surfaceestablishing of the insulator a collision sheds deposition was regarded model. asFor an the infinitely same reason, large the plate inclination placed verticallyangle for anwhen insulator establishing a collision deposition model. For the same reason, the inclination angle for an insulator establishinginstalled a collisionobliquely deposition was assumed model. to beFor φthe, and same the reason, insulator the was inclination regarded angle as an for infinitely an insulator large flat installedinstalled obliquely obliquely was was assumed assumed to be to beφ,ϕ and, and the the insulator insulator was was regarded regarded as as an infinitelyinfinitely largelarge flat flat plate plate with an inclination angle of 90φ . Figure 2 illustrates the collision model between the with an inclination angle of 90 ϕ. Figure2 illustrates the collision model between the particles and plate with an inclination angle of◦ −90φ . Figure 2 illustrates the collision model between the insulatorparticles surface. and insulator surface. particles and insulator surface.

Insulator Insulator Insulatorsurface Insulator surface surface surface

Particle Particle vx1 vx1 Particle Particle vxθ1 vxθ1 θ θ

1 v1 vy1 v vy1 1 v1 vy1 v vy1

Horizontal installation Oblique installation Horizontal installation Oblique installation FigureFigure 2. 2.Collision Collision model model between between the the particles particles and and insulator insulator surface. surface. Figure 2. Collision model between the particles and insulator surface. The assumption was that the particles collide with the insulator surface at the horizontal and The assumption was that the particles collide with the insulator surface at the horizontal and vertical velocities of vx1 and vy1, respectively, and assumed that the particles were round spheres, Thevertical assumption velocities was of vthatx1 and the v yparticles1, respectively, collide and with assumed the insulator that the surface particles at werethe horizontal round spheres, and and and adopted a hard ball model (i.e., particles do not deform when they collide). This study took a verticaladopted velocities a hard of vx 1ball and modelvy1, respectively, (i.e., particles and assumeddo not deform that the whenparticles they were collide). round This spheres, study and took a horizontally installed insulator as an example to analyze the collision deposition process between the adoptedhorizontally a hard ball installed model insulator (i.e., particles as an example do not todeform analyze when the collision they collide). deposition This process study tookbetween a the particles and insulator surface. horizontallyparticles installed and insulator insulator surface. as an example to analyze the collision deposition process between the particles and insulator surface.

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TheThe collision collision deposition deposition process process of of the the particles particles and and insulator insulator surface surface can can be be divided divided into into four four stages:stages: injection, injection, collision, collision, recovery recovery deformation, deformation, and and ejection. When When the the cantilever cantilever insulator insulator is is installedinstalled horizontally, horizontally, the the insulator insulator can can be be assumed as as an an infinitely inﬁnitely large large flat ﬂat plate with the the particle sizesize relative relative to to the insulator surface. Figure Figure 3 showsshows thethe schematicschematic ofof thethe collisioncollision depositiondeposition ofof thethe particles and insulator surface. InjectionInjection stage: stage: The The particles particles are are injected injected on on the the insulator insulator surface at a horizontal velocity vx11,, vertical velocity vy11, ,and and collision collision angle angle of of θθ.. CollisionCollision stage: stage: The The particles particles collide collide with with the theinsulator insulator surface surface in an in inelastic an inelastic manner. manner. The horizontalThe horizontal velocity velocity of the particles of the particles gradually gradually decreases. decreases. When the elastic When deformation the elastic deformationon the insulator on surfacethe insulator is the surfacemaximum, is the the maximum, normal velocity the normal of the velocity particles of is the 0. particles is 0. RecoveryRecovery deformation deformation stage: stage: When When the the horizontal horizontal velocity velocity is is 0, 0, the the particle particle receives receives the the largest largest elasticelastic force onon thethe insulator insulator surface. surface. At At this this time, time, the the particle particle moves moves in in a horizontal a horizontal direction. direction. When When the theinsulator insulator wall wall is restored is restored to deformation, to deformation, the elastic the elastic force becomesforce becomes 0, and 0, the and horizontal the horizontal and vertical and verticalvelocities velocities of the particles of the particles are vx2 and are vxy22 and, respectively. vy2, respectively. EjectionEjection stage: The particlesparticles areare ejected ejected outward outward at at a velocitya velocityv2 vand2 and are are bound bound by by adhesion. adhesion. If the If theparticles particles can can overcome overcome the the adhesion adhesion of the of the insulator insulator surface, surface, then then they they will will bounce bounce back back in thein the air. air.However, However, if the if the particles particles cannot cannot overcome overcome the the adhesion adhesion of of the the insulator insulator surface, surface, thenthen they will be be depositeddeposited on on the the insulator surface.

Insulator Insulator Insulator Insulator surface surface surface surface

Particle x1 Particle vx1 Particle Particle v vx2 vx3 θ θ

vy1 v1 vy1 v1 v2 vy2 v3 vy3

Injection Collision Recovery deformation Ejection Figure 3. Schematic of the particle collision deposition. Figure 3. Schematic of the particle collision deposition. After the particles are injected on the insulator surface at the horizontal and vertical velocities of After the particles are injected on the insulator surface at the horizontal and vertical velocities of vx1 and vy1, respectively, then the particles are subjected to gravity, friction, and gas drag in the vertical vx1 and vy1, respectively, then the particles are subjected to gravity, friction, and gas drag in the vertical direction, and the adhesion and elastic force of the insulator surface in the horizontal direction. direction, and the adhesion and elastic force of the insulator surface in the horizontal direction. Some of the particles will adhere to the surface of the insulator when it comes into contact Some of the particles will adhere to the surface of the insulator when it comes into contact with with the insulator surface. The adhesion force mainly includes the Van der Waals, electrostatic, the insulator surface. The adhesion force mainly includes the Van der Waals, electrostatic, and and capillary forces. The Van der Waals force action begins to appear only when the distance between capillary forces. The Van der Waals force action begins to appear only when the distance between the the particle and insulator surface is below 100 nm and increases as the distance decreases. This action particle and insulator surface is below 100 nm and increases as the distance decreases. This action is is the main component of adhesion. The electrostatic force is due to the potential diﬀerence between the main component of adhesion. The electrostatic force is due to the potential difference between the particles and plate, and other factors dominate after adhesion occurs. For the capillary force, the particles and plate, and other factors dominate after adhesion occurs. For the capillary force, the the particles and insulator surface will form a liquid bridge after the relative humidity is above 50%, particles and insulator surface will form a liquid bridge after the relative humidity is above 50%, and and the main inﬂuencing factor is related to air humidity. Figure4 shows the schematic of the adhesion the main influencing factor is related to air humidity. Figure 4 shows the schematic of the adhesion of particles to the surface of objects. of particles to the surface of objects.

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FigureFigure 4.4. SchematicSchematic ofof thethe surfacesurface adhesion.adhesion.

TheThe catenarycatenary insulator insulator studied studied in this in paperthis paper is designed is designed to be in ato dry be and in wind-sanda dry and environment, wind‐sand soenvironment, the inﬂuence so of the capillary influence force of capillary on the insulator force on surface the insulator is ignored, surface and is Van ignored, der Waals and Van forces der are Waals the mainforces factor are the of main the adhesion factor of force. the adhesion force. TheThe calculationcalculation methodmethod ofof the Van derder WaalsWaals forceforce onon particlesparticles isis relatedrelated toto thethe didifferentﬀerent contactcontact formsforms betweenbetween thethe particles.particles. The expression of the Van derder WaalsWaals forceforce betweenbetween thethe ballball andand plateplate isis shownshown inin EquationEquation (1)(1) [[19]:19]: AR Fw = (1) 6AHR2 Fw = 2 (1) where Fw is the Van der Waals force between the ball6H and plate, N; A is the Hamaker constant of the particle; H is the distance between the particle and plate, m; and R is the particle radius, µm. where Fw is the Van der Waals force between the ball and plate, N; A is the Hamaker constant of the particle;During H is the the collision distance between between the the particles particle and and insulator plate, m; surface, and R is the the particles particle squeeze radius, the μm. insulator surfaceDuring to produce the collision a small deformation,between the therebyparticles producing and insulator an elastic surface, force the perpendicular particles squeeze to the wall. the F Equationinsulator (2)surface shows to the produce elastic a force small adeformation,based on Hertz thereby elastic producing theory [20 an]: elastic force perpendicular

a to the wall. Equation (2) shows the elastic force F4 based 3on Hertz elastic theory [20]: Fa = √RS 2 (2) 3kπ 3 4 2 FRSa = (2) where Fa is the elastic force, N; S is the amount of3 deformationkπ that occurs during collision; and k is the elastic deformation coefficient. where Fa is the elastic force, N; S is the amount of deformation that occurs during collision; and k is The deposition of particles on the insulator surface mainly depends on whether the particles can the elastic deformation coefficient. complete the ejection. If they can be ejected, then the particles will rebound into the air against the The deposition of particles on the insulator surface mainly depends on whether the particles can adhesion of the insulator surface. If the particles cannot overcome the adhesion of the insulator surface, complete the ejection. If they can be ejected, then the particles will rebound into the air against the then they will be deposited on the insulator surface. During the entire collision process, the energy loss adhesion of the insulator surface. If the particles cannot overcome the adhesion of the insulator suffered by the particles mainly includes the losses caused by the friction with the insulator surface in surface, then they will be deposited on the insulator surface. During the entire collision process, the the vertical direction and the collision loss caused by the inelastic collision in the horizontal direction. energy loss suffered by the particles mainly includes the losses caused by the friction with the These energy losses will reduce the ejection velocity of particles. insulator surface in the vertical direction and the collision loss caused by the inelastic collision in the In the vertical direction, the sliding friction between the particles and insulator surface produces horizontal direction. These energy losses will reduce the ejection velocity of particles. relative displacement. Eventually, the combined force of the particle’s gravity, friction, and aerodynamic In the vertical direction, the sliding friction between the particles and insulator surface produces resistance is 0. relative displacement. Eventually, the combined force of the particle’s gravity, friction, and During the ejection process, the particles are affected by Van der Waals forces in the horizontal aerodynamic resistance is 0. direction and slow down. If the particles overcome the Van der Waals forces, then the ejection is During the ejection process, the particles are affected by Van der Waals forces in the horizontal completed; otherwise, the particles will be deposited on the insulator surface. The condition of the direction and slow down. If the particles overcome the Van der Waals forces, then the ejection is particle ejection is v > 0. completed; otherwise,x3 the particles will be deposited on the insulator surface. The condition of the When the particle adopts the hard ball model, which states that the collision process is particle ejection is vx3 > 0. instantaneous, and the velocity change before and after the collision depends on the recovery When the particle adopts the hard ball model, which states that the collision process is coefficient e [21]. Equation (3) shows the expression of the velocity relationship before and after instantaneous, and the velocity change before and after the collision depends on the recovery particle collision: coefficient e [21]. Equation (3) shows the expression of the velocity relationship before and after v = ev particle collision: x2 x1 (3)

vevxx21 (3)

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1 1 2 8 σ 2 mV /2 − e = 3.8( s ) ( ) (4) 3 γ σsR where vx1 and vx1 are the velocities of the particles before and after collision, respectively, m/s; e is the recovery coeﬃcient; σs is the ultimate yield; γ is the Young’s modulus; V is the velocity at which the particles collide with the insulator, m/s; m is the mass of the particles, kg. When the particles are ejected in the horizontal direction, the Van der Waals forces must be overcome to complete the ejection. The work to overcome the Van der Waals force is Wa, and the calculation expression of Wa is shown in Equation (5):

Wa = Fw(hmax h ) (5) − min where Wa is the work to overcome the Van der Waals force, J; hmax is the maximum distance where Van der Waals forces occur, m; and hmin is the minimum distance where the Van der Waals forces occur, m. We obtain the following equation according to the preceding analysis and kinetic energy theorem:

1 2 1 2 Wa = mv mv (6) 2 x2 − 2 x3

From Equations (3) and (6), vx3 can be obtained as follows: r 2 2Wa vx = (ev ) (7) 3 x1 − m

If the particle horizontal ejection velocity vx3 > 0, then the particles are ejected. If vx3 < 0, then the particles are deposited on the insulator surface. According to the analysis of the horizontal installation method of the insulator, the horizontal and vertical velocities can be decomposed in the collision model of the oblique cantilever insulator to obtain the velocity vx3 of the particle ejection of the oblique installation method as in Equation (8). r 2 2Wa vx = [e(v cos ϕ + v sin ϕ)] (8) 3 x1 y1 − m

Therefore, the particle ejection velocity vx3 on the surface of the insulator under different installation methods is shown in Equation (9):  q  2 2Wa  (evx1) horizontal installation v =  q − m (9) x3   [e(v cos ϕ + v sin ϕ)]2 2Wa oblique installation x1 y1 − m According to the ejection velocity of the particles on the surface of the insulator, when the insulators are of the same material and the particle size is the same, the work done by the adhesion force and the particle mass are the same; the lower the ejection velocity, the easier the particles are deposited on the insulator surface. According to the analysis of the particle movement in the air, the velocity vx1 of the particles is an order of magnitude above vy1. Hence, vx1 > vx1 cos ϕ + vy1 sin ϕ. Compared with the horizontally and obliquely installed insulators, the particles are easier to deposit on the surface of the oblique cantilever insulator. That is, when the insulator structure is completely the same, the degree of contamination accumulation of the insulator surface installed obliquely at the same particle size and wind velocity is more serious than that of the insulator installed horizontally. Different factors such as external electric field, particle shape, humidity, the insulator shed material, and so on, differently affect the collision and deposition characteristics of particles on the insulator surface. More influencing factors will be discussed in future research. Coatings 2020, 10, 697 7 of 19

3. Mathematical Model of the Insulator Contamination

3.1. Euler Dual-Fluid Model The movement of contamination particles carried by air is a typical gas–solid two-phase flow movement, which can be numerically simulated using the Euler two-fluid model. Euler’s double fluid aims to treat the air and particles as continuous fluids. The two fluids move according to their own laws and introduce volume fractions to describe the existence of each phase. The basic equation of Euler’s double fluid is as follows: αg + αs = 1 (10) where αg and αs are the volume fraction of the air and particle phases, respectively. Each phase satisfies the mass conservation equation (i.e., fluid continuity equation) and momentum conservation equation. The mass conservation equation of the air and particle phases (i.e., continuity equation) is as follows: ∂αiρ i + (α ρ →v ) = 0 (11) ∂t ∇ · i i i 3 where ρi is the density of the i-th phase, kg/m ; →v i is the velocity of the i-th phase, m/s; and i = g represents the air phase and i = s represents the particle phase. The momentum conservation equation of air phase and particle phase is as follows:

∂(αgρg→v g) + (αgρ →v g→v g) = αg p + τg + αgρ →g + Kgs(→v g →v s) (12) ∂t ∇ · g − ∇ ∇ · g −

∂(αsρs→v s) + (αsρ →v s→v s) = αs p + τs + αsρs→g + Ksg(→v s →v g) (13) ∂t ∇ · s − ∇ ∇ · − 2 where p is the pressure, Pa; →g is the acceleration of gravity, m/s ; τg and τs are the stress tensors of the air and particle phases, respectively; and Kgs = Ksg is the momentum exchange coeﬃcient of the particle and air phases. The expression is as follows:

3C α α ρ D s g g 2.65 Ksg = →v s →v g α−g (14) 4ds − where CD is the drag coefficient between phases and ds is the particle diameter, µm. The air flow around the insulator is incompressible viscous turbulent flow. To adapt to the complex shape of the insulator, this study used the RNG k-ε model to solve it as it can better handle the flow with high strain rate and large degree of streamline bending [22]. The k and ε equations in the RNG k-ε model are as follows:

∂(ρk) ∂(ρkui) ∂ ∂k + = (αkµe f f ) + Gk + ρε (15) ∂t ∂xi ∂xj ∂xj

2 ∂(ρε) ∂(ρεui) ∂ ∂ε C1εε C2ερε + = (αεµe f f ) + Gk (16) ∂t ∂xi ∂xj ∂xj k − k where Gk is the turbulent ﬂow energy generated by the average velocity, J; αk and αε are the Prandtl number corresponding to the turbulent kinetic energy k and dissipation rate ε, respectively; C1ε and C2ε are the empirical constants; and µe f f is the turbulent viscosity coeﬃcient.

3.2. Insulator Model and Meshing This study selected the FQBG-25/12 composite cantilever composite insulator of the rod type as the research object. The schematic of the insulator structure is shown in Figure5. The insulator structure included nine large sheds and eight small sheds. The height of the structure was 800 mm, Coatings 2020, 10, x FOR PEER REVIEW 8 of 19

3.2. Insulator Model and Meshing This study selected the FQBG‐25/12 composite cantilever composite insulator of the rod type as the research object. The schematic of the insulator structure is shown in Figure 5. The insulator structure included nine large sheds and eight small sheds. The height of the structure was 800 mm, creepage distanceCoatings was 2020, 10 1800, x FOR PEERmm, REVIEW diameter of the large shed was 180 mm, and the8 of diameter19 of the small shed was 128 mm. 3.2. Insulator Model and Meshing

CoatingsThis2020 study, 10, 697 selected the FQBG‐25/12 composite cantilever composite insulator of the rod type8 of as 19 the research object. The schematic of the insulator structure is shown in Figure 5. The insulator structure included nine large sheds and eight small sheds. The height of the structure was 800 mm, creepagecreepage distance waswas 18001800 mm, mm, diameter diameter of of the the large large shed shed was was 180 180 mm, mm, and and the diameterthe diameter of the of small the smallshed wasshed 128 was mm. 128 mm.

Figure 5. Schematic of the FQBG‐25/12 cantilever composite insulator.

The existing insulator contaminationFigureFigure 5. 5. SchematicSchematic of of depositionthe the FQBG FQBG-25‐25/12/12 cantilever cantilevercharacteristics composite composite insulator. insulator. mainly study the distribution of contamination particlesTheThe existing existing on insulatorthe insulator surface contamination contamination of the depositionshed. deposition This characteristics characteristics research mainly mainly disregarded study study the the distribution distribution the hardware of of fittings at both ends of thecontaminationcontamination insulator particles particles when on on the the the modelsurface surface of of was the the shed. shed. built. This This SolidWorksresearch research disregarded disregarded software the the hardware hardware was fittings ﬁttingsused at atto build the 3D bothboth ends ends of of the the insulator insulator when when the the model model was was built. built. SolidWorks SolidWorks software software was was used used to to build build the the 3D 3D model of the insulator.modelmodel of of the the Figure insulator. insulator. 6 Figure Figure shows 6 shows the thetheestablished established three-dimensionalthree three‐dimensional‐dimensional modelmodel ofof themodelthe insulator.insulator. of the insulator.

Figure 6. Schematic of the three‐dimensional insulator.

The established three‐dimensional model of the insulator was imported into the mesh generation softwareFigure and 6. theFigure Schematic calculation 6. Schematic domainof the of the threesize three-dimensional and‐dimensional mesh were insulator. set. insulator. The size of the calculation domain has immense influence on the accuracy of the calculation result. Given that computational The established three-dimensional model of the insulator was imported into the mesh generation fluid mechanics generally requires that the blocking probability is not over 3%, the blocking software and the calculation domain size and mesh were set. The size of the calculation domain has The establishedprobability threeζ was‐ defineddimensional as follows [23]:model of the insulator was imported into the mesh immense influence on the accuracy of the calculation result. Given that computational fluid mechanics generation softwaregenerally and requires the that calculation the blocking probabilitydomain is size notL over and 3%, mesh the blocking were probability set. Theζ wassize defined of the calculation ζ = 1 (17) domain has immenseas follows [influence23]: on the accuracy of Lthe calculation result. Given that computational L ζ = 1 (17) fluid mechanicswhere generally L1 is the projected requires area of thatthe insulator the blockingat the Linlet of probability the calculation domain,is not m 2over; and L is3%, the the blocking 2 cross‐sectional area of the inlet of the calculation domain, m . 2 probability ζ wherewas definedL1 is the projected as follows area of the[23]: insulator at the inlet of the calculation domain, m ; and L is the The insulator structure indicates that L1 = 180 mm × 530 mm = 0.0954 m2, the inlet area of the cross-sectional area of the inlet of the calculation domain, m2. 2 calculation domain set in this research was 2000 mm × 2000 mm = 4 m , and the2 blocking probability The insulator structure indicates that L1 = 180 mm 530 mm = 0.0954 m , the inlet area of the was 0.024. To completely develop the fluid and preventL1 × backflow, the length of the calculation calculation domain set in this research was 2000ζ = mm 2000 mm = 4 m2, and the blocking probability (17) domain was appropriately increased. Therefore, the ×size of the calculation domain was eventually was 0.024. To completely develop the fluid and preventL backflow, the length of the calculation domain determined to be 2000 mm × 2000 mm × 3000 mm. Airflow and contamination particles flow in from was appropriately increased. Therefore, the size of the calculation domain was eventually determined the left side of the calculation domain and flow out from the right side. For the convenience of the 2 where L1 is theto projected be 2000 mm area2000 of mm the3000 insulator mm. Airflow at andthe contamination inlet of the particles calculation flow in from domain, the left side m ; and L is the subsequent mesh× division, ×the calculation domain was divided into two areas (see Figure 7). cross‐sectional ofarea the calculation of the inlet domain of andthe flowcalculation out from the domain, right side. m For2. the convenience of the subsequent mesh division, the calculation domain was divided into two areas (see Figure7). The insulator structure indicates that L1 = 180 mm × 530 mm = 0.0954 m2, the inlet area of the calculation domain set in this research was 2000 mm × 2000 mm = 4 m2, and the blocking probability was 0.024. To completely develop the fluid and prevent backflow, the length of the calculation domain was appropriately increased. Therefore, the size of the calculation domain was eventually determined to be 2000 mm × 2000 mm × 3000 mm. Airflow and contamination particles flow in from the left side of the calculation domain and flow out from the right side. For the convenience of the subsequent mesh division, the calculation domain was divided into two areas (see Figure 7).

Coatings 2020, 10, 697 9 of 19 Coatings 2020, 10, x FOR PEER REVIEW 9 of 18

Coatings 2020, 10, x FOR PEER REVIEW 9 of 19 interface out_flow interface out_flow

velocityvelocity_inlet_inlet wallwall

FigureFigureFigure 7. Schematic7. 7. SchematicSchematic of of of the the calculationcalculation calculation domain domain domain division. division. division.

DueDue to to the the different different mesh mesh division division accuracies accuracies of of the the different different parts parts and and to to balance balance the the calculation calculation Dueaccuracyaccuracy to the differentand and calculation calculation mesh resources, resources,division the theaccuracies use use of of a a tetrahedraltetrahedral of the different unstructured unstructured parts mesh meshand into in the balance the area area near nearthe the calculation the accuracysurfacesurface and calculationof of the the insulator insulator resources, can can substantially substantially the use fit fitof the thea tetrahedralcomplex complex shape shape unstructured of of the the insulator. insulator. mesh Starting Starting in the from from area the the near the surface insulatorofinsulator the insulator surface, surface, it it can was divideddividedsubstantially by by the the near nearfit andthe and far, complex far, and and the the qualityshape quality of of the of the tetrahedralthe insulator. tetrahedral mesh Startingmesh was above was from the 0.33. The outer area used a hexahedral structured mesh, which effectively reduced the number of mesh insulatorabove surface, 0.33. The it was outer divid area useded bya hexahedral the near structured and far, mesh,and thewhich quality effectively of thereduced tetrahedral the number mesh was ofand mesh saved and on saved calculation on calculation resources. resources. The quality The quality of the hexahedral of the hexahedral mesh was mesh 1. Thewas number 1. The number of mesh above 0.33. The outer area used a hexahedral structured mesh, which effectively reduced the number ofwas mesh approximately was approximately 1.6 million. 1.6 million. Figure8 Figure shows 8 the shows meshing the meshing results. results. of mesh and saved on calculation resources. The quality of the hexahedral mesh was 1. The number of mesh was approximately 1.6 million. Figure 8 shows the meshing results.

(a) (b)

FigureFigure 8. 8.MeshingMeshing results. results. (a ()a Overall) Overall insulator insulator meshing meshing result; result; ( (bb)) x = 0 planar insulatorinsulator meshing meshing result. result. 3.3. Boundary Condition Setting 3.3. Boundary Condition Setting(a) (b) The divided mesh was imported into the fluent fluid mechanics software, and boundary conditions Figurewere 8.The Meshing set divided for each results mesh surface.. (awas) O This verallimported study insulator involved into themeshing three fluent types resultfluid of ; boundarymechanics(b) x = 0 planar conditions.software, insulator and The boundary leftmeshing side of conditionsthe calculation were set domain for each was surface. defined This as study the velocity involved inlet three boundary types of condition, boundary theconditions. right side The of left the result. sidecalculation of the calculation domain was domain defined was as defined the fully as developed the velocity out inlet flow boundary boundary, condition, and the the insulator right side surface of theand calculation the other fourdomain surfaces was ofdefined the calculation as the fully domain developed were definedout flow as boundary, the wall boundary and the insulator condition. 3.3. BoundarysurfaceThe insulator Condition and the surface other Setting wasfour setsurfaces to the boundaryof the calculation condition domain of the no-slipwere defined wall. When as the the wall particles boundary move Thecondition. from divided the airThe mesh to insulator the insulator was surface imported surface was set of into the to the insulator, the boundary fluent the particlecondition fluid mechanics velocity of the isno 0,‐ slip software, which wall. means When and that the boundary it particlesremains move on the from surface the ofair the to insulator.the insulator surface of the insulator, the particle velocity is 0, which conditionsmeans wereAccording that set it remains for to each the on related surface. the surface research This of on the study the insulator. measurement involved ofthree the particle types sizeof boundary of the insulator conditions. surface in The left side of thethe calculation naturalAccording contamination to domain the related test,was research the defined particle on the as size measurement the distribution velocity of oninlet the insulator particle boundary surface size of condition, the is logarithmic insulator the surface normal right side of the calculationindistribution, the natural domain and contamination the was particle defined test, size distribution the as particle the fully issize mainly developed distribution around out15on µinsulator m.flow The boundary, average surface value is logarithmic and of particle the insulator surface normalandsize Dthe10 distribution,(i.e., other particle four and size surfaces the when particle the of cumulativesize the distribution calculation probability is mainlydomain distribution around were 15 number μdefinedm. The reaches averageas the 10%) valuewall on theofboundary µ µ condition.particlecomposite The size insulator insulatorD10 (i.e., particlesurface surface size iswas 2.90 when setm, the to the cumulative the average boundary value probability of conditionD50 distributionis 8.25 ofm, the andnumber no the-slip averagereaches wall. 10%) value When the on the composite insulator surface is 2.90 μm, the average value of D50 is 8.25 μm, and the average particles move from the air to the insulator surface of the insulator, the particle velocity is 0, which value of D90 is 22.58 μm [24]. Therefore, in this paper, the particle size was set to 5, 10, 15, 20, and 25 means thatμm. itAccording remains to o then the statistics, surface the oforder the of insulator. magnitude of contamination particle density (unit: g/m3) Accordingwas generally to the about related 10−5, and research the particle on the phase measurem was sparseent phase. of the The particle particle phasesize of volume the insulator fraction surface in the natural contamination test, the particle size distribution on insulator surface is logarithmic normal distribution, and the particle size distribution is mainly around 15 μm. The average value of particle size D10 (i.e., particle size when the cumulative probability distribution number reaches 10%) on the composite insulator surface is 2.90 μm, the average value of D50 is 8.25 μm, and the average value of D90 is 22.58 μm [24]. Therefore, in this paper, the particle size was set to 5, 10, 15, 20, and 25 μm. According to the statistics, the order of magnitude of contamination particle density (unit: g/m3) was generally about 10−5, and the particle phase was sparse phase. The particle phase volume fraction

Coatings 2020, 10, x FOR PEER REVIEW 10 of 19 can be used to distinguish different environments. The volume fraction of contamination particles in the Gobi,Coatings sandy,2020 and, 10, 697 desert landforms are 0.02, 0.04 and 0.05, respectively [25]. As the research10 of 19 object of this paper was the catenary insulator in northwest China, the volume fraction of contamination particlesof underD90 is 22.58the Gobiµm [24 landform]. Therefore, was in thisset paper,as 0.02 the as particle the simulation size was set condition to 5, 10, 15, 20,in this and 25paper.µm. It was According to the statistics, the order of magnitude of contamination particle density (unit: g/m3) was assumed that the particles5 were mainly affected by drag force and gravity in the air. generally about 10− , and the particle phase was sparse phase. The particle phase volume fraction can be used to distinguish diﬀerent environments. The volume fraction of contamination particles in 3.4. Characterizationthe Gobi, sandy, Parameters and desert of landforms Contamination are 0.02, 0.04 and 0.05, respectively [25]. As the research object Thisof research this paper used was the the catenary volume insulator fraction in northwestto characterize China, the the volume degree fraction of particle of contamination accumulation on particles under the Gobi landform was set as 0.02 as the simulation condition in this paper. It was the insulator surface. The volume fraction refers to the percentage of the particle volume on the assumed that the particles were mainly aﬀected by drag force and gravity in the air. insulator surface to the present total volume of air and particles. The volume fraction can characterize the deposition3.4. Characterization and distribution Parameters of of Contaminationparticles on the insulator surface. The volume fraction of the particles hasThis a positive research correlation used the volume with fraction the amount to characterize of contamination the degree of particle[26]. The accumulation contamination on the volume fraction insulatorexpression surface. is as The follows: volume fraction refers to the percentage of the particle volume on the insulator surface to the present total volume of air and particles. The volume fraction can characterize the deposition and distribution of particles on the insulatorVparticle surface. The volume fraction of the particles  = (18) has a positive correlation with the amount of contaminationVV+ [26]. The contamination volume fraction expression is as follows: particle air Vparticle where Vparticle is the contamination volume,φ m=3 and Vair is the air volume, m3. (18) Vparticle + Vair For the subsequent analysis of the distribution of contamination particles on the insulator 3 3 surface, whereeach shedVparticle shouldis the contamination be divided into volume, four m parts:and V windwardair is the air volume, side, leeward m . side, crosswind side 1, For the subsequent analysis of the distribution of contamination particles on the insulator and crosswindsurface, eachside shed 2, each should of be which divided takes into fouran angle parts: windward of 90° [27]. side, Figure leeward 9 side, shows crosswind the division side 1, of the shed. and crosswind side 2, each of which takes an angle of 90◦ [27]. Figure9 shows the division of the shed.

Figure 9. Figure 9. DivisionDivision of thethe insulator insulator shed. shed. To accurately express the amount of the surface area contamination of the insulator, the To contaminationaccurately express volume fractions the amount at diﬀerent of locationsthe surface were calculated.area contamination The calculation of result the used insulator, the the contaminationarea-weighted volume average fractions of the at contamination different locations volume fractions were calculated. to represent the The degree calculation of contamination result used the area‐weightedaccumulation. average The expressionof the ofcontaminationx is as follows: volume fractions to represent the degree of Z n contamination accumulation. The expression1 of x is as follows:1 X φave = φdM = φiMi (19) M M n 11i=1   ave =d= M  iiM (19) MM2 i=1 where M is the area of the selected part, m ; φi is the contamination volume fraction on the discrete M n M mesh nodes; i is the micro-element area;2 and is the discrete number on . where M is the area of the selected part, m ; i is the contamination volume fraction on the discrete mesh nodes; Mi is the micro‐element area; and n is the discrete number on M.

4. Deposition Characteristics of Particles on the Insulator Surface

4.1. Effects of the Insulator Installation Method on Contamination Deposition Characteristics The current research used the cantilever insulator with two different installation methods (i.e., horizontal and oblique installations) as the research object. The inlet velocity was 10 m/s, particle size was 15 μm, airflow angle was 0°, and volume fraction of the particle phase was 0.02. Figure 10 shows the particle deposition cloud chart of the particles on the cantilever insulator surface. The

Coatings 2020, 10, 697 11 of 19

4. Deposition Characteristics of Particles on the Insulator Surface

4.1. Effects of the Insulator Installation Method on Contamination Deposition Characteristics The current research used the cantilever insulator with two different installation methods (i.e., horizontal and oblique installations) as the research object. The inlet velocity was 10 m/s, particleCoatings 2020 size, 10 was, x FOR 15 PEERµm, REVIEW airflow angle was 0◦, and volume fraction of the particle phase was11 0.02.of 19 Coatings 2020, 10, x FOR PEER REVIEW 11 of 19 CoatingsFigure 202010 shows, 10, x FOR the PEER particle REVIEW deposition cloud chart of the particles on the cantilever insulator surface.11 of 19 Thecontaminated contaminated volume volume data data on onthe the creepage creepage distances distances along along the the windward, windward, leeward, leeward, and and crosswind contaminated volume data on the creepage distances along the windward, leeward, and crosswind surfaces were selectedselected forfor comparison.comparison. Figures 1111–13–13 show thethe simulationsimulation results.results. surfaces were selected for comparison. Figures 11–13 show the simulation results.

(a) (b) (a) (b) Figure 10. Particle deposition cloud chart of the cantilever insulator. (a) Horizontal cantilever Figure 10. Particle deposition cloud chart of the cantilever insulator. (a) Horizontal cantilever Figureinsulator. 10. (Particleb) Oblique deposition cantilever cloud insulator. chart of the cantilever insulator. (a) Horizontal cantilever insulator. insulator. (b) Oblique cantilever insulator. (insulator.b) Oblique (b cantilever) Oblique cantilever insulator. insulator.

Figure 11. Contamination volume fraction changes with the distance along the windward side. Figure 11. Contamination volume fraction changes with the distance along the windward side.

Figure 12. Contamination volume fraction changes with the distance along the leeward side. Figure 12. Contamination volume fraction changes with the distance along the leeward side.

Coatings 2020, 10, 697 12 of 19

Coatings 2020, 10, x FOR PEER REVIEW 12 of 19

Figure 13.13. Contamination volume fraction changes with the distance alongalong thethe crosswindcrosswind side.side.

FigureFigure 1111 showsshows thatthat thethe contamination volumevolume fractionfraction ofof thethe windward surfacesurface ofof thethe insulator oscillatesoscillates upup andand downdown withwith thethe creepage distance.distance. These reasons are mainly relatedrelated toto thethe shape and structurestructure ofof thethe cantilevercantilever insulator.insulator. TheThe horizontalhorizontal andand obliqueoblique installationinstallation methodsmethods werewere similarsimilar withwith thethe creepagecreepage distancedistance alongalong thethe surface,surface, andand certaincertain didifferencesfferences inin thethe contaminationcontamination volumevolume fractionfraction existedexisted atat certaincertain positions.positions. The maximum contamination volume fractionfraction on thethe surfacesurface ofof thethe insulatorinsulator was was 0.543, 0.543, which which is is nearly nearly 30 30 times times the the contamination contamination volume volume fraction fraction in thein the air. air. Figure Figure 11 illustrates11 illustrates that that the the installation installation method method of the of the insulator insulator has has a certain a certain effect effect on theon the particle particle deposition deposition on theon the insulator insulator surface. surface. FigureFigure 12 12 shows shows that that the the leeward leeward surface surface contamination contamination volume volume fraction fraction changes changes with the creepagewith the distancecreepage were distance similar were to similar the windward to the windward surface. The surface. leeward The surfaceleeward contamination surface contamination volume fractionvolume withfraction the with creepage the creepage distance distance presented presented a high value a high in value the middle in the middle and low and values low atvalues both at ends. both When ends. nearWhen the near two the ends two of ends the insulator, of the insulator, the oblique the oblique installation installation insulator insulator had a larger had a contamination larger contamination volume fractionvolume thanfraction the horizontal than the installation horizontal insulator. installation In the insulator. middle of theIn shed,the middle the contamination of the shed, volume the fractioncontamination of the horizontal volume fraction installation of the insulator horizontal surface installation was higher insulator than surface that of thewas oblique higher than installation that of insulator.the oblique The installation maximum insulator. contamination The maximum volume fraction contamination of the leeward volume surface fraction was of 0.180, the whichleeward is relativelysurface was smooth 0.180, in which value is compared relatively with smooth that in of value the windward compared surface. with that of the windward surface. FigureFigure 1313 showsshows thatthat thethe contaminationcontamination volumevolume fractionfraction ofof thethe obliqueoblique installationinstallation insulatorinsulator crosswindcrosswind sideside waswas higherhigher thanthan that of thethe horizontalhorizontal installation insulator at the same position. ComparedCompared withwith thethe windwardwindward andand leewardleeward surfaces,surfaces, thethe crosswindcrosswind surfacesurface hadhad thethe lowestlowest contaminationcontamination volumevolume fractionfraction alongalong thethe creepagecreepage distance.distance. In summary, thethe contaminationcontamination volumevolume fractionfraction ofof thethe windward, leeward,leeward, andand crosswindcrosswind surfacessurfaces ofof thethe insulatorinsulator changeschanges oscillatedoscillated upup andand downdown withwith thethe creepagecreepage distancedistance alongalong thethe surface.surface. TheThe unevenuneven distributiondistribution ofof thethe contaminationcontamination particlesparticles onon thethe insulatorinsulator surfacesurface waswas evident.evident. The shed structure of the insulator will lead to different different contaminationcontamination volume volume fractions fractions at diatff differenterent positions, positions, and theand collision the collision mode ofmode the particles of the particles at different at positionsdifferent positions of the insulator of the isinsulator different. is different. The installation The installation method has method a certain has eaff ectcertain on the effect degree on the of contaminationdegree of contamination accumulation accumulation on the insulator on the insulator surface. surface. When the When insulator the insulator is installed is installed in the in same the manner,same manner, the contamination the contamination volume volume fraction fraction of di ffoferent different parts parts with with the creepage the creepage distance distance along along the surfacethe surface changes changes as follows: as follows: windward windward side side> leeward > leeward side side> crosswind > crosswind side. side. TheThe changechange inin thethe contaminationcontamination volumevolume fractionfraction ofof thethe particlesparticles withwith thethe creepagecreepage distancedistance alongalong thethe surfacesurface indicatedindicated thatthat thethe installationinstallation methodmethod has a significantsignificant eeffectffect onon thethe contaminationcontamination accumulationaccumulation characteristicscharacteristics ofof thethe insulator.insulator. ThisThis studystudy tooktook thethe horizontalhorizontal installationinstallation andand obliqueoblique installationinstallation of of insulators insulators as as the the research research object, object, and selected and selected the middle the middle group of group sheds forof sheds the numerical for the simulationnumerical analysissimulation at di ffanalysiserent particle at different sizes and particle wind velocities sizes and to comparewind velocities the contamination to compare volume the fractionscontamination of the windward,volume fractions leeward, of the crosswind, windward, and overallleeward, surfaces crosswind, of the and insulator. overall surfaces of the insulator. This study selected five working conditions: wind velocity of 10 m/s, particle phase volume fraction of 0.02, airflow angle of 0°, and particle sizes of 5, 10, 15, 20, and 25 μm. The contamination volume fraction data at different parts of the horizontal and oblique cantilever insulators were collected as well as the contamination volume fractions of the windward side, leeward side,

Coatings 2020, 10, 697 13 of 19

This study selected five working conditions: wind velocity of 10 m/s, particle phase volume fraction of 0.02, airflow angle of 0◦, and particle sizes of 5, 10, 15, 20, and 25 µm. The contamination volume fraction data at different parts of the horizontal and oblique cantilever insulators were collected as well as the contamination volume fractions of the windward side, leeward side, crosswind side 1, crosswind side 2, and the entire insulator. Table1 presents the contamination volume fraction data at different parts.

Table 1. Contamination volume fraction of the insulator surface in diﬀerent parts under diﬀerent particle sizes.

Insulator Parts 5 µm 10 µm 15 µm 20 µm 25 µm Windward side of the horizontal installation 0.0222 0.0299 0.0415 0.0566 0.0715 Windward side of the oblique installation 0.0221 0.0298 0.0421 0.0598 0.0783 Leeward side of the horizontal installation 0.0175 0.0140 0.0151 0.0212 0.0263 Leeward side of the oblique installation 0.0173 0.0136 0.0122 0.0156 0.0199 Crosswind side 1 of the horizontal installation 0.0191 0.0187 0.0204 0.0232 0.0273 Crosswind side 1 of the oblique installation 0.0192 0.0188 0.0204 0.0241 0.0293 Crosswind side 2 of the horizontal installation 0.0190 0.0185 0.0201 0.0233 0.0273 Crosswind side 2 of the oblique installation 0.0192 0.0188 0.0211 0.0255 0.0305 Entire insulator of the horizontal installation 0.0192 0.0206 0.0268 0.0344 0.0437 Entire insulator of the oblique installation 0.0193 0.0211 0.0269 0.0355 0.0453

Table1 shows that the contamination volume fractions of the horizontal and oblique cantilever insulators at the same location were different under different particle sizes, and that slight differences were evident. On the windward side, when the particle size was below 10 µm, the degree of contamination accumulation of the horizontal and oblique cantilever insulators was the same. When the particle size was above 10 µm, the contamination volume fraction of the oblique cantilever insulator surface was higher than that of the horizontal cantilever insulator. For the leeward surface, the contamination volume fraction of the oblique cantilever insulator surface was lower than that of the horizontal cantilever insulator. For the crosswind surface, the contamination volume fraction of the horizontal and oblique cantilever insulator surfaces was the same when the particle size was below 15 µm. When the particle size was above 15 µm, the contamination volume fraction of the oblique cantilever insulator surface was higher than that of the horizontal cantilever insulator. For the entire insulator surface, the contamination volume fraction of the oblique cantilever insulator surface was higher than that of the horizontal cantilever insulator; the larger the particle size, the larger the difference in value. Accordingly, the installation method has a certain effect on the deposition characteristics of the particles on the insulator surface. The effects of the installation method on the deposition characteristics of particles on the insulator surface were further studied. This research selected four working conditions for the simulation test: particle size of 15 µm, particle phase volume fraction of 0.02, airflow angle of 0◦, and wind velocities of 5, 10, 15, and 20 m/s. The contamination volume fraction data at different parts of the horizontal and oblique cantilever insulators were collected as well as the contamination volume fractions of the windward side, leeward side, crosswind side 1, crosswind side 2, and the entire insulator. Table2 shows the contamination volume fraction data at the different parts. Coatings 2020, 10, 697 14 of 19

Table 2. Contamination volume fraction of the insulator surface in diﬀerent parts under diﬀerent wind velocities.

Insulator Parts 5 m/s 10 m/s 15 m/s 20 m/s Windward side of the horizontal installation 0.0314 0.0418 0.0509 0.0590 Windward side of the oblique installation 0.0317 0.0421 0.0517 0.0612 Leeward side of the horizontal installation 0.0147 0.0152 0.0226 0.0240 Leeward side of the oblique installation 0.0114 0.0122 0.0203 0.0229 Crosswind side 1 of the horizontal installation 0.0189 0.0204 0.0218 0.0240 Crosswind side 1 of the oblique installation 0.0188 0.0204 0.0230 0.0254 Crosswind side 2 of the horizontal installation 0.0186 0.0202 0.0219 0.0242 Crosswind side 2 of the oblique installation 0.0186 0.0211 0.0241 0.0271 Entire insulator of the horizontal installation 0.0211 0.0268 0.0312 0.0359 Entire insulator of the oblique installation 0.0213 0.0269 0.0325 0.0378

Table2 shows that the contamination volume fractions of the horizontal and oblique cantilever insulators at the same location were different under different wind velocities and slight differences were evident. For the windward surface, the contamination volume fraction of the oblique cantilever insulator surface was higher than that of the horizontal cantilever insulator at different wind velocities. For the leeward surface, the contamination volume fraction of the oblique cantilever insulator surface was lower than that of the horizontal cantilever insulator at different wind velocities. For the crosswind surface, the contamination volume fraction of the insulator surface increased with the increase of wind velocity, and those of the horizontal and oblique cantilever insulator surfaces were not substantially different from each other. For the entire insulator surface, the contamination volume fraction of the oblique cantilever insulator surface was consistently higher than that of the horizontal cantilever insulator at different wind velocities. Moreover, the higher the wind velocity, the larger the difference in the contamination volume fraction of the oblique and horizontal cantilever insulator surfaces. In summary, this study comparatively analyzed the difference in the deposition characteristics of particles on the surfaces of the horizontal and oblique cantilever insulator surfaces. Our results indicate that the installation method has a significant effect on the deposition characteristics of the particles on the insulator surface. When the particle size and wind velocity are fixed for the same insulator, the degree of contamination accumulation on the insulator surface installed obliquely is higher than the insulators installed horizontally. This result is consistent with the conclusion (in Section2) drawn by the collision deposition model of the particles with insulator surfaces in different installation methods. In the past, the horizontal and oblique cantilever insulators of the catenary usually used to be of the same type and the same creepage distance, so the creepage distance of the oblique cantilever insulator in the same catenary could be increased to prevent flashover. For example, the oblique cantilever insulator can replace an insulator with larger creepage distance or attach a booster shed, and the cleaning frequency of the oblique insulator should be greater than that of the horizontal insulator. For an area where the wind direction is relatively fixed all year round, during the cleaning process of the maintenance personnel, or during the cleaning process of the mechanized work tools, different cleaning schemes, strengths, and methods are formulated for the windward, leeward, and crosswind sides of the insulator.

4.2. Effects of Shed Structure on the Contamination Deposition Characteristics The positive feeder insulators also belong to the catenary insulator, which are vertically connected into an insulator string to hang the positive feeder of the catenary. The aforementioned cantilever insulator is different from the positive feeder insulator in shed shape, so this paper will study the effects of shed structure on the contamination deposition characteristics of catenary insulator. The U70BS insulator can be used as a positive feeder insulator, and this study selected the U70BS porcelain insulator of disc type as the research object. The inclination angle of the U70BS insulator shed is larger than that of the cantilever insulator. Moreover, the lower surface of the shed has a number of ribs. Coatings 2020, 10, 697 15 of 19

Coatings 2020The, 10 disc, x FOR diameter PEER REVIEW of the U70BS insulator was 255 mm, height of the structure was 146 mm, and the 15 of 19 Coatings 2020creepage, 10, x FOR distance PEER was REVIEW 295 mm. Figure 14 shows the three-dimensional structure of the U70BS insulator. 15 of 19

Figure 14.Figure Three 14. ‐Three-dimensionaldimensional structure structure diagram diagram of of the the U70BS U70BS insulator. insulator. Figure 14. Three‐dimensional structure diagram of the U70BS insulator. In the simulation, the wind velocity was 10 m/s, particle concentration was 0.02, airﬂow angle was In the simulation, the wind velocity was 10 m/s, particle concentration was 0.02, airflow angle In the0◦, andsimulation, particle size the was wind 15 µm. velocity A piece ofwas insulator 10 m/s, in the particle middle concentration was selected for analysis.was 0.02, Figure airflow 15 angle was 0°, and particle size was 15 μm. A piece of insulator in the middle was selected for analysis. was 0°, andshows particle the particle size deposition was 15 μ cloudm. chartA piece of the of particles insulator on the in U70BS the middle insulator was surface. selected for analysis. Figure 15 shows the particle deposition cloud chart of the particles on the U70BS insulator surface. Figure 15 shows the particle deposition cloud chart of the particles on the U70BS insulator surface.

(a) (b) (a) (b) Figure 15.Figure Particle 15. depositionParticle deposition cloud cloudchart chart of the of theU70BS U70BS insulator. insulator. (a (a) )Upper Upper surfacesurface of of the the shed; shed; (b) Figure 15. Particle deposition cloud chart of the U70BS insulator. (a) Upper surface of the shed; (b) lower surface(b) lower of the surface shed. of the shed. lower surface of the shed. Figure 15 shows that for the upper surface, the particles were mainly deposited on the windward Figure 15 shows that for the upper surface, the particles were mainly deposited on the windward Figureand leeward15 shows surfaces, that for and the the upper crosswind surface, surface the was particles relatively small.were Themainly contamination deposited accumulation on the windward and leewardof the leewardsurfaces, surface and was the more crosswind extensive compared surface with was those relatively of the windward small. and leewardThe contamination surfaces. and leeward surfaces, and the crosswind surface was relatively small. The contamination accumulationFor the of lower the leeward surface, the surface particles was were more also mainly extensive deposited compared on the leeward with surface,those of and the the windward particles and accumulation of the leeward surface was more extensive compared with those of the windward and leeward surfaces.were deposited For the minimally lower insurface, other areas. the particles The contamination were also volume mainly fractions deposited of the windward,on the leeward leeward leeward,surfaces. crosswind For the 1, lower and crosswind surface, 2 werethe particles extracted, andwere their also values mainly were 0.0350,deposited 0.0480, on 0.0202, the leeward surface, and the particles were deposited minimally in other areas. The contamination volume surface, andand 0.0196, the particles respectively. were The deposited degree of contamination minimally accumulationin other areas. on the The diff erentcontamination parts of the volume fractions of the windward, leeward, crosswind 1, and crosswind 2 were extracted, and their values fractionsinsulator of the windward, surface is as follows: leeward, leeward crosswind side > windward 1, and crosswind side > crosswind 2 were side. extracted, and their values were 0.0350, 0.0480,To study 0.0202, the deposition and 0.0196, characteristics respectively. of particles The on thedegree positive of feeder contamination insulator under accumulation different on were 0.0350, 0.0480, 0.0202, and 0.0196, respectively. The degree of contamination accumulation on the differentconditions, parts of this the research insulator simulated surface and analyzedis as follows: the distribution leeward of side particles > windward on the insulator side surface > crosswind the different parts of the insulator surface is as follows: leeward side > windward side > crosswind side. under different wind velocities and different particle sizes. The effects of wind velocity on the particle side. deposition characteristics of the positive feeder insulator surface were analyzed. In the simulation, To study the deposition characteristics of particles on the positive feeder insulator under To thestudy fixed the particle deposition size was 15characteristicsµm, airflow angle of wasparticles 0◦, particle on the concentration positive wasfeeder 0.02 andinsulator wind under different conditions, this research simulated and analyzed the distribution of particles on the different conditions, this research simulated and analyzed the distribution of particles on the insulator surface under different wind velocities and different particle sizes. The effects of wind insulator surface under different wind velocities and different particle sizes. The effects of wind velocity on the particle deposition characteristics of the positive feeder insulator surface were velocity on the particle deposition characteristics of the positive feeder insulator surface were analyzed. In the simulation, the fixed particle size was 15 μm, airflow angle was 0°, particle analyzed. In the simulation, the fixed particle size was 15 μm, airflow angle was 0°, particle concentration was 0.02 and wind velocities were 1, 5, 10, 15, and 20 m/s. Given the top effects at both concentration was 0.02 and wind velocities were 1, 5, 10, 15, and 20 m/s. Given the top effects at both ends of the insulator, the second shed in the middle was selected to calculate the contamination ends of the insulator, the second shed in the middle was selected to calculate the contamination volume fractions of the windward, leeward, crosswind 1, and crosswind 2 surfaces at different wind volume fractions of the windward, leeward, crosswind 1, and crosswind 2 surfaces at different wind velocities. Figure 16 shows the changes of the contamination volume fraction of the positive feeder velocities. Figure 16 shows the changes of the contamination volume fraction of the positive feeder insulator surface with wind velocity. insulator surface with wind velocity.

Coatings 2020, 10, x FOR PEER REVIEW 16 of 19 Coatings 2020, 10, 697 16 of 19

velocities were 1, 5, 10, 15, and 20 m/s. Given the top eﬀects at both ends of the insulator, the second shed in the middle was selected to calculate the contamination volume fractions of the windward, leeward, Coatings crosswind2020, 10, x FOR 1, and PEER crosswind REVIEW 2 surfaces at diﬀerent wind velocities. Figure 16 shows the changes of the 16 of 19 contamination volume fraction of the positive feeder insulator surface with wind velocity.

Figure 16. Positive feeder insulator surface contamination volume fraction changes with wind velocity.

Figure 16 shows that the contamination volume fraction of the windward, leeward, and crosswind Figuresurfaces 16. Positive of the feeder positive insulator feeder surface insulator contamination increased volume fraction with changes an increase with wind in velocity. wind velocity. This resultFigure was the16. samePositive as thefeeder change insulator of the surface cantilever contamination insulator surfacevolume withfraction wind changes velocity. with At wind the same windvelocity. velocity,Figure the16 shows contamination that the contamination volume volume fraction fraction of ofthe the windward windward, leeward, side of and the crosswind positive feeder surfaces of the positive feeder insulator increased with an increase in wind velocity. This result was insulator was consistently less than the leeward side, and the contamination volume fraction of the Figurethe same 16 asshows the change that of the the contamination cantilever insulator volume surface withfraction wind of velocity. the windward, At the same windleeward, and windwardvelocity, side the of contamination the cantilever volume insulator fraction of was the windward constantly side higher of the positive than feederthe leeward insulator wasside, thereby crosswindformingconsistently a surfacessharp lesscontrast. of than the the positiveEvidently, leeward side,feeder the and shedinsulator the contamination structure increased has volume substantial with fraction an increase of effects the windward inon wind the side deposition velocity. of This law resultof particles wasthe cantilever the on same the insulatorwindward as the waschange constantlyand ofleeward the higher cantilever sides than of the insulatorthe leeward insulator. side, surface thereby with forming wind a sharp velocity. contrast. At the same windThe velocity,Evidently, effects thethe of shed contaminationparticle structure size has on substantial volume the deposition e fffractionects on the characteristicsof deposition the windward law of of particles theside positive on of the the windward feederpositive insulator feeder and leeward sides of the insulator. insulatorsurface were was likewiseconsistently analyzed. less than In the the simulation, leeward side, the and fixed the wind contamination velocity was volume 10 m/s, fraction airflow of angle the windward Theside eff ectsof the of particle cantilever size on insulator the deposition was characteristics constantly of higher the positive than feeder the insulator leeward surface side, thereby was 0°,were particle likewise concentration analyzed. In the was simulation, 0.02, theand fixed particle wind velocity sizes waswere 10 5, m /s,10, airflow 15, angle20, and was 025, μm. The forming a sharp contrast. Evidently, the shed structure has substantial effects on the deposition◦ law contaminationparticle concentration volume fractions was 0.02, of and the particle windward, sizes were leeward, 5, 10, 15, 20,crosswind and 25 µm. 1, Theand contamination crosswind 2 surfaces ofwith particles differentvolume on fractions theparticle windward of sizes the windward, were and leewardalso leeward, calculated. sides crosswind of Figurethe 1,insulator. and 17 crosswindshows the 2 surfaceschange with in the diff erentcontamination volumeTheparticle fractioneffects sizes of were theparticle also positive calculated. size feeder on Figure the insulator 17deposition shows surface the changecharacteristics with in the the contamination particle of the size. positive volume fraction feeder of insulator surfacethe were positive likewise feeder analyzed. insulator surface In the with simulation, the particle the size. fixed wind velocity was 10 m/s, airflow angle was 0°, particle concentration was 0.02, and particle sizes were 5, 10, 15, 20, and 25 μm. The contamination volume fractions of the windward, leeward, crosswind 1, and crosswind 2 surfaces with different particle sizes were also calculated. Figure 17 shows the change in the contamination volume fraction of the positive feeder insulator surface with the particle size.

FigureFigure 17. Positive 17. Positive feeder feeder insulator insulator surface surface contamination contamination volume volume fraction fraction changes changes with particle with size. particle size.

Figure 17 shows that the contamination volume fractions of the windward, leeward, and crosswind surfaces of the positive feeder insulators increased with the gradual increase of the particle size, and the windward and leeward surfaces grew faster than the crosswind 1 and crosswind 2. The law Figureof the contamination17. Positive feeder volume insulator fraction surface on contamination the insulator volume surface fraction with changesthe particle with sizeparticle is consistent size. with the wind velocity law. At the same particle size, the windward surface contamination volume fractionFigure of the17 positiveshows thatfeeder the insulator contamination was constantly volume lessfractions than the of leewardthe windward, surface contaminationleeward, and crosswindvolume fraction, surfaces and of thethe positivecantilever feeder insulator insulators windward increased surface with contamination the gradual increase volume of fraction the particle was size,constantly and the higher windward than theand leeward leeward surface surfaces contamination grew faster than volume the crosswind fraction, thereby 1 and crosswind forming a 2. sharp The law of the contamination volume fraction on the insulator surface with the particle size is consistent with the wind velocity law. At the same particle size, the windward surface contamination volume fraction of the positive feeder insulator was constantly less than the leeward surface contamination volume fraction, and the cantilever insulator windward surface contamination volume fraction was constantly higher than the leeward surface contamination volume fraction, thereby forming a sharp

Coatings 2020, 10, 697 17 of 19

Figure 17 shows that the contamination volume fractions of the windward, leeward, and crosswind surfaces of the positive feeder insulators increased with the gradual increase of the particle size, and the windward and leeward surfaces grew faster than the crosswind 1 and crosswind 2. The law of the contamination volume fraction on the insulator surface with the particle size is consistent with the wind velocity law. At the same particle size, the windward surface contamination volume fraction of the positive feeder insulator was constantly less than the leeward surface contamination volume fraction, and the cantilever insulator windward surface contamination volume fraction was constantly higher than the leeward surface contamination volume fraction, thereby forming a sharp contrast. Evidently, the insulator shed structure has substantial effects on the deposition characteristics of particles on the insulator surface. The preceding analysis indicated that when the wind velocity and particle size are fixed, the positive feeder insulator has a distinct difference from the windward and leeward sides of the cantilever insulator. This result is considerably related to the structure of the insulator shed. The possible reason is that the inclination angles of the upper and lower sheds of the cantilever insulator is close to the horizontal, thereby resulting in difficulty forming a large vortex area on the leeward surface. The majority of the particles are deposited on the windward surface of the insulator, and the particles are difficult to deposit on the leeward surface. However, the leeward area forms a large vortex area due to the larger disc diameter of the positive feeder insulator, and the particles are mainly deposited on the leeward surface. In the same environment, the contamination characteristics of insulators with different shed shapes are different, so the description of the contamination characteristics of insulators should be based on a certain shed structure.

5. Conclusions According to the above results, the following conclusions can be obtained:

(1) From a microscopic point of view, the gas–solid two-phase flow theory was used to establish the collision deposition model of particles and the surfaces of the horizontal and oblique cantilever insulators. The deposition conditions of the particles on the insulator surface were obtained according to the conservation of kinetic energy. When particle size and wind speed are fixed, the ejection velocity of the oblique cantilever insulator surface is less than that of the horizontal cantilever insulator, and the particles are easily deposited on the surface of the oblique cantilever insulator. (2) In the horizontal and oblique installation methods, the contamination volume fractions of the windward, leeward, and crosswind surfaces showed up and down oscillations with the creepage distance. The uneven distribution of contamination particles on the insulator surface was evident. At the same location, a certain difference existed in the contamination volume fraction of the insulator surface of the horizontal and oblique cantilever insulators. For the entire insulator surface, the degree of contamination accumulation on the oblique cantilever insulator surface was consistently higher than that of the horizontal cantilever insulator. The installation method of the insulator had a significant effect on the contamination deposition characteristics. (3) It is recommended to increase the creepage distance of the oblique cantilever insulator or attach a booster shed to deal with the situation of large contamination accumulation and easy contamination flashover. For an area where the wind direction is relatively fixed all year round, during the cleaning process of the maintenance personnel, or during the cleaning process of the mechanized work tools, different cleaning schemes, strengths, and methods can be formulated for the windward, leeward and crosswind sides of the insulator. (4) The shed structure of the insulator has a significant effect on the contamination deposition characteristics of the insulator. With the increase in wind velocity and particle size, the contamination volume fraction on the windward side of the cantilever insulator is constantly higher than the leeward side, the contamination volume fraction of the positive feeder insulator on Coatings 2020, 10, 697 18 of 19

the windward side is constantly less than the leeward side. The description of the contamination characteristics of insulators should be based on a certain shed structure.

Author Contributions: The research concepts were proposed by S.Z., C.Z., D.Z., and Y.Z. Data processing and manuscript preparation were conducted by Y.Z. and D.Z. Data analysis and interpretation were implemented by S.Z., C.Z., and D.Z. Manuscript editing and visualization were performed by S.Z. and C.Z. All authors have read and agreed to the published version of the manuscript. Funding: This work was financially supported by the Natural Science Foundation of China (Grant Nos. 51867013; 51767014; 51567014). Conflicts of Interest: The authors declare no conflicts of interest.

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