A predictive 0-D HCCI combustion model for ethanol, natural gas, gasoline, and primary reference fuel blends

Homogeneous Charge Compression Ignition (HCCI) is a promising combustion technology that might help mitigate the effects of global climate change.

Higher compression ratios (CR), rapid near-constant-volume combustion, the use of a lean fuel-air mixture, and unthrottled operation all lead to the high thermal efficiency characteristics of HCCI.

Low combustion temperatures and the use of a homogeneous and lean fuel-air mixture result in ultra-low exhaust emissions for HCCI.

Numerical studies of HCCI have been widely conducted in recent years to better understand HCCI combustion and the benefits and drawbacks.

Typical numerical methods include computational fluid dynamics (CFD) with fluid mechanics and chemical kinetics, multi-zone quasi-dimensional and single-zone zero-dimensional (0-D) chemical kinetics simulations, and other 0-D simulations without chemical kinetics.

CFD simulations provide detailed insights of the flow field, combustion process, and emissions formation by solving partial differential equations (Navier-Stokes equations, etc.) for fluid flow and a system of ordinary differential equations (ODEs) for the chemical kinetics.

0-D chemical kinetics models only solve the ordinary differential equations to understand the chemical reactions during the combustion process.

However, the fidelity of a given model is generally proportional to the computational cost and solving a large system of differential equations requires substantial computational resources.

Generally, CFD models take hours to days to simulate one engine cycle while 0-D chemical kinetics models take seconds to minutes to solve one engine cycle.

Nevertheless, the computational times on the order of seconds is still sometimes unacceptable.

For control-oriented models, the calculations must be completed in real-time; thus, solving differential equations is not a viable solution.

In computational time-sensitive applications, only simple explicit algebraic formulas for combustion modeling can be solved quickly enough.

The Wiebe function is a widely-used model with a simple mathematical form and is often used to describe burn rate for various combustion modes.

Heywood et al. used a single Wiebe function to describe spark-ignition (SI) engine combustion in 1979.

For some combustion processes governed by more complicated mechanisms, multiple Wiebe functions are necessary.

For instance, spark-assisted compression ignition (SACI) is governed by initial flame propagation stage and then autoignition of the end-gas.

Hellström et al. used a double Wiebe function and a transition function to fit SACI combustion.

HCCI can generally be described by a single Wiebe function since it has a rapid combustion process that is governed by a single mechanism: chemical kinetics.

Chang et al. Soylu et al. and Shaver et al. used a single Wiebe function to study HCCI combustion.

Babajimopoulos et al. performed CFD simulations and developed a predictive combustion model for isooctane.

The model predicted CA0 with an ignition delay correlation.

Then, CA50 and CA90 were predicted from correlations that used CA0 and the charge-mass equivalence ratio ϕ′.

With CA0, CA50, and CA90 known, a single Wiebe function was developed to describe combustion.

Blomberg et al. used single-zone chemical kinetics and CFD to develop a predictive HCCI combustion model with a triple Wiebe function and an ignition delay correlation for multiple fuels in a virtual rapid compression and expansion machine.

In this paper, a computationally-efficient, predictive 0-D HCCI combustion model is purposed based on experimental results.

This model does not require numerical methods to solve any differential equations; therefore, it is ideal for system-level engine modeling and control-oriented programs, such as the work of M. Shahabakhti et al. and Chiang et al.

Ethanol, natural gas, E10-gasoline and Primary Reference Fuel (PRF) blends are studied.

The experimental setup and post-processing techniques will be discussed in Section 2.

The predictive burn rate modeling procedure and results are shown in Section 3.

Next, existing ignition delay correlations are tested against the experimental data and suggested modifications are made to better match the experimental results, which is included in Section 4.

Finally, a full model validation with the self-built burn rate model and modified ignition delay correlations is shown in Section 5.


HCCI is an advanced combustion technology that can achieve high thermal efficiencies and low engine-out emissions. In this paper, a computationally-efficient, 0-D HCCI burn rate model for ethanol, natural gas, E10-gasoline, and PRF blends is purposed.

The model can calculate the burn rate in the form of Wiebe function with CA0 and ϕ′ as inputs. The correlation is built from experimentally measured individual-cycle MFB curves. Correlations of CA0-50 and CA50-90 are established with a dependence on ϕ′. The constructed correlations generally displayed a good fit of the data, with R2 usually higher than 0.97. The correlations can accurately determine the burn duration based on the ignition timing and the equivalence ratio. Earlier CA0 will have an eariler CA50 and CA90 with shorter burn duration. Higher ϕ′ will also reduce the burn duration.

PRF blends exhibit two-stage heat release and hence a double-Wiebe function model with a weighting function is developed. The weighting function determines the fraction of the total heat release that occurs during the low temperature heat release period. The LTHR Wiebe function describes the low-temperature combustion and does not include a dependence on ϕ′ or PRF number.

In addition to the self-built burn rate model, multiple ignition delay correlations from the literature were tested and suggested modification are provided. The ignition correlations have an acceptable level of accuracy considering the difficulty in accurately determining the temperature in the cylinder and the sensitivity of the autoignition integral to temperature. However, the accuracy is not as high as the burn rate model.

In summary, this computationally-efficient 0-D HCCI model can accurately predict the combustion phasing and burn rate without solving any differential equations, which can benefit system-level modeling efforts or control-oriented program development.

Reference: Y. Zhou, D. Hariharan, R. Yang, S. Mamalis, B. Lawler, A predictive 0-D HCCI combustion model for ethanol, natural gas, gasoline, and primary reference fuel blends, Fuel. 237 (2019) 658–675. doi:10.1016/j.fuel.2018.10.041.

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