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Large Eddy Simulation of Diesel Engine Combustion

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Modelling Diesel Combustion

Part of the book series: Mechanical Engineering Series ((MES))

Abstract

This chapter introduces the basic concept of large eddy simulation (LES) and the sub-grid-scale models. Specific treatments on the spray models and turbulent combustion models in the framework of LES are discussed. The combustion process of a heavy-duty diesel engine that operates under low-temperature combustion mode with early fuel injection is simulated using LES with a dynamic structure model and unsteady RANS with the RNG k-epsilon model. The SAGE model, a direct chemistry model, is used as the combustion model. Two different skeleton n-heptane reaction mechanisms, the ERC mechanism, and the Chalmers mechanism are considered. The results are compared with available experimental data. It is found that the predictions of pressure trace and heat release rate depend more on the reaction mechanism. With the ERC mechanism, both LES and RANS can reproduce the pressure trace. The LES shows a more detailed flow structure and a larger area of the flame front. The LES is a good tool to investigate some transient phenomena but is still not suitable for design optimization purposes.

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Abbreviations

a 4 , b 3 , b 1 :

Model constants (–)

C :

Model constant (–)

C k , σ k , C ε :

Model constants (–)

C s :

Adjustable model constant (–)

C s , dyn :

Model constant (–)

C ν :

Model constant in the formulation of turbulent viscosity in the SGS model (–)

Da:

Damkohler number (–)

DNS:

Direct numerical simulation (–)

ERC:

Engine Research Center at University of Wisconsin–Madison (–)

F b :

Body force (Nm−3)

F s :

Source term due to spray (Nm−3)

FTS:

Flamelet timescale (–)

G (x; y) :

Classical filters include box (top-hat) filter, Gaussian filter (–)

k :

Sub-grid turbulent kinetic energy (m2s−2)

K :

“Grid”-level turbulent kinetic energies (m2s−2)

LES:

Large Eddy simulation (–)

L ij :

Double-filtered grid-level sub-grid stress tensor is the Leonard stress term (m2s−2)

l τ :

Turbulent length scale (m)

M ij :

Deviatory part of Lij (m2s−2)

QSF:

Quasi-steady flamelet mode (–)

RANS:

Reynolds-averaged Navier–Stokes equations (–)

RNG:

Renormalization group (–)

SGS:

Sub-grid scale (–)

S ij :

Strain rate tensor (s−1)

s l :

Laminar flame speed (m/s)

s t :

Turbulent flame speed (m/s)

T c :

Cut-off temperature (K)

T ij :

Sub-grid stress tensor based on the test filter (m/s)

u :

Turbulent velocity (m/s)

u' :

Root mean square of the turbulent fluctuating velocity (m/s)

V :

Local cell volume (m3)

α :

First combustion index is used to distinguish the slow-chemistry regime from the fast-chemistry regime, i.e. depending on the chemical timescale (–)

Δ :

The grid filter that is computed from the local cell volume (m)

ε :

Sub-grid turbulent dissipation of sub-grid kinetic energy (m2s−2)

ν t :

Turbulent viscosity (m2/s)

ρ :

Density (kg/m3)

σ ij :

The viscous term (Pa)

τ chem :

Characteristic timescale describing the duration that the current flamelet proceeds towards its steady state (s)

τ ij :

Sub-grid stress tensor (Pa)

τ ij :

“Grid”-level modelled stress tensor (Pa)

φ :

Arbitrary flow variable (–)

ω :

Specific turbulent dissipation rate (m2/s3)

\({\mathcal{H}}\) :

Heaviside function (–)

\(\hat{\Delta }\) :

Another test filter with a length scale. Usually, this test filter is twice the grid filter (). (m)

\(\hat{K}\) :

“Test” level turbulent kinetic energies (m2s−2)

\(\hat{\tau }_{ij}\) :

“Test” level modelled stress tensor (Pa)

\(\tilde{\xi }\) :

Mean mixture fraction (–)

\(\tau_{{u_{j} \xi }}\) :

Flux of the mean of mixture fraction (s−1)

\(\chi_{{{\text{SGS}}}}\) :

Sub-grid-scale scalar dissipation rate (m2/s3)

\(\tilde{Y}_{i}^{{{\text{lib}}}}\) :

Mass fraction calculated from the flamelet library (–)

\(\chi\) :

Local scalar dissipation rate (m2/s3)

\(\chi_{c}\) :

Criterion of scalar dissipation rate between the diffusion flamelet regime and the partially premixed regime (m2/s3)

\(\gamma\) :

Local mixture homogeneity, second combustion index used to distinguish the quasi-steady homogeneous regime from the quasi-steady diffusion flamelet regime (–)

u :

An unburnt region (–)

i, j, k :

Component along x-, y-, and z-directions (–)

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  1. Department of Mechanical Engineering, Texas Tech University, Lubbock, United States

    Haiwen Ge

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Ge, H. (2022). Large Eddy Simulation of Diesel Engine Combustion. In: Modelling Diesel Combustion. Mechanical Engineering Series. Springer, Singapore. https://doi.org/10.1007/978-981-16-6742-8_18

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  • DOI: https://doi.org/10.1007/978-981-16-6742-8_18

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