2004 ABAQUS Users’ Conference 1

Coupled CFD-FE-Analysis for the Exhaust Manifold of a Diesel Engine

Yasar Deger*, Burkhard Simperl*, Luis P. Jimenez**

*Sulzer Innotec, Sulzer Markets and Technology Ltd, Winterthur, Switzerland

**Guascor I+D S.A., Miñano, Spain

Abstract: The rapid advances in computer and simulation technology make it possible to model complex geometrical shapes, material behavior and load cases, and to analyze the associated deformations and stresses under simulated operational conditions close to the real situation. The efficiency of the interdisciplinary multiphysics-analyses and the quality of their results are however highly dependent on the possibility to access the knowledge and expertise of company specialists in finite element applications, materials sciences and fluid dynamics. A typical example of such a close cooperation at Sulzer Innotec was the numerical investigation of the thermo-mechanical stresses in the exhaust manifold of a diesel engine with active water cooling system. In a first step, CFD analyses for three stationary operational conditions with variable cooling flow were performed for this exhaust manifold aiming to determine specific temperature and pressure distributions. The fluid flow and the heat transfer through the exhaust manifold were computed correspondingly by CFD analyses including the conjugate heat transfer. The temperature distributions of the solid part of the CFD mesh were the “load cases” in a second step. They were analysed subsequently using the ABAQUS-FE-model of this solid part, consisting of 600’000 elements, to quantify related deformations and thermally induced stresses, in a one-way-coupling approach and considering nonlinear material behaviour. The interpolation of the temperature data for 10-node-elements of type tetrahedron was done by algorithms developed by Sulzer Innotec. Selected details and results of the overall investigation are presented and discussed within the framework of this paper.

Keywords: CFD Coupling, Heat Transfer, Thermal Stress

1. Introduction

Exhaust manifolds are parts of diesel engines sensitive to crack damage. Even improved materials like cast alloys suffer from relatively high operational temperatures which can lead to significant stresses and displacements. The aim of a series of coupled CFD-FE simulations performed by Sulzer Innotec for Guascor was to investigate the thermo-mechanical behaviour of an exhaust

2 2004 ABAQUS Users’ Conference

Figure 1. Exhaust manifold of a diesel engine.

manifold (Figure 1) which has an active cooling system. The following three cases of cooling were analysed:

• Full water flow • Partial water flow (by 50% reduced cooling flow) • Vapour flow

Fluid flow, thermal heat transfer and stress analysis are coupled for each case using a one-way-coupling approach. Selected results are given below in form of temperature, stress and displacement distribution plots. The arrows in Figure 1 indicate potentially critical areas of the component. The investigation was focusing on potential structural optimisation measures. Therefore some suggestions for design improvements are presented also, which are presumably effective to reduce the temperature peaks and temperature gradients and to ensure a longer service life for the exhaust manifold.

2. CFD Analysis

The fluid flow and the heat transfer through the exhaust manifold are computed by a CFD analysis using the CFD code STAR-CD. The temperatures of the solid parts are interpolated subsequently on the ABAQUS-FE-mesh and used to obtain corresponding thermal deformations and stresses. This interpolation is done by algorithms developed by Sulzer Innotec. The CFD calculations are based on selected operating points concerning cooling conditions which are described below in detail:

• Full cooling water flow

2004 ABAQUS Users’ Conference 3

Figure 2. Longitudinal section plot of the exhaust manifold showing exhaust tube, cooling jacket and the casing.

• Partial cooling water flow (Due to higher temperatures in the cooling jacket, the cooling

water can partially evaporate. Based on this assumption the second analysis is done with a one-phase model and using a coolant medium with the material properties of water, equivalent to 50% reduced cooling flow. A possible occurrence of vapour phase is therefore not simulated explicitly, but potentially critical zones are expected to be identifiable by this simplified modelling.)

• Vapour flow (Extremely, the further increase of the temperature in the cooling jacket can lead to evaporation of the entire cooling water. This operation point is investigated with a one phase model with water vapour as coolant medium.)

2.1 Preparation of the numerical model and mesh generation The hot exhaust gas enters the manifold from two sides and is cooled by a cooling jacket (Figure 2). In order to carry out the CFD-calculation with simultaneous consideration of conjugate heat transfer, a multi-purpose model containing the fluid parts (exhaust gas, cooling medium) and the solid part (cast shell) has been created. For the FE analysis, only the solid part of the model is used. In spite of the relatively symmetric geometry of the exhaust manifold, due to the asymmetrical cooling flow the full-scale model has been taken into account for the entire investigation. The unstructured grid, shown in Figure 3, consists of approximately 1.800.000 cells. These are divided in 600.000 solid cells and 1.200.000 fluid cells. Great importance was attached to implement prism layers with a fine resolution at the interface between fluid and solid part to get a proper simulation of flow in the wall boundary layer and of the heat transfer to the wall.

Exhaust gas inlet

Exhaust gas inlet

Exhaust gas outlet Cooling water inlet

Cooling water outlet

4 2004 ABAQUS Users’ Conference

Figure 3. Longitudinal section of the numerical grid. The zoomed view shows the implemented prism layer on fluid contact areas to ensure proper calculation of the heat transfer between solid and fluid parts.

2.2 Thermal material properties and boundary conditions Temperature, pressure and mass flow of the exhaust gas and of the cooling water at the inlet to the manifold were specified for all three operating points. Furthermore, material properties of cast iron and the surface temperature at the interface between cylinder head and exhaust manifold were defined. The heat transfer between the hot exhaust gases, the manifold shell, the cooling water and the environment is calculated by the CFD code. The surfaces attached to the engine or to a neighbouring manifold have a fixed temperature of 150°C. The ambient temperature was assumed to be 30°C with a heat transfer coefficient of α = 5 W/m2K. This is a usual value to simulate natural convection.

2.3 CFD-simulations StarCD, the numerical code used to simulate the CFD part of this study, operates by solving the governing differential equations of the flow physics using a finite-volume approach. The turbulent flow of both fluids (exhaust gas and cooling water) is modelled by the standard k-ε-model. Internal algorithms address conjugate heat transfer problems, involving simultaneous fluid convection and solid conduction. Not considered are effects, which suddenly occur when water evaporates at a hot wall like film boiling or bubble boiling. This study provides information only, - if any - where evaporation can arise.

2.4 Results of the CFD-analyses The temperature distribution for the three operating points in the solid part, resulting from the exhaust gas flow and the cooling water flow, is the main output of the each CFD simulation performed for the exhaust manifold.. It is used as load input for the subsequent FE analysis. Plots of the temperature distribution for the three operating points, in a horizontal and a vertical cross section of the solid part, are presented in Figures 4 and 5.

2004 ABAQUS Users’ Conference 5

Figure 4. Temperature distribution in a longitudinal horizontal cross section. The temperature distributions for full cooling flow and partial cooling flow are similar. For the vapour flow however the temperatures in the solid part are significantly higher, compared to the water flow cooling (please note the different scales of the legend in Figures 4 and 5). Temperature peaks occur near the exhaust gas outlet, especially in the rib between the two exhaust streams. This is caused by the fact that the cooling water has no access to this rib. Thermal strains caused by these high temperatures can lead to significant stresses, if the corrsponding displacements are suppressed. Therefore, this area is of special interest and will be investigated in detail by means of the FE analyses.

3. FE Analysis

To simulate the thermally induced stresses and deformations induced by the temperature distributions FE simulations have been performed using ABAQUS (Version 6.4) for the same three operating points (full water flow, partial water flow, vapour flow). The model consisted of 600.000 10 nodes tetraeder elements of type C3D10.

3.1 Boundary Conditions The investigated manifold is mounted to two other manifolds on both sides, to the cylinder head and to the turbocharger. All of these devices are practically fixed. This means that no

Full cooling flow Partial cooling flow

Vapour flow

Temperature [°C]

Temperature [°C]

Partial cooling flow

6 2004 ABAQUS Users’ Conference

Figure 5. Temperature distribution in a vertical cross section through the rib at gas outlet. displacements are possible in normal direction to the surfaces which are connected to adjacent devices. Figure 6 shows the FE-Model with corresponding boundary conditions.

3.2 Loads Temperature fields as output from CFD analyses were the main load cases to investigate. As stress free environmental temperature 30°C (303 K) has been assumed. The pressure of the cooling flow and the exhaust flow in the exhaust manifold vary between 1.0 and 3.0 bar depending on the operating point. The stresses induced by these pressures are relatively low in comparison to the thermal stresses induced by the temperature distribution. Therefore they are considered to be negligible within the scope of this investigation.

3.3 Material properties As shown in Table 1, the material properties of GGG Si-Mo 5.1 are sensitively dependent on the temperature. Considering the avarage temperature under operational conditions and as a conservative approach, a modulus of elasticity equal to 135000 MPa, a Poisson’s ratio of 0.25 and a linear coefficient of thermal expansion equal to 1.22.10-5 K-1 were used for simulation purposes.

Full cooling flow

Temperature [°C]

Temperature [°C]

Partial cooling flow

Vapour flow

2004 ABAQUS Users’ Conference 7

Figure 6. FE model with boundary conditions. The nonlinear material behaviour above the proportionality limit (here: yield stress) has been accounted for according to the curve plotted in Figure 7.

Figure 7. Elastoplastic material model.

570

390

Stress [MPa]

Strain [%]

8.5

8 2004 ABAQUS Users’ Conference

Table 1. Material properties relevant for the FE analysis. Temperature

[°C] UTS

[MPa] Yield stress

[MPa] Modulus of elasticity

[MPa] A (lo=5do)

[%] 20 580 470 145000 8.8

400 570 390 130000 8.8 600 170 170 80000 8.8

3.4 Results of the FEM-Simulation

All three thermal load cases were evaluated in terms of von Mises stresses and maximal principal strain. Figure 8 shows a typical deformation plot and Figure 9 the corresponding stress distribution. As one can easily see, the maximum stresses are of the same order of the magnitude as the yield stress. In the cases of partial water cooling and vapour cooling the critical areas remain the same and stresses are even higher. Furthermore, surprisingly it was found with an additional analysis that the influence of boundary conditions on the stress distribution is rather of minor importance.

One of the major advantages of the coupled CFD-FE simulations as performed in the presented case is that the model can be easily adapted to potential modifications and be utilized for any “what, if…”-analyses. Most probably, the existing representative FE model of the exhaust manifold will be re-used for further investigations in this way.

Figure 8. Thermally induced deformation of the exhaust manifold under normal cooling conditions. The displacements are given in mm

2004 ABAQUS Users’ Conference 9

Figure 9. Thermally induced von Mises stresses in the exhaust manifold under normal cooling conditions (plotted in N/mm2).

4. Discussion / Conclusions

The modelling with the elements of type C3D10, the use of at least 2 elements across the wall thickness of the exhaust manifold and the nonlinear analysis enable a reasonable simulation of a rather complex problem and ensure relativly realistic predictions of the thermal gradients occurring under extreme conditions (Deger, 2002). The results of this investigation confirm that significant stresses can be expected at selected areas of the component (especially, outlet section of the exhaust gas, near rib). The stress concentrations can be interpreted as remarkable indices for extreme level of temperatures and temperature gradients and show at the same time the sensitive areas for potential enhancement measures. Next development steps of the exhaust manifold will be taken based on these information.

In the following, some suggestions are listed, which could possibly lead to significant improvements in terms of the reduction of thermal stresses:

10 2004 ABAQUS Users’ Conference

Figure 10. Thermally induced von Mises stresses (N/mm2) in the exhaust manifold under normal cooling conditions (detail plot of the rib area).

• Additional cooling at the rib region.

• Choise of an other material with more adequate mechanical properties at high temperatures.

• Local modification of the design.

• Any combination of the measures mentioned above.

5. References

1. Deger, Y., “Simulation of Thermomechanical Load Cases”, Sulzer Technical Review, 3/2003. 2. Deger, Y., “Die Methode der Finiten Elemente”, 2nd Ed., Expert Verlag, Germany, 2002. 3. Simperl, B., Schöck, J., Deger Y., “Thermal Deformation and Stresses in an Exhaust

Manifold”, Technical Report Nr. TB03_0123, Sulzer Innotec, Oct. 2003, (not public). 4. ABAQUS User’s Manual, Version 6.4.