# Parametric Knocking Performance Investigation of Spark Ignition Natural Gas Engines and Dual Fuel Engines

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## Abstract

**:**

## 1. Introduction

## 2. Model Description

- (1)
- The cylinder is modelled by employing two zones—the burnt zone and the unburnt zone.
- (2)
- The pressure at any time is considered to be uniform within the cylinder.
- (3)
- Each cylinder zone has its own uniform temperature. There is no heat transferred between the two zones.
- (4)
- Gas in each zone is assumed to be homogenously distributed and the basic species are considered as ideal but non-perfect gases.
- (5)
- Blowby and valves leakage in the engine cylinders are not considered.

#### 2.1. Fuel Injector Model

#### 2.1.1. NG Injector Model for the Investigated SI NG Engine

#### 2.1.2. NG and Pilot Diesel Injector Models for the Investigated DF Engine

#### 2.2. Combustion Model

_{IT}, ${f}_{{x}_{rg}}$, f

_{n}, f

_{wi}, g

_{IT}, ${g}_{{x}_{rg}}$, g

_{n}, g

_{wi}, h

_{IT}, ${h}_{{x}_{rg}}$, h

_{n}and h

_{wi}are functions of ignition timing, residual gas portion, rotational speed and indicated work, which were reported in Witt [63].

_{1}represents the weight factor of the pilot diesel fuel combustion, 0 < b

_{1}< 1; τ

_{1}and τ

_{2}are the normalised combustion time of pilot diesel and NG, respectively; m

_{1}and m

_{2}are the Wiebe exponents of pilot diesel and NG, respectively.

_{1}is unburnt zone mass; u

_{1}is unburnt zone energy; ${\dot{m}}_{g}^{ent}$ is the mass flow from unburnt zone to burnt zone; ${h}_{g}^{ent}$ is enthalpy of the gas that leaves unburnt zone; ${\dot{m}}_{sg}^{exit}$ is the mass flow from burnt zone to unburnt zone; ${h}_{sg}^{exit}$ is the enthalpy of the gas that leaves burnt zone; p is the cylinder pressure; V

_{1}is the unburnt zone volume; Q

_{1}is the unburnt zone heat transfer rate.

#### 2.3. Heat Transfer Model

_{a}, T

_{a}and V

_{a}are the pressure (bar), temperature (K) and volume (m

^{3}) at the inlet valve closure, respectively; V

_{s}is the cylinder displacement (m

^{3}); p

_{0}is the in-cylinder pressure at motoring conditions (bar); c

_{m}is the average piston speed (m/s); C

_{1}is the coefficient depending on the airflow velocity; C

_{2}is the coefficient related to combustion chamber shape.

#### 2.4. Knocking Prediction Model

_{k}) and a constant parameter K, which are calculated according to the following equations, as reported in [60]:

_{CS}signifies the crank angle of calculation start, whilst θ

_{K}is the crank angle of knocking occurrence; a, b, c, a

_{IK}, a

_{K}, b

_{K}and c

_{K}are coefficients provided by [60]; θ

_{50mfb}and θ

_{75mfb}are the crank angle of 50% and 75% mass fraction burnt points, respectively; subscript ref represents values obtained at the reference operating condition.

_{k}and K, a set of reference parameters including the crank angles at 75% and 50% of burnt fuel mass fraction, the air-fuel ratio and a reference K-value that are calculated for a known cycle in the knocking boundary. Then the knocking sub-model calculates at each operating point, a characteristic crank angle (θ

_{E}), based on the calculated K-value, as well as the crank angle (θ

_{k}) at which I

_{k}becomes equal to one. θ

_{E}is calculated according to the following equation

_{SOC}is the crank angle where combustion starts; Δθ

_{CD}is the combustion duration.

_{k}with a probability when the following inequality holds: θ

_{k}< θ

_{E}. This probability derives from the model uncertainty that I

_{k}and K have a dispersion range of 15% and 5%, respectively. In this respect, the knocking probability is calculated according to the following equation:

_{KDR}is the crank angle resulting from the superimposition of I

_{k}and K dispersion ranges; a

_{kp}and b

_{kp}are coefficients provided by [60].

#### 2.5. Model Layout

#### 2.5.1. Engine A

#### 2.5.2. Engine B

## 3. Engine Setup and Model Validation

#### 3.1. Experimental Set up

#### 3.2. Model Validation

_{max}) and the corresponding crank angle (α

_{1}), the cylinder pressure at the spark timing (p

_{com}), the pressure at the EVO (p

_{EO}) as well as the Indicated Mean Effective Pressure (IMEP). p

_{com,}p

_{max}and p

_{EO}are critical parameters that determine the diagram characteristic of in-cylinder pressure during the compression stage, combustion stage and expansion stage, respectively. IMEP is a valuable measure indicating an engine’s power capacity independent of engine displacement, which should be considered for validating the combustion model.

#### 3.2.1. Engine A

_{max}, α

_{1}, p

_{com}, p

_{EO}and IMEP are shown in Table 5. The error of α

_{1}is presented in the form of absolute difference (°CA), whilst those of p

_{max}, p

_{com}, p

_{EO}and IMEP are indicated by the relative percentage error (%). As can be deduced from Table 5, the relative errors of p

_{max}, p

_{com}, p

_{EO}and IMEP are below 3%, whilst the absolute difference of the peak pressure position is less than 1°CA. Thus, it can be inferred that the developed model is able to predict with adequate accuracy the performance of the Engine A.

#### 3.2.2. Engine B

_{1}, SOC

_{1}, Δφ

_{1}, m

_{1}, SOC

_{2}, Δφ

_{2}and m

_{2}) for four operating points (100%, 74%, 42% and 32% load) were calibrated by analysing the experimentally obtained HRR curve. The calibration procedure is described below.

_{1}, which is used to specify the energy percentages of pilot fuel, can be acquired by dividing the pilot fuel energy by the total energy of pilot diesel and NG. The energy provided by each fuel is calculated by multiplying the injection mass and the respective LHV. In order to reduce the Wiebe parameters, the pilot fuel and natural gas are assumed to start their combustion at the same crank angle. The SOC was obtained from the measured cylinder pressure diagrams (abrupt rising of pressure in comparison with the motoring cylinder pressure). As the natural gas is the primary fuel in the DF Engine and exhibits a much slower combustion speed than the pilot diesel, the total combustion duration obtained from the experimentally obtained HRR was used as the combustion duration for the natural gas. The remaining three Wiebe parameters, namely the combustion duration, the Wiebe exponent for diesel fuel and the Wiebe exponent of natural gas, can be obtained by a curve fitting method. Although the experimentally obtained heat release rate (HRR) diagram represents the overall HRR, the heat release contribution of pilot diesel and natural gas can be separated by the weight factor b

_{1}. After defining the exponential function shown in Equation (6), the remaining three Wiebe parameters were obtained by using the Fit function in MATLAB.

_{max}, α

_{1}, p

_{com}, p

_{EO}and IMEP are shown in Table 7. As the combustion in Engine B starts after the TDC, the pressure at TDC is selected as the p

_{com}. As can be deduced from Table 7, the relative errors of p

_{max}, p

_{com}, p

_{EO}and IMEP are below 4%, whilst the absolute difference of the peak pressure position is less than 1°CA. Therefore, it is inferred that the developed model is capable of adequately predicting the performance of the Engine B, and can be used with fidelity for the knocking analysis presented in the next section.

## 4. Knocking Performance Parametric Investigation

_{k}= θ

_{E}. Thus, a knocking probability of 20% is set to be the knocking upper limit for the investigated parameters.

#### 4.1. Engine A

#### 4.1.1. Compression Ratio Effect on Knocking Performance

_{k}> 20%) for CR values above 11. The knocking onset position is presented in Figure 5c (knocking position equal to 0 demonstrates the engine operating without knocking). As can be deduced from Figure 5c, the knocking onset is advanced from 1°CA BTDC (−1°CA) to 7.5°CA BTDC (−7.5°CA) as the compression ratio increases from 10 to 16. Figure 5d shows the cylinder unburnt mass fraction (unburnt zone mass over the total mass) for the investigated CR range. The cylinder UMF varies from 0% to 75% as the CR increases from 7 to 16. UMF equal to 0 represents knocking free engine operation. Generally, a higher UMF value means that more energy will be released in a short period of time, thus indicating a stronger knocking phenomenon.

#### 4.1.2. Air-Fuel Equivalence Ratio Effect on Knocking Performance

#### 4.1.3. Ignition Timing Effect on Knocking Performance

_{k}< 20%) when the ignition timing is retarded after −38°CA. Figure 7c indicates that the knocking occurs later when the ignition timing is retarded. In Figure 7d, the UMF decreases from 36% to 18% with the SOC retarded from −44°CA to −37°CA.

#### 4.2. Engine B

#### 4.2.1. Compression Ratio Effect on Knocking Performance

_{k}= 20%), the compression ratio of Engine B should be limited up to around 16.5 in order to operate safely. The knocking onset position is presented in Figure 8c, which indicates that the knocking occurrence is advanced from 25°CA ATDC to 3°CA ATDC with a higher compression ratio value. The unburnt mass fraction exhibits a monotonically increasing trend as indicated in Figure 8d, which indicates that the knocking gets stronger with a larger compression ratio.

#### 4.2.2. Air-fuel Equivalence Ratio Effect on Knocking Performance

#### 4.2.3. Ignition Timing Effect on Knocking Performance

#### 4.2.4. Pilot Fuel Energy Proportion Effect on Knocking Performance

_{1}as in Equation (6)) varied, whilst the Wiebe functions parameters of both diesel and natural gas were kept the same with those provided in Table 6.

_{k}> 20%) 100% load when the pilot diesel energy proportion increases above 9%. In order to avoid knocking caused by the increase in pilot fuel energy proportion, the SOC must be retarded according to the analysis in Section 4.2.3. As can be deduced from Figure 11c, the knocking onset position at 100% load condition is advanced by around 5°CA when the diesel energy proportion varies from 8% to 15%. Figure 11d shows an increasing unburnt mass fraction from 48% to 57%, indicating a stronger knocking phenomenon with the increased diesel energy proportion.

## 5. Discussion

_{1}. In addition, the knocking onset position is advanced with a stronger knocking intensity for the cases where the pilot fuel mass increases while keeping a constant total fuel energy input. A similar trend was experimentally observed in [80], where a greater pilot fuel quantity increases the knock tendency at high loads. It can be concluded that when DF engines operate at high load conditions, increasing the pilot fuel mass would not be recommended unless the SOC is retarded to suppress the knocking occurrence.

## 6. Conclusions

- Increasing the compression ratio results in higher cylinder peak pressure and IMEP for the SI natural Engine and the DF engine, and therefore increases the knocking occurrence tendency. The compression ratio upper limits of Engine A and Engine B are 11 and 16.5, respectively.
- The knocking boundary for the SI natural gas engines does not exhibit an explicit variation trend with the air-fuel equivalence ratio, whilst that of the DF engine indicates a descending trend with the increase in the air-fuel equivalence ratio. The nominal air-fuel equivalence ratio for the Engine B is suggested to be reduced below 2, however experimental verification for this knocking limit is required.
- The ignition timing delay exhibits a diminishing effect on the IMEP and peak pressure of both the investigated engines. The knocking occurrence for the Engine A and the Engine B could be suppressed by retarding the ignition timing after −38°CA and 3°CA, respectively.
- A higher energy proportion (between 5% and 15%) of the pilot fuel increases the knocking tendency and intensity of DF engines at high loads. It is suggested to maintain the pilot fuel energy ratio less than 9% for Engine B.

- Prior to attempting to improve the performance of an engine (SI NG or DF) by increasing the compression ratio or advancing ignition timing, knocking behaviour analysis must be performed by considering the knocking occurrence, onset position and intensity as well as the cylinder peak pressure upper limit.
- The ignition timing of the SI natural gas engines and DF engines must be controlled precisely after the knocking limit in order to suppress knocking occurrence.
- When operating at high load conditions, the pilot fuel mass of DF engine is suggested to remain at a low level to avoid deteriorating the knocking behaviour.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Simulated and measured in-cylinder pressure for the Engine A at different operating conditions: (

**a**) 25% load; (

**b**) 50% load.

**Figure 4.**In-cylinder pressure comparison of Engine B at different operation conditions: (

**a**) 50% load; (

**b**) 85% load.

**Figure 6.**Knocking IMEP variation with the air–fuel equivalence ratio at different compression ratios (Engine A).

**Figure 9.**Knocking IMEP variation with air–fuel equivalence ratio under different compression ratios (Engine B).

**Figure 11.**Pilot fuel energy proportion effect on engine performance and knocking parameters (Engine B).

Parameters | Unit | 2135 | YC6K |
---|---|---|---|

Cylinder number | - | 2 | 6 |

Bore | mm | 135 | 129 |

Stroke | mm | 140 | 155 |

Compression ratio | - | 11 | 16.5 |

Displacement per cylinder | L | 2 | 2.03 |

Nominal engine speed | rpm | 1200 | 1800 |

Nominal power per cylinder | kW | 9.5 | 50.5 |

Air-fuel equivalence ratio | - | 1.2 | 2.1 |

Ignition timing | °CA | −36 | - |

Pilot injection timing | °CA | - | −5 |

Equipment | Type | Measured Error/Uncertainty/Linearity |
---|---|---|

In-cylinder pressure sensor | AVL GU22CK [67] | ≤ ±0.3% |

Combustion analyser | KiBox To Go 2893 [68] | Approx. 5 ms (<< 1 combustion cycle) |

Diesel consumption meter | AVL 735C [69] | ≤ 0.12% |

Gas consumption meter | E+H 83F25-XRW2/0 [70] | ≤ ±0.05 |

Air-mass flow meter | ABB FMT 700 [71] | ≤ 0.8% |

Inlet/Exhaust pressure sensor | AVL LP11DA [72] | ≤ ±0.1% |

Emission analyser | AVL AMA i60 R1 [73] | ≤ ±2% |

Compositions | Volumetric fraction (%) |
---|---|

CH_{4} | 86.37 |

C_{2}H_{6} | 3.67 |

C_{3}H_{8} | 0.02 |

n-C_{4}H_{10} | 0.01 |

CO_{2} | 4.70 |

N_{2} | 2.55 |

CO | 2.68 |

Load | SOC (°CA, BTDC) | Combustion Duration (°CA) | Wiebe Exponent (-) |
---|---|---|---|

25% | 36 | 58 | 4 |

50% | 34 | 60 | 4 |

Load | Parameters | p_{max} (bar) | α_{1} (°CA) | p_{com} (bar) | p_{EO} (bar) | IMEP (bar) |
---|---|---|---|---|---|---|

25% | Simulation | 19.71 | 11.70 | 2.90 | 1.31 | 1.74 |

Measurement | 19.68 | 11.80 | 2.89 | 1.33 | 1.79 | |

Error (% or °CA) | 0.15 | 0.80 | 0.34 | 1.50 | 2.79 | |

50% | Simulation | 30.47 | 8.87 | 7.43 | 1.85 | 3.64 |

Measurement | 31.07 | 9.00 | 7.34 | 1.90 | 3.72 | |

Error (% or °CA) | 1.93 | 0.13 | 1.22 | 2.60 | 2.15 |

Load | Unit | 100 | 85 | 74 | 50 | 42 | 32 | |
---|---|---|---|---|---|---|---|---|

b_{1} | - | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | |

Diesel fuel | SOC | °CA, ATDC | 2.9 | 3.1 | 3.6 | 3.9 | 3.9 | 4.0 |

Combustion Duration | °CA | 14 | 9.5 | 7.5 | 7.5 | 7.5 | 7.5 | |

Wiebe Exponent | - | 0.2 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | |

Natural gas | SOC | °CA, ATDC | 2.9 | 3.1 | 3.6 | 3.9 | 3.9 | 4.0 |

Combustion Duration | °CA | 97 | 87.5 | 87 | 87 | 84.5 | 84.5 | |

Wiebe Exponent | - | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.4 |

Load | Parameters | p_{max}(bar) | α_{1}(°CA) | p_{com}(bar) | p_{EO}(bar) | IMEP (bar) |
---|---|---|---|---|---|---|

50% | Simulation | 99.37 | 8.02 | 94.87 | 7.25 | 12.84 |

Experiment | 100.08 | 7.80 | 95.06 | 7.48 | 12.39 | |

Error (% or °CA) | 0.7 | 0.22 | 0.2 | 3.07 | 3.63 | |

85% | Simulation | 128.43 | 5.64 | 128.09 | 10.46 | 17.89 |

Experiment | 128.00 | 6.23 | 127.42 | 10.56 | 18.00 | |

Error (% or °CA) | 0.33 | 0.59 | 0.52 | 0.95 | 0.61 |

Parameter | Unit | Range |
---|---|---|

Compression ratio | - | 7~16 |

Air–fuel equivalence ratio | - | 0.8~1.5 |

Ignition timing | °CA | −44~−26 |

Parameter | Unit | Range |
---|---|---|

Compression ratio | - | 12~21 |

Air-fuel equivalence ratio | - | 0.8~2.8 |

SOC | °CA | −6~8 |

Pilot fuel energy proportion | % | 5~15 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xiang, L.; Theotokatos, G.; Cui, H.; Xu, K.; Ben, H.; Ding, Y.
Parametric Knocking Performance Investigation of Spark Ignition Natural Gas Engines and Dual Fuel Engines. *J. Mar. Sci. Eng.* **2020**, *8*, 459.
https://doi.org/10.3390/jmse8060459

**AMA Style**

Xiang L, Theotokatos G, Cui H, Xu K, Ben H, Ding Y.
Parametric Knocking Performance Investigation of Spark Ignition Natural Gas Engines and Dual Fuel Engines. *Journal of Marine Science and Engineering*. 2020; 8(6):459.
https://doi.org/10.3390/jmse8060459

**Chicago/Turabian Style**

Xiang, La, Gerasimos Theotokatos, Haining Cui, Keda Xu, Hongkai Ben, and Yu Ding.
2020. "Parametric Knocking Performance Investigation of Spark Ignition Natural Gas Engines and Dual Fuel Engines" *Journal of Marine Science and Engineering* 8, no. 6: 459.
https://doi.org/10.3390/jmse8060459