Survey of the Streamlined and Thermal Behaviour of a Ventilated Disc Brake

International Journal of Mechanics and Applications 014, 4(): 1-8 DOI: 10.593/j.mechanics.014040.01 Survey of the Streamlined and Thermal Behaviour of a Ventilated Disc Brake Hassene Djemel 1, Mohamed Kaffel 1, Zied Driss,*, Hedi Kchaou, Mounir Baccar 1 1 Unité de Dynamique des Fluides Numérique et Phénomènes de Transfert, University of Sfax, Department of Mechanical Engineering, National Engineering School of Sfax, Road Sokra, B P <1173>, 3038 Sfax, Tunisia Laboratoire des Systèmes Electromécaniques (LASEM), University of Sfax, Department of Mechanical Engineering, National Engineering School of Sfax, Road Sokra, B P <1173>, 3038 Sfax, Tunisia Abstract Knowledge finalized the thermal behavior of friction parts (disc and pad) braking system, has become indispensable in order to develop tropological studies to improve materials. The frictional heat generated on the disk-pad interface induces high temperature which can cause disk brake fade phenomena, local scoring, thermal cracking and thermo elastic instabilities. In this work, a thermo-mechanical modelling of an automotive braking system was presented. For this purpose, three dimensional calculations are carried out in laminar, transitional and turbulent flow in ventilation ducts of brake disc. The calculations are founded on the finite volume method. Model taking into account the friction of the pad against the movable disk, developing a new so-called "Sliding Boundary Condition" technique that allowed us to take into account the spatial and temporal variability of heat flux generated by friction, and update its depending on the amount and speed of braking scenario. Indeed, we have approached the problem in two calculation phases completely independent. In a preliminary calculation phase, the speed and the temperature of the disk are maintained constant. Correlations giving the kinetics of cooling necessary for the calculation of conductive transfer in the disc are established. In a second calculation phase, we have used the equations giving the kinetics of the cooling disk for the thermal loading of the disc resulting in calculation of the transient temperature field. The numerical results were presented in the form of cartographies showing the temperature fields versus time in the r-θ and r-z planes. The results obtained by the simulation are satisfactory compared with those of the specialized literature. Keywords Numerical simulation, Disc brake, Out-flow, Heat transfer 1. Introduction The conception optimization of a ventilated disc brake requires the deep knowledge of the hydrodynamics of the air out-flow in the ventilation channels of the disk. This is to determine the shape and the relative measurements to the smooth transfer of heat so as to lower the disk temperature. A large bibliographic consultation carried out on the analysis of the disk performance allows us to note that the concretized progress does not have any important repercussions on the hydrodynamic calculation of the air outflow in the channels of ventilation of the disk. Actually, only one recent research work in tribological systems was computed by Graf et al. [1]. These authors used the efficient approach for the boundary conditions between pad and disk, which takes into account the rigid body motions of the pad. The thermal stress analyses on a ventilated locomotive wheel-mounted brake disc were investigated by Ghadimi * Corresponding author: zied_driss@yahoo.fr (Zied Driss) Published online at http://journal.sapub.org/mechanics Copyright 014 Scientific & Academic Publishing. All Rights Reserved et al. []. Belhocine et al. [3] analysed the thermal behavior of the full and ventilated brake discs of the vehicles using computing code ANSYS. Yevtushenko et al. [4] concluded that with the increase in pressure the coefficient of friction decreases, and the intensity of thermo-mechanical wear increases. The three-dimensional temperature distributions caused by mutual sliding of two members of the disc brake system were studied by Adamowicz et al. [5]. The temperature and the thermal constriction resistance as a function of geometric characters and velocity were determined. Park et al. [6] investigated the heat transfer enhancement in the automobile ventilated disc brake using helically fluted surface. Der Wiesche [7] established correlations providing the exchange coefficient air-disk of a full disk in rotation. Indeed, the majority of the research studies of the thermal behaviour of the disk are founded on the coefficients of empiric exchange taken from the literature [8-14]. In this context, the present study lies to carry out a survey oriented according to two axes. In the first step, we study the turbulent air outflow through the ventilation channel of the disk to determine the superficial coefficient of exchange. In the second step, we develop the unsteady thermal behaviour

Hassene Djemel et al.: Survey of the Streamlined and Thermal Behaviour of a Ventilated Disc Brake of the disc brake in decelerated movement during a braking phase. In order to achieve these objectives, we have developed two three-dimensional computer codes. The first calculates the exchange coefficient for air-disc of a ventilated disc brake. The second calculates the temperature of the disk, while taking into account the variation of the imposed instantaneous thermal flux in function of the vehicle speed during an operation of any braking operation. The calculation of the temperature field is initiated by imposing the previously calculated exchange coefficients as boundary conditions in channel and on the disk facets.. Geometrical System The system under investigation is a ventilated disc brake consisting of two plates connected by twenty-six solid nervures having twenty-six channels of ventilation between them (figure 1). Figure 1. Studied device The calculations are undertaken in two independent stages. Regarding the first one, it is a preliminary calculation stage permitting the simulation of the outflow and the thermal transfer of the cooling air in its movement in the channel. For the second stage, it takes advantage from the results obtained from the preliminary calculations in function of the simulation of the thermal behaviour of the disk. For each stage, the corresponding calculation domains are constituted of only one channel transporting the cooling and disk air as a whole. The determined local result integration in the first stage allows for the establishment of correlations, giving the superficial coefficients of exchange between the disk facets and air, on the one hand, and between the air currents entering into channels and their internal partitions, on the other hand. These correlations will then be used to express the boundary conditions at the thermal loading of the disc. 3. Mathematical Formulation The equations describing the air outflow through the channels and the heat transfer in turbulent flow emanate from the Reynolds decomposition of the hydrodynamic and thermal variables followed by taking the temporal average of Navier-Stokes equations and instantaneous energy. While using the concept of turbulent diffusion for the turbulent flow modelling, the movement and energy equations are written in vector form that is suitable to the discretization to the finite volumes of the average dimensionless sizes U, V, W and T. The radial velocity component is written as follow: U d e p + div V U ϑ e grad U = + t π Rer r U 1 V 1 U ϑ e + r + ϑe d r r r r r e Θ Re ( V (1) π r ) W + ϑ e r + ϑ e r Θ r z r V + + r+ V r Where ϑ e = 1+ϑ t is the effective dimensionless viscosity and ϑ t is the dimensionless turbulent viscosity. The tangential velocity component is written as follow: V d e p + div V V ϑ e grad V = t π Rer r Θ 1 U V 1 U ϑ e + e V d r r + ϑ r r e r Θ Θ + () π Re V U W + ϑ e + + ϑe r Θ r Θ r z r Θ UV U r The axial velocity component is written as follow: W d e p + div V W ϑ e grad W = t π Rer z 1 U V r ϑ e + ϑ (3) e de r r z r z Θ 1 + + π Re W Fr + ϑe z z The closure of these equations is performed by the first-order turbulence of the k-ε type. Two equations are thus written, one of which controls the turbulent kinetic energy,

International Journal of Mechanics and Applications 014, 4(): 1-8 3 and the other the dissipation rate of this energy. ( σ +ϑ ) k d e k t de + div V k grad k = G ε(4) t π Re σ k π Re ( σ +ϑ ) ε d + e ε t div V ε grad ε = t π Re σ ε ε C G C k π Re de 1 ε Thermal energy equation relating to the fluid: T d e + div V T ( 1+ λ t ) grad T = 0 t π Pe (5) (6) undergoes a centrifugation marked by the dominance of the radial velocity component forming a fluid vein with an almost flat profile. This phenomenon is a characteristic of the turbulent out-flow. Indeed, the air is drawn in the central part of the disk. After that, it is blown along the ventilation channel, before driven back towards the outside. Also, it seems that the entrance as well as in the exit of the channel, the rotation of the disk is felt by a clean increase of the tangential velocity component. Figure 3. Field of speed in the r-θ plane Figure. Portion of the ventilated disc 4. Results and Discussion This section is interested in the determination of the superficial coefficients of exchange of the air-disk, as well as the thermal survey of the disk. 4.1. Hydrodynamic Survey For reasons of clear periodicity, the hydrodynamic survey is limited exclusively to a π/nc sector, where Nc represents the number of ventilation channels. The results are drawn for a maintenance braking to a constant speed of 100 km/h, which corresponds to a Reynolds number of Re = 60768. 4.1.1. Velocity Field Figure 3 presents the distribution of the tangential and radial components of velocity in the r-θ plane situated in the median plane of the disk. This presentation is provided in a mobile reference mark. In this plane cutting the ventilation channels in their mid-height, it appears that the fluid Figure 4. Velocity field in the r-z plane The distribution of the velocity field in the r-z plane is plotted in figure 4. According to these results, it is clear that the rotation of the disc provides the fluid with kinetic energy resulting from the centrifugal forces along the channel formed by two consecutive nervures. These results bring to mind the behaviour of a centrifugal pump. Indeed, it has been noted firstly a strong aspiration of the outside air at the center, then a strong engagement of the fluid in the different channels. Finally, it has been observed a strong repression current of the fluid vein towards the outside. In the periphery of the disk, the outflow is coming out of all openings and it presents a radial dominance. 4.1.. Turbulence Characteristics Figure 5.a replicates the spatial evolution of the turbulent kinetic energy in the r-z plane, thus cutting a channel of ventilation at the level of its median. Indeed, it shows that the maximal value of the turbulent kinetic energy is localized in the exit of the channel at the level of which the velocity gradients are most important. On all sides of the disk, the turbulent kinetic energy is very weak. This result is quite

4 Hassene Djemel et al.: Survey of the Streamlined and Thermal Behaviour of a Ventilated Disc Brake normal because the velocity of the outflow is more important inside the channel than in the neighbourhood of the disk. The distribution of the dissipation rate of the turbulent kinetic energy in the r-z plan is given in figure 5.b. According to these results, a resemblance between representation is clear. Indeed, it has been noted that the maximum values of the dissipation rate of turbulent kinetic energy is concentrated in the exit of the channel at the outside radius level of the disk. Also, it s clear that the dissipation rate of the turbulent kinetic values is very weak outside the channel. In figure 5.c, the distribution of the turbulent viscosity is reproduced in the same r-z plane mentioned previously. According to these results, it is clear that the most intense viscosity values are centralized in the entrance and in the exit of the channel, at the level of the outside radius of the disk. The maximal value of the viscosity is about 140 and is localized at the level exit of the channel. Indeed, at the level of the channel inlet, a relatively important value of the turbulent viscosity can be distinguished. However, in the neighbourhood of the disk, the turbulent viscosity is practically null. Figure 6. Adimensional temperature field 4... Evolution of the Nusselt Number and Superficial Coefficient of Exchange Taking advantage of the hydrodynamic results, we are able to calculate the temperature field in the cooling fluid traversing the canal. The average coefficients of exchange is calculated by the integration of temperature fields, on the one hand, between the surfaces of the disk and ambient air bathing these surfaces, and between the air traversing the canal and the inner walls. In fact, it should be born in mind that the disk is assumed to be kept at a constant temperature equal to the dimensionless unit size. Figure 7 shows the evolution of the superficial coefficients of exchange in function of the car speed at the disc surfaces. In these conditions, h1 is the superficial coefficient of exchange for the left disc surface, h represents the superficial coefficient of exchange for the right disc surface, and h3 represents the superficial coefficient of exchange between the air ratio in its travel in a channel and the inner wall of a channel. Figure 5. Spatial evolution of the turbulent kinetic energy, its dissipation rate and the turbulent viscosity in the r-z plane 4.. Thermal Survey of the Channel 4..1. Temperature Field Figure 6 presents distribution of the adimensional temperature in the r-θ plane cutting the channel to mi-width, for a disk rotating at a constant speed of 100 km/h. In these conditions, the Reynolds number value is equal to Re=60768. According to these results, the temperature increases inside of the channel with the increase of the disk radius. Outside the channel, for a radius superior to the outside radius of the disk, the temperature decreases again. Thus, at the hub level, the temperature is very weak. In the r-z plane, distribution of the adimensional temperature shows that the most elevated temperatures are localized at the level of the two plates constituting the disk as well as at the exit level of the channel. Outside the disk, the temperature is relatively very weak. Figure 7. Evolution of the superficial coefficient of exchange in function of the speed According to these curves it has been noted that the left surface of the disc is cooled better than the right one. This is quite normal because the left surface is in direct contact with the ambient air, while the right one is enclosed by the hub. Concerning the outer surfaces, we can see that the transfer at the internal walls of the cannelures is smaller than the one taking place at the disk surfaces.

International Journal of Mechanics and Applications 014, 4(): 1-8 5 surfaces in the left and in the right plat, a clear difference of about 15 C can be discerned (Figures 10.a and 10.g). Indeed, while the maximum value of the temperature on the left surface is about 95 C, it is equal to 110 C on the right surface. This fact can be explained because the board is better in the left exposed to the air, while the surface of the right plat is sheltered by the wheel hub. Figure 8. Set of the disk hub To determine the superficial coefficients of exchange in function of the vehicle speed, we have drawn the corresponding curves by adopting a logarithmic scale (Figure 9). Moreover, it is shown that above the speed of 0.6 km/h, the curves are almost straight. The equations giving the variation of the superficial coefficient of exchange in function of the vehicle speed can be obtained by linear regression. In these conditions, we found h1=5.9, h=0.3 and h3=.60 at V=0.78. Figure 9. Variation of the superficial coefficient of exchange in function of the speed 4.3. Thermal Study of the Disk An ideal or optimal braking is a purely theoretical scenario in which the driver must exert effort so as to maintain a constant deceleration and a slip rate between the wheels of the car and the floor of the order of 18%. 4.3.1. Temperature Distribution within the Disk The temperature fields in the stopping of the vehicle at t = 3.43 s are shown in figure 10 in different planes located at different depths from the surface of the left disk. With respect to the contact surfaces with pads figure 10.a and 10.g, it appears that the highest temperatures are positioned at the pad-swept sectors, which are the seats of the dissipative heat flows attributable to the degradation of the kinetic energy. Comparing the temperature levels reached on both contact Figure 10. Distribution of the temperature inside the disc By penetrating more and more into the disc material, we can see a cooling trend, and find that the friction impact disappears or almost in the symmetry plane of the ventilation channel (Figure 10.d). This fact gives rise the periodic temperature distribution along the tangential direction θ. Thus, we can clearly distinguish the shape of the 6 solid nervures and predict the location of ventilation channels on the disc. These channels are marked on the map in figure 10.d, by isolines resulting in cylindrical segments of low

6 Hassene Djemel et al.: Survey of the Streamlined and Thermal Behaviour of a Ventilated Disc Brake temperature levels and similarly reproduced on the entire circumference. 4.3.. Temperature Profile Figure 11.a draws the axial development curve of the temperature of a corresponding angular position in the hot zone of the disk when it is stopped. This curve shows that the temperature decreases rapidly from both left and right surfaces of the disk in contact with both calliper brakes to be stabilized at a low temperature in the form of a plate illustrating the effectiveness of the ventilation channels. Figure 11. Evolution of the temperature inside the disc Figure 11.b presents the evolution of the temperature along the tangential direction when the vehicle stops, and this is pertaining to the circumference belonging to the area swept by the skating surface and another at a depth Z=8e/3 calculated from the left surface contact. According to these results, it has been noted that the temperature level on the right disc surface Z=e is relatively high and is marked by a slight increase particularly in the area of contact with the hub when the car stops. The second curve proves the effect of ventilation on the disc in which the temperature difference between the two planes is about 0 C. Even at the disc surface, the effect of solid nervures and ventilation channels existence appears on the curve of the tangential evolution of the temperature and results in a slight fluctuation in the passage frequency by the 6 nervures. These fluctuations are more obvious on the second curve corresponding to a nearest ventilation channels plane. 4.3.3. Temporal Evolution of the Temperature on the Warmest Surface Figure 1. Temporal evolution of temperature on the hottest surface Figure 1 illustrates the temperature distribution on the surface of the right disc plate for an initial speed of 100 km/h and a target deceleration of 8 m/s². Theoretically, these data lead to a braking time t = 3.43 s. Outside the swept area by the calliper brake, it seems that the temperature level is relatively very low, as it is in direct and continuous contact with the surrounding air in relative motion. Moreover, the calliper brake footprint on the disc by the heating effect due to friction can be clearly distinguished. This contributes to a progressive increase in temperature from the inlet of a sector of the disc into contact with the calliper brake to its outlet. For thus, the maximum temperature at a footprint is about 40 C and is located just before the release of the disc from its contact area with the calliper brake. Around the calliper brake printed on the disc, as well as on the outlines of the area swept by the calliper brake, it has been noted that the temperature gradients are very high, indicating that the thermal and mechanical constraints are very large. These temperature gradients are the highest at the

International Journal of Mechanics and Applications 014, 4(): 1-8 7 beginning of the braking process. Indeed, it seems that the part coming out of the area of contact with the calliper brake, undergoes a brief cooling with ambient air. This behaviour is reproduced on a periodic basis to the frequency of the contact area-calliper brake and leads to the heating area swept by the pad. It is also worthwhile to note that the scrolling of the hot spots on the friction track and at the frequency of angular distribution of the nervures. The appearance of these spots is due to the return of the heat accumulated on the nervures level. In figure 13, the evolution of the maximum temperature in function of time, is presented on the surface of the right plate as well as on the surface of the left plate of the disc. It seems that the temperature reaches a maximum value of 40 C, just one second after the start of braking, and then gradually decreases until it stops. 4.3.4. Temporal Evolution of the Axial Temperature Distribution The distribution of temperature during time in the r-z plane, which intersects the calliper brake, is illustrated by a series of maps reproduced in figure 14. These maps show clearly that during the braking process, the temperature and the temperature gradients are the highest on the outer left and right surfaces of the disc, located around the area of the calliper brake-disc contact. On the other hand, we can see that the thermal penetration depth is rather limited, especially at the beginning of the braking when the vehicle speed is very important. Indeed, at the beginning of the braking process, the generated heat does not have time to penetrate sufficiently. This fact is due to resulting in a very tight isotherm at the start of the heating process (Figure 14.a). Throughout time, these isotherms become less frequent though still concentrated in the immediate vicinity of the fingerprints. Also, it appears that the ventilation channels contribute to the radial and axial heat dissipation in the disc by the effect of the pulsating flow of air through these channels. To support the heat propagation and dissipation, the disc material has a high thermal diffusivity. Therefore, according to this viewpoint, the steel is not the best choice. Figure 13. Temporal evolution of temperature in the contact zone 5. Validation of the Code Calculation In order to check our results, we have compared the evolution of the Nusselt number (Nu) on the left surface of the disc in function of Reynolds number, with anteriores results [7]. A very good agreement has been found in Figure 15. Figure 15. Evolution of the Nusselt number as a function of Reynolds number Figure 14. Temporal evolution of the temperature distribution in the r-z plane Figure 16.a shows the temperature field at t = 3.87 s, calculated by our code for a stop braking duration t f = 4.74 s from a speed of 100 km/h. Figure 16.b shows the temperature field at the same time and for the same braking conditions given by Gao et al. [15]. According to these results, similarity appears at the isothermal level as well as a qualitative resemblance appears at the level of the temperature values between the distributions.

8 Hassene Djemel et al.: Survey of the Streamlined and Thermal Behaviour of a Ventilated Disc Brake thermal stresses in a locomotive ventilated brake disc based on a conjugate thermo-fluid coupling boundary conditions, International Communications in Heat and Mass Transfer, 49, (013), pp.104-109. [3] A. Belhocine, M. Bouchetara, Investigation of temperature and thermal stress in ventilated disc brake based on 3D thermomechanical coupling model, Ain Shams Engineering Journal, 4, (013), pp. 475-483. 6. Conclusions Figure 16. Temperature field at t = 3,87s In this work, we have developed a local knowledge of the heat transfer phenomenon in ventilated brake discs. The equation of transfer of heat in unsteady state governing the thermal behaviour of the disc is solved by the method with finite volumes. Particularly, we have built a computer code to simulate the laminar, transitional and turbulent flow in the ventilation channels of the brake disc. In addition, the modelling of the friction of the calliper brake against the movable disc, developing a new technique called "Sliding Boundary Condition" that allowed us not only to take into account the spatial and temporal variability of the heat flow generated by friction, but also to update its amount in function of the speed and braking scenario. The numerical simulation shows that the visualization in unsteady state of the temperature fields which conforms following any braking scenarios. The results resulting from the application of our computer code, shows that the most elevated temperatures are localized at the level of the two plates constituting the disk as well as at the exit level of the channel. Outside the disk, the temperature is relatively very weak. Also, it appears that the ventilation channels contribute to the radial and axial heat dissipation in the disc by the effect of the pulsating flow of air through these channels. The obtained results are very useful for the study of the thermomechanical behaviour of the disc brake. REFERENCES [1] M. Graf, G.-P. Ostermeyer, Efficient computation of thermoelastic instabilities in the presence of wear, Wear, 31, (014), pp.11-0. [] B. Ghadimi, R. Sajedi, F. Kowsary, 3D investigation of [4] A.A. Yevtushenko, P. Grzes, Axisymmetric FEA of temperature in a pad/disc brake system at temperaturedependent coefficients of friction and wear, International Communications in Heat and Mass Transfer, 39, (01), pp. 1045-1053. [5] A. Adamowicz, P. Grzes, Analysis of disc brake temperature distribution during single braking under non-axisymmetric load, Applied Thermal Engineering, 31, (011), pp. 1003-101. [6] S. B. Park, K. S. Lee, D. H. Lee, An investigation of local heat transfer characteristics in a ventilated disc brake with helically fluted surfaces, J. Mech. Sci.Technol, 1, (007), pp. 178-187. [7] Stefan Aus Der Wiesche, Heat transfer from a rotating disk in a parallel air crossflow, International Journal of Thermal Sciences, 46, (007), pp. 745-754. [8] A. Floquet and M. Dubourg, Realistic braking operation simulation of ventilated disk brakes, ASME J. of Tribology, pp. 466-47, 1996. [9] J. H. Choi, In Lee, Finite element analysis of transient thermoelastic behaviors in disk brakes, Wear, Vol. 57, pp. 47-58, 004. [10] T. NGUYEN-TAJAN, Modélisation thermomécanique des disques de frein par une approche eulérienne, Thesis of Ecole Polytechnique, 00. [11] D. Thuresson, Influence of material properties on sliding contact braking applications, Wear, 004. [1] D. Severin, S. Dörsch, Friction mechanism in industrial brakes. Wear, Vol. 49, pp. 771-779, 001. [13] M. Eriksson, F. Bergman, S. Jacobson, On the nature of tribological contact in automotive brakes, Wear, Vol. 5, pp. 6-36, 00. [14] P.J. Blau, J.C. McLaughlin, Effects of water films and sliding speed on the frictional behavior of truck disc brake materials, Tribology International, Vol. 36, pp. 709-715, 003. [15] C. H. Gao, X.Z. Lin, Transient temperature field analysis of a brake in a non-axisymmetric three-dimensional model, Journal of Materials Processing Technology, Vol. 19, pp. 513-517, 00.