Towards multiobjective Nelder-Mead optimization of a HSDI diesel engine: Application of Latin hypercube design-explorer with SVM modeling approach

Energy Conversion and Management 143 (2017) 150–161

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Towards multiobjective Nelder-Mead optimization of a HSDI diesel engine: Application of Latin hypercube design-explorer with SVM modeling approach Hadi Taghavifar Young Researchers and Elite Club, Urmia Branch, Islamic Azad University, Urmia, Iran

a r t i c l e

i n f o

Article history: Received 23 January 2017 Received in revised form 21 March 2017 Accepted 1 April 2017 Available online 7 April 2017 Keywords: Combustion noise Diesel engine Nelder-Mead algorithm Design of experiment SVR

a b s t r a c t Optimization process of energy-related devices is gaining an undivided attention of industrial sectors due to cost effectiveness and practicality attributes. Diesel engines are the most efficient in producing power, although there is a great capacity that has not been fully exploited. Therefore the simplex-based optimization is addressed to enhance the indicated torque (IT), combustion noise (CN), and swirl ratio (SR) of the engine at the same time. The optimum solution is reached at RunID 27, which demonstrates 7.7% increase in IT, 0.19% decrease in CN, and 21.98% increase in SR compared to those of baseline mode. In the present study, IT and CN vary inversely, thus the modification in injection schemes and chamber geometry have to be considered without putting a penalty on another. It was indicated that Min. swirl and torque cases have significantly reduced bowl volume, however, the case with the lowest swirl has lower centerline depth. In addition, it is determined that Max. torque and swirl are obtainable with a big bowl segment, although it was observed that a shallow combustion chamber is expected to induce higher torque. The higher torque is associated with more uniformity of mixture (0.8484) and pressure peak (13.98 MPa) that is plausible with a fitted spray injection with chamber walls coordination, reducing the spray-wall impingement. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Nowadays, diesel engines constitute an indispensable part of industrial and transportation segments of the globe. Enhancement of the engine efficiency offers several benefits from low emissions to higher output power to low combustion noise and fuel consumption. The energy optimization researches are in rapid progress due to the shortage of fuel sources and concerns about the health care of humans exposed to hazardous combustion products. The optimization studies are usually classified into evolutionary methods, gradient/simplex based methods, and Pareto optimization. For the optimization procedure, either experimental data pool or CFD-driven (computational Fluid Dynamics) dataset can be used. Furthermore, parametric optimization has been implemented experimentally or numerically to determine the ideal combination of several operating parameters in combination [1–4]. The majority of studies are focused on the design and geometry of combustion chamber, while the objective is to reduce emissions or increase the engine performance. Chen and Lv [5] applied a multi-dimensional optimization on 8.9 L Cummins diesel engine E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.enconman.2017.04.008 0196-8904/Ó 2017 Elsevier Ltd. All rights reserved.

to find an optimum set of chamber structure and their results suggested that a smaller diameter, shallower combustion chamber cause lower soot emission. The design of experiment (DoE) can be utilized integrated with optimization algorithms to find better starting points. For instance, in Refs. [6,7], the DoE technique has been performed with multi-objective optimization algorithms to modify injection/chamber structure parameters in order to achieve predefined goals. Jafari et al. [8] have employed a new entropy generation minimization in diesel engines where they analyzed the second law efficiency surface plots to deduce that start of injection is dominant for the first law and duration of injection is significant for the second law. Several papers can be found trying to optimize the engine in a dual fuel mode [9–10]. Benajes et al. [11,12] reported optimization results on diesel and reactively controlled compression ignition (RCCI) engines in which for a diesel engine it was concluded that 40% decrease in NOx is possible while keeping fuel consumption and soot constant through CFD + DoE, and about RCCI engine, dual fuel mode optimization provided 7% higher efficiency. Wang et al. [13] carried out an optimization work by non-dominated sorting genetic algorithm (NSGA II) algorithm with the enhanced architecture of chamber. The main achievement was to reduce HC and CO emissions by 56.47% and 33.55%, respec-

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151

Nomenclature CA CFD CN Dm dnozzle DFT DoE ECFM HSDI HRR IT LB lh

crank-angle (deg) computational fluid dynamics combustion noise (db) bowl middle diameter (m) nozzle hole outer diameter (m) discrete Fourier transform design of experiment extended coherent flame model high speed diesel engine heat release rate (J/deg) indicated torque (Nm) lower bound injector tip protrusion (m)

tively. A numerical investigation is carried out on the basis of Latin hypercube sampling and Pareto optimization on a dual-fueled compression ignition (CI) engine [14]. The optimization is done to maximize the torque, and minimize the NOx and fuel consumption. Lee et al. [15] optimized the geometry of combustion chamber and relevant operational conditions of a compression ignition engine fueled with pre-blended gasoline-diesel fuel. The micro genetic coupled with KIVA-CHEMKIN code suggested that reentrainment type into shallow bowl could contribute to better fuel consumption with reduced maximum pressure rise rate. Park et al. [16] performed 1D simulation on the performance and NOx emission of a diesel-methanol dual fuel engine and its optimization by multi-objective Pareto optimization. It was found that the exhaust gas recirculation (EGR) had a greater effect than injection timing on the optimal Pareto front. For the engine optimization field, little has been investigated with the simplex-based Nelder-Mead algorithm to search for the optimum chamber/injector configuration. The comprehensive collection of design variables including injector tip protrusion (lh), half spray cone angle (h), nozzle hole diameter (dnozzle), bowl middle diameter (Dm), and bowl center depth (Tm) are taken into consideration to maximize the indicated torque and swirl while to minimize the combustion noise. The aforementioned variables have been varied during 30 RunIDs to find an optimum case among feasible designs with an emphasis put on torque. The next phase of the investigation is using Latin hypercube type of DoE method and then l-SVR prediction model is build to predict the objective based on design variables. The flowchart diagram of the procedural operation is illustrated in Fig. 1. At first, an engine model was created based on a real operating engine, with which a set of data are generated. The dataset is then classified to design variables (inputs) and objectives (outputs) used for building a l-SVR model for prediction and optimization + DoE for an exhaustive search of the best design of interest. 2. Simulation of HSDI diesel engine The original experimental engine exploits a flexible fuel injection and air charge, variable-geometry turbocharging (VGT) and high-pressure common rail (HPCR) systems. The HPCR system promises fuel injection pressure to be independent of crankshaft speed, which therefore, better air/fuel mixture can be attained. The experiments were performed under limiting torque condition (LTC) of 1.8 L prototype direct injection diesel engine with a baseline build comprised of a fixed-geometry turbocharging (FGT) with a distributor electronic fuel injection system. HSDI (high-speed direct injection) Ford Diesel engine was equipped with a prototype Lucas CAV HPCR system, and an allied Signal VGT.

LHS N NMA SR SVM RMSE

Latin hypercube sampling engine speed, number of vertices Nelder-Mead algorithm swirl ratio support vector machine root mean square error

Greek symbols reflection coefficient b expansion coefficient c contraction coefficient h half spray cone angle (deg)

a

Since a needle lift transducer was not available, start of injection (SOI) was regulated from the instant where the raise pressure trace shows its first sharp reduction. All results were obtained at the limiting torque curve with limits set to the following parameters over different speed ranges [17]: Air-fuel ratio, A/F:
19 for Ne (engine speed) between: 1250 and 1500 rpm. Maximum cylinder pressure, Pmax: 140 bar for Ne between: 1500 and 3000 rpm. Pre. Turbine temperature, Texhaust  800 °C for Ne: 3000– 4000 rpm. The numerical simulation has been performed based on a 1.8 L Ford diesel engine, variable geometry turbo-charging (VGT) type of direct injection diesel engine. The engine runs at medium load, 2500 rpm engine speed and the compression ratio and fuel injection mass ratio is kept constant during all optimization cases. Table 1 elaborates the engine’s operational characteristics. The experimental validation as well as grid independency of results have been detailed and described thoroughly in [17–19]. The applied mesh comprised 23 K cells at TDC, which are mostly hexagonal elements and it is refined for the injector and spray blocks to give a robust computation. The injector and spray blocks change with variation of injection parameters of each RunIDs since there are different designs for each run cases. The simulation and optimization job is performed using AVL-FIRE software. The semi implicit method for pressure linked equations (SIMPLE) incorporated to pressure implicit with splitting of operator (PISO) [20,21] is adopted to solve the governing Navier-Stokes equations in pressure-velocity field in a discretized domain. In addition, k-zeta-f model [22] is selected to simulate the in-cylinder turbulence. The spray breakup process is based on standard WAVE model [23], which considers both primary and secondary atomization mechanisms. Finally, the extended coherent flame model- 3zones (ECFM-3Z) is used for combustion of charge [24]. 3. Nelder-Mead optimization technique This algorithm runs simplex method for finding local optima by minimization of the objective function relying on mathematical rules to complete the process. For a function of N design variables, there should be N + 1 vertices on N-dimensional space. In the case of having two variables, the simplex is a triangle, where the searching process is an attempt to compare the values of the function at the vertices of the triangle. The worst vertex (the one with the largest value) is discarded and replaced with new a new vertex. The searching process is continued by the generation of series of

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Fig. 1. Flow chart diagram of the optimization/modeling procedures.


 Ph Þ Pr ¼ P
þ aðP

Table 1 Main operational condition of the base diesel engine. Bore  stroke Displacement Compression ratio Swirl ratio @ IVC Rail pressure Nozzle geometry Number of nozzles Conrod Clearance Injection start timing Injection spray angle

82.5  82 mm 438 cm3/cylinder 19.5:1 3 54–125.5 MPa (based on engine speed) 5  0.15 mm 4 130 mm 0.86 mm 3°CA ATDC 160 deg

triangles whereby the function values keep being smaller and smaller. In this manner, the triangle approaches toward the coordinate of the minimum point. This method is effective and computationally robust. The bounds of design variables and constraints of objectives are considered by setting a penalty term that is embedded in the objective function. The steps of the Nelder-Mead are briefly as follows [25]: Assume yi as the value of the objective function at point Pi, and yl and yh are considered as the worst and best objective functions. First, the centroid of N best points is evaluated by: N X
¼1 P Pi N i¼1

ð1Þ

At each stage of the algorithm, Ph is replaced by implementation of three operations: reflection, expansion, and contraction. The coordinate of reflection point is:

ð2Þ

Here Pr is located on the line connecting P to Ph. If yr is within (yl, yh), Ph is replaced by Pr, else yr < yl, i.e. via reflection a new minimum is produced, then the expansion coordinate has to be introduced:


 Ph Þ Pe ¼ P
þ bðP

ð3Þ

Again, if ye < yl, Pe should be replaced by Ph, otherwise if expansion fails Pr is replaced by Ph. If yr > yh is true during reflection, we apply contraction operation by:


 Ph Þ Pc ¼ P
þ cðP

ð4Þ

If the contraction is successful, Pc will be replaced by Ph, unless the contracted point is worse than Pr and Ph. In this case, all Pi have to be replaced by (Pi + Pl)/2 and restart the algorithm. The coefficients a, b, and c are reflection, expansion, and contraction coefficients, respectively that are user defined parameters. The tuning parameters of the multi-objective Nelder-Mead algorithm for the HSDI diesel engine under study are gathered in Table 2. The weighted um multi-objective optimization is used and the weights are such selected to outline the importance of each design goal, therein the final objective function is minimized and the lowest value has the best characteristics as given below:

Objectiv e ¼ 2:0 Obj swirl þ 1:0 Obj combustion noise  3:0 Obj indicated torque

ð5Þ

The base, lower, and upper bounds of design variables and objectives, which they are allowed to change, are mentioned in Table 3.

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H. Taghavifar / Energy Conversion and Management 143 (2017) 150–161 Table 2 The main tuning specifications of the NMA. Max. number of function evaluations Max. number of iterations Function tolerance Variable tolerance Linear constant factor Exponential constant factor

IT ¼ 10 15 0.0001 0.0001 100.0 2.0

5. Latin hypercube design The type of DoE method used for generation of initial design points in this study is Latin hypercube sampling. Latin hypercube designs split the design space for each factor evenly into n levels. One must note that only one design point exists on each level of every factor. In this sense, n! different permutations of the n levels are possible for each factor. The design matrix of the Latin hypercube comprises one column for each factor and the column is determined by a randomly chosen permutation of the n levels [28]. In other words, Latin hypercube is a statistical way to produce randomly chosen samples from a multidimensional space. A Number of experiments in current research is 20 and the randomized seeds are equal to 100.

Combustion noise reduction is an important process of engine design for a smooth engine operation, especially in diesel engines. High-pressure rise rate makes higher combustion noise and knocking [26], therefore calculation and quantification of this parameter is implemented by pressure-time data written on simulation files. In this regard, a discrete function is presented as Yi = Y (xi), i = 0, . . ., M  1, where M represents the number data registered on the file, xi, i = 1, . . ., M is time data and Yi, i = 0, . . ., M is pressure data. First, the x-values have to be distributed uniformly for the interpolation of the function. Thereafter, the function is transformed from time domain to frequency domain by discrete Fourier transform (DFT). Then the frequencies, amplitudes, and phases for the transformed function should be computed. From these values, noise will be obtained. Based on available filters, four different values can be prepared for combustion noise. The swirl/tumble can be quantified as affected by different water injection modes. Accordingly, the angular swirl velocity, xsx, and a swirl ratio, SRx [27] are given to estimate the strength of swirl induced by each injection configuration. The swirl angular velocity is represented by:

Pn

mi ½ðyi  y0 Þwi  ðzi  z0 Þv i 

i¼1 mi ½ðzi

6. Data analysis by support vector machine Support vector machine (SVM) has been first introduced by Vapnik [29] postulated upon the statistical learning theory that primarily performs the classification operation though support vector regression (SVR) is considered as subsystem of the SVM. The SVR principally is tied with SVM concept. As for regression, it is of interest to construct a hyper-plane best fitted with the majority of data. Therefore, the target is to achieve a hyper-plane with small norm while simultaneously reducing the sum of the distances from the data sets to the hyper-plane. This means the error must be decreased steadily when the hyper-plane is adapted to fit with the desired data. The e-insensitive loss function is considered as a tube equal to the approximation accuracy that surrounds the training data [30]. The regression evaluation with SVR is to assess a function corresponding to a data set fðxi ; yi Þgn wherein xi, yi and n are input, output and number of data points, respectively. There are two chief kinds of linear and nonlinear SVR.

ð6Þ

 z0 Þ2  ðyi  y0 Þ2 

Here n signifies the total cell numbers in the computational domain, mi gives the mass inside the computational cell, (x0, y0) is used to determine the cylinder axis, and the local cell in the Cartesian system has the following coordination (xi, yi, zi). The velocity components aligned with x, y, and z directions are ui, vi, and wi, respectively. The swirl ratio or swirl number (SR) is described as below:

SRx ¼

xsx

6.1. Linear SVR For the linear system, the regression model is as follows [31]:

ð7Þ

N

f ðxÞ ¼ hw; xi þ b

1  VD



Le ðyÞ ¼

Z

PC :dV

ð10Þ

where f(x) is an unknown target function. The h.,.i symbol denotes the dot product in X and w is the weight vector. The most prevalent loss function is the e-insensitive one proposed by Vapnik [31] and is defined by the following function:

Therein, SRx is the swirl ratio around the x-axis, and N is the engine angular velocity. Indicated mean effective pressure (IMEP) is a valuable indication of the engine ability to deliver work and is defined as an average pressure generated during the power course. This factor can be described as following:

IMEP ¼

ð9Þ

where kcycle is cycle parameter equal to 2 for two-stroke engines and 4 for four-stroke engines.

4. Calculation of objective values

xsx ¼ Pi¼1n

IMEP  V D kcycle  p

ð8Þ

0;

forjfðxÞ  yj 6 e



ð11Þ

jfðxÞ  yj  e; otherwise

As a convex optimization problem, it can be written as:

where VD is displacement volume and Pc represents the cylinder pressure. The indicated torque is:

minimize

l X 1 kwk2 þ C ðni þ ni Þ 2 i¼1

ð12Þ

Table 3 The base, lower, and upper bound values of design variables and objective functions.

Base Lower bound Upper bound *

dnozzle (m)

lh (m)

h (deg)

Dm (m)

Tm (m)

IT* (–)

SR* (–)

CN* (–)

0.00016 0.000135 0.000195

0.0 0.001 0.002

6.0 5.6 6.4

0.005671 0.00464 0.00773

0.05139 0.04727 0.0555

1.83788 0.91894 2.75682

3.82333 1.91166 7.64666

2.24818 1.12409 4.49636

Signifies scaled characteristics.

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8 9 > < yi  hw; xi i  b 6 e þ ni > = Subject to hw; xi i þ b  yi 6 e þ ni > > : ; ni ; ni P0

ð13Þ

where ni and n⁄i variables have to satisfy the function constraints. The corresponding dual optimization problem is defined as:

max   a;a

l X l l X 1X ðai  ai Þðaj  aj Þhxi ; xj i  yi ðai  ai Þ 2 i¼1 j¼1 i¼1

l X  e ðai þ ai Þ

7. Results and discussion

ð14Þ

i¼1

The imposed constraints are:

0 6 ai ; ai 6 C; i ¼ 1; . . . ; l l X ðai  ai Þ ¼ 0

ð15Þ

i¼1

where a and a⁄ signify the Lagrange variables and w and b are defined by the following equation while xr and xs are support vectors [32]. l X w¼ ðai  ai Þxi

ð16Þ

i¼1

b¼

 12 hw; ðxr

þ xs Þi

6.2. Nonlinear SVR In nonlinear regression problems, there is a nonlinear mapping / of the input space onto a higher dimension space, and then linear regression can be implemented in this space [33]. The nonlinear model is given

f ðxÞ ¼ hw; /ðxÞi þ b

ð18Þ

i¼1 l l X X ðai  ai Þh/ðxi Þ; /ðxÞi ¼ ðai  ai ÞKðxi ; xÞ i¼1

b¼

7.1. Multi-objective Nelder-Mead optimization The model parameters that are varied during an optimization process are illustrated in multi-history plots of Fig. 3. The variation of both design variables and objectives with regard to RunID cases show that the minimum of objective value (optimal case) coincides with RunID 27 having a value of -13.0221. Out of 30 design points, some are classified as feasible or infeasible based on their potential to meet the constraints as Const_Swirl
LB1 and Const_Torque
LB2 where LB1 and LB2 are lower bounds of swirl and torque set to 3.88 and 1.9. Fig. 4 demonstrates that feasible

Table 4 Adjustment of SVR method parameters.

l X ðai  ai Þ/ðxi Þ

hw; /ðxÞi ¼

The engine geometrical parameters, as well as injection system factors, are regarded as design variables to decide an ideal configuration based on which the maximum torque and swirl with minimum combustion noise can be satisfied. In order to obtain the unbiased decision-making strategy, the values of sub-objectives have to be brought into the same level. This operation can be achieved by non-dimensional data of quantities performed by response editor interface. In this regard, the data set has been scaled and shifted to get them within a desirable range.

ð17Þ

where

w¼

The modeling has been performed by Nu-SVR method and its performance is estimated by the power of predictability of output results. According to Fig. 2, it is seen that the predicted values are well mapped to standard line and the value of root mean square error (RMSE) is negligible amount of 0.02893, which assures the effectiveness of model. The specification of the SVM model to represent a reliable predictability is listed in Table 4.

ð19Þ

i¼1

l 1X ðai  ai ÞðKðxi ; xr Þ þ Kðxi ; xs ÞÞ 2 i¼1

ð20Þ

SVR type Epsilon/Nu value Cost value Tolerance value SVM kernel type Degree of kernel Gamma value of kernel Coefficient value of kernel Normalization type Number of folds

where xr and xs are support vectors.

Fig. 2. Statistical scatter plot of predicted objective vs. optimized results.

l-SVR 0.1 2.2525 0.001 Polynomial function 3.0 1.0 0.0 Min/Max. normalization 10

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155

Fig. 3. Multi-history plot variation of (a) objectives and (b) design variables with RunID during optimization process.

designs have higher swirl and torque and this assures the functionality of feasible designs since infeasible ones are removed from the further investigation. Fig. 5 shows the geometrical feature of the standard design and the best design, Moreover, the best and worst configuration of the combustion chamber for swirl and torque are depicted in outlined mode. The injection characteristics along with the chamber shape constitute the fundamentals of flow regime and combustion quality in an engine. It can be noticed that a bigger bowl radius and bowl center depth (Tm), as well as smaller bowl middle diameter (Dm), can demonstrate better performance than

the baseline case. This geometrical feature of chamber shows better overall performance in torque, swirl, and combustion noise with rather lower spray cone angle and greater nozzle hole diameter (features that are not appropriate for spray injection). Fig. 6 shows the variation of swirl ratio and uniformity indices as a function of CA for the best and worst cases. It is evident from Fig. 6a that larger bowl radius and lower bowl distance can induce larger swirl motion. The uniformity of air/fuel mixture that can be created by adopting a proper chamber configuration and injection strategy is the key factor for the stronger torque and engine power.

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Fig. 4. 2D scatter plot of torque vs. swirl for feasible and infeasible designs.

Fig. 5. (a) Comparison of standard and optimum topology, (b) comparison of extremum cases of torque and swirl.

This issue is depicted in Fig. 6b, where a bigger bowl and centerline depth are in favor of uniform mixture formation since it makes fuel jet-wall collision improbable. The cylinder pressure of different configurations in the extreme conditions of objectives, baseline, and optimum arrangements are plotted in Fig. 7a, while HRR

curves of the baseline, optimum (RunID 27), and Max. torque (RunID 29) is presented in Fig. 7b. The peak pressure of maximum torque has the highest value, and the peak pressures of optimum design, baseline, and minimum combustion noise come in the next places. The optimum design found by Nelder-Mead has lower peak

H. Taghavifar / Energy Conversion and Management 143 (2017) 150–161

157

Fig. 6. Variation of (a) swirl ratio and (b) uniformity index with crank-angle.

pressure than RunID 29 since it is responsible for establishing a trade-off between conflicting objectives of torque, swirl, and combustion noise. This issue can be confirmed with reference to HRR curves, where the peak HRR of RunID 29 is 32.271 J/deg while for optimum it amounts to 31.07 J/deg. Fig. 7c demonstrates that in addition to cylinder pressure, the cylinder temperature undergoes dramatic rise when optimum mode and Max. torque designs are applied. It should be noted that the increase in thermodynamic parameters are obtained solely due to change in injection system and chamber shape while compression ratio, the amount of fuel injection, equivalence ratio were kept constant.

7.2. DoE evaluation results with LHS method integrated with l-SVR surrogate model For further analysis of optimization results a surrogate model by support vector machine methodology is specified as Objective = f(Dm, lh, h, dnozzle, Tm) to predict the objective influenced by design variables. The surface plots in Fig. 8 demonstrate the relationship between objective and design variables established by modeling predictability potential. It can be seen that for a compromise between combustion noise and torque, a bigger spray cone angle and bigger nozzle hole diameter is recommendable. The

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H. Taghavifar / Energy Conversion and Management 143 (2017) 150–161

Fig. 7. Variation of the baseline, optimum, and maximum IT with crank-angle for (a) pressure, (b) HRR and (c) temperature.

modeling results suggest that decline in both Dm and Tm would decrease the objective value and this benefits the overall minimum combustion noise and maximum torque and swirl. The particular case with low Tm and high Dm increases the risk of spray to wall impingement. The spray-wall interaction deteriorates the combustion quality, which has a direct impact on the engine torque. The contour plots of Fig. 9 indicate the effect of injectionchamber design effects in combination on the objective. Fig. 9a shows that decreasing Dm and dnozzle simultaneously is of interest for achieving better overall engine performance in terms of combustion noise, torque, and swirl. It can be observed that by the reduction in nozzle hole diameter, the objective is decreasing, which means the spray droplets (SMD) become smaller and this makes more fuel diffusion into the air and a smoothed combustion.

Fig. 9b infers that the injector tip protrusion is not a dominant factor because the range of objective variation is limited, albeit it is advisable that either high or low lh-Tm combination should be applied together for slightly better prescribed objective. Contrarily, spray cone angle and bowl middle diameter are dominant factors in changing the engine condition for combustion (see Fig. 9c). Moreover, decreasing Dm together with an increase in the spray cone angle lead to minimum objective amounts, thus higher torque and swirl as well as lower combustion noise. A greater Dm induces a high swirl in the chamber, while a bigger spray cone angle implies better spray atomization. Overall, enhanced spray disintegration and swirl motion give a steady burning of charge (decreased rate of pressure rise i.e. lower combustion noise) with an efficient engine performance.

H. Taghavifar / Energy Conversion and Management 143 (2017) 150–161

Fig. 7 (continued)

Fig. 8. Surface plot representation of (a) injection and (b) chamber geometry parameters.

159

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Fig. 9. Contour plot representation of combinatory injection-chamber variables: (a) dnozzle-Dm, (b) lh-Tm and (c) h-Dm.

H. Taghavifar / Energy Conversion and Management 143 (2017) 150–161

8. Conclusions The study is numerically performed with 3D CFD code (AVLFIRE package) to simulate the basic experimental DI test engine. The attempts are then concentrated on finding optimum solutions on how it is possible to modify the injection system and combustion chamber configuration by resorting multi-objective NelderMead algorithm to maximize indicated torque and swirl motion, whereas combustion noise is being reduced. The important findings are: It was shown that the model with the lowest statistical merit is credible and shows a high level of confidence in the output prediction (RMSE = 0.02893). The solutions with the highest torque (RunID 29) and swirl (RunID 9) cannot alone fulfill the best case considering the defined objective since a rapid combustion with a high rate of pressure rise will increase the combustion noise. By applying Nelder-Mead algorithm, a 0.192% decrease in combustion noise, 7.7% increase in torque, and 21.98% increase in swirl motion with respect to baseline is obtained. Handling the injection system is desirable for controlling the combustion noise (reduced spray cone and increased nozzle hole diameter). The chamber modification (bigger bowl radius with a small outer wall diameter) is suited for increasing the engine torque.

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