J. Cent. South Univ. Technol. (2011) 18: 271-278

DOI: 10.1007/s11771-011-0690-x

Effect of heat transfer space non-uniformity of combustion chamber components on in-cylinder soot emission formation in diesel engine

L? Ji-zu(吕继组)^{1, 2}, BAI Min-li(白敏丽)², LI Xiao-jie(李晓杰)¹, ZHOU Long(周龙)²

1. State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian University of Technology, Dalian 116023, China;

2. School of Energy and Power Engineering, Dalian University of Technology, Dalian 116023, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2011

 Abstract: Combustion chamber components (cylinder head, cylinder liner, piston assembly and oil film) are treated as a coupled body. Based on the three-dimensional numerical simulation of heat transfer of the coupled body, a coupled three-dimensional calculation model for the in-cylinder working process and the combustion chamber components was built with domain decomposition and boundary coupling method, in which the coupled three-dimensional simulation of in-cylinder working process and the combustion chamber components was adopted. The simulation was applied in the influence investigation of the space non-uniformity in heat transfer among combustion chamber components on the generation of in-cylinder emissions. The results show that the space non-uniformity in heat transfer among the combustion chamber components has great influence on the generation of in-cylinder NO_x emissions. The heat transfer space non-uniformity of combustion chamber components has little effect on soot formation, and far less effect on soot formation than on NO_x. Under two situations of different wall temperature distributions, the soot in cylinder is different by 1.3% when exhaust valves are open.

Key words: heat transfer; space non-uniformity; soot emission; in-cylinder; diesel

1 Introduction

As one of the most significant contaminants, soot formed in reacting fuel jets and not completely oxidized at the end of the combustion process is a major component of the particulate matter emitted by direct-injection diesel engines [1]. How to reduce PM emissions to the levels required by stringent new regulations is a big challenge for diesel engine manufacturers. In addition, engine performance, in-cylinder combustion and other emission formation are also influenced by soot formation.

In cylinder working process of diesel, soot deposition is a function of gas temperature and the temperature gradient normal to the wall [2]. The local gas temperature in cylinder mainly depends on in-cylinder gas flow and the heat transfer intensity of the wall, and the heat transfer intensity of walls is directly influenced by the temperature distribution on the walls of the combustion chamber. From the calculation results of three-dimensional steady coupled simulation of the combustion chamber solid components, it can be clearly seen that the wall temperature distribution of combustion chamber components is characterized by significant space non-uniformity, and the local temperature difference may even exceed 100 °C [3]. Thus, the wall temperature distribution space non-uniformity of the combustion chamber components inevitably exerts vital influence on the in-cylinder working process of diesel engine, and affects the rate of soot formation and oxidation [4-5].

In this work, coupled complete model simulation technology for multi-dimensional multi-physical-field simulation and calculation is adopted, i.e., combining the working process of internal combustion engine, combustion chamber components, cooling system and lubrication system, etc. into an integral whole. Coupled simulation is used to assist the study of the influence of space non-uniformity in heat transfer among combustion chamber components on the generation of in-cylinder emissions in diesel engine, especially on soot emission.

2 Model formulation

Some of the supporting submodels used are described in this study. They include a modified k-ζ-? turbulence model, a turbulent wall heat transfer model,as well as spray, combustion model and emission model.

2.1 Turbulence model

In the compression and expansion stroke of diesel engine, extremely complicated and intensive transient turbulent movements happen in cylinder and require a kind of turbulence model to compute. The model used in this study is k-ζ-? in AVL-Fire [6] which is developed from -f of DURBIN [7], where  is replaced by velocity scale  After being modified, k-ζ-? model compared with -f is more stable and the convergence is also improved.

2.2 Heat transfer model

The turbulent wall heat transfer model of HAN- REITZ [8] is used to predict heat transfer between gas and wall surfaces. This model takes variable density and turbulent flows into account and allows a coarse grid size to be used near the wall while maintaining the accuracy. The wall heat flux is computed as

                                                 (1)

where c_p is the specific heat of the gas, T and T_w are the gas and wall temperature, respectively, and y⁺ is the dimensionless distance:

                                                                     (2)

where y is the distance normal to the wall, v is the gas kinematic viscosity, and u_τ is the friction velocity:

                                                                 (3)

In Eq.(5), k is turbulent kinetic energy, C_μ is a constant.

Hybrid wall treatment is accepted to ensure a gradual change between viscous sub-layer formulations and the wall functions. The production of turbulence kinetic energy near the wall is modified as well to ensure that results are the same for the small y⁺ as provided by low-Re models and the results are the same as the standard wall function for the high y⁺ [9].

2.3 Spray and combustion model

Spray model includes sub-models for spray, breakup and vaporization, and droplet coalescence. In this work, the sub-model involved is as follows: GOSMAN [10] model is used for fuel turbulent dissipation, O’ROUKE [11] model is used for particle interaction, DUKOWICZ [12] model is used for evaporation, Wave [13] model is used for breakup, and WALLJET1 [14] model is used for droplet coalescence.

It is important to choose combustion model for computing in-cylinder process in diesel engine, which directly determines the accuracy of the whole computation. A characteristic time scale combustion model (CTM) [15] is used to simulate the combustion process of diesel in this work. This model is activated when the temperature of a computational cell exceeds   1 000 K.

2.4 Emission model

The generation of NO_x by diesel engine is a complex process. A great deal of the knowledge acquired was obtained from direct measurements by simplified studies of flame. The thermal or Zeldovich mechanism [16] is responsible for the majority of emissions of NO_x originating from a diesel engine. The NO production was modeled using the extended Z’edlovich NO model in this work. The reaction mechanism for this model is

                                                  (4)

                                                    (5)

                          (6)

The amount of soot presented in a computational cell at a given time, neglecting convection and diffusion transport processes, is governed by two competing reactions: soot formation and soot oxidation. The soot formation model implemented in the version of AVL-Fire used for the present research is based on the HIROYASU and NISHIDA mode [17] and is given by

                                         (7)

where M_soot, M_form and M_oxid present the net reaction, formation and oxidation rates of soot mass, respectively.

The soot formation rate is given in Arhennius form as

                               (8)

where A_f =450, m_fv is the fuel vapor mass, p is the gas pressure and E_f is the activation energy.

The NAGLE and STRICKLAND-CONSTABLE model [18] is used for the soot oxidation:

                       (9)

               (10)

                                              (11)

where M_C is the relative molecular mass of carbon, ρ_S is the soot density, D_S is the soot diameter, R_tot is the net reaction rate[19], p(O₂) is the partial pressure of oxygen and x is the ratio of more reactive sites versus less reactive sites on the soot particle due to surface variation, K_A, K_Z, K_B and K_T are constants.

3 Implementation of multi-dimensional numerical simulation of fluid-solid coupled in in-cylinder working process and combustion chamber components

In-cylinder working process and heat transfer among the solid components of combustion chamber belong to typical fluid-solid coupled heat-transfer problems. Therefore, domain decomposition and boundary-coupled method were applied in the three- dimensional coupled simulation calculation for the in-cylinder working process and combustion chamber components. The implementation steps are as follows.

1) Control equations corresponding to the physical models concerning the domains of in-cylinder working process and combustion chamber components (piston assembly, cylinder liner, cylinder head, cylinder gasket and cylinder body, etc.) were established.

2) The boundary conditions for each domain were listed, where the coupling boundary included the bottom wall of the cylinder head in contact with the gas in cylinder, the inner-wall part of the cylinder liner in contact with the gas in cylinder, and the top face of piston. The following two conditions were met on the coupled boundary:

Temperature continuity

                            (12)

Heat-flux continuity

                          (13)

where “cylinder” represents the domain of in-cylinder working process; “solid” represents the domain of the solid components of combustion chamber; x, y and z are the three direction components of coordinates.

3) First, multi-dimensional transient numerical simulation calculation for the in-cylinder working

process was performed based on a presumed temperature distribution on the coupled boundary (fixed wall temperature). Then, time-average method was applied to obtain the spatial distribution of heat-flux density on the coupled boundary. Eq.(15) was applied to obtain the surface heat-flux density distribution of the combustion chamber components, which was regarded as the heat boundary condition for the three-dimensional finite element simulation calculation of the combustion chamber components. The complete simulation method for the coupled heat-transfer of integral combustion chamber components was applied in the three- dimensional steady finite-element simulation calculation for all combustion chamber components, so that the temperature field distribution on the coupled boundary of the combustion chamber components could be obtained. Afterwards, the temperature field was transformed into the heat boundary condition for the multi-dimensional transient numerical simulation calculation of the in-cylinder working process according to Eq.(14), so that the three-dimensional coupled heat-transfer numerical simulation calculation for in-cylinder working process and combustion chamber components could be implemented (as shown in Fig.1).

4 Computational conditions

4.1 Real diesel model

The test engine considered in this work is a single cylinder version of a six-cylinder truck diesel engine. Engine parameters are given in Table 1. Valve timings are given relative to top dead center where 0° ATDC (after top dead center) is the top of the compression stroke.

4.2 Computational mesh

For multi-dimensional numerical simulation in in-cylinder working process, due to piston movement, the dynamic cell should be applied in order to really

Fig.1 Schematic diagram of integrate analysis

reflect the true working case. So, a kind of special dynamic cell formation tool, AVL-Fire software of ICE, was used to form the computation cell in this work. Structured hexahedron was adopted for improving the calculation precision. On one hand, the hexahedron mesh is not only easy to control and can result in a high-precision simulation, but also compatible to many kinds of arithmetic. The cell formation is given in Fig.2, when the piston is in the BDC, which is constructed with hexahedral mesh and contains 194 084 cells and 201 570 vertices.

Fig.2 In-cylinder mesh at crank angle of -180° (ADTC)

4.3 Initial conditions

For diesel engine, in-cylinder computation starts at the time of intake valve closing, so the initial condition has to be given. In the initial multi-dimensional numerical simulation of in-cylinder working process, in-cylinder airflow state proceeded at intake valve closing, including in-cylinder pressure, density, temperature, flow velocity, turbulence etc. In this work, the initial conditions of multi-dimensional numerical simulation of in-cylinder working process are obtained by multi-dimensional simulation of intake process for improving the calculation accuracy [20].

4.4 Heat boundary conditions

All computations are done under the same engine working condition. In order to compare the effects of heat transfer space non-uniformity of combustion chamber on in-cylinder soot, two kinds of wall heat boundary conditions are applied.

1) Specified wall temperature (Run A)

In the specified wall temperature mode, the temperature of all combustion chamber components does not vary with time and space. The surface of all combustion chamber components is divided into three zones: surface of cylinder head bottom, surface of piston dome and inner surface of cylinder liner, and different zones are given different temperatures. Surface temperatures of different combustion chamber components are listed in Table 2.

Table 2 Surface temperatures of combustion chamber

2) Actual wall temperature distribution mode (Run B)

In the actual wall temperature distribution mode, it is defined that the surface temperature of combustion chamber components does not vary with time, and actual wall temperature distribution is obtained by coupled heat transfer computations of combustion chamber solid components (see Ref.[21]). Then, by liquid-solid coupled heat transfer model, this temperature would be taken as boundary condition for in-cylinder multi- dimensional transient simulation computation. Fig.3 shows the temperatures of piston and cylinder liner surfaces at the time that intake valve is closed.

5 Results and discussion

Fig.4 shows the predicted value of in-cylinder mean effective pressure compared with experimental value under two kinds of heat transfer conditions on the combustion chamber surface. It can be seen that under the two conditions, the predicted values are both close to experiment ones. The space non-uniformity of wall temperature of combustion chamber components has

Fig.3 Temperatures of piston and cylinder liner surfaces

Fig.4 Comparison of predicted and experimental in-cylinder pressure

little effect on the predicted value of in-cylinder pressure for normal mental made diesel engine and in the actual wall temperature mode the predicted values are closer to the experimental ones.

For diesel engine, changes in NO_x concentration are affected in two regions: the main chamber and the near wall region. The non-uniform temperature of the combustion chamber components mainly affects the near wall region. The predicted in-cylinder NO_x levels, as a function of crank angle, are shown in Fig.5. The non- uniform temperature of combustion chamber components affects the NO_x concentration mainly during the process of its rapid production. The non-uniform wall temperature leads to the increase of heat transfer rate in the near-wall region, thus the local gas temperature drops and the NO_x concentration reduces. In the whole, the quantity of NO_x is different by 6% when the exhaust valve opens. Changes in predicted in-cylinder soot levels are affected by the non-uniform temperature distribution as well, and are shown in Fig.6. However, the predicted change in in-cylinder soot levels is not as great as the change in predicted NO_x. In the whole, the quantity of soot is different by 1.3% when the exhaust valve opens. The lower temperatures associated with a non-uniform wall temperature distribution produce slightly higher levels of soot compared with the case when these effects

Fig.5 Change of predicted in-cylinder NO_x concentration as function of crank angle

Fig.6 Change of predicted in-cylinder soot levels

are neglected.

Whereas from global analysis, it can be seen that the heat transfer space non-uniformity of combustion chamber components has slight effect on the production of soot, and the non-uniform temperature distribution has significant effect on soot deposition rates. For local area, the effect needs to be analyzed by cross sectional distribution of soot content at different crankshaft angles. So, the cross sectional distribution diagrams of soot content at different crankshaft angles are given in Fig.7. It can be seen that, with the crankshaft angle varing, the

Fig.7 Cross sectional distribution diagrams of soot mass fraction at different crankshaft angles: (a) 6°; (b) 18°; (c) 30°; (d) 45°;     (e) 60°

heat transfer space non-uniformity of combustion chamber components mainly influences the formation of soot near combustion chamber wall surface. Soot has been mainly generated in this zone. So, there exist some differences in the soot content.

Fig.8 shows the mass fraction distribution of soot near piston dome at different crankshaft angles. For the gas in cylinder, its temperature distribution near the wall area would be affected by heat transfer of the combustion chamber directly, so the space non-uniformity of wall temperature of combustion chamber components would affect the production of soot in the area greatly. It can be seen that there is apparent difference from the comparison of mass fraction distribution of soot at different crankshaft angles. The space non-uniformity decreases the content of soot in local area and influences the production of soot in cylinder in the whole.

In conclusion, the heat transfer space non- uniformity of combustion chamber components has less effect on the production of soot in cylinder, mainly in the zone near the surface of combustion chamber and has nearly no effects in the center area.

Fig.8 Mass fraction distributions of soot near piston dome at different crankshaft angles: (a) 18°; (b) 30°; (c) 45°; (d) 90°

6 Conclusions

1) It is obvious that the heat transfer space non-uniformity of combustion chamber components has great effect on the production of NO_x in cylinder, mainly in the zone near the surface of combustion chamber; and has nearly no effect in the center area. In the whole, the quantity of NO_x is different by 6% when the exhaust valves are open.

(2) The predicted change of in-cylinder soot levels is not as great as the change in predicted NO_x concentration. In the whole, the quantity of soot is different by 1.3% when the exhaust valve is open. The lower temperature associated with a non-uniform wall temperature distribution produces slightly higher levels of soot content compared with the case when these effects are neglected.

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(Edited by YANG Bing)

Foundation item: Projects(50576008, 50876016, 51006015) supported by the National Natural Science Foundation of China; Project(20062180) supported by the Natural Science Foundation of Liaoning Province, China; Project(20100470070) supported by China Postdoctoral Science Foundation

Received date: 2009-01-06; Accepted date: 2009-04-21

Corresponding author: L? Ji-zu, PhD Candidate; Tel: +86-13942601557; E-mail: lvjizu2002@yahoo.com.cn