Aerodynamic and Thermal Modelling of Disc Brakes—Challenges and Limitations
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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 experimentalexperimental 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 teststests areare usuallyusually performedperformed to ensureensure thethe correctcorrect brakesbrakes systemsystem cooling performance,performance, some of themthem lastlast severalseveral minutesminutes andand somesome cancan lastlast muchmuch longer.longer. Moreover,Moreover, thethe 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 glowingas a glowing brake brake disc. 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 processis a slow [10 process]; however, [10] it; however, will be dominant it will be if dominant the 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, CFDCFD codes werewere usedused toto computecompute 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 solidsolid domainsdomains withinwithin the same finitefinite volumevolume solversolver [[16]16];; however, theythey stillstill experience most ofof thethe issuesissues presentedpresented inin thisthis paper.paper. 2.1. Coupling Approaches The datadata exchangeexchange processprocess betweenbetween twotwo models,models, alsoalso knownknown asas coupling,coupling, usuallyusually involvesinvolves transferringtransferring HTCs and reference fluidfluid temperatures from aerodynamic solver solver to to the the thermal thermal solver. solver. TheThe thermalthermal solver solver uses uses these these data data to estimate to estimate the convection the convection heat fluxes heat forfluxes part surfacesfor part andsurfaces 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. T wall isis the the temperature temperature of the surfacessurfaces whilewhile TTfluidfluid is thethe 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