Modeling and Optimization of Fuel-Mode Switching and Control Systems for Marine Dual-Fuel Engine
Abstract
:1. Introduction
1.1. The Research Background
1.2. Technical Parameters and Characteristics of Dual-Fuel Engines
2. Dual-Fuel Engine Model
2.1. Simulation Theory and Mathematical Models
2.2. Basic Equations for In-Cylinder Processes
2.3. Mathematical Model of Intake and Exhaust Processes
2.4. Engine Speed Control Principle
2.5. Joint Simulation Modeling
2.6. Simulation Model Calibration
3. Simulation of a Dual-Fuel Engine Fuel-Mode Switching Process
3.1. Switching from Gas Mode to Diesel Mode
3.2. Switching from Diesel Mode to Gas Mode
4. Cuckoo-Search-Algorithm-Based Control Parameter Tuning
4.1. Cuckoo Search Algorithm
- (a)
- The cuckoo chooses a random nest location and lays only one egg in a single nest at a time.
- (b)
- Eggs in the better-placed nests will be kept and hatched.
- (c)
- The number of nests available to cuckoos and the probability that each nest owner will find an intrusive egg is fixed.
- (a)
- The initial definition of the algorithm parameters: for the number of nests, Q, the larger the Q, the greater the number of nest options for the cuckoo to lay eggs; in this paper, Q = 500. The problem dimension, H, also known as the number of optimization parameters, is the three control parameters in the controller; in this paper, H is taken as 3, 2, and 1 in this order. The discovery probability, Pa, refers to the likelihood of the original nest owner finding exotic cuckoo eggs; in this paper Pa = 0.25. The number of iterations is C; in this paper C = 100. The nest’s location is randomly initialized, and the fitness function is defined.
- (b)
- The fitness function values for each existing nest location are calculated and compared with each other to select the current optimal function value.
- (c)
- In addition to the optimal nest, the nest location and nest state are updated using Levy flight for the other nest locations while generating a random number of r(r ∈ [0,1]).
- (d)
- The value of the function calculated in step (c) is compared with the optimal function value in step (b) to generate a new optimal function value. The random number r generated in step (c) is compared with the discovery probability, Pa, defined in step (a). If r > Pa, a new nest position is generated randomly; otherwise, the nest position remains unchanged. In addition, add one to the number of iterations.
- (e)
- If the maximum number of iterations set in step (a) has been met, the global optimal nest position is output at that point; if the maximum number of iterations is not satisfied, return to step (c).
4.2. Simulation Verification of PID Parameter Tuning Based on the Cuckoo Search Algorithm
5. Conclusions
- A simulation model of the 7X82DF dual-fuel engine was built using GT Power and MATLAB/Simulink coupling. The model was calibrated and verified by using the steady-state data of the engine running in diesel and gas modes and the bench report provided by the shipyard. Each error was within 5%, which verified the model’s accuracy. It was demonstrated that the developed model met the requirements for further research.
- According to the manufacturer’s requirements, the engine needs to be switched from running in gas mode to diesel mode within 2 s, which places high demands on the engine and its control system. The rapid cut-off of the gas and the lag in the diesel supply cause an instantaneous lack of engine power, which results in an instantaneous drop in engine speed. In order to quickly restore engine power and speed, the control system increases the diesel supply and overshoots the speed, after which the engine gradually stabilizes. This process is more prone to safety accidents as the engine speed fluctuates due to the short switching time and the high mechanical and thermal loads on the engine components.
- The changeover from diesel to gas mode is longer, and the change in fuel supply is smoother, so the simulation gives a smoother transition in engine parameters. The changeover process is less volatile and less demanding on the engine and its control system than the changeover from gas to diesel mode. Therefore, the possibility of a safety incident during this process is also low.
- The cuckoo search algorithm was introduced and used to optimize the parameters of a PID controller for a conventional fuel supply system. The optimized controller is then used to simulate the switching process from gas to diesel mode at 80% and 100% loads on the main engine. The results show that the optimized controller is able to significantly suppress the engine speed fluctuations when performing the fuel-mode switch.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
PID | Proportion Integral Differential |
CS | Cuckoo search algorithm |
LNG | Liquefied natural gas |
IMO | International Maritime Organization |
PID | Proportional–Integral–Derivative controller |
TDC | Top dead center |
ATDC | After top dead center |
Fuel inject timing | |
Ignition delay time | |
P | Pressure in the cylinder |
T | Temperature in the cylinder |
k | Chemical kinetic rate constant |
m | Mass of oil and gas mixture generated during the ignition delay |
Calibration factor | |
Taylor microscale length | |
, | GT Power built-in function |
Volume of cylinders | |
Concentration of oxygen | |
Diffusion combustion coefficient | |
Energy that enters or exits the system | |
Heat exchanged through the system boundary | |
W | Mechanical work of the gas in the cylinder acting on the piston |
Specific enthalpy | |
U | Internal energy of the system |
V | Working volume of the air cylinder |
Crank angle | |
Heat enters or leaves the walls of the cylinder | |
Heat release of fuel into the cylinder | |
Specific enthalpy at the intake valve and exhaust valve | |
Mass of the working substance flowing into and out of the cylinder | |
Instantaneous fuel mass in the cylinder | |
V | Volume of the working substance in the system |
n | Amount of substance of the working substance in the system |
T | Temperature of the working substance in the system |
R | Gas constant |
Mass flow through the control body boundary | |
Density | |
A | Area cross section |
u | Velocity of the working substance crossing the boundary |
Surface area of the heat transfer surface | |
e | Internal energy per unit mass |
H | Enthalpy per unit mass |
h | Heat transfer coefficient |
Temperature of the fluid and the temperature of the wall | |
Pressure loss coefficient | |
Surface friction coefficient | |
dx | Mass element length in the flow direction |
dp | Pressure difference before and after dx |
D | Equivalent diameter |
Output value | |
Difference between the target value and the measured value | |
Proportionality coefficient | |
Integral coefficient | |
Differential coefficient | |
MCR | Maximum continuous rating |
BSFC | Brake-specific fuel consumption |
ITAE | Time-multiplied absolute error integration criterion |
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Engine Parameters | Unit | Values |
---|---|---|
Cylinder | - | 7 |
Bore | mm | 820 |
Stroke | mm | 3375 |
Compression ratio | - | 12.4 |
Power | kW | 22,531 |
Speed | rpm | 62.5 |
Firing order | - | 1-6-3-4-5-2-7 |
Pilot-injection pressure | bar | 755 |
Gas-injection pressure | bar | 14.8 |
Pilot timing | °CA ATDC | −8.5 |
Gas-valve timing | °CA ATDC | 224 |
Load (%) | 25 | 50 | 75 | 80 | 100 |
Pilot consumption (g/kWh) | 1.0 | 0.5 | 0.4 | 0.3 | 0.3 |
Load (%) | 25 | 50 | 75 | 80 | 100 |
Pilot consumption (g/kWh) | 1.9 | 0.4 | 0.3 | 0.3 | 0.3 |
Load (%) | 25 | 50 | 75 | 80 | 100 |
---|---|---|---|---|---|
Error (%) | |||||
Power (kW) | −0.267 | −3.556 | 2.518 | 1.828 | 1.133 |
Maximum Combustion Pressure (bar) | 1.154 | −1.936 | 1.201 | 1.525 | 0.909 |
BSFC (g/kWh) | 2.425 | 1.625 | 2.414 | 2.295 | 1.889 |
Scavenging Air Temperature (K) | −0.362 | −0.599 | −0.597 | −0.463 | −0.692 |
Exhaust Temperature (K) | 1.357 | −1.003 | 1.231 | 0.988 | 1.4 |
Load (%) | 25 | 50 | 75 | 80 | 100 |
---|---|---|---|---|---|
Error (%) | |||||
Power (kW) | −0.781 | −3.759 | 1.124 | 1.289 | 1.025 |
Maximum Combustion Pressure (bar) | −1.445 | −1.191 | 1.336 | 1.148 | 2.178 |
BSFC (g/kWh) | 1.012 | 1.089 | 1.054 | 1.623 | −0.128 |
Scavenging Air Temperature (K) | 0.758 | 0.466 | 0.431 | 0.465 | 0.397 |
Exhaust Temperature (K) | −1.378 | −1.485 | 1.285 | 1.660 | 1.781 |
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Shu, Z.; Gan, H.; Ji, Z.; Liu, B. Modeling and Optimization of Fuel-Mode Switching and Control Systems for Marine Dual-Fuel Engine. J. Mar. Sci. Eng. 2022, 10, 2004. https://doi.org/10.3390/jmse10122004
Shu Z, Gan H, Ji Z, Liu B. Modeling and Optimization of Fuel-Mode Switching and Control Systems for Marine Dual-Fuel Engine. Journal of Marine Science and Engineering. 2022; 10(12):2004. https://doi.org/10.3390/jmse10122004
Chicago/Turabian StyleShu, Zepeng, Huibing Gan, Zhenguo Ji, and Ben Liu. 2022. "Modeling and Optimization of Fuel-Mode Switching and Control Systems for Marine Dual-Fuel Engine" Journal of Marine Science and Engineering 10, no. 12: 2004. https://doi.org/10.3390/jmse10122004