Aerodynamic and Thermal Modelling of Disc Brakes—Challenges and Limitations

energies

Review Aerodynamic and Thermal Modelling of Disc Brakes—Challenges and Limitations

Alexey Vdovin 1,* and Gaël Le Gigan 2 1 Department of Mechanics and Maritime Sciences, Chalmers University, 412 96 Göteborg, Sweden 2 Volvo Car Corporation, 418 78 Göteborg, Sweden; [email protected] * Correspondence: [email protected]; Tel.: +46-31-772-3626

Received: 28 November 2019; Accepted: 25 December 2019; Published: 1 January 2020

Abstract: The brake system is a critical component for any passenger vehicle as its task is to convert the kinetic and potential energy of the vehicle into heat, allowing the vehicle to stop. Heat energy generated must be dissipated into the surroundings in order to prevent brake overheating. Traditionally, a lot of experimental testing is performed to ensure correct brake operation under all possible load scenarios. However, with the development of simulation techniques, many vehicle manufacturers today are looking into partially or completely replacing physical experiments by virtual testing. Such a transition has several substantial beneﬁts, but simultaneously a lot of challenges and limitations need to be addressed and understood for reliable and accurate simulation results. This paper summarizes many of such challenges, discusses the eﬀects that can and cannot be captured, and gives a broader picture of the issues faced when conducting numerical brake cooling simulations.

Keywords: brake cooling; computer-aided engineering (CAE) simulations; test replication; computational ﬂuid dynamics (CFD); thermal simulations

1. Introduction Friction brakes are used to convert the kinetic, and sometimes potential energy of the vehicle, into thermal energy, hence, allowing the vehicle to decelerate or stop when required. Since brakes can generate a substantial amount of heat energy in a short instance, overheating of the brake discs is a possible scenario to be avoided. Overheating can cause brake fading, brake judder, increased wear, as well as thermal cracking and even brake fluid vaporization [1,2], which constitutes a serious safety issue. Furthermore, other parts of wheel suspension, wheel cover or tire, can also be affected by high temperatures, especially during the thermal soak process [3,4]. In order to avoid brake system overheating, it is a necessity that the brake assembly is appropriately dimensioned and designed as to store and dissipate energy without reaching critical temperatures, even in the most extreme braking scenarios. Traditionally, the brake systems have been tested experimentally using different test benches, such as full-scale brake dynamometer, as well as through complete vehicle testing. However, nowadays, some tests can be replicated by CAE simulations, which are cheaper and can also provide information difficult to obtain in real life tests. Moreover, the simulations can be performed at much earlier stages, such as concept phase, hence, avoiding possible later problems in vehicle development, reducing both prototyping costs and lead time for parts and by that reducing the total length of vehicle development. The complexity of the computer-aided design (CAD) models for numerical simulations can vary significantly. Simple studies looked into modelling of a single channel inside the brake disc [5], a sector of the brake disc [6,7] or just the brake disc with some surrounding geometries [8–10]. More complex studies would include more geometrical parts [11,12], which have been shown to be more representative of the on-road conditions [11]. At the same time, from the physics perspective, these simulations

Energies 2020, 13, 203; doi:10.3390/en13010203 www.mdpi.com/journal/energies Energies 2020, 13, x FOR PEER REVIEW 2 of 12

Energies 2020, 13, 203 2 of 12 representative of the on-road conditions [11]. At the same time, from the physics perspective, these simulations would often focus either on computing convection heat transfer coefficients from a wouldcomputational often focus fluid either dynamics on computing (CFD) convectionpoint of view heat or transfer on conduction coefficients modelling from a computational through the solid fluid dynamicsparts. Simulations (CFD) point that ofinclude view or both on conductioneffects are more modelling challenging through and the demanding solid parts. in Simulations terms of setup that includesince they both require effects coupling are more between challenging fluid and and demanding thermal solvers in terms to of account setup since for changes they require in both coupling flow betweenand temperature fluid and fields thermal [12– solvers14]. to account for changes in both flow and temperature fields [12–14]. Complete replacement of the brake cooling experimental experimental tests by numerical simulations is a demanding task as itit requiresrequires accurateaccurate modellingmodelling ofof allall threethree heatheat transfertransfer mechanisms:mechanisms: convectionconvection (through(through airflowairflow passingpassing insideinside andand aroundaround thethe disc),disc), conductionconduction (through(through thethe supportsupport andand contactcontact areas) and,and, atat last,last, radiation.radiation. This paper addresses the complexity of this modelling and discussesdiscusses simplificationssimplifications andand limitationslimitations thatthat needneed toto bebe accountedaccounted for.for.

2. Complications of Modelling Aero-ThermalAero-Thermal Problems Several didifferentfferent tests tests are are usually usually performed performed to ensure ensure the the correct correct brakes brakes system system cooling performance,performance, some of them them last last several several minutes minutes and and some some can can last last much much longer. longer. Moreover,Moreover, the the dominant heatheat transfertransfer mechanismmechanism wouldwould didifferffer dependingdepending onon thethe testtest scenario.scenario. Convection isis usuallyusually the the most most important important mechanism mechanism for for cooling. cooling. Radiation Radiation is importantis important only only for highfor high temperatures, temperatures, such such as a glowing as a glowing brake brakedisc. The disc. contribution The contribution of conduction of conduction through through the support the issupport less important is less important since it is since a slow it process is a slow [10 process]; however, [10] it; however, will be dominant it will be if dominantthe test includes if the test the soakingincludes phasethe soaking when thephase vehicle when is the stopped vehicle and is stopped forced convection and forced isconvection replaced byis replaced natural convection. by natural Nevertheless,convection. Nevertheless, all these mechanisms all these mechanisms need to be modelled need to forbe modelled every test for scenario every iftest the scenario test results if the are test to beresults replicated are to accurately.be replicated accurately. Historically, CFD CFD codes were were used used to to compute compute convection heat transfertransfer coecoefficientsfficients (HTCs),(HTCs), whilewhile separateseparate thermalthermal solverssolvers werewere usedused toto modelmodel conductionconduction andand radiationradiation [[12,13,1512,13,15].]. SpecificsSpecifics ofof aerodynamic and thermal models are discussed in later chapters;chapters; here,here, the focus is onon thethe couplingcoupling processprocess andand datadata exchangeexchange between didifferentfferent solvers.solvers. It should be noted that there are studies that combine fluidfluid andand solid solid domains domains within within the same finite finite volume volume solver solver [ [16]16];; however, they they still still experience most ofof thethe issuesissues presentedpresented inin thisthis paper.paper.

2.1. Coupling Approaches The data data exchange exchange process process between between two two models, models, also also known known as as coupling, coupling, usually usually involvesinvolves transferringtransferring HTCs and reference fluidfluid temperatures from aerodynamic solver solver to to the the thermal thermal solver. solver. TheThe thermal thermal solver solver uses uses these these data data to estimate to estimate the convection the convection heat fluxes heat for fluxes part surfacesfor part and surfaces combines and itcombines with computed it with conductioncomputed conduction and radiation and fluxes radiation to estimate fluxes the to changesestimate in the components changes in temperatures components duringtemperatures a specified during time a period.specified New time surface period. temperatures New surface are temperatures then being transferred are then being to the transferred aerodynamic to solverthe aerodynamic for recalculating solver thefor airflowrecalculating around the the airflow simulated around components, the simulated see Figurecomponents,1. see Figure 1.

Figure 1. 1. SimpliﬁedSimplified couplingcoupling process. process. Twall isis the the temperature temperature of the surfaces surfaces while while T Tﬂuidfluid is the the referencereference airair temperaturetemperature nextnext toto thethe surfaces.surfaces.

The communicationcommunication between between two two separate separate solvers solvers can can be setbe upset inup several in several diﬀerent different ways. ways. The most The accuratemost accurate method method would would be to use be ato fully-transient use a fully-transient approach approach when changes when inchanges the airﬂow in the and airflow HTCs and are

Energies 2020, 13, 203 3 of 12 continuously modelled for the whole duration of the test. However, simulating several minutes of the transient airflow around the vehicle can be extremely expensive in terms of computational resources; therefore, other simulation approaches have been developed. One of the popular approaches is to consider the flow around the rotating brake disc to be independent of the surface temperatures. This assumption allows performing only a few aerodynamic simulations with different vehicle velocities. Interpolation is then used to obtain surface HTC dependency curves for all vehicle velocities. These curves are then used in the thermal model without any additional flow recalculation loops required. Such simplification works relatively well for high speed scenarios [13]; however, if the simulated vehicle velocities are slow, the buoyancy effects become more pronounced, and this approach thereby becomes invalid. More accurate simulation approaches, usually referred to as “semi-transient”, use two-way coupling between thermal and aerodynamic solvers, i.e., the airflow and HTCs are being updated several times during one simulation. In this case, surface HTCs are considered dependent on both the vehicle velocity and component surface temperatures. An important parameter for semi-transient simulations is the coupling frequency. Some approaches would assume a step curve for HTCs of the parts and require frequent recalculations of them, while others would assume linear behaviour of the surface HTCs and, hence, allow much longer time intervals between coupling [13,14,17]. Both methods have pros and cons, depending on the test scenario being simulated.

2.2. Data Mapping Addressing the complications of a coupling process, it is important to remember the data mapping between codes. Even though having a conformal mesh on the two sides of the aero-solid interface would be advantageous for matching heat fluxes between solid and fluid cells, quite often non-conformal interfaces are being used. This occurs because the mesh requirements for two solvers are quite different and having coarser mesh for thermal simulations reduces the computational effort. At the same time, non-conformal interfaces mean that a single cell from the thermal simulation would need to be mapped to several cells from the CFD side. HTCs on the aerodynamic side can be quite sensitive to the CFD mesh quality; hence, extra attention is needed when mapping them. Furthermore, it is important to make a good selection for the reference temperatures to be mapped in parallel with the HTCs as some of the parts are going to be heated up and some cooled down by the air.

3. Aerodynamic Modelling Simulating wheelhouse flows is a topic of many scientific publications as it is a very complex problem by itself. Moreover, standard aerodynamic simulations do not include the energy equation or any temperature related effects. To obtain the convection heat transfer coefficients required for coupling process, the aerodynamic simulations need to be enhanced with energy and gravity models to account for temperature gradients in the air and their influence on the airflow. The following chapter summarizes some of the main considerations and limitations for such type of simulations.

3.1. Level of Model Details The level of details in the virtual model would depend on the type of braking test being simulated, for example, emergency brake test and drag braking. Unfortunately, to simulate an actual on-road test scenario, a fully detailed vehicle model is required. The airflow in the wheelhouses depends not only on external air entering from underneath the vehicle and from the sides but also on the air coming from the engine bay. Therefore, due to asymmetrical packaging and heat distribution inside the engine compartment, the velocity and temperature fields inside the wheelhouses would be significantly Energies 2020, 13, 203 4 of 12

Energiesdifferent 2020 [18, 13]., x Consequently, FOR PEER REVIEW the cooling performance of brakes on the left and right sides would4 of be12 different as well. 3.2. Airflow Simulation Approaches 3.2. Airflow Simulation Approaches In standard aerodynamic simulations, brake discs are often simulated with moving wall boundaries,In standard which aerodynamic can significantly simulations, affect brakethe amount discs are of oftenmass simulatedflow through with the moving discs walland, boundaries, hence, the calculatedwhich can cooling significantly performance. affect the There amount are of two mass more flow advanced through the approaches discs and, to hence, simulate the brake calculated disc rotation:cooling performance. There are two more advanced approaches to simulate brake disc rotation:  Multiple Reference Frame (MRF) approach, when the the additional additional forces forces imposed imposed by by rotation rotation are are • introducedintroduced to the volumetric region inside the disc;  Rigid Body Motion (RBM) approach, when the the mesh mesh of the vanes (cooling channels inside the • disc) is physically rotated in space.

BothBoth approaches can can be be applicable, applicable, but but the the latter, latter, though being being more more accurate, requires requires using using unsteadyunsteady methods methods for for simulating simulating the the airflow, airflow, hence, hence, it is it much is much more more computationally computationally expen expensive.sive. The MRFThe MRF method method,, on the on theother other hand, hand, is beneficial is beneficial since since it allows it allows to touse use steady steady-state-state Reynolds Reynolds Averaged Averaged NavierNavier Stokes Stokes simulations simulations,, which which are are significantly significantly faster faster and and at at the the same same time time provide provide good good enough enough accuracyaccuracy for the mass-flowmass-flow throughthrough the the vanes vanes and and surface surface HTCs HTCs [19 [19].]. A A typical typical volume volume of rotationof rotation for forany any of theseof these methods methods would would be limitedbe limited tothe to the vanes vanes ofthe of the disc, disc as, presented as presented in Figure in Figure2. 2.

FigureFigure 2. RotatingRotating region region inside inside the the brake brake disc. disc.

ItIt should should be be mentioned mentioned that that this this rotating rotating region region is is only only an an addition that that is is required required for correct correct airflowairflow simulation simulation around around the the brake brake discs. discs. Other Other rotating rotating parts parts like like rims, rims, tires tires and and even even the the cooling cooling fansfans inside the engine baybay stillstill needneed toto bebe treated treated appropriately appropriately as as they they should should be be in in any any other other type type of ofaerodynamic aerodynamic simulation. simulation. Moreover, Moreover, both both the the airflow airflow inside inside and and aroundaround brakebrake discsdiscs and the surface heatheat transfer coefficients coefficients are quite sensitive to the mesh settings. 3.3. HTC Averaging 3.3. HTC Averaging Independently of using steady-state or unsteady methods for the airflow simulations, it is Independently of using steady-state or unsteady methods for the airflow simulations, it is important to remember that coupling between aerodynamic and thermal codes usually happen only a important to remember that coupling between aerodynamic and thermal codes usually happen only certain amount of times during a simulation of one test cycle. Moreover, the outer disc surfaces are still a certain amount of times during a simulation of one test cycle. Moreover, the outer disc surfaces are typically modelled as moving wall boundaries. This means that it may be necessary to average the still typically modelled as moving wall boundaries. This means that it may be necessary to average heat transfer coefficients of the rotating parts not to introduce any unrealistic temperature gradients on the heat transfer coefficients of the rotating parts not to introduce any unrealistic temperature the disc surfaces. As the airflow for the inboard and outboard side of the disc is usually significantly gradients on the disc surfaces. As the airflow for the inboard and outboard side of the disc is usually different, a recommendation is to split the brake disc surfaces to at least three regions: two outer significantly different, a recommendation is to split the brake disc surfaces to at least three regions: surfaces and the vanes. two outer surfaces and the vanes. 3.4. Simulating Tests with Soaking Phases 3.4. Simulating Tests with Soaking Phases Some of the test scenarios, for example, mountain descent test, include the soaking phase when Some of the test scenarios, for example, mountain descent test, include the soaking phase when the vehicle is standing still and the thermal energy from the disc is dissipated into the rest of the the vehicle is standing still and the thermal energy from the disc is dissipated into the rest of the braking system and the surrounding air. For the cases of pure natural convection, the velocity field braking system and the surrounding air. For the cases of pure natural convection, the velocity field inside the wheelhouse is directly affected by the temperatures of different parts; hence, it is necessary inside the wheelhouse is directly affected by the temperatures of different parts; hence, it is necessary to recompute the flow field during this phase. to recompute the flow field during this phase. Moreover, extra attention is needed for the transition between driving and soaking phases. First, it is important to have some data about the fan after-run curves and temperature distribution inside the engine compartment, as the fan is going to push warm air from the engine bay to the wheel arches.

Energies 2020, 13, 203 5 of 12

Moreover, extra attention is needed for the transition between driving and soaking phases. First, itEnergies is important 2020, 13, x to FOR have PEER some REVIEW data about the fan after-run curves and temperature distribution inside5 of 12 the engine compartment, as the fan is going to push warm air from the engine bay to the wheel arches. ItIt shouldshould bebe noted that such an additional air circulation waswas shownshown toto increaseincrease thethe rate of the soaking processprocess forfor thethe brakebrake systemsystem inin comparison to a case without fan after-runafter-run [[18].18]. Secondly, oneone shouldshould keepkeep inin mindmind thatthat the the switch switch to to natural natural convection convection does does not not happen happen instantaneously, instantaneously and, and hence, hence, it can it becan advantageous be advantageous to simulate to simulate this transitionthis transition period period using using transient transient approaches. approaches.

4.4. Thermal Modelling AA typicaltypical thermal thermal model model usually usually includes includes all all parts parts that that are inare immediate in immediate proximity proximity to the to hot the brake hot discbrake and disc participate and participate in the heat in the dissipation heat dissipation from it: brake from disc,it: brake brake disc, pads brake with pads shims with and backplates, shims and calliperbackpla withtes, calliper all internal with parts, all internal wheel parts, rim and wheel tire, rim dust and shield, tire, wheel dust shield, hub and wheel knuckle. hub and A typical knuckle. mesh A fortypical the modelmesh for will the contain model 3 will to 5 contain million cells.3 to 5 Anmillion example cells. is An given example in Figure is given3. in Figure 3.

Figure 3. Typical thermal model ofof a brake assemblyassembly includingincluding wheelwheel rimrim andand tire.tire.

AsAs mentionedmentioned previously, the the mainmain task task ofof thethe thermalthermal solver solver is is toto calculatecalculate conductionconduction andand radiationradiation heatheat ﬂuxes,fluxes, combinecombine themthem withwith the convective data obtained from the aerodynamic solver andand advanceadvance inin time,time, calculatingcalculating newnew temperaturetemperature distributionsdistributions insideinside thethe partsparts modelled.modelled.

4.1.4.1. Conduction Modelling DependingDepending on on the the brake brake test testthat is that being is modelledbeing modelled and the vehicleand the setup, vehicle the brake setup, disc the temperature brake disc cantemperature reach up to can 500–700 reach ◦ upC or to higher. 500–700 Other °C parts, or higher. even though Other reaching parts, even lower though temperatures, reaching are lower still subjectedtemperatures, to significant are still subjected spatial and to significant temporal temperaturespatial and temporal gradients, temperature and as a result, gradients their, materialand as a propertiesresult, their are material going properties to be affected. are going Hence, to tobe modelaffected. thermal Hence, conduction to model thermal within conduction parts, it is of within high importanceparts, it is of to high obtain importance temperature to obtain dependent temperatur properties,e dependent mainly specific properties, heat andmainly thermal specific conductivity, heat and forthermal all parts conductivity, participating for inall the parts heat participating dissipation, in or the at leastheat fordissipation, the brake or disc at andleast brake for the pads. brake These disc propertiesand brake canpads. also These often properties be anisotropic, can also especially often be foranisotropic, the pads. especially for the pads. TheThe conductionconduction betweenbetween partsparts inin typicallytypically handledhandled byby thermalthermal interfacesinterfaces oror thermalthermal links.links. Two surfacessurfaces in in contact contact always always have have a certain a certain amount amount of thermal of thermal contact contact resistance. resistance. This resistance This resistance depends ondepends many parameters, on many parameters including, materialincluding properties, material surface properties, roughness, surfaceand roughness the contact, and pressure the contact [20], whichpressure can [20], change which substantially can change substantially even depending even depending on the position on the of position tightening of tightening bolts [10 bolts]. In [10]. the simulation,In the simulation, the contact the contact resistance resistance can be can added be added to thermal to thermal links or links modelled or modelled by adding by adding virtual virtual layers oflayers material of material between between components. componen It cants. also It can be also used be to used replace to replace thin parts thin that parts would that require would toorequire fine meshingtoo fine meshing otherwise, otherwise, for example, for example brake pad, brake shims. pad However, shims. However, the assumed the values assumed to be values used forto be contact used resistancefor contact are resistance quite diffi arecult quite to estimate difficult as there to estimate are many as variables there are that many must variables be considered that [must21]. be consideredOne area [21]. that requires particular attention is the contact between the piston and calliper body whereOne they area are that separated requires by particular a thin brake attention fluid film. is the contact between the piston and calliper body where they are separated by a thin brake fluid film. 4.2. Radiation Modelling 4.2. RadiationOne of the Modelling easiest approaches to model radiation between parts is to use surface-to-surface radiation model. This model requires emissivity coefficients being assigned for every surface participating in the One of the easiest approaches to model radiation between parts is to use surface-to-surface radiation model. This model requires emissivity coefficients being assigned for every surface participating in the heat transfer process. These coefficients can be measured (e.g., using reflectometer) or estimated most of the times, but for some of the surfaces, it can be a challenging task.

Energies 2020, 13, 203 6 of 12 heatEnergies transfer 2020, 13 process., x FOR PEER These REVIEW coeffi cients can be measured (e.g., using reflectometer) or estimated6 most of 12 of the times, but for some of the surfaces, it can be a challenging task. The brake disc is is a a part part that that is is mostly mostly affected affected by by the the radiation radiation heat heat transfer transfer as asit is it subjected is subjected to tothe the highest highest temperatures. temperatures. Therefore, Therefore, the authors the authors have have measured measured emissivity emissivity of a large of a var largeiety variety of brake of brakediscs (alldiscs made (all made of similar of similar cast cast iron iron alloy alloy material), material), new new and and used, used, and and found found that that the the emissivity emissivity coecoefficientsfficients cancan varyvary between 0.150.15 to 0.9 depending on the disc surface conditions. This finding finding is also supported by other investigations availableavailable in literatureliterature [[10,2210,22].]. Furthermore, operating brake disc would have didifferentfferent emissivityemissivity values compared to one that is standing still. This is due to the fact that the emissivity values are temperature dependent and also because there is usually an oxidation layer atat thethe surfacessurfaces ofof the the brake brake that that is is being being cleaned cleaned away away by by the the brake brake pads pads as soonas soon as theas the brakes brakes are appliedare applied while while the vehiclethe vehicle is moving is moving [23]. [23]. As the the mesh mesh of of the the brake brake disc disc is often is often modelled modelled stationary stationary in a thermal in a thermal model modeleven during even driving during scenarios,driving scenarios, an extra an step extra is requiredstep is required to account to account for the for rotation the rotation and avoid and localavoid hot local and hot cold and spots cold formationspots formation on the on disc the surfaces. disc surfaces. The radiation The radiation patches patches on each on of each the twoof the sides two of sides the brake of the disc brake should disc beshould combined be combined to work to as work a single as a source single/ receiversource/receiver of radiation. of radiation.

4.3. Brake Fluid Modelling There are several approaches to model the brake fluidfluid and the selectionselection between them would depend on on the the importance importance of ofthe the brake brake fluid fluid simulation simulation for a for particular a particular test scenario test scenario that is that being is beingsimulated. simulated. The firstfirst and the simplest method is to use a single concentrated mass node representing brake fluidfluid inside the calliper.calliper. In this case case,, thermal links need to be set up in between this node and the corresponding surfaces of the piston and calliper.calliper. This met methodhod implies that the entire brake fluidfluid volume has the same temperature. The second approach is to have the brake fluidfluid volume wrapped and meshed so that the brake fluidfluid can be simulated as a a solidsolid bodybody with with fluid fluid materialmaterial properties.properties. This method is much m moreore accurate, but as the mixing of the fluidfluid due to convection is not allowed,allowed, it can result in rather high temperature gradients inside the fluid fluid;; see Figure4 4.. Consequently,Consequently, oneone shouldshould paypay attentionattention toto thethe position of the measurement sensorsensor duringduring thethe experimentexperiment andand itsits equivalentequivalent inin thethe simulation.simulation.

Figure 4. Example of temperature gradients inside the brake fluid volume. Figure 4. Example of temperature gradients inside the brake fluid volume. Another option is to try simulating brake fluid as fluid together with the brake lines, but that wouldAnother increase option the computational is to try simulating cost of brake such simulations fluid as fluid even together more. with the brake lines, but that would increase the computational cost of such simulations even more. 4.4. Energy Input and Disc-to-Pads Contact 4.4. Energy Input and Disc-to-Pads Contact Measuring the amount of energy that goes into the brakes and its distribution between inboard and outboardMeasuring sides the amount of the disc of energy are rather that hardgoes issuesinto the that brakes are goingand its to distribution be discussed between in the inboard Testing section.and outboard From thesides simulation of the disc side, are itrather is possible hard toissues address that thisare problemgoing to usingbe discussed finite element in the methodTesting (FEM)section. approach From the [ 24simulation,25]. However, side, it not is possible to increase to address the complexity this problem of the using simulations, finite element the amount method of (FEM) approach [24,25]. However, not to increase the complexity of the simulations, the amount of thermal energy added to the system can be estimated. Yet, even the application of this energy inside the thermal model may be a challenging task.

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thermalEnergies 20 energy20, 13, x FOR added PEER to REVIEW the system can be estimated. Yet, even the application of this energy inside7 of 12 the thermal model may be a challenging task. One of the approaches to add energy to the brake system is to apply volumetric heat fluxflux to the circular area of the disc that passes underunder the brake pads. At the same time, in real life life,, the energy is generated by friction in the contact pair between the brake disc andand brakebrake pads.pads. The energyenergy is then distributed between the contacting surfaces. Ther Therefore,efore, the volumetric fluxflux approach may lead to overprediction ofof the disc temperatures and incorrect energy flowsflows for the contacts between the brake disc and brake pads. An alternative approach is to use virtual thermal nodes in between the brake disc and the brake pad surfaces that go inin contact when the brakes are applied.applied. Figure 55 shows shows anan exampleexample ofof howhow thisthis type ofof surfacessurfaces can be defined.defined. The energy is then “added” directly to the virtual node, allowing to have heat fluxes,fluxes, that go into the brake padspads andand the brake disc, changing over time based on the material properties and temperaturestemperatures ofof thethe correspondingcorresponding partsparts asas theythey wouldwould inin reality.reality.

(a) (b)

Figure 5. ExtraExtra surface surface part part IDs IDs (PIDs) (PIDs) assigned assigned for for brake brake disc disc in ingreen green (a), ( aand), and the thebrake brake pad pad in purple in purple (b). (b). If the simulated test involves stages of driving without braking or soaking phases, the thermal linksIf between the simulated the disc test and involves the pads stages must ofbe driving adjusted without accordingly. braking or soaking phases, the thermal links between the disc and the pads must be adjusted accordingly. 5. Testing 5. Testing The numerical models and methods developed for replicating any physical test need to be The numerical models and methods developed for replicating any physical test need to be validated against real life experimental data. Therefore, it is important to know and understand the validated against real life experimental data. Therefore, it is important to know and understand the limitations and possible issues with the experimental testing. This chapter covers some of the vital limitations and possible issues with the experimental testing. This chapter covers some of the vital testing issues that are difficult to predict or incorporate into numerical models. testing issues that are diﬃcult to predict or incorporate into numerical models. 5.1. Typical Test Scenarios and On-Road Testing 5.1. Typical Test Scenarios and On-Road Testing One of the easiest ways to test brake cooling performance is to do it on a component level, for One of the easiest ways to test brake cooling performance is to do it on a component level, for example, using brake dynamometer for reduced brake assembly. Unfortunately, component tests, example, using brake dynamometer for reduced brake assembly. Unfortunately, component tests, even even with partial vehicle geometry [11], do not represent the on-road driving as there are many with partial vehicle geometry [11], do not represent the on-road driving as there are many uncertainties uncertainties that must be accounted for one way or the other. that must be accounted for one way or the other. Two typical full-scale on-road vehicle tests scenarios validating brake cooling performance are: Two typical full-scale on-road vehicle tests scenarios validating brake cooling performance are: mountain descent (also known as alpine descent) and the “Auto Motor und Sport” (AMS) test. mountain descent (also known as alpine descent) and the “Auto Motor und Sport” (AMS) test. Mountain descent test, as the name implies, is conducted on mountains and includes two phases: Mountain descent test, as the name implies, is conducted on mountains and includes two phases:

1. HeatHeat-up-up phase: phase: low low speed speed down-hill down-hill driving driving with with constantly constantly engaged engaged brakes brakes on a slope on a of slope around of around10%; 10%; 2. Thermal soaking phase: the vehicle stands still, and the heat from the brakes is transferred into 2. Thermal soaking phase: the vehicle stands still, and the heat from the brakes is transferred into the brake system and the environment. the brake system and the environment. AMS test consists of 10 repeated cycles of accelerating up to 130 km/h and braking from 130 to 0 km/h on a flat surface that are sometimes followed by the cool-down phase with constant speed driving or standing still.

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AMS test consists of 10 repeated cycles of accelerating up to 130 km/h and braking from 130 to 0 km/h on a ﬂat surface that are sometimes followed by the cool-down phase with constant speed driving or standing still. Any of the on-road tests will inevitably suﬀer from the lack of repeatability due to unpredictable and uncontrollable environment. The main considerations are the following:

Air temperature and humidity variations: outside air conditions are changing every day; moreover, • considering mountain descent, these conditions can be significantly different at the top and the bottom of the mountain, which in some cases could be compensated by proper monitoring of the driving conditions and calibration of potential numerical factors; Wind conditions: wind speed and direction change all the time. Considering the cases of low • speed driving and especially soaking phase when the vehicle is standing still, the presence of wind can significantly affect the cooling performance of the brake system; Initial part temperature variations: quite often, several tests are conducted one after another to • test various brake and wheel specifications or counteract repeatability issues. Unfortunately, it is almost impossible to get the vehicle into the same exact initial state as it was in before the first run; Road variations and driver behaviours: none of the roads or drivers are the same, and even if • driving the same road with the same driver there will be variations in how the vehicle behaves and what forces it is subjected to. The usage of a driving robot may remove driver behaviour from the equation, but even there, the road will never be exactly the same and neither will the weather conditions.

A lot of these variations can be removed if the tests are simplified and ran in a more controlled environment, but it also means that some of the important variables can be lost. Another approach to tackle repeatability issues is to use statistical analysis; however, testing is expensive and repeating a test 100 times may not be an option. Other important considerations for matching the simulations and on-road testing are the fan control strategies and the vehicle body movement during various parts of the tests. The first has already been discussed, as for the body movement, when driving downhill, the weight distribution of the vehicle is shifted forwards affecting ground clearance and, hence, affecting the flow inside the wheelhouses. Addition of the braking only increases this effect. Moreover, even on the flat road, inertial radial expansion of tires and aerodynamic lift forces would significantly increase the ground clearance of the vehicle [26,27]. Furthermore, the magnitude of this effect depends on the vehicle velocity, which can be of high importance for the AMS tests.

5.2. Wind Tunnel Testing One of the ways to reduce uncertainties is to conduct tests in a controlled environment. The best option available is to do it in the wind tunnel. This does not only allow choosing the vehicle and wind velocity precisely but also permits to have much better instrumentation as the vehicle is fixed in its position. Many modern wind tunnels are equipped with various moving ground systems that exist to prevent the formation of the boundary layer and to simulate the ground movement under the vehicle. Unfortunately, wheel drive units are often not powerful enough to withstand the high torque required to replicate braking scenarios. Therefore, braking tests need to be conducted without ground simulation with only the wheel rotating on the dynamometer, see Figure6. In the example given, a dynamometer part of the wind tunnel test section has a stationary floor, the rear wheels are standing still, and some additional pipes are present to remove the exhaust gasses. All these modifications are providing extra uncertainties as they alter the airflow compared to on-road conditions. Energies 2020, 13, 203 9 of 12 Energies 2020, 13, x FOR PEER REVIEW 9 of 12

Figure 6. Test object during the wind tunnel braking investigation.investigation.

When imitating mountain descent test in the wind tunnel, constant braking force has to be maintained. Unfortunately, Unfortunately, increasing increasing temperatures temperatures of ofthe the brake brake pads pads and and the thebrake brake discs discs alter alter the thefriction friction coefficient coeﬃcient between between these theseparts; parts;hence, hence,the pressure the pressure in the braking in the system braking must system be constantly must be constantlyadjusted. adjusted. Most of the full-scalefull-scale wind tunnels have a closed loop setup, which means that the air continues to move inside in a circular circular motion, motion, and and it it is is impossible impossible to to bring bring the the air air speed speed to to full full stop stop immediately. immediately. Consequently, in order toto imitateimitate a vehiclevehicle stopping at the beginning of the soaking phase, a windwind shield can be used to protect thethe frontfront ofof thethe vehicle.vehicle.

5.3. Sensors and Measurements Thermocouples are are widely widely used used in in industry industry to to measure measure local local component component temperatures. temperatures. They They are arecheap, cheap, easy easy to mount,to mount, accurate accurate,, and and reliable. reliable. There There are are two two types types of thermocouples: thermocouples: embedded embedded thermocouple and rubbing (also calledcalled sliding)sliding) thermocouple.thermocouple. In general, thermocouples are wired to measuring equipment,equipment, which records the voltage produced and maps the results to calibrated temperatures. Wireless thermocouples can also be used,used, but they are less reliable due to possible loss of connection and not convenient because of the added weigh weightt and space taken by by the the wireless wireless unit. unit. However, theythey allowallow measuringmeasuring temperaturetemperature onon rotatingrotating partsparts easily.easily. Thermal cameras can be used in laboratory,laboratory, butbut theythey havehave thethe emissivityemissivity issue:issue: the temperature measurement needs to be compensated at high values due to the change of emissivity emissivity,, which as for today,today, cannotcannot bebe dynamicallydynamically modifiedmodified whilewhile recording.recording. Moreover, the thermal cameras cannot be usedused for for brake brake disc disc temperature temperature measurements measurements as the as wheel the wheel rim blocks rim blocks the view. the Furthermore, view. Furthermore, thermal camerasthermal cameras are very expensiveare very expensive (for the wide (for temperaturethe wide temperature ranges observed ranges atobserved braking), at bulky, braking), and fragile.bulky, and fragile.The usual approach is to embed one thermocouple 2 mm below the outer brake pad friction surface,The i.e., usual the approach brake pad, is whichto embed is closer one tothermocouple the wheel rim. 2 mm The be thermocouplelow the outer is brake inserted pad from friction the backplate,surface, i.e. making, the brake sure pad that, which the piston is closer or calliperto the wheel finger rim. will The not thermocouple put pressure is on inserted the wire, from which the couldbackplate damage, making it or sure in the that worst the piston case, cut or it.calliper Embedding finger will the not thermocouple put pressure at theon the friction wire, surface which cancould destroy damage it sinceit or in embedded the worst thermocouples case, cut it. Embedding are not meant the thermocouple to be subjected at the to friction. friction Also,surface when can insertingdestroy it the since thermocouple, embedded thethermocouples hole can go through are not ormeant stop to 2 mm be subjected before the to friction friction. surface, Also, so when that theinserting thermocouple the thermocouple, is not exposed the hole to frictional can go through debris. or stop 2 mm before the friction surface, so that the thermocoupleWhen brake disc is not temperatures exposed to frictional are recorded debris. in some of the experiments, rubbing thermocouples are oftenWhen used brake to disc measure temperatures the average are surfacerecorded temperature in some of the on experiments, a certain radius rubbing at the thermocouples contact patch. Also,are often pyrometers used to canmeasure be used the for average the same surface result. temperature Alternatively, on thea certain brake discradius can at also the becontact drilled patch. with thermocouplesAlso, pyrometers embedded can be used under for itsthe surface. same result. This setupAlternatively, would require the brake a slip disc ring can connector also be drilled on the outsidewith thermocouples of the wheel toembedded transfer theunder signal its surface. from the This rotating setup disc, would similar require to the a slip one ring in Figure connector6. on the outsideWhen theof the brake wh fluideel to temperature transfer the needssignal to from be measured, the rotating a special disc, similar thermocouple to the one embedded in Figure in 6. the brakeWhen calliper the bleeding brake fluid screw temperature is normally needs used; to see be Figure measured7. This, a isspecial not where thermocouple the brake fluidembedded reaches in itsthe highest brake calliper temperature, bleeding but screw this is is the normally only location used; thatsee Figure is safe enough7. This is to not measure where the the temperature brake fluid withoutreaches a itsffecting highest the temperature, strength of the but calliper. this is Brake the only fluid location temperature, that is as safe provided enough by tothe measure experiment, the willtemperature be a single without point measurement,affecting the strength while as of it wasthe calliper mentioned. Brake earlier fluid in temperature Section 4.3, CAE, as provided simulations by allowthe experiment seeing the, will brake be fluid a single temperature point measurement, gradient. while as it was mentioned earlier in Section 4.3, CAE simulations allow seeing the brake fluid temperature gradient.

EnergiesEnergies 20202020,,13 13,, 203x FOR PEER REVIEW 1010 ofof 1212

FigureFigure 7.7. A modiﬁedmodified bleeding screw forfor measuringmeasuring brakebrake ﬂuidfluid temperature.temperature.

CapturingCapturing spatialspatial temperature temperature gradients gradients of of the the brake brak ﬂuide fluid experimentally experimentally is hardly is hardly possible, possible and, evenand even for the for parts the parts that are that easier are easier to access, to access, there isthere always is always a limit a of limit how of many how thermocouplesmany thermocouples can be used.can be Any used. additional Any additional thermocouples thermocouples do not do only not increaseonly increase the time the time required required for test for preparationtest preparation but alsobut also alter al theter airﬂowthe airflow around around parts. parts.

5.4.5.4. Disc Deformations andand Hot-SpottingHot-Spotting MostMost ofof thethe partsparts willwill experienceexperience thermalthermal expansionexpansion whenwhen subjectedsubjected toto highhigh temperatures.temperatures. ForFor thethe brakebrake coolingcooling tests,tests, thethe mostmost importantimportant deformationsdeformations happenhappen toto thethe discdisc asas itit experiencesexperiences highesthighest temperaturetemperature changes. changes. Unfortunately, Unfortunately, thermal thermal expansion expansion is not is the not only the deformation only deformation that occurs that during occurs braking.during braking. Conning Conningis the type is of the deformation type of deformation that occurs when that the occurs brake when disc deforms the brake elastically disc deforms and/or plasticallyelastically atand/or the neck plastically due to cyclicat the coolingneck due and to heating.cyclic cooli Anotherng and important heating. Another effect is hot-spotting.important effect is hotHot-spotting-spotting. is related to a phenomenon called Thermo-Elastic Instabilities (TEI) [28]. When braking,Hot the-spotting pair of is brake related pads to is apushed phenomenon towards called the brake Thermo disc,-Elastic which, Instabilities in return, generates (TEI) [28]. frictional When heatbraking, flux the at thepair sliding of brake interface, pads is pushed which istowards proportional the brake to thedisc contact, which, pressure.in return, generates Therefore, frictional if some unevenheat flux pressure at the sliding distribution interface arises, which at the is frictionproportional surface, to the the contact areas where pressure. the pressureTherefore, is if higher some experienceuneven pressure a higher distribution temperature arises increase. at the This, friction in turn, surface, causes the greater areas where local thermal the pressure expansion is higher and, thereby,experience leads a higher to further temperature local pressure increase. increase This, [ 29in]. tur Hot-spotn, causes positions greater local change thermal with everyexpansion new loadand, cycle;thereby, therefore, leads to measuring further local the pressure disc temperatures increase [29]. with Hot embedded-spot positions thermocouples change with can every have new serious load repeatabilitycycle; therefore, issues measuring even when the testing disc temperatures in the wind tunnel.with embedded thermocouples can have serious repeatabilitAny uneveny issues pressure even when distribution testing in at the the wind contact tunnel. between the brake disc and brake pads leads to unevenAny uneven deformations pressure and, distribution consequently, at the non-uniform contact between heat the fluxes brake at thedisc contact and brake interface. pads leads These to eunevenffects are deformations typically unaccounted and, consequently, for in the brake non- coolinguniform simulations heat fluxes but at should the contact be kept interface. in mind Thesewhen comparingeffects are thetypical resultsly unaccounted between real for and in virtual the brake models. cooling simulations but should be kept in mind when comparing the results between real and virtual models. 5.5. Energy Input Estimation 5.5. EnergyTemperatures Input Estimation in the brake system are directly affected by the amount of energy that goes into contact between the brake disc brake and pads. However, estimating this amount for each pad-to-disc Temperatures in the brake system are directly affected by the amount of energy that goes into contact is not a trivial task. contact between the brake disc brake and pads. However, estimating this amount for each pad-to- disc Whencontact the is not vehicle a trivial brakes, task. one can have a good estimation of changes in kinetic and potential energies. Unfortunately, not all of this energy goes into the braking system. Some of it is spent on When the vehicle brakes, one can have a good estimation of changes in kinetic and potential overcoming rolling and aerodynamic resistance and some ends up in drivetrain and other losses. energies. Unfortunately, not all of this energy goes into the braking system. Some of it is spent on Moreover, depending on the vehicle weight distribution and brake system setup, front and rear brakes overcoming rolling and aerodynamic resistance and some ends up in drivetrain and other losses. wouldMoreover, have depending an uneven split on the between vehicle them. weight Typically, distribution front brakes and brake take most system of the setup, load front due to an higherd rear vertical force on front wheels and vehicle stability reasons. Additionally, since the vehicles are not brakes would have an uneven split between them. Typically, front brakes take most of the load due symmetrical, brakes on the left and right side of the vehicle may have slightly different temperatures, to higher vertical force on front wheels and vehicle stability reasons. Additionally, since the vehicles whichare not would symmetrical, lead to changing brakes onfriction the left and and different right energy side of input the forvehicle them. may The have same slightly principle different applies totemperatures inboard and, which outboard would sides lead of to the changing brake disc friction where and the different energy inputenergy would input di forffer. them. Furthermore, The same theprinciple ratios applies in these to splits inboard would and change outboard during sides the of the braking brake test disc cycle, where making the energy it almost input impossible would differ. to estimate them exactly at any given moment. Furthermore, the ratios in these splits would change during the braking test cycle, making it almost impossible to estimate them exactly at any given moment.

Energies 2020, 13, 203 11 of 12

During the tests in the wind tunnel, the amount of energy added to the braking system is easier to estimate as the braking force is recorded by the dynamometer. Nevertheless, the amount of losses in various system parts and the distribution between two contact surfaces of the disc are still unclear.

6. Concluding Remarks Brake cooling performance evaluation is important since it allows safe vehicle operation in even the most extreme circumstances. Currently, most of this evaluation is performed using expensive experimental testing methods; however, there is extensive ongoing work to replicate such testing using CAE simulations. In this paper, some important effects, findings, and issues needed to be considered during this process were summarized. Brake cooling CAE simulations are complex since a large amount of material data and other properties are missing or even impossible to estimate. Additionally, there are several simulation approaches, all having different advantages and disadvantages, and a common denominator that they all require considerable simplifications. Nevertheless, it has been shown that CAE simulations give satisfactory results, especially when comparing different design choices. The simulations are not only cheaper but can also be performed at earlier stages of the vehicle development process, even when there are no prototypes available. Furthermore, as the simulations have perfect control over used boundary conditions, they provide perfect repeatability, which is something that the experimental testing is certainly struggling with. In addition, virtual models give important physical insights into the complicated heat dissipation process. The CAE simulations provide not only the temperature gradients within parts, but also the heat flux distributions for convection, conduction, and radiation for every part surface or part contact at any given time. For instance, experimentally determined brake fluid temperature is measured in a single point, while CAE simulations offer spatial temperature gradients inside the calliper. At this time, it is not yet possible to replace the experimental testing with simulations, but two approaches can be used together to complement each other. Moreover, as the computational resources become more affordable, the amount of virtual testing will increase. However, much more work is still needed to improve the existing methods and develop new ones before they can completely replace the physical testing.

Author Contributions: Most of the writing was performed by A.V., G.L.G. contributed with a substantial part of the “Testing” chapter as well as provided feedback, editing and proof-reading for the other parts of the article. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to thank engineers from Brakes, Thermodynamics and Aerodynamics groups at Volvo Car Corporation for their time and support that made this work possible. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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