Numerical Investigations of Brake
Cooling Performance
Master’s Thesis in Automotive Engineering
TIM DEKKER
VIGNESH KRISHNAN
Department of Mechanics and Maritime Sciences
CHALMERS UNIVERSITY OF TECHNOLOGY
G¨oteborg, Sweden 2018
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CFD Simulation of Brake Disc Cooling Performance: Analysis and Optimization, Guías, Proyectos, Investigaciones de Electrotecnia
This study uses computational fluid dynamics (cfd) simulations to analyze and optimize brake disc cooling performance. It investigates factors affecting cooling, heat transfer coefficient definitions, and the effects of brake disc design and rotation direction changes. The research also examines the influence of surrounding parts and proposes approaches for brake cooling simulations using star-ccm+. Key findings include the utility of the virtual local heat transfer coefficient for early comparisons, performance behavior predictability through heat transfer coefficient linearization, and identification of optimal design parameters for maximizing cooling. This research offers valuable insights into brake system design and thermal management, providing a cost-effective alternative to experimental methods. It is relevant for students and professionals in mechanical engineering, automotive engineering, and thermal sciences.
Tipo: Guías, Proyectos, Investigaciones
2024/2025
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Numerical Investigations of Brake
Cooling Performance
Master’s Thesis in Automotive Engineering
TIM DEKKER
VIGNESH KRISHNAN
Department of Mechanics and Maritime Sciences CHALMERS UNIVERSITY OF TECHNOLOGY G¨oteborg, Sweden 2018
Numerical Investigations of Brake Cooling Performance TIM DEKKER VIGNESH KRISHNAN
©c TIM DEKKER, VIGNESH KRISHNAN, 2018
Master’s Thesis 2018: Department of Mechanics and Maritime Sciences Division of Vehicle Engineering and Autonomous System Chalmers University of Technology SE-412 96 G¨oteborg Sweden Telephone: +46 (0)31-772 1000
Cover: Vector plot of flow field around the disc with velocity streamlines travelling out through the disc. The disc surfaces are coloured with the Specified Temperature Heat Transfer Coefficient.
Chalmers Reproservice G¨oteborg, Sweden 2018
Numerical Investigations of Brake Cooling Performance Master’s Thesis in Automotive Engineering TIM DEKKER VIGNESH KRISHNAN Department of Mechanics and Maritime Sciences Division of Vehicle Engineering and Autonomous System Chalmers University of Technology
Abstract
In the modern world, tough legislation on lowered emissions, leads the manufacturers to apply innovative strategies which involve aerodynamic improvements, such as covered rims. A covered rim is a good solution from an aerodynamics point of view, but poses serious constraints on the cooling performances of the brake discs, as it somewhat affects the cooling ability of the brake discs. To prevent critical situations that could lead to safety issues, such as decreased friction coefficients, brake hot-judder, increased wear, thermal cracking or even brake fluid boiling, the heat must be dissipated and hence, there is a demand for efficient cooling of brakes.
Traditionally, brake performance investigations were performed experimentally. However, with the computational power available today, these experiments can be simulated to save physical test time and resources. CAE simulations have shown good correlation with experimental results and can aid in incorporation of design changes at early stages of development. At Volvo Cars, these simulations are carried out using co-simulation where the aerodynamic and thermal solutions are calculated in parallel to get an estimate of the cooling performance.
This work examines the possibility to run mono-simulations using the CFD tool Star-CCM+ to test different approaches and investigate important parameters for brake disc cooling performance. During the project, investigations were carried out pertaining to:
- Various factors affecting the cooling performance
- Applicability of different Heat Transfer Coefficient definitions
- Effects of changes in brake disc design and rotation direction
- Influence of parts around the brake disc
- Approaches for brake cooling simulations using Star-CCM+
Some important observations made during the course of the project suggests that: the Virtual Local Heat Transfer Coefficient can be used for early comparison investigations which saves simulation time, the performance behavior due to rotational velocity variation can be predicted by linearization of the Heat Transfer Coefficient and there is an optimal point in variation of the design parameters where the best cooling performance of a brake disc type is achieved. This work was carried out at Chalmers University and with the support and valuable feedback from the brakes department at Volvo Cars.
Keywords: Brake cooling, CFD, heat transfer, vane designs, ventilated discs, rotation modelling, virtual local heat transfer coefficient
i
Preface
In this report, the results of the project work carried out during spring 2018 are reported. The work was carried out at Chalmers University of Technology in collaboration with the Brakes department at Volvo Cars Corp. The project aimed at developing a method to simulate the cooling performance of brake discs and also study the influence of external and geometric parameters on the cooling performance. The work was supervised by Ga¨el Le Gigan and Alessandro Travagliati at Volvo Cars and by Alexey Vdovin at Chalmers. This work was examined by Associate Professor Simone Sebben at the Vehicle Engineering and Autonomous System(VEAS) division at Chalmers University of Technology.
Acknowledgements
We would like to thank everybody involved directly or indirectly for their support and contribution that helped in the successful completion of this project. Our sincere thanks to our supervisors Ga¨el Le Gigan and Alessandro Travagliati at the Brakes department at Volvo Cars Corp., for sharing their experience and knowledge throughout the project. We would also like to thank Randi Franzke and Athanasios Tzanakis from Volvo Cars Corp., for contributing with strategies and a model, when we needed help.
Our sincere gratitude to our examiner, associate professor Simone Sebben for her invaluable input, guiding us through the technical know hows and for providing us with the information we needed.
We are highly indebted to our supervisor, Alexey Vdovin for spending all the precious time imparting his knowledge and expertise to us throughout the duration of the project. His continuous inputs have enhanced our thinking ability, the way we present our results and application of concepts. His support has motivated us to try and experiment different concepts.
It would not be fair on us if we did not acknowledge Emil Ljungskog and Magnus Urquhart for all their help and support, both with the workstations and with other technical inputs.
We would like to thank Chalmers University of Technology for letting us use the resources and providing licenses for softwares that aided in the successful completion of the project. We would like to extend our sincere gratitude to the members at VEAS division for making us feel home and comfortable during the course of the project work.
iii
iv
h energy [J]
H heat transfer coefficient [W/m^2 · K]
jn diffusional flux of species n [mol/m^2 · s]
k turbulent kinetic energy [J/kg]
κ thermal conductivity [W/m · K]
L length [m]
m mass [kg]
m˙ mass flow rate [kg/s]
μ dynamic viscosity of the fluid [P a · s]
∇ gradient operator [−]
N u Nusselt number [−]
ν kinematic viscosity [kg/m · s]
ω turbulence dissipation [1/s]
P pressure [P a]
φ scalar [−]
P r Prandtl number [P a]
q heat flux [W/m^2 ]
qs local surface heat flux [W/m^2 ]
Ra Rayleigh number [−]
Re Reynolds number [−]
ρ density [kg/m^3 ]
Sh source term in the energy equation [−]
σ Stefan-Boltzmann constant [W/m^2 · K^4 ]
σk closure coefficient in the k − ω turbulence model equation [−]
σω closure coefficient in the k − ω turbulence model equation [−]
τ shear stress [P a]
θ vane tangent [◦]
T temperature [K]
t time [s]
U velocity [m/s]
u∗ friction velocity [−]
u, v, w velocity components [m/s]
y+^ dimensionless wall distance [−]
yc height of near wall cell [m]
vi
Contents
Abstract i
Preface iii
Acknowledgements iii
Nomenclature v
1 Introduction
This master thesis is carried out as a part of the Masters program in Automotive Engineering at Chalmers University of Technology. The work was executed over a time period of 20 weeks.
The following report is structured into five chapters: Introduction, Theory, Methodology, Results and Discussions and Conclusions. The Introduction covers the background to explain the problem as well as the purpose and the specific questions that will be answered at the end of the project. Thereafter, a section covering the necessary theory merged with literature findings follows, for the reader to better understand the project. Then, the applied methodology and settings used are presented in the Methodology section. Based on the methodology, the findings are presented and discussed with regards to theory as well as literature findings in the Results and Discussion section. Lastly, the report ends with conclusions deduced from achieved results and discussions.
1.1 Background
One of the most critical features of a vehicle, is the ability to decelerate which is taken care of by the brake system. Brake systems can broadly be classified into friction, pumping or electromagnetic brake systems. The most commonly used brake system in the automotive industry is friction brakes. The brake system converts kinetic and potential energy into heat, which in turn is dissipated from the brake system into the surroundings. The heat transfer from the brake system can occur by three means i.e., conduction, convection and radiation. If the heat addition to the brake system is not dissipated at a high enough rate, the temperature could rapidly increase and in turn, result in overheating of brake components. This can result in brake fluid vaporization, reduced friction coefficient, brake judder, brake squeal, increased wear and thermal cracking. It then comes as no surprise, that it is important for vehicle manufacturers to investigate and thoroughly understand the thermal braking process to avoid these problems from occurring.
Traditionally, real world experiments were the primary method to investigate brake performance, although they are expensive and time-consuming. With the introduction of computer aided engineering (CAE), in particular computational fluid dynamics (CFD), these drawbacks can be overcome. Furthermore, CFD also makes it possible to visualize and perform investigations that are difficult to carry out in real life, it can be applied in early stages of development and is easily repeatable, yet again reducing cost and time.
Commonly, the computational investigations are carried out coupling two software, i.e. co-simulations; one software solving the heat transfer and the other software solving the aerodynamic flow [1, 2, 3]. For co- simulations, the boundary conditions play a key role since the two software exchange data. The reason being that, if erroneous boundary conditions are applied, an erroneous solution may be achieved. On the contrary, simulating both parts in one software may result in a higher modeling effort and larger models, thereby a larger computational cost, but can, when set up correctly, result in a more detailed solution [4].
1.2 Purpose
This project aims at defining a simulation methodology for brake cooling investigations, i.e. creating a mesh independent solution, recommend a rotation technique and turbulence model using a CFD solver, such as STAR-CCM+ which is used in this study. The established configuration will then be used to investigate heat transfer coefficients, the effect of adjacent parts on the flow field, brake disk designs, rotational direction and parameter dependencies on brake cooling performance.
1.3 Limitations
This work is performed as a master thesis by two students and is limited to a time period of 20 weeks. The main focus is on the brake discs and few adjacent parts, meaning that the influence of e.g. the wheelhouse, cooling duct or full car simulations will not be investigated. Furthermore the simulations will consider the aerodynamic and thermodynamic field, but do not cover structural analysis. Consequently, effects such as
warping, stress concentrations and cracks will not be examined in this work. The brake disc will have properties of a used, but not worn out or damaged disc. To verify the work, the obtained results and used models will be compared to literature and previous studies, but no real-world testing will be involved in the project.
1.4 Specification of the Question
Based on the outcome of the project, it should be possible to answer the following questions,
- How should the optimal configuration be defined for a limited computational resource?
- How should the Heat Transfer Coefficient be defined to reflect the heat transfer of the prescribed application?
- How does the flow field and cooling performance change with altered velocity and temperature?
- How does the flow field and cooling performance change for different brake disc designs, such as radial, tangential and curved vanes?
- How is the flow field and cooling performance affected by rotation direction?
- How does addition of adjacent parts, such as brake shield and brake calliper, affect the flow field and cooling performance?
Brake Shield
The brake shield’s (also known as the dust shield), main function is to protect the inner friction surface of the brake disc from debris and dirt, such as sand and mud. If dirt accumulates or gets trapped between the brake disc and the brake pads, the friction between the two could decrease, thereby decreasing the performance of the brake system. Another hazard is that dirt can damage the surfaces, thereby decreasing the performance and lifetime of the brake parts. However, despite the advantages of having a brake shield, the brake shield will influence the flow around the disc and hence, the heat transfer. The main disadvantage is that it will cover the inner friction surface and disturb the flow field and as found in literature, thereby lower the disc’s cooling performance [6, 7, 8]. Additionally, the dust shield may introduce noise due to stones getting trapped between the brake disc and the dust shield.
Brake Pad
The brake pads are the parts being pushed against the friction surfaces in order to stop the brake discs and thereby the vehicle. Therefore it is imperative that the friction between the two is high and consistent, and that the pad can withstand high temperatures.
Commonly, brake pads were made with asbestos since this resulted in a high friction coefficient, and thereby high brake system performance. However, since asbestos is carcinogenic, it is not used in brake pads developed today. Generally, brake pads are made out of four components; reinforcing fibres, binders, fillets and frictional additives [9].
Brake Calliper
The brake callipers houses the piston(s), which pushes the brake pads against the brake discs due to the increase in the pressure of the brake fluid. Two calliper types that can be found in vehicles today are fixed callipers and floating callipers, also known as sliding callipers. A fixed calliper uses pistons on both sides, whilst a floating calliper uses a one or more pistons on only one side. When the floating calliper pushes the brake pad against the disc, the calliper will slide along the rotation axis of the disc, until the pad on the opposite side also is pushed against the brake disc. On passenger vehicles, floating callipers are more commonly applied since these are less expensive and occupy less volume around the brake disc. On the contrary, fixed callipers can apply a more evenly distributed clamping force right away and give a better brake feel. This is why fixed callipers are more commonly applied on performance and luxury vehicles.
Similar to the brake shield, the brake calliper will decrease the cooling performance of the brake disc since it interferes with the flow field and covers approximately 15-35 % of the brake disc. As an example of this, it has been shown that by moving the calliper from facing the flow to not facing the flow behind the axle, the heat transfer can be increased both for the brake disc and the calliper [8].
Brake Disc
Equally important to the brake pads, are the brake discs, which help in bringing the vehicle to a stand still. Previously, solid brake discs were used, but, due to the increased performance and high speeds that today’s cars can reach, ventilated brake discs are becoming a first design choice. Ventilated, or vented, brake discs work in such a way that air is pumped through the brake disc due to a centrifugal force generated by rotation, similar to a centrifugal pump, improving the cooling capability of the brake disc. Many different materials have been and are in use, such as aluminum, cast steel, high carbon cast iron and even ceramic composite materials, although, grey cast iron is most frequently used for automotive brake discs.
Many different types of vented brake discs exist. Not only can the vanes be different, e.g. radial, tangential, curved, pillar or diamond vanes to mention a few, but, the surface of the disc can also vary, e.g. drilled or slotted/grooved disc. Studies have shown that the vane configuration and the brake disc parameters have a big impact on the cooling capacity of the brake disc [10].
2.1.2 Brake Discs
Three common type of brake disc designs are radial, tangential and curved vane design brake discs, as displayed in Figure 2.2. Radial vane design brake discs are the most simple and commonly used ventilated brake discs. They can be said to be non-directional, i.e. they can be mounted on either side of the vehicle and still perform equally well. The reason for their wide application is that they perform better than solid discs, are lighter compared to tangential and curved vane discs and are non-directional. However, it has been shown that when the vane angle is low, i.e. for radial vanes, a high mass flow through the disc is necessary and separation and recirculation may occur on the inlet of the vanes, resulting in less flow through the vanes [11].
(a) Radial vane design (b) Tangential vane de- sign
(c) Curved vane design
Figure 2.2: Radial, Tangential and Curved vane type brake disc.
The tangential vane design is similar to the radial vane design as they have straight vanes, but placed at an angle, defined by θ in Figure 2.2, and the curved vane type can be described as bent tangential vanes. Both these types of vanes are directional, meaning that the manufacturer either has to generate two different brake disc designs for the two sides of the vehicle, or has brakes that will perform better on one side of the vehicle. These brake discs generally have longer vanes compared to the vanes of radial vane design and perform better when rotated in the correct direction. Having a longer vane introduces more material and more cooling area, hence better interaction with the flow. A disadvantage is that the brake discs become heavier and will be more expensive to manufacture, especially if the manufacturer creates one disc for each side of the car.
To produce non-directional high performance brake discs, pillared and diamond vane type discs, as displayed in Figure 2.3, were introduced. These discs partly include the superior performance that curved vane discs have without having to take rotational direction into consideration. However, they come with the drawback of an increased manufacturing cost and casting scrapping rate due to the fact that the core is less stable. Lately, performance vehicle manufacturers have started mixing different patterns, e.g. combining curved with discontinuous curved vanes.
Figure 2.3: Vane-layout for a mix pattern vane brake disc [12].
The common parameters varied between brake discs are the vane width, vane angle (for tangential vane design brake discs), vane curvature (for curved vane designs brake discs) and the number of vanes, as shown in Figure 2.2. When the vane width is increased and the number of vanes are kept constant, the volume through which
2.3 Turbulent Flow
Turbulence is omnipresent in our daily lives. It is one of the most commonly occurring flow phenomenon and is one of the key elements in CFD. Turbulence significantly affects mass, momentum and heat transfer rates. It is a decaying process where large disturbances in the flow are formed by absorbing energy from the bulk flow which break down to smaller disturbances and eventually become laminar in nature. Turbulent flows can be characterized by being diffusive, irregular, chaotic and consist of a wide range of length scales, velocity scales and timescales.
Solving turbulent flow is very time-consuming, hence it is commonly modelled in the form of mathematical equations which can model the disturbances and its effect on the flow. Sometimes the information near the wall regions cannot be captured and needs extra steps in modelling, especially in the boundary layer region. The turbulent boundary layer can be divided into inner region and outer region based on the thickness from the wall. As shown in Figure 2.4, the inner region of the boundary layer can further be divided into viscous layer, buffer sub-layer and fully turbulent layer. The level upto which the flow properties have to be resolved is decided by the user and influences how the geometry is discretized.
Figure 2.4: Sub-layers in the turbulent boundary layer [18]
Discretizing a geometry means dividing the geometry into smaller elements/cells of a known shape. In order to capture the flow properties in the boundary layer, care has to be taken during discretization. Each sub-layer in the boundary layer has an associated dimensionless distance from the wall, i.e., y+ value that helps in determining the first cell height. The user can decide upto which sublayer the flow properties have to be captured. This lets the user know the associated y+ value of the sublayer and in turn the first cell height. The y+ value is a function of the velocity of the flow in the first cell, u∗, the kinematic viscosity ν, and the distance to the wall, y as given in equation 2.4 and equation 2.5.
u∗ =
τw ρ
y+ =
u∗y ν
The choice of the first cell height is dependent on the requirements of the turbulence model and wall function that are being used. Wall functions are semi-empirical rules that are based on the logarithmic law of the wall [18]. These functions help in avoiding dense meshes near the wall and are needed when a particular turbulence model is not valid in the viscosity affected region near the wall. They are used to estimate properties in the first cell close to the wall and hence demand a wise choice of first cell height near the wall. Taking into account the level of detail needed and computational time, a choice of wall treatment can be made between low y+, high y+ or an all y+ wall treatment, each having a different requirement of the first cell height. For a varying geometry with difficulty in achieving a consistent y+, an all y+ treatment can be used.
Some turbulence models solve one transport equation while others use two equations. In this work, a two- equation turbulence model will be used, which are discussed in more detail, in the following section.
2.3.1 RANS
Reynolds Averaged Navier Stokes equation (RANS) is based on statistical averaging of Navier Stokes (NS) equation. In RANS equation, each term of NS equation is decomposed to mean and fluctuating components, as can be represented by equation 2.6. φ = φ′^ + φ¯ (2.6)
Where, φ can be e.g. velocity component, pressure, energy or species concentration. Since NS equation is non-linear, a non-linear acceleration term appears when averaging NS equation. This term is known as Reynolds Stress and cannot be solved directly, which is why it has to be modelled. The turbulence models for RANS provide the terms that are required to calculate the eddy viscosity νT , which is then used in Boussinesq approximation, equation 2.7, to model the Reynolds stresses. Two commonly applied turbulence models to do so, are the Realizable Two-Layer k − ε and SST Menter k − ω, which will be introduced in the following two subsections.
Realizable Two-Layer k − ε
k − ε is a model to close RANS by introducing transport equations for the turbulent kinetic energy, k, and dissipation rate of k, ε, to obtain the eddy viscosity. In the standard k − ε model, the normal stress can become negative for flows with large mean strain rates. In a realizable model, a correction factor that is a function of the local state of the flow, Cμ, is introduced in the turbulent kinetic energy equation. This is done by introducing Boussinesq approximation, equation 2.7, to analyze the normal components of the Reynolds stress and ensures that the normal stresses are positive for all flow conditions, making it realizable.
〈uiuj 〉 = Σi
u^2 i
k − 2 νT
δ 〈Ui〉 δxj
Another difference is that ε equation is modified in realizable k − ε model, that makes the model not only predict planar flows, but also axi-symmetric flows. This also makes the realizable k − ε model suitable for flows involving rotation and separation. The advantage of using a two layer model is that the entire boundary layer is resolved until the viscous sub-layer.
SST Menter k − ω
In the k − ω turbulence model, transport equations are introduced for k and ω, to solve eddy viscosity, and thereby close RANS. The specific dissipation, ω, is used as the length-determining quantity, where ω ∝ (^) kε.
The use of Shear Stress Turbulence (SST) Menter k − ω model, combines the best of two models i.e, it uses both k − ε and k − ω. The low Re turbulence near the wall is modelled using the k − ω model and is switched to k − ε in the free-stream, making the SST model less sensitive to free-stream turbulence properties, as is a problem when using k − ω model alone. This property makes it usable in flows involving adverse pressure gradients and separating flow, although there is a risk of erroneous predictions in stagnation zones and regions with strong acceleration.
The use of this model has been proved advantageous, especially in the near wall regions as it eliminates the need for wall functions in the viscous sub-layer. However at low Re, there is a requirement of a very fine mesh close to the wall.
2.3.2 URANS
Unsteady Reynolds Averaged Navier Stokes (URANS) can be used when a long-term periodical oscillation is to be investigated. Turbulence fluctuations of flow quantities are not resolved in URANS approach. In this model, turbulence stress is introduced in the Navier-Stokes equation and have to be modelled using the available two equation models [19].