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Feb 1, 2017 - COEFFICIENT TRANSFER FOR AUTOMOTIVE DISC ... 1Department of Mechanical Engineering, University of Sciences and Technology of ...
Computational Thermal Sciences, 10(1):1–21 (2018)

COMPUTATIONAL FLUID DYNAMICS MODELING AND COMPUTATION OF CONVECTIVE HEAT COEFFICIENT TRANSFER FOR AUTOMOTIVE DISC BRAKE ROTORS Ali Belhocine1,∗ & Wan Zaidi Wan Omar2 1

Department of Mechanical Engineering, University of Sciences and Technology of Oran, L.P. 1505 El-Mnaouer, USTO 31000 Oran, Algeria 2 Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Malaysia *Address all correspondence to: Ali Belhocine, Department of Mechanical Engineering, University of Sciences and Technology of Oran, L.P. 1505 El-Mnaouer, USTO 31000 Oran, Algeria; Tel.: +213 790 092 648, E-mail: [email protected] Original Manuscript Submitted: 2/1/2017; Final Draft Received: 6/16/2017 The braking network of an automobile is one of its most important control systems. For many years, disc brakes have been used for safe retardation of a vehicle. During braking, an enormous amount of heat is generated, and for effective braking, sufficient heat dissipation is essential. The thermal performance of a disc brake depends on characteristics of the airflow around the brake rotor; hence, aerodynamics is key in the region of brake components. Using ANSYS CFX software, we performed a computational fluid dynamics (CFD) analysis on a brake system to study the behavior of airflow distribution around disc brake components. We were interested in the determination of the heat-transfer coefficient on each surface of a ventilated disc rotor, varying with time in a transient state. Using CFD analysis, we imported surface film condition data into a corresponding finite-element method for disc temperature analysis.

KEY WORDS: CFD, heat flux, convection, heat-transfer coefficient, gray cast iron 1. INTRODUCTION The ever-increasing need for effective transportation presents challenges for automobile manufacturers to maintain and improve safety systems. A vehicle’s brake system has always been one of its most critical active safety networks, and brake cooling is an important aspect when considering brake disc durability and performance. Brake disc convective cooling is significant, because it can be improved by trivial design changes and contributes to a major part of total dissipated heat flux during normal driving conditions. Components of the brake system are undeniably significant, especially when slowing or stopping the rotation of a wheel by pressing brake pads against rotating wheel discs (Valvano and Lee, 2000). Commonly used for improving brake cooling is a ventilated brake disc that improves convective cooling by means of air passages that separate braking surfaces. For years, ventilated brake rotors have been incorporated into brake systems for their weight savings and additional convective heat transfer from air channels among rotor hub cheeks (these passages lack solid rotors). However, the amount of additional cooling needed due to this internal airflow is not well defined and depends on the brake rotor’s geometry and cooling airflow conditions around the brake assembly. Flow analysis and heat dissipation have fascinated many researchers. Earlier work on ventilated and solid discs addressed both aerodynamics (David et al., 2003; Anders and Christer, 2001; Lisa et al., 2002; Hudson and Ruhl, 1997; Parish and MacManus, 2005) and heat transfer (Voller et al., 2003; Lisa et al., 2002; Valvano and Lee, 2000; Eisengraber et al., 1999). Investigation of localized thermal phenomena such as hot spotting and hot banding

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(Anderson and Knapp, 1990; Lee and Dinwiddie, 1998) requires a fully coupled thermo-elastic analysis and is thus beyond the scope of the current study. However, separate work that is underway to include localized thermal effects in the proposed design process will be reported on in the future. As mentioned, vehicle braking performance can be significantly affected by temperature rise in brake components. Frictional heat generated at the interface of the disc and pads can result in high temperatures. In particular, the temperature can exceed the critical value for a given material and lead to undesirable effects, such as brake fade, local scoring, thermo-elastic instability, premature wear, brake fluid vaporization, bearing failure, thermal cracks, and thermally excited vibration (Abu Bakar et al., 2010). Dufr´enoy (2004) proposed a structural macro model of the thermo-mechanical behavior of the disc brake, taking into account the real three-dimensional (3D) geometry of disc–pad coupling. Contact surface variations, distortions, and wear were taken into account. Formation of hot spots as well as the nonuniform distribution of contact pressure are unwanted effects that can emerge in disc brakes during the course of braking or engagement of the transmission clutch. In work carried out by S¨oderberg and Anderson (2009), a 3D finite-element model (FEM) of the brake pad and rotor was developed primarily for calculating contact pressure distribution of the pad onto the rotor. If sliding velocity is high enough, this effect can become unstable and result in disc material damage, frictional vibration, and wear (Voldrich, 2006). Gao and Lin (2002) cited considerable evidence showing that contact temperature is an integral factor, reflecting specific power friction influence of the combined effect of load, speed, friction coefficient, and thermo-physical and durability properties of materials in a frictional couple. Lee and Yeo (2000) reported that uneven distribution of temperature at the surfaces of the disc and friction pads brings about thermal distortion, known as coning, which was found to be the main cause of judder and disc thickness variation. In recent work, Ouyang et al. (2009) found that temperature could also affect vibration level in a disc brake assembly. In other studies, Ouyang et al. (2009) and Hassan et al. (2009) used FEM to investigate thermal effects on disc brake squeal, using dynamic transient and complex eigenvalue analysis, respectively. A brake system is composed of many parts, including friction pads on each wheel, a master cylinder, wheel cylinders, and a hydraulic control system (Sivarao et al., 2009). A disc brake consists of a cast-iron disc that rotates with the wheel, a caliper that is fixed to the steering knuckle, and friction material (brake pads). When the braking process occurs, hydraulic pressure forces the piston, causing the pads and disc brake to be in a sliding contact. Setup force resists the movement so that the vehicle slows or eventually stops. Friction between the disc and pads always opposes motion, and heat is generated due to conversion of kinetic energy (Kuciej and Grzes, 2011). The three-dimensional (3D) simulation of thermo-mechanical interactions on the automotive brake, showing the transient thermo-elastic instability phenomenon, was presented for the first time by Cho and Ahn (2001). Recently, Belhocine and Wan Omar (2017) investigated the structural and mechanical behavior of a 3D disc–pad model during the braking process under dry contact slipping conditions. Subsequently, Belhocine (2017) investigated structural and contact behaviors of the brake disc and pads during the braking phase with and without thermal effects. When a vehicle brakes, part of the friction temperature escapes into the air through convection and radiation. Therefore, the determination of heat-transfer coefficients is very important. However, it is difficult to calculate the coefficients precisely, because they depend on braking system shape, speed of vehicle movement, and consequently, air circulation. The modeling of convection proves to be a main problem, because it is related to the aerodynamic conditions of the disc. In this work, we are interested in this part of the calculation of the heat exchange coefficient (h). This parameter must be evaluated to visualize the 3D distribution of disc temperature. The strategy of our calculation is based on ANSYS CFX 11 software, which performs numerical simulation of the transient thermal field (Zhang et al., 2009). A comparison was made between temperature of full and ventilated brake discs, showing the importance of the cooling mode in the design of automobile discs. 2. PRINCIPLE OF DISC BRAKES The principle of a disc brake is very simple: A metal disc (the rotor) is firmly mounted to the rotating wheel. The pads grip the rotating disc when the brakes are applied. The disc brake system consists of the following parts (see Fig. 1):

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FIG. 1: Parts of the brake system

• Pads. Two flat elements that are comprised of friction material, the pads run perpendicular to the disc and grip the disc when brake force is applied. Rubbing on the moving disc surface causes the vehicle to slow. • The caliper, which is mounted to the chassis, contains a piston that presses the pads against the disc surface. • The rotor is mounted to the hub and therefore rotates with the wheel. A vehicle in motion may be considered to be a permanent energy conversion system, because chemical energy is transformed through combustion into mechanical energy. This energy is then transformed into the kinetic or potential energy of the car. When braking, the vehicle’s kinetic energy is entirely converted into thermal energy by the frictional interaction between brake pads and rotor. Generated heat is distributed between rotor and pads. This partition between pads and disc largely depends on the physio-chemical properties of the two materials. More than 95% of thermal energy flows into the rotor and is stored, conducted to the hub and wheel, and, for longer brake applications, convected to the surrounding air. 3. BRAKE DISC TYPES The two types of brake discs are full and ventilated. The full discs, of simple geometry and thus simple manufacture, are generally placed on the rear axle of the car. Full discs are comprised of a solid crown connected to a “bowl” that is fixed to the hub of the car [Fig. 2(a)]. Ventilated discs, which are more complex in geometry and appeared later,

FIG. 2: Full disc (a); ventilated disc (b)

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were mostly found at first on the front axle. However, ventilated discs are now increasingly found in the rear and front of high-end cars. Ventilated discs have two crowns, called flanges, that are separated by fins [Fig. 2(b)]. These discs cool more efficiently than full discs, thanks to ventilation among the fins, and they promote convective heat transfer by increasing exchange surfaces. A ventilated disc contains more material than a full disc, and this improves its heat-absorption capacity. The number, size, and shape (radial, curved, circular pins, etc.) of the fins vary. The gradients in the throat of the bowl are explained in the same way. At the beginning of braking, the temperature of the bowl is at 20◦ C, whereas that of the tracks is at a few hundred degrees. To prevent the hub temperature from becoming too high (which would cause tire temperature increases, which is quite critical), the throat is machined to prevent it from transmitting too much heat to the hub bowl (Fig. 3). With this machining, the temperature of the bowl actually decreases, but the thermal gradients increase consequently in this zone. This give rise to thermal stresses, which explains the bowl rupture that can be observed during severe experimental tests. Disc rotation results in air circulation in the channels that causes improvement in cooling (Fig. 4). 4. TRANSIENT HEAT CONDUCTION EQUATION Transient heat conduction in the 3D heat-transfer problem is governed by the following differential equation: ( ) ∂qx ∂qy ∂qz ∂T − + + + Q = ρCp , ∂x ∂y ∂z ∂t

(1)

where qx , qy , and qz are the conduction heat fluxes in the x, y, and z directions, respectively; Cp is the specific heat; ρ is the specific mass; Q is the internal heat-generation rate per unit volume; and T is the temperature that varies with coordinates and time t. Conduction heat fluxes may be written in terms of temperature using Fourier’s law. Assuming constant and uniform thermal properties, the relationships are qx = −kx

∂T , ∂x

qy = −ky

∂T , ∂y

qz = −kz

∂T , ∂z

(2)

where kx , ky , and kz are the thermal conductivities in the x, y, and z directions, respectively. Heat-transfer boundary conditions include several heat-transfer modes that can be written in different forms. Boundary conditions that are frequently encountered are Ts = T1 (xyzt), (3) −qs = h (Ts − T∞ ) ,

(4)

where T1 is the specified surface temperature; qs is the specified surface heat flux (this is positive when entering into a surface); h is the convective heat-transfer coefficient; Ts is the unknown surface temperature; and T∞ is the convective exchange temperature.

FIG. 3: Calorific throat

FIG. 4: Circulation of air in the channels of a ventilated disc

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5. CALCULATING HEAT FLUX ENTERING THE DISC 5.1 Forces Acting on Wheels during Braking The parameters appearing in Fig. 5 can be defined as follows: FRA is the aerodynamic force acting on the body of the vehicle; h is the height of the center of gravity (CG) from the ground; FG is the weight of the vehicle acting at its CG; FQV and FQH are the dynamic weights carried on the front and rear wheels; FRRV and FRRH are the rolling resistances at the tire contact patch; FD is the inertia force; FRP is the resistance force from the slope; FF V and FF H are the tractive force; L is the wheel base length; LH is the distance of the CG to the back of the front axle; and LV is the distance of the CG at the front of the front axle. The longitudinal and transverse equilibria of the vehicle can be written along the local x and y axes of the car: ∑ FX = 0 =⇒FRRV + FF V + FRRH + FF H + FRA − (FRP + FD ) = 0 (5) FF = FRP + FRF FRR FRA

(6)

with FF = FF V + FF H , ∑ ∑

FRR = FRRV + FRRH , FY = 0 =⇒ FG cos α − (FQV + FQH ) = 0

(7)

MB = 0 =⇒ FQV L + FRA h − h (FRF + FRP ) − LV FG cos α = 0,

(8)

[(FRF + FRP ) h + FG LH − FRA h] (9) L For a road vehicle, the rolling force FRR = FG fr cos α is due to the flat that was formed in a tire on the road, and fr is the rolling resistance coefficient. For a high-pressure tire (fr = 0.015), FQV =

FRP = FG sin α The aerodynamic force is given by FRA = CX AF

ρa 2 v , 2

(10)

(11)

with CX the coefficient of form that is equal to 0.3–0.4 in the car, and AF (m2 ) is the frontal surface. With this approach, for a road passenger vehicle, we can take AF = 0.8 × height × width S and ρa to be the air density.

FIG. 5: Definition of the forces acting on an automobile during braking. Please see text for description of parameters in figure.

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5.2 Total Braking Power Ptot = PR + PF , ∑ PF = FF v = (FF V + FF H ) v, ∑ PR = FR v = (FRR + FRP + FRA ) v,

(12) (13) (14)

where v is the velocity of the vehicle. In the case of flat braking (Fig. 6), the resistances due to rolling and slope are neglected (FRR and FRP = 0), and FRP = 0) the penetration into the air is generally negligible. For these reasons (FRA = 0), ∑ PR = FR v = (FRR + FRP + FRA ) v = 0, (15) PF =



FF v = (FF V + FF H ) v,

(16)

(FF V + FF H ) = FD = ma,

(17)

Ptot = PF = m a v.

(18)

Let ϕ be the coefficient that represents the proportion of the braking force relative to the rear wheels; PF H = ϕmav, and then PF V = (1 − ϕ)mav. If a is constant, we have v (t) = v0 − at,

(19)

PF = (1 − ϕ) ma (v0 − at).

(20)

The braking power delivered to the brake disc is equal to half the total power: PF V I =

(1 − ϕ) ma (v0 − at). 2

(21)

At t = 0, we have

(1 − ϕ) mav0 . 2 The braking efficiency is then defined by the ratio between deceleration (a) and acceleration (g): PF V I =

Z=

ad , g

(22)

(23)

FIG. 6: Efforts acting on a car using stop braking when a tire is flat

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(1 − ϕ) mZg v 0 . (24) 2 The purpose of the brake discs is to dissipate mechanical energy into heat. For trains or cars, it is the kinetic energy of the vehicle that is dissipated by the friction of the skates on the discs. Disc–pad assembly heats up under this action and cools in ambient air. As the brakes are repeatedly applied, the brake discs are subjected to thermomechanical fatigue. In the automotive industry, many studies have shown that braking can generate temperatures in excess of 700◦ C in a matter of seconds. Considering that the brake disc can totally absorb the amount of heat produced, [ ] (1 − ϕ) Nm Qv = mtot gv = [W ] . (25) 2 s PF V I =

The expression of the transformed friction power per unit area is thus [ ] [ ] (1 − ϕ) mtot gv N m W ′ Qv= = . 2 2Ad sm2 m2

(26)

The quantity Q′ v characterizes the heat flux injected into the disc and must therefore be located only on the actual contact surface, where Ad is the disc surface swept by a brake pad. If we introduce the factor of exploitation εp of the friction surface, Q′ (27) εp = ′ v . Q vmax Thus, the equation of the initial thermal flow of friction entering the disc is calculated as follows: [ ] [ ] (1 − ϕ) mtot gv N m W ′ Q vmax = = . 2 2Ad εp sm2 m2

(28)

5.3 Heat Flux Entering the Disc In the course of braking, an automobile’s kinetic and potential energy are converted into thermal energy through frictional heating behavior among the interfaces of the friction pair; frictional heat is generated on the interfaces of the brake disc and brake pads. The initial heat flux q0 into the rotor face is directly calculated using the following formula (Reimpel, 1998): 1 − ∅ m g v0 z , (29) q0 = 2 2Ad εp where z = a/g is the braking effectiveness, a is the deceleration of the vehicle (ms−2 ), and g is the acceleration of gravity (9.81) (ms−2 ). Our work studies the thermal behavior of a 3D brake disc that includes heat flux generated inside the brake disc, maximum and minimum temperatures, and additional parameters. Here, we analyze a scenario that involves a stop brake. In practice, the braking system bathes in an airflow, more or less forced according to the system that participates in the cooling of the disc and plates. Airflow is governed by the laws of aerodynamics. The values of the heat exchange coefficient h as a function of time are calculated using the ANSYS CFX code. These values are then used to determine the thermal behavior of the disc in a transient mode. The brake disc consumes the major part of the heat, usually > 90% (Cruceanu, 2007), by means of the effective contact surface of the friction couple. Considering the complexity of the problem and the limitations of average data processing, one identifies the pads by their effect, represented by an entering heat flux (Fig. 7). Loading corresponds to the heat flux on the disc surface, and the study is based on a ventilated brake disc of high-carbon, gray cast iron (FG – Fonte Grise); this type of disc (262 × 29 mm) is fitted to certain versions of vehicles (Fig. 8). To facilitate comparison of simulation results, the geometric dimensions of the two disc variants (full and ventilated) are equal. The dimensions and parameters used in the thermal calculation are described in Table 1. The disc material is gray cast iron (FG 15) with high carbon content (Gotowicki et al., 2005), both useful thermo-physical

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FIG. 7: Application of flux

FIG. 8: Ventilated disc (contour view)

TABLE 1: Geometrical dimensions and application parameters of automotive braking Inner disc diameter, mm Outer disc diameter, mm Disc thickness (T H), mm Disc height (H), mm Vehicle mass (m), kg Initial speed (v0 ), m/s Deceleration (a), m/s2 Braking time (tb ), s Effective rotor radius (Rrotor ), mm Rate distribution of braking forces (ϕ), % Factor of charge distribution of the disc (εp ) Surface disc swept by the pad (Ad ), mm2

66 262 29 51 1385 28 8 3.5 100.5 20 0.5 35993

characteristics. The thermo-elastic characteristics that are adopted in this simulation in the transient analysis of the disc are listed in Table 2. It is very difficult to exactly model the brake disc, but ongoing research is aimed at determining transient thermal behavior of the disc brake during braking applications. To simplify the analysis, several assumptions are made (Khalid et al., 2011): • All kinetic energy at the disc brake rotor surface is converted into frictional heat or heat flux. • The heat transfer involved in this analysis is only for conduction and convection processes. Heat-transfer radiation can be neglected in this analysis because of its small amount (5% to 10%) (Limpert, 1999). • The disc material is considered to be homogeneous and isotropic.

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TABLE 2: Thermo-elastic properties used in simulation Material Properties Thermal conductivity (k), W/m◦ C Density (ρ), kg/m3 Specific heat (c), J/Kg◦ C Poisson’s ratio (ν) Thermal expansion (α), 10−6 /◦ C Elastic modulus (E), GPa

Disc 57 7250 460 0.28 10.85 138

• The domain is considered to be axis symmetric. • Inertia and body force effects are negligible during the analysis. • The disc is stress-free before the application of the brake. • In this analysis, the ambient and initial temperature have been set to 20◦ C. • All other possible disc brake loads are neglected. • Only certain parts of the disc brake rotor will apply with convection heat transfer, such as cooling vanes area, outer-ring diameter area, and disc brake surface. The thermal conductivity and specific heat are a function of temperature (see Figs. 9 and 10). 6. MODELING IN ANSYS CFX The airflow characteristics around brake components are highly complex, and they can vary significantly with the underbody structure as well as the component shapes. Instead of using empirical equations, which are commonly used in thermal analysis (Dittrich and Lang, 1984; Fukano and Matsui, 1986), the average heat-transfer coefficients are calculated from the measured cooling coefficients by an iteration algorithm. Because cooling coefficients account for all three modes of heat transfer, the estimated heat-transfer coefficients include the equivalent radiation heattransfer coefficient. The solution scheme uses the κ–ε model with scalable wall function and sequential load steps. For the preparation of the mesh of the CFD model, one initially defines various surfaces of the disc in ANSYS ICEM 60 800 750 700

50

Specific heat J/kg°C

Thermal conductivity W/m°C

55

45

40

650 600 550 500

35

450

0

100

200

300 400 500 600 Temperature °C

700

800

FIG. 9: Thermal conductivity versus temperature

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0

100

200

300

400

500

600

Temperature °C

FIG. 10: Specific heat versus temperature

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CFD as shown in Figs. 11 and 12; we used a linear tetrahedral element with 30,717 nodes and 179,798 elements. This refers only to the fluid flow mesh or the area surrounding the disc. To prevent weighing down the calculations, we used an irregular (nonuniform) mesh, in which the meshes are broader where the gradients are weaker (Fig. 13). As mentioned above, the CFD models were constructed and solved using ANSYS CFX software. The model applies periodic boundary conditions on the section sides and the radial and axial lengths of the air domain surrounding the disc. The disc is attached to an adiabatic shaft whose axial length spans that of the domain. The air around the disc is considered at T∞ = 20◦ C, and open boundaries with zero relative pressure are used for the upper, lower, and radial ends of the domain. 6.1 Preparation of the Mesh This stage consists of preparing the mesh of the fluid field. In our case, we used a linear tetrahedral element with 30,717 nodes and 179,798 elements (Fig. 14). Considering symmetry in the disc, we took only 25% of the geometry of the fluid field (Fig. 15) by using ANSYS ICEM CFD. In this step, we declare all of the physical characteristics of the fluid and solid and introduce the physical properties of the materials used into the library. We selected three gray cast-iron materials (FG 25 AL, FG 20, and FG 15) with thermal conductivities of 43.7, 55, and 57 W/m◦ C, respectively. Because the aim is to determine the temperature field in a disc brake during the braking phase of an

FIG. 11: Definitions of full-disc surfaces

FIG. 12: Definitions of ventilated disc surfaces

FIG. 13: Irregular mesh in the wall

FIG. 14: Mesh of the fluid field

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FIG. 15: Definitions of the fluid-field surfaces

average-class vehicle, we use the following temporal conditions (measured in seconds): Braking time, 3.5; increment time, 0.01; and initial time, 0. The disc is attached to four adiabatic surfaces and two surfaces of symmetry in the fluid domain, with an ambient air temperature of 20◦ C. Figure 16 shows the elaborated CFD model used for ANSYS CFX preanalysis. After the airflow through and around the brake disc is analyzed, the solver automatically calculates the heat-transfer coefficient at the wall boundary. Heat-transfer coefficients considering convection are calculated and organized in such a way that they can be used as a boundary condition in thermal analysis. The average heat-transfer coefficient must calculated for all discs using ANSYS CFX postanalysis, as is indicated in Figs. 17–20. The heat transfer coefficient values obtained from the calculations for full disc are listed in Table 3. Figures 18–20 show the distribution fields of the exchange coefficient h for the three types of cast-iron materials. We found that the behavior of h in the disc does not depend on the material chosen and that the distribution of h in the disc is not the same as that found in the literature. Table 4 shows the mean values of h calculated by the minimum and maximum values of the various surfaces of the ventilated disc. The heat-transfer coefficient is not a thermo-physical property; it depends on many factors including geometry, flow conditions, fluid temperature, and other thermo-physical properties such as viscosity and thermal conductivity. The values of h converge and are almost substantially identical for the three materials. We found that the type of the material does not have a great influence on the variation of h. Contrary to the first case, the value of h is strongly influenced by the ventilation system for the same material (FG 15).

FIG. 16: Brake disc CFD model

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FIG. 17: Distribution of the heat-transfer coefficient on a full disc in the steady-state case (FG 15)

FIG. 18: Distribution of the heat-transfer coefficient on a ventilated disc in the stationary case (FG 25 AL)

FIG. 19: Distribution of the heat-transfer coefficient on a ventilated disc in the stationary case (FG 20)

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FIG. 20: Distribution of the heat-transfer coefficient on a ventilated disc in the stationary case (FG 15)

TABLE 3: Heat-transfer coefficient values for different surfaces in the stationary case for a full disc (FG 15) Surface SC1 SC2 SC3 SC4 SF1 SF3 ST2 ST3 ST4 SV1 SV2 SV3 SV4

FG 15 hmean = (W m–2 k–1 ) 25.29168 5.18003 2.922075 11.77396 111.20765 53.15547 23.22845 65.6994 44.26725 81.37535 71.75842 41.83303 65.82545

6.2 Results of the Calculation of h The heat-transfer coefficient is a parameter that relates to the velocity of the air, the shape of the brake disc, and many other factors. In different air velocities, the heat-transfer coefficient in different parts of the brake disc changes with time (Zhang and Xia, 2012). The heat-transfer coefficient depends on airflow in the region of the brake rotor and on vehicle speed, but it does not depend on material. Comparing Figs. 21 and 22 on the variation of h in the nonstationary mode for full and ventilated discs, we note that the introduction of ventilation system directly influences the value of this coefficient for the same surface. This is logically significant because this mode of ventilation results in a reduction of differences in wall-fluid temperatures. Figures 23 and 24 show, by way of example, the change in h for the surfaces SPV2 and SV1 during each time step.

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TABLE 4: Heat-transfer coefficient values for different surfaces in the stationary case for a ventilated disc (FG 25 AL, FG 20, and FG 15)

-2

-1

Coefficient of transfer h [W.m .°C ]

Materials Surface SC1 SC2 SC3 SF1 and 2 SF3 SPV1 SPV2 SPV3 SPV4 ST1 ST2 ST3 ST4 SV1 SV2 SV3 SV4

FG 25 AL FG 20 FG 15 hmean = (W m–2 k–1 ) 54.16235 53.926035 53.8749 84.6842 83.7842 83.6516 44.4171 44.3485 44.32945 135.4039 135.0584 135.00065 97.17095 95.0479 94.8257 170.64715 171.4507 171.56955 134.08145 134.3285 134.3615 191.2441 191.9436 192.0391 175.16665 176.13395 176.2763 113.6098 114.3962 114.391555 35.0993 34.47225 34.3473 68.33155 66.33155 66.0317 75.09445 72.1235 71.6642 135.5299 131.11825 131.20745 119.25715 118.464835 118.20395 46.70225 44.8195 44.52635 111.57685 108.5044 108.1817

120 110 100 90 80 70 60 50 40 30 20 10 0 -0.5

SC1 SC2 SC3 SC4 SF1 SF3 ST2 ST3 ST4 SV1 SV2 SV3 SV4

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Time [s]

FIG. 21: Variation of the heat-transfer coefficient (h) of various surfaces for a full disc in the transient case (FG 15)

7. DETERMINATION OF THE LOAD Modeling the disc temperature is performed by simulating stop braking of a middle-class car (braking type 0). Vehicle speed decreases linearly with time until it reaches 0. Braking down from the maximum speed of 100.8 km/h to a standstill is shown in Fig. 25. Variation of the heat flux during the simulation time is represented in Fig. 26.

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250 SC1 SC2 SC3 SF1 SF3 SPV1 SPV2 SPV3 SPV4 ST1 ST2 ST3 ST4 SV1 SV2 SV3 SV4

-1

200

-2

Coefficient of transfer h [W m °C ]

225

175 150 125 100 75 50 25 0 -0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

FIG. 22: Variation of the heat-transfer coefficient (h) of various surfaces for a ventilated disc in the transient case (FG 15)

8. MESHING DETAILS The goal of meshing in ANSYS Workbench is to provide robust, easy-to-use tools that simplify the mesh-generation process. The model must be divided into a number of small pieces known as finite elements. Because the model is divided into discrete parts, we performed a finite-element analysis. The generated finite-element mesh model is shown in Fig. 27. 9. THERMAL BOUNDARY CONDITIONS The boundary conditions were introduced into ANSYS Workbench (multiphysics) by choosing the mode of the first simulation (permanent or transitory) and defining the physical properties of the materials; these conditions constituted the initial conditions of our simulation. After having fixed these parameters, we introduced a boundary condition associated with each surface. The total time of the simulation was 45 s. • Increment of initial time = 0.25 s. • Increment of minimal initial time = 0.125 s. • Increment of maximal initial time = 0.5 s. • Initial temperature of the disc = 20◦ C. • Material: Three types of gray cast iron (FG 25 AL, FG 20, FG 15). • Convection: We introduced the values of the heat-transfer coefficient (h) obtained for each surface in the shape of a curve (Figs. 21 and 22). • Flux: We entered the values obtained by flux by means of the code in CFX. 10. RESULTS AND DISCUSSION 10.1 Thermal Analysis In Figs. 28 and 29, for each type of material selected (FG 25 Al, FG 20, FG 15), we show the evolution of the disc temperature at the moment the temperature is reached. Disc material with low thermal conductivity results in a temperature rise on the disc surface. It can be seen that material FG 15 has a maximum temperature (345.44◦ C) that

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FIG. 23: Variation of the heat-transfer coefficient (h) on the surface (SPV2) and as a function of time for a ventilated disc (FG 15)

23.Variation of the heat transfer coefficient (h) on the surface (SPV2) and as a Computational Thermal Sciences

CFD Modeling and Computation of Convective Heat Coefficient Transfer

FIG. 24: Variation of the heat-transfer coefficient (h) on the surface (SV1) and as a function of time for a full disc (FG 15)

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18

Belhocine & Wan Omar

6

30

5x10

Heat Flux

6

20 -2

Heat Flux [W m ]

Braking Power P(t) [W]

4x10

10

6

3x10

6

2x10

6

1x10

0 0

0

10

20

30

Time [s]

FIG. 25: Stop braking load

40

0

10

20 Time [s]

30

40

FIG. 26: Heat flux versus time

FIG. 27: Finite-element analysis mesh model for the (a) full disc (172,103 nodes; 114,421 elements) and (b) ventilated disc (154,679 nodes; 94,117 elements)

FIG. 28: Temperature distribution for the ventilated disc. Materials: FG 25 AL, FG 20, and FG 15

Computational Thermal Sciences

CFD Modeling and Computation of Convective Heat Coefficient Transfer

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FIG. 29: Temperature distribution of the full (a) and ventilated (b) cast-iron disc (FG 15)

is less than those of materials FG 25 AL and FG 20, which had of temperatures 380.2◦ C and 351.58◦ C, respectively. From this figure, FG 15 shows better thermal behavior. The full disc temperature reached its maximum value of 401.55◦ C at t = 1.8839 s, and then decreased exponentially at 4.9293 s once it reached the end of braking (t = 45 s). Figures 30 and 31 illustrate that the time difference (0–3.5 s) indicates a forced convection cycle. Free convection was carried out at the end of the latter until the close of the simulation time limit (t = 45 s). We observed that the ventilated disc had a reduced temperature of almost 60◦ C compared to that of the full disc. We conclude that ventilated brake discs in vehicle design represent a more effective ventilation system and better means of cooling and then decreasing temperatures than full discs. 11. CONCLUSIONS The present work presents a complex brake disc model using ANSYS CFX software to determine values for the heat exchange coefficient h by convection during the phase and braking conditions of a vehicle. The numerical results of this investigation were geared to solving a transient thermal scenario of full and ventilated brake discs, in which their 3D temperature was visualized using ANSYS (multiphysics) 11.0 finite-element software. The purpose of our contribution is to show the impact of ventilation in the cooling of discs during vehicular use. It is our hope that such data that shows better thermal resistance will guarantee safer and more effective of braking systems. Regarding our calculation results, they are satisfactorily and commonly found in the literature. It would be interesting to solve the

of cast iron (FG 15).

Variation of temperature of the full disc of theof timethe (FG 15) Figure FIG. 30.30:Variation of temperature full disc

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Belhocine & Wan Omar

FIG. 31: Variation of temperature of the ventilated disc of the time (FG 15)

problem of thermo-mechanical disc brakes with an experimental study to validate our numerical results, for example, on test benches to show agreement between model and reality.

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