The development of thermal stress in the exhaust manifold of a gasoline engine is considered. The problem is addresses in the frame of a combined approach where fluid and structure are coupled using the GT-POWER and STAR-CCM+ software. First, the external characteristic curve of the engine is compared with a one-dimensional simulation model, then the parameters of the model are modified until the curve matches the available experimental values. GT-POWER is then used to transfer the inlet boundary data under transient conditions to STAR-CCM+ in real-time. The temperature profiles of the inner and outer walls of the exhaust manifold are obtained in this way, together with the thermal stress and thermal deformation of the exhaust manifold itself. Using this information, the original model is improved through the addition of connections. Moreover, the local branch pipes are optimized, leading to significant improvements in terms of thermal stress and thermal deformation of the exhaust manifold (a 7% reduction in the maximum thermal stress).

Using software simulations, Zhu et al. [

The CFD and FEM methods are already widely employed in thermal stress analyses of exhaust manifolds, and the accuracy of these models is steadily improving [

Fluid-solid coupling heat transfer refers to the interaction between solids and fluids, accompanied by heat exchange. Therefore, it involves the joint action of mechanical load and thermal load. When coupling data is extracted from the coupling interface between the solid domain and the fluid domain, the solid domain uses the oil film temperature and heat transfer coefficient transmitted by the fluid, while the fluid uses the wall temperature transmitted by the solid domain as the boundary condition [

In order to accurately obtain the temperature distribution, flow characteristics and the thermal stress distribution on the solid wall of the exhaust manifold. The temperature variation, the turbulent mixing, the transport of fluid components and the convection diffusion should also be taken into account when establishing the mathematical model. The basic governing equations of the fluid domain include the energy conservation equation, the momentum conservation equation and the mass conservation equation.

The mass conservation equation is given by [

The momentum conservation equation is given by

The energy conservation equation is given by

Due to heat transfer between the fluid and the solid wall, the exhaust manifold needs to be divided into the fluid and solid domains [

In the fluid domain, the

There are three basic methods for heat transfer: thermal conduction, thermal radiation and thermal convection. Thermal convection widely exists in various fluids, it refers to the process of heat transfer between various parts of the fluid due to relative displacement. The heat transfer that causes heat movement is called thermal conduction. Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material is converted to electromagnetic radiation. In this paper, the effect of thermal radiation is ignored because it has little effect on this study [

Thermal conduction follows Fourier law is given by

Thermal convection equation can be described as

Assuming that the manifold is a circular tube, the convective heat transfer coefficient between the high-temperature exhaust gas and the inner wall surface is given by

Physical models are often divided into a large number of units in finite element analysis. The governing equation of thermal conduction of the unit body can be written as follows:

By utilizing a combination of GT-POWER and STAR-CCM+ fluid software, the inlet boundary conditions (Inlet mass flow of the four cylinders and gas temperature at the four cylinder inlets) solved by GT-POWER are transferred to STAR-CCM+ in real-time under transient conditions. Then the node temperature of the temperature field distribution in the fluid domain is calculated by STAR-CCM+. The node temperature is directly defined by some commands, and then it is used as the body load as the input to solve the wall thermal stress.

The STAR-CCM+ program has a variety of built-in physical models. The Three-Dimensional model is selected to represent space and the Implicit Unsteady model is chosen for time. Through analysis of the geometric model, we can see that large memory resources are required for performing calculations using the model. Therefore, to reduce the number of calculations, we select Segregated Flow as the flow item. Since the Reynolds number of the gas in the engine exhaust manifold is greater than 2300, the flow state of the gas in the exhaust manifold is three-dimensional turbulent flow. The

Physics model | |
---|---|

Space | Three dimensional |

Time | Implicit unsteady |

Material | Gas |

Flow | Segregated flow |

Equation of state | Ideal gas |

Energy | Segregated fluid temperature |

Viscous regime | Turbulent |

Reynolds-averaged turbulence | |

Enabled models | Realizable K-epsilon two-layer |

Reynolds-averaged navier-stokes | |

Two-layer all wall treatment | |

Wall distance | |

Gradient | |

Interpolation |

To facilitate CFD transient analysis, the parameters of the calculation domain and the wall boundary parameters at zero time are set as the initial conditions of the analysis. The setting of these parameters has a substantial impact on the convergence of the model and the accuracy of the calculation results. Therefore, the initial conditions of the thermal analysis flow field are: initial pressure of 1.01 × 10^{5} N/m^{2}; ambient initial temperature set at 300 K; initial velocity of 0 m/s; and the convective heat transfer coefficient of the outer wall of the exhaust manifold is 11 W/m^{2}∙k). The values of constants are listed in

Constant parameter | Value |
---|---|

0.09 | |

1.44 | |

1.9 | |

1.0 | |

1.0 | |

1.2 | |

2.0 | |

1.0E-10 | |

1.0E-10 | |

60 | |

10 |

According to the design parameters of engines and exhaust manifolds shown in

Item | Unit | Parameter |
---|---|---|

Cylinder diameter | mm | 82.3 |

Stroke | mm | 92.6 |

Engine displacement | L | 2 |

Compression ratio | 9.6:1 | |

Max speed | r/min | 5000 |

Max torque | N·m | 282 |

Rated power | kW | 145 |

When the exhaust manifold works, the internal air flow and solid wall heat transfer change dynamically with time. In order to avoid the non convergence of the exhaust manifold in the first cycle, the transient calculation of the exhaust manifold for three cycles (2160°CA) is carried out in this paper. Because the time of each crank angle is 3.3 × 10^{−5} s under the maximum speed of 5000 r/min, the time step is set to 3 × 10^{−5} s. The maximum iteration number is set to 10, which can ensure the full transmission of data between nodes.

In this study, we compare the external characteristic curve of the engine with that of the one-dimensional simulation model. Then, we gradually modify the parameters of the simulation model until the external characteristic curve calculated by the one-dimensional simulation model is in good agreement with the experimental value. As

According to the calculations of the GT-POWER simulation, we obtain values for the inlet mass flow and gas temperature at the four cylinder inlets, as

The instantaneous velocity in engine exhausts can reach hundreds of meters per second, with high Reynolds numbers. This produces non-negligible viscous forces, and the velocity gradient is very large along the normal direction. Therefore, to ensure the accuracy of the calculation results and capture the flow characteristics in this region more effectively, it is necessary to divide the boundary layer. In this paper, the target y+ value is 30, and a three-layer boundary layer grid with a thickness of 0.56 mm is generated on the interface between fluid domain and solid domain by calculation.

Taking the exhaust manifold inlet wall temperature as the evaluation index, we compare the modeling results of 0.91 million, 1.12 million, 1.44 million, and 2.04 million grids. Ultimately, we select 1.12 million grids as the optimal value. Of the total number of 1.12 million grids, 0.32 million are in the fluid domain, while 0.8 million are in the solid domain, as

The temperature distribution in the solid domain of the manifold has a tremendous impact on the thermal stress and thermal deformation of the entire exhaust manifold. This can, as a result, seriously affect the service performance and service life of the exhaust manifold [

The outer wall surface of the exhaust manifold directly generates convective heat transfer with the external environment, so the temperature is relatively low. In contrast, the inner wall surface is in direct contact with high-temperature gas, resulting in high convective heat transfer intensity and temperature. Moreover, the temperature range in the exhaust manifold wall surface is unevenly distributed, and there is a certain temperature gradient between the inner and outer wall surfaces. The maximum wall temperature of the exhaust manifold is shown in

The thermal deformation and thermal stress of the structure can be calculated by adding appropriate figures to the model for solving the temperature field. First, the temperature field in the solid domain is used as the applied load for thermal stress analysis, then the thermal deformation and thermal stress of the structure are calculated by the load step of the static analysis. The nonlinear parameters of the material are set according to the temperature variation range. Besides, the material of the exhaust manifold wall is QTANi35si5Cr2. Mechanical properties of the material include a yield strength greater than 220 MPa and a tensile strength greater than 370 MPa. Other material property parameters are presented in

Item | Unit | Parameter |
---|---|---|

Elasticity modulus | N/mm | 1.38 × 10^{5} |

Poisson ratio | 0.283 | |

Density | Kg/m^{3} |
7450 |

Thermal conductivity | W/(m·k) | 19.95 |

Thermal expansion coefficient | K^{−1} |
1.51 × 10^{−5} |

Specific heat capacity | J/(kg·K) | 500 |

As

In this paper, we improve the original manifold model by strengthening the connecting rib plate to increase the overall stiffness of the manifold. The purpose of this is to reduce the thermal stress at the exhaust manifold without changing the internal flow field, thereby making the stress in the exhaust manifold more uniform and increasing overall structural stiffness. The improved model is displayed in

The maximum thermal strain decreases from 1.64 to 1.57 mm, primarily because the connecting ribs between the branch pipes somewhat restrict the deformation of the exhaust manifold, where the maximum thermal strain decreases by 0.07 mm, which is a 4.3% reduction.

To highlight the differences between the original model and the improved model,

Item | Original model | Optimized model | Optimization results |
---|---|---|---|

Temperature field | 1047.70 K | 1041.51 K | 0.6% |

Thermal stress | 205.03 MPa | 190.59 MPa | 7.0% |

Thermal deformation | 1.64 mm | 1.57 mm | 4.3% |

In this study, we established a one-dimensional model of the engine using GT-POWER software, then completed a calibration verification of the model. After calibration, the errors regarding torque and power between the simulation and the test were 2.8% and 3.7%, respectively. Coupled with STAR-CCM+ software, GT-Power calculated fluid-structure coupling with inlet temperature and mass flow rate as boundary conditions, thereby solving the problem of setting dynamic boundary conditions in a transient analysis. The temperature field of the exhaust manifold wall under actual working conditions was obtained by directly analyzing coupled heat transfer. According to the calculation results of thermal stress and thermal deformation under a transient temperature field, we optimized the original model by adding connections. After optimization, the maximum thermal stress fell by 14.44 MPa, or 7.0%, which demonstrates that the optimization scheme is feasible. These results provide a useful reference for optimizing designs of gasoline engine exhaust manifolds.

This work is supported by the Basic Ability Improvement Project for Young and Middle-Aged Teachers in Guangxi Universities, Project No. 2021KY0792.

The authors declare that they have no conflicts of interest to report regarding the present study.