The Simulation of Brake Dust Deposition A P Gaylard and D Lynch Jaguar Land Rover J Amodeo and R Amunugama Exa Abstract The application of brakes on a vehicle leads to the generation of a cloud of heated particles ejected from brake discs and pads, which can be entrained by the flow around the wheels and deposited on their surfaces. Under some circumstances, this may be considered inconvenient or unsightly. This paper describes the development of a brake-dust deposition simulation, using a commercially available CFD code. A range of approaches was investigated to account for the effect of wheel rotation and the propagation of brake dust particles. A comparison to simplified laboratory dynamometer experiments is presented and the most successful CFD method is applied to a full car model, providing insight into the brake-dust deposition mechanisms. Introduction As customer expectations of premium automotive product rise and the need to optimise wheel design for aerodynamics becomes more pressing, it is important to have a virtual toolset available that can assess brake dust deposition alongside brake heating and wheel system drag. This paper describes the development of a CFD brake dust deposition assessment method, using a commercially available Lattice Boltzmann (LBM) CFD method (Exa PowerFLOW). Three different approaches to accounting for wheel-rotation were investigated: applying a rotational velocity boundary condition (VBC), moving reference frame (MRF) or a sliding (rotating) mesh (RM). Additionally, two simulation techniques for modelling the propagation of the brake-dust through the flow field were examined: time-averaged Lagrangian particle tracking (ALPT) and transient Lagrangian particle tracking (TLPT). These were compared to a simplified laboratory experiment. The combination of rotating (wheel) mesh and transient Lagrangian particle tracking (RM/TLP) is shown to produce a wheel-soiling pattern that most closely resembles the experimental data. The RM/TLPT model was applied to a whole-car aerodynamic CFD model, providing an assessment method integrated into the vehicle aerodynamics / thermal management toolset, as well as insights into the brake-dust soiling mechanism.

Previous Relevant Work The authors have been unable to locate any previous attempt to model the deposition of brake dust on wheel rim surfaces. However, this work does require the accurate representation of the local flow induced by wheel rotation. The simulation of wheel rotation has received much attention within the context of automotive aerodynamics CFD. The complexity of modelling rotating wheels and the computational limitations of the time, led to the initial studies focussing on simple, solid, isolated wheels. For example, Axon, Garry, and Howell [1] reported such a simulation using a steady-state RANS solver and exploiting centreline symmetry. Wheel rotation was accounted for by applying a rotational velocity to the wheel surface. Skea, Bullen and Qiao [2] adopted a similar approach, but eschewed the use of a symmetry plane. It was quickly appreciated that the flow structures generated by a wheel in isolation differed to those seen with the wheel installed in a wheelarch. Axon, Garry, and Howell [3] extended their work to include a simple wheel housing contained within an aerodynamically neutral idealised body; as did Skea, Bullen and Qiao [4]. In both cases, a rotational velocity was applied to the surface of a simple, solid wheel. Wäschle et al [5] examined the flow structures and aerodynamic forces generated by an isolated 'Formula-1' wheel in both 'rotating' and stationary configurations. They compared two CFD codes: a RANS and a Lattice Boltzmann (LBM) solver. In the case of the RANS solver, wheel rotation was simulated using the Multiple Reference Frame (MRF) technique and a steady-state simulation was performed. They were only able to apply the rotational velocity approximation, when using the LBM solver, though a transient flow field solution was obtained. Comparing to both Laser Doper Anemometry (LDA) and force balance measurements, they concluded that the CFD codes were, "able to reproduce the main flow structure measured with LDA as well as integral coefficients for the chosen test cases. The achieved results show an excellent agreement with the wind tunnel results"; though local discrepancies remained. Earlier work had shown the importance of simulating wheel induced flows in the context of the local vehicle body. Huminic and Chiru [6] published the results of a study using a simplified car and applying a rotational velocity to the wheel surfaces; though this work did not include any comparable experimental data. Dimitriou and Klussmann [7] also reported the results of a limited study of a wheel in situ. Using CFD as a flow visualisation tool, they explored the flow topology for the wheel related flows seen on a BMW Z4 model (at 1:2 scale). Their conclusion on the viability of numerical simulation was that, "the basic problems associated with the use of a CFD code, such as the solution dependency on the chosen turbulence model and the inability to simulate the actual rotating wheel, would not allow us to reliably draw conclusions regarding the vertical forces that a rotating wheel experiences" This view has been contradicted by the work of Wäschle [8]. This study used a Mercedes-Benz E-Class limousine, simplified to provide a reduced scale model (1:4)

and fully detailed production geometry (1:1 scale). Closed, simplified, and detailed wheel rims were investigated using a steady-state RANS simulation. Wheel rotation was accounted for using the MRF technique. The results were characterised as showing, "good agreement in force coefficient changes and time-averaged topology". Finally, Duncan et al [9] recently reported on a study using the same LBM CFD solver relied on in this work to model the effect of wheel styles on vehicle aerodynamic forces, accounting for wheel rotation using both the simple rotational velocity boundary condition and a true wheel rotation using a sliding mesh-multi-domain technique. They found that actual wheel rotation was required to capture local changes in transient flow structure. This brief, and necessarily incomplete, literature review highlights the importance of modelling wheel-related flows in situ, using detailed geometry. Whilst apparently, acceptable results have been obtained using the rotational velocity boundary condition and MRF approaches, it is likely that brake dust propagation is strongly influenced by transient local flow structures. Hence, the approach of Duncan et al [9] could be expected to be the most realistic. The second element of this study is the modelling of brake dust particles moving under the influence of a combination of their own (limited) momentum and the local flow. Particle models have been combined with automotive aerodynamics simulations to investigate water-contamination of (principally) mirrors and front side glass. Generally, a Lagrangian particle-tracking model has been combined with a thin (surface) film model [10, 11, 12] though simple Lagrangian approaches have also been studied [13]. Kuthada and Cyr [14] provided a comprehensive overview of vehicle soiling issues and the use of the ALPT approach for road spay driven off the vehicle's tyres. Finally, Jeli� et al [15] recently reported brake-cooling simulations for a mid-size sport utility vehicle exploiting the LBM solver used in this study. This work fully resolved the brake system geometry and reported simulations at different vehicle and airflow velocities. Conduction, radiation, and convection effects were accounted for by automated coupling between the flow and separate thermal solvers. The method was shown to be able to predict the brake temperatures of both the full braking cycle and the cool-down within the limits of experimental uncertainty. Simulation Concept It is difficult to obtain reliable experimental data on wheel soiling from brake dust. In-service assessments contain large uncertainties in both environmental conditions and brake usage. Test track experiments can overcome these issues, but still share the common limitation that the material deposited on the wheel surfaces is a combination of brake dust, tyre, and road debris. Therefore a CFD simulation method is attractive, particularly one that can be run within the aerodynamic (drag reduction) and thermal management (brake cooling) process [15].

To seek to overcome the limitations of vehicle-based experimental data, a simplified dynamometer experiment was devised. This had the advantage of ensuring that only brake-dust soiling was being assessed, within the context of known brake usage and controlled environmental conditions. Facility limitations meant that this correlation experiment did not include a realistic (compared to the wheel in situ) onset flow, neither could a tyre be included. However, it was assumed that a CFD approach, which could reproduce the pattern of soiling on a wheel under these conditions, would have validity within the context of a whole car CFD model. Hence, this approach was used to prototype a CFD method that could subsequently be applied to a wheel in place on a vehicle. Correlation Experiment A schematic of the correlation experiment is shown in Figure 1(a), along with the representation used in the initial CFD model development (b). This set-up mounts the styled alloy wheel (outer face) onto a shaft, along with some elements of the suspension and the brake system. The powered shaft allows the wheel to be spun up to a set speed and the brake applied to bring it to a stop. This process can be repeated, producing known brake cycles and any dust deposited on the brake surface assessed colourimetrically. The rig also has the ability to introduce a cross-flow through the wheel, though the results reported here refer to rotation only.

Figure 1 (a) Simplified Correlation Experiment Schematic (Plan View) and

(b) CFD Model.

(a)

(b)

A typical result is shown in Figure 2 (all dark and discoloured surfaces are soiled), for three braking cycles, from 100 km/h to a stop. This shows that the rim is the main area of deposition, whilst on the spokes particles accumulate on the leading edge, with the heaviest concentration closest to the rim.

Figure 2 Typical Dynamometer Rig Result, Showing Soiling (Dark and

Discoloured Surfaces) on the Wheel Rim CFD simulation

The use of a simplified dynamometer experiment meant that the wheel rotation and brake dust modelling aspects of the method could be prototyped on a small CFD model (Figure 1(b)). This enabled the least complex way of accounting for wheel rotation to be identified along with the best available approach to modelling the particle release and propagation. Wheel Rotation Three modelling options were trailed to account for the effects of wheel rotation, in order of increasing complexity, computational cost, and physical realism, these were: (a) rotational velocity boundary condition (VBC), (b) multiple reference frame (MRF) and a sliding (rotating) wheel mesh (RM). The VBC method applies a rotational velocity to the wall boundary, and defines an axis of rotation. It is predicated on the assumption of rotational symmetry, which is violated by the wheel spokes seen in these cases. Whilst computationally simple, it is unlikely to provide an adequate model in this case. The MRF approach provides a more physically accurate simulation. The wheel hub is contained within a local rotating reference frame. Forces consistent with rotation (centrifugal and Coriolis forces) are applied to the fluid within the region, and fluid velocities are transformed across the boundary between the rotating frame and the global reference frame. This does not provide an actual rotation of the geometry, so will introduce artefacts when flow properties are not axisymmetric. The final option examined (RM) actually rotates the wheel hub and so provides a complete model of wheel rotation – but at a higher computational cost. Figures 3 to 6 illustrate the flow simulations provided by each of these approaches.

Monitoring Locations

Direction of rotation

Figure 3 Instantaneous Surface Flow Pattern Generated by the Simulated

Rig Model with (a) Velocity Boundary Condition, (b) Moving Reference Frame and (c) Rotating Wheel Mesh

As expected the VBC approach generates a flow field that is very different to the two more physically realistic approaches (Figure 3(a)). In particular, the radial velocity gradient is not captured by the VBC method. The MRF and rotating mesh approaches yield similar velocity distributions; with more evidence of small-scale flow structures seen using the RM method.

Figure 4 Surface Static Pressure Distribution Generated by the Simulated

Rig Model with (a) Velocity Boundary Condition, (b) Moving Reference Frame and (c) Rotating Wheel Mesh

(a) (b) (c)

(a) (b) (c)

Comparing the surface pressure distributions (Figure 4), supports the observations made on the near-surface velocity plots: the VBC does not provide a physically convincing representation of the flow, whilst the MRF and RW approaches show similar trends. Specifically, high-pressure regions are seen on the leading faces of the spokes, with suction generated on the outboard surface of the leading spokes – associated with a high-speed attached flow. Some 'pockets' of high pressure are apparent at the forward-facing intersections of the spokes and inner rim surface. Also, some cross flow is present, unlike the VBC simulation.

Figure 5 Flow Velocity in Two Perpendicular Planes Generated by the

Simulated Rig Model with (a) Velocity Boundary Condition, (b) Moving Reference Frame and (c) Rotating Wheel Mesh

In Figure 5 the velocity magnitude is plotted on two perpendicular planes through the wheel. The VBC (a) generates little flow near the wheel, the simulated rotation only producing a boundary layer over the external surface of the rim. The MRF (b) and RW (c) models both produce a significant radial flow, which is stronger in the case of the RW model. Streamlines are used in Figure 6 to visualise the flow structure generated by the three approaches trialled to represent the effect of wheel rotation. They show that MRF and RW models force cross flow inside the hub, though much of this is directed inboard, leaving open the question of how brake dust, released at the brake disc, is deposited on the outer rim surface.

(a) (b) (c)

Figure 6 Flow Structure Generated by the Simulated Rig Model with (a)

Velocity Boundary Condition, (b) Moving Reference Frame and (c) Rotating Wheel Mesh

Brake Dust Time-Averaged Lagrangian Particle Tracking (ALPT) The CFD simulation software uses a basic Lagrangian particle tracking approach; however, it does exploit the transient aerodynamic flow field to some degree. A series of contiguous short-time average flow fields are recorded during the simulation. Particles are then released into the first of these 'data frames' and their path calculated using the force balance illustrated in Figure 7. They are assumed to be spherical, of a given dimension and density. When released into the flow their velocity is also prescribed a priori. The particles are tracked through the 'frozen' flow field until they leave the flow domain or impact on a surface. The distribution of particle impacts on the surfaces is recorded and the same process repeated on the next 'data frame'. The cumulative particle impact distribution is then updated. This approach assumes one-way coupling that is the flow affects the trajectory of the particle, but the particle's presence does not affect the flow. This is an economic

(a) (b) (c)

assumption, which can be justified if the mass loading of particulate matter in the airflow is relatively low. It has several important limitations in this application. First, this representation is not truly transient. The particles are convected through a series of 'frozen' time-averaged flow fields, rather than tracked through the instantaneous flow field. Also, the particles are assumed to 'stick' where they hit surfaces.

Figure 7 Forces Experienced By Individual Particles (after Kuthada and Cyr

[14]) The brake dust was represented by particles with diameters normally distributed over a range of (1 – 10) × 10-6 m with a density of approximately 5000 kg·m-3. The particles were released from a surface constructed with the same diameter as the wheel rim, having a depth reaching from the centre of the brake disc to just past its outside face. This is shown in Figure 8. The assumption inherent in this approach is that the spread of brake dust through the flow field is not dominated by the local mechanisms of its release (i.e. 'lathing' from the brake disc / pad contact patch): particles are released uniformly across the disc surface. Transient Lagrangian Particle Tracking (TLPT) During the course of this work, it became possible to use an enhanced particle-tracking algorithm. Rather than track particles through 'frozen' flow fields a true transient simulation was used, in conjunction with the rotating wheel model. For each rotational time step (2.224 × 10-3 s – 1/10th of a spoke rotation at 50 km/h) 20,000 particles were released and tracked. The mass deposition distribution was recorded for the rim and then the next time step was calculated – updating the rim soiling distribution. This process was repeated for 862 time steps (1.9 s in total).

Figure 8 Particle Release Surface for the Particle-Based Models Final Model Choice Given the potential importance of local small-scale transient structures in transporting the simulated brake-dust particles, the wheel rotation model was selected. As seen in the work of Duncan et al [9], only this approach accounts for the local flow disturbance caused by the movement of the spokes. This conclusion is further supported by the surface pressure distribution presented in Figure 4. The particle mass distribution shown provided in Figure 9 also highlights the importance of using a true transient simulation of the particle dynamics. The ALPT method (a) shows much less soiling than the TLPT approach (b). Comparing the deposition patterns seen in Figure 9(b) with the experimental data of Figure 2 reveals that both predict the same general trend: most soiling on the rim, whilst on the spokes particles accumulate on the leading edge, with the heaviest concentration closest to the rim. Having validated, to the extent possible, the approach to be used for simulating wheel rotation, brake dust particle transport, and deposition this was applied to an aerodynamics CFD model of a complete vehicle; in this case the Jaguar S Type.

Figure 9 Surface Deposition Pattern for the (a) ALPT and (b) TLPT Methods Whole Car Model Vehicle Two key changes were made to the prototype method outlined. Due to the geometric complexity of the whole car model, the rotation was applied to the wheel only, whilst a rotational velocity was applied to the tyre. Also, to match more closely the braking process, after establishing a fully developed flow field for a steady speed, the wheel was decelerated from 50 km/h to rest in 1.5 s. The vehicle chosen for this part of the study was the Jaguar S Type, a model that is now out of production (see [16] for further details). However, a fully detailed, open-cooling aerodynamics model was available. The vehicle surfaces used are shown in Figure 10.

Figure 10 S Type CFD Model Surfaces Showing (a) Brake Disc and (b)

Caliper

(a) (b)

(a) (b)

CFD Model Details

Figure 11 Car in Computational Domain with Main Variable Resolution (VR)

Regions Shown. The computational domain used in illustrated in Figure 11. The edge lengths (�Vx) of the cubic volume elements used in nested regions of increased resolution (VR) are also provided for the zones most distant from the car. This strategy delivered a 0.1% solid blockage in the flow domain.

Figure 12 Local Variable Resolution (VR) Regions. VR6 (0.02 m), VR7

(0.01 m), VR8 (5 mm), VR9 (2.5 mm) and VR10 (1.25 mm) In the immediate vicinity of the car, high levels of spatial resolution were provided (Figure 12). Figure 13 shows that particular attention was paid to resolving the flow through the grille, and the front wheel (�Vx = 1.25 mm), with the smallest volume elements around the braking system (�Vx = 0.625 mm). In total, the model comprised 50 × 106 volume elements and 10.4 × 106 surface elements. A moving ground boundary condition was used across the complete floor. Centre-line symmetry was exploited to reduce the computational effort.

Inle

t

VR1 (0.64 m)

VR2 (0.32 m)

VR3 (0.16 m)

VR0 (1.28 m)

VR4 (0.08 m) VR5 (0.04 m) VR6 (0.02 m)

Out

let

Ceiling

VR8

VR6

VR7 VR9

VR10 (Intake & chin)

Car

Figure 13 Variable Resolution Regions Close To The Front Wheel. VR9 (2.5

mm), VR10 (1.25 mm), and VR11 (0.625 mm) The simulation was run with an onset flow velocity of 50 km/h, equivalent to a Reynolds number (based on vehicle height) of 1.43 × 106. The time step length for the transient flow solution was 6.95 × 10-6 s. Results The predicted flow structure obtained from the S Type simulation is summarised by the instantaneous plots provided in Figures 14 and 15. These reveal a very different flow topology than that seen in the correlation experiment. Given that this did not include a tyre, ground plane, onset flow or car body, this is entirely expected. The presence of these realistic elements in the CFD model, result in a local flow around the wheel that shows flow both outboard through the wheel (Figure 14(a)) and inboard into the rim (Figure 14(b)). The former provides a mechanism for the transport and deposition of brake dust particles onto the outboard wheel surfaces. Figure 15(a) provides evidence of flow structures moving axially through the wheel, as well as some radial flow into the upper part of the wheel arch (at close to the 90° position). The surface velocity plot (Figure 15(b)) indicates the presence of small-scale transient structures on the tyre wall and wheel rim.

VR9

VR9 VR10 (Chin & front wheel deflector)

VR10 VR11

Figure 14 Flow Streamlines Around The Rotating Wheel (a) With S Type

Body Shown and (b) With The Body Hidden.

Figure 15 Instantaneous Flow Velocities (a) In Two Perpendicular Planes

Through The Wheel Centre and (b) On The Wheel Surface.

(a) (b)

(a)

(b)

Figure 16 Final Brake Dust Deposition Pattern Finally, the resultant brake-dust particle deposition pattern is shown in Figure 16. Comparing this to Figure 9(b) shows that the inclusion of physically realistic geometry and boundary conditions leads to the prediction of more soiling, particularly on the spokes, as well as near-uniform soiling of the rim. Conclusions Within the (admittedly significant) limitations of the experimental data, it appears possible to simulate the deposition of brake dust onto wheel surfaces. The particle transport process appears to be driven by small-scale, local, transient structures in the flow. Given this, accurate representation of wheel rotation (via a rotating mesh) along with a transient flow simulation and particle tracking approach are essential. The flow structures which appear to be responsible for the dust transport are generated by the rotation of the spokes; so it is likely that wheels with bluff spoke designs (like the one shown in this work) may be more vulnerable to soiling. Conversely, aerodynamic profiling of the spokes may reduce susceptibility to soiling. A simple Lagrangian particle tracking method appears to be sufficient to capture this phenomenon, although it must be coupled with a transient flow solution.

Finally, it should be noted that this method assumes a level of brake-dust particle release from the disc surface. Hence, it can only help assess the relative vulnerability of wheel designs to soiling, given a particular level of brake dust generation. Acknowledgements The authors would like to thank Jaguar Land Rover for granting permission to publish this paper. Further, they would like to recognise the contribution of Irena Ndindabahizi (Exa) to this project. References

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