Zero-dimensional modelling of a four-cylinder turbocharged diesel engine with variable compression ratio and its effects on emissions
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With emission legislation becoming ever more stringent, declining fossil resources and an increase in greenhouse effect caused by CO2 emissions, manufacturers are exploring new ways to match the emissions regulations without compromising on the performance of the engine. This study included development of zero-dimensional model of a 2.0 L turbocharged diesel engine and then study the effects of changing its compression ratio in the numerical model. This paper gave a framework in determining the effect of compression ratios in different operational conditions of the engine. Implementation of variable compression ratio technology on a numerical model proved to be very cost-effective, time saving and validated the fact that numerical models can be used to study different parameters of the engines during the development stage. The main effect of an increase in compression ratio, was found to be as expected, a decrease in brake specific fuel consumption and an increase in thermal efficiency with a greater impact at low rpm-low load regions. Assuming, that the variable compression ratio technology can be utilized in the engine, this work found the best combination of compression ratios around the engine map, giving a best fit of trade-offs between the emissions and performance of the engine. This study also validates the fact that variable compression ratio technology, if implemented in the engine could not only reduce emissions of the engine but can be given as an option to the end-user to switch to more economic fuel consumption values during idling or cruising at long distant journeys.
KeywordsInternal combustion engine Variable compression ratio Numerical modelling Combustion Emissions Zero dimensional
Bottom dead centre
Brake mean effective pressure
Brake specific fuel consumption
Charge air cooler
Digital analogue convertor
Diesel particulate filter
Exhaust aftertreatment system
Electronic control unit
Exhaust gas recirculation
Homogeneous charge compression ignition
Hardware in the loop
Indicated mean effective pressure
Lean NOx trap
Mass flow of fuel
Mass fuel of intake air
Mass fuel burnt 50%
Model in the loop
Model based engine optimization
Oxides of nitrogen
Pressure at engine out
Peak firing pressure
Wall heat transfer
Real driving emissions
Revolutions per minute
Rate of heat release
Selective catalytic reduction
Specific fuel consumption
Software in the loop
Start of combustion
SAAB variable compression
Temperature at engine out
Top dead centre
Variable compression ratio
Variable geometry turbo
Variable nozzle turbine
Variable valve timing
With emission legislation becoming ever more stringent, declining fossil resources and an increase in greenhouse effect, manufacturers are exploring new ways to match the emissions regulations without compromising on the performance of the engine. A “Not-To-Exceed” zone is also being introduced as a part of these legislations, where tail pipe emissions must not exceed a specific value. Legislations like these break the stronghold of keeping these engines economical under the same performance circle. Although new technologies like the control methods, exhaust gas recirculation (EGR), and variable valve timing (VVT), have helped to reduce the NOx and soot emissions considerably [1, 2, 3, 4, 5, 6, 7, 8], further measures are to be taken to meet the increasingly restrictive emission standards.
It is of no contradiction that diesel engines are in the top list to face emission limitations in near future and the trade-offs between NOx–CO2–Soot emissions must be handled without compromising on the performance outputs [9, 10].
Several techniques and methodologies have been introduced in making combustion leaner and lower the emission levels. One way to reduce these pollutant emissions is using the technology called homogenous charge compression ignition (HCCI) combustion. It consists of preparing a highly homogenous air/fuel mixture that will result in a homogenous and efficient in-cylinder combustion. Thus, a complete and controlled combustion would mean better performance, lower emissions and above all no soot is produced .
Among many other factors, compression ratio is a direct influencer on the performance of the engine. In engines, a fixed compression ratio over the whole load and rpm range caps a limit on its operational efficiency and emissions over different regions. In conventional engines, a fixed compression ratio is selected which successfully operates it at variable rpms and loads meanwhile achieving a reliable self-ignition when starting the engine at cold-start.
The real problem is the fact that a fixed compression ratio of internal combustion engine is not optimal for all operating conditions. It is normally set as a compromise between partial and full-load requirements. A very high compression ratio could improve high part-load efficiency but will result in a knock (gasoline engines) and peak pressure limitations in diesel engines. An engine a fixed with low compression ratio provides performance with low maximal cylinder pressure which in turn means low frictional losses, costs and weight of the engine but limits the maximum achievable torque. An engine like this requires a glow plug which gives it a cold start ability resulting in a more stable idle operation and less smoke [11, 12, 13, 14]. Therefore, the new technology of variable compression ratio (VCR) offers more flexibility in terms of controlling power and emissions at different operating load conditions.
Turbocharged diesel engines are usually also restricted by the stress levels in moving mechanical components. With an increase in boost pressure, maximum pressure, thermal loading and friction losses also increase proportionally, unless engine design and operating conditions are changed. Practically, compression ratio is often reduced in turbocharged engines to maintain peak pressures and thermal loading at acceptable levels .
VCR technology could not provide a cold-start ability but also could change the engine’s combustion capability in such a way to get the optimal trade-offs of emissions, performance and fuel consumption at desired rpm and loads . Different VCR methodologies implemented in the industry are also critically being examined to understand its applications and scope and a thorough study in this context can be found in .
A study comparing the experimental results with numerical modelling results was performed before in . But as per our knowledge, no previous study has been done comprising of a detailed model especially implementing VCR directly in the numerical model and comparing the performance parameters in terms of engine maps.
According to theoretical studies, the overall efficiency of internal combustion engines can be improved: up to 40% for otto and up to 50% for diesel engines. Efficiency of over 50% is achieved only by two-stroke marine diesel engines [19, 20].
Early stage calibration is a way to assure meeting of the emission requirements at various ambient conditions while still delivering the desired engine performance and fuel consumption. In this process the major concern always remains to find the optimal compromise between emission, performance and fuel consumption targets under all ambient conditions and to achieve this with very limited access to non-standard engine tests beds.
Modern numerical models and tools help to pre-calibrate these engine correction functions at a virtual testbed embedded with numerical models of the engine. This delivers an identical environment as on real testbeds, while saving time and money. With emission standards becoming narrower every day, these simulation tools can prove to be very effective in development process to meet the standard called real driving emission (RDE). The virtual test-bed is setup with high precision empirical and physical models/components to simulate the real working of the engine under different scenarios as accurately as possible. This widely helps in combustion refinement and pre-optimizing the thermodynamic cycle of the engine.
‘Concept-to-Road’ calibration is therefore considered an important part of the pre-prototyping phase. A baseline requirement of numerical validation is based on data of the base model of the engine from real testbed. Therefore, numerical modeling tools play a crucial part in the optimization and validation of the powertrain development process providing a very swift and cost-effective way at the early development stages, before even the prototype becomes available.
The aim of this work is to develop a zero-dimensional numerical model of a 2.0 L four-cylinder turbocharged diesel engine in AVL Cruise-M (MoBEO-model based engine optimization)  which will then be simulated with VCR technology to understand the effect of this technology on the performance and emissions of the engine.
Modelling of the thermodynamic cycles of the engine is very easy and understandable. However, these cycles become more complex when combustion refinement is being performed by tuning various parameters of the engine. Thus, there are limits to which these parameters can be altered in the thermodynamic processes. The influence of compression ratios on the changes in thermodynamic combustion process in an engine has been studied in  and is considered while modelling the engine.
The first part of this study will focus on the methodologies for correlating dynamic simulations with any performance parameter in the dynamic engine operation with insights on the emissions data. This correlation can be performed using simulated test runs within AVL’s mean value engine model, MoBEO. Using this approach, the main objective will be to explain how the correlated engine values and the small differences between measure and simulated results can be sourced by specific dynamic phenomena and how they impact the obtained results. It will also help to understand that having a correlation between the model and measurement data, can help in achieving front-load calibration with a very high level of confidence. This study will also summarize the factors which are influenced by changing compression ratio in diesel engine, which may be used in developing a strategy towards the concept of ‘One Engine for all fuels or One Fuel for all engines’ .
This work can help in developing an industrial approach towards zero-dimensional numerical model of a real engine and could add to the confidence on relying at such models. One of the main aims of the work is also to show the load conditions of the engine terms of various regions on engine maps. This would help in framing the zones in the engine map where VCR technology has the maximum and minimum effect on the emissions and performance of the engine. An optimal compression ratio specific to each region can also be suggested through this process.
Effects of several operating parameters will also be studied using the obtained results which can act as a solid rung towards showing the strategies to be utilized for further studies.
2.1 Zero-dimensional modelling approach
Cruise-M was used to create the numerical model of the engine. MoBEO is a tool developed by AVL GmbH which integrates empirical and physical models. This means that the airpath of the modelled engine was fully physical whereas, the cylinder model was based on semi-physical modeling approach as can also be seen in Fig. 5. Instead of complex cylinder configurations, MoBEO enables ‘concept model capability’—tune the cylinder using fit-parameters based on ten thousand of engine test bed measurements. Thus, it demands 25 basic cylinder and fueling parameters measured from the testbed in order to perform the combustion refinement based on previously embedded data. Emission models are a part of this semi-physical approach. More details regarding the empirical, semi-physical and physical based models used by MoBEO can be accessed from .
A numerical diesel engine generally deals with mean engine values of performance and emission parameters (pressures, flow rates, temperatures, boundary conditions etc.). Moreover, the aftertreatment system can also be integrated and dealt in detail within the model. Since the complexity of the engine increases when testing change of compression ratios on physical testbeds, a numerical approach to study the trending technology of VCR can be useful in validating the circumstances which give the optimal trade-off of performance and emissions. One of the most vital advantage of engine modelling is the cut-off in both costs and time. Virtual test beds with engine models can save a lot of expenses that could otherwise incur during modification and testing process on real testbeds.
Numerical models cannot always replace the test-bed engine testing but could produce very close estimates of changes in the operational conditions, emissions and performance. This vastly helps in predicting the relevant parameters and selecting the best case during the engine development stage.
Basis of powertrain engineering is to enable a rapid setup of numerical model and to use it in a wide variety of applications. The engine domain is the heart of the entire multi-disciplinary model-based development solution. This becomes possible because of dedicated numerical solvers that work at explicit constant time step and implicit adaptive time step integration using transient and steady-state zero-dimensional component models. A steady-state approach is normally applied in modelling the basic flow characteristics. Numerical models are not only capable of being faster than real-time but also support a very high amount of cycle simulations with different hardware variants. They are also capable of transient system operation which makes it easier to study stochastic changes of the engine and exhaust gas aftertreatment system.
2.2 Single zone combustion model
2.3 Variable compression ratio
There are three direct methodologies through which an efficient combustion can be achieved in the engine: downsizing, supercharging and varying the compression ratio .
Varying the compression ratio in a running engine is a new technology that has been developed called variable compression ratio, which radically improves the fuel consumption without impairing engine performance at certain regions of the engine map. VCR engines have been categorized into several classes in .
VCR is a technology which directly changes the compression ratio of the engine by changing the stroke under the same operating conditions. This phenomenon diversifies the engine to adjust its compression ratio directly according the load and performance need. Diesel engines have high thermal efficiencies as compared to gasoline engines mainly because of their higher compression ratios. As compression ratio decreases, both the gas pressure and temperature decrease at the end of compression stroke, thus it has a very critical influence on the combustion process and ultimately the performance of the engine.
Diesel engines normally have compression ratios between 14:1 to 25:1. Higher compression ratios mean a higher thermal efficiency, which means that theoretically maximum efficiency can be achieved at an infinite compression ratio. However, a high compression ratio results in higher cylinder pressures and temperatures which limit it to a certain value.
A higher compression ratio also results in an increase in frictional losses and lowers down the mechanical efficiency . Furthermore, it also increases heat transfer to the combustion chamber walls due to small clearance volume resulting in a very high temperature gradient. High compression ratio also comes with shortened ignition delays as both pressure and temperature in the cylinder increase during fuel injection. Moreover, not only the weight and cost of the engine increases but it also introduces more complexity, frictional losses and unburnt hydrocarbons. Theoretically, the brake thermal efficiency increases with an increase in compression ratio, reaches an optimal maximum value and does not show any further increase after a certain compression ratio value.
In conventional engines, the minimum compression ratio is calculated such that it supports the start of engine with little amount of fuel (very low load operation) or cold start (when temperatures are below 0 °C). Starting from that minimum compression ratio, a single compression ratio value is then determined which gives a perfect trade-off between the emissions and performance at different operational conditions. One of the important facts is that diesel engines do not run at the same loads. For instance, at a long-distance motorway journey, the engine will operate at low load/idling condition while during acceleration, it will work under full load conditions.
With a VCR engine, compression ratio can be increased at start-up and low power operations to get a stable ignition and operation, while the compression ratio can be lowered during high load operations to get more power by burning more fuel. Therefore, the VCR concept can be considered as a very reliable solution to the problems being faced by engineers in varying the combustion conditions in the engine during different load conditions. An engine with VCR makes it possible to increase its overall efficiency, by choosing high compression ratios at low loads to maximize the efficiency, and low compression ratios at high loads to avoid knock (in case of gasoline engines).
Volvo/Alvar engine varies the volume of the combustion chamber through a secondary piston in the cylinder head . The constrain to this design was that since it had four valves per cylinder, supercharging was also necessary to achieve the effect completely.
SAAB practiced variable compression ratio technology through its SVC Engine. The technology was implemented by repositioning of the cylinder or cylinder head .
FEV is also realized this technology by working on different methods. One of them was to use a connecting rod with variable length . While the other one used eccentric bearings that change the TDC and BDC positions of the piston .
3 Specifications of engine
2.0 L (1996 cc)
Number of turbochargers
Single stage turbocharged
Type of turbocharger
Variable geometry turbocharger
Number of cylinders
In-line four cylinders
Fuel injection type
One pilot and one main
125 kW @ 3500 rpm
Max torque/speed range
405 Nm @ 1750–2500 rpm
Idle engine speed
Maximum engine speed
4 Model setup
Numerical Modelling was performed using AVL Cruise-MoBEO tool with measurement data of actual engine obtained by dynamometer tests.
A standard AVL engine development testbed with 220 kW dyno and inhouse sensors was used in the collection of different parameters. The sensors were mounted on the test bed upstream and downstream of all the engine components in order to record all the maximum possible pressure, temperature, emissions readings of a running engine on the required test points. The data was collected using AVL PUMA software interface.
Steady-state data collection requires a waiting time for the engine to reach that desired steady state and the readings were then recorded for a certain amount of time. Several readings of the same point were taken, and log-point average of the obtained readings was used.
An intensive data check of the raw data from sensors was performed using post-processing software, AVL Concerto, in order to make sure that the collected data correlated with each other as well as general trends expected to be observed. Out of 300 logged points, only 236 points were filtered to be usable for steady-state characterization of the numerical model.
4.1 Standalone model simulation
Standalone model approach is used to check if MoBEO model configuration fits the combustion parameters of the engine.
4.2 Full model characterization and simulation
After the creation of general engine model, sizing of components including their volumes, dimensions, heat transfer coefficients and other parameters are set to concede with the physical components. The model consists of plenums, restrictions, solid walls, turbo components, heat transfers and other components like functions and constant table blocks. PID controllers are used to characterize the required components.
After the whole model is characterized, a full open-loop (without PID control) simulation is given to see the proximity of the model with the actual measurement data. Some tunings/refinements are also performed after this stage to eliminate minor characterization errors. The obtained 236 steady-state log points at different load conditions were validated at steady-state and transient conditions to make sure they pass the quality gates of the characterized parameters of the engine model.
4.3 VCR simulation setup
5 Results and discussion
5.1 Results from steady state simulation
VCR Simulation study was conducted after the validation of the correct working of the open loop numerical model of the engine.
5.2 Results from numerical model with VCR
5.2.1 Strategy of VCR implementation in numerical model
All the maps of the engine are given in terms of rpm on x-axis, torque on y-axis and percentage change on z-axis. The main strategy applied to the model was to keep the torque and rpm constant with the operational map of CR16.5. At different compression ratios, torque was expected to increase or decrease for the same fuel quantity, thus a shift in the whole map can occur and could make the comparison of the graphs complicated and more difficult. Therefore, the same set-point torque was achieved by connecting a PID to control the fuel quantity.
5.2.2 Mass flow of fuel
As explained earlier, the torque was kept constant at every set-point by changing the fuel quantity using a PID.
As the compression ratio increases, the torque produced for the same fuel quantity also increased, thus PID decreased the torque to the original point by decreasing the fuel quantity.
5.2.3 Brake specific fuel consumption
The effect of this change is seen to be more at low load-low rpm conditions and this trend decreases at high load-high rpm conditions.
5.2.4 Mass flow of intake air
5.2.5 Thermal efficiency
Matching the inverse proportionality of the formula shown above and trend shown in BSFC values in Fig. 23, it can be clearly observed that the thermal efficiency increases as compression ratio increases and decreases as the compression ratio decreases.
This change is seen to be more prominent at low load-low rpm conditions and becomes less prominent towards high load-high rpm conditions.
This phenomenon is based on the fact that a higher compression ratio means a more complete combustion and combining it with the observation from Fig. 20, less fuel is needed to achieve the same torque, means less heat energy will be produced which will ultimately result in a lower temperature; reducing the production of NOx.
The effect is more prominent at low load-low rpm conditions while some of its prominence can also be seen at high torque-low rpm values.
5.2.7 Mechanical efficiency
5.2.10 Engine out temperature
5.2.11 Engine out pressure
In the early stage design of the engine, the pressure difference between the intake and exhaust manifolds of the engine is always considered and studied with importance, to make sure it remains within an acceptable threshold.
A wide difference could result in malfunctioning of various engine components. For instance, if the difference is too high, a slight opening of EGR valve could result in massive flow of air to pass by it and could ultimately lead to a malfunction of airflow control.
5.3 Summary of results based on zones
Zone 1-covering low load area from low until normal operating rpm values;
Zone 2-covering middle load area from normal until high operating rpm values;
Zone 3-covering high load area (including rated power) with very high rpm values
A high compression ratio in these zones only increases it by 0.71% and 0.30% with CR18 and 1.57% and 0.40% with CR20. Thus, this change is not as much as can be observed at low load conditions, where normal thermal efficiency was around 25% and was observed to increase by 9.70% at CR20.
BSFC decreases by 8.14%, 1.54% and 0.37% in Zone 1, 2 and 3 respectively when compression ratio is 20. Observing changes in emissions at the same set point, it is seen that NOx decreases by 8.33%, CO2 by 8.50% while Soot increases by 6.91%. This clearly suggests that a higher compression ratio should be preferable in Zone 1.
Observing soot and BSFC values with CR20 in Zone 2 and 3 clearly suggest that it is not preferable as a good trade-off. Soot values clearly suggest that a low compression ratio is preferable for Zone 2 and 3. For a smooth transition between Zone 1 and 2, a compression ratio lower than 18 for Zone 2 may result in a sudden jerk produced by the engine. Keeping this in mind, a compression ratio of 18 is preferred for Zone 2.
The transition of compression ratios between the zones is always kept as smooth as possible to avoid any sudden unwanted behaviour from the engine.
Finally, to keep up with the smoothness trend and to avoid any further decrease in performance, the default compression ratio of 16.5 is preferred in Zone 3.
The main effect of an increase in compression ratio, was found to be, as expected, a decrease in brake specific fuel consumption (BSFC) and increase in thermal efficiency. However, this trend comprised on the best efficiency-emissions trade-off for low rpm-low load region of the map (Region 1). With an increase in load and rpm (Region 2 to Region 3), the trade-off gap between efficiency and emissions becomes wide off since soot starts to become a prominent factor leading to uncompromisable level.
Assuming, that the instantaneous VCR changing technology can be utilized in the engine, this work found the best combination of compression ratios around the engine load map, giving a best fit of trade-offs of the engine.
The developed numerical model of the engine proved to be a great help in studying VCR concept on an existing engine and proved that numerical modelling can save a lot of expenses in studying concepts like these in the development phase of the vehicle. However, there are some limitations to the numerical model approach such as; not having a complete insight of all the emissions, as improving one factor of emission can prove to vastly effect the emissions which are not given by the numerical model. Moreover, the aging factor of the engine also could not be taken into account using this approach.
Numerical modelling can greatly aid in getting an idea on the engine being developed at initial stages before the prototype becomes available. The numerical model can also be used in calibration of the engine if soft-ECU is developed in the model;
An engine equipped with VCR technology can increase the efficiency and decrease the emissions at different operational conditions;
Increasing compression ratio at low load operations highly increases the thermal efficiency and decreases NOx. At the same time, soot emissions increase in the same operational conditions;
Future vehicles with the concept of ‘one engine all fuels–one fuel all engines’ will be key option in development of future transport in the world.
First, I would like to thank my family for supporting me at all times. I would also like to thank everyone at Marmara University and AVL Research and Engineering Turkey for a nice and stimulating time, especially to my supervisor, Prof. Dr. M. Zafer Gül and Department Manager, Mr. Caner Bayburtlu for their encouragement and valuable ideas. Further, I would like to thank Ramazan Şener for all help in the lab, and Oğuz Ulutürk for his precious time and aid in modelling of the engine. Furthermore, I would like to thank BAPKO (Bilimsel Araştirma Proje Komisyonu) for their support through Project Number: FEN-C-YLP-200318-0113.
Compliance with ethical standards
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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