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A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach
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A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach
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Hamid Taghavifar a,⇑, Hadi Taghavifar b, Aref Mardani a, Arash Mohebbi a, Shahram Khalilarya b a b
Department of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Urmia, Iran Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran
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h i g h l i g h t s The wall heat flux modeling of n-heptane fueled direct injection (DI) diesel engine was performed.
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The coupled computational fluid dynamics (CFD) and artificial neural network (ANN) approach was developed.
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A 6-17-1 ANN topology yielded the MSE equal to 0.5217 and R equal to 0.99.
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a r t i c l e 2 3 0 3 21 22 23 24 25 26 27 28 29 30 31 32
i n f o
Article history: Received 21 June 2014 Received in revised form 5 September 2014 Accepted 23 September 2014 Available online xxxx Keywords: ANN CFD Wall heat flux Equivalence ratio Turbulence kinetic energy
a b s t r a c t The primitive purpose of the present paper is to address the wall heat flux modeling of n-heptane fueled direct injection (DI) diesel engine with the application of a coupled computational fluid dynamics (CFD) and artificial neural network (ANN) approach. The numerical model was established for a Ford 1.8 l DI diesel engine equipped with a prototype Lucas CAV HPCR system, and an Allied Signal VGT. The turbulent flows within the combustion chamber were simulated using the RNG k–e turbulence model. The input parameters of crank angle, mass flux, liquid mass evaporated, equivalence ratio, turbulence kinetic energy, and pressure were included in the system. It was concluded that more wall heat flux was transferred with fuel injection around TDC and along with combustion initiation for 2000 rpm and the higher pressure can be achieved at the same engine speed. Furthermore, a feed-forward with back propagation learning algorithm and Levenberg–Marquardt training technique were employed for various ANN modeling implementations. At 17 neurons in the hidden layer, the MSE equal to 0.5217 was yielded and the coefficient of determination values of 0.99 and 0.99 were obtained for training and testing phases. The optimum values of the learning rate and momentum were also yielded at 0.6 and 0.7, respectively. Ó 2014 Elsevier Ltd. All rights reserved.
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1. Introduction Extensive information on engine performance facilitates the design of modern machinery and processing equipment with modified quality specifications. The automotive research industry world-wide investigates various techniques to improve internal combustion engine efficiency and exploit alternative fuels [1]. Aiming this, a detailed investigation into the combustion phenomenon and energy balance is required. One beneficial approach is to assess the heat flux or thermal flux of combustion chamber wall. The rate of heat energy transfer through a given surface is recognized as heat flux which is most typically quantified by measuring a temperature ⇑ Corresponding author at: Department of Mechanical Engineering in Farm Machinery, Faculty of Agriculture, Urmia University, P.O. Box 165, Urmia, Iran. Tel.: +98 9143882707; fax: +98 441 277 19 26. E-mail addresses: [email protected], [email protected] (H. Taghavifar).
difference over a piece of material with known thermal conductivity. From the beginning of Diesel engine development, the significance of the heat transfer through the combustion chamber walls has been recognized [2–4]. The phenomenon is complex to analyze owing to its nonlinearity encompassing transient three-dimensional behavior, rapid temperatures wings, piston motion, cooling passages, and turbulent reactive fluid dynamics [4]. In internal combustion (IC) engines, heat transfer is one of the most important topics as it directly affects the main distinguishing parameters of the engine, such as in-cylinder pressure and temperature [5]. The development of a highly efficient global heat transfer model for the application of ICEs was the main objective behind the efforts of Ref. [6]. In real-world disciplines one cannot understand the precise heat flux at every point on the surface; however, approximation schemes can be utilized to compute the integral, for example Monte Carlo integration.
http://dx.doi.org/10.1016/j.fuel.2014.09.092 0016-2361/Ó 2014 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Taghavifar H et al. A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.09.092
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@Ein @Eout @Eaccumulated ¼0 @t @t @t
where the three @E terms are the representatives of the time rate of @t change of respectively the total amount of incoming energy, the total amount of outgoing energy and the total amount of accumulated energy. If the single approach that the system exchanges energy with its surroundings is through heat transfer, the heat rate can be used to calculate the energy balance;
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ð1Þ
@Ein @Eout ¼ @t @t
I
! ! /q : dS
ð2Þ
s
! where we have integrated the heat flux density /q over the surface S of the system. The computational fluid dynamics (CFD) codes [7] can further assist such research efforts, describing with great detail the incylinder phenomena [8], such as the flame kernel development, and the in-cylinder heat and mass transfer processes. There are also some investigations centered on the development of adiabatic engines, using the ceramic coatings on the combustion chamber walls and other high thermal resistive ingredients [9,10]. In this manner, the heat losses are decreased and/or could be partially converted into useful work [11–13]. A study was carried out for the development of more exact theoretical models for predicting the propagation of heat through the combustion chamber walls of reciprocating (internal combustion) IC engines while a fast response thermocouple was included in the combustion chamber of a single cylinder engine to measure the dynamic wall temperatures [14]. The heat flux was obtained by solving the one-dimensional transient energy equation with transient boundary conditions using the Fast Fourier Transform. Additionally, a study was conducted to validate an experimental facility to establish a technique to assess the influence of some of the engine parameters on local engine heat transfer behavior under motored steady-state conditions [15]. Instantaneous temperature measurements were carried out in order to estimate heat fluxes on a modified diesel single cylinder combustion chamber. To the best knowledge of authors, little is known about the assessment of wall heat flux of n-heptane fueled DI diesel engine under the effect of crank angle, mass flux, liquid mass evaporated, equivalence ratio, turbulence kinetic energy and pressure. A developed CFD code coupled with the predicting ability of artificial neural network (ANN) approach would be beneficial to predict the wall heat flux of n-heptane fueled DI diesel engine. Hence, the primitive objective of the present study was to cover the aforementioned aspects and furnish the needed information in this regard.
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2. Experimental description and modeling validation
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The experimental work is carried out for diesel fuel, noting that the numerical work was replicated for n-heptane fuel while fixing the operational and simulative conditions of engine running. In order to set up flexible fuel injection and air charge, variablegeometry turbocharging (VGT) and high-pressure common rail (HPCR) systems are applied. The HPCR system assures fuel injection pressure to be independent of crankshaft speed, which accordingly better air/fuel mixture can be obtained. The experiments were carried out 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. The experimental results were obtained with the aid of the AVL data acquisition system and
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Concerto software [16] is represented for each of the engine speeds by the following traces: 1. 2. 3. 4. 5.
Cylinder pressure (bar). Apparent rate of heat release (kJ/m3 °CA). Cumulative apparent heat release (kJ/m3). Rail pressure (bar). Electrical output of injector needle actuator.
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All dataset were measured at relatively early stages of the commissioning process of the equipment. Since a needle lift transducer was not available, the start of injection had to be interred from the instant where the raise pressure trace shows its first reduction. AVL 409 SMOKE (Bosch) and AVL AFR (Spindt) was used for measurement of smoke and air/fuel ratio. All results were obtained at the limiting torque curve with limits set to the following parameters over different speed ranges: Air–fuel ratio, A/F: P19 for Ne (engine speed) between: 1250– 1500 rpm. Maximum cylinder pressure, Pmax: 6140 bar for Ne between: 1500–3000 rpm. Pre turbine temperature, Texhaust 6 800 °C for Ne: 3000– 4000 rpm. More details about experimental setup and information about data acquisition apparatus and procedure are mentioned in [17,18]. The results of simulation was compared with the experimental data when running with diesel fuel in terms of pressure course (over CA), air–fuel ratio (AFR), and average fuel flow for different engine speeds. Fig. 1 demonstrates the validity of simulation results for diesel fueled engine. The simulation was extended for n-heptane fuel since no experimental data was available for n-heptane fueled engine. The predictability of ANN tool in the subsequent sections once again confirmed the validity of obtained data for alternative fuel.
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3. CFD simulation procedure
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The numerical model was established for a Ford 1.8 l DI diesel engine with the specifications listed in Table 1. The engine was operated at medium load for every operational condition of both engine speeds of 2000 and 3000 rpm. The diesel engine was equipped with a prototype Lucas CAV HPCR system, and an Allied Signal VGT. The numerical grid of combustion chamber is shown in Fig. 2(a) at TDC position with 101,327 cells (enough resolution is given for the convergence of desired results). The calculations for unsteady equations of mixtures on closed system were carried out from IVC (52 °CA BTDC) to EVO (110 °CA ATDC). The turbulent flows within the combustion chamber were simulated using the RNG k–e turbulence model [19]. In addition, the standard WAVE model was adopted for the primary and secondary breakup of the spray. For treating the heating up and evaporation of the droplets, the Dukowicz model [20] was taken into account. The interaction between the particles and the turbulent eddies as a result of fluctuating velocity was added to the mean gas velocity by a stochastic dispersion model [21]. The assumption of this model is postulated on the fact that the fluctuating velocity has a randomly Gaussian distribution. The Extend Coherent Flame Model, 3-Zone (ECFM-3Z Model) is developed based on the turbulent mixing was selected for the combustion process simulation in the combustion chamber [22,23]. Fig. 2(b) illustrates three zones mentioned in the modeling. The model is according to a flame surface density transport equation and a mixing model, which describes inhomogeneous turbulent premixed and diffusion combustion phases. In this model, the fuel is considered as combination
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Fig. 1. (a) Comparison between simulated and experimental pressure courses for diesel fuel @ 1500 rpm and (b) model validation for fuel flow rate and AFR over engine speeds.
Table 1 Engine operational condition. Bore stroke Displacement Compression ratio Swirl ratio @ IVC Rail pressure Nozzle geometry Number of nozzles Conrod Clearance Injection start timing Injection spray angle Operational mode
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82.5 82 mm 438 cm3/cylinder 19.5:1 3 540–1255 bar (based on engine speed) 5 0.15 mm 4 130 mm 0.86 mm 3 °CA ATDC 160 deg Medium load @ 2000 and 3000 rpm
of more than one chemical species. The rate of reaction for each fuel component is finally divided. In this way, it is possible to calculate the consumption of each component separately. The development of the combustion products is based on the consumption of the
single components. The combustion model is based on Coherent Flame Model that is coupled to the spray model and has the capacity of stratified combustion modeling and NO formation [24]. The extended combustion flame model is based on ECFM-3Z [25] that constitutes and recognizes three zones of unmixed air plus EGR (if any exists), the mixed air and fuel zone, and unmixed fuel. In this approach, flame propagation occurs from burned gas to unburned gas section and takes into account the three main combustion modes, i.e. Auto Ignition, Premixed Flame (oxidation), and Diffusion Flame. For a diesel spray, the fuel droplets have close proximity to each other and the fuel droplets can be classified at unmixed fuel part of the computational cell. After evaporation of droplet fuels, a definite period is needed to transfer from the pure fuel area to mixed fuel and air region. In this situation, the mixing of fuel with air is modeled by initially placing the fuel into the ‘unmixed fuel’ zone of the ECFM-3Z model [25]. The transport equation from the unmixed to the mixed zone is solved and presented in detail in Ref. [25].
Please cite this article in press as: Taghavifar H et al. A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.09.092
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Fig. 2. (a) Meshing model of combustion chamber and (b) illustration of 3 zones of ECFM-3Z.
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The simulation is performed with n-heptane fuel in a diesel engine having the cetane number of 56, H/C ratio of 2.28, lower heating value equaling 44.9 (MJ/kg), and density of 0688 (g/mL, 20 °C). This fuel undergoes two-stage combustion. The ignition of n-heptane is controlled by some reactions during the combustion phase of low temperature stage. The low temperature reactions are initiated with the following reactions among others as well:
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n-C7 H16 þ O2 ! C7 H15 þ HO2
ð3Þ
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n-C7 H16 þ OH ! C7 H15 þ H2 O
ð4Þ
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Noting that the latter reaction is dominating through the process, whereas at the high temperature stage the chain branching reaction H + O2 = O + OH is controlling the reaction rate.
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4. Artificial neural network
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Artificial neural network (ANN) is a robust paradigm of artificial intelligence (AI) scope commonly considered as a universal approximator, which has been broadly acceptable and applicable across variety of scientific and engineering contexts. The scope of modeling has been the dynamic studying interest for the researchers and ANN has approved its robustness and promising ability to deal with the systems of stochastic and nonlinear systems with high degree of complexity. ANN is an emulation of biological neural system that is mimicking the biological behavior of the nervous system and approximates the operation of the human brain. In an
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ANN system neurons, each of which includes assigned weight and bias, are closely interconnected in various layers while the complexity of the problems decides the number of needed layers. This type of neural networks is so called multilayer neural networks whose most prominent representative is the Multi-Layered Perception (MLP). The layers which are sandwiched between the input layer and output layer are called hidden layers which play a substantial role on the predicting ability of the developed ANN. ANN system is a structure that receives an input, process the data, and provides an output while the input encompasses in a data array. When an input is transmitted to the neural network, and a corresponding desired or target response is set at the output, an error is composed from the difference of the desired response and the real system output. The error is fed back (back propagation) to the system which makes all adjustments to their parameters in a learning rule. This process is repeated (iteration or epoch) until the desired output is acceptable. The back propagation algorithm optimizes the model by convergence of the predicted values to the actual values using the gradient descent method. The schematic configuration of the developed ANN including the input and output parameters as well as the single hidden layer is demonstrated in Fig. 3. The total available data points of 520 in the present study were shuffled into three portions of 70%, 20% and 10% for training, testing and cross-validation, respectively. Levenberg–Marquardt training algorithm of trainlm was employed during modeling implementations owing to its well-documented ability dealing with combustion phenomenon of the DI engines [26,27]. A feed-forward ANN
Please cite this article in press as: Taghavifar H et al. A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.09.092
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Fig. 3. The schematic configuration of the developed ANN.
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with back propagation (BP) learning algorithm was used where the four introduced training algorithms were applied to the implementations where gradient descent approach was used for error minimization. MLP neural network with one hidden layer and varying number of neurons was considered while the number of neurons where increased in each layer from 1 to 20 in order to avoid the randomly selection of ANN architecture. At the start of network training, initial weights and biases of neurons are chosen randomly. Therefore, for each number of hidden neurons (each network structure), network was trained for 100 times to overcome this drawback. The mean value based on the performance criterion was then considered as the predicting ability of the corresponding model. In each system training network was trained for 1000 epochs as the stopping parameter. For the normalization step, the following function was applied.
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Xn ¼
X r X r;min ðX h X l Þ þ X l X r;max X r;min
ð5Þ
where Xn denotes normalized input variable, Xr is raw input variable, and Xr,min and Xr,max denote minimum and maximum of input variable. Moreover, Xh and Xl are set to be 0 and 1. Since that the normalization outputs would be in compliance with the logsig transfer function. In modeling purposes, it is essential to assess the performance of developed representation by various statistical criteria. The mean square error (MSE) and the coefficient of determination (R2), are adopted for analysis of model quality as following.
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n 1X MSE ¼ ðY predicted Y actual Þ2 n i¼1
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R ¼
Pn
ð6Þ
2
i¼1 ðY predicted Y actual Þ Pn 2 i¼1 ðY predicted Y mean Þ
ð7Þ
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where Yactual and Ypredicted are measured and predicted values by the developed models.
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5. Results and discussion
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The wall heat flux through the combustion chamber wall is predicted and calculated by the Annand’s correlation, which is consisted of the several components such as Reynolds number, wall temperature, cylinder bore, cylinder mixture temperature, and
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the thermal conductivity of gas. The current study establishes a new modeling for the prediction of wall heat flux by consideration of other elements having of superior significance over the processes of flow field formation and combustion phenomenon. These factors include the chemical interactions of reactants, thermodynamic properties of in-cylinder mixture, the air–fuel mixture quality, and the CA position. In this sense the transfer of heat can be predicted via the evolution of reaction over the CA period, fuel mass flow rate, pressure, turbulence kinetic energy, equivalence ratio, and liquid mass evaporated. Fig. 4 depicts the concentration distribution of input parameters at two CA values of 730 and 740 and engine speeds of 2000 and 3000 rpm. It is deducible that the increased CA leads to the increment of equivalence ratio and mass flux in contradictory to that of pressure. During expansion stroke of actual engine the heat was transferred from the combustion chamber wall. The amount of heat generation depends on air compression and especially combustion, which utilizes the chemical reaction of air/fuel mixture with oxidizer components. In this regard, the most effective parameters were taken into account as to analyze the heat transfer in the form of convection that explains the main reason of irreversibility in the engine and deviation from the ideal diesel cycle. After injection of spray, the mixing of spray droplets with air happens. Having all droplets evaporated by the heat transfer from the surrounding air to fuel droplets, the combustion process initiates. The input parameters were such chosen to have the most influence on the combustion duration and intensity. Fig. 5 demonstrates the variation of heat flux and injected mass flux as a function of crankangle at 2000 and 3000 rpm engine speeds. It is clear that more wall heat flux was transferred with fuel injection around TDC and along with combustion initiation for 2000 rpm due to more mixing time of fuel and air that leads to higher combustion and heat generation. Moreover, the amount of mass fuel injection was plotted for different engine speeds. It is seen that higher rate of overall mass injection is of 3000 rpm especially at late combustion period denoting higher equivalence ratio originated from more fuel provided for combustion. At premixed combustion phase, the higher mass flux corresponds to lower 2000 rpm, which affects the equivalence ratio with more fuel proportion compared to air at the mixture. Fig. 6 demonstrates the equivalence ratio and in-cylinder pressure course within the combustion chamber at different times (crank-angles) under 2000 and 3000 rpm engine speeds. As shown, the higher pressure can be achieved for
Please cite this article in press as: Taghavifar H et al. A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.09.092
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Fig. 4. The contour plots of the input parameters at two CA values.
Fig. 5. The variation of heat flux and injected mass flux as a function of crank-angle at 2000 and 3000 rpm engine speeds.
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2000 rpm since better mixture can be obtained because of more homogeneous mixture distribution denoted by lower equivalence ratio accompanied with better combustion and hence higher pressure. As it is appreciated from Fig. 7, applying higher engine speed can actively induce the turbulence amplitude whereby more uniform mixture can be expected; therefore, more fuel is expected to be evaporated. One has to note the contrary effect of lower engine speed on better mixture quality with more mixing time and poor mixing quality as a result of lower TKE. The superposition of input parameters with opposing effects on heat flux of combustion chamber was incorporated to develop a model to predict the output parameter based on neural network approach. Fig. 8 is a box plot of data in the x-axis which is the representative of the output vector of the data. On this box, the central mark is the median at 9050.94 W and the edges of the box are the 25th
and 75th percentiles. The whiskers extend to the most extreme data points not considered outlier and outliers are plotted individually. In the statistics’ discipline, a histogram is a graphical demonstration of the distribution of data while it gives an estimate of the probability distribution of a continuous variable. The histogram in Fig. 9 shows the distribution of data values where the superimposed normal distribution line is fitted. It is deducible that the data distribution has a satisfactory level of accordance with that of normal distribution line, however, the k-fold cross validation ensured the contributing role of any random share of data in the final result of the developed representation. The inclusion of the various numbers of neurons in the hidden layer has significant effect on the obtained result. In order to avoid the random selection of ANN configuration, the number of neurons in the hidden layer varied to observe the change of MSE (Fig. 10). At 17 neurons in the hidden
Please cite this article in press as: Taghavifar H et al. A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.09.092
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Fig. 6. The variation of pressure and equivalence ratio as a function of crank-angle at 2000 and 3000 rpm engine speeds.
Fig. 7. The variation of turbulence kinetic energy and liquid mass evaporated as a function of crank-angle at 2000 and 3000 rpm engine speeds.
Fig. 8. The statistical box plot of data to show the maximum, minimum and median.
Please cite this article in press as: Taghavifar H et al. A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.09.092
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Fig. 9. The histogram of data distribution of data and the superimposed normal distribution line.
Fig. 10. The variations of MSE versus the number of neurons in the hidden layer for Levenberg–Marquardt training algorithm.
Fig. 11. The variations of MSE versus the momentum and learning rate.
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Fig. 12. The scattering of data points around the best fitting line for training, testing and validation.
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layer, the MSE equal to 0.5217 was yielded among 1–20 neuron numbers being employed. Therefore, an ANN with 6-17-1 topological configuration using trainlm training algorithm and feed-forward with back propagation learning algorithm with logsig transfer function was chosen as the best model. The learning rate, which has influence on a portion of the individual adjustment to the previous weight, deals with the intensity of decreasing the error after iterations. In the case that the learning rate is set to a great value a quick learning procedure is resulted. Wherein a large instability in the input set occurs, the network may not learn preferably. In real terms, setting the learning rate to a large value is improper and counter-productive to learning [28]. It is therefore advised to set the factor to a lower level and gradually increase it where the learning rate seems slow. Momentum performs similar a low-pass filter to reduce the fluctuations in the progress while it allows a change to the weights to act against a number of adjustment cycles [28] and the degree of the persistence is controlled by the momentum factor. The adoptions of differently selected momentums and learning rates to minimize the representation error were performed. The variations of MSE versus learning rate and momentum changes are plotted in Fig. 11. The results showed that the optimum values of the learning rate and momentum were obtained at 0.6 and 0.7, respectively. The satisfactory performance of the developed ANN model is also recognized from Fig. 12 which is concerned with the scattering of data points around the best fitting line regarding the relationship of developed model prediction values versus the experimental data for the three portions of training, testing and validation. The promising values of correlation coefficient further confirm the robustness and satisfactory performance of the proposed ANN model. Fig. 12 reveals that the data points are distributed normally and not in heteroskedastic style. The coefficient of determination (R2) value equal to 0.99 and 0.99 were obtained for training and testing phases.
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6. Concluding remarks
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The present paper investigated the wall heat flux modeling of nheptane fueled direct injection (DI) diesel engine with the application of a coupled computational fluid dynamics (CFD) and artificial neural network (ANN) approach. The numerical model was established for a Ford 1.8 l DI diesel engine equipped with a prototype Lucas CAV HPCR system, and an Allied Signal VGT. The turbulent flows within the combustion chamber were simulated using the RNG k–e turbulence model. The input parameters of crank angle, mass flux, liquid mass evaporated, equivalence ratio, turbulence
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kinetic energy, and pressure were included in the system. It was concluded that more wall heat flux was transferred with fuel injection around TDC and along with combustion initiation for 2000 rpm and the higher pressure can be achieved at the same engine speed. Furthermore, a feed-forward with back propagation learning algorithm and Levenberg–Marquardt training technique was employed for various ANN modeling implementations. At 17 neurons in the hidden layer, the MSE equal to 0.5217 was yielded and the coefficient of determination values of 0.99 and 0.99 were obtained for training and testing phases and the optimum values of the learning rate and momentum were yielded at 0.6 and 0.7, respectively.
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References
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[14] Desantes JM, Torregrosa AJ, Broatch A, Olmeda P. Experiments on the influence of intake conditions on local instantaneous heat flux in reciprocating internal combustion engines. Energy 2011;36(1):60–9. [15] Torregrosa AJ, Bermúdez V, Olmeda P, Fygueroa O. Experimental assessment for instantaneous temperature and heat flux measurements under diesel motored engine conditions. Energy Convers Manage 2012;54(1):57–66. [16] AVL Concerto Software Operating Manual, Version 3.2; February 2000. [17] Hawley JG, Wallace FJ, Cox A, Cumming B, Capon G. An experimental study of the application of variable-geometry turbocharging and high-pressure common rail to an automotive diesel engine. J Inst Energy 2001;74(501): 124–33. [18] Khalilarya SH. An extended zero-dimensional simulation for HPCR diesel engines. Bath University, Doctorate thesis, February 2002. [19] Han Z, Reitz RD. Turbulence modeling of internal combustion engines using RNG K-e models. Combust Sci Technol 1995;106:267–95. [20] Liu AB, Reitz RD. Modeling the effects of drop drag and break-up on fuel sprays. SAE Paper NO. 930072; 1993.
[21] Dukowicz JK. Quasi-steady droplet change in the presence of convection. Informal Report Los Alamos Scientific Laboratory. LA7997-MS. [22] Halstead M, Kirsch L, Quinn C. The auto ignition of hydrocarbon fueled at high temperatures and pressures – fitting of a mathematical model. Combust Flame 1977;30:45–60. [23] AVL FIRE user manual V. 8.5; 2010. [24] Fire Software help, AVL, version 8.5; 2005. [25] Colin O, Benkenida A. The 3-zones extended coherent flame model (ECFM3Z) for computing premixed/diffusion combustion. Oil Gas Sci Technol Rev IFP 2004;59(6):593–609. [26] Taghavifar H, Taghavifar H, Mardani A, Mohebbi A. Exhaust emissions prognostication for DI diesel group-hole injectors using a supervised artificial neural network approach. Fuel 2014;125:81–9. [27] Roy S, Banerjee R, Bose PK. Performance and exhaust emissions prediction of a CRDI assisted single cylinder diesel engine coupled with EGR using artificial neural network. Appl Energy 2014;119:330–40. [28] Taghavifar H, Mardani A. Use of artificial neural networks for estimation of agricultural wheel traction force in soil bin. Neural Comput Appl 2013:1–10.
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Contents lists available at ScienceDirect
Fuel journal homepage: www.elsevier.com/locate/fuel 5 6
A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach
3 4 7 8 9
Q1
Hamid Taghavifar a,⇑, Hadi Taghavifar b, Aref Mardani a, Arash Mohebbi a, Shahram Khalilarya b a b
Department of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Urmia, Iran Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran
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h i g h l i g h t s The wall heat flux modeling of n-heptane fueled direct injection (DI) diesel engine was performed.
16
The coupled computational fluid dynamics (CFD) and artificial neural network (ANN) approach was developed.
17
A 6-17-1 ANN topology yielded the MSE equal to 0.5217 and R equal to 0.99.
2
18
a r t i c l e 2 3 0 3 21 22 23 24 25 26 27 28 29 30 31 32
i n f o
Article history: Received 21 June 2014 Received in revised form 5 September 2014 Accepted 23 September 2014 Available online xxxx Keywords: ANN CFD Wall heat flux Equivalence ratio Turbulence kinetic energy
a b s t r a c t The primitive purpose of the present paper is to address the wall heat flux modeling of n-heptane fueled direct injection (DI) diesel engine with the application of a coupled computational fluid dynamics (CFD) and artificial neural network (ANN) approach. The numerical model was established for a Ford 1.8 l DI diesel engine equipped with a prototype Lucas CAV HPCR system, and an Allied Signal VGT. The turbulent flows within the combustion chamber were simulated using the RNG k–e turbulence model. The input parameters of crank angle, mass flux, liquid mass evaporated, equivalence ratio, turbulence kinetic energy, and pressure were included in the system. It was concluded that more wall heat flux was transferred with fuel injection around TDC and along with combustion initiation for 2000 rpm and the higher pressure can be achieved at the same engine speed. Furthermore, a feed-forward with back propagation learning algorithm and Levenberg–Marquardt training technique were employed for various ANN modeling implementations. At 17 neurons in the hidden layer, the MSE equal to 0.5217 was yielded and the coefficient of determination values of 0.99 and 0.99 were obtained for training and testing phases. The optimum values of the learning rate and momentum were also yielded at 0.6 and 0.7, respectively. Ó 2014 Elsevier Ltd. All rights reserved.
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1. Introduction Extensive information on engine performance facilitates the design of modern machinery and processing equipment with modified quality specifications. The automotive research industry world-wide investigates various techniques to improve internal combustion engine efficiency and exploit alternative fuels [1]. Aiming this, a detailed investigation into the combustion phenomenon and energy balance is required. One beneficial approach is to assess the heat flux or thermal flux of combustion chamber wall. The rate of heat energy transfer through a given surface is recognized as heat flux which is most typically quantified by measuring a temperature ⇑ Corresponding author at: Department of Mechanical Engineering in Farm Machinery, Faculty of Agriculture, Urmia University, P.O. Box 165, Urmia, Iran. Tel.: +98 9143882707; fax: +98 441 277 19 26. E-mail addresses: [email protected], [email protected] (H. Taghavifar).
difference over a piece of material with known thermal conductivity. From the beginning of Diesel engine development, the significance of the heat transfer through the combustion chamber walls has been recognized [2–4]. The phenomenon is complex to analyze owing to its nonlinearity encompassing transient three-dimensional behavior, rapid temperatures wings, piston motion, cooling passages, and turbulent reactive fluid dynamics [4]. In internal combustion (IC) engines, heat transfer is one of the most important topics as it directly affects the main distinguishing parameters of the engine, such as in-cylinder pressure and temperature [5]. The development of a highly efficient global heat transfer model for the application of ICEs was the main objective behind the efforts of Ref. [6]. In real-world disciplines one cannot understand the precise heat flux at every point on the surface; however, approximation schemes can be utilized to compute the integral, for example Monte Carlo integration.
http://dx.doi.org/10.1016/j.fuel.2014.09.092 0016-2361/Ó 2014 Elsevier Ltd. All rights reserved.
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@Ein @Eout @Eaccumulated ¼0 @t @t @t
where the three @E terms are the representatives of the time rate of @t change of respectively the total amount of incoming energy, the total amount of outgoing energy and the total amount of accumulated energy. If the single approach that the system exchanges energy with its surroundings is through heat transfer, the heat rate can be used to calculate the energy balance;
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ð1Þ
@Ein @Eout ¼ @t @t
I
! ! /q : dS
ð2Þ
s
! where we have integrated the heat flux density /q over the surface S of the system. The computational fluid dynamics (CFD) codes [7] can further assist such research efforts, describing with great detail the incylinder phenomena [8], such as the flame kernel development, and the in-cylinder heat and mass transfer processes. There are also some investigations centered on the development of adiabatic engines, using the ceramic coatings on the combustion chamber walls and other high thermal resistive ingredients [9,10]. In this manner, the heat losses are decreased and/or could be partially converted into useful work [11–13]. A study was carried out for the development of more exact theoretical models for predicting the propagation of heat through the combustion chamber walls of reciprocating (internal combustion) IC engines while a fast response thermocouple was included in the combustion chamber of a single cylinder engine to measure the dynamic wall temperatures [14]. The heat flux was obtained by solving the one-dimensional transient energy equation with transient boundary conditions using the Fast Fourier Transform. Additionally, a study was conducted to validate an experimental facility to establish a technique to assess the influence of some of the engine parameters on local engine heat transfer behavior under motored steady-state conditions [15]. Instantaneous temperature measurements were carried out in order to estimate heat fluxes on a modified diesel single cylinder combustion chamber. To the best knowledge of authors, little is known about the assessment of wall heat flux of n-heptane fueled DI diesel engine under the effect of crank angle, mass flux, liquid mass evaporated, equivalence ratio, turbulence kinetic energy and pressure. A developed CFD code coupled with the predicting ability of artificial neural network (ANN) approach would be beneficial to predict the wall heat flux of n-heptane fueled DI diesel engine. Hence, the primitive objective of the present study was to cover the aforementioned aspects and furnish the needed information in this regard.
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2. Experimental description and modeling validation
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The experimental work is carried out for diesel fuel, noting that the numerical work was replicated for n-heptane fuel while fixing the operational and simulative conditions of engine running. In order to set up flexible fuel injection and air charge, variablegeometry turbocharging (VGT) and high-pressure common rail (HPCR) systems are applied. The HPCR system assures fuel injection pressure to be independent of crankshaft speed, which accordingly better air/fuel mixture can be obtained. The experiments were carried out 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. The experimental results were obtained with the aid of the AVL data acquisition system and
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Concerto software [16] is represented for each of the engine speeds by the following traces: 1. 2. 3. 4. 5.
Cylinder pressure (bar). Apparent rate of heat release (kJ/m3 °CA). Cumulative apparent heat release (kJ/m3). Rail pressure (bar). Electrical output of injector needle actuator.
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All dataset were measured at relatively early stages of the commissioning process of the equipment. Since a needle lift transducer was not available, the start of injection had to be interred from the instant where the raise pressure trace shows its first reduction. AVL 409 SMOKE (Bosch) and AVL AFR (Spindt) was used for measurement of smoke and air/fuel ratio. All results were obtained at the limiting torque curve with limits set to the following parameters over different speed ranges: Air–fuel ratio, A/F: P19 for Ne (engine speed) between: 1250– 1500 rpm. Maximum cylinder pressure, Pmax: 6140 bar for Ne between: 1500–3000 rpm. Pre turbine temperature, Texhaust 6 800 °C for Ne: 3000– 4000 rpm. More details about experimental setup and information about data acquisition apparatus and procedure are mentioned in [17,18]. The results of simulation was compared with the experimental data when running with diesel fuel in terms of pressure course (over CA), air–fuel ratio (AFR), and average fuel flow for different engine speeds. Fig. 1 demonstrates the validity of simulation results for diesel fueled engine. The simulation was extended for n-heptane fuel since no experimental data was available for n-heptane fueled engine. The predictability of ANN tool in the subsequent sections once again confirmed the validity of obtained data for alternative fuel.
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3. CFD simulation procedure
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The numerical model was established for a Ford 1.8 l DI diesel engine with the specifications listed in Table 1. The engine was operated at medium load for every operational condition of both engine speeds of 2000 and 3000 rpm. The diesel engine was equipped with a prototype Lucas CAV HPCR system, and an Allied Signal VGT. The numerical grid of combustion chamber is shown in Fig. 2(a) at TDC position with 101,327 cells (enough resolution is given for the convergence of desired results). The calculations for unsteady equations of mixtures on closed system were carried out from IVC (52 °CA BTDC) to EVO (110 °CA ATDC). The turbulent flows within the combustion chamber were simulated using the RNG k–e turbulence model [19]. In addition, the standard WAVE model was adopted for the primary and secondary breakup of the spray. For treating the heating up and evaporation of the droplets, the Dukowicz model [20] was taken into account. The interaction between the particles and the turbulent eddies as a result of fluctuating velocity was added to the mean gas velocity by a stochastic dispersion model [21]. The assumption of this model is postulated on the fact that the fluctuating velocity has a randomly Gaussian distribution. The Extend Coherent Flame Model, 3-Zone (ECFM-3Z Model) is developed based on the turbulent mixing was selected for the combustion process simulation in the combustion chamber [22,23]. Fig. 2(b) illustrates three zones mentioned in the modeling. The model is according to a flame surface density transport equation and a mixing model, which describes inhomogeneous turbulent premixed and diffusion combustion phases. In this model, the fuel is considered as combination
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Fig. 1. (a) Comparison between simulated and experimental pressure courses for diesel fuel @ 1500 rpm and (b) model validation for fuel flow rate and AFR over engine speeds.
Table 1 Engine operational condition. Bore stroke Displacement Compression ratio Swirl ratio @ IVC Rail pressure Nozzle geometry Number of nozzles Conrod Clearance Injection start timing Injection spray angle Operational mode
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82.5 82 mm 438 cm3/cylinder 19.5:1 3 540–1255 bar (based on engine speed) 5 0.15 mm 4 130 mm 0.86 mm 3 °CA ATDC 160 deg Medium load @ 2000 and 3000 rpm
of more than one chemical species. The rate of reaction for each fuel component is finally divided. In this way, it is possible to calculate the consumption of each component separately. The development of the combustion products is based on the consumption of the
single components. The combustion model is based on Coherent Flame Model that is coupled to the spray model and has the capacity of stratified combustion modeling and NO formation [24]. The extended combustion flame model is based on ECFM-3Z [25] that constitutes and recognizes three zones of unmixed air plus EGR (if any exists), the mixed air and fuel zone, and unmixed fuel. In this approach, flame propagation occurs from burned gas to unburned gas section and takes into account the three main combustion modes, i.e. Auto Ignition, Premixed Flame (oxidation), and Diffusion Flame. For a diesel spray, the fuel droplets have close proximity to each other and the fuel droplets can be classified at unmixed fuel part of the computational cell. After evaporation of droplet fuels, a definite period is needed to transfer from the pure fuel area to mixed fuel and air region. In this situation, the mixing of fuel with air is modeled by initially placing the fuel into the ‘unmixed fuel’ zone of the ECFM-3Z model [25]. The transport equation from the unmixed to the mixed zone is solved and presented in detail in Ref. [25].
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Fig. 2. (a) Meshing model of combustion chamber and (b) illustration of 3 zones of ECFM-3Z.
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The simulation is performed with n-heptane fuel in a diesel engine having the cetane number of 56, H/C ratio of 2.28, lower heating value equaling 44.9 (MJ/kg), and density of 0688 (g/mL, 20 °C). This fuel undergoes two-stage combustion. The ignition of n-heptane is controlled by some reactions during the combustion phase of low temperature stage. The low temperature reactions are initiated with the following reactions among others as well:
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n-C7 H16 þ O2 ! C7 H15 þ HO2
ð3Þ
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n-C7 H16 þ OH ! C7 H15 þ H2 O
ð4Þ
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Noting that the latter reaction is dominating through the process, whereas at the high temperature stage the chain branching reaction H + O2 = O + OH is controlling the reaction rate.
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4. Artificial neural network
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Artificial neural network (ANN) is a robust paradigm of artificial intelligence (AI) scope commonly considered as a universal approximator, which has been broadly acceptable and applicable across variety of scientific and engineering contexts. The scope of modeling has been the dynamic studying interest for the researchers and ANN has approved its robustness and promising ability to deal with the systems of stochastic and nonlinear systems with high degree of complexity. ANN is an emulation of biological neural system that is mimicking the biological behavior of the nervous system and approximates the operation of the human brain. In an
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ANN system neurons, each of which includes assigned weight and bias, are closely interconnected in various layers while the complexity of the problems decides the number of needed layers. This type of neural networks is so called multilayer neural networks whose most prominent representative is the Multi-Layered Perception (MLP). The layers which are sandwiched between the input layer and output layer are called hidden layers which play a substantial role on the predicting ability of the developed ANN. ANN system is a structure that receives an input, process the data, and provides an output while the input encompasses in a data array. When an input is transmitted to the neural network, and a corresponding desired or target response is set at the output, an error is composed from the difference of the desired response and the real system output. The error is fed back (back propagation) to the system which makes all adjustments to their parameters in a learning rule. This process is repeated (iteration or epoch) until the desired output is acceptable. The back propagation algorithm optimizes the model by convergence of the predicted values to the actual values using the gradient descent method. The schematic configuration of the developed ANN including the input and output parameters as well as the single hidden layer is demonstrated in Fig. 3. The total available data points of 520 in the present study were shuffled into three portions of 70%, 20% and 10% for training, testing and cross-validation, respectively. Levenberg–Marquardt training algorithm of trainlm was employed during modeling implementations owing to its well-documented ability dealing with combustion phenomenon of the DI engines [26,27]. A feed-forward ANN
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Fig. 3. The schematic configuration of the developed ANN.
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with back propagation (BP) learning algorithm was used where the four introduced training algorithms were applied to the implementations where gradient descent approach was used for error minimization. MLP neural network with one hidden layer and varying number of neurons was considered while the number of neurons where increased in each layer from 1 to 20 in order to avoid the randomly selection of ANN architecture. At the start of network training, initial weights and biases of neurons are chosen randomly. Therefore, for each number of hidden neurons (each network structure), network was trained for 100 times to overcome this drawback. The mean value based on the performance criterion was then considered as the predicting ability of the corresponding model. In each system training network was trained for 1000 epochs as the stopping parameter. For the normalization step, the following function was applied.
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Xn ¼
X r X r;min ðX h X l Þ þ X l X r;max X r;min
ð5Þ
where Xn denotes normalized input variable, Xr is raw input variable, and Xr,min and Xr,max denote minimum and maximum of input variable. Moreover, Xh and Xl are set to be 0 and 1. Since that the normalization outputs would be in compliance with the logsig transfer function. In modeling purposes, it is essential to assess the performance of developed representation by various statistical criteria. The mean square error (MSE) and the coefficient of determination (R2), are adopted for analysis of model quality as following.
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n 1X MSE ¼ ðY predicted Y actual Þ2 n i¼1
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R ¼
Pn
ð6Þ
2
i¼1 ðY predicted Y actual Þ Pn 2 i¼1 ðY predicted Y mean Þ
ð7Þ
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where Yactual and Ypredicted are measured and predicted values by the developed models.
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5. Results and discussion
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The wall heat flux through the combustion chamber wall is predicted and calculated by the Annand’s correlation, which is consisted of the several components such as Reynolds number, wall temperature, cylinder bore, cylinder mixture temperature, and
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the thermal conductivity of gas. The current study establishes a new modeling for the prediction of wall heat flux by consideration of other elements having of superior significance over the processes of flow field formation and combustion phenomenon. These factors include the chemical interactions of reactants, thermodynamic properties of in-cylinder mixture, the air–fuel mixture quality, and the CA position. In this sense the transfer of heat can be predicted via the evolution of reaction over the CA period, fuel mass flow rate, pressure, turbulence kinetic energy, equivalence ratio, and liquid mass evaporated. Fig. 4 depicts the concentration distribution of input parameters at two CA values of 730 and 740 and engine speeds of 2000 and 3000 rpm. It is deducible that the increased CA leads to the increment of equivalence ratio and mass flux in contradictory to that of pressure. During expansion stroke of actual engine the heat was transferred from the combustion chamber wall. The amount of heat generation depends on air compression and especially combustion, which utilizes the chemical reaction of air/fuel mixture with oxidizer components. In this regard, the most effective parameters were taken into account as to analyze the heat transfer in the form of convection that explains the main reason of irreversibility in the engine and deviation from the ideal diesel cycle. After injection of spray, the mixing of spray droplets with air happens. Having all droplets evaporated by the heat transfer from the surrounding air to fuel droplets, the combustion process initiates. The input parameters were such chosen to have the most influence on the combustion duration and intensity. Fig. 5 demonstrates the variation of heat flux and injected mass flux as a function of crankangle at 2000 and 3000 rpm engine speeds. It is clear that more wall heat flux was transferred with fuel injection around TDC and along with combustion initiation for 2000 rpm due to more mixing time of fuel and air that leads to higher combustion and heat generation. Moreover, the amount of mass fuel injection was plotted for different engine speeds. It is seen that higher rate of overall mass injection is of 3000 rpm especially at late combustion period denoting higher equivalence ratio originated from more fuel provided for combustion. At premixed combustion phase, the higher mass flux corresponds to lower 2000 rpm, which affects the equivalence ratio with more fuel proportion compared to air at the mixture. Fig. 6 demonstrates the equivalence ratio and in-cylinder pressure course within the combustion chamber at different times (crank-angles) under 2000 and 3000 rpm engine speeds. As shown, the higher pressure can be achieved for
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Fig. 4. The contour plots of the input parameters at two CA values.
Fig. 5. The variation of heat flux and injected mass flux as a function of crank-angle at 2000 and 3000 rpm engine speeds.
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2000 rpm since better mixture can be obtained because of more homogeneous mixture distribution denoted by lower equivalence ratio accompanied with better combustion and hence higher pressure. As it is appreciated from Fig. 7, applying higher engine speed can actively induce the turbulence amplitude whereby more uniform mixture can be expected; therefore, more fuel is expected to be evaporated. One has to note the contrary effect of lower engine speed on better mixture quality with more mixing time and poor mixing quality as a result of lower TKE. The superposition of input parameters with opposing effects on heat flux of combustion chamber was incorporated to develop a model to predict the output parameter based on neural network approach. Fig. 8 is a box plot of data in the x-axis which is the representative of the output vector of the data. On this box, the central mark is the median at 9050.94 W and the edges of the box are the 25th
and 75th percentiles. The whiskers extend to the most extreme data points not considered outlier and outliers are plotted individually. In the statistics’ discipline, a histogram is a graphical demonstration of the distribution of data while it gives an estimate of the probability distribution of a continuous variable. The histogram in Fig. 9 shows the distribution of data values where the superimposed normal distribution line is fitted. It is deducible that the data distribution has a satisfactory level of accordance with that of normal distribution line, however, the k-fold cross validation ensured the contributing role of any random share of data in the final result of the developed representation. The inclusion of the various numbers of neurons in the hidden layer has significant effect on the obtained result. In order to avoid the random selection of ANN configuration, the number of neurons in the hidden layer varied to observe the change of MSE (Fig. 10). At 17 neurons in the hidden
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Fig. 6. The variation of pressure and equivalence ratio as a function of crank-angle at 2000 and 3000 rpm engine speeds.
Fig. 7. The variation of turbulence kinetic energy and liquid mass evaporated as a function of crank-angle at 2000 and 3000 rpm engine speeds.
Fig. 8. The statistical box plot of data to show the maximum, minimum and median.
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Fig. 9. The histogram of data distribution of data and the superimposed normal distribution line.
Fig. 10. The variations of MSE versus the number of neurons in the hidden layer for Levenberg–Marquardt training algorithm.
Fig. 11. The variations of MSE versus the momentum and learning rate.
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Fig. 12. The scattering of data points around the best fitting line for training, testing and validation.
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layer, the MSE equal to 0.5217 was yielded among 1–20 neuron numbers being employed. Therefore, an ANN with 6-17-1 topological configuration using trainlm training algorithm and feed-forward with back propagation learning algorithm with logsig transfer function was chosen as the best model. The learning rate, which has influence on a portion of the individual adjustment to the previous weight, deals with the intensity of decreasing the error after iterations. In the case that the learning rate is set to a great value a quick learning procedure is resulted. Wherein a large instability in the input set occurs, the network may not learn preferably. In real terms, setting the learning rate to a large value is improper and counter-productive to learning [28]. It is therefore advised to set the factor to a lower level and gradually increase it where the learning rate seems slow. Momentum performs similar a low-pass filter to reduce the fluctuations in the progress while it allows a change to the weights to act against a number of adjustment cycles [28] and the degree of the persistence is controlled by the momentum factor. The adoptions of differently selected momentums and learning rates to minimize the representation error were performed. The variations of MSE versus learning rate and momentum changes are plotted in Fig. 11. The results showed that the optimum values of the learning rate and momentum were obtained at 0.6 and 0.7, respectively. The satisfactory performance of the developed ANN model is also recognized from Fig. 12 which is concerned with the scattering of data points around the best fitting line regarding the relationship of developed model prediction values versus the experimental data for the three portions of training, testing and validation. The promising values of correlation coefficient further confirm the robustness and satisfactory performance of the proposed ANN model. Fig. 12 reveals that the data points are distributed normally and not in heteroskedastic style. The coefficient of determination (R2) value equal to 0.99 and 0.99 were obtained for training and testing phases.
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6. Concluding remarks
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The present paper investigated the wall heat flux modeling of nheptane fueled direct injection (DI) diesel engine with the application of a coupled computational fluid dynamics (CFD) and artificial neural network (ANN) approach. The numerical model was established for a Ford 1.8 l DI diesel engine equipped with a prototype Lucas CAV HPCR system, and an Allied Signal VGT. The turbulent flows within the combustion chamber were simulated using the RNG k–e turbulence model. The input parameters of crank angle, mass flux, liquid mass evaporated, equivalence ratio, turbulence
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kinetic energy, and pressure were included in the system. It was concluded that more wall heat flux was transferred with fuel injection around TDC and along with combustion initiation for 2000 rpm and the higher pressure can be achieved at the same engine speed. Furthermore, a feed-forward with back propagation learning algorithm and Levenberg–Marquardt training technique was employed for various ANN modeling implementations. At 17 neurons in the hidden layer, the MSE equal to 0.5217 was yielded and the coefficient of determination values of 0.99 and 0.99 were obtained for training and testing phases and the optimum values of the learning rate and momentum were yielded at 0.6 and 0.7, respectively.
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Please cite this article in press as: Taghavifar H et al. A numerical investigation on the wall heat flux in a DI diesel engine fueled with n-heptane using a coupled CFD and ANN approach. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.09.092