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Applied Thermal Engineering 52 (2013) 293e303

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Multiphase CFDeCHT optimization of the cooling jacket and FEManalysis of the engine head of a V6 diesel engine

Stefano Fontanesi*, Matteo GiacopiniUniversity of Modena and Reggio Emilia, Department of Engineering “Enzo Ferrari”, via Vignolese 905, 41125 Modena, Italy

h i g h l i g h t s

< CFDeFEM heat transfer/fatigue-strength analyses of an internal combustion engine.< Multi-domain CHTeCFD model covering both the coolant and the metal components.< Detailed CFD modeling of the phase transition within the coolant galleries.< Combined high-cycle and low-cycle fatigue analysis.< Energetic criterion for low-cycle fatigue analysis of the combustion dome region.

a r t i c l e i n f o

Article history:Received 9 July 2012Accepted 7 December 2012Available online 20 December 2012

Keywords:Engine headHeat transferBoilingFatigue analysis

* Corresponding author. Tel.: þ39 (0)59 2056114; fE-mail address: stefano.fontanesi@unimore.it (S. F

1359-4311/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.applthermaleng.2012.12.00

a b s t r a c t

The present paper proposes a numerical methodology aiming at analyzing and optimizing an internalcombustion engine water cooling jacket, with particular emphasis on the assessment of the fatiguestrength of the engine head.

Full three-dimensional CFD and FEM analyses of the conjugate heat transfer and of the thermo-mechanical loading cycles are presented for a single bank of a currently made V6 turbocharged Dieselengine under actual operating conditions.

A detailed model of the engine, consisting of both the coolant galleries and the surrounding metalcomponents is employed in both fluid-dynamic and structural analyses to accurately mimic the influenceof the cooling system layout on the thermo-mechanical behavior of the engine.

In order to assess a proper CFD setup useful for the optimization of the thermal behavior of the engine,the experimentally measured temperature distribution within the engine head is compared to the CFDforecasts. Particular attention is paid to the modeling of the phase transition and of the vapor nucleiformation within the coolant galleries.

Thermo-mechanical analyses are then carried out aiming at addressing the design optimization of theengine in terms of fatigue strength. Because of the wide range of thermal and mechanical loadings actingon the engine head, both high-cycle and low-cycle fatigue are considered. An energy-based multi-axialcriterion specifically suited for thermal fatigue is employed in the low-cycle fatigue region (i.e. thecombustion dome) while well-established multi-axial stress/strain-based criteria are adopted to inves-tigate the high-cycle fatigue regions of the engine head (i.e. the coolant galleries).

The proposed methodology shows very promising results in terms of point-wise detection of possibleengine failures and proves to be an effective tool for the accurate thermo-mechanical characterization ofinternal combustion engines under actual life-cycle operating conditions.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Internal combustion engines undergo cyclic thermo-mechanicalloadings and are subjected to a wide range of operating conditions,

ax: þ39 (0)59 2056126.ontanesi).

All rights reserved.5

in terms of both temperature distribution and frequency/amplitudeof mechanical and thermo-mechanical loading cycles.

Consequently, in order to accurately evaluate the mechanicalstrength of engine components, two different fatigue cycles must bemodeled: (i) the fatigue cycle related to the combustion process,whose frequency is strictly related to the crankshaft revving speed,(ii) the thermally induced fatiguecyclewhose frequency isdependenton the ignition/engine warm up/switch off/engine cool down cycle.

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303294

On one side, traditional and well-established stress-based [1] orstrain-based [2] fatigue criteria can be proficiently employed toanalyze the effects of the application of high-frequency loadings.On the other side, low-frequency thermo-mechanical loadings arestill an open challenge for the designers. In fact, a unique andwidely recognized procedure for the low-cycle fatigue strengthassessment of engine components is not yet available. Relying ona formerly developed energy-based criterion [3], analyses of low-cycle fatigue phenomena in engine components such as cast-ironengine manifolds [4] or aluminum alloy engine heads [5] havebeen performed, whose predictive capability in terms of consis-tency between numerical forecasts and experimental evidences isconfirmed by recent applications [6].

Since the temperature-induced stress field is the major cause ofmaterial damage in the low-cycle fatigue regions, high accuracy isrequired for the evaluation and application of thermal boundaryconditions.

A detailed CFD investigation on the point-wise fluid/solid heattransfer becomes therefore of crucial importance in order tocorrectly estimate the local thermal conditions, since it providesa deep knowledge on both global and local thermal phenomena anda good understanding of the effect of the cooling system designmodifications on the thermal behavior of the engine. In fact, even ifexperimental investigations on internal combustion engine coolingsystems can provide useful information for the understanding of theglobal thermal behavior of the engine, as well as a useful set ofvalidation parameters for the numerical simulations [7], the use ofexperimental techniques for thedesign and theoptimizationprocessof an engine head is not feasible from an industrial point of view.Therefore, the use of numerical simulations for the design and theoptimization process becomes strategic, where a relevant reductionof both time to market and development costs are required.

For an accurate representation of the heat transfer between theengine head and the coolant, many key numerical parameters andsub-models must be correctly defined and tuned. In particular,a proper modeling of both the thermal boundary layer and thevapor nuclei formation is widely recognized to play a crucial role inthe temperature distribution calculation inside both aluminumalloy [8] and cast iron [9] engine components.

In the present paper a deep investigation on the role played bythe fluid boundary layer modeling is carried out. In particular,a phase-change model is introduced in order to increase theaccuracy of the numerical forecasts. It is in fact widely recognizedthat engine cooling typically relies on convection and boiling heattransfer within the engine cooling jacket. The geometricalcomplexity of typical engine heads makes it extremely difficult toclearly identify the heat transfer regime in the cooling systemmostcritical regions.

From a general perspective, heat transfer modes can be dividedin: a) pure convection, b) nucleate boiling and c) film boiling.

a) The heat transfer mechanism that occurs in the coolantgalleries under low thermal loads is mainly dominated byforced convection: under this situation, coolant physicalproperties and flow rate rule the effectiveness of the heatremoval from the engine metal surfaces.

b) When the heat flux increases (e.g. for high-load engine oper-ating conditions typical of the last generation of downsized/turbocharged HSDI Diesel engines), a surface temperature isreached that promotes the vapor bubble formation at the fluid/solid interface, despite the coolant bulk temperature is stillbelow the saturation temperature at the cooling system oper-ating pressure. Thus, nucleate boiling arises.

c) A further increase in the heat flux causes a speed up of thevapor nuclei formation at the fluid/solid interface, which can

eventually lead to an undesired formation of a vapor filmpreventing the circumstance that the coolant reaches thesurface. This phenomenon, widely termed as film boiling, leadsto a sudden and non-negligible reduction in the ability of thecoolant to remove heat and, therefore, to a rapid increase in thelocal metal temperature [10].

The ability of the liquid coolant to promptly remove heat fromthe nucleate boiling regions strongly depends on a complexcombination of flow characteristics and coolant channel design.Therefore, in order to evaluate the actual design efficiency and toimprove the system performance, both these aspects must bedeeply investigated to improve the cooling performance and,consequently, to reduce the thermal stresses arising in the engine.

In the present paper a previously proposedmethodology [8,9] issubstantially improved in the capability of correctly mimicking thelocal coolant behavior and detecting the correct location of fatiguecrack initiations.

The paper is organized as follows. First, the whole modelingstrategy is presented. Then the CFD simulations are described indetails and a validation of the CFD forecasts versus experimentaltemperature measurements is reported. The influence of the phasetransition modeling and the vapor nuclei formation within thecoolant galleries on the temperature distribution estimation isdiscussed. Then, thermo-mechanical FEM analyses of the enginehead are described where CFD validated results are employed asexternal thermal boundary conditions. Results in terms of bothlow-cycle fatigue and high-cycle fatigue life estimation are pre-sented. The proposed approach is validated versus some crackinitiations observed during bench tests of a high specific power VMMotori turbocharged HSDI six cylinder diesel engine for automotiveapplications.

2. Modeling strategy

The methodology presented in this paper is based on CFD andFEM decoupled simulations.

The CFD analyses constitute the first step of the proposedmodeling strategy. Two different aspect are investigated in details:i) the fluid-dynamic behavior of the cooling circuit is firstlyanalyzed and optimized aiming at improving the cooling efficiencyand the flow distribution among the different cylinders; ii) thepoint-wise fluid/solid heat transfer is then evaluated. In particular,benefits on the overall predicting capability brought in by theadoption of a proper phase-changemodel are highlighted bymeansof a preliminary comparison with a simplified model where phase-change is neglected and by a subsequent validation of the meth-odology against experimental measurements of the temperaturedistribution within the engine head.

The second step of the proposed methodology consists in theimplementation of a FEM procedure able to properly account forthe different mechanical and thermal boundary conditions appliedto the engine components. An ad-hoc user routine is employed tomap point-wise coolant/metal interface thermal boundary condi-tions from the CFD to the FEM realm. In order to correctly assess thefatigue strength of the engine, proper damage criteria are adoptedto estimate the behavior of the different engine regions.

3. CFD analyses

3.1. Cooling circuit layout optimization

Fig. 1 shows the fluid region of both the engine head and theblock: the coolant enters the circuit from the engine block and exitsout of the head; both inlet and outlet lay on the same side of the

Fig. 1. Cooling circuit layout.

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303 295

cooling circuit. Two additional coolant outlets are visible in Fig. 1,one serving the turbocharger cooler and the other serving the EGRcooler.

The circuit layout is characterized by a cross flow distributionaround each cylinder: as a consequence, a relevant coolant fractionleaves the circuit before reaching the cylinder furthest from theentrance.

All the analyses presented in this paper are carried out simu-lating the engine at full load and at peak power revving speed, i.e.4000 rpm, since this situation represents the most critical engineoperating condition from the engine head thermo-mechanicalloading point of view. A coolant flow rate through the circuitequal to about 150 l/min is considered as a mass flow entering theblock and it is then split among the three different outlets, see Fig.1,in accordance with experimental measurements provided by theengine manufacturer. The cooling pressure is derived from thefeeding pump performance curve, while the inlet averagetemperature is again derived from experiments at the engine testbench. The coolant is a 50/50 mixture of water and ethylene glycol.Literature-based physical properties [11] and boiling curves [12] aresubsequently recomputed by means of a purposely developedspreadsheet [13] for the specific operating pressure, temperatureand mixture composition suggested by the engine manufacturer.

Fig. 2. Gasket op

The cooling circuit has been extensively analyzed from a fluid-dynamic point of view using the methodology described in [8,9] towhich the interested reader is referred. The definitive jacket layout(with particular regard to the apertures through the gasket) is theresult of a set of analyses aimed at improving the cooling efficiencyand the flow distribution homogenization among the three cylin-ders of the analyzed engine portion.

Fig. 2 depicts a comparison between some gasket configura-tions, highlighting in particular the most promising solution(named “Optimized”) in terms of flow distribution uniformityamong the cylinders and flow resistance.

3.2. Evaluation of the point-wise fluid solid heat transfer

The CFD computational domain employed for the evaluation ofthe coolant/solid heat transfer covers a full engine bank, i.e. thecoolant galleries, the aluminum alloy engine head, the cast ironblock and the gasket. To properly take into account the materialdiscontinuities, press fit components are also included.

In order to speed up the grid generation process, the CFDdomain is generated using the STAR-CCMþ polyhedral mesher byCD-Adapco. The resulting grid is made up of polyhedral shapedcells, which constitute a good tradeoff between cell mean size,computational demand and effort requested to discretize sucha geometrically complex domain.

Particular care is used to model the fluid-dynamic boundarylayer, discretized by prismatic layers whose thickness is properlychosen according to the adopted near-wall treatment. Particularly,this paper reports the results obtained using the keu SST low-Reynolds model [14]. On one hand, because of the high flow non-uniformity near the walls and the small cooling passage dimen-sions, it is extremely complex to satisfy the requirements of a high-Reynolds wall treatment, i.e. yþ > 30. On the other hand, the highgeometrical complexity and the wide extent of the calculationdomain make the use of a low-Reynolds approach extremelyexpensive from the computational demand point of view. There-fore, to limit the overall number of cells, it is necessary to coarsenthe grid far away from the areas of major interest. The resultingdomain consists of about 14.000.000 cells.

timization.

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303296

It is important to note that local grid refinements in the soliddomain are adopted in the regions subjected to high thermalgradients, i.e. the combustion chamber, the valve guides and thevalve seats walls.

Fig. 3 shows the CHTeCFD portion for the sole engine head,where the press fit components, i.e. valve seats and valve guides,and the gasket are highlighted.

3.2.1. Thermal boundary conditionsSince the accuracy of the simulations in terms of temperature

estimation within the engine, and therefore of its thermo-mechanical behavior, heavily depends on the choice of properthermal boundary conditions, particular care is paid to the subdi-vision of the combustion heat flux among the many componentsfacing the combustion chamber.

In particular, boundary conditions accounting for the combus-tion and gas/solid heat fluxes are derived from a combination ofthree-dimensional simulations of the in-cylinder processes, one-dimensional simulations results of the whole engine and experi-mental measurements.

It is well known that temperature oscillations can be observed atthe walls facing the combustion chamber [15]. Nevertheless,because of the relevant thermal inertia of the metal components,these temperature oscillations due to the instantaneous heat fluxvariation are expected to moderately affect the heat transferbetween the engine and the coolant. Therefore, the actual time-varying heat flux can be cycle-averaged and converted intoa time-independent thermal load. If accurate predictions of walltemperature oscillations were required, a correction factor shouldbe introduced in the heat fluxes/heat transfer coefficients basedeither on multi-zone models [16] or on instantaneous three-dimensional models of the whole combustion process [17].

In this case, three-dimensional simulations of the whole enginecycle are used to derive a cycle-averaged point-wise thermal heatflux distribution on the engine surfaces directly facing thecombustion chamber, i.e. the combustion dome, the cylinder linerand the piston.

The heat flux entering the combustion chamber walls is thensimultaneously applied to all the cylinders and split among themany components following the above mentioned 3D simulations.In particular, the overall heat flux lost through the combustionchamber walls results as follows:

(i) 35% on the combustion dome;(ii) 22% on a certain portion of the cylinder liner;(iii) 43% on the piston top.

Fig. 3. Press fit components and gasket.

which is consistent with data available in literature [18].While the above described point-wise specific heat flux is

directly applied to the combustion dome, intake valves and exhaustvalves surfaces, a fictitious specific heat flux varying as a function ofthe cylinder axis coordinate is applied to the liner, adoptinga strategy similar to the one reported in [19].

In fact, following a 3D Finite Element thermal analysis of thepiston, a portion of the heat flux entering the piston top is trans-ferred to the cylinder liner as a consequence of the contact betweenthe piston skirt and the liner. Therefore, the overall flux applied tothe liner results from the superposition of the direct flux derivingfrom the combustion process and that related to the piston/linercontact [20].

In particular, since the heat flux transferred to the cylinder linerdecreases with the increase of the distance from the combustiondome, the specific heat flux _q is assumed as a parabolic function ofthe axial coordinate x, where x ¼ 0 corresponds to the gasket planeaxial coordinate.

Results from one-dimensional simulations of the whole enginein terms of gas temperatures and heat transfer coefficients are thenused for the intake and exhaust ports. For these components, theuse of one-dimensional derived boundary conditions is a standardpractice and is based on widely recognized assumptions [21].

Finally, the simulation is performed considering actual test-cellroom conditions.

3.2.2. Phase-change modelAs already stated in the Section Introduction, boiling effects

have been included in the CFD procedure to improve the accuracyof the local heat transfer forecasts. The model implemented in thecommercial software STAR-CCMþ to mimic the onset of vaporformation within the fluid domain is constituted of various sub-models.

First, the heat transfer at solideliquid interface is used tocompute the rates of fluid evaporation and condensation. Thetemperature of vapor bubbles is assumed to be equal to the satu-ration temperature Tsat, while the liquid temperature Tl can beapproximated to the mixture temperature T. The whole heat fluxexchanged between the liquid and the vapor is converted into massflow rate subjected to phase transition (i.e. evaporation orcondensation):

_mEC ¼ CHTCxAreaðT � TsatÞhlat

(1)

where hlat is the latent heat of vaporization and CHTCxArea is the heattransfer coefficient between vapor bubbles and the surroundingliquid multiplied by the contact surface separating the two phases.

Secondly, if a liquid is in contact with a solid surface witha temperature Twall higher than Tsat, boiling occurs at the liquid/solid interface. In this case, boiling undergoes three characteristicregimes:

(i) nucleate boiling: characterized by the formation and growthof vapor bubbles on a heated surface. The bubbles rise up froma discrete number of points whose temperature is slightlyhigher than the liquid saturation temperature Tsat. In general,the number of nucleation sites increases as the surfacetemperature increases. Augmenting the surface roughness canlead to a higher number of nucleation sites, while an extremesmoothing of the surfaces can lead to surface overheating;

(ii) film boiling: once a critical heat flux is reached, the heatedsurface is covered by a continuous vapor film. Because of thelow thermal conductivity of the vapor layer, the surface can beconsidered insulated;

Fig. 4. Coolant threshold above the boiling temperature.

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303 297

(iii) transition boiling: it describes the mechanism occurring fortemperatures ranging between the maximum temperature ofnucleate boiling regime and minimum temperature of filmboiling.

Although many heat transfer models can be found in literaturedealing with the nucleate boiling regime [22], none of them isaccepted as a standard. A common characteristic of all thesemodelsis the mimicking of the main mechanisms of nuclei formation, i.e.evaporation (latent heat), transport, micro convection, liquidevapor exchange, surface extinction, etc. In particular, the empiricrelationship proposed by Rohsenow [23] is used in the presentwork to calculate the boiling heat flux on a certain surface:

qbw ¼ mlhlat

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigðrl � rvÞ

s

r cPlðTw � TsatÞcqwhlatPr

1:7l

!3:03

(2)

where ml, cPl, rl and Prl are the dynamic viscosity, the specific heat,the density and the Prandtl number of the liquid phase, respec-tively, g is the gravity, rv is the density of the vapor phase, s is thesurface tension at the liquid/vapor interface, Tw is the walltemperature and cqw is an empirical coefficient whose value isdependent on the corresponding liquid/surface properties, previ-ously calibrated by one of the authors by means of comparisonsbetween CFD predictions and experimental measurements forengine coolants and aluminum alloys in simplified geometries [13].The vapor mass flow rate generated on a surface covered bynucleation sites can be written as follows:

_mew ¼ cewqbwhlat

(3)

where cew is a model constant which tunes the amount of boilingheat flux percentage converted into bubble formation.

3.2.3. Methodology validationAs a preliminary step, results obtained from a single-phase

analysis are compared with those computed employing theproposed multiphase model: some non-negligible limitations inthe representation of local thermal phenomena can be observedwhen the CFDmodel is not suitable to take into account the coolantphase transition.

Nevertheless, it is important to point out that the adoption ofa phase transition model implies the use of a transient simulationapproach, despite the application of cycle-averaged heat fluxes. Theonset of a transient simulation requires the convergence of thesolution to be obtained for both the computational domains (fluidand solid). Considering that, in order to limit the fluid domainconvective Courant number, the computing time step is about0.005 s, and that the solution stabilizes only after an analysis timeclose to 120 s, a huge number of iterations has to be run. Asa consequence, the methodology requires extremely high compu-tational times, which can reach 200 h on a 14 CPU linux cluster.Therefore, the use of a simplified single-phase steady-stateapproach, neglecting the effects of vapor formation, would beextremely advantageous in order to limit the computationaldemand. On the other side, the impossibility by the coolant tosubtract latent heat during phase transition could lead to a relevantlocal overestimation of the maximum temperature levels withinthe fluid domain, since all the heat flux is converted into sensibleheat.

As a result, when the simplified single-phase steady-stateapproach is employed for the CFD heat transfer simulations of theengine under investigation, coolant maximum temperature

appears to be strongly overestimated, severely limiting the physicalsoundness of the CFD forecast. Although the amount of coolantvapor can be limited both in terms of spatial extent and totalamount, vapor nuclei arise at the engine most critical locations.Moreover, the surrounding metal can also be affected by thedescribed coolant temperature overestimation, similarly reachingtemperature peaks far beyond the measured ones.

Fig. 4 shows the portion of the fluid domain whose temperaturerises above the boiling temperature threshold at the cooling systemoperating pressure within the simplified single-phase approachframework.

The above described shortcome, is completely overcome thanksto the adoption of a proper phase-change sub-model, which is ableto capture vapor nuclei formation at the most critical locations. Thesubsequent heat removal mechanism, named as “boiling heat flux”is shown in Fig. 5.

In order to assess the predictive capability of the proposedmethodology, CFD computed temperatures are then comparedwith experimental measurements obtained by means of eightthermocouples locatedwithin the engine head covering at the headmost critical regions, i.e. for example the exhaust valve bridge.Considering the limited number of available experimental data, thecomparison between CFD predictions and measurements is carriedout with the specific aim of correctly capturing the thermal fieldwithin the head solid domain. An extensive validation of thephysical soundness of the coolant behavior would require the use ofmore detailed experimental techniques far away from the standardindustrial practice. Nevertheless, since the aim of the overallsimulation process is the correct representation of the thermo-mechanical behavior of the engine head, the experimentalevidences are considered to be very useful. Temperaturemeasurements have been carried out along two section planescutting the engine head at a different distance from the gasketplane. Fig. 6 illustrates the position of the thermocouples: even-numbered thermocouples are located at a distance equal to2.5 mm from the gasket plane, while odd-numbered ones arelocated at a distance equal to 8 mm from the gasket plane.

Fig. 7 reports a comparison between the numerical forecasts andthe experimental available data set.

Fig. 8 shows the temperature distribution on the walls of thecombustion dome and intake and exhaust ports, with the coolantjacket portion undergoing vapor bubble formation superimposed.

Adopting the above described numerical procedure it is possibleto correctly reproduce the temperature distribution within theengine head. The ability of the simulations to accurately representboth the thermal boundary layer and the convective heat transferphenomena, as well as the effects of local vapor bubble formation atthe fluid/solid interface and subsequent condensation within the

Fig. 5. Heat flux due to phase-change (a) and vapor volume fraction (b).

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303298

liquid core, is a crucial aspect. In fact, the agreement betweenpredicted andmeasured temperatures is very satisfactory for all themeasurement locations.

4. Finite Element results

Thermo-mechanical simulations are performed using thecommercial Finite Element softwareMSC.Marc2010.2�. For optimalaccuracy and numerical stability, new grids have been adopted forFinite Element calculations.

To achieve a more faithful representation of the engine headbehavior under actual operating conditions, a former modelemployed in Ref. [9] is improved including the non-linear modelingof the gasket behavior and a full discretization of the engine block.Fig. 9 shows the Finite Element discretization of the investigatedDiesel engine components. The FEM model consists of approxi-mately 1,740,000 elements and 560,000 node.

4.1. Mechanical loading

The same set of mechanical boundary conditions already used inRef. [9] are adopted in all the simulations involved in this work andare briefly reported in the following for the sake of clarity:

(i) bolt tightening between the different components;(ii) press fit of valve seats and valve guides;(iii) pressures within the combustion chamber.

Fig. 6. Thermocouple positions.

4.2. Thermal loading

Due to material expansion under a non-uniform temperaturedistribution, thermal stresses are induced in the engine head. Inorder to properly predict the fatigue life of the component, thecorrect temperature distribution has to be taken into account. Astatic thermal Finite Element calculation is therefore performed, tocompute the temperature distribution map directly on the gridcreated for Finite Element calculations. The same thermal loads usedfor CFD simulations are applied to this FEM thermal model, exceptfor the metal/coolant interface, where heat transfer coefficients areprecisely mapped from the CFD solution to the FEMmodel using anad-hoc Fortran routine. Fig. 10 pictorially represents the tempera-ture distribution inside the engine head computed with FE.

4.3. Load Cases

Many different consecutive Load Cases are subsequently appliedto the thermo-mechanical model of the engine in order to take intoaccount both high-frequency cycles and low-frequency cycles [24]:

- Load Case 1: including only press fits and bolt tightening;- Load Case 2: including press fits, bolt tightening and combus-tion pressure;

- Load Case 3: including all mechanical and thermal loads;- Load Case 4: including all loads except for combustionpressure:

- Load Case 5: thermal loading is removed;- Load Case 6: thermal loading is applied again.

Each different Load Case represents a different engine oper-ating condition. In particular, Load Case 1 simulates engineassembling, Load Case 2 simulates engine cold start, while Load

150

170

190

210

230

250

270

290

Tsx1 Tsx2 Tsx3 Tsx4 Tsx5 Tsx6 Tsx7 Tsx8

Tem

pe

ra

tu

re

°C

Experimental k-omega

Fig. 7. Comparison between CFD forecasts and experimental measurements.

Fig. 8. Temperature distribution and vapor fraction.

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303 299

Cases 3 and 4 describe the engine operating at full load conditionand the corresponding stress distributions represent the envelopeof the high-cycle fatigue (HCF). Load Cases 5 and 6 represent thestart/operate/stop cycle related to the low-cycle fatiguephenomena (LCF).

4.4. Fatigue criteria

To correctly predict the fatigue behavior of the whole enginehead, specific failure criteria must be employed at different loca-tions. In fact, because of the superimposition of mechanical andthermal loading, both high-cycle and low-cycle fatigue phenomenahave to be taken into account. In particular, two main areas can bedetected that exhibit different behaviors:

Fig. 9. Finite Element model of (a) the engine head, (b) the engine block,

(i) under normal loading conditions, the walls of the coolantjacket do not undergo any plastic strain; therefore, this regionscan be treated with usual high-cycle fatigue criteria (stress-based [1] or strain-based [2] criteria);

(ii) the area of the combustion dome exposed to the combustiongases is subjected to the highest thermal loads, and displayssubstantial plastic deformations, which can be traced back tothe drop of mechanical properties at high temperature.

In this second region, an energetic approach can be employed topredict the most critical locations in term of fatigue life. In fact, in[3] Skelton states that crack growth can arise when a given amountof energy has been dissipated in a certain zone. Similarly, Charkalukand Constantinescu [4] observe that the fatigue life of a material isstrongly correlated with the amount of dissipated energy per cycle:

(c) the gasket and (d) the valve seats, the valve guides and the bolts.

Fig. 10. FEM computed temperature distribution inside the engine head.

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303300

DWS ¼ZtþT

t

sdεp (4)

where s is the local stress tensor and εp is the local plastic straintensor.

The advantages stemming from the use of an energetic approachare manifold:

(i) it can be easily employed in a multi-axial situation;(ii) it can be applied with non-isothermal loading (e.g. start/

operating/stop cycles of an engine) as the dissipated energyper cycle is evaluated taking into account the whole loadinghistory and his value is approximately temperature-independent.

The fatigue criterion is expressed by the relation:

DWSNb ¼ C (5)

where N is the number of cycles at which crack propagation isexpected to occur and b and C are experimentally determinedconstants [25].

Table 1Chaboche parameters K and g as a function of temperature for the aluminum alloyA356 T6.

T [�] Rs [MPa] K g

20 200 5556 68.7150 190 5282 68.8200 162 4011 69.8250 104 2285 70.9300 71 1160 73

4.5. Non-linear material behavior

Low-cycle fatigue phenomena are mainly related to thetemperature evolution within the components. The implementa-tion of a robust procedure for the cyclic application of subsequentmechanical, thermal, and thermo-mechanical loads to the model istherefore essential, since the accuracy of these data directly affectsthe quality of the structural response and the numerical predic-tions. In order to accurately account for the peculiar behavior of thematerial subjected to high temperature cyclic loading, the Cha-boche stressestrain relationships for both plasticity [26] and visco-plasticity [27] are employed, based on the non-linear kinematichardening rule expressed by:

X�εp� ¼ a

Kg��X0 � a

Kg

�e�agðε0�εp0Þ (6)

where:a ¼ signðs� XÞ, K and g are experimentally determined

material properties depending on temperature and εp is again thelocal plastic strain.

The fundamental parameters of the model have to be adjustedto accurately reproduce the actual experimental material behaviorin the elasticeplastic region. Therefore, a virtual Finite Elementtensile specimen has been generated. A non-linear optimizationprocedure has been employed in order to correctly fit the numericalforecast to the experimental data during cyclic loading, Fig. 11.

Table 1 reports the values of K and g as a function of temperaturefor the aluminum alloy A356 T6 employed for the engine headproduction.

4.6. High-cycle fatigue results

Numerical predictions display ample regions of highly stressedmaterial. Looking at the fillets of the walls of the coolant jacket,different highly stressed points with high values of tensile stresscan be detected. In particular, a confined region is investigatedwhere the maximum value of tensile principal stress is evaluated.Such a high value of stress classifies this region as the most likelysource of failure. The comparatively low temperatures of the wallsof the coolant jacket allow the employment of a stress-basedcriterion in the prediction of the local fatigue behavior. In partic-ular, the Dang Van criterion is adopted in this study [1].

Fig. 11. Stresseplastic strain path evaluated by Finite Element analysis on a simple specimen at different temperatures with the Chaboche model.

Fig. 12. HCF. Dang Van criterion. Comparison between experimental cracks and numerical predictions.

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303 301

Fig. 12 shows a comparison between the actual propagation ofa crack and the map of high-cycle fatigue safety factors among theregions of interest. A very satisfactory match between the locationof minimum safety factors and the experimentally assessed point ofcrack initiation supports the validity of the present methodologyand of the underlying hypotheses.

A

B

C

D

E

-200

-150

-100

-50

0

50

100

150

200

250

-0.003 -0.0025 -0.002 -0.0015 -0.001 -0.0005 0 0.0005

stress [M

Pa]

plastic strain

stress - plastic strain hystory curve

Fig. 13. Longitudinal stresseplastic strain history curve at valve bridge between intakevalves.

4.7. Low-cycle fatigue results

The flame-plate zone usually represents the area exposed to thehighest thermo-mechanical loads. In particular, the regions thatundergo the most severe cyclic loading are located between thevalve seats (valve bridges), where the stresses due to press fit andmaximum temperature cyclic loading overlap.

With reference to Fig. 13, the effect of the loading history on thematerial, between for example the intake valves, can be qualita-tively described as follows:

AeB segment: due to the press fit of the valve seats, the materialis subjected to a tensile stress state;BeC segment: when the highly non-uniform temperature fieldis applied, the material undergoes a compressive stress state,entering plastic regime;CeD segment: while the uniform ambient temperature issmoothly re-established, the material is ultimately subject toresidual stress, reaching a tensile plastic regime;DeE segment: a second application of the working temperaturedistribution again induces compressive plasticization, thuscompleting a full hysteresis cycle.

The employment of the energetic approach described in Section4.4 requires the computation of DWs defined in Eq. (4). In order tobe able to assess the damage index for multi-axial states oncomplex geometries, a general technique is required. Therefore

Fig. 14. LCF. Energy dissipated per cycle. Comparison between experimental cracks and numerical predictions.

S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303302

a post-processing procedure based on a custom-coded Fortranprogram has been developed to post-process the FEM solutioncomputing DWs for each integration point. A different user routineis then employed to display the computed damage index as contourbands, providing a much more practical tool for quick detection ofthe regions subjected to critical LCF cycles.

Fig. 14 compares the actual experimental crack propagations inthe flame-plate zone with the distribution of the energy dissipatedper cycle. Again, a perfect matching is detected.

5. Conclusion

The combined CFD and FEManalyses the present paper describesaim at accurately predicting the temperature field and the resultingthermo-mechanical loading cycle affecting internal combustionengine components under actual operating conditions. This decou-pled CFD and FEM methodology correctly estimates the fatiguestrength of the engine head of a V6 turbocharged Diesel engine.

A detailed model of the engine, covering both the coolantgalleries and the surrounding metal components is at firstemployed for the fluid-dynamic analyses to accurately capture theinfluence of the cooling system layout on the thermal and thermo-mechanical behavior of the engine. The comparison between anexperimentally measured temperature distribution within theengine head and the CFD forecasts highlights the importance of anaccurate modeling of both the coolant phase transition and thevapor nuclei formation within the coolant galleries.

Finite Element analyses are then performed in order to estimatethe fatigue strength of the investigated engine head. Again,a comparisons between numerical forecasts and experimentalevidences show that the proposed methodology is able to preciselypredict the engine failure loci by means of the application ofdifferent fatigue criteria properly accounting for the superimposi-tion of mechanical and thermal loadings, which result in both high-cycle and low-cycle fatigue phenomena.

The accuracy of the numerical forecasts allows the methodologyto be applied not only as a useful tool for the investigation andunderstanding of detected engine failures, but also as a design toolof both the water cooling jacket and the engine structural parts.

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