Numerical Study of Heat Transfer and Speed Air Flow on Performance of an Auto-Ventilated Disc Brake

fluids

Article Numerical Study of Heat Transfer and Speed Air Flow on Performance of an Auto-Ventilated Disc Brake

R. A. García-León * , N. Afanador-García and J. A. Gómez-Camperos

Facultad de Ingeniería, Universidad Francisco de Paula Santander Ocaña, 546552 Norte de Santander, Colombia; [email protected] (N.A.-G.); [email protected] (J.A.G.-C.) * Correspondence: [email protected]; Tel.: +57-315-289-8250

Abstract: In the braking system, the heat dissipation generated by the friction between the disc and pad should be evacuated as quickly as possible. In this work, ﬁve common different automotive disc brakes were studied through mathematical theories of heat transfer and numerical methods using the ANSYS software. In addition, a direct comparison between experimental, theoretical, and simulation values found in the open literature was performed to propose a disc brake with an improved geometry in terms of dissipation of heat transfer. The numerical results were considered to propose two possible solutions of disc brake geometries using N-38 ventilation blades used in aeronautic engineering. An improvement in temperature dissipation was achieved by approximately 23.8% compared to the ﬁve geometries analyzed with a simple type N-38 ventilation blade. The heat dissipation in the brakes strongly depends on the geometry of the disc, the geometry of the blades,

the material from which it is manufactured, the material of the pad, the weight of the vehicle, and the operating conditions, as can be veriﬁed with mathematical calculations and experiments. The

Citation: García-León, R.A.; results obtained demonstrate that the discs can be used effectively in extreme working conditions ◦ Afanador-García, N.; (80 km/h and 33 C), without affecting the safety of the occupants and the braking system. Gómez-Camperos, J.A. Numerical Study of Heat Transfer and Speed Air Keywords: temperature; disc brakes; blades; friction; heat transfer; CFD Flow on Performance of an Auto-Ventilated Disc Brake. Fluids 2021, 6, 160. https://doi.org/ 10.3390/ﬂuids6040160 1. Introduction Brakes are essential elements to maintain maneuverability and safety in any vehicle, Academic Editors: Diego Angeli and whether they are rotary or linear. Braking systems work by taking advantage of the friction V’yacheslav Akkerman between two surfaces (the disc and the pad), to slow down the moving vehicle. There are various types of brakes: drum, band, disc, and conical, and they have different applications. Received: 12 March 2021 In particular, the most common ones in the automotive sector are the self-ventilated disc Accepted: 13 April 2021 Published: 16 April 2021 type in the front part of the vehicle and the drum type for the rear part [1]. Disc brakes differ from the other types as the applied force is normal to the disc instead of being radial.

Publisher’s Note: MDPI stays neutral Another distinctive feature of the disk brakes is that the friction moment does not aid the with regard to jurisdictional claims in actuation moment (self-energizing effect), as occurs in drum and bevel brakes. This allows published maps and institutional affil- slight changes in the friction coefficient to not dramatically affect the braking force required iations. to stop the car. For example, a 30% variation in the friction coefficient, which is a normal condition in humid environments, causes at least a 50% increase in the force of the braking system [2]. The disc brake is the element that is attached to the wheel hub and rotates with it, forming the mobile element of the braking system. Against the surface or friction area of Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. the disc brake the pads interact, and thus the vehicle is stopped thanks to the continuous This article is an open access article friction established between the pads and the disc. During this process, the hydraulic pump distributed under the terms and is activated when actuating the brake pedal, which transports the brake fluid to its calipers. conditions of the Creative Commons The pressure transmitted by the liquid causes the caliper piston to push the pads against Attribution (CC BY) license (https:// the disc brake generating friction. The kinetic energy (accumulated in the vehicle due to its creativecommons.org/licenses/by/ speed) is transformed into thermal energy due to the friction between the disc and pad, 4.0/). which is evacuated by natural convection to the environment; thus, the vehicle gradually

Fluids 2021, 6, 160. https://doi.org/10.3390/ﬂuids6040160 https://www.mdpi.com/journal/ﬂuids Fluids 2021, 6, 160 2 of 24

decelerates. In this way, it is normal in vehicles to use self-ventilated brake discs in all four wheels (discs with ventilation channels). However, the safety triangle intervenes, which refers to the components of the vehicle that influence the movement, such as the shock absorbers, the braking system, and the tires [3,4]. The efficiency of the braking process depends significantly on the type of material, the disc geometry, and the ventilation blades’ configuration for heat dissipation. In conclusion, the braking system is a device directly coupled to the vehicle tires, whose main objective is to transform the kinetic energy of the vehicle into thermal energy to totally or partially reduce its speed. Likewise, the bigger the vehicle, the greater its mass; therefore, more effort is made by the braking system to reduce the kinetic energy caused by the movement [5]. This generates an increase in the temperature of the braking system in many cases. The study conducted by Wallis et al. [6] evaluated the thermal behavior of three types of rotors: straight radial blades (SRV), straight blades with a rounded edge (SRV-R), and with teardrop-shaped diamond blades (DTDP). They concluded that the capacity of heat transfer of round edge straight vane rotors (SRV-R) and teardrop diamond vane rotors (DTDP) is ~20% higher than that of straight radial vane rotors (SRV). This is because of the improved pumping in the rotors for this configuration, evidencing the importance of the design in the geometry. McPhee and Johnson [7] evaluated heat transfer and fluid movement using a transient-state experiment to quantify the internal convection between the ventilation vanes in terms of external convection (rotor surface) for three different speeds. The results showed that conduction and radiation were negligible. On the other hand, for higher rotor speeds, the heat transfer by convection increases, showing a linear relationship. The flow analysis of the experiment involved the determination of the speed field through the internal passages formed by the radial of the disc brake [8]. Atkins et al. [9] studied the local temperature and the experimentally obtained distributions of the heat transfer coefficient on the internal surfaces of a rotor brake with rotating blades at realistic angular velocities. The results validated that the bulk of the airflow within the vented channel of a rotating disc flows mostly backward from the ventilation blades, and the internal heat transfer is distributed non-uniformly during the motion. In addition, the outer surfaces of the disc brake generate an average cooling of approximately twice that of the inner surface. Park et al. [10] carried out a study to increase the heat transfer rate in the ventilated disc brake. The surface geometry in the disc brake flow path was modified from a smooth surface to a surface with helical grooves. The results of the numerical analysis showed that the local Nusselt numbers decreased monotonically with the distance between the crests and the helical groove. This shows that the increase in the surface area provided by the helical grooved geometry improves the recirculation behavior of the airflow and the swirls formed. Therefore, when the helical groove is too deep, it causes the rate of heat transfer to decrease. To demonstrate the numerical simulation of steady-state braking, Nejat et al. [11] modeled the various airflow geometries by simulation of computational fluid dynamics (CFD). Furthermore, some detailed analyses for the speed and temperature distribution around the ventilation blades were made. The result of the CFD analysis showed an increase in the airflow, limiting the flow separation region, especially near the leading edge of the ventilation blades. These factors are essential in the overall improvement of the heat transfer coefficient (HTC). Likewise, a new design was introduced using two air blades, which notably increased the airflow efficiency, improving the HTC between 17 and 29% for different angular speeds. Duzgun [12] modeled three different ventilated disc brakes employing finite element analysis (FEA) to study their thermo-structural behavior. The FEA results showed that heat generation on the solid surfaces of the brake discs is reduced to a maximum of 24% due to the geometries of the ventilation blades. The experimental study for the dissipation of heat generated on the discs’ surfaces was verified through the FEA and a range between Fluids 2021, 6, 160 3 of 24

1.13 and 10.87% was found for the analysis of the temperature. This behavior aided in the improvement of the braking performance, maintaining the friction coefficient between the pad and the disc surface and stabilizing the pads surface wear rate, especially under continuous braking conditions. Lee et al. [13] numerically analyzed the fluid flow and heat transfer characteristics of ventilated disc brakes under real conditions. Due to higher heat dissipation compared to drum brake or solid brake discs; the results showed that when the incoming cooling air collides with the ventilation blades the airflow is deflected due to the Coriolis force. In addition, reverse airflow is generated, which has a negative influence on heat transfer. The inverted airflow for all cases is identified close to the suction side of the blades, obtaining conclusions and comparisons between different blade configurations to propose an alternative model. Belhocine and Afzal [14] carried out a transient thermal analysis of two types of disc brakes, one solid and one ventilated. This analysis was performed using the finite element method (FEM). During the braking process, the material must have a lower thermal conductivity, which generates large thermal gradients and, consequently, an increase in the disc brake surface temperature. From the results obtained by FEM, the ventilated disc brakes made of FG20 and FG25AL will have temperatures around 351.5 to 380.2 ◦C, respectively. These are higher than that of the ventilated disc made of FG15, which has a maximum temperature of 345.4 ◦C. Therefore, the most suitable material in this case for the brake discs is FG15 gray cast iron, since it presents the best thermal performance. Belhocine and Bouchetara [15] analyzed the thermal behavior of the solid and ventilated brake discs of automotive vehicles using the ANSYS simulation software. The temperature distribution in the disc brake was modeled to identify all the factors and the corresponding input parameters at the time of braking operation, such as the type of braking, the geometric design of the disc, and the material used. The study concluded that FEA presents satisfactory results, compared to those of the specialized literature. Through the particular manufacturing process of the SiC3D/Al alloy, Jiang et al. [16] carried out thermal and stress analysis on the disc brake during emergency braking with a speed of 350 km/h. The authors considered the cooling air using FEM and computational fluid dynamics (CFD). The alloy improved the temperature generated by friction by 14% (517 ◦C and 192 MPa in 63 s) due to its high thermal conductivity. Topouris et al. [17] conducted an experimental investigation on the heat dissipation of stationary brake discs concentrated on four disc designs: a ventilated disc with radial blades, two ventilated type discs with curved blades (a non-perforated and cross-drilled disc), and a solid disc. The experiments were performed on a specially designed thermal spin platform and provided accurate, repeatable, and reliable temperature measurements to predict total, convective, and radiative heat dissipation coefficients. The values obtained were compared with the results obtained through CFD, and thus the four disc brake designs show that the disc with radial blades has the highest convection heat dissipation. It was around 30% lower compared to the solid disc. Lakkam et al. [18] investigated the temperature gradient of the disc brake to evaluate the heat convection coefficients (h) through experimental and numerical tests. The value of h was modified by changing the temperature distribution in disc brakes under steady-state forced heat convection. Numerical and finite methods were applied to study the distribution and dissipation of heat transfer, and the results obtained were validated by the experimental results. To provide a broader perspective on the behavior of the brake discs, García-León [19] selected three classes of commonly used disc brakes to perform mathematical and simulation calculations for evaluating the behavior of each disc geometry. The results showed that the discs with a superficial temperature higher than 80 ◦C could dissipate the heat in 40–60 min through natural convection and airspeed air in the surroundings equaled to zero. Likewise, García-León and Flórez-Solano [20] studied the dynamics and kinet- ics of the brake system with the mathematical calculation of the pedal to simulate the behavior through FEA with the aid of the Solidworks simulation software. The results Fluids 2021, 6, 160 4 of 24

of their simulations showed that the geometry of the ventilation blades is an essential point for the design of disc brakes. García -León and Flórez-Solano [21] analyzed under different theories of heat transfer the evacuation of the heat to the surroundings (air) for three different disc brakes. The brake discs work under two types of movement, rotational and translational. The first is generated by the engine and transmitted by the axles to the wheels, and the second is the movement that the vehicle creates when moving. Therefore, different types of heat transfer by convection occur at the same time. Using CFD in the Solidworks simulation software, the distribution of heat transfer by convection in a disc rotating at high temperature through a horizontal airflow duct was studied, obtaining the behavior of the speed and temperature inside the ventilation blades, along with the geometry of the three brake discs. On the other hand, García-León et al. [22] proposed a new geometric arrangement to improve airflow in a vehicular disc brake, considering the ventilation blades based on NACA 66–209 type aerodynamic profiles. To validate this design proposal, they constructed a 1:1 prototype with the aid of additive manufacturing. To calculate the speed field produced in the suction and discharge area, they designed a structure for the disc and a particle image velocimetry (PIV), the speed field produced in the suction and discharge areas. The validation of this geometric design was developed under five levels for the angular velocity: 541, 641, 741, 841, and 941 rpm. These are proportional to the linear speeds of the vehicle at 60, 70, 80, and 90 km/h. Numerical tests were performed with three different quantities of ventilation blades, which were 10, 15, and 20. They proved that a configuration of 20 blades improves heat dissipation [23,24]. A similar study proposed a new geometric arrangement to enhance the airflow in a vehicular disc brake, considering the ventilation pillars based on N-38 type aerodynamic profiles. It was evidenced that as the speed of the vehicle increases, the suction force is greater, that is, the test length is shorter for each one. In addition, for a higher speed, the airflow counteracts the amount of heat generated at the moment of braking, as there is more energy to reduce [25]. Hwang et al. [26] studied the behavior of the disc brake surface temperature during single-stop braking, finding that the temperature rises more in the brake ventilation wall. The results were validated through the 3D model of the ventilated disc brake through a transient thermal analysis. Likewise, the results evidenced the importance of the ventilation blades’ geometry on the performance efficiency during heat dissipation, being compared to experimental results. Volchenko et al. [27] found that one way to increase the forced air and the cooling intensity of the disc pad friction torques during vehicle movement is by increasing the area of the disc brake ventilation blades. Whereas, if the ventilation blade area increases by approximately 20%, the cooling intensity increases by 7 to 10%. On the other hand, different factors are involved in the efficiency of the braking process, such as the amount of energy in the disc, the speed of heat dissipation, the efficiency of the disc geometry, among others. Those can be evaluated by applying mathematical concepts or numerical simulations [2,28]. This study presents the thermal and fluid dynamic behavior of two geometric proposals of automotive disc brakes. There are not enough open investigations reported in the literature about the geometry study of the ventilation blades in the disc brakes and their heat dissipation behavior [29]. The results are analyzed through heat transfer laws, mathematical concepts (conduction and convection phenomena), and the FEA to select a new geometry considering five different disc brake ventilation blades studied by different authors. Finally, the heat generated by friction on the disc brakes is modeled via CFD as a way of designing disc brakes, improving the braking process’s performance, safety and providing a better theoretical basis to evaluate the heat dissipation and the disc fluid dynamic behavior. Fluids 2021, 6, x FOR PEER REVIEW 5 of 25 Fluids 2021, 6, 160 5 of 24

2. Materials and Methods 2. Materials and Methods 2.1.2.1. Auto-Ventilated Auto-Ventilated Disc Disc Brake Brake ThisThis type type of of disc disc has has radial radial channels channels in in the the middle middle of of the the friction friction surfaces. surfaces. In Insuch such a waya way that that an an air air current current is isproduced produced in in the the middle middle of of the the frictional frictional area area to to improve improve the the dissipationdissipation of of the heatheat generatedgenerated during during breakings. breakings. These These discs discs can can be be used used on theon the front front and andrear rear wheels wheels as they as they are designed are designed to withstand to withstand up to 700up ◦toC. 700 If the °C. vehicle If the vehicle has ventilated has venti- and latedsolid and discs, solid the discs, ventilated the ventilated ones will beones located will be on located the front on axle the sincefront theaxle most since signiﬁcant the most significantbraking force braking falls onforce them falls [5 on]. them [5]. TheThe brake brake disc disc is is formed formed by by a a round round shape shape with with a a large large surface surface that that is is exposed exposed and and ventilated.ventilated. This This enables enables successive successive cooling cooling and and therefore therefore allows allows all all the the heat heat produced produced causedcaused by by friction friction to to be be dissipated. dissipated. Figure Figure 1 shows the main parts of a disc brake.

FigureFigure 1. 1. PartsParts of of an an auto-ventilated auto-ventilated disc disc brake. brake. Source: Source: [5]. [5].

GrayGray cast cast iron iron receives receives its its name name for for the the appearance appearance of of its its fracture fracture surface, surface, which which is is graygray in in color. color. Carbon Carbon is is commonly commonly found found in in the the form form of of lamellar lamellar graphite graphite and and usually usually containscontains approximately approximately 11 toto 3.8%3.8% silicon. silicon. In In pearlite pearlite gray gray cast cast irons, irons, the the carbon carbon is combined is com- binedto produce to produce cementite cementite and the and free the part free in part the in form the ofform graphite. of graphite. It should It should be noted be thatnoted in thatpractice in practice it is too it difficult is too difficult to obtain to castingsobtain castings in which in all which the carbon all the iscarbon manifested is manifested in the form in theof graphite.form of graphite. Gray cast Gray iron cast differs iron fromdiffers steel from because steel because there arethere graphite are graphite inclusions inclusions on its onstructure its structure with extensivewith extensive variations variations in quantity, in quantity, shape, shape, size, andsize, distribution. and distribution. This givesThis givesrise to rise different to different gray castgray iron cast that iron is that a composite is a composite material material of graphite of graphite with a with matrix a matrix that is thatregularly is regularly composed composed of cementite of cementite and ferrite and ferrite [30]. [30]. TheThe mechanical, mechanical, physical, physical, and and thermal thermal properti propertieses of gray cast iron to perform mathe-math- matical and numerical calculations are summarized in Table1. ematical and numerical calculations are summarized in Table 1. Table 1. Main mechanical, physical, and thermal properties of nodular gray cast iron. Table 1. Main mechanical, physical, and thermal properties of nodular gray cast iron. Property Symbol Magnitude Property Symbol Magnitude Brinell hardness H 170–250 Brinell hardness H 170–250 Shear strength G 151 MPa ImpactShear resistance strength J G 2.0 151 J/mm MPa2 CoefficientImpact of friction resistance µ J 2.00.30–0.50 J/mm2 ThermalCoefficient conductivity of friction k µ 41–57 0.30–0.50 W/m × K 10.5 µm/m between 0–100 ◦C ThermicThermal dilatation conductivity coefficient - k 41–57 W/m × K 13 µm/m between 0–500 ◦C Melting point P10.5 µm/m 1130–1250 between◦C 0–100 °C Thermic dilatation coefficient - ◦ Specific heat Cp 13 µm/m434–460 between J/Kg 0–500C °C VolumetricMelting mass density point ρ P 7250–8131 1130–1250 Kg/m °C 3 α × 6 2 ThermalSpecific diffusivity heat Cp 11.60 434–46010 J/Kgm /s°C Thermal transmission J 3 Volumetric mass density U ρ 7250–813132 Kg/m◦ coefficient m2×s× C Thermal diffusivity α 11.60 ×10 m2/s Source: [14,31–33]. 32 Thermal transmission coefficient U ×× ° Source: [14,31–33]. Fluids 2021, 6, 160 6 of 24 Fluids 2021, 6, x FOR PEER REVIEW 6 of 25 FluidsFluids 2021 2021, 6,, x6 ,FOR x FOR PEER PEER REVIEW REVIEW 6 of6 of25 25 Fluids Fluids 20212021,, 66,, xx FORFOR PEERPEER REVIEWREVIEW 66 ofof 2525 Fluids 2021, 6, x FOR PEER REVIEW 6 of 25 Fluids 2021, 6, x FOR PEER REVIEW 6 of 25

2.2.2.2. Disc2.2. Disc Brakes Disc Brakes Brakes Geometry Geometry Geometry 2.2.2.2.2.2. DiscDisc Disc BrakesBrakes Brakes GeometryGeometry Geometry 2.2. DiscTableTable Brakes 2 shows2 shows Geometry the the geometries geometries of of the the disc disc brakes studiedstudied togethertogether with with the the specifications specifica- 2.2. DiscTableTable Brakes 2 shows2 showsGeometry the the geometries geometries of of the the disc disc brakes brakes studied studied together together with with the the specifica- specifica- TableusedTable in 22 shows theshows mathematical thethe geometriesgeometries and numericalofof thethe discdisc analysis. brakesbrakes studiedstudied togethertogether withwith thethe specifica-specifica- tionstions usedTable used in in 2the shows the mathematical mathematical the geometries and and numerical ofnumerical the disc analysis. brakesanalysis. studied together with the specifica- tionstionstionsTable usedused used in2in shows in thethe the mathematicalmathematical mathematicalthe geometries andand and of numericalnumerical numericalthe disc brakesanalysis.analysis. analysis. studied together with the specifications used in the mathematical and numerical analysis. tions Tableused 2.in Geometriesthe mathematical and specifications and numerical of the studiedanalysis. disc brakes. TableTable 2. 2.Geometries Geometries and and specifications specifications of ofthe the studied studied disc disc brakes. brakes. TableTableTable 2.2. Geometries2.Geometries Geometries andand and specificationsspecifications specifications ofof of thethe the studiedstudied studied discdisc disc brakes.brakes. brakes. Disc IsometricTableTable View 2. Geometries2. Geometries and and specifications specifications X-ray of Viewofthe the studied studied disc disc brakes. brakes. Specifications DiscDisc IsometricIsometric View View X-rayX-ray View View Specifications Specifications DiscDiscDisc IsometricIsometricIsometric ViewView View X-rayX-rayX-ray ViewView View Specifications Specifications Specifications Disc Isometric View X-ray View D = 0.2362 Specifications m Disc Isometric View X-ray View DD== 0.2362 Specifications 0.2362 m m D DD=External= 0.2362 0.2362= m0.2362 m m DD == 0.2362 0.2362 m m D D=D= 0.1352 0.1352= 0.2362= m0.1352 m m m DD== 0.1352=Inner 0.1352 0.2362 m mm DD== 0.1352 0.1352 mm D=D= 0.0598Bell 0.1352= 0.0598 m m m DD=== 0.0598 0.1352 0.0598 m m m DD== 0.0598 0.0598= m m DD == 0.0598E 0.0598Disc m0.0154 m m 11 DE ED== 0.05980.0154 0.05980.0154 m m 1 1 EE== 0.0154EBell 0.0154= m0.0224 m m 11 1 E= 0.0154 m 1 E == 0.0224 0.0154 mm 1 EE== 0.0224=0.0154N 0.0224 0.0154Blade m=m m 30m 1 EE== 0.0224 0.0224 m m EE == 0.0224 0.0224 m m N NE=30==30 0.0224 m NEN==30 0.0224=30 m NN=30=30 N =30Rim designation: 195/65/R-15 NRim=30Rim designation: designation: 195/65/R-15 195/65/R-15 RimRim designation: designation: 195/65/R-15 195/65/R-15 RimRim designation: designation: 195/65/R-15 195/65/R-15 RimRim designation: designation: 195/65/R-15 195/65/R-15 D = 0.254 m DD== 0.254 0.254 m m D DD== 0.254 0.254= m 0.254 m m DD =External= 0.254 0.254 m m D D== 0.1226 0.1226= 0.254 m m m DD=D= 0.1226=Inner 0.1226 0.254= m 0.1226m m m DD== 0.1226 0.1226 mm D=D= 0.0838 0.1226= 0.0838 m m m DD=== 0.0838= 0.1226 0.0838Bell 0.1226 m m m m DD== 0.0838 0.0838 m m DD == 0.0838E 0.0838Disc = m0.0175 m m E ED== 0.0175 0.08380.0175 m m 2 22 EDE== 0.08380.0175E 0.0175= m0.0158 m m 2 2 EE== 0.0175 0.0175Bell mm 2 E == 0.0158 0.0175 mm 2 EE== 0.0158=0.0175N 0.0158 0.0175 m=m m 36m 2 EE== 0.0158 0.0158Blade m m EE == 0.0158 0.0158 m m N NE=36==36 0.0158 m NEN==36 0.0158=36 m NN=36=36 N =36 N=36 Rim designation: 205/70/R-15 Rim designation: 205/70/R-15 RimRim designation: designation: 205/70/R-15 205/70/R-15 RimRim designation: designation: 205/70/R-15 205/70/R-15 D RimRim designation:= designation: 0.3001 m 205/70/R-15 205/70/R-15 DD== 0.3001 0.3001 m m D DD== 0.3001 0.3001= m0.3001 m m DD =External= 0.3001 0.3001 m m D D== 0.1801 0.1801= 0.3001 m m m DD=D= 0.1801=Inner 0.1801 0.3001= m0.1801 mm m DD== 0.1801 0.1801 mm D=D= 0.1001 0.1801= 0.1001 m m m DD=== 0.1001 0.1801 0.1001Bell m m m DD== 0.1001 0.1001 m m DD == 0.1001E 0.1001Disc = m0.0283 m m 3 E ED== 0.0283 0.10010.0283 m m 3 33 EDE== 0.10010.0283 0.0283= m m 33 3 EE== 0.0283 0.0283EBell mm0.0152 m 3 E == 0.0152 0.0283 mm 3 3 EE== 0.0152=0.0283N 0.0152 0.0283 m=m m 24m EE== 0.0152 0.0152Blade m m EE == 0.0152 0.0152 m m N NE=24==24 0.0152 m NEN==24 0.0152=24 m NN=24=24 N =24Rim designation: 275/60/R-18 NRim=24Rim designation: designation: 275/60/R-18 275/60/R-18 RimRim designation: designation: 275/60/R-18 275/60/R-18 RimRim designation: designation: 275/60/R-18 275/60/R-18 D DRimRim= designation:= 0.3473 designation: 0.3473 m m 275/60/R-18 275/60/R-18 DD== 0.3473 0.3473 m m DD== 0.3473 0.3473 mm DD=External 0.2217= 0.3473= m0.3473 m m DD=== 0.2217 0.2217= 0.3473 0.3473 m mm m DD== 0.2217 0.2217 m m DD =D= 0.2217Inner 0.2217= m0.2217 m m D D== 0.085= 0.085 0.2217 m m m DD=== 0.085D 0.2217 0.085 =m 0.085mm m DD== 0.085 0.085Bell mm ED = 0.0850.006 m 4 4 DEE== 0.0850.006EDisc 0.006 =m 0.006m m 4 4 EE== 0.006 0.006 m m 44 4 EE == 0.006 0.006= m m 4 E E== 0.028=E 0.028Bell 0.006 m 0.028 mm m 4 EE=== 0.028 0.006 0.028 mm m EE== 0.028 0.028N mm= 20 NE ==20 0.028Blade m ENNE==20= 0.028=20 0.028 m m NN=20=20 NN =20=20 N N=20=20 RimRim designation: Rimdesignation: designation: 275/30/R-19 275/30/R-19 275/30/R-19 RimRimRim designation:designation: designation: 275/30/R-19275/30/R-19 275/30/R-19 Rim designation: 275/30/R-19 D DRimRim=0.36 designation:=0.36 designation: m m 275/30/R-19 275/30/R-19 DD=0.36=0.36 m m DD=0.36=0.36 mm D=0.26=0.36 m m DD=0.26=0.26=0.36=0.36 m mm m DD=0.26D=0.26External m m= 0.36 m DD =0.26=0.26 m m D D== 0.20D=0.26 0.20 m m= m 0.26 m DD==0.26= 0.20 0.20Inner m m m DD== 0.20 0.20 mm ED =D 0.200.024Bell = m 0.20m m DEED== 0.200.024 0.200.024 m m m m 5 5 E E== 0.024 0.024 m m 5 5 EE == 0.024EDisc 0.024= m 0.024m m 5 E E== 0.022= 0.022 0.024 m mm 55 EE=== 0.022 0.024E 0.022 = mm 0.022 m m 5 EE== 0.022 0.022Bell mm NE ==26 0.022 m ENNE==26= 0.022N=26 0.022Blade m = m26 NN=26=26 NN =26=26 N N=26=26 RimRim designation: designation: 215/60/R-17 215/60/R-17 RimRimRim designation:designation: designation: 215/60/R-17215/60/R-17 215/60/R-17 Rim Rimdesignation: designation: 215/60/R-17 215/60/R-17 Source:Source: Disc Disc brake brake 1 (Renault), 1 (Renault), Disc Disc brak brake 2e (Toyota), 2 (Toyota), Disc Disc brake brake 3 (Mitsubishi), 3 (Mitsubishi), Disc Disc brake brakeRim 4 (Naca/66-209), 4 designation: (Naca/66-209), and 215/60/R-17 and Disc Disc brake brake Source:Source:Source: DiscDisc Disc brakebrake brake 11 (Renault), (Renault),1 (Renault), DiscDisc Disc brakbrak brakee 22e (Toyota), (Toyota),2 (Toyota), DiscDisc Disc brakebrake brake 33 (Mitsubishi), (Mitsubishi),3 (Mitsubishi), DiscDisc Disc brakebrake brake 44 (Naca/66-209), (Naca/66-209),4 (Naca/66-209), andand and DiscDisc Disc brakebrake brake 5 (double5Source: (double blade).Disc blade). brake Source: Source: 1 (Renault), [11,19,34]. [11,19,34]. Disc brake 2 (Toyota), Disc brake 3 (Mitsubishi), Disc brake 4 (Naca/66-209), and Disc brake 5Source: (double5 (doubleSource: Disc blade). blade). Discbrake brakeSource: 1 Source: (Renault), 1 (Renault), [11,19,34]. [11,19,34]. Disc Disc brak brakee 2 (Toyota), 2 (Toyota), Disc Disc brake brake 3 (Mitsubishi), Disc Disc brake brake 4 (Naca/66-209),4 (Naca/66-209), and and Disc Disc brake brake 5 (double 5 (double5 (double blade). blade). Source: Source: [11,19,34]. [11,19,34]. 5 (double5 (doubleblade). blade). Source:blade). Source: [11Source:,19,34 [11,19,34].]. [11,19,34]. Fluids 2021, 6, 160 7 of 24

2.3. Mathematical Calculations The dynamic and thermal analysis of the brake system was made starting from the calculation of the particles in motion to later determine operating conditions based on the mass of the vehicles and the geometries of the disc brakes. The mathematical calculations and the theories of heat transfer were considered as proposed by Garcia-León et al. [20,21,35]. The braking force is the one that the driver exerts on the brake pedal to stop the vehicle. The efficiency of that process depends on the force applied to the pedal. In many cases the driver cannot exert enough force to stop the vehicle at the ideal distance; so, the force is multiplied through levers or hydraulic circuits to obtain a greater friction force. During real braking conditions, it is difficult to achieve the maximum braking force on all four wheels of the vehicle simultaneously due to the weight distribution on the vehicle (affected by passengers, road inclination, undulations, among others), and this determines its limit of adhesion that varies dynamically during the braking process. The weight distribution on the wheels is not constant, and the operating conditions change every fraction of a second. On the other hand, the conditions of mathematical and experimental calculations are considered suitable. The kinetic and potential energy of the vehicle generates the power of the system, which is transformed into thermal energy generated by the operating conditions. The energy accumulated in the disc brake in the form of heat due to the friction between the brake and the pad must be dissipated as quickly as possible to avoid overheating. The heat transfer rate depends on the geometry of the disc brake, its material, and the operating conditions. The heat generated must be evacuated as quickly as possible so repetitive braking does not generate high temperatures that could lead to reduced efficiencies and lower safety in the braking process. The vehicle displacement aids the heat dissipation through the phenomena of convection and radiation. The braking efficiency is the magnitude of the braking system performance, where the vehicle must stop at a required time and distance, according to the operating conditions and the force applied on the brake pedal. The efficiency of the braking system is considered to reach 100% when the measured deceleration is equal to the acceleration due to gravity (9.8 m/s2). During the braking process, the disc absorbs approximately 90% of the wheel energy and the pad absorbs 10%, according to theoretical assumptions [1,12]. In this way, Equation (1) was used to calculate the total energy in the disc brake.

ETotal in disc = EEach disc × 0.9 (1)

The rise in temperature of a brake assembly is mathematically governed by Equation (2), and to calculate the temperature on the surface of the disc, Equation (3) was used [8].

E ∆T = Disc brake (2) mD × Cp

Ti − T∞ = ∆T (3) Equation (4) is known as Newton’s law of cooling, which states that a disc at a temperature Ti (the instantaneous temperature at all times) will cool by natural convection if it is left at room temperature for a particular time. This equation helps to determine the instantaneous temperature until the disc cools down, which will depend on the geometry of the disc brake and its material. The results of the cooling calculation were carried out using the properties summarized in Table1.

− A×U ×t m ×Cp Ti − T∞ = (Ti − T∞) × e D (4)

For the calculation of the heat transfer coefﬁcients (h), the disc brake geometries were considered. The thermal convection and transfer coefﬁcients generated on the disc brakes Fluids 2021, 6, x FOR PEER REVIEW 8 of 25

reported by Cengel [36]. The total convection generated during the braking process is a sum of the frontal convection (bell and periphery), lateral convection, rotary effect convection, and ducts convection, based on each disc brake geometry. For these estimations, Equations (5) and (6) were used. K h = ×Nu (5) D

h =h +h +h +h (6) To estimate the convection, the Reynolds number expressed in Equation (7) is used. The automobile speed is 80 km/h ≌ 22.22 m/s, the environment temperature is T∞ = 33 °C, and the diameters of the different disc brakes studied can be found in Table 2 [37]. V × D R = (7) Ʋ Fluids 2021, 6, 160 Frontal convection is performed between braking tracks/bell and the air and 8is of rep- 24 resented as the sum of the peripheral convection (Figure 2a) and the bell convection (Figure 2b) of the disc. To determine the air properties, it was necessary to obtain the average temperature using Equation (8). were calculated for a speed peak of 80 km/h and with common air physical properties reported by Cengel [36]. The total convectionT generated+T during the braking process T = (8) is a sum of the frontal convection (bell and periphery),2 lateral convection, rotary effect convection,The rotary and ducts convection convection, appears based between on each the disc di brakesc brake geometry. and the Forairflow. these Figure estimations, 2c rep- Equationsresents how (5) andthe airflow (6) were convection used. wraps up the disc brake contour, where it develops a K boundary layer that surrounds the disc.h = Air× paNurticles collide with the disc generating (5) an increase in the pressure inside the disc. ToD obtain this calculus, it is necessary to calculate thehTotal Reynolds= hFrontal number convection for+ rotaryhLateral convection convection + usinghRotary Equation effect convection (9). + hDucts convection (6) To estimate the convection, the Reynolds numberD ×ω expressed in Equation (7) is used. ∼ Re = ◦ (9) The automobile speed is 80 km/h = 22.22 m/s, the environmentυ temperature is T∞ = 33 C, and the diameters of the different disc brakes studied can be found in Table2[37]. Lateral convection occurs thanks to the air flux on the disc walls (Figure 2d). In this case, the airflow on the flat plates is studied.V Notice× D that the transmission from laminar to R = (7) turbulent flow depends on the surface’se geometricυ configuration, its roughness, and the fluidFrontal circulating convection on the isdisc. performed The Reynolds between number braking varies tracks/bell along the and stream the air until and it isreaches rep- resentedthe end asof the plate. sum ofIt can the be peripheral considered convection that the transmission (Figure2a) and from the laminar bell convection to turbulent (Figureflow has2b) toof be the given disc. a critical To determine Reynolds the numb air properties,er that is estimated it was necessary using Equation to obtain (7). the averageDuct temperature convection using happens Equation inside (8). the ventilation blades, as shown in the schematic representation in Figure 2e. In this case, the ducts on the disc were considered as non- rounded with two walls. Besides, the geometriesT∞ + T iof the ducts were considered to estimate TP = (8) the inlet and outlet speeds and the angles using2 the theory of radial fans from the book mechanics of fluids and hydraulic machines. (a) (b)

(c)

Fluids 2021, 6, x FOR PEER REVIEW 9 of 25

(d) (e)

FigureFigure 2. (2.a) (a Peripheral) Peripheral convection, convection, (b ()b bell) bell convection, convection, ( c(c)) airair ﬂuxflux onon thethe disc brake brake (rotary (rotary convection), convection), (d (d) )lateral lateral con- convection,vection, and (e) duct convection.

TheIn rotary this way, convection the heat appears transfer between only was the calculated disc brake by and the the convection airﬂow. Figureeffect, 2usingc representsEquations how (10) the and airﬂow (11) respectively convection wraps [38]. up the disc brake contour, where it develops a boundary layer that surrounds the disc. Air particles collide with the disc generating an increase in the pressure inside the disc.Q To=h×A obtain × this(T calculus,−T∝) it is necessary to calculate(10) the Reynolds number for rotary convection using Equation (9). Q =Q +Q +Q (11) The heat dissipation of the disc brakeD 2is× maωinly attributable to the action of the con- Re = (9) vection coefficient. When temperaturesg of atυ least 300 °C are generated in the braking process, the radiation coefficient acts to dissipate the heat. The calculations developed at 80 km/h do not generate enough heat on the braking area for the radiation to act. This also depends on the material properties of the disc brake [39,40].

2.4. Computational Fluid Dynamics (CFD Simulation) The numerical simulations developed in this study consider the interaction of the fluid-disc brake without its rotation, where the air is the same speed as the automobile, and thus perform the CFD analysis in a transient state. Initially, the Solidworks 2017 student version software was used, which is a CAD-3D design program, to design 2D parts and 3D assemblies. Likewise, it provides a complete group of tools to produce, reproduce, and publish, as well as manage data, projects, and processes, and increase innovation and the efficiency of engineering resources. All these solutions work together to allow institutions to design better products quickly and productively [41]. Subsequently, the CAD-3D designs of the disc brakes were imported into AN- SYS/2020-R2 student version software, which was used for the design, analysis, and simulation of parts through FEA and CFD, performing the stages of execution of the simulations shown in Figure 3. In order to solve the mechanical problems, this graphic interface processor includes, for the development of this research, heat and mass transfer analysis [42].

(a) The properties 1. Pre- Creation of the Mesh and time of the material model. independence processing are established.

2. Assignment of Acquisition of experimental the problem Processing parameters. solution.

Obtaining and 3. Post- Interpretation analyzing of results. processing results.

Fluids 2021, 6, x FOR PEER REVIEW 9 of 25 Fluids 2021, 6, 160 9 of 24

(d) Lateral convection occurs thanks to the air(e) flux on the disc walls (Figure2d). In this case, the airflow on the flat plates is studied. Notice that the transmission from laminar to turbulent flow depends on the surface’s geometric configuration, its roughness, and the fluid circulating on the disc. The Reynolds number varies along the stream until it reaches the end of the plate. It can be considered that the transmission from laminar to turbulent flow has to be given a critical Reynolds number that is estimated using Equation (7). Duct convection happens inside the ventilation blades, as shown in the schematic

representation in Figure2e. In this case, the ducts on the disc were considered as non- Figure 2. (a) Peripheral roundedconvection, with (b) twobell convection, walls. Besides, (c) air the flux geometries on the disc of brake the ducts(rotary were convection), considered (d) lateral to estimate convection, and (e) duct convection.the inlet and outlet speeds and the angles using the theory of radial fans from the book mechanics of ﬂuids and hydraulic machines. In thisIn this way, way, the the heat heat transfer transfer only only was was calculated calculated by theby the convection convection effect, effect, using using EquationsEquations (10) (10) and and (11) (11) respectively respectively [38 ].[38].

. Q =h×A ×(T −T∝) (10) Q = h × As × (Ti − T∝) (10) Q =Q +Q +Q (11) Q = Q + Q + Q (11) The heat dissipationTotal of in the disc disc Bellbrake isPeripheral mainly attributableRotary to the action of the con- vectionThe heat coefficient. dissipation When of temperatures the disc brake of at is least mainly 300 attributable°C are generated to the in actionthe braking of the pro- ◦ convectioncess, the coefficient.radiation coefficient When temperatures acts to dissipate of at least the 300heat.C The are calculations generated in developed the braking at 80 process,km/h thedo radiationnot generate coefficient enough acts heat to dissipateon the brak theing heat. area The for calculations the radiation developed to act. This at 80 also km/hdepends do not on generate the material enough properti heat ones of the the braking disc brake area [39,40]. for the radiation to act. This also depends on the material properties of the disc brake [39,40]. 2.4. Computational Fluid Dynamics (CFD Simulation) 2.4. Computational Fluid Dynamics (CFD Simulation) The numerical simulations developed in this study consider the interaction of the The numerical simulations developed in this study consider the interaction of the fluid-disc brake without its rotation, where the air is the same speed as the automobile, fluid-disc brake without its rotation, where the air is the same speed as the automobile, and and thus perform the CFD analysis in a transient state. Initially, the Solidworks 2017 stu- thus perform the CFD analysis in a transient state. Initially, the Solidworks 2017 student dent version software was used, which is a CAD-3D design program, to design 2D parts version software was used, which is a CAD-3D design program, to design 2D parts and 3D and 3D assemblies. Likewise, it provides a complete group of tools to produce, reproduce, assemblies. Likewise, it provides a complete group of tools to produce, reproduce, and and publish, as well as manage data, projects, and processes, and increase innovation and publish, as well as manage data, projects, and processes, and increase innovation and the the efficiency of engineering resources. All these solutions work together to allow institu- efficiency of engineering resources. All these solutions work together to allow institutions tions to design better products quickly and productively [41]. to design better products quickly and productively [41]. Subsequently, the CAD-3D designs of the disc brakes were imported into AN- Subsequently, the CAD-3D designs of the disc brakes were imported into ANSYS/2020- SYS/2020-R2 student version software, which was used for the design, analysis, and sim- R2 student version software, which was used for the design, analysis, and simulation of ulation of parts through FEA and CFD, performing the stages of execution of the simula- parts through FEA and CFD, performing the stages of execution of the simulations shown in Figuretions shown3. In order in Figure to solve 3. In the order mechanical to solve the problems, mechanical this problems, graphic interface this graphic processor interface includes,processor for theincludes, development for the devel of thisopment research, of heatthis research, and mass heat transfer and analysismass transfer [42]. analysis [42].

(a) The properties 1. Pre- Creation of the Mesh and time of the material model. independence processing are established.

2. Assignment of Acquisition of experimental the problem Processing parameters. solution.

Obtaining and 3. Post- Interpretation analyzing of results. processing results.

Figure 3. Cont. Fluids 2021Fluids, 6, 2021x FOR, 6 ,PEER 160 REVIEW 10 of 25 10 of 24

(b)

Figure 3. a b Figure 3. (a) Stages( ) of Stages finite of element finite element analysis analysis in Computational in Computational Fluid Fluid Dynamics Dynamics (CFD) (CFD) and and(b) ( ) method. method.Source: Source: [5 [5].]. Ansys Flow Simulation solves the Navier–Stokes equations, which are formulations of Ansys Flow Simulation solves the Navier–Stokes equations, which are formulations the laws of conservation of mass, momentum, and energy and are presented below [43,44]. of the laws of conservation of mass, momentum, and energy and are presented below Three-dimensional models of the disc brake and fluid domain (air) were constructed to [43,44]. Three-dimensional models of the disc brake and fluid domain (air) were con- develop the CFD cooling analysis. FLUENT was used to solve the equations of continuity, structed to develop the CFD cooling analysis. FLUENT was used to solve the equations of momentum, and energy for pressure and velocity coupling. The turbulent model was continuity, momentum, and energy for pressure and velocity coupling. The turbulent solved based on the Reynolds-Averaged Navier–Stokes equations (RANS) approach with model was solved based on the Reynolds-Averaged Navier–Stokes equations (RANS) ap- an achievable k-ε model, which is a variant of the standard k-ε model. The continuity and proach with an achievable k-ε model, which is a variant of the standard k-ε model. The moment expressions are described according to energy Equations (12) and (13), used to continuity and moment expressions are described according to energy Equations (12) and calculate the high-velocity incompressible flows and ripple flow: (13), used to calculate the high-velocity incompressible flows and ripple flow: ∂ρ ∂(ρu ) ∂ρ ∂(ρu+) i = 0 (12) + ∂t =∂x 0 (12) ∂t ∂x i → h ∂u i ∂ ∂ ∂ ∂ ∂p ∂∂p ∂u ∂ ∂u ∂ui2 ∂uj 2 ∂u∂l ∂ 0 0 (ρui) + ρuiuj = − + ρg + µ + − δij + − ρu iu j (13) (ρu) + ∂ρut u=−∂xj +ρg⃗ + ∂xi μ ∂+xj −∂xj δ∂xi 3 +∂xl −ρu∂xju (13) ∂t ∂x ∂x ∂x ∂x ∂x 3 ∂x ∂x In this case, the density is a function of the temperature according to the ideal gas law. The Inrealizable this case, k- theε turbulent density is model a function is given of by the the temperature transport expressions according for to thethe turbulentideal gas kinetic law. Theenergy realizable (k) and k- theε turbulent turbulent model dissipation is given rate by (ε), the respectively transport byexpressions Equations for (14) the and tur- (15): bulent kinetic energy (k) and the turbulent dissipation rate (ε), respectively by Equations " # (14) and (15): ∂ ∂ ∂p µ ∂k (ρk) + ρku = µ + t + G + G − ρε − Y + S (14) ∂t ∂x j ∂x σ ∂x k b M k ∂ ∂ j ∂p j μ ∂kk j (ρk) + ρku = μ + +G +G −ρε−Y +S (14) ∂t ∂x ∂x σ ∂x h i 2 ∂ ∂ ∂p µt ∂ε ε ε (ρε) + ρεu = µ + + ρC Sε − ρC √ + C ε C3εG + Sε (15) ∂t ∂xj j ∂xj σε ∂xj 1 2 k+ νε 1 k b ∂ ∂ ∂p μ ∂ε ε ε (ρε) + ρεu= μ + +ρCS −ρC +C CG +S (15) ∂t where:∂x ∂x σ ∂x k+√νε k η k q C = max 0.43, , η = S ,S = 2S S (16) where: 1 η + 5 ε ij ij Additional details of the realizableη k-ε modelk and parameters using the above equa- C =max0.43, ,η=S ,S=2S S (16) tions can be found in [45]. To obtainη+5 the temperatureε field, the energy equation was solved as presented in Equation (17): Additional details of the realizable k-ε model and parameters using the above equations can be found in [45]. To obtain the temperature field, the energy" # equation was solved ∂ ∂ ∂ ∂T as presented in Equation (17): ρCpT + (ρuih) = λ (17) ∂t ∂xi ∂xj ∂xj ∂ ∂ ∂ ∂T λ ρCT + (ρuh) = λ λ (17)λ λ where is the thermal∂t conductivity,∂x which for∂x the fluid∂x domain becomes + t, and t is the turbulent thermal conductivity. Likewise, the temperature distribution in the disc where brakeλ is the was thermal obtained conductivity, by solving which Equations for the (12)–(17). fluid domain becomes λ + λt, and λt is the turbulentThe thermal boundary conductivity. conditions wereLikewise, established the temperature as follows according distribution to the in analytical the disc model. brake was obtained by solving Equations (12)–(17). T Specified disc surface temperature ST × T = T*. Heat flux entering the disk SQ: [Q ][n] = −Q*. Fluids 2021, 6, x FOR PEER REVIEW 11 of 25

Fluids 2021, 6, 160 The boundary conditions were established as follows according to the analytical11 of 24 model. Specified disc surface temperature ST × T = T*. Heat flux entering the disk SQ: [QT][n] = −Q*. Specified convection on the surface of the disc SC: [QT][n] = h (TS − TF). Where ST is the surface temperature, T is the temperature, T* is the specific surface temperature, T SpecifiedSQ is the surface convection heat, onQ* theis the surface surface-specific of the disc heat, SC: [QSC is][n] the = disc h (T surfaceS − TF convection,). Where S Th isis thethe surfaceconvection temperature, coefficient T of is the the air, temperature, TS is the surface T* is the temperature, specific surface and T temperature,F is the fluid Stem-Q is theperature. surface heat, Q* is the surface-specific heat, SC is the disc surface convection, h is the convectionThe initial coefficient conditions of the for air, the TS issimulations the surface ar temperature,e the speed and(80 km/h), TF is the the fluid air temperature temperature. (33 °CThe and initial T(x,y,z) conditions = 100 K), for the the disc simulations brake surface are the temperature, speed (80 km/h), and a the disc air without temperature rota- ◦ (33tion.C Surface and T(x,y,z) temperatures = 100 K), are the shown disc brake in Table surface 4, and temperature, considerations and a discin Section without 3.2. rotation. Surface temperatures are shown in Table 4, and considerations in Section 3.2. 2.5. Grid Type 2.5. Grid Type For the transient-state simulations, a tetrahedral mesh was selected in the computa- For the transient-state simulations, a tetrahedral mesh was selected in the computational domain of the fluid (Figure 4). This mesh has a more significant number of elements tional domain of the fluid (Figure4). This mesh has a more significant number of elements compared to the polyhedral type [46]. The grid was adjusted to the unstructured solid compared to the polyhedral type [46]. The grid was adjusted to the unstructured solid through the construction of nodes distributed in an irregular way. In addition, with this through the construction of nodes distributed in an irregular way. In addition, with this type of mesh, it is much easier to perform complex structures, achieving more efficiency type of mesh, it is much easier to perform complex structures, achieving more efficiency in in computational time when performing the respective numerical analyzes on the disc computational time when performing the respective numerical analyzes on the disc brakes. brakes.

FigureFigure 4.4. MeshMesh typetype used used in in the the simulation. simulation. (a ()a Initial) Initial and and boundary boundary conditions, conditions, and and (b) ( meshb) mesh used. used. Source: Source: own own elaboration. elaboration. 2.5.1. Mesh Independence Study 2.5.1.In Mesh Figure Independence5 the mesh independence Study study is presented. The fluid exit temperature of the computationalIn Figure 5 the domain mesh independence was evaluated study for 500,000is presented. elements. The fluid It was exit observed temperature that inof orderthe computational to obtain an errordomain of less was than evaluated 5%, the for mesh 500,000 must elements. have from It 450,000was observed to 500,000 that ele- in ments.order to Moreover, obtain an the error air of outlet less temperaturethan 5%, the and mesh velocity must have are not from influenced 450,000 byto the500,000 number ele- ofments. elements Moreover, in the meshthe air for outlet a number temperature of 450,000 and to velocity 500,000 are elements. not influenced by the number of elements in the mesh for a number of 450,000 to 500,000 elements. 2.5.2. Independence of Time In Figure6 the temperature behavior as a function of the data points and the time behavior for each disc brake is observed, where the different sections of the discs were measured. On the other hand, it was confirmed that the temperature does not change as a function of time, ranging from 1, 0.1, and 0.01 s. Considering the results obtained from the time step not varies using whatever time step (1, 0.1, and 0.01 s, presented the same behaviors in the plot), for this reason, 0.1 s was selected to perform the simulations of the thermal behavior and fluid dynamic behavior. Notice that the simulation was configured under the following parameters: 0.1 s of the time step, 1200 time step number, and 500 maximum interactions by time step. With these parameters, the total time of Fluids 2021, 6, 160 12 of 24

Fluids 2021, 6, x FOR PEER REVIEW 12 of 25 simulation was 120 s. With time independence, the aim is to ensure that the results are reliable for the different time intervals used depending on the number of elements.

Fluids 2021, 6, x FOR PEER REVIEW 13 of 25

FigureFigure 5.5. MeshMesh independenceindependence study study for for the the disc disc brakes brakes outlet outlet air temperature.air temperature. Source: Source: own own elaboration. elaboration.

2.5.2. Independence of Time In Figure 6 the temperature behavior as a function of the data points and the time behavior for each disc brake is observed, where the different sections of the discs were measured. On the other hand, it was confirmed that the temperature does not change as a function of time, ranging from 1, 0.1, and 0.01 s. Considering the results obtained from the time step not varies using whatever time step (1, 0.1, and 0.01 s, presented the same behaviors in the plot), for this reason, 0.1 s was selected to perform the simulations of the thermal behavior and fluid dynamic behavior. Notice that the simulation was configured under the following parameters: 0.1 s of the time step, 1200 time step number, and 500 maximum interactions by time step. With these parameters, the total time of simulation was 120 s. With time independence, the aim is to ensure that the results are reliable for the different time intervals used depending on the number of elements.

FigureFigure 6. 6. TimeTime independence independence for for brakes brakes ( a)) Disc Disc 1, 1, ( (bb)) Disc Disc 2, 2, ( (cc)) Disc Disc 3, 3, ( (dd)) Disc Disc 4, 4, and and ( (ee)) Disc Disc 5. 5. Source: Source: own own elaboration. elaboration.

3.3. Results Results and and Discussions Discussions ForFor the the development development of ofthe the numerical numerical model, model, heat heat transfer transfer equations equations were wereused, used,con- sideringconsidering parameters parameters such such as braking as braking time, time, vehicle vehicle speed, speed, geometries geometries and and dimensions dimensions of theof thebrake brake components, components, the disc the brake disc brakerotor materials, rotor materials, and the anddistribution the distribution of pad and of con- pad tactand pressure. contact pressure. The results The show results a heat show split a heat at the split contact at the surface contact of surface two sliding of two compo- sliding nentscomponents due to thermal due to thermal resistance. resistance. This happens This happens because because of the accumulation of the accumulation of wear of parti- wear cles between the contact surfaces. This phenomenon prevents the discs from absorbing more heat and makes the brake lining hot [47].

3.1. Mathematical Results of Heat Transfer Each of the proposed equations were developed considering the theories of heat transfer. Table 3 summarizes the calculation of the total energy in the disc brake, the heat generated during braking, and the rate of overall heat loss in the disc and the ducts using Equations (1)–(11). For the value of QTotal in disc, the rate of heat loss in the bell, the periphery, and the rotating effect of each disc brake were considered. The same considerations were taken for the convection coefficient. Notice that the disc brake geometry affects all those variables, but it affected E in a greater way. It means that a big disc brake provides better performance during the braking process and thus improves heat dissipation, but it will depend on the blade type. These results agree with those presented by [38,48], which concluded that the type of the pad and frequency of braking also affects the braking process during wear with the disc. In addition, convective values are between 0 and 100 W/m2 × K [49]. It is worth noting that the behavior and Q values of the disc brake ducts have not been reported. In addition, the total Q in the ducts is less than the total Q in a disc brake. Thus, there is a correspondence with the theories related to heat transfer.

Fluids 2021, 6, 160 13 of 24

particles between the contact surfaces. This phenomenon prevents the discs from absorbing more heat and makes the brake lining hot [47].

3.1. Mathematical Results of Heat Transfer Each of the proposed equations were developed considering the theories of heat transfer. Table3 summarizes the calculation of the total energy in the disc brake, the heat generated during braking, and the rate of overall heat loss in the disc and the ducts using Equations (1)–(11). For the value of QTotal in disc, the rate of heat loss in the bell, the periphery, and the rotating effect of each disc brake were considered. The same considerations were taken for the convection coefﬁcient. Notice that the disc brake geometry affects all those variables, but it affected E in a greater way. It means that a big disc brake provides better performance during the braking process and thus improves heat dissipation, but it will depend on the blade type. These results agree with those presented by [38,48], which concluded that the type of the pad and frequency of braking also affects the braking process during wear with the disc. In addition, convective values are between 0 and 100 W/m2 × K[49]. It is worth noting that the behavior and Q values of the disc brake ducts have not been reported. In addition, the total Q in the ducts is less than the total Q in a disc brake. Thus, there is a correspondence with the theories related to heat transfer.

Table 3. Mathematical results of disc brake heat transfer.

Variable Disc 1 Disc 2 Disc 3 Disc 4 Disc 5 E (J) 102,188.97 159,278.04 183,879.84 158,160.77 237,443.24 Total in disc W 212.89 220.84 207.88 191.48 285.14 hTotal m2×◦C Q W/m2 × 106 1.5881 2.4754 2.8577 2.4417 3.6992 QTotal in disc (W) 94.11 132.39 174.77 159.15 229.46 QDuct (W) 1.9204 1.6723 1.8218 3.7197 1.1496 QTotal in ducts (W) 57.61 60.20 43.72 74.39 29.89 Angular speed (rad/s) 70 66.79 57.45 68.77 102.60 Source: own elaboration. According to Lakkam et al. [40], a surface temperature of at least 300 ◦C on the disc brake increases with the pressure applied during the braking process at a speed of 80 Km/h, and changes with the operational conditions of the automobile such as weight, speed, tire and roadway conditions. However, the heat generated during the braking process is approximately 5.4% higher because the braking time in this research is shorter (around ~2.38 s for all discs), and the energy dissipated in the disc is smaller (Table3). On the other hand, the rate of heat loss inside the ventilation ducts had an increase of 9%, compared to that calculated by García- León [19]. This happens because the characteristics of the ventilation ducts are similar and the assumed and ambient temperature is 13 ◦C higher, affecting the values of the air properties and therefore the Reynolds number, which consequently affects the calculation of the convective coefﬁcient, which depends on the car capacity and the geometry of the disc brake. The angular speed is higher (between 57 to 102 rad/s) on the disc brake which depends on the tire characteristic and designation (width, radius and others), which aids the process of heat dissipation to the environment by natural convection [6]. Similar results to Echavez-Díaz and Quintero-Orozco were found [34]. Table4 summarizes the temperature results on the surface of the discs using Equations (4) and (5). Note that the temperature differential between the disc brake and the ambient temperature must be known. This was taken as 33 ◦C for an arid region (Aguachica, Colombia), where the mathematical calculations and numerical simulations were carried out. The temperature difference is 1.1% less and 34% greater than that calculated by [19,34]. It occurs because the mass and total energy in the disc are similar. This indicates that a vehicle with a mass of ~1650 Kg and speed of 80 km/h, circulating in an environment of 33 ◦C, with a friction surface between the disc and the pad, generates a disc brake Fluids 2021, 6, 160 14 of 24

temperature of approximately 84.96 to 119 ◦C to stop the vehicle, obtaining results similar to those found by Topouris, et al. [17] and Lakkam et al. [18].

Table 4. Surface temperature of the disc brakes.

Fluids 2021, 6, x FOR PEER REVIEW Variable Disc 1 Disc 2 Disc 3 Disc 4 Disc15 5 of 25

Ti (◦C) 95 119 102 84.69 110.6 Source: own elaboration. 3.2. Newton’s Newton’s Law of Cooling Results Figure 77 shows the behavior behavior of of the the disc disc br brakesakes under under the the calculations calculations performed performed us- ingusing Equation Equation (4) (4)for for100 100 s intervals. s intervals. Natural Natural convection convection during during heat heat dissipation dissipation from from the brakingthe braking track track is the is sum the sumof the of convection the convection in the in bell the and bell at and the atperiphery the periphery of the disc. of the These disc. resultsThese resultsare based are basedon theon speed the speedlimit allowe limit allowedd in Colombia in Colombia and the and average the average ambient ambient tem- peraturetemperature in the in city the cityof Aguachica, of Aguachica, Colombia. Colombia.

Figure 7. Newton’sNewton’s law law of of cooling cooling for the five-disc ﬁve-disc brakes. Source: own own elaboration. elaboration.

◦ The disc brake will reach an ambient temperature of 33 °CC in around 30 min after being subjected toto thethe differentdifferent temperatures temperatures on on the the surface surface of of the the braking braking track track during during the thefriction friction process process between between the disc the anddisc the and pad. the Itpad. will It happen will happen as long as as long the cooling as the cooling process processoccurs by occurs natural by natural convection, convection, that is, that the airis, inthe the air environmentin the environment must have must a have speed a speed equal equalto zero to [ 1zero,24,50 [1,24,50].]. From FigureFrom Figure6, Disc 6, 2 reachesDisc 2 reaches the environmental the environmental temperature temperature at 6700 at s, 6700while s, the while other the discs other at discs approximately at approximately ~7200 s. ~7200 s. The speed of the vehicle influences influences the kine kinetictic energy that is generated during the movement. It does not affect it linearly but increases its value exponentially. This means movement. It does not affect it linearly but increases its value exponentially. This means that a vehicle of the same weight but twice the speed of another vehicle does not require that a vehicle of the same weight but twice the speed of another vehicle does not require twice the braking force to stop the vehicle, but four times more. Therefore, the stopping twice the braking force to stop the vehicle, but four times more. Therefore, the stopping distance will be longer, as long as the vehicle rides on a flat road [51]. On the other distance will be longer, as long as the vehicle rides on a flat road [51]. On the other hand, hand, the material of the brake pad influences the thermodynamic properties of the disc the material of the brake pad influences the thermodynamic properties of the disc brake, brake, and thus the increase in temperature. However, the material of the disc brake, the and thus the increase in temperature. However, the material of the disc brake, the geom- geometry, and the configuration of the blades are relevant factors in the heat dissipation to etry, and the configuration of the blades are relevant factors in the heat dissipation to the the environment, so they affect the useful life of the brake pad components of the braking environment, so they affect the useful life of the brake pad components of the braking system [39]. system [39]. 3.3. CFD Results of Temperature and Fluid Speed Behavior 3.3. CFD Results of Temperature and Fluid Speed Behavior CFD analyses show the temperature and fluid behavior through colored bars. The temperatureCFD analyses dissipated show duringthe temperature the braking and process fluid behavior and the speedthrough of colored the air insidebars. The the temperatureventilation ducts dissipated are presented during inthe a braking color scale proc whereess and red the represents speed of the the highest air inside trend, the lightven- tilationgreen refers ducts to are an presented intermediate in a value, color scale and dark where blue red represents represents the the lowest highest trend trend, for light both greenvariables. refers The to valuesan intermediate of grind and value, time and independence dark blue represents are similar the to thoselowest reported trend for by both [29]. variables. The values of grind and time independence are similar to those reported by [29]. In this way, Figures 8 and 9 show the heat flow behavior and the airspeed of the five- disc brakes, respectively, using the student version of ANSYS FEA software, which was measured in two time intervals of 0 and 120 s [13]. The mechanical, physical, and thermal properties of lamellar graphite nodular gray cast iron are presented in Table 1.

Fluids 2021, 6, 160 15 of 24

In this way, Figures8 and9 show the heat ﬂow behavior and the airspeed of the ﬁve-disc brakes, respectively, using the student version of ANSYS FEA software, which was measured in two time intervals of 0 and 120 s [13]. The mechanical, physical, and thermal properties of lamellar graphite nodular gray cast iron are presented in Table1.

Disc t = 0 s t = 120 s

Figure 8. Thermal behavior of disc brakes at different time intervals. Source: own elaboration.

Fluids 2021, 6, 160 16 of 24

In the developed simulation, a thermal and fluid dynamic analysis was carried out. In the time intervals used it can be observed that the thermal behavior of Disc 4 is the best as the surface temperature reached 69.1 ◦C. This value decreased after activating the brake system for a time of 120 s. This can be verified by observing the airspeed of ~6.55 m/s in the fluid dynamic analysis (Figure9). Therefore, it can be seen that this is the highest compared to the other speeds of the other discs, checking with the heat dissipation values [16].

Disc t = 0 s t = 120 s

Figure 9. Fluid dynamic behavior of disc brakes at different time intervals. Source: own elaboration.

Fluids 2021, 6, 160 17 of 24

Fluids 2021, 6, x FOR PEER REVIEW 18 of 25

From Table4 and Figure8, the analytically calculated temperature and that obtained by ANSYS FEA software student version are presented. The temperatures in a time of 0 s are 95, 119, 102, 84.69, and 110.6 ◦C, while the ones obtained in the simulation were 101.4, 91.5, 80, and 108 °C. The◦ percentage differences between the temperatures mathe- matically92.9, 101.4, calculated 91.5, 80, and and the 108 onesC. obtained The percentage by numerical differences simulation between are 2.2, the 14.8, temperatures 10.3, 5.5, andmathematically 2.4%, respectively calculated for each and the disc ones brake. obtained This margin by numerical of error simulation is acceptable are 2.2, because 14.8, 10.3,it is 5.5, and 2.4%, respectively for each disc brake. This margin of error is acceptable because it less than 15%. It can be observed that Disc 4 reaches a temperature of 69.1 °C◦ after 120 s ofis lessoperating than 15%. the brake It can system, be observed while that the Discother 4 discs reaches reach a temperature a temperature of 69.1of 76.5,C after79.6, 12077.5, s of operating the brake system, while the other discs reach a temperature of 76.5, 79.6, 77.5, and 108.1 °C, which allows us to deduce that Disc 4 is the optimal disc brake. and 108.1 ◦C, which allows us to deduce that Disc 4 is the optimal disc brake. In the same way, it was determined by simulation that the airspeed values inside the In the same way, it was determined by simulation that the airspeed values inside the ventilation ducts, which are presented in Figure 8, are 4.35, 3.11, 1.91, 6.55, and 5.02 m/s. ventilation ducts, which are presented in Figure8, are 4.35, 3.11, 1.91, 6.55, and 5.02 m/s. This confirms that the highest airspeed inside the ventilation ducts occurs in Disc 4, which This conﬁrms that the highest airspeed inside the ventilation ducts occurs in Disc 4, which causes the temperature to decrease more quickly (see Figure 7). causes the temperature to decrease more quickly (see Figure7). Considering the heat transfer values summarized in Table 3, it was evident that the Considering the heat transfer values summarized in Table3, it was evident that the rate rate of heat dissipated by Disc 2 is higher compared to that of the other discs brakes. It can of heat dissipated by Disc 2 is higher compared to that of the other discs brakes. It can be be explained as Disc 2 reaches a higher surface temperature before and after applying the explained as Disc 2 reaches a higher surface temperature before and after applying the brake brake system, which increases the rate of heat evacuated. On the other hand, the afore- system, which increases the rate of heat evacuated. On the other hand, the aforementioned mentioned results were compared with those calculated analytically by García-León [19], results were compared with those calculated analytically by García-León [19], in which inheat which loss valuesheat loss of values 405.66, of 644.24, 405.66, and 644.24, 595.71 and W are595.71 presented W are inpresented Disc 1, Disc in Disc 2, and 1, Disc Disc 2, 3, andrespectively. Disc 3, respectively. The results The of Disc results 4 were of Disc compared 4 were compared with the results with the of results Echavez-D of Echavez-íaz and DíazQuintero-Orozco and Quintero-Orozco [34], where [34], the where surface the temperature surface temperature was 60.5 ◦ wasC and 60.5 the °C evacuated and the evac- heat uatedrate was heat 337.26 rate was W in337.26 Disc W 4. in In Disc this investigation,4. In this investigation, the surface the temperature surface temperature is 84.69 ◦ isC 84.69and the°C and evacuated the evacuated heat rate heat is 919.95rate is 919.95 W, which W, which represents represents a difference a difference of 28.5 of and28.5 62%,and 62%,respectively. respectively. The contrast The contrast in the in results the results resides resides in the differentin the different values forvalues the surroundingfor the sur- roundingtemperature, temperature, being 20 ◦ Cbeing in the 20 Echavez-D °C in the íazEchavez-Díaz and Quintero-Orozco and Quintero-Orozco research and research 33 ◦C in andthis 33 one. °C Figure in this 10 one. summarizes Figure 10 thesummarizes results obtained the results by CFDobtained for temperature by CFD for andtemperature airspeed. andNotice airspeed. that this Notice ﬁgure that was this obtained figure was with obtained the temperature with the temperature generated by generated the disc by brake the discwhich brake was which calculated was mathematicallycalculated mathematically under ideal under conditions, ideal andconditions, the relationship and the relation- with the shipairspeed with forthe the airspeed different for discthe different brakes studied disc brakes aids the studied heat dissipation.aids the heat dissipation.

FigureFigure 10. 10. GraphicalGraphical results results obtained obtained by by CFD. CFD. Source: Source: own own elaboration. elaboration.

Finally,Finally, for for a a geometric geometric configuration configuration with with a more a more significant significant number number of profiles, of profiles, air- flowairflow blocking blocking can can occur occur at low at low rotation rotation speeds. speeds. This This is mainly is mainly duedue to the to thereduction reduction of the of effectivethe effective surface surface of the of disc the brake. disc brake. That is, That the is, number the number of profiles of profiles directly directly affects affects air circu- air lationcirculation [25]. [25].

Fluids 2021, 6, x FOR PEER REVIEW 19 of 25

Fluids 2021, 6, 160 3.4. Proposal for a New Disc Brake Geometry 18 of 24 Two new geometries that improve heat dissipation during the braking process are proposed after having analyzed the previous results. The first one is an automotive disc brake3.4. Proposal with N-38 for a type New Discventilation Brake Geometry blades and a single wing and the second has a double wing. These configurations have a more aerodynamic profile compared to the automotive Two new geometries that improve heat dissipation during the braking process are disc brake with the NACA 66–209 type ventilation blades, which makes the airflow inside proposed after having analyzed the previous results. The first one is an automotive disc the ventilation blades circulate with better efficiency, and the rate of heat evacuated brake with N-38 type ventilation blades and a single wing and the second has a double higher, thus increasing the efficiency of the disc brake. According to the authors of [22], wing. These configurations have a more aerodynamic profile compared to the automotive an increase in the number of blades in the disc brake geometry design does not promote disc brake with the NACA 66–209 type ventilation blades, which makes the airflow inside the block effect at low speeds and also provides better performance for heat dissipation. the ventilation blades circulate with better efficiency, and the rate of heat evacuated higher, Table 5 presents the most relevant parameters and dimensions of the proposed brake thus increasing the efficiency of the disc brake. According to the authors of [22], an increase discs. in the number of blades in the disc brake geometry design does not promote the block effect at low speeds and also provides better performance for heat dissipation. Table5 Table 5. Parameters and dimensions of the new disc brake proposal. presents the most relevant parameters and dimensions of the proposed brake discs. Parameters Disc Brake Proposal 1 Disc Brake Proposal 2 Table 5. Parameters and dimensions of the new disc brake proposal. D (m) 0.356 0.350 D Parameters (m) Disc Brake0.226 Proposal 1 Disc Brake 0.200 Proposal 2 D (m) 0.085 0.080 DExternal (m) 0.356 0.350 E (m) 0.006 0.005 DInner (m) 0.226 0.200 E DBell(m)(m) 0.026 0.085 0.030 0.080 ENDisc(m) 15 0.006 12 0.005 TiEBell (°C)(m) 117.12 0.026 115.14 0.030 NBlade 15 12 E (J) 143,769.678 213,592.385 Ti ( ◦C) 117.12 115.14 Q (W/m) ×106 2.2343 3.3194 ETotal in disc (J) 143,769.678 213,592.385 2 6 QQ (W/m ) ×(W)10 1236.742.2343 1306.17 3.3194 QTotalQ in disc(W)( W) 8.221236.74 8.08 1306.17 QDuct (W) 8.22 8.08 Q (W) 123.21 96.96 Q (W) 123.21 96.96 Source: ownTotal elaboration. in duct Source: own elaboration. FigureFigure 1111 shows shows the the geometry geometry of ofthe the ventilation ventilation blades blades which, which, depending depending on the on con- the figurationconfiguration of the of disc the disc brake, brake, achi achieveseves the thehighest highest heat heat dissipation. dissipation.

0.15 N-38 Naca 66-209 0.10

0.05

0.00 Width (units)

-0.05 -0.01 0.19 0.39 0.59 0.79 0.99 Length (units)

FigureFigure 11. 11. GeometryGeometry of of the the N-38 N-38 and and Naca Naca 66-209 66-209 type type ventilation blades. Source: Source: [52]. [52].

TheThe simulation waswas carriedcarried out out in in the the ANSYS ANSYS software, software, having having established established two two possible pos- sibleoptimal optimal disc brakedisc brake configurations, configurations, obtaining obtaining the results the results shown shown in Figures in Figures 12 and 12 13 and. 13. In the simulations presented in Figures 12 and 13, a thermal and ﬂuid dynamic analysis

was carried out, which was carried out in two time intervals of 0 and 120 s, where it is observed that the disc of the disc brake proposal 2 reaches a lower temperature of ~66.3 ◦C. In comparison, disc brake proposal 1 reaches a higher temperature, which is 114.7 ◦C. Likewise, it was possible to observe that the airspeed inside the ventilation blades in disc brake proposal 1 reaches values of ~7.014 m/s. In contrast, disc brake proposal 2 reaches a higher airspeed of ~10.41 m/s, which conﬁrms what has been said above regarding the dissipated temperature because the higher airspeed inside the ventilation blades leads to a signiﬁcantly lower surface temperature. Likewise, these two new geometries were compared with the previously analyzed geometries, for which it was possible to deduce Fluids 2021, 6, 160 19 of 24

that disc brake proposal 2 improved by approximately 23.8% on average for the dissipated temperature. This is because the ventilation blades of the two disc proposals have a more aerodynamic tendency, which makes the air circulate more quickly inside them, and therefore, the dissipated heat transfer rate is higher.

Disc brake proposal 1 (P1)

t = 0 s t = 120 s

Figure 12. Simulations for disc brake proposal 1. Source: own elaboration.

On the other hand, the behavior of Newton’s law of cooling for the two brake proposals is shown in Figure 14. It is evident how the disc brake proposal 2 (N-38 simple) dissipates heat faster by natural convection. This process is generated in less than 100 min, being much lower compared to the ﬁve-disc brakes studied in this research (Figures8 and9). The rotation of the disc brake is directly regulated by the blade angle, and the method

that deﬁnes the displacement of the rotor angle at a given moment is different. In this way,

some considerations are important to recall: the contact pressure leads to non-uniform

temperature when the pressure applied is not constant. The high local temperature results

in greater thermal expansion and leads to an increase in the local pressure, generating more friction on the braking track. The convection in the disc impacts the temperature ﬁeld during the cooling process, and thus the temperature is reduced with the aid of the cooling channels [26].

Fluids 2021, 6, 160 20 of 24 Fluids 2021, 6, x FOR PEER REVIEW 21 of 25

Disc brake proposal 2 (P2)

m/s m/s t = 0 s t = 120 s

Figure 13. Simulations for disc brake proposal 2. Source: own elaboration.

In the simulations presented in Figures 12 and 13, a thermal and fluid dynamic analysis was carried out, which was carried out in two time intervals of 0 and 120 s, where it is observed that the disc of the disc brake proposal 2 reaches a lower temperature of ~66.3 °C. In comparison, disc brake proposal 1 reaches a higher temperature, which is 114.7 °C. Likewise, it was possible to observe that the airspeed inside the ventilation blades in disc brake proposal 1 reaches values of ~7.014 m/s. In contrast, disc brake proposal 2 reaches a higher airspeed of ~10.41 m/s, which confirms what has been said above regarding the dissipated temperature because the higher airspeed inside the ventilation blades leads to a significantly lower surface temperature. Likewise, these two new geometries were compared with the previously analyzed geometries, for which it was possible to deduce that disc brake proposal 2 improved by approximately 23.8% on average for the dissipated temperature. This is because the ventilation blades of the two disc proposals have a more aerodynamic tendency, which makes the air circulate more quickly inside them, and therefore, the dissipated heat transfer rate is higher. On the other hand, the behavior of Newton’s law of cooling for the two brake proposals is shown in Figure 14. It is evident how the disc brake proposal 2 (N-38 simple) dissipates heat faster by natural convection. This process is generated in less than 100 min, being much lower compared to the five-disc brakes studied in this research (Figures 8 and Figure 13. Simulations for disc9). brake proposal 2. Source: own elaboration. Figure 13. Simulations for disc brake proposal 2. Source: own elaboration.

FigureFigure 14. 14. Newton’sNewton’s law law of ofcooling cooling for for the the two two disc disc brake brake proposals. proposals. Source: Source: own own elaboration. elaboration.

TheAccording rotation toof thethe authorsdisc brake of [is6 ],directly the type regulated of geometry by the of blade the disc angle, brake and blades the method improves thatthe defines total heat the transfer displacement up to 20%,of the more rotor with angle teardrop at a given pillars, moment depending is different. on the In this rotor way, speed. someIn this considerations way, the new are geometry important proposed to recall: in the this contact work increases pressure theleads total to heatnon-uniform transfer by around 24% due to the air ﬂux speed generated on the N-38 type blades, promoting the Fluids 2021, 6, 160 21 of 24

mass flow rate in the quick heat dissipation. In addition, the internal convection increases linearly with speed, which increases much more quickly compared with the external convection [53]. Notice that, due to the discontinuity of the profile design in the disc brake proposal 1 (double blade), the flow has the largest contact on the disc surface, which is reduced due to the turbulence of the flow generated between the blades. In contrast, in the disc brake proposal 2, the profile design is continuous to the center of the disc, which promotes the flow along the duct disc related to the lines of continuity of the flow. Compared with the results obtained in Figures8 and9, for the thermal and fluid-dynamic behavior of the common disc brakes, it is evident that a delay in the heat dissipation on the behavior of the disc brakes with these parameters reduces the performance of the disc brake.

4. Conclusions The results obtained for the contact surface temperatures between the disc and the pad demonstrate a distribution of heat between two components in sliding contact due to the high-temperature gradients and the operating conditions that affect the ventilation of the disc, and; therefore, heat dissipation to the environment. It was evidenced through the calculations that the increase in the temperature in the braking track is mainly inﬂuenced by the pressure exerted during braking, as well as the time in which this action is executed. On the other hand, the wear of the brake pad is inﬂuenced by the braking actuation time, and thus by the mechanical properties of the brake pad and the disc brake materials. With the different mathematical calculations and theories of heat transfer, it was possible to determine the surface temperature in the braking track and the rate of heat loss for each disc brake. The surface temperature values determined in a time equal to zero are 95, 119, 102, 84.69, and 110.6 ◦C. Likewise, the values of the rate of heat evacuated in a time of zero are 745.11, 1463.64, 1320.56, 919.95, and 1399.22 W. These results allowed concluding that the higher the surface temperature, the higher the rate of heat transfer evacuated during the braking process. Thus, using the Solidworks design software, the different geometries of the discs were developed and later imported into the student version of the ANSYS simulation software to carry out the respective simulations of airspeed and surface temperature on the braking tracks. The results of the simulations were analyzed and compared with the mathematical calculations previously made. It was possible to observe the surface temperatures on the braking track after 120 s, with values of 76.6, 79.3, 77.5, 69.1, and 108.1 ◦C, respectively, for each disc brake. It was observed that Disk 4 reaches the lowest temperature compared to the other geometries. This occurs because the area of the braking track is smaller, as a result, the friction surface is also smaller, which makes the temperature lower. Likewise, in the simulation, the airspeed inside the ventilation ducts was determined, where values of 4.31, 3.11, 1.91, 6.55, and 5.02 m/s were found. The speed inside the ventilation ducts in Disk 4 is higher. Finally, two proposals for new geometries were made. It was observed that in disk proposal 2, with a simple type N-38 ventilation blade, an improvement in temperature dissipation was achieved by approximately 23.8%, compared to the previous geometries analyzed. This is due to the aerodynamics of the ventilation blade, which makes the air circulate more quickly, and therefore, the generated temperature is evacuated faster.

Author Contributions: R.A.G.-L.: supervision, project administration, sources, conceptualization, methodology, formal analysis, writing—original draft preparation, writing—review and editing. N.A.-G. and J.A.G.-C.: formal analysis, funding acquisition, sources, visualization, validation, other contribution. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Fluids 2021, 6, 160 22 of 24

Data Availability Statement: Not applicable. Acknowledgments: This work was supported by the Universidad Francisco de Paula Santander Ocaña, Colombia. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature DExternal Disc brake outer diameter. (m). DInner Disc brake inner diameter. (m). DBell Disc brake bell diameter. (m). EDisc Disc thickness. (m). EBell Bell thickness. (m). ETotal in disc Total energy in the disc brake. (J). EEach disc Energy in each disc brake. (J). NBlades Number of blades. (N) Q Heat generated during braking on the disc. (W/m2). QTotal in disc Total heat loss rate in the disc brake. (W). QBell Rate of total heat loss in the brake disc bell. (W). QPeripheral Total heat loss rate at the periphery of the disc brake. (W). QRotary Total heat loss rate by rotating effect of the disc brake. (W). ∆T Temperature differential between the disc brake and the environment. (◦C). EDisc brake Disc brake energy. (J). mD Disc brake mass. (Kg). ◦ CP Speciﬁc heat of the material. (J/Kg × C). ◦ Ti Instantaneous temperature at all times. ( C). T∞ Ambient temperature. (33 ◦C). A Heat transfer area. (m2). U Coefﬁcient of surface thermal transmission of the material. (J/s × m2 × ◦C). g Acceleration of gravity. (9.81 m/s2). t Newton cooling time. (s). Nu Nusselt number. (Dimensionless). K Thermal conductivity. (w/m× ◦C). D Disc brake diameter. (m). υ Fluid kinematic viscosity. (m2/s). ω angular speed. (Rad/s). Reg Reynolds number for rotary convection. (Dimensionless). Tp Disc periphery temperature. (m).

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