Main Chamber Jet Ignition Calibration
6.2 Genetic Algorithm
The calibration was carried out by using the Integrated Optimizer provided by Gamma Technologies, which proposes the use of a Genetic Algorithm (GA) for calibrating other predictive combustion models, likewise the SITurb. A genetic al-gorithm is a search heuristic that is inspired by Charles Darwin’s theory of natural evolution. Five phases are considered in a genetic algorithm:
1. Initial population 2. Fitness function 3. Selection
4. Crossover 5. Mutation
Turbulent Jet Ignition (TJI) Combustion Modelling in GT-Suite
The process begins with a set of individuals which is called a Population. Each individual is a solution to the problem that has to be solved. An individual is characterized by a set of parameters (variables) known as Genes. The fitness function gives to each individual a fitness score, concerning the probability that an individual will be selected for reproduction is determined. The idea of the selection phase is to select the fittest individuals and let them pass their genes to the next generation.
After the selection phase, hybrid solutions are generated through the crossover phase, during which some parts of the genes of the selected individuals are mixed to gain new solutions. Basing on some coefficients previously defined, a mutation is applied to some individuals of the population obtained by casually changing some Genes.
The mutation is applied to either improve the value of the fitness function or extend the research space to avoid local optimum configurations. After the mutation phase, the procedure is restarted from point 2.
There are some parameters that characterize the GA setup (i.e. the ones shown Table 6.2). If the optimization setup is not adequate, the evolution of the optimization could be unsuccessful. As an example, the generic function shown in Figure 6.9 can be considered. Assumed that a GA is used for finding the global minimum of this function, if the GA setting is not adequate, it is possible that the local minimum is given as a result of the optimization. This condition is enhanced by the high complexity of our case study, characterized by a high number of calibration parameters (7).
Figure 6.9: Case Sweep Optimization - min. ANHRR RMSE
In our case, the fitness function aims to minimize either the MC ANHRR RMSE (eq. (5.3)), or the MC Pressure RMSE (eq (5.4)). The software allows to run either an independent optimization for each case considered, or a case-sweep optimization.
The former is able to find a set of calibration parameters for each operating point that minimizes the ANHRR/Pressure RMSE of that point; the latter permits to define a unique set of calibration parameters able to minimize the value of RMSE averaged over all the operating points.
6.3 Calibration Results
As described in chapter 5, the MC Jet Ignition model was tuned through the usage of the Integrated Design Optimizer with the III genetic algorithm. NSGA-III algorithm performs a broad search of the design space and is the recommended choice for problems with any moderate to high complexity: when using three or more factors, for multi-modal problems, and/or when working with very non-linear problems ([3]). The calibration was performed on two operating points: 3000x100%
and 6500x100%.
At first, since no reference was available, the Jet Ignition combustion was calibrated by imposing the upper and lower limits shown in Table 6.1. The set-up of the optimizer is described in Table 6.2, and it is inherited from the GT-manual guidelines for the SITurb combustion calibration ([3]).
Parameter Value
Population Size 30
Number of Generations 34
Crossover Rate default (=1) Crossover Rate Distribution Index default (=15)
Mutation Rate 0.5
Mutation Rate Distribution Index 15 Table 6.2: Genetic Algorithm Optimization - Setup
The number of combinations investigated by the optimizer is given by the multiplica-tion of the populamultiplica-tion size and the number of generamultiplica-tion (1020 cases). As suggested by Gamma Technologies, the calibration was initially conducted with the aim of minimizing the main chamber Apparent Net Heat Release Rate RMS error. In the
Turbulent Jet Ignition (TJI) Combustion Modelling in GT-Suite
prechamber, the Wiebe profiles able to match the timing of the jet were chosen (Figures 5.18 and 5.19 - blue curves). The results of the case-sweep optimization, which have room for improvement, are shown in Figure 6.10.
Figure 6.10: Case Sweep Optimization - min. ANHRR RMSE
In order to evaluate the differences of the Jet Ignition combustion model between the operating points considered, an independent optimization aimed to minimize the ANHRR RMSE was run (Figure 6.11 - blue lines).
As shown at 6500x100%, the set of multipliers that best fits the ANHRR provides a bad fit of the main chamber pressure, despite the strong relationship between the pressure and the heat release rate profile.
This behaviour can be explained by the equation (5.3): the integration starts from t0, the predicted combustion start, without considering the mismatch with the measured
ANHRR of the first phase. For this reason, the optimizer attempts to fit the peak of the release rate by delaying the predicted start of combustion.
Figure 6.11: Independent Optimization - min. ANHRR RMSE vs min. Pressure RMSE
Due to this, a user-defined routine, which is able to calculate an error between the measured and the predicted main chamber pressures, was manually built (Figure 6.12 - equation (5.4)).
The results of an independent optimization carried on with the aim of minimizing the pressure RMSE are displayed in Figure 6.11 - green lines. As shown, the fit on the 6500x100% operating point improves, being the pressure RMSE objective function more adequate than the ANHRR RMSE to describe the match between the measured and the predicted combustion.
Turbulent Jet Ignition (TJI) Combustion Modelling in GT-Suite
Figure 6.12: Pressure error calculation routine
In both cases, the results obtained on the 3000x100% point are unsatisfactory, mak-ing necessary an assessment of the GA settmak-ing described in Table 6.2. In order to understand if the optimizator provided a set related to a local minimum, a DoE anal-ysis was run. The DoE analanal-ysis allows to assess several combinations of calibration parameters.
The DoE setup is summarized in Table 6.3.
Calibration Parameter Lower Lim. Upper Lim. # of levels
Entrainment Rate Multiplier 0.95 1.25 4
Ignition Delay Multiplier 1 1.6 5
Premixed Combustion Rate Multiplier 0.05 0.25 3
Diffusive Combustion Rate Multiplier 0.4 1 3
Turbulent Flame Speed Multiplier 0.5 0.9 9
Taylor Length Scale Multiplier 1.5 3 6
Dilution Effect Multiplier 1.5 2.5 6
Table 6.3: Jet Ignition Model - Calibration Parameters - DoE setup
The number of levels indicates the number of cases investigated for a given calibra-tion parameter. The cases explored are evenly-spaced (i.e. the PCRM can take the values: 0.05 - 0.15 - 0.25). The upper and lower limits and the number of levels of each multiplier were accurately chosen in order to limit the number of cases to be run. The ranges of values considered were defined on the basis of the results obtained from several optimizations previously carried out. The DoE setup led to the assessment of 58320 cases, hence this approach to the minimum search requires a large amount of time and is suitable only when the operating points are few.
The set of calibration parameters which minimizes the pressure RMSE (for each case) obtained through the DoE resulted in the green lines (Figure 6.13).
Figure 6.13: Min. Pressure RMSE - Optimization VS DoE analysis - Ranges of values of Table 6.3
In the meanwhile, a pressure RMSE-based independent optimization was run, con-sidering the same ranges of values of the DoE analysis (Table 6.3), resulting in the blue lines (Figure 6.13).
An important results can be earned from Figure 6.13: for the ranges of values shown in Table 6.3, the optimizer setup is robust enough, being the optimum configuration provided by the optimizer very close to the optimum from the DoE analysis.
The results obtained from two optimizations carried on aiming at minimizing the pressure RMSE on the ranges of values shown in Table 6.1 and Table 6.3, are dis-played in Figure 6.14.
Turbulent Jet Ignition (TJI) Combustion Modelling in GT-Suite
Figure 6.14: Optimization - min. Pressure RMSE - different ranges of multipliers
If the ranges are more extended (fuchsia curve), at 3000x100%, the optimizer pro-vides a result related to a local minimum (the pressure RMSE of the fuchsia curve is higher than the one of the blue case). This occurs because the optimizer has to explore a wider region of the objective function, increasing the likelihood of finding a local minimum. The combinations of calibration parameters which give the fuchsia curves is external to the ranges of the DoE analysis.
Hence, the GA setting used (Table 6.2) should be improved when the ranges of values to be explored are wider (likewise the one shown in Table 6.1).
The set of calibration parameters, obtained from the DoE analysis, which minimizes the pressure RMSE averaged over the two cases, results in the blue curves of Figure 6.14, which allows to state that for the ranges of values shown in Table 6.3, a single set of calibration parameter values able to properly describe the Jet Ignition
combustion at both operating points does not exist in this version of the software (v2020).
Figure 6.15: DoE analysis - Case sweep optimum - min. Pressure RMSE
Finally, a case sweep optimization was conducted on both operating points, with the aim of minimizing the pressure RMSE, considering the ranges shown in Table 6.1.
The results are displayed in Figure 6.16. In this case, the pressure RMSE is lower than the one of Figure 6.15, but the results have ample room for improvement.
Turbulent Jet Ignition (TJI) Combustion Modelling in GT-Suite
Figure 6.16: Case sweep Optimization - min. Pressure RMSE
Chapter 7
Methodology
In this chapter a brief description of the methodology developed is provided. This workflow takes into account the tool potentialities, the limitations encountered and the results obtained. It is assumed that a detailed model of the engine considered is already available and validated.
1. Building of a simplified model
The construction of a simplified model (likewise the one shown in Figure 7.1) from the detailed one, allows to:
• Reduce the computational cost;
• Set a Three Pressure Analysis (TPA) in the Main Chamber, useful for the following steps.
The main inputs of the simplified model are the prechamber and the main chamber measured pressure traces (obtained, in our case, from 3D-CFD), and the intake and the exhaust instantaneous pressures. The predictive combustion model in the main chamber resulted to be dependent on the simulation time-step; for this reason, the simulation time-step used in the simplified model should be similar to that resulting from the detailed one. It is possible to impose a user-defined time-step through the General folder of the Advanced Setup. Further information regarding the simplified model is given in chapter 4.
Figure 7.1: Simplified Model of engine - Input Data
2. Prechamber Modelling
The SITurb is not able to properly describe the PC combustion in GT-ISE v2020, as confirmed by Gamma Technologies. The prechamber geometry has to be modelled; since the only adequate prechamber combustion model is non-predictive (SI Wiebe Model), a simple geometry description of the precham-ber (volume and surface) is sufficient. In case of predictive combustion in the prechamber, the advanced setting should be used coupled to a calibrated flow model. A procedure similar to chapter 5.1 can be used either for the prechamber.
3. Prechamber Connector Modelling
The nozzle number and the nozzle diameter have to be defined in the precham-ber connector (Figure 7.3). Before starting with the prechamprecham-ber Wiebe com-bustion calibration phase, a reasonable value of nozzle discharge coefficients (Cd) can be defined. The software considers the prechamber nozzles as a single equivalent hole. If sufficient data from 3D-CFD are available, the prechamber connector will be defined in order to define an effective passage area equiva-lent to that of 3D-CFD. During this work, the reverse and forward Cd were considered equal.
Turbulent Jet Ignition (TJI) Combustion Modelling in GT-Suite
Figure 7.2: PreChamber Object - Main Folder
Figure 7.3: PreChamber Connector Object - Main Folder
4. Prechamber Wiebe Combustion Calibration
The Wiebe combustion models have been calibrated. The Wiebe profile has a very simplified shape in comparison with the measured data, so the match on the gas exchange PC-MC can be searched in order to avoid excessive impacts on the Jet Ignition combustion. During this phase, a TPA analysis mode should be active in the main chamber, with the scope of replicating the measured MC pressure cycle as well as possible. For the future versions, in the case of an adequate SITurb model for the prechamber, an RLT that describes the match between the measured and the predicted data better than the ANHRR RMSE shown in equation (5.3) should be defined also for the prechamber combustion. To this aim, the user-defined pressure RMSE (equation (5.4)) or a more adequate start of integration for the ANHRR error should be used.
5. Main Chamber Flow Model Calibration
The Main Chamber Flow Model should be calibrated, basing on the 3D-CFD data (section 5.1). This step is useful due to the evident impact of the turbu-lence on the predictive Jet Ignition combustion. Since the prechamber com-bustion was modelled in the previous steps, the impact of the jet PC-MC on
the turbulence is taken into account.
6. Building of a routine for the calculation of the MC pressure RMSE For performing the next steps, a routine for the calculation of the Root Mean Square error between the measured and the predicted pressure traces in the main chamber has to be built. This calculation can be inherited from this work, with reference to Figure 6.12 and equation (5.4). An alternative could have been to build a user-defined ANHRR RMSE considering a more adequate start of integration, but the pressure RMSE was preferred, being this output less noisy. Generally, the model has to show a good level of correlation (trapped mass, thermal status, etc.) for using the pressure RMSE with reliability.
7. Main Chamber Jet Ignition Model Setup
Once calibrated the prechamber combustion, the Jet Ignition combustion can be modelled (chapter 6). Since a predictive model is employed, a Flame Object containing information regarding the combustion chamber geometry has to be defined. The Flame Object also contains a "spark location"; since the software treats the combustion as a single flame propagating from this "spark location", this latter indicates the average position of the nozzles with respect to the head.
8. Main Chamber Jet Ignition Model Optimization
The optimization should be carried on with the aim of minimizing the user-defined pressure RMSE, user-defined at step 6. The GA algorithm can be used for the scope. Note that its robustness is improved by using the user defined error function, but a special attention should be deserved since the number of independent variables is high and the GA settings were not deeply assessed on others operating points combinations.
Chapter 8 Conclusions
The aim of the thesis work was to investigate the JetIgnition model in GT-ISE v2020 and build a methodology for its calibration. In this perspective, several analyses were performed defining a step-by-step workflow (Figure 8.1) and showing the current modelling limitations.
1) The objective of having a fully predictive model (with an SITurb model in the prechamber and a Jet Ignition model in the main chamber) cannot be accomplished, due to the impossibility to properly model a predictive combustion in the precham-ber: as shown in chapter 3.3.1, the Flame Kernel Growth Multiplier (FKGM) does not have any impact when the SITurb is modeled in the prechamber, so the flame is fully turbulent as soon as the spark occurs. Moreover, it was assumed that the flame was planar immediately after the spark, which resulted in a significant over-estimation of the flame area. The combination of these two issues made it impossible to match the measured data when the actual spark timing input is used. As has been explained by Gamma Technologies, the v2021 of the software should allow the user to overcome these problems, since in this version the FKGM has an impact again and a ‘Flame Area Transition’ attribute, which makes the flame spherical during the first phase of the combustion, has been added.
2) The Jet Ignition calibration based on the MC Apparent Net Heat Release, which is advised by Gamma Technologies, resulted to be not robust due to the definition of the ANHRR RMS error (given in equation (5.3)), as explained in chapter 6.3.
In order to overcome this problem, the optimizer has to be set up with the aim of minimizing the error between measured and predicted pressure. An RLT that
reports the pressure RMS error is not provided by the software when using the HRBC, so a user-defined routine for calculating the error between predicted and measured MC pressure was built (equation (5.4)).
3) Also, when considering the pressure error-based optimization of the Jet Ignition model, the DoE analysis carried out on the 3000x100% operating point (FL) showed the existence of better sets of calibration parameters than the one provided by the optimizer. Hence, when the ranges of values shown in Table 6.1 are considered, the optimizer setup described in Table 6.2 should be improved. Further investigations on the optimizer setup are necessary.
4) The DoE analysis confirmed that a single set of Jet Ignition multipliers able to properly model a TJI combustion in both the operating points considered (3000x100%
and 6500x100% - FL) does not exist, for the ranges of values shown in Table 6.3.
The results obtained have room for improvement which is expected for the v2021, since the Jet Ignition modelling in GT-ISE seems to be very promising.
The next steps are the following:
1) The GT-SUITE v2021 potentialities assessment, with reference to the predictive combustion (SITurb) in the PC and the Jet Ignition model in the main chamber.
2) An investigation on the Genetic Algorithm setting parameters, aimed at gaining a more robust MC Jet Ignition calibration.
Finally, the methodology built and the main limitations encountered are summarized in Figure 8.1.
Turbulent Jet Ignition (TJI) Combustion Modelling in GT-Suite
Figure 8.1: JI combustion predictive model - methodology
Bibliography
[1] Sayan Biswas, Physics of Turbulent Jet Ignition, Springer, 2018.
[2] J. B. Heywood, Internal Combustion Engine Fundamentals, McGraw Hill Inter-national edition, 1988.
[3] GT-SUITE, Engine Performance Application Manual, Gamma Technologies, 2020.
[4] Wenig, M., Fogla, N. and Roggendorf, K., Towards Predictive Dual-Fuel Combus-tion Prechamber Modeling for Large Two-Stroke Engine in the Scope of 0D/1D Simulation, CIMAC Congress, 2019.
[5] N. Fogla, M. Bybee, M. Mirzaeian, F. Millo, and S. Wahiduzzaman, Develop-ment of a k-k- phenomenological model to predict in-cylinder turbulence, SAE International Journal of Engines, vol. 10, pp. 562–575, 2017.