Journal of
Marine Science
and Engineering
Article
Towards Marine Dual Fuel Engines Digital
Twins—Integrated Modelling of Thermodynamic
Processes and Control System Functions
Sokratis Stoumpos, Gerasimos Theotokatos * , Christoforos Mavrelos and
Evangelos Boulougouris
Maritime Safety Research Centre, Department of Naval Architecture, Ocean and Marine Engineering, University
of Strathclyde, 100 Montrose Street, Glasgow G4 0LZ, Scotland, UK
* Correspondence: gerasimos.theotokatos@strath.ac.uk; Tel.: +44 (0)-141-548-3462
Received: 25 February 2020; Accepted: 12 March 2020; Published: 14 March 2020
Abstract: This study aims at developing an integrated model that combines detailed engine thermodynamic
modelling and the control system functional modelling paving the way towards the development of
high-fidelity digital twins. To sufficiently represent the combustion process, a multi-Wiebe function
approach was employed, whereas a database for storing the combustion model parameters was
developed. The developed model was employed for the systematic investigation of a marine four-stroke
dual fuel engine response during demanding transient operation with mode switching and load
changes. The derived results were analysed to identify the critical engine components and their
effect on the engine operational limitations. The results demonstrate that the developed model can
sufficiently represent the engine and its subsystems/components behaviour and effectively capture
the engine control system’s functionality. The appropriate turbocharger matching along with the
sufficient design of the exhaust gas waste gate valve and fuel control systems are crucial for ensuring
the smooth engine operation of dual fuel engines.
Keywords: marine dual fuel engines; 0D/1D simulation; control system functional modelling;
operating modes switching; GT-ISE modelling; digital twins
1. Introduction
As the reduction of greenhouse and non-greenhouse emissions is amongst the high priority
issues that the shipping industry has to endure on account of the stricter environmental standards
imposed [1], the use of alternative fuels including natural gas, methanol and bio-fuels have been
proposed for improving the environmental sustainability of maritime operations [2]. In specific, natural
gas (NG) as a fuel has proven to be a viable solution for vessels operating both inside and outside
the Emission Control Areas (ECAs) owing to the rapid development of the global liquefied natural
gas (LNG) infrastructure [3], the lower LNG fuel price levels [4] compared to other fossil fuels [5] as
well as the clean nature of lean combustion [6], which leads to the reduction of nitrogen oxides (NOx),
carbon dioxide (CO2 ) due to the low carbon to hydrogen ratio and the almost complete elimination of
particulate matters (PM) and sulphur oxides (SOx) emissions [3].
The economic and environmental benefits of using LNG as an alternative fuel led the marine
engine manufacturers to develop dual fuel (DF) versions of both the large two-stoke slow-speed
engines and the four-stroke engines [7]. The marine DF engines run with a small amount of pilot diesel
fuel used for initiating combustion and natural gas as the main fuel; they can operate according to
either the premixed combustion concept (with the natural gas injected in the inlet ports during the
cylinder induction phase [8,9] or within the cylinders during the compression phase [10]) or the gas
J. Mar. Sci. Eng. 2020, 8, 200; doi:10.3390/jmse8030200
www.mdpi.com/journal/jmse
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direct injection concept with the natural gas injected after the pilot fuel injection [11]. Other engine
types include the spark ignited pure gas engines as well the gas–diesel engines [12]; the latter can
operate with a variety of gas to diesel fuel fractions. The marine DF engines can operate either in the
diesel mode by burning diesel fuel—heavy fuel oil (HFO) or marine gas oil (MGO)—or in the gas mode
by burning natural gas and pilot diesel fuel (for initiating combustion); thus providing additional fuel
flexibility for the vessel operation. In this respect, they are currently becoming the industry standard
not only for LNG carriers but also for all LNG-fuelled vessels, as reported in [13,14].
In this respect, the continuous engine development and optimisation procedures, which are
usually based on a number of techniques including experimentation, design, prototyping and engine
mathematical modelling, are essential to the marine industry [12]. The advent of Internet of Things (IoT)
and digitalisation has enabled the effective application of the digital twins in various industries including
shipping, with expected benefits on the systems safety, maintenance, efficiency and environmental
footprint [15]. The use of marine engines thermodynamic models as digital twins is reported in [16].
In this respect, high-fidelity integrated models combining the engine thermodynamic processes
modelling with the control and safety system modelling are required as a first step prior to developing
an intelligent digital twin as defined in [15].
As reported in [17,18], very few studies have been published focusing on the modelling/simulation
or experimental analysis of marine DF engines. The more recent authors’ studies [19,20] presented
the transient simulation of a large marine DF engine and the derived results were employed for the
safety analysis of the engine operations. In addition, to the best of authors’ knowledge, other simulation
studies on the transient operation of marine DF engines are not available in the open literature.
In [21], a marine DF engine was studied experimentally at steady state conditions complemented
by a liquid fuel injection model to obtain a better understanding of the local combustion conditions.
In Li et al. [22], a small marine DF four-stroke engine was experimentally investigated for comparison
with the engine performance/emissions characteristics in the diesel and the gas operating modes.
Boeckhoff et al. [23] presented the experimental investigation of a large marine DF four-stroke engine
of the premixed combustion type at both steady state conditions (studying the effect of the engine
and fuel parameters variations on the engine performance and emissions) and transient conditions
(with fuel switching), reporting the engine operational experience. Banck et al. [24] conducted an
experimental analysis of a large DF four-stroke engine optimised for marine applications discussing the
engine load acceptance at various load ramp slopes and the engine operational requirements at the low
load range. Portin [25] reported the development of DF four-stroke engines for offshore applications
and presented experimental data for the engine load acceptance test from 40% to 80% load for the gas
mode. In Mohr et al. [26], the experimental investigation of a large size four-stroke single cylinder
engine at steady state conditions was reported and the influence of the engine settings variation on the
engine performance and emissions was discussed.
Previous investigations reported that DF engines have operational limitations in marine and
offshore applications due to the expected considerable transient loading requirements. In particular,
during the load increase phase of premixed combustion DF engines running in the gas mode, the
engine delivered power initially increases due to the injection of an additional amount of gas fuel,
whilst the amount of combustion air increases more slowly due to the turbocharger lag effect. Thus, the
engine runs temporarily with a rich gas fuel−air mixture until the turbocharger delivers the required
air flow. In principle, the same takes place in a diesel engine, but due to the different combustion
process, the load acceptance is subject to different limitations. Thus, over-fuelling a gas engine leads
to a rich combustion (i.e., lower air−fuel ratio), which at low loads improves the engine combustion
efficiency [25], whereas at higher loads, over-fuelling causes the engine operating point to shift towards
the knocking limit, as the range between the misfiring and knocking borderlines becomes narrower at
higher engine loads [21]. In contrast, over-fuelling a diesel engine at low loads reduces the combustion
efficiency and leads to black smoke, if not controlled. However, at higher loads, the turbocharger’s
faster response improves the diesel engine load acceptance.
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Considering the size, complexity and cost of the marine DF engines, experimental studies require
significant resources. Thus, engine modelling as well as simulation is employed as one of the most effective
methods for obtaining a better understanding of the engine operation and components interactions as
well as predicting the engine performance and emission characteristics. In Stoumpos et al. [18], a large
marine DF four-stroke engine steady state model was developed in the GT-ISE™ software and used for
the parametric investigation of the engine settings and the study of the engine performance/emissions
trade-offs. The employed models were of the zero-dimensional (0D) type for modelling the engine
cylinders processes and the one-dimensional (1D) type for modelling the intake and exhaust manifolds.
Theotokatos et al. [20] reported the extension of the model presented in [18] and simulated critical
situations of the engine operation considering normal and delayed exhaust gas waste gate valve
control providing recommendations for enhancing the engine safety. In Mavrelos and Theotokatos [17],
a large marine DF two-stroke engine of the premixed combustion type was investigated based on
a steady state 0D model developed in the GT-ISE software and the parametric optimisation of the
engine settings was performed with the aim of simultaneously reducing the CO2 and NOx emissions.
In Ritzke et al. [27], a combined 0D/1D and computational fluid dynamics (CFD) three-dimensional
(3D) approach was proposed for modelling a four-stroke dual fuel marine engine in the AVL Boost
and FIRE software tools. The 0D/1D engine model was used to generate information regarding the
initial and boundary conditions, and subsequently these conditions were used for the 3D CFD model.
In Sixel et al. [28], a physical model for modelling the premixed combustion process of marine DF
engines along with its integration with the engine 0D/1D model developed in the GT-Power software
was reported. The model was used for the investigation of two engines (a single cylinder engine and a
large marine DF four-stroke engine) operation at steady state conditions considering both natural gas
and methanol as the main fuel. Based on the comparison with experimental data, the developed model
accuracy was considered adequate for allowing its usage at the design phase of dual fuel or gas-diesel
engines. Wenig et al. [29] developed a quasi-dimensional phenomenological combustion model to
calculate the burning rate of a lean premixed mixture marine DF two-stroke engine with a pre-chamber.
Following a process for the model constants calibration based on a set of experimental data, it was
concluded that the model provided sufficient accuracy for a wide range of engine operating conditions.
In addition, a limited number of studies investigating the transient operation (including load
chances and fuel changes) of small vehicles or heavy-duty DF engines by using simulation tools were
published. Xu et al. [30] developed a one-dimensional model of an automotive four-stroke dual fuel
engine in the GT-ISE software to study and improve the engine transient response by optimising
the engine fuel injection. This model was validated against a comprehensive set of experimental
data, from which a lag in the engine power delivery under transient loading with dual fuel operation
was identified, and subsequently was applied to generate the required insight and to design control
strategies for smooth torque delivery under dynamic conditions. For modelling the combustion
process, a triple Wiebe function was employed, the constants of which were correlated with the engine
indicated mean effective pressure based on the acquired experimental data as reported in [31]. Barroso
et al. [32] modelled a heavy-duty DF compression ignition (CI) engine by employing a 1D model in
GT-Power; the model was calibrated by using engine mapping experimental data and used in both
steady state and transient conditions. Georgescu et al. [33] investigated the transient behaviour of gas
and DF engines running on natural gas by employing two mean value dual cycle models. The first
model was used to gain insight into the DF engine in-cylinder combustion process, whilst the second
was used to simulate the entire engine system. The simulation results were used to discuss the engine
limitations and transient response. In Mayr et al. [34], the development and implementation of a
methodology was presented for simulating the transient response of large gas engines on a single
cylinder engine test bed. Simple and fast models and algorithms based on lookup tables were employed
to provide the boundary of the investigated engine components conditions. The simple model results
were compared with the results from a 1D model developed in the GT-Power software demonstrating
sufficient accuracy.
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For operating a marine DF engine in a broad envelope as well as accommodating the demands
during the fuels switching, the engine control system design as well as sufficient control strategies
development is required. Wang et al. [35] studied the design of a marine DF engine fuel control system
to accommodate effective fuel transitions by employing a mean value model-based approach. It was
concluded that a Multiple Input Single Output (MISO) control system architecture with feedback
corrections applied to both the gas and diesel fuels is advantageous compared with architectures
that apply corrections to only one fuel command (either diesel or gas). Schmid et al. [36] focused
on the marine four-stroke gas and DF engines cylinder individual combustion control by employing
an anti-knock approach, determining ways of combining combustion balancing (which is currently
a challenging task due to the extreme sensitivity of the modern engines to the cylinder-to-cylinder
variations) with conventional control functions. Ott et al. [37] investigated the cylinder combustion
individual feedback control of a four-stroke DF engine. The centre of combustion and maximum
pressure rise was controlled by actuating the start and duration of the pilot diesel fuel injection. Engine
experimental analysis indicated that the proposed controller was able to compensate the influence of
various disturbances. An applicable and comprehensive control strategy for an automotive natural
gas/diesel engine was presented in [38]. Roecker et al. [39] demonstrated a method for controlling the
diesel fuel injection in DF four-stroke engine in order to overcome the shortcomings of the natural gas
port injection and improve the engine transient performance and implemented the developed control
in two vehicles engines. Fathi et al. [40] discusses the homogeneous charge compression ignition
(HCCI) engine control structure in order to effectively control these engines and obtain acceptable
performance and emissions characteristics. However, the complete detailed modelling of the engine
and its control system has not been reported in pertinent literature.
From the preceding literature review, the following research gaps were identified: (a) the lack of a
detailed model to adequately represent the marine DF engines’ behaviour along with their control
system functionalities; (b) the need for the detailed engine control system description and modelling;
(c) the lack of a thorough investigation of the marine DF engine processes during transient operations
including modes switching; and (d) the need for mapping the engine components’ limitations and the
control system requirements for ensuring reliable and smooth engine operation during transients with
load changes and modes switching.
For addressing these gaps, the present study aims at systematically investigating a marine DF
four-stroke engine response by developing a detailed model for both the engine and its control system.
The developed model is an extension of the versions presented in [18,20] for simulating the engine
steady state and transient operation, respectively. The focus of the present study is on the analysis of
the engine response and the engine subsystems/components interactions as well as the identification of
the engine operational limitations.
The model was developed in the GT-ISE software [41], as this software provides the tools, libraries and
functionalities to address the inherent complexity of the engine and its control system modelling as well as
the interfaces required for the programming of the controller logical functions. A similar implementation
by using an in-house software would be more time-consuming. In addition, GT-ISE is a tool that has been
extensively used in both academia and industry for modelling a considerable variety of engine types/sizes
and fuels. Following validation under steady state and transient conditions, the developed model
was used for a systematic analysis of the engine response under the investigated transient operating
conditions. By comparing the engine performance parameters metrics, the critical engine components
are identified, and the engine operational limitations are discussed, which provided valuable information
for the understanding of the engine response and the control system design improvement.
The original contribution of this study is summarised as follows: (a) it is the first time that the
detailed DF engine control system functional analysis and modelling is presented in pertinent literature;
(b) the development and extensive validation of the complete engine and its control system model,
which allows for simulation of the engine performance/emission and response at both steady state and
transient operation including modes switching; (c) the investigation of a large four-stroke marine DF
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engine transient operation in detail, enabling greater understanding of the involved processes and the
interactions between the engine components; (d) the study of the control system response effects on
the engine components’ operation; and (e) the identification of the engine operational limitations.
2. Investigated Engine Description
In the present study, the four-stroke, non-reversible, turbocharged and intercooled Wärtsilä
9L50DF engine was investigated [42]. The engine is capable of operating in two distinct modes, in
specific: (a) the gas mode running on natural gas and light fuel oil (LFO) (which is used as pilot fuel
for initiating combustion) and (b) the diesel mode, in which either heavy fuel oil (HFO) or LFO is
used as the main fuel. The engine control system must be capable of smoothly switching between
fuels during the engine operation. The engine’s high-power output along with the fuel flexibility, low
emissions, high efficiency and reliability renders this engine an attractive solution for both electric
power generation and ship propulsion [43]. Its main advantage is the lean-burn combustion, which
provides an increased engine efficiency with reduced in-cylinder peak temperatures, thus resulting in
reduced NOx emissions and engine thermal loading.
In the gas mode, the investigated DF engine operates at a much lower NOx emission level (compared
to diesel mode) complying with the IMO Tier III limits. However, to achieve stable combustion conditions,
an air−fuel ratio operating window between the limits of misfiring and knocking combustion needs to
be targeted. The engine cylinders air−fuel ratio is adjusted via an electronically controlled exhaust gas
waste gate (WG), which bypasses a part of the exhaust gas along the turbocharger (TC) turbine [42].
Each engine cylinder is equipped with a combined diesel and pilot fuel injector. Gas is injected by
using solenoid gas admission valves at each cylinder inlet port (upstream the intake valves) during the
engine induction process. The gas admission valves as well as the diesel fuel injectors are electronically
controlled (in the gas and diesel operating modes, respectively) to adjust the engine power output
in order to keep the ordered engine speed. The injected pilot fuel amount depends on the engine
operating mode and load. The engine advanced automation system controls the engine functions,
counting for the prevailing ambient conditions and the used fuel properties (including fuel quality,
methane number, etc.), so that optimal running conditions are obtained [25].
In this study, the examined engine was considered as a part of a generator set operating at a
constant speed of 514 r/min. The engine details are reported in the manufacturer product guide [42],
the main engine characteristics are illustrated in Table 1, whilst the engine layout and components
are presented in Figure 1. To allow for the engine’s smooth operation, an adequate control strategy
for governing the injected fuels amount as well as their injection timing and duration has to be
implemented. This also includes the waste gate control, which is essential to adjust the combustion
air−fuel equivalence ratio (λ) by regulating the boost pressure, when the engine operates in the
gas mode.
Table 1. Main engine characteristics.
MCR Power/Speed
kW/r/min
8775/514
BSEC at MCR (gas mode)
BSFC at MCR (Diesel mode)
No. of cylinders
Bore/Stroke
Turbocharger units
kJ/kWh
g/kWh
mm
-
7300
190
9
500/580
1
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Figure 1. Wärtsilä 9L50DF engine layout.
Engine Transient Operation Requirements
For ensuring the engine integrity and smooth running during transient operations, the ECS needs
to satisfy the engine response requirements as determined by the engine manufacturer [42]. With
regard to the load transition, for load steps in the gas mode, the maximum acceptable step load increase
is as illustrated in Figure 2 (left), whilst the maximum allowed step load decrease should be according
to the following schedule: 100–75–45–0% (for the intermediate engine loads, the nearest lower load
threshold needs to be used). In addition, the recovery time (i.e., the time required for the engine
to reach its steady state operating point following a transient) should be less than 10 s, whilst the
recommended time between consecutive load steps should be greater than 30 s. In the diesel mode, the
maximum acceptable step load increase is as indicated in Figure 2 (left) and there are no limitations
in terms of step load reductions. In this case, the recovery time after a load change decreases to 5 s,
whereas the recommended time between consecutive load steps is greater than 10 s.
Figure 2. Maximum allowed step load increase in percentage of MCR for the gas mode and the diesel
mode (left); Maximum allowed ramp load increase for engine operating at nominal speed (right).
≤
≥
≤
≥
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For ramp load changes in the gas mode, the engine control system must not permit a load reduction
from 100% to 0% faster than 20 s prior to automatic transfer to the diesel mode. The maximum allowed
ramp load increase for various engine operating conditions is shown in Figure 2 (right). The curve
“preheated, normal gas” is used as the default ramp load increase for the gas mode, whereas the curve
“max capacity gas” indicates the maximum allowed ramp load increase.
Furthermore, considering the fuel change at any fixed load, the gas to diesel (GTD) mode switching
needs to take place at any load within 1 s. The switch from the diesel mode to the gas mode (DTG)
needs to be completed within 2 min for the minimization of disturbances to the gas fuel supply systems.
In both cases, the maximum allowed speed drop is 10%. These manufacturer transient requirements
are summarised in Table 2.
Table 2. Engine transient response requirements [42].
Load Change
Diesel Mode
Gas Mode
Recovery time
≤5 s
≤10 s
Time between load steps
≥10 s
≥30 s
Maximum allowed speed drop
10%
10%
Maximum step-wise load increase
33% of MCR
shown in Figure 2
Maximum step-wise load decrease
No limitation
100–75–45–0%
Mode switching
Diesel to Gas
Gas to Diesel
Required time
2 min
1s
Maximum allowed speed drop
10%
10%
3. Investigated Engine and Controls System Modelling
The present study focuses on the modelling of the investigated engine and its control system for
further study of the engine response at transient conditions by employing the GT-ISE software, which
is a widely used simulation program for engine modelling and analysis [41]. The complete engine
model was realised by using the following assemblies of the GT-ISE software: (a) the 0D/1D engine
model; (b) the user input; (c) the engine control system (ECS); and (d) the engine monitors and alarms.
In the developed model, the user can order a specific transient operation (i.e., load changes at either
the gas or the diesel modes, a mode switching at constant load or extreme load changes that may result
in a mode switching) by employing the user input assembly.
3.1. Engine Modelling
The 0D/1D engine model for the investigated engine simulation at steady state conditions (for both
the gas and diesel operating modes in a number of operating points) was previously developed in the
GT-ISE software and was used for the engine settings optimisation as described in [18]. The extension
of the existing model to accommodate the engine transient conditions was realised by: (a) setting up
the input data block for providing the ordered engine operating schedule in terms of mode and load
versus time (i.e., no fuel change, GTD or DTG mode switching and/or load change); (b) modelling the
engine control system by developing the ECS assembly (based on the available published manufacturer
data [25,42] as described in Section 3.3) to control the engine mode switching as well as the injected
fuels; and (c) extending the engine model assembly to accommodate the modelling of the combustion
process in transient conditions (as described in the Section 3.2).
The complete engine layout of the model in GT-ISE is presented in Figure 3. The engine model uses
a number of elements available in the GT-ISE software libraries, which are appropriately interconnected.
In specific, cylinder elements are used, connected upstream and downstream the intake and exhaust
valves, respectively, whereas pipes and junctions are used for modelling the inlet and exhaust manifolds.
The turbocharger (TC) unit is modelled by using the compressor and turbine elements; the former is
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connected between the ambient and the air cooler, whereas the latter is connected between the exhaust
pipe and the exhaust ambient. The compressor and turbine elements are mechanically connected
with the TC shaft element. An air cooler element is connected between the compressor and the inlet
manifold pipes, whereas the waste gate (WG) valve element is connected in the exhaust manifold
for bypassing the turbine and is controlled by the boost pressure (acquired from the inlet manifold
connected downstream the air cooler). The gas admission valves (one per cylinder) are connected
in the engine inlet port (upstream the engine intake valves). The gas injection takes place during
the respective cylinder induction process after the exhaust valves closing, so that all the injected gas
remains into the engine cylinders. The diesel fuel and the pilot fuel injectors are directly connected to
the engine cylinders. The engine cylinders are mechanically connected to the engine crankshaft, which
is also connected to the engine load.
Figure 3. Engine model layout in the GT-ISE environment.
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The engine cylinders are modelled by using a zero-dimensional method using a two-zone approach
for modelling the combustion and expansion processes (one zone containing the combustion products
and an unburned mixture zone), as well as a single zone approach for the remaining of the cycle [44].
The following mass and energy conservation equations were employed for modelling each zone along
with the ideal gas equation and the cylinder volume time derivative equation:
X .
dm
=
m
dt
(1)
.
d(me)
dV X .
= −p
+
(mH ) − Qht
dt
dt
(2)
i
i
where m and V denote the working medium mass and cylinder volume, respectively; ṁ is the mass
flow rate entering or exiting the cylinder; p denotes the cylinder pressure; e is the working medium
total specific internal energy (internal energy plus kinetic energy per unit mass); H is the working
.
medium total specific enthalpy; and Qht is the heat flow rate from the gas to the cylinder walls.
According to the employed two-zone approach [41], the unburned gas zone consists of air and
combustion products from the previous cycle, whereas the burned gas zone is generated after the start
of combustion. At each time step, the amount of fuel and air is transferred from the unburned zone to
the burned zone as dictated by the burning rate, which is calculated with the employed combustion
model. The chemical kinetics calculation considering dissociation effects is carried out in the burned
gas zone taking into account the used fuel(s) combustion and the assumption that the combustion
products consist of the following 13 species: N2 , O2 , H2 O, CO2 , CO, H2 , N, O, H, NO, OH, SO2 and Ar.
The gas properties are calculated by using the species mass fractions and the respective property, the
latter is calculated as algebraic functions of temperature.
Appropriate heat transfer, combustion and friction models [41] are employed. In particular,
for calculating the gas to wall heat transfer coefficient, the Woschni heat transfer model is used [45].
The Chen–Flynn friction model is employed for calculating the engine friction mean effective pressure [46].
The cylinders volume is calculated by using the engine kinematic mechanism geometry. The employed
combustion process modelling approach is described in the following section. For estimating the NOx
emissions, the extended Zeldovich mechanism is employed, which is described in [47,48], taking into
account the temperature of the burned gas zone. The model constants are calibrated for a discrete load at
each operating mode.
A one-dimensional approach is used to model the pipes and junction elements by solving the
following momentum conservation equation along with the mass and energy conservation equations
described by Equations (1) and (2) in each discretised pipe element of the intake and exhaust manifolds [41]:
.
dm
=
dt
Adp +
P
.
i (mu) −
4C f dx
D
dx
+ Kp
1
2 ρu|u|A
(3)
where ṁ is the boundary mass flux (ṁ = ρAu); ρ is the density; A is the pipe cross-sectional flow area; u
denoted the velocity at the boundary; Cf is the friction factor; Kp is the pressure loss coefficient; D is
the pipe equivalent diameter; dx is the discretization length; and dp is the pressure differential acting
across dx.
The pipe elements model solver employs an explicit time integration method, which provides a
compromise between the required computational time and accuracy. The model variables include the
working medium mass flow, density and internal energy. The pipe elements employed for representing
the engine intake and exhaust manifolds are divided into a number of discrete elements considering a
discretisation length of 0.4 to 0.55 times the cylinder bore diameter for the intake and exhaust manifolds,
respectively. The scalar variables (pressure, temperature, density, internal energy, enthalpy, species
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concentrations, etc.) are assumed to be uniform over each discrete element, whereas the vector variables
(mass flux, velocity, mass fraction fluxes, etc.) are calculated for each discrete element boundary.
The compressor and turbine models use the steady state maps of the respective elements in a
digitised format. The inlet and exhaust valves elements use the respective valves’ profiles, employing
the quasi-steady adiabatic flow equation for calculating the respective flow rates. The intake valves
employ the Miller timing, closing before the cylinder bottom dead centre (BDC), which reduces the
required compression work and the combustion temperature and results in higher engine efficiency
and lower NOx emissions.
The angular momentum conservation equations are employed in the engine mechanical elements
(shafts) in order to calculate the respective rotational speeds. Furthermore, the WG valve element
employs a simplified PID controller with predefined proportional and integral constants for controlling
the valve area considering the engine boost pressure as the input. This PID controller constant, which
affects the WG valve response, is calibrated during the model calibration phase. The engine air cooler
element is modelled by using multiple pipes connected in parallel that are treated according to the 1D
model described above, where the heat transfer from the air to their walls is calculated considering the
overall heat transfer coefficient. This heat transfer coefficient, as well as the heat transfer area and the
cooling water temperature, are the model input parameters; the latter was considered constant for
simulating both steady state and transient conditions.
The input data required to set up the engine model includes the engine geometric data, the
cylinder valves profiles, the compressor and turbine maps, the WG valve area, the constants of engine
sub-models (combustion, heat transfer and friction), the ambient conditions as well as the engine load
and mode time variation. Initial conditions need to be provided for the temperature, pressure and
composition of the working medium contained in the engine cylinders, pipes and receivers. The input
data were acquired from the engine manufacturer product guide and the three-dimensional engine
drawings were available from the engine manufacturer in [42].
3.2. Combustion Process Modelling
For calculating the fuel burning rate at the diesel operating mode, the single Wiebe combustion
model is employed along with the Sitkey equation for estimating the ignition delay [44]. For modelling
the combustion process at the gas operating mode, a triple Wiebe function is employed with each
function representing the premixed combustion of a portion of the pilot fuel, the diffusive combustion
of the remaining pilot fuel and the rapid burning of the gaseous fuel as well as the tail combustion
of the cylinder residuals [6]. The ignition delay for the gas mode is approximated by using the
equations and data reported in [28,49]. The gas admission valves are modelled by controlling the pulse
width/duration (taking values in the region from 38 to 68 ◦ CA from low to high loads) considering that
the respective fuel pressure linearly varies with the engine load. The injected gaseous fuel mass flow
rate is calculated as a function of the solenoid valve nozzle area, pressure ratio and the gaseous fuel
properties upstream the gas admission valve. The main diesel fuel injected amount is modelled as a
function of the engine load, whereas the pilot fuel amount is considered to be a function of the engine
load and operating mode (diesel or gas).
The cumulative fuel burnt for the gas mode is calculated according to the following equation [41]:
xb,g (θ) =
3 h
X
i=1
FF g,i xb,g,i (θ)
i
where i denotes the Wiebe function; FF denotes the weight of each Wiebe function (
and θ denotes the crank angle (top dead centre (TDC) of the closed cycle is at 0◦ CA).
(4)
P3
i=1 FF g,i
= 1);
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Each individual Wiebe function is calculated by the following equation [44], which is also used
for calculating the cumulative fuel burnt at the diesel operating mode:
!
θ − θSC_i m g,i +1
xb,g,i (θ) = 1 − exp −a
∆θ g,i
(5)
where i denotes the Wiebe function; a is the Wiebe function parameter (considered 6.9); θSC_i is the start
of combustion; ∆θg,i is the combustion duration; and mg,i denotes the i-th Wiebe function shape factor.
The combustion heat release rate is calculated using the derived fuel burning rate, which is the
time derivative of the cumulative fuel burnt from Equation (4), and the total energy from all the injected
fuels, according to the following equation:
.
.
.
Qb = xb E f ,total = xb
3
X
m f ,i LHVi
(6)
i=1
.
where xb denotes the fuel burning rate, Ef,total is the total energy of all the injected fuels, mf is the
burnt fuel amount, LHV denotes the fuel lower heating value and i denotes the fuel (gas, diesel, pilot).
In this study, marine gas oil (MGO) was considered for the main and pilot fuels, whereas methane was
considered for the gaseous fuel.
It was reported in the previous authors’ studies [18,19] that the single Wiebe function can sufficiently
capture the combustion processes in the diesel mode, as the maximum cylinder pressure, the brake
specific fuel consumption (BSFC) and the indicated mean effective pressure (IMEP) were predicted
with adequate accuracy. However, the triple Wiese function model was required to provide sufficient
accuracy in the gas mode as reported in pertinent literature [18,19,30,31]. Hence, the Wiebe function
modelling approach was also employed in this study, instead of a predictive combustion model, as the
latter requires a considerable set of the model constants calibration [28,29].
The combustion model parameters (weights, start of combustion, combustion duration and shape
factor for each Wiebe function), which determine the combustion profile for both the diesel and the
gas modes, were calibrated at 25%, 50%, 75% and 100% loads (at steady state conditions), so that
the predicted engine cylinder parameters (maximum pressure, IMEP and brake specific fuel/energy
consumption) sufficiently matched their respective experimental values. The calibrated values of
the combustion model parameters (controlled parameters) are stored in a database in the format of
three-dimensional matrices (or dependency templates) as functions of the following two controlling
parameters: (a) the engine load, and (b) the engine operating mode (diesel or gas).
The procedure illustrated in the flowchart of Figure 4 is employed for modelling the combustion
process in each engine cylinder when the engine operates in transient conditions. The combustion
model controlling parameters, which are taken from the ECS model, include the engine load and the
operating mode (diesel, gas, GTD change, DTG change) as well as the fuels injected amounts (the
values of fuels amount are used only for the case of the DTG change). For the engine operation in
the diesel mode, the gas mode and the GTD change, quadratic interpolation is used (considering the
engine load as the controlling parameter) for calculating the values of the respective combustion model
parameters for each engine cylinder (single Wiebe function model for the diesel mode; triple-Wiebe
function for the gas mode). It needs to be noted that during the GTD mode switching, the engine
cylinders operate either in the gas mode for the cylinders in which combustion or injection processes
already started prior to the implementation of the change, or the diesel mode for the cylinders in which
combustion or injection processes started after the mode switching order (as in this case the gas fuel
is cut off instantly and only diesel fuel is injected). Based on the combustion model parameters, the
fuel burning rate and the heat release rate are calculated by using Equations (4) and (6), respectively.
This calculation procedure is depicted in the interior box shown in the left-hand side in Figure 4.
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The controlled combustion model parameters for each engine cylinder are updated at every cycle
based on the controlling parameters derived from ECS described in 3.3.
The modelling of each cylinder combustion process for the DTG mode switching requires a more
sophisticated approach as the engine cylinders operate for a considerable period (around 2 minutes)
with the main diesel fuel, the gas fuel and the pilot fuel. The employed calculation procedure is
described in the flowchart included in the exterior box in Figure 4. First, the total burning rates at
the specific engine load are calculated considering separately the diesel mode and the gas mode by
employing the procedure described in the previous paragraph (the procedure illustrated by interior
box flowchart in Figure 4). In addition, the fuels amounts (derived from the ECS model) and the fuels
lower heating values are used for calculating the fuels energy ratios for the diesel and gas modes
according to the following equation:
+
= m LHV,
= m g LHV g + mp LHV g
d
d
,
ERd = ,
, ER g =
(7)
E f ,total
E f ,total
Subsequently, the total fuel burning rate is calculated by using Equation (8), which provides
an adequate approximation of the total heat release rate for gas–diesel engines as deduced from the
analysis of the experimental results reported in [50]. Finally, the heat release rate is calculated using
Equation (6).
=
+ + ER ,x
xb = ERd, xb,d
(8)
g b,g
Figure 4. Combustion model procedure flowchart. Abbreviations: md : diesel fuel mass; mg : gas fuel
mass; mp : pilot fuel mass; xb : fuel burning rate, ECS: engine control system.
3.3. Engine Control System Modelling
The developed ECS model controls the gas admission valves, the diesel and pilot fuel injectors as
well as the engine waste gate at both steady state and transient conditions with fuel or load changes.
For the gas mode, the model is capable of identifying imposed step-wise load changes that exceed
the maximum allowed load change (via comparison against the manufacturer maximum step load
increase limitations), and subsequently implementing a mode switch from gas to diesel as specified
by the engine manufacturer requirements. In such scenarios, the engine operation is immediately
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switched to the diesel mode via a fast-acting signal, for the fuels and the waste gate controls. In addition,
requests for a diesel to gas mode switching above 80% engine load are not allowed as indicated by the
manufacturer [42]. The ECS operating mode controller was modelled to identify either the engine load
or the fuel transition (based on the manual input for ordered operation mode) and accordingly calculate
the respective combustion model parameters.
The developed ECS model assembly consists of the fuels (diesel main, diesel pilot and gas) and
the exhaust waste gate controllers. A flowchart illustrating the modelling philosophy and the logical
conditions of the developed ECS model is provided in Figure 5, whereas the structure and functionality
of the developed fuel control system is illustrated by using the flow chart diagram presented in Figure 6.
The ECS model includes the following elements: the logic controllers, the PID controllers for adjusting
the injected fuels amount, the fuel transition profiles (i.e., GTD and DTG) as well as the exhaust waste
gate (WG) controller. The ECS model employs two discrete control switches, which can be activated
or deactivated though a logic controller (mode controller) based on the fuel or the fuels employed at
the time (i.e., diesel or gas and pilot). In specific, for a load change at any operating mode, only one
of the two switches is activated based on the operating mode. However, during the fuel transition
operations, both switch controls are used in order to control the gas fuel, the pilot fuel and the diesel
fuel injection timing. Additionally, the injection controllers for each engine cylinder were set to adjust
the amount of all cylinder injected fuels and determine a suitable fuel change timing for each cylinder,
based on each cylinder phase angle.
Upon an ordered operating mode, the developed fuel control system actuates the gas, the diesel
and the pilot fuels injectors via a set of controllers, so that the engine is able to operate at: (a) steady
state conditions in the diesel or the gas modes (i.e., fixed load and no mode switching); (b) load changes
(transient operations) in the diesel or the gas modes; and (c) mode switching (transient operations)
from the diesel mode to the gas mode and vice versa.
In particular, for the diesel mode simulation at steady state conditions, a PID controller (Diesel
PID in Figure 5) adjusts the rack position of each cylinder diesel fuel pump that determines the fuel
amount of the respective diesel fuel injector, based on the engine speed feedback signal. This controller
employs a lambda limiter, thus preventing the engine to operate with low air–fuel equivalence ratio
values, which may cause incomplete combustion issues and high thermal loading. According to
the engine manufacturer [42], the pilot fuel is always injected in both engine operating modes, so
that wear and damage of the pilot injectors are avoided. Hence, the pilot fuel injection control (Pilot
controller in Figure 5) was set to appropriately adjust the pilot fuel amount in both the investigated
operating modes.
For the gas mode, the gas fuel supply pressure is assumed to linearly change as function of the
engine load, whilst an additional PID controller (Gas PID in Figure 5) adjusts the duration of the gas
admission valve opening based on the engine speed feedback signal, thus adjusting the mass of the
gas fuel injected per cylinder. The pilot fuel pressure is considered constant and the pilot fuel injection
amount is controlled for each cylinder. Moreover, the rack position of the diesel fuel pumps is set to its
minimum position (i.e., no diesel fuel is injected). It is expected that the engine speed error signal (i.e.,
difference between the ordered and the actual average engine speed) is zero during the engine steady
state operation in either the diesel or the gas modes, and as a result the employed controllers set the
corresponding controlling parameters. The employed PID controllers’ settings were tuned by using
the Ziegler–Nichols method according to the guidelines provided in [51].
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Figure 5. ECS model logical structure flowchart. Abbreviations: GAV: gas admission valve; GTD: gas
to diesel; DTG: diesel to gas; CRM: Current Running Operating Mode.
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Figure 6. Fuel control system functional diagram.
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For controlling the engine transient operation with load changes in the diesel or the gas modes, the
fuel control system follows a similar control strategy as described above for the steady state operation.
The controllers use the engine speed error (ordered speed to actual speed difference) as the input and
eventually control the injected fuel amounts depending on the operating mode, aiming to minimise the
engine speed error by adjusting either the rack position of each cylinder diesel fuel pump, or the gas
admission and the pilot fuel injection duration. Additionally, the fuel control system is also designed
to immediately change the engine operation to the diesel mode in cases where the ordered engine load
change exceeds the investigated engine maximum load acceptance criteria when the engine operates
in the gas mode. In this case, the transient operation involves both the load change and the mode
switching from the gas to the diesel modes. The fuel control system performs all the necessary control
actions (described in the following paragraphs) to initially achieve the mode switching (i.e., gas to
diesel) and subsequently to respond to the ordered engine load change.
For the control of the engine transient operation with a mode switching from diesel to gas (DTG),
the engine control system actually controls both the gas and diesel fuels (gas fuel pressure and injection
duration and diesel rack position), whilst the pilot fuel injection duration is also adjusted to control
the amount of the pilot fuel injected per cylinder. However, for the modelled engine control system,
the amount of the gas fuel injected per cylinder is controlled via an imposed profile with a positive
rate of change (slope) depending on the engine load, whilst the pilot fuel amount is calculated by
interpolation, employing a lookup table with the measured values for each engine operating point.
At the same time, the diesel PID controller adjusts the diesel fuel rack position based on the engine
speed feedback signal, and thus, determines the mass of the diesel injected per cylinder and per cycle.
It should be noted that the ECS model allows for the gas fuel injection only for the cylinders operating
in their open cycle period.
In the case of an ordered gas to diesel mode switching (GTD), the rack position of each cylinder
diesel fuel pump (determining the fuel amount of the respective diesel injector) is adjusted based on
the feedback of the diesel PID controller. The gas admission valves of the engine cylinders, in which
the injection has not started yet, are ordered to immediately close, based on an imposed step input
signal, whilst a step change input signal governs the amount of pilot fuel injected in each cylinder.
In either the diesel or the gas modes, the fuel control system takes into account each cylinder
phase angle during mode switching in order to determine if the ordered fuel change in each cylinder is
permitted and, hence, define the timing for implementing this fuel change. This is considered in order
to avoid a fuel change during the cylinders closed cycle or when the gas fuel injection is ongoing, which
may lead to engine speed and power fluctuations. The fuel control system was set to perform the fuel
change of each cylinder during the corresponding intake phase, prior to the gas fuel injection start.
The completion of the ordered engine fuel change is achieved when the fuel change is implemented
to all the engine cylinders. In this respect, the injection controllers were set to serve the purpose of
identifying whether the fuel change is permitted in each consecutive fired cylinder and whether the
fuel change has been applied to all cylinders. If the fuel change is not permitted in a cylinder due to
its ongoing operating phase, the initial fuel settings are applied until it reaches the intake phase of
the next cycle. The fuel change control actions are repeated until the fuel change is applied to all the
engine cylinders [25].
It must be noted that in the ECS model, the crank angle (CA) position information was taken from
the engine crankshaft block whilst considering the phase angle of each cylinder. The actual engine
control system employs two CA sensors (encoders) for measuring the crank angle; the first is located
in the flywheel, whereas the second is located in the free end.
4. Results and Discussion
Steady state runs were performed in a number of operating points, so that the derived performance
and emission parameters are compared with the respective experimental data from the engine testbed
trials. The steady state simulation results, along with a parametric investigation of the engine settings
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effect on the performance–emissions trade-offs, are reported in an author’s previous study [18]. From
the data presented in [18], it can be inferred that the model accuracy is sufficient in all the investigated
engine steady state operating points with the maximum value of the absolute percentage error being
smaller than 3.5%.
Following the engine simulation at steady state conditions, the developed model in GT-ISE was
used for simulating the engine transient operation including load and mode switching. Three cases,
for which published experimental data are available, were investigated in specific:
(a)
(b)
(c)
Case 1—the engine operation at 100% load in the gas mode and a mode switch to the diesel
mode [52];
Case 2—the engine operation at 80% load in the diesel mode and a mode switch to the gas
mode [52]; and
Case 3—the engine operation at 40% load in the gas mode and a step-wise load increase to 80%
engine load [25]. For this case, due to the large ordered load increase, a mode switch from the gas
mode to the diesel mode also takes place [25].
The first two cases were also presented in the authors’ previous study [20], where the validation
of the model results is discussed. However, the focus of that study was the safety analysis of the engine
systems, whereas this study focuses on analysing the engine response and the engine components
interactions as well as identifying the engine operational limitations.
For the three investigated cases, the predicted variations of the engine parameters including the
normalised rotational speed, the engine load and the normalised fuels amount (for the gas and diesel
fuels), the engine boost pressure, the exhaust gas temperature before the TC turbine, the TC shaft speed,
the waste gate opening, the air−fuel equivalence ratio (λ), as well as the locus of the TC compressor
superimposed on the compressor map are presented in Figures 7–9, respectively. In these figures, the
available experimentally measured parameter variations are also presented to serve the purpose of the
developed model’s validation. All the parameters except for the exhaust gas WG valve opening were
normalised by using their corresponding values at 100% load for the diesel mode, whereas the WG
valve opening was normalised by using its maximum area. It can be inferred from the presented results
that the model can predict the engine parameter responses with an adequate accuracy as discussed in
detail in the following paragraphs.
4.1. Case 1—100% Load-GTD Mode Switching
For the first investigated case, the engine parameter variations are sufficiently predicted as illustrated
in Figure 7. Both the simulation and experimental results show that the change of the engine operating
mode from gas to diesel took place within 1 s, whereas the engine recovery time was less than 3 s after
the ordered mode switching. The maximum engine speed and load drops from their initial values
were approximately 5% and 4%, respectively. The gas fuel was cut within 1 s in the consecutive firing
cylinders with a simultaneous fast increase of the injected diesel fuel, which exhibited an overshoot
(obtaining its maximum value at the 11th s of the simulation run) and a subsequent gradual reduction
until it reached its steady state value at the 14th s of the simulation run. This is attributed to the
PID diesel fuel governor model that detected and appropriately responded to an increased error
between the ordered and the actual speed (due to the engine speed drop). Based on the above, it can
be concluded that the engine operation complies with the manufacturer specifications/requirements
shown in Table 2, according to which the mode switch must occur within 1 s, the acceptable maximum
speed drop must be less than 10% and the acceptable maximum recovery time must be 5 s.
It can be observed from Figure 7 that a considerable reduction in the exhaust gas temperature
before TC turbine occurred immediately after the gas fuel cut off between the 10.5th s and the 11th s of
the simulation run. This is attributed to the fact that the gas fuel was immediately cut off, whilst the
diesel fuel rack position response was not as fast (i.e., the diesel fuel cannot instantly reach its required
value). This, in turn, resulted in the under-powering of a number of engine cylinders for a number
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of engine cycles after the gas full cut off at the 10.5th s associated with a temporary considerable
increase of the air−fuel equivalence ratio between the 10.5th s and 11th s of the simulation run, as
well as the temporary loss of the engine power, which reached its minimum value at the 11th s of the
simulation run. The gradually increasing injection of the diesel fuel (following the gas fuel cutting
off) resulted in the recovery of the engine power within 1 s after the time of its minimum value (the
engine load almost reached its steady state value at the 12th s of the simulation run), however it caused
a notable decrease of the air−fuel equivalence ratio to 1.5 at the 11.5th s. The latter is attributed to
the fact that the WG valve was open in the gas mode operation, and therefore− the air mass flow rate
was less that the one required for the engine to operate in the diesel mode. The lower exhaust gas
energy at the TC turbine resulted in corresponding reductions of the TC speed and the boost pressure,
which in turn moved the compressor operating point closer to the surge line of the compressor map.
For this investigated case, compressor surge did not occur, as the surge margin was adequate; however
careful consideration is required during the engine–turbocharger matching procedure to account for
the fast-transient phenomena
taking place during the GTD mode switching. It must be noted that
−
the predicted temporary engine boost pressure drop is also observed in the experimental results [52]
indicating that the simulation effectively captures this feature of the engine operation during the GTD
mode switching.
Figure 7. Case 1—GTD mode switching at 100% load; predicted engine parameters and comparison
with experimental data taken from [52].
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The fast increase of the injected diesel fuel in conjunction with the air−fuel equivalence ratio
drop resulted in a peak of the exhaust gas temperature (due to the diesel combustion with less air).
Following the mode switching order, the engine control system reacted by closing the WG valve, thus
increasing the exhaust gas flow rate (hence the energy rate) entering the TC turbine, which in turn
increased the TC shaft speed. The gradual increase in the TC shaft speed resulted in a respective
increase of the engine boost pressure (hence the engine air flow), which as a consequence gradually
increased the engine air−fuel equivalence ratio and reduced the exhaust gas temperature before the
TC turbine. All the engine performance parameters reached their steady state values approximately
8 s after the mode switching order; therefore, the engine restored its operation at steady conditions in
the diesel mode in the 18th s of the simulation run.
Based on the above analysis, the following points must be noted: (a) a GTD mode switching takes
place in a very short space of time (within 1 s) and therefore it is quite challenging for the engine and
its control system; (b) the WG valve control along with the engine–turbocharger matching are critical
parameters for the successful completion of the GTD mode switching as they affect the compressor
normal operation and the turbocharger response time (compressor surging as well as incomplete
combustion at the diesel fuel operation must be avoided) with implications to the engine air flow rate,
the combustion conditions, and the engine thermal loading; (c) considering that gas fuel operation
takes place only for the cylinders initially operating in either the closed cycle or gas injection phase,
knocking or misfiring do not seem as an issue during the GTD mode switching.
4.2. Case 2—80% Load-DTG Mode Switching
For the second investigated case where the engine operates at 80% load, it can be observed from the
respective plots of Figure 8 that the engine speed and load are also predicted with sufficient accuracy;
the maximum observed error between the predicted and measured results is less than 2%. However,
fluctuations are observed both in the engine speed and load from the experimental measurements,
which are attributed to the more considerable cycle to cycle variations of the engine gas mode operation.
A notable deviation in the prediction of the diesel fuel amount during this mode switching is observed;
however, this can be justified based on the employed method for the gas fuel amount estimation
in the modelled engine control system. In the actual engine control system, the gas pressure and
the gas valve opening duration are controlled; however, in the model only the latter is controlled,
whereas the gas pressure profile is assumed to linearly vary with engine load. In this respect, the
fuel transition is gradually performed within 2 min (approximately 100 s) where the gas, diesel and
pilot fuels are controlled. Based on the above, it can be concluded that the engine operation complies
with the manufacturer specifications shown in Table 2, according to which, the mode switching must
occur within 2 min, the acceptable maximum speed drop should be less than 10% and the acceptable
maximum recovery time should be 10 s.
In this case, the DTG mode switching is completed within 2 min and as a result, the transition
from the diesel engine mode to the gas mode is much slower and smoother compared with the GTD
mode switching. In the diesel mode, the engine operates with closed the WG valve, which results
in greater values of the boost pressure, the TC shaft speed, as well as the air−fuel equivalence ratio
and lower exhaust gas temperature before the TC turbine in comparison with the respective values of
these parameters at the gas operating mode. Following the mode switching order, the engine control
system reacted by increasing the WG valve opening to its maximum value (considering a WG valve
opening limiter in order to avoid compressor surging) at the 11th s of the simulation run; subsequently,
the WG valve opening was gradually reduced reaching its steady state value at the end of mode
switching (at the 112th s of the simulation run). The WG valve opening resulted in a decrease of
the TC shaft speed, and as a consequence, the boost pressure drop, as also can be observed in the
experimental results reported in [52]. In turn, this reduced the air flow into the engine cylinders, thus
decreasing the air−fuel equivalence ratio whilst increasing the exhaust gas temperature before the TC
turbine. The challenges for the engine operation during the DTG mode switching include the knocking
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condition avoidance due to the change of the air−fuel equivalence ratio as well as the compressor
surging avoidance. Therefore, it can be inferred that the WG valve control is critical for the smooth
engine DTG fuel switching.
Figure 8. Case 2—DTG mode switching at 80% load; predicted engine parameters and comparison
with experimental data taken from [52].
4.3. Case 3—Step Load Increase from 40% to 80%
For the third investigated case, the engine parameter response is examined under a rather abnormal
step-wise load increase from 40% to 80% in the gas mode. As this ordered load change is not permitted
in the gas mode according to the engine manufacturer (the maximum allowed step-wise load increase
is 20% for the case where the engine operates at 40% load in the gas mode as shown in Figure 2), the
engine control system orders a fuel transition from gas to diesel. The measured parameters were
taken from [52], where it is reported that they acquired from a plant with two generator sets initially
operating at 40% load. One of these two units exhibited an emergency shutdown, so that all the
electric load was transferred to the generator set in operation, thus resulting in its almost instantaneous
load increase. These engines are of the same type as the investigated engine in this study, however
the number of cylinders and their power are double the respective values of the investigated engine
herein. Thus, a greater inertia and a relatively slower response is expected in the measured data, as
also verified by the results presented in Figure 9. However, as [52] is the only available study in open
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literature with published measured results of such a considerable load increase that induces a GTD
mode switching, it was chosen to be used for validating the developed model herein.
Figure 9. Case 3—40–80% load change in the gas mode including a GTD mode switching; predicted
engine parameters and comparison with experimental data taken from [25].
The comparison of the derived engine parameter response with the respective experimentally
measured variations, which is illustrated in Figure 9, demonstrates that the model can adequately
predict the engine response during this transient operation. In specific, the results presented
− in
Figure 9 show that the mode switching from gas to diesel took place within 1 s, whereas the engine
recovery time was found to be slightly higher than 5 s. The maximum engine speed drop was found
to be 4% and 6% in the simulated and experimental cases, respectively. However, the engine speed
response is sufficiently captured.
Similarly, to the first investigated case, the gas fuel was cut within
−
1 s with a simultaneous rapid increase of the injected diesel fuel that retains its maximum value for
approximately 3 s due to the PID diesel fuel governor response following the detected increased error
between the ordered and the actual speed. The −diesel fuel amount started reducing from the 14th
s of the simulation run obtaining its steady state value corresponding to 80% load almost after 2 s.
An additional characteristic of this case (in comparison with the first investigated case) is the activation
of the lambda limiter to confine the injected diesel fuel for values of air−fuel equivalence ratio lower
than 1.1. This resulted in the slight drop of the injected diesel fuel amount between the 10.7th and 11th
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s of the simulation run. Based on the above discussion, it can be concluded that the engine response
complies with the engine manufacturers specifications as described in Table 2.
Similarities of the plotted engine parameters variations with the ones presented and discussed
for the first investigated case were observed. The rapid reduction of the gas fuel along with the
slower increase of the injected diesel fuel resulted in a temporary considerable increase of the air−fuel
equivalence ratio (slightly above 3) as well as a considerable decrease of the exhaust gas temperature
before the TC turbine and the corresponding decreases of the TC shaft speed and the boost pressure.
Due to the almost instantaneous increase of the engine load and the respective increase of the injected
diesel fuel amount, the air−fuel equivalence ratio reduced to very low values close to 1 at the 11th s of
the simulation run, denoting that the engine operation temporarily reached the limits for incomplete
combustion and smoke appearance. As explained above, the lambda limiter was slightly engaged,
reducing the injected diesel fuel amount. The air−fuel equivalence ratio increased after the 11th s of
the simulation run as a result of the effect of the WG valve closing and the increase of the exhaust
gas temperature (due to the diesel fuel combustion), which resulted in the increase of the exhaust
gas energy in the TC turbine and the corresponding increases of the TC shaft speed and the boost
pressure (also leading to the reduction of the exhaust gas temperature after the 12th s of the simulation
run). The engine speed was restored to its original value at the 15th s of the simulation run, which in
turn caused the decrease of the injected fuel to its steady state value and the corresponding changes
of the engine parameters slopes variations. The engine operation obtained steady state conditions
around the 25th s (7 s longer than what was required for the first investigated case). Similarly to the
first investigated case, this run is also quite demanding for both the fuels control system (due to the
fast mode switching) and the smooth compressor operation (compressor surging avoidance).
4.4. Engine Operational Limitations
In order to identify and map the engine operational limitations for the three investigated cases,
a number of engine performance parameters were considered along with their limits (upper or lower) as
proposed by the engine manufacturer [53]. These parameters were the following: engine speed, air−fuel
ratio equivalence ratio (lambda), exhaust gas temperature before the TC turbine, maximum cylinders
WG valve opening/closing area change rate. The employed metrics to characterise the criticality of the
engine operation include the percentage difference of each parameter from the respective limit and are
provided in Table 3.
From Table 3 results, it can be inferred that, in all the investigated cases, the engine speed drops
were within the allowed limits ranges, the cylinders maximum pressure was below its upper limit,
whereas the TC shaft speed was kept below its maximum allowed value. On the other hand, the
exhaust gas temperature exceeded the respective upper alarm limit for a very limited time for the
investigated cases with the GTD mode switching, however the engine shut down limit conditions
(alarm limit and duration) were not exceeded. Specifically, for the GTD mode switching in 100% engine
load (Case 1) the exhaust gas temperature (before the TC turbine) exceeded the manufacturer limit for 3
s with its maximum value being 5% above the limit. In Case 3 (GTD mode switching and load increase
from 40 to 80%), the exhaust gas temperature exceeded the limit for 4.5 s with its maximum value
being above the limit value by 26%. In the GTD mode switching, the air–fuel equivalence ratio in the
diesel mode exceeded the corresponding lower limit; for Case 1, the lambda exceeded the respective
smoke limit for less than 1 s with its minimum value being 6% below this limit; in Case 3, the lambda
exceeded the respective smoke (lower) limit for approximately 3 s with its minimum value being 27%
below this limit. It should be noted that the usage of a WG valve controller with a slower response or
stricter lambda limiter for the diesel fuel can be considered an option to mitigate this operational issue;
however, greater speed and power drops are expected in these cases. For the DTG mode switching, the
lower air–fuel ratio limit for the gas mode (knocking limit) was critically approached with the lambda
value being 6% above this limit. The compressor surge line was also approached for all the investigated
cases as shown in Figures 7–9 and the surge margin values presented in Table 3. The most critical cases
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for compressor surging were Cases 1 and 2, as the engine operates at high loads. This is connected
with the WG valve area change rate, which controls how quickly the WG valve opens or closes. In this
respect, it can be inferred that the WG valve almost instant closing is needed for avoiding compressor
surging issues and lambda values below the smoke limit for the GTD mode switching, whereas for the
DTG mode switching, a slower WG valve opening is required, so that compressor surging and lambda
mismatch (leading to knocking or misfiring) are avoided. In cases where the WG valve control fails to
provide the specified opening/closing area rates, compressor surging is highly likely to occur.
Table 3. Engine operating parameters deviations compared to the respective manufacturer limits.
Case 1
Case 2
Case 3
Engine speed
Within limits;
minimum value 5.3% above
the lower limit
Within limits;
minimum value 9.9% above
the lower limit
Within limits;
minimum value 7% above the
lower limit
Lambda
For the diesel mode: below the
lower limit for less than 1 s;
minimum value 6% below the
smoke (lower) limit
For the gas mode: minimum
value 6% above the knocking
(lower) limit
For the diesel mode: below the
lower limit for 3 s; minimum
value 27% below the smoke
(lower) limit
Exhaust Gas
temperature
before TC
Above the upper limit for 3 s;
maximum value 5% above the
upper limit; engine shut down
limit was not exceeded
Within limits;
maximum value 5% below the
upper limit
Above the upper limit for 4.5 s;
maximum value 26% above
the upper limit;
engine shut down limit was
not exceeded
Maximum
cylinder pressure
Within limits;
Maximum value 18% below
the upper limit
Within limits;
Maximum value 27% below
the upper limit
Within limits;
Maximum value 29% below
the upper limit
TC speed
Within limits;
Maximum value 5% below the
upper limit
Within limits;
Maximum value 14% below
the upper limit
Within limits;
Maximum value 13% below
the upper limit
Compressor
surge margin
Minimum value: 5.8%
Surge did not occur
Minimum value: 10.5%
Surge did not occur
Minimum value: 15.2%
Surge did not occur
The identification of these limitation metrics is quite useful to investigate solutions for mitigating
the potential engine safety and operational implications by considering both design measures and
engine settings optimisation. Examples of such solutions, which have been adapted by the engine
manufacturer in recent engine versions for reducing the likelihood for compressor surging, include the
modification of the engine manifolds design to introduce an air bypass loop and a bypass valve for
controlling the air flow from the compressor outlet to the turbine inlet [54], as well as the replacement
of the exhaust gas WG valve electric actuators by fast acting hydraulic actuators [55].
5. Conclusions
The integrated modelling (including the engine thermodynamic model and the control system
functional model) of a large marine DF four-stroke engine and its control system was developed in
GT-ISE to allow the simulation of the engine transient operation with fuel switching and load changes.
The engine control system and component functions were analysed based on the engine manufacturer
requirements, thus allowing for the development of the ECS model (also in GT-ISE) to adjust the
employed fuels (gas, diesel and pilot) and the exhaust gas WG valve under both steady state and
transient operating conditions. The developed integrated model was used for the investigation of three
representative engine operating cases with fuel and load changes for which experimental results were
published. Based on the analysis of the results, the developed model was validated, the engine and its
control system operation were delineated, and the engine operation limitations were discussed taking
into consideration the difference in the engine performance parameters from the manufacturer alarm
limits. The main findings of the conducted research are summarised as follows.
J. Mar. Sci. Eng. 2020, 8, 200
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The model extension/upgrading to accommodate the simulation of the transient conditions with
mode switching included: (a) the development of the control functional system model along with the
exhaust waste gate control and the fuels control modules; (b) the database development for storing the
Wiebe functions parameters as well as the combustion modelling during the various modes switching,
and; (c) addition of the transient simulations input parameters.
The challenge for the control system functional modelling was mainly attributed the complexity
of this system as well as the limited information available in literature.
The combustion modelling was challenging, as the model needed to accommodate the combustion
process of the employed engine fuels (gas, diesel and pilot) during the mode switching.
The followed approach for predicting the engine combustion performance during transients,
which included a database for storing the Wiebe functions parameters validated at steady state
conditions and the use of quadratic interpolation for predicting the combustion characteristics during
the fuel and load changes, proved to be sufficient for capturing the involved phenomena.
The developed engine control system represented the actual ECS operation realistically. However,
it was a demanding task, requiring attention to all the engine control subsystems and components as well
as their interactions, the sequence of the involved processes and the engine manufacturer requirements.
From the performed validation study, it was inferred that the developed model is capable
of sufficiently predicting the engine parameters response during transient operating conditions,
including fuel and load changes. Even for the almost instantaneous GTD mode switching, in which
modelling and simulation are fairly demanding tasks, the developed model succeeded in providing
sufficient predictions.
The developed tool provides the required accuracy and can be used with fidelity for investigating
both the steady state and transient engine operation.
The engine response for the investigated operating cases were found to satisfy the engine
manufacturer requirements.
The mode switching from gas to diesel (GTD) is rapid and must be completed within 1 s; therefore,
it is demanding for both the engine and its control system operation. The quick gas fuel cut off in
conjunction with the slower diesel fuel increase resulted in a temporary loss of power, associated with
a slight reduction in the TC shaft speed and the engine boost pressure. The subsequent reduction of
the air−fuel equivalence ratio and the increase of the exhaust gas temperature can result in smoke and
engine component thermal loading, respectively.
The mode switching from diesel to gas (DTG) has to be completed in a longer period (within
2 min), and as a result, smoother engine parameters variations were observed. The WG valve control
is critical for avoiding compressor surging issues as well as air−fuel equivalence ratio mismatching
between the diesel and the gas operating modes.
The exhaust gas WG valve control is a crucial part of the sophisticated and complex ECS for
ensuring the smooth and reliable marine DF engine transient operation with fuel and changes.
Careful consideration is required during the engine–turbocharger matching and the engine control
system design to accommodate the contradictory requirements for the GTD and DTG fuel changes.
The developed model’s computational time on a modern desktop computer with a single
processing unit is approximately 20–25 times the real time. The simulation time can be significantly
reduced by using a parallel computing approach. It must also be noted that the GT-ISE offers a tool to
develop a real time model, which can be used in future work for developing the real time digital twin
of the investigated engine.
In conclusion, the results of the derived analysis revealed the engine’s and its systems’ characteristics
during transients with fuel and load changes, enlightening the involved processes and associated
phenomena. In this respect, the developed model will be a useful tool for further developing, testing
and designing engine control system components. This model could form the basis to develop an engine
real-time digital twin, which can be combined with the engine monitoring system and machine learning
algorithms to provide new directions that ensure smooth, reliable and efficient engine operation.
J. Mar. Sci. Eng. 2020, 8, 200
25 of 29
Author Contributions: Conceptualization, S.S., G.T.; methodology, S.S., G.T., C.M.; software, S.S., C.M.; validation,
S.S., G.T., C.M.; formal analysis, S.S., G.T., C.M.; writing—original draft preparation, S.S., G.T., C.M.; writing—
review and editing, G.T., E.B.; visualization, S.S.; supervision, G.T., E.B.; project administration, G.T. All authors
have read and agreed to the published version of the manuscript.
Funding: No funding was received for this research.
Acknowledgments: The authors greatly acknowledge the funding from DNV GL AS and RCCL for the MSRC
establishment and operation. The opinions expressed herein are those of the authors and should not be construed
to reflect the views of DNV GL AS and RCCL. Gamma Technologies support is also greatly acknowledged by
the authors.
Conflicts of Interest: No potential conflict of interest was reported by the authors.
Nomenclature List
A
BMEP
BSEC
BSFC
Cf
D
dp
dx
Ef,total
e
FF
H
Kp
LHV
m
ṁ
md
mf
mg
mp
p
.
Qht
.
Qb
u
V
Greeks
a
.
xb
∆θg,i
θ
θSC_i
λ
ρ
Pipe cross-sectional flow area (m2 )
Brake Mean Effective Pressure (bar)
Brake Specific Energy Consumption (kJ/kWh)
Brake Specific Fuel Consumption (g/kWh)
Friction factor (−)
Pipe diameter (m)
Pressure differential acting across dx (Pa)
Discretization length (m)
Total fuel energy (J)
Total specific internal energy (J/kg)
Weight of Wiebe function (−)
Total specific enthalpy (J/kg)
Pressure loss coefficient (−)
Lower heating value (J/kg)
Mass (kg); Wiebe function parameter m (−)
Mass flow rate (kg/s)
Diesel fuel mass (kg)
Burnt fuel amount (kg)
Gas fuel mass (kg)
Pilot fuel mass (kg)
Pressure (Pa)
Heat flow rate (W)
Combustion heat release rate (W)
Velocity (m/s)
Volume (m3 )
Wiebe function parameter (−)
Fuel burning rate (−)
Combustion duration (deg)
Crank angle (deg)
Start of combustion (deg)
Air−fuel equivalence ratio (−)
Density (kg/m3 )
Abbreviation List
0D
1D
3D
BMEP
BSEC
BSFC
Zero-dimensional
One-dimensional
Three-dimensional
Brake Mean Effective Pressure
Brake Specific Energy Consumption
Brake Specific Fuel Consumption
J. Mar. Sci. Eng. 2020, 8, 200
CA
CO
CO2
DF
DTG
ECA
ECS
EEDI
EEOI
GTD
HC
HCCI
HFO
IMO
LHV
LNG
MARPOL
MCR
MGO
MISO
NG
NOx
PID
PM
SOx
TC
WG
26 of 29
crank angle
Carbon Monoxide
Carbon Dioxide
Dual Fuel
Diesel to Gas fuel change
Emission Control Area
Engine Control System
Energy Efficiency Design Index
Energy Efficiency Operational Indicator
Gas to Diesel fuel change
Hydrocarbons
Homogeneous Charge Compression Ignition
Heavy Fuel Oil
International Maritime Organization
Lower Heating Value
Liquefied Natural Gas
International Convention for the Prevention of Marine Pollution
Maximum continuous rating
Marine Gas Oil
Multiple Input Single Output
Natural Gas
Nitrogen Oxides
Proportional–Integral–Derivative controller
Particulate Matter
Sulphur Oxides
Turbocharger
Exhaust gas waste gate
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