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Multiphase CFD–CHT optimization of the cooling jacket and FEM analysis of the engine head of a V6 diesel engine
Applied Thermal Engineering 52 (2013) 293e303
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Multiphase CFDeCHT optimization of the cooling jacket and FEM analysis of the engine head of a V6 diesel engine Stefano Fontanesi*, Matteo Giacopini University 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
a b s t r a c t
Article history: Received 9 July 2012 Accepted 7 December 2012 Available online 20 December 2012
The present paper proposes a numerical methodology aiming at analyzing and optimizing an internal combustion engine water cooling jacket, with particular emphasis on the assessment of the fatigue strength of the engine head. Full three-dimensional CFD and FEM analyses of the conjugate heat transfer and of the thermomechanical loading cycles are presented for a single bank of a currently made V6 turbocharged Diesel engine under actual operating conditions. A detailed model of the engine, consisting of both the coolant galleries and the surrounding metal components is employed in both fluid-dynamic and structural analyses to accurately mimic the influence of 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 CFD forecasts. Particular attention is paid to the modeling of the phase transition and of the vapor nuclei formation within the coolant galleries. Thermo-mechanical analyses are then carried out aiming at addressing the design optimization of the engine in terms of fatigue strength. Because of the wide range of thermal and mechanical loadings acting on the engine head, both high-cycle and low-cycle fatigue are considered. An energy-based multi-axial criterion specifically suited for thermal fatigue is employed in the low-cycle fatigue region (i.e. the combustion dome) while well-established multi-axial stress/strain-based criteria are adopted to investigate 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 possible engine failures and proves to be an effective tool for the accurate thermo-mechanical characterization of internal combustion engines under actual life-cycle operating conditions. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Engine head Heat transfer Boiling Fatigue analysis
1. Introduction Internal combustion engines undergo cyclic thermo-mechanical loadings and are subjected to a wide range of operating conditions,
* Corresponding author. Tel.: þ39 (0)59 2056114; fax: þ39 (0)59 2056126. E-mail address: [email protected] (S. Fontanesi). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.12.005
in terms of both temperature distribution and frequency/amplitude of mechanical and thermo-mechanical loading cycles. Consequently, in order to accurately evaluate the mechanical strength of engine components, two different fatigue cycles must be modeled: (i) the fatigue cycle related to the combustion process, whose frequency is strictly related to the crankshaft revving speed, (ii) the thermally induced fatigue cycle whose frequency is dependent on the ignition/engine warm up/switch off/engine cool down cycle.
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On one side, traditional and well-established stress-based [1] or strain-based [2] fatigue criteria can be proficiently employed to analyze the effects of the application of high-frequency loadings. On the other side, low-frequency thermo-mechanical loadings are still an open challenge for the designers. In fact, a unique and widely recognized procedure for the low-cycle fatigue strength assessment of engine components is not yet available. Relying on a formerly developed energy-based criterion [3], analyses of lowcycle fatigue phenomena in engine components such as cast-iron engine manifolds [4] or aluminum alloy engine heads [5] have been performed, whose predictive capability in terms of consistency between numerical forecasts and experimental evidences is confirmed by recent applications [6]. Since the temperature-induced stress field is the major cause of material damage in the low-cycle fatigue regions, high accuracy is required for the evaluation and application of thermal boundary conditions. A detailed CFD investigation on the point-wise fluid/solid heat transfer becomes therefore of crucial importance in order to correctly estimate the local thermal conditions, since it provides a deep knowledge on both global and local thermal phenomena and a good understanding of the effect of the cooling system design modifications on the thermal behavior of the engine. In fact, even if experimental investigations on internal combustion engine cooling systems can provide useful information for the understanding of the global thermal behavior of the engine, as well as a useful set of validation parameters for the numerical simulations [7], the use of experimental techniques for the design and the optimization process of an engine head is not feasible from an industrial point of view. Therefore, the use of numerical simulations for the design and the optimization process becomes strategic, where a relevant reduction of both time to market and development costs are required. For an accurate representation of the heat transfer between the engine head and the coolant, many key numerical parameters and sub-models must be correctly defined and tuned. In particular, a proper modeling of both the thermal boundary layer and the vapor nuclei formation is widely recognized to play a crucial role in the temperature distribution calculation inside both aluminum alloy [8] and cast iron [9] engine components. In the present paper a deep investigation on the role played by the fluid boundary layer modeling is carried out. In particular, a phase-change model is introduced in order to increase the accuracy of the numerical forecasts. It is in fact widely recognized that engine cooling typically relies on convection and boiling heat transfer within the engine cooling jacket. The geometrical complexity of typical engine heads makes it extremely difficult to clearly identify the heat transfer regime in the cooling system most critical regions. From a general perspective, heat transfer modes can be divided in: a) pure convection, b) nucleate boiling and c) film boiling. a) The heat transfer mechanism that occurs in the coolant galleries under low thermal loads is mainly dominated by forced convection: under this situation, coolant physical properties and flow rate rule the effectiveness of the heat removal from the engine metal surfaces. b) When the heat flux increases (e.g. for high-load engine operating conditions typical of the last generation of downsized/ turbocharged HSDI Diesel engines), a surface temperature is reached that promotes the vapor bubble formation at the fluid/ solid interface, despite the coolant bulk temperature is still below the saturation temperature at the cooling system operating pressure. Thus, nucleate boiling arises. c) A further increase in the heat flux causes a speed up of the vapor nuclei formation at the fluid/solid interface, which can
eventually lead to an undesired formation of a vapor film preventing the circumstance that the coolant reaches the surface. This phenomenon, widely termed as film boiling, leads to a sudden and non-negligible reduction in the ability of the coolant to remove heat and, therefore, to a rapid increase in the local metal temperature [10]. The ability of the liquid coolant to promptly remove heat from the nucleate boiling regions strongly depends on a complex combination of flow characteristics and coolant channel design. Therefore, in order to evaluate the actual design efficiency and to improve the system performance, both these aspects must be deeply investigated to improve the cooling performance and, consequently, to reduce the thermal stresses arising in the engine. In the present paper a previously proposed methodology [8,9] is substantially improved in the capability of correctly mimicking the local coolant behavior and detecting the correct location of fatigue crack initiations. The paper is organized as follows. First, the whole modeling strategy is presented. Then the CFD simulations are described in details and a validation of the CFD forecasts versus experimental temperature measurements is reported. The influence of the phase transition modeling and the vapor nuclei formation within the coolant galleries on the temperature distribution estimation is discussed. Then, thermo-mechanical FEM analyses of the engine head are described where CFD validated results are employed as external thermal boundary conditions. Results in terms of both low-cycle fatigue and high-cycle fatigue life estimation are presented. The proposed approach is validated versus some crack initiations observed during bench tests of a high specific power VM Motori turbocharged HSDI six cylinder diesel engine for automotive applications. 2. Modeling strategy The methodology presented in this paper is based on CFD and FEM decoupled simulations. The CFD analyses constitute the first step of the proposed modeling strategy. Two different aspect are investigated in details: i) the fluid-dynamic behavior of the cooling circuit is firstly analyzed and optimized aiming at improving the cooling efficiency and the flow distribution among the different cylinders; ii) the point-wise fluid/solid heat transfer is then evaluated. In particular, benefits on the overall predicting capability brought in by the adoption of a proper phase-change model are highlighted by means of a preliminary comparison with a simplified model where phasechange is neglected and by a subsequent validation of the methodology against experimental measurements of the temperature distribution within the engine head. The second step of the proposed methodology consists in the implementation of a FEM procedure able to properly account for the different mechanical and thermal boundary conditions applied to the engine components. An ad-hoc user routine is employed to map point-wise coolant/metal interface thermal boundary conditions from the CFD to the FEM realm. In order to correctly assess the fatigue strength of the engine, proper damage criteria are adopted to 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 the block: the coolant enters the circuit from the engine block and exits out of the head; both inlet and outlet lay on the same side of the
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The cooling circuit has been extensively analyzed from a fluiddynamic point of view using the methodology described in [8,9] to which the interested reader is referred. The definitive jacket layout (with particular regard to the apertures through the gasket) is the result of a set of analyses aimed at improving the cooling efficiency and the flow distribution homogenization among the three cylinders of the analyzed engine portion. Fig. 2 depicts a comparison between some gasket configurations, highlighting in particular the most promising solution (named “Optimized”) in terms of flow distribution uniformity among the cylinders and flow resistance. 3.2. Evaluation of the point-wise fluid solid heat transfer Fig. 1. Cooling circuit layout.
cooling circuit. Two additional coolant outlets are visible in Fig. 1, one serving the turbocharger cooler and the other serving the EGR cooler. The circuit layout is characterized by a cross flow distribution around each cylinder: as a consequence, a relevant coolant fraction leaves the circuit before reaching the cylinder furthest from the entrance. All the analyses presented in this paper are carried out simulating the engine at full load and at peak power revving speed, i.e. 4000 rpm, since this situation represents the most critical engine operating condition from the engine head thermo-mechanical loading point of view. A coolant flow rate through the circuit equal to about 150 l/min is considered as a mass flow entering the block and it is then split among the three different outlets, see Fig. 1, in accordance with experimental measurements provided by the engine manufacturer. The cooling pressure is derived from the feeding pump performance curve, while the inlet average temperature is again derived from experiments at the engine test bench. The coolant is a 50/50 mixture of water and ethylene glycol. Literature-based physical properties [11] and boiling curves [12] are subsequently recomputed by means of a purposely developed spreadsheet [13] for the specific operating pressure, temperature and mixture composition suggested by the engine manufacturer.
The CFD computational domain employed for the evaluation of the coolant/solid heat transfer covers a full engine bank, i.e. the coolant galleries, the aluminum alloy engine head, the cast iron block and the gasket. To properly take into account the material discontinuities, press fit components are also included. In order to speed up the grid generation process, the CFD domain is generated using the STAR-CCMþ polyhedral mesher by CD-Adapco. The resulting grid is made up of polyhedral shaped cells, which constitute a good tradeoff between cell mean size, computational demand and effort requested to discretize such a geometrically complex domain. Particular care is used to model the fluid-dynamic boundary layer, discretized by prismatic layers whose thickness is properly chosen according to the adopted near-wall treatment. Particularly, this paper reports the results obtained using the keu SST lowReynolds model [14]. On one hand, because of the high flow nonuniformity near the walls and the small cooling passage dimensions, it is extremely complex to satisfy the requirements of a highReynolds wall treatment, i.e. yþ > 30. On the other hand, the high geometrical complexity and the wide extent of the calculation domain make the use of a low-Reynolds approach extremely expensive from the computational demand point of view. Therefore, to limit the overall number of cells, it is necessary to coarsen the grid far away from the areas of major interest. The resulting domain consists of about 14.000.000 cells.
Fig. 2. Gasket optimization.
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It is important to note that local grid refinements in the solid domain are adopted in the regions subjected to high thermal gradients, i.e. the combustion chamber, the valve guides and the valve 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 conditions Since the accuracy of the simulations in terms of temperature estimation within the engine, and therefore of its thermomechanical behavior, heavily depends on the choice of proper thermal boundary conditions, particular care is paid to the subdivision of the combustion heat flux among the many components facing the combustion chamber. In particular, boundary conditions accounting for the combustion and gas/solid heat fluxes are derived from a combination of three-dimensional simulations of the in-cylinder processes, onedimensional simulations results of the whole engine and experimental measurements. It is well known that temperature oscillations can be observed at the 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 flux variation are expected to moderately affect the heat transfer between the engine and the coolant. Therefore, the actual timevarying heat flux can be cycle-averaged and converted into a time-independent thermal load. If accurate predictions of wall temperature oscillations were required, a correction factor should be introduced in the heat fluxes/heat transfer coefficients based either on multi-zone models [16] or on instantaneous threedimensional models of the whole combustion process [17]. In this case, three-dimensional simulations of the whole engine cycle are used to derive a cycle-averaged point-wise thermal heat flux distribution on the engine surfaces directly facing the combustion chamber, i.e. the combustion dome, the cylinder liner and the piston. The heat flux entering the combustion chamber walls is then simultaneously applied to all the cylinders and split among the many components following the above mentioned 3D simulations. In particular, the overall heat flux lost through the combustion chamber 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 exhaust valves surfaces, a fictitious specific heat flux varying as a function of the cylinder axis coordinate is applied to the liner, adopting a strategy similar to the one reported in [19]. In fact, following a 3D Finite Element thermal analysis of the piston, a portion of the heat flux entering the piston top is transferred to the cylinder liner as a consequence of the contact between the piston skirt and the liner. Therefore, the overall flux applied to the liner results from the superposition of the direct flux deriving from the combustion process and that related to the piston/liner contact [20]. In particular, since the heat flux transferred to the cylinder liner decreases with the increase of the distance from the combustion dome, the specific heat flux q_ is assumed as a parabolic function of the axial coordinate x, where x ¼ 0 corresponds to the gasket plane axial coordinate. Results from one-dimensional simulations of the whole engine in terms of gas temperatures and heat transfer coefficients are then used for the intake and exhaust ports. For these components, the use of one-dimensional derived boundary conditions is a standard practice and is based on widely recognized assumptions [21]. Finally, the simulation is performed considering actual test-cell room conditions. 3.2.2. Phase-change model As already stated in the Section Introduction, boiling effects have been included in the CFD procedure to improve the accuracy of the local heat transfer forecasts. The model implemented in the commercial software STAR-CCMþ to mimic the onset of vapor formation within the fluid domain is constituted of various submodels. First, the heat transfer at solideliquid interface is used to compute the rates of fluid evaporation and condensation. The temperature of vapor bubbles is assumed to be equal to the saturation temperature Tsat, while the liquid temperature Tl can be approximated to the mixture temperature T. The whole heat flux exchanged between the liquid and the vapor is converted into mass flow rate subjected to phase transition (i.e. evaporation or condensation):
_ EC ¼ m
CHTCxArea ðT Tsat Þ hlat
(1)
where hlat is the latent heat of vaporization and CHTCxArea is the heat transfer coefficient between vapor bubbles and the surrounding liquid multiplied by the contact surface separating the two phases. Secondly, if a liquid is in contact with a solid surface with a temperature Twall higher than Tsat, boiling occurs at the liquid/ solid interface. In this case, boiling undergoes three characteristic regimes: (i) nucleate boiling: characterized by the formation and growth of vapor bubbles on a heated surface. The bubbles rise up from a discrete number of points whose temperature is slightly higher than the liquid saturation temperature Tsat. In general, the number of nucleation sites increases as the surface temperature increases. Augmenting the surface roughness can lead to a higher number of nucleation sites, while an extreme smoothing of the surfaces can lead to surface overheating; (ii) film boiling: once a critical heat flux is reached, the heated surface is covered by a continuous vapor film. Because of the low thermal conductivity of the vapor layer, the surface can be considered insulated;
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(iii) transition boiling: it describes the mechanism occurring for temperatures ranging between the maximum temperature of nucleate boiling regime and minimum temperature of film boiling. Although many heat transfer models can be found in literature dealing with the nucleate boiling regime [22], none of them is accepted as a standard. A common characteristic of all these models is the mimicking of the main mechanisms of nuclei formation, i.e. evaporation (latent heat), transport, micro convection, liquide vapor exchange, surface extinction, etc. In particular, the empiric relationship proposed by Rohsenow [23] is used in the present work to calculate the boiling heat flux on a certain surface:
qbw ¼ ml hlat
!3:03 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gðrl rv Þ cPl ðTw Tsat Þ
s
cqw hlat Pr1:7 l
(2)
where ml, cPl, rl and Prl are the dynamic viscosity, the specific heat, the density and the Prandtl number of the liquid phase, respectively, g is the gravity, rv is the density of the vapor phase, s is the surface tension at the liquid/vapor interface, Tw is the wall temperature and cqw is an empirical coefficient whose value is dependent on the corresponding liquid/surface properties, previously calibrated by one of the authors by means of comparisons between CFD predictions and experimental measurements for engine coolants and aluminum alloys in simplified geometries [13]. The vapor mass flow rate generated on a surface covered by nucleation sites can be written as follows:
_ ew ¼ m
cew qbw hlat
(3)
where cew is a model constant which tunes the amount of boiling heat flux percentage converted into bubble formation. 3.2.3. Methodology validation As a preliminary step, results obtained from a single-phase analysis are compared with those computed employing the proposed multiphase model: some non-negligible limitations in the representation of local thermal phenomena can be observed when the CFD model is not suitable to take into account the coolant phase transition. Nevertheless, it is important to point out that the adoption of a phase transition model implies the use of a transient simulation approach, despite the application of cycle-averaged heat fluxes. The onset of a transient simulation requires the convergence of the solution to be obtained for both the computational domains (fluid and solid). Considering that, in order to limit the fluid domain convective Courant number, the computing time step is about 0.005 s, and that the solution stabilizes only after an analysis time close to 120 s, a huge number of iterations has to be run. As a consequence, the methodology requires extremely high computational times, which can reach 200 h on a 14 CPU linux cluster. Therefore, the use of a simplified single-phase steady-state approach, neglecting the effects of vapor formation, would be extremely advantageous in order to limit the computational demand. On the other side, the impossibility by the coolant to subtract latent heat during phase transition could lead to a relevant local overestimation of the maximum temperature levels within the fluid domain, since all the heat flux is converted into sensible heat. As a result, when the simplified single-phase steady-state approach is employed for the CFD heat transfer simulations of the engine under investigation, coolant maximum temperature
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appears to be strongly overestimated, severely limiting the physical soundness of the CFD forecast. Although the amount of coolant vapor can be limited both in terms of spatial extent and total amount, vapor nuclei arise at the engine most critical locations. Moreover, the surrounding metal can also be affected by the described coolant temperature overestimation, similarly reaching temperature peaks far beyond the measured ones. Fig. 4 shows the portion of the fluid domain whose temperature rises above the boiling temperature threshold at the cooling system operating pressure within the simplified single-phase approach framework. The above described shortcome, is completely overcome thanks to the adoption of a proper phase-change sub-model, which is able to capture vapor nuclei formation at the most critical locations. The subsequent heat removal mechanism, named as “boiling heat flux” is shown in Fig. 5. In order to assess the predictive capability of the proposed methodology, CFD computed temperatures are then compared with experimental measurements obtained by means of eight thermocouples located within the engine head covering at the head most critical regions, i.e. for example the exhaust valve bridge. Considering the limited number of available experimental data, the comparison between CFD predictions and measurements is carried out with the specific aim of correctly capturing the thermal field within the head solid domain. An extensive validation of the physical soundness of the coolant behavior would require the use of more detailed experimental techniques far away from the standard industrial practice. Nevertheless, since the aim of the overall simulation process is the correct representation of the thermomechanical behavior of the engine head, the experimental evidences are considered to be very useful. Temperature measurements have been carried out along two section planes cutting the engine head at a different distance from the gasket plane. Fig. 6 illustrates the position of the thermocouples: evennumbered thermocouples are located at a distance equal to 2.5 mm from the gasket plane, while odd-numbered ones are located at a distance equal to 8 mm from the gasket plane. Fig. 7 reports a comparison between the numerical forecasts and the experimental available data set. Fig. 8 shows the temperature distribution on the walls of the combustion dome and intake and exhaust ports, with the coolant jacket portion undergoing vapor bubble formation superimposed. Adopting the above described numerical procedure it is possible to correctly reproduce the temperature distribution within the engine head. The ability of the simulations to accurately represent both the thermal boundary layer and the convective heat transfer phenomena, as well as the effects of local vapor bubble formation at the fluid/solid interface and subsequent condensation within the
Fig. 4. Coolant threshold above the boiling temperature.
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Fig. 5. Heat flux due to phase-change (a) and vapor volume fraction (b).
liquid core, is a crucial aspect. In fact, the agreement between predicted and measured temperatures is very satisfactory for all the measurement locations. 4. Finite Element results Thermo-mechanical simulations are performed using the commercial Finite Element software MSC.Marc2010.2Ò. For optimal accuracy and numerical stability, new grids have been adopted for Finite Element calculations. To achieve a more faithful representation of the engine head behavior under actual operating conditions, a former model employed in Ref. [9] is improved including the non-linear modeling of the gasket behavior and a full discretization of the engine block. Fig. 9 shows the Finite Element discretization of the investigated Diesel engine components. The FEM model consists of approximately 1,740,000 elements and 560,000 node. 4.1. Mechanical loading The same set of mechanical boundary conditions already used in Ref. [9] are adopted in all the simulations involved in this work and are 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.
4.2. Thermal loading Due to material expansion under a non-uniform temperature distribution, thermal stresses are induced in the engine head. In order to properly predict the fatigue life of the component, the correct temperature distribution has to be taken into account. A static thermal Finite Element calculation is therefore performed, to compute the temperature distribution map directly on the grid created for Finite Element calculations. The same thermal loads used for CFD simulations are applied to this FEM thermal model, except for the metal/coolant interface, where heat transfer coefficients are precisely mapped from the CFD solution to the FEM model using an ad-hoc Fortran routine. Fig. 10 pictorially represents the temperature distribution inside the engine head computed with FE. 4.3. Load Cases Many different consecutive Load Cases are subsequently applied to the thermo-mechanical model of the engine in order to take into account 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 combustion pressure; - Load Case 3: including all mechanical and thermal loads; - Load Case 4: including all loads except for combustion pressure: - Load Case 5: thermal loading is removed; - Load Case 6: thermal loading is applied again. Each different Load Case represents a different engine operating condition. In particular, Load Case 1 simulates engine assembling, Load Case 2 simulates engine cold start, while Load
Experimental
k-omega
290
Temperature °C
270 250 230 210 190 170 150 Tsx1 Fig. 6. Thermocouple positions.
Tsx2
Tsx3
Tsx4
Tsx5
Tsx6
Tsx7
Tsx8
Fig. 7. Comparison between CFD forecasts and experimental measurements.
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Fig. 8. Temperature distribution and vapor fraction.
Cases 3 and 4 describe the engine operating at full load condition and the corresponding stress distributions represent the envelope of the high-cycle fatigue (HCF). Load Cases 5 and 6 represent the start/operate/stop cycle related to the low-cycle fatigue phenomena (LCF).
4.4. Fatigue criteria To correctly predict the fatigue behavior of the whole engine head, specific failure criteria must be employed at different locations. In fact, because of the superimposition of mechanical and thermal loading, both high-cycle and low-cycle fatigue phenomena have to be taken into account. In particular, two main areas can be detected that exhibit different behaviors:
(i) under normal loading conditions, the walls of the coolant jacket do not undergo any plastic strain; therefore, this regions can be treated with usual high-cycle fatigue criteria (stressbased [1] or strain-based [2] criteria); (ii) the area of the combustion dome exposed to the combustion gases is subjected to the highest thermal loads, and displays substantial plastic deformations, which can be traced back to the drop of mechanical properties at high temperature. In this second region, an energetic approach can be employed to predict the most critical locations in term of fatigue life. In fact, in [3] Skelton states that crack growth can arise when a given amount of energy has been dissipated in a certain zone. Similarly, Charkaluk and Constantinescu [4] observe that the fatigue life of a material is strongly correlated with the amount of dissipated energy per cycle:
Fig. 9. Finite Element model of (a) the engine head, (b) the engine block, (c) the gasket and (d) the valve seats, the valve guides and the bolts.
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Fig. 10. FEM computed temperature distribution inside the engine head.
DWS ¼
ZtþT
sdεp
(4)
t
where s is the local stress tensor and εp is the local plastic strain tensor. The advantages stemming from the use of an energetic approach are 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 energy per cycle is evaluated taking into account the whole loading history and his value is approximately temperatureindependent. The fatigue criterion is expressed by the relation:
DWS Nb ¼ C
K K agðε0 εp0 Þ e X εp ¼ a X0 a
g
(6)
g
where: a ¼ signðs XÞ, K and g are experimentally determined material properties depending on temperature and εp is again the local plastic strain. The fundamental parameters of the model have to be adjusted to accurately reproduce the actual experimental material behavior in the elasticeplastic region. Therefore, a virtual Finite Element tensile specimen has been generated. A non-linear optimization procedure has been employed in order to correctly fit the numerical forecast to the experimental data during cyclic loading, Fig. 11. Table 1 reports the values of K and g as a function of temperature for the aluminum alloy A356 T6 employed for the engine head production. 4.6. High-cycle fatigue results
(5)
where N is the number of cycles at which crack propagation is expected to occur and b and C are experimentally determined constants [25].
4.5. Non-linear material behavior Low-cycle fatigue phenomena are mainly related to the temperature evolution within the components. The implementation of a robust procedure for the cyclic application of subsequent mechanical, thermal, and thermo-mechanical loads to the model is therefore essential, since the accuracy of these data directly affects the quality of the structural response and the numerical predictions. In order to accurately account for the peculiar behavior of the material subjected to high temperature cyclic loading, the Chaboche stressestrain relationships for both plasticity [26] and viscoplasticity [27] are employed, based on the non-linear kinematic hardening rule expressed by:
Numerical predictions display ample regions of highly stressed material. Looking at the fillets of the walls of the coolant jacket, different highly stressed points with high values of tensile stress can be detected. In particular, a confined region is investigated where the maximum value of tensile principal stress is evaluated. Such a high value of stress classifies this region as the most likely source of failure. The comparatively low temperatures of the walls of the coolant jacket allow the employment of a stress-based criterion in the prediction of the local fatigue behavior. In particular, the Dang Van criterion is adopted in this study [1]. Table 1 Chaboche parameters K and g as a function of temperature for the aluminum alloy A356 T6. T [ ]
Rs [MPa]
K
g
20 150 200 250 300
200 190 162 104 71
5556 5282 4011 2285 1160
68.7 68.8 69.8 70.9 73
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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.
Fig. 12 shows a comparison between the actual propagation of a crack and the map of high-cycle fatigue safety factors among the regions of interest. A very satisfactory match between the location of minimum safety factors and the experimentally assessed point of crack initiation supports the validity of the present methodology and of the underlying hypotheses.
stress - plastic strain hystory curve D
200 150
stress [MPa]
100 50 0 -0.0025
-0.002
-0.0015
-0.001
-0.0005
A 0
0.0005
-50 -100 E -150
C
The flame-plate zone usually represents the area exposed to the highest thermo-mechanical loads. In particular, the regions that undergo the most severe cyclic loading are located between the valve seats (valve bridges), where the stresses due to press fit and maximum temperature cyclic loading overlap. With reference to Fig. 13, the effect of the loading history on the material, between for example the intake valves, can be qualitatively described as follows:
250
B
-0.003
4.7. Low-cycle fatigue results
-200
plastic strain
Fig. 13. Longitudinal stresseplastic strain history curve at valve bridge between intake valves.
AeB segment: due to the press fit of the valve seats, the material is subjected to a tensile stress state; BeC segment: when the highly non-uniform temperature field is applied, the material undergoes a compressive stress state, entering plastic regime; CeD segment: while the uniform ambient temperature is smoothly re-established, the material is ultimately subject to residual stress, reaching a tensile plastic regime; DeE segment: a second application of the working temperature distribution again induces compressive plasticization, thus completing a full hysteresis cycle. The employment of the energetic approach described in Section 4.4 requires the computation of DWs defined in Eq. (4). In order to be able to assess the damage index for multi-axial states on complex geometries, a general technique is required. Therefore
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Fig. 14. LCF. Energy dissipated per cycle. Comparison between experimental cracks and numerical predictions.
a post-processing procedure based on a custom-coded Fortran program has been developed to post-process the FEM solution computing DWs for each integration point. A different user routine is then employed to display the computed damage index as contour bands, providing a much more practical tool for quick detection of the regions subjected to critical LCF cycles. Fig. 14 compares the actual experimental crack propagations in the flame-plate zone with the distribution of the energy dissipated per cycle. Again, a perfect matching is detected. 5. Conclusion The combined CFD and FEM analyses the present paper describes aim at accurately predicting the temperature field and the resulting thermo-mechanical loading cycle affecting internal combustion engine components under actual operating conditions. This decoupled CFD and FEM methodology correctly estimates the fatigue strength of the engine head of a V6 turbocharged Diesel engine. A detailed model of the engine, covering both the coolant galleries and the surrounding metal components is at first employed for the fluid-dynamic analyses to accurately capture the influence of the cooling system layout on the thermal and thermomechanical behavior of the engine. The comparison between an experimentally measured temperature distribution within the engine head and the CFD forecasts highlights the importance of an accurate modeling of both the coolant phase transition and the vapor nuclei formation within the coolant galleries. Finite Element analyses are then performed in order to estimate the fatigue strength of the investigated engine head. Again, a comparisons between numerical forecasts and experimental evidences show that the proposed methodology is able to precisely predict the engine failure loci by means of the application of different fatigue criteria properly accounting for the superimposition of mechanical and thermal loadings, which result in both highcycle and low-cycle fatigue phenomena. The accuracy of the numerical forecasts allows the methodology to be applied not only as a useful tool for the investigation and understanding of detected engine failures, but also as a design tool of both the water cooling jacket and the engine structural parts.
[2] [3] [4]
[5] [6] [7]
[8]
[9]
[10]
[11]
[12]
[13]
[14] [15]
[16]
[17]
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K.J. Miller (Eds.), Biaxial and Multiaxial Fatigue, Mechanical Engineering Publications, London, 1989, pp. 459e478. M.W. Brown, K.J. Miller, A theory for fatigue failure under multiaxial stresse strain conditions, Proc. Inst. Mech. Eng. 187 (1973) 745e755. R.P. Skelton, Energy criteria for high temperature low cycle fatigue, Mater. Sci. Technol. 7 (1991) 427e439. E. Charkaluk, A. Bignonnet, A. Constantinescu, K. Dang Van, Fatigue design of structures under thermomechanical loadings, Fatig. Fract. Eng. Mater. Struct. 25 (12) (2002) 1199e1206. J.J. Thomas, L. Verger, A. Bignonnet, E. Charkaluk, Thermomechanical design in the automotive industry, Fatig. Fract. Eng. Mater. Struct. 27 (2004) 887e895. W.M. Zhao, W. Zhang, Study on thermal fatigue life prediction of cylinder head, Adv. Mater. Res. 3 (2012) 433e440. G. Cantore, M. Giacopini, R. Rosi, A. Strozzi, P. Pelloni, C. Forte, M. Achiluzzi, G.M. Bianchi, L. Ceschini, A. Morri, Validation of a combined CFD/FEM methodology for the evaluation of thermal load acting on aluminum alloy pistons through hardness measurements in internal combustion engines, Metall. Sci. Technol. 29 (1) (2011) 16e25. D. Carpentiero, S. Fontanesi, V. Gagliardi, S. Malaguti, S. Margini, M. Giacopini, A. Strozzi, L. Arnone, M. Bonanni, D. Franceschini, Thermomechanical Analysis of an Engine Head by Means of Integrated CFD and FEM, SAE Paper 2007-24-0067, Society of Automotive Engineers, Warrendale, PA, 2007. S. Fontanesi, D. Carpentiero, S. Malaguti, M. Giacopini, S. Margini, L. Arnone, A New Decoupled CFD and FEM Methodology for the Fatigue Strength Assessment of an Engine Head, SAE Paper 2008-01-0972, Society of Automotive Engineers, Warrendale, PA, 2008. S. Nukiyama, Maximum and minimum values of heat transmitted from metal to boiling water under atmospheric pressure, Jpn. Soc. Mech. Eng. 37 (1934) 367e374. M. Gollin, E.V. McAssey, C. Stinson, Comparative Performance of Ethylene Glycol/Water and Propylene Glycol/Water Coolants in the Convective and Forced Flow Boiling Regimes, SAE Paper 950464, Society of Automotive Engineers, Warrendale, PA, 1995. H.S. Lee, A.T. O’Neill, Comparison of Boiling Curves Between a Standard S.I. Engine and a Flow Loop for a Mixture of Ethylene Glycol and Water, SAE Paper 2006-01-1231, Society of Automotive Engineers, Warrendale, PA, 2006. S. Fontanesi, E.V. McAssey, Experimental and Numerical Investigation of Conjugate Heat Transfer in a HSDI Diesel Engine Water Cooling Jacket, SAE Paper 2009-01-0703, Society of Automotive Engineers, Warrendale, PA, 2009. F.R. Menter, Zonal two equation keu turbulence models for aerodynamic flows, in: AIAA Paper 93-2906, 1993. C.D. Rakopoulos, D.C. Rakopoulos, G.C. Mavropoulos, E.G. Giakoumis, Experimental and theoretical study of the short term response temperature transients in the cylinder walls of a diesel engine at various operating conditions, Appl. Therm. Eng. 24 (2004) 679e702. C.D. Rakopoulos, D.T. Hountalas, Development of a new 3-D multi-zone combustion model for indirect injection diesel engines with a swirl type prechamber, Trans. SAE J. Engines 109 (2000) 718e733. S. Fontanesi, G. Cicalese, A. D’Adamo, G. Pivetti, Validation of a CFD Methodology for the Analysis of Conjugate Heat Transfer in a High Performance SI Engine, SAE Paper 2011-24-0132, Society of Automotive Engineers, Warrendale, PA, 2011. C.D. Rakopoulos, G.C. Mavropoulos, Experimental instantaneous heat fluxes in the cylinder head and exhaust manifold of an air-cooled diesel engine, Energ. Convers. Manag. 41 (2000) 1265e1281.
S. Fontanesi, M. Giacopini / Applied Thermal Engineering 52 (2013) 293e303 [19] E. Carvajal Trujillo, F.J. Jiménez-Espadafor, J.A. Becerra Villanueva, M. Torres García, Methodology for the estimation of cylinder inner surface temperature in an air-cooled engine, Appl. Therm. Eng. 31 (2011) 1474e1481. [20] V. Esfahanian, A. Javaheri, M. Ghaffarpour, Thermal analysis of an SI engine piston using different combustion boundary condition treatments, Appl. Therm. Eng. 26 (2006) 277e287. [21] C. Borgnakke, V.S. Arpaci, R.J. Tabaczynski, A Model for the Instantaneous Heat Transfer and Turbulence in a Spark Ignition Engine, SAE Paper 800287, Society of Automotive Engineers, Warrendale, PA, 1980. [22] Gopinath R. Warrier, Vijay K. Dhir, Heat transfer and wall heat flux partitioning during subcooled flow nucleate boilingea review, Trans. ASME J. Heat Trans. 128 (2006) 1243e1256.
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[23] W.M. Rohsenow, A method of correlation heat transfer data for surface boiling of liquid, Trans. ASME J. Heat Trans. 74 (1952) 969e976. [24] I.C. Finlay, G.R. Gallacher, T.W. Biddulph, R.A. Marshall, The Application of Precision Cooling to the Cylinder-head of a Small Automotive Petrol Engine, SAE Paper 880263, Society of Automotive Engineers, Warrendale, PA, 1988. [25] T. Takahashi, K. Sasaki, Low cycle thermal fatigue of aluminum alloy cylinder head in consideration of changing metrology microstructure, Procedia Eng. 2 (2010) 767e776. [26] J.L. Chaboche, Time-independent constitutive theories for cyclic plasticity, Int. J. Plasticity 2 (1986) 149e188. [27] J.L. Chaboche, Constitutive equations for cyclic plasticity and cyclic viscoplasticity, Int. J. Plasticity 5 (1989) 247e302.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Multiphase CFDeCHT optimization of the cooling jacket and FEM analysis of the engine head of a V6 diesel engine Stefano Fontanesi*, Matteo Giacopini University 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
a b s t r a c t
Article history: Received 9 July 2012 Accepted 7 December 2012 Available online 20 December 2012
The present paper proposes a numerical methodology aiming at analyzing and optimizing an internal combustion engine water cooling jacket, with particular emphasis on the assessment of the fatigue strength of the engine head. Full three-dimensional CFD and FEM analyses of the conjugate heat transfer and of the thermomechanical loading cycles are presented for a single bank of a currently made V6 turbocharged Diesel engine under actual operating conditions. A detailed model of the engine, consisting of both the coolant galleries and the surrounding metal components is employed in both fluid-dynamic and structural analyses to accurately mimic the influence of 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 CFD forecasts. Particular attention is paid to the modeling of the phase transition and of the vapor nuclei formation within the coolant galleries. Thermo-mechanical analyses are then carried out aiming at addressing the design optimization of the engine in terms of fatigue strength. Because of the wide range of thermal and mechanical loadings acting on the engine head, both high-cycle and low-cycle fatigue are considered. An energy-based multi-axial criterion specifically suited for thermal fatigue is employed in the low-cycle fatigue region (i.e. the combustion dome) while well-established multi-axial stress/strain-based criteria are adopted to investigate 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 possible engine failures and proves to be an effective tool for the accurate thermo-mechanical characterization of internal combustion engines under actual life-cycle operating conditions. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Engine head Heat transfer Boiling Fatigue analysis
1. Introduction Internal combustion engines undergo cyclic thermo-mechanical loadings and are subjected to a wide range of operating conditions,
* Corresponding author. Tel.: þ39 (0)59 2056114; fax: þ39 (0)59 2056126. E-mail address: [email protected] (S. Fontanesi). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.12.005
in terms of both temperature distribution and frequency/amplitude of mechanical and thermo-mechanical loading cycles. Consequently, in order to accurately evaluate the mechanical strength of engine components, two different fatigue cycles must be modeled: (i) the fatigue cycle related to the combustion process, whose frequency is strictly related to the crankshaft revving speed, (ii) the thermally induced fatigue cycle whose frequency is dependent on the ignition/engine warm up/switch off/engine cool down cycle.
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On one side, traditional and well-established stress-based [1] or strain-based [2] fatigue criteria can be proficiently employed to analyze the effects of the application of high-frequency loadings. On the other side, low-frequency thermo-mechanical loadings are still an open challenge for the designers. In fact, a unique and widely recognized procedure for the low-cycle fatigue strength assessment of engine components is not yet available. Relying on a formerly developed energy-based criterion [3], analyses of lowcycle fatigue phenomena in engine components such as cast-iron engine manifolds [4] or aluminum alloy engine heads [5] have been performed, whose predictive capability in terms of consistency between numerical forecasts and experimental evidences is confirmed by recent applications [6]. Since the temperature-induced stress field is the major cause of material damage in the low-cycle fatigue regions, high accuracy is required for the evaluation and application of thermal boundary conditions. A detailed CFD investigation on the point-wise fluid/solid heat transfer becomes therefore of crucial importance in order to correctly estimate the local thermal conditions, since it provides a deep knowledge on both global and local thermal phenomena and a good understanding of the effect of the cooling system design modifications on the thermal behavior of the engine. In fact, even if experimental investigations on internal combustion engine cooling systems can provide useful information for the understanding of the global thermal behavior of the engine, as well as a useful set of validation parameters for the numerical simulations [7], the use of experimental techniques for the design and the optimization process of an engine head is not feasible from an industrial point of view. Therefore, the use of numerical simulations for the design and the optimization process becomes strategic, where a relevant reduction of both time to market and development costs are required. For an accurate representation of the heat transfer between the engine head and the coolant, many key numerical parameters and sub-models must be correctly defined and tuned. In particular, a proper modeling of both the thermal boundary layer and the vapor nuclei formation is widely recognized to play a crucial role in the temperature distribution calculation inside both aluminum alloy [8] and cast iron [9] engine components. In the present paper a deep investigation on the role played by the fluid boundary layer modeling is carried out. In particular, a phase-change model is introduced in order to increase the accuracy of the numerical forecasts. It is in fact widely recognized that engine cooling typically relies on convection and boiling heat transfer within the engine cooling jacket. The geometrical complexity of typical engine heads makes it extremely difficult to clearly identify the heat transfer regime in the cooling system most critical regions. From a general perspective, heat transfer modes can be divided in: a) pure convection, b) nucleate boiling and c) film boiling. a) The heat transfer mechanism that occurs in the coolant galleries under low thermal loads is mainly dominated by forced convection: under this situation, coolant physical properties and flow rate rule the effectiveness of the heat removal from the engine metal surfaces. b) When the heat flux increases (e.g. for high-load engine operating conditions typical of the last generation of downsized/ turbocharged HSDI Diesel engines), a surface temperature is reached that promotes the vapor bubble formation at the fluid/ solid interface, despite the coolant bulk temperature is still below the saturation temperature at the cooling system operating pressure. Thus, nucleate boiling arises. c) A further increase in the heat flux causes a speed up of the vapor nuclei formation at the fluid/solid interface, which can
eventually lead to an undesired formation of a vapor film preventing the circumstance that the coolant reaches the surface. This phenomenon, widely termed as film boiling, leads to a sudden and non-negligible reduction in the ability of the coolant to remove heat and, therefore, to a rapid increase in the local metal temperature [10]. The ability of the liquid coolant to promptly remove heat from the nucleate boiling regions strongly depends on a complex combination of flow characteristics and coolant channel design. Therefore, in order to evaluate the actual design efficiency and to improve the system performance, both these aspects must be deeply investigated to improve the cooling performance and, consequently, to reduce the thermal stresses arising in the engine. In the present paper a previously proposed methodology [8,9] is substantially improved in the capability of correctly mimicking the local coolant behavior and detecting the correct location of fatigue crack initiations. The paper is organized as follows. First, the whole modeling strategy is presented. Then the CFD simulations are described in details and a validation of the CFD forecasts versus experimental temperature measurements is reported. The influence of the phase transition modeling and the vapor nuclei formation within the coolant galleries on the temperature distribution estimation is discussed. Then, thermo-mechanical FEM analyses of the engine head are described where CFD validated results are employed as external thermal boundary conditions. Results in terms of both low-cycle fatigue and high-cycle fatigue life estimation are presented. The proposed approach is validated versus some crack initiations observed during bench tests of a high specific power VM Motori turbocharged HSDI six cylinder diesel engine for automotive applications. 2. Modeling strategy The methodology presented in this paper is based on CFD and FEM decoupled simulations. The CFD analyses constitute the first step of the proposed modeling strategy. Two different aspect are investigated in details: i) the fluid-dynamic behavior of the cooling circuit is firstly analyzed and optimized aiming at improving the cooling efficiency and the flow distribution among the different cylinders; ii) the point-wise fluid/solid heat transfer is then evaluated. In particular, benefits on the overall predicting capability brought in by the adoption of a proper phase-change model are highlighted by means of a preliminary comparison with a simplified model where phasechange is neglected and by a subsequent validation of the methodology against experimental measurements of the temperature distribution within the engine head. The second step of the proposed methodology consists in the implementation of a FEM procedure able to properly account for the different mechanical and thermal boundary conditions applied to the engine components. An ad-hoc user routine is employed to map point-wise coolant/metal interface thermal boundary conditions from the CFD to the FEM realm. In order to correctly assess the fatigue strength of the engine, proper damage criteria are adopted to 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 the block: the coolant enters the circuit from the engine block and exits out of the head; both inlet and outlet lay on the same side of the
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The cooling circuit has been extensively analyzed from a fluiddynamic point of view using the methodology described in [8,9] to which the interested reader is referred. The definitive jacket layout (with particular regard to the apertures through the gasket) is the result of a set of analyses aimed at improving the cooling efficiency and the flow distribution homogenization among the three cylinders of the analyzed engine portion. Fig. 2 depicts a comparison between some gasket configurations, highlighting in particular the most promising solution (named “Optimized”) in terms of flow distribution uniformity among the cylinders and flow resistance. 3.2. Evaluation of the point-wise fluid solid heat transfer Fig. 1. Cooling circuit layout.
cooling circuit. Two additional coolant outlets are visible in Fig. 1, one serving the turbocharger cooler and the other serving the EGR cooler. The circuit layout is characterized by a cross flow distribution around each cylinder: as a consequence, a relevant coolant fraction leaves the circuit before reaching the cylinder furthest from the entrance. All the analyses presented in this paper are carried out simulating the engine at full load and at peak power revving speed, i.e. 4000 rpm, since this situation represents the most critical engine operating condition from the engine head thermo-mechanical loading point of view. A coolant flow rate through the circuit equal to about 150 l/min is considered as a mass flow entering the block and it is then split among the three different outlets, see Fig. 1, in accordance with experimental measurements provided by the engine manufacturer. The cooling pressure is derived from the feeding pump performance curve, while the inlet average temperature is again derived from experiments at the engine test bench. The coolant is a 50/50 mixture of water and ethylene glycol. Literature-based physical properties [11] and boiling curves [12] are subsequently recomputed by means of a purposely developed spreadsheet [13] for the specific operating pressure, temperature and mixture composition suggested by the engine manufacturer.
The CFD computational domain employed for the evaluation of the coolant/solid heat transfer covers a full engine bank, i.e. the coolant galleries, the aluminum alloy engine head, the cast iron block and the gasket. To properly take into account the material discontinuities, press fit components are also included. In order to speed up the grid generation process, the CFD domain is generated using the STAR-CCMþ polyhedral mesher by CD-Adapco. The resulting grid is made up of polyhedral shaped cells, which constitute a good tradeoff between cell mean size, computational demand and effort requested to discretize such a geometrically complex domain. Particular care is used to model the fluid-dynamic boundary layer, discretized by prismatic layers whose thickness is properly chosen according to the adopted near-wall treatment. Particularly, this paper reports the results obtained using the keu SST lowReynolds model [14]. On one hand, because of the high flow nonuniformity near the walls and the small cooling passage dimensions, it is extremely complex to satisfy the requirements of a highReynolds wall treatment, i.e. yþ > 30. On the other hand, the high geometrical complexity and the wide extent of the calculation domain make the use of a low-Reynolds approach extremely expensive from the computational demand point of view. Therefore, to limit the overall number of cells, it is necessary to coarsen the grid far away from the areas of major interest. The resulting domain consists of about 14.000.000 cells.
Fig. 2. Gasket optimization.
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It is important to note that local grid refinements in the solid domain are adopted in the regions subjected to high thermal gradients, i.e. the combustion chamber, the valve guides and the valve 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 conditions Since the accuracy of the simulations in terms of temperature estimation within the engine, and therefore of its thermomechanical behavior, heavily depends on the choice of proper thermal boundary conditions, particular care is paid to the subdivision of the combustion heat flux among the many components facing the combustion chamber. In particular, boundary conditions accounting for the combustion and gas/solid heat fluxes are derived from a combination of three-dimensional simulations of the in-cylinder processes, onedimensional simulations results of the whole engine and experimental measurements. It is well known that temperature oscillations can be observed at the 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 flux variation are expected to moderately affect the heat transfer between the engine and the coolant. Therefore, the actual timevarying heat flux can be cycle-averaged and converted into a time-independent thermal load. If accurate predictions of wall temperature oscillations were required, a correction factor should be introduced in the heat fluxes/heat transfer coefficients based either on multi-zone models [16] or on instantaneous threedimensional models of the whole combustion process [17]. In this case, three-dimensional simulations of the whole engine cycle are used to derive a cycle-averaged point-wise thermal heat flux distribution on the engine surfaces directly facing the combustion chamber, i.e. the combustion dome, the cylinder liner and the piston. The heat flux entering the combustion chamber walls is then simultaneously applied to all the cylinders and split among the many components following the above mentioned 3D simulations. In particular, the overall heat flux lost through the combustion chamber 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 exhaust valves surfaces, a fictitious specific heat flux varying as a function of the cylinder axis coordinate is applied to the liner, adopting a strategy similar to the one reported in [19]. In fact, following a 3D Finite Element thermal analysis of the piston, a portion of the heat flux entering the piston top is transferred to the cylinder liner as a consequence of the contact between the piston skirt and the liner. Therefore, the overall flux applied to the liner results from the superposition of the direct flux deriving from the combustion process and that related to the piston/liner contact [20]. In particular, since the heat flux transferred to the cylinder liner decreases with the increase of the distance from the combustion dome, the specific heat flux q_ is assumed as a parabolic function of the axial coordinate x, where x ¼ 0 corresponds to the gasket plane axial coordinate. Results from one-dimensional simulations of the whole engine in terms of gas temperatures and heat transfer coefficients are then used for the intake and exhaust ports. For these components, the use of one-dimensional derived boundary conditions is a standard practice and is based on widely recognized assumptions [21]. Finally, the simulation is performed considering actual test-cell room conditions. 3.2.2. Phase-change model As already stated in the Section Introduction, boiling effects have been included in the CFD procedure to improve the accuracy of the local heat transfer forecasts. The model implemented in the commercial software STAR-CCMþ to mimic the onset of vapor formation within the fluid domain is constituted of various submodels. First, the heat transfer at solideliquid interface is used to compute the rates of fluid evaporation and condensation. The temperature of vapor bubbles is assumed to be equal to the saturation temperature Tsat, while the liquid temperature Tl can be approximated to the mixture temperature T. The whole heat flux exchanged between the liquid and the vapor is converted into mass flow rate subjected to phase transition (i.e. evaporation or condensation):
_ EC ¼ m
CHTCxArea ðT Tsat Þ hlat
(1)
where hlat is the latent heat of vaporization and CHTCxArea is the heat transfer coefficient between vapor bubbles and the surrounding liquid multiplied by the contact surface separating the two phases. Secondly, if a liquid is in contact with a solid surface with a temperature Twall higher than Tsat, boiling occurs at the liquid/ solid interface. In this case, boiling undergoes three characteristic regimes: (i) nucleate boiling: characterized by the formation and growth of vapor bubbles on a heated surface. The bubbles rise up from a discrete number of points whose temperature is slightly higher than the liquid saturation temperature Tsat. In general, the number of nucleation sites increases as the surface temperature increases. Augmenting the surface roughness can lead to a higher number of nucleation sites, while an extreme smoothing of the surfaces can lead to surface overheating; (ii) film boiling: once a critical heat flux is reached, the heated surface is covered by a continuous vapor film. Because of the low thermal conductivity of the vapor layer, the surface can be considered insulated;
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(iii) transition boiling: it describes the mechanism occurring for temperatures ranging between the maximum temperature of nucleate boiling regime and minimum temperature of film boiling. Although many heat transfer models can be found in literature dealing with the nucleate boiling regime [22], none of them is accepted as a standard. A common characteristic of all these models is the mimicking of the main mechanisms of nuclei formation, i.e. evaporation (latent heat), transport, micro convection, liquide vapor exchange, surface extinction, etc. In particular, the empiric relationship proposed by Rohsenow [23] is used in the present work to calculate the boiling heat flux on a certain surface:
qbw ¼ ml hlat
!3:03 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gðrl rv Þ cPl ðTw Tsat Þ
s
cqw hlat Pr1:7 l
(2)
where ml, cPl, rl and Prl are the dynamic viscosity, the specific heat, the density and the Prandtl number of the liquid phase, respectively, g is the gravity, rv is the density of the vapor phase, s is the surface tension at the liquid/vapor interface, Tw is the wall temperature and cqw is an empirical coefficient whose value is dependent on the corresponding liquid/surface properties, previously calibrated by one of the authors by means of comparisons between CFD predictions and experimental measurements for engine coolants and aluminum alloys in simplified geometries [13]. The vapor mass flow rate generated on a surface covered by nucleation sites can be written as follows:
_ ew ¼ m
cew qbw hlat
(3)
where cew is a model constant which tunes the amount of boiling heat flux percentage converted into bubble formation. 3.2.3. Methodology validation As a preliminary step, results obtained from a single-phase analysis are compared with those computed employing the proposed multiphase model: some non-negligible limitations in the representation of local thermal phenomena can be observed when the CFD model is not suitable to take into account the coolant phase transition. Nevertheless, it is important to point out that the adoption of a phase transition model implies the use of a transient simulation approach, despite the application of cycle-averaged heat fluxes. The onset of a transient simulation requires the convergence of the solution to be obtained for both the computational domains (fluid and solid). Considering that, in order to limit the fluid domain convective Courant number, the computing time step is about 0.005 s, and that the solution stabilizes only after an analysis time close to 120 s, a huge number of iterations has to be run. As a consequence, the methodology requires extremely high computational times, which can reach 200 h on a 14 CPU linux cluster. Therefore, the use of a simplified single-phase steady-state approach, neglecting the effects of vapor formation, would be extremely advantageous in order to limit the computational demand. On the other side, the impossibility by the coolant to subtract latent heat during phase transition could lead to a relevant local overestimation of the maximum temperature levels within the fluid domain, since all the heat flux is converted into sensible heat. As a result, when the simplified single-phase steady-state approach is employed for the CFD heat transfer simulations of the engine under investigation, coolant maximum temperature
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appears to be strongly overestimated, severely limiting the physical soundness of the CFD forecast. Although the amount of coolant vapor can be limited both in terms of spatial extent and total amount, vapor nuclei arise at the engine most critical locations. Moreover, the surrounding metal can also be affected by the described coolant temperature overestimation, similarly reaching temperature peaks far beyond the measured ones. Fig. 4 shows the portion of the fluid domain whose temperature rises above the boiling temperature threshold at the cooling system operating pressure within the simplified single-phase approach framework. The above described shortcome, is completely overcome thanks to the adoption of a proper phase-change sub-model, which is able to capture vapor nuclei formation at the most critical locations. The subsequent heat removal mechanism, named as “boiling heat flux” is shown in Fig. 5. In order to assess the predictive capability of the proposed methodology, CFD computed temperatures are then compared with experimental measurements obtained by means of eight thermocouples located within the engine head covering at the head most critical regions, i.e. for example the exhaust valve bridge. Considering the limited number of available experimental data, the comparison between CFD predictions and measurements is carried out with the specific aim of correctly capturing the thermal field within the head solid domain. An extensive validation of the physical soundness of the coolant behavior would require the use of more detailed experimental techniques far away from the standard industrial practice. Nevertheless, since the aim of the overall simulation process is the correct representation of the thermomechanical behavior of the engine head, the experimental evidences are considered to be very useful. Temperature measurements have been carried out along two section planes cutting the engine head at a different distance from the gasket plane. Fig. 6 illustrates the position of the thermocouples: evennumbered thermocouples are located at a distance equal to 2.5 mm from the gasket plane, while odd-numbered ones are located at a distance equal to 8 mm from the gasket plane. Fig. 7 reports a comparison between the numerical forecasts and the experimental available data set. Fig. 8 shows the temperature distribution on the walls of the combustion dome and intake and exhaust ports, with the coolant jacket portion undergoing vapor bubble formation superimposed. Adopting the above described numerical procedure it is possible to correctly reproduce the temperature distribution within the engine head. The ability of the simulations to accurately represent both the thermal boundary layer and the convective heat transfer phenomena, as well as the effects of local vapor bubble formation at the fluid/solid interface and subsequent condensation within the
Fig. 4. Coolant threshold above the boiling temperature.
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Fig. 5. Heat flux due to phase-change (a) and vapor volume fraction (b).
liquid core, is a crucial aspect. In fact, the agreement between predicted and measured temperatures is very satisfactory for all the measurement locations. 4. Finite Element results Thermo-mechanical simulations are performed using the commercial Finite Element software MSC.Marc2010.2Ò. For optimal accuracy and numerical stability, new grids have been adopted for Finite Element calculations. To achieve a more faithful representation of the engine head behavior under actual operating conditions, a former model employed in Ref. [9] is improved including the non-linear modeling of the gasket behavior and a full discretization of the engine block. Fig. 9 shows the Finite Element discretization of the investigated Diesel engine components. The FEM model consists of approximately 1,740,000 elements and 560,000 node. 4.1. Mechanical loading The same set of mechanical boundary conditions already used in Ref. [9] are adopted in all the simulations involved in this work and are 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.
4.2. Thermal loading Due to material expansion under a non-uniform temperature distribution, thermal stresses are induced in the engine head. In order to properly predict the fatigue life of the component, the correct temperature distribution has to be taken into account. A static thermal Finite Element calculation is therefore performed, to compute the temperature distribution map directly on the grid created for Finite Element calculations. The same thermal loads used for CFD simulations are applied to this FEM thermal model, except for the metal/coolant interface, where heat transfer coefficients are precisely mapped from the CFD solution to the FEM model using an ad-hoc Fortran routine. Fig. 10 pictorially represents the temperature distribution inside the engine head computed with FE. 4.3. Load Cases Many different consecutive Load Cases are subsequently applied to the thermo-mechanical model of the engine in order to take into account 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 combustion pressure; - Load Case 3: including all mechanical and thermal loads; - Load Case 4: including all loads except for combustion pressure: - Load Case 5: thermal loading is removed; - Load Case 6: thermal loading is applied again. Each different Load Case represents a different engine operating condition. In particular, Load Case 1 simulates engine assembling, Load Case 2 simulates engine cold start, while Load
Experimental
k-omega
290
Temperature °C
270 250 230 210 190 170 150 Tsx1 Fig. 6. Thermocouple positions.
Tsx2
Tsx3
Tsx4
Tsx5
Tsx6
Tsx7
Tsx8
Fig. 7. Comparison between CFD forecasts and experimental measurements.
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Fig. 8. Temperature distribution and vapor fraction.
Cases 3 and 4 describe the engine operating at full load condition and the corresponding stress distributions represent the envelope of the high-cycle fatigue (HCF). Load Cases 5 and 6 represent the start/operate/stop cycle related to the low-cycle fatigue phenomena (LCF).
4.4. Fatigue criteria To correctly predict the fatigue behavior of the whole engine head, specific failure criteria must be employed at different locations. In fact, because of the superimposition of mechanical and thermal loading, both high-cycle and low-cycle fatigue phenomena have to be taken into account. In particular, two main areas can be detected that exhibit different behaviors:
(i) under normal loading conditions, the walls of the coolant jacket do not undergo any plastic strain; therefore, this regions can be treated with usual high-cycle fatigue criteria (stressbased [1] or strain-based [2] criteria); (ii) the area of the combustion dome exposed to the combustion gases is subjected to the highest thermal loads, and displays substantial plastic deformations, which can be traced back to the drop of mechanical properties at high temperature. In this second region, an energetic approach can be employed to predict the most critical locations in term of fatigue life. In fact, in [3] Skelton states that crack growth can arise when a given amount of energy has been dissipated in a certain zone. Similarly, Charkaluk and Constantinescu [4] observe that the fatigue life of a material is strongly correlated with the amount of dissipated energy per cycle:
Fig. 9. Finite Element model of (a) the engine head, (b) the engine block, (c) the gasket and (d) the valve seats, the valve guides and the bolts.
300
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Fig. 10. FEM computed temperature distribution inside the engine head.
DWS ¼
ZtþT
sdεp
(4)
t
where s is the local stress tensor and εp is the local plastic strain tensor. The advantages stemming from the use of an energetic approach are 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 energy per cycle is evaluated taking into account the whole loading history and his value is approximately temperatureindependent. The fatigue criterion is expressed by the relation:
DWS Nb ¼ C
K K agðε0 εp0 Þ e X εp ¼ a X0 a
g
(6)
g
where: a ¼ signðs XÞ, K and g are experimentally determined material properties depending on temperature and εp is again the local plastic strain. The fundamental parameters of the model have to be adjusted to accurately reproduce the actual experimental material behavior in the elasticeplastic region. Therefore, a virtual Finite Element tensile specimen has been generated. A non-linear optimization procedure has been employed in order to correctly fit the numerical forecast to the experimental data during cyclic loading, Fig. 11. Table 1 reports the values of K and g as a function of temperature for the aluminum alloy A356 T6 employed for the engine head production. 4.6. High-cycle fatigue results
(5)
where N is the number of cycles at which crack propagation is expected to occur and b and C are experimentally determined constants [25].
4.5. Non-linear material behavior Low-cycle fatigue phenomena are mainly related to the temperature evolution within the components. The implementation of a robust procedure for the cyclic application of subsequent mechanical, thermal, and thermo-mechanical loads to the model is therefore essential, since the accuracy of these data directly affects the quality of the structural response and the numerical predictions. In order to accurately account for the peculiar behavior of the material subjected to high temperature cyclic loading, the Chaboche stressestrain relationships for both plasticity [26] and viscoplasticity [27] are employed, based on the non-linear kinematic hardening rule expressed by:
Numerical predictions display ample regions of highly stressed material. Looking at the fillets of the walls of the coolant jacket, different highly stressed points with high values of tensile stress can be detected. In particular, a confined region is investigated where the maximum value of tensile principal stress is evaluated. Such a high value of stress classifies this region as the most likely source of failure. The comparatively low temperatures of the walls of the coolant jacket allow the employment of a stress-based criterion in the prediction of the local fatigue behavior. In particular, the Dang Van criterion is adopted in this study [1]. Table 1 Chaboche parameters K and g as a function of temperature for the aluminum alloy A356 T6. T [ ]
Rs [MPa]
K
g
20 150 200 250 300
200 190 162 104 71
5556 5282 4011 2285 1160
68.7 68.8 69.8 70.9 73
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301
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.
Fig. 12 shows a comparison between the actual propagation of a crack and the map of high-cycle fatigue safety factors among the regions of interest. A very satisfactory match between the location of minimum safety factors and the experimentally assessed point of crack initiation supports the validity of the present methodology and of the underlying hypotheses.
stress - plastic strain hystory curve D
200 150
stress [MPa]
100 50 0 -0.0025
-0.002
-0.0015
-0.001
-0.0005
A 0
0.0005
-50 -100 E -150
C
The flame-plate zone usually represents the area exposed to the highest thermo-mechanical loads. In particular, the regions that undergo the most severe cyclic loading are located between the valve seats (valve bridges), where the stresses due to press fit and maximum temperature cyclic loading overlap. With reference to Fig. 13, the effect of the loading history on the material, between for example the intake valves, can be qualitatively described as follows:
250
B
-0.003
4.7. Low-cycle fatigue results
-200
plastic strain
Fig. 13. Longitudinal stresseplastic strain history curve at valve bridge between intake valves.
AeB segment: due to the press fit of the valve seats, the material is subjected to a tensile stress state; BeC segment: when the highly non-uniform temperature field is applied, the material undergoes a compressive stress state, entering plastic regime; CeD segment: while the uniform ambient temperature is smoothly re-established, the material is ultimately subject to residual stress, reaching a tensile plastic regime; DeE segment: a second application of the working temperature distribution again induces compressive plasticization, thus completing a full hysteresis cycle. The employment of the energetic approach described in Section 4.4 requires the computation of DWs defined in Eq. (4). In order to be able to assess the damage index for multi-axial states on complex geometries, a general technique is required. Therefore
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Fig. 14. LCF. Energy dissipated per cycle. Comparison between experimental cracks and numerical predictions.
a post-processing procedure based on a custom-coded Fortran program has been developed to post-process the FEM solution computing DWs for each integration point. A different user routine is then employed to display the computed damage index as contour bands, providing a much more practical tool for quick detection of the regions subjected to critical LCF cycles. Fig. 14 compares the actual experimental crack propagations in the flame-plate zone with the distribution of the energy dissipated per cycle. Again, a perfect matching is detected. 5. Conclusion The combined CFD and FEM analyses the present paper describes aim at accurately predicting the temperature field and the resulting thermo-mechanical loading cycle affecting internal combustion engine components under actual operating conditions. This decoupled CFD and FEM methodology correctly estimates the fatigue strength of the engine head of a V6 turbocharged Diesel engine. A detailed model of the engine, covering both the coolant galleries and the surrounding metal components is at first employed for the fluid-dynamic analyses to accurately capture the influence of the cooling system layout on the thermal and thermomechanical behavior of the engine. The comparison between an experimentally measured temperature distribution within the engine head and the CFD forecasts highlights the importance of an accurate modeling of both the coolant phase transition and the vapor nuclei formation within the coolant galleries. Finite Element analyses are then performed in order to estimate the fatigue strength of the investigated engine head. Again, a comparisons between numerical forecasts and experimental evidences show that the proposed methodology is able to precisely predict the engine failure loci by means of the application of different fatigue criteria properly accounting for the superimposition of mechanical and thermal loadings, which result in both highcycle and low-cycle fatigue phenomena. The accuracy of the numerical forecasts allows the methodology to be applied not only as a useful tool for the investigation and understanding of detected engine failures, but also as a design tool of both the water cooling jacket and the engine structural parts.
[2] [3] [4]
[5] [6] [7]
[8]
[9]
[10]
[11]
[12]
[13]
[14] [15]
[16]
[17]
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