Chemistry acceleration with tabulated dynamic adaptive chemistry in a realistic engine with a primary reference fuel

Fuel 171 (2016) 186–194

Contents lists available at ScienceDirect

Fuel journal homepage: www.elsevier.com/locate/fuel

Chemistry acceleration with tabulated dynamic adaptive chemistry in a realistic engine with a primary reference fuel Lei Zhou ⇑, Haiqiao Wei State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China

h i g h l i g h t s
Efficient chemistry calculation via combined ISAT–DAC.
Chemistry acceleration effected by temperature inhomogeneity.
Performance of ISAT–DAC with different error tolerance values.
Low temperature chemistry is very important.

a r t i c l e

i n f o

Article history: Received 25 September 2015 Received in revised form 22 December 2015 Accepted 24 December 2015 Available online 31 December 2015 Keywords: ISAT–DAC HCCI Computational cost Temperature inhomogeneity

a b s t r a c t Detailed kinetic reaction mechanisms are necessary for accurate prediction of combustion characteristics such as ignition and emissions in realistic engines. However, the calculation of chemically reacting flows with detailed chemistry is computational expensive due to the large number of species and reactions involved. In this study, a combined approach of dynamic adaptive chemistry (DAC) and in situ adaptive tabulation (ISAT) for efficient chemistry calculations has been implemented into a three-dimensional flow solver to simulate a homogenous charged compression ignition (HCCI) engine with a primary reference fuel (PRF). In the combined method, ISAT speeds up the chemistry calculation by reducing the number of integrations of ordinary differential equations (ODEs) governing chemical kinetics through tabulating and re-using the ODE solutions. At the meantime, DAC accelerates the necessary ODE integrations via the use of locally valid reduced mechanisms, which are obtained using the direct relation graph (DRG) method. The study shows that ISAT–DAC can achieve a speedup factor of about three with accurate prediction of composition and heat release even for the pressure-varying transient engine simulation with significant composition inhomogeneity resulting from wall heat loss. A detailed analysis reveals that the combined method effectively reduces the computational cost through taking advantage of the respective acceleration characteristics of DAC and ISAT at different combustion stages. In the low temperature combustion stage between about 650 K and 1000 K, even though the reduction in the mechanism size and consequently the ODE integration of the chemical kinetics by DAC is not significant, the combined method can still reach a speed-up factor of more than 100 due to the fact that the tabulated entries can effectively be reused. For the high temperature region, even though the tabulated entries cannot be reused due to the rapid change of the pressure and large composition inhomogeneity resulting from the active combustion and heat loss, DAC can effectively reduce the size of the needed ODE integrations by freezing a significant number of unimportant species and reactions. The study further quantifies the effect of composition inhomogeneity on the computation efficiency in detailed chemistry calculations in realistic engine simulations. For the case considered, the temperature inhomogeneity due to the wall heat loss obviously increases at around top dead center (TDC), reaching a level of 350 K difference in temperature within the combustion chamber. Consequently, the overall computational efficiency in chemistry calculation by the combined method has been reduced by 40% compared to the case without heat loss. Ó 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: 92 Weijin Road, Nankai District, Tianjin, China. E-mail address: [email protected] (L. Zhou). http://dx.doi.org/10.1016/j.fuel.2015.12.055 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.

L. Zhou, H. Wei / Fuel 171 (2016) 186–194

1. Introduction Practical engine fuels, such as gasoline and diesel, consist of multi-component with variant classes of chemical structures [1]. It is widely accepted that the oxidation processes of n-heptane and iso-octane can represent the ignition and combustion characteristics of diesel and gasoline fuels well. The multi-component surrogate fuels of diesel and gasoline, such as primary reference fuel (PRF) [2–6], n-heptane/toluene/ethanol blends [7], and toluene reference fuel (TRF) [8], are applied in numerical simulation researches. PRF is widely used as a surrogate fuel of practical fuels, which is a mixture of n-heptane and iso-octane [2] with the octane number ranging from 0 to 100. It provides detailed chemical information with detailed chemistry kinetic mechanisms to predict the ignition, flame propagation, and emission processes in internal combustion engine (ICE) accurately. The major computational challenge of the IC engine simulations with detailed chemistry is the time-intensive nature of chemical integration, which may account for more than 90% of the overall simulation time [9]. Over the last decades, significant progresses have been made to accelerate the chemistry calculations in engine combustion simulations [9–19], such as in situ adaptive tabulation (ISAT) [16]; cell agglomeration methods such as multi-zone models [11], and dynamic adaptive chemistry (DAC) [20,21]. The DAC approach accelerates the time-integration of ODEs through the use of locally (spatially and temporally) valid skeletal mechanisms, which are obtained by invoking the directed relation graph method [22,23] or its variants [24–26] for each CFD cell to perform on-thefly mechanism reduction at the local thermochemical condition. DAC has been successfully demonstrated for chemistry acceleration in internal combustion engine (ICE) simulations [9]. In contrast, ISAT algorithm presented by Pope [27] offers the unique feature of storing and retrieving the chemical integration results. By tabulating solutions of ordinary differential equations (ODEs) system governing chemical kinetics and reusing them, ISAT can substantially reduce the number of direct chemical kinetic integrations and significantly speedup the chemistry calculations. The computational efficiency of the ISAT algorithm is higher when the tabulated information can be re-used more frequently. For instance, speedup factors of 100–1000 can be achieved using ISAT for statistically stationary reactive flows [27]. More recently, the combined use of ISAT and DAC (ISAT–DAC) was employed by Contino et al. [28] and Ren et al. [13] for highly efficient ICE simulations with detailed chemistry. For example, with ISAT–DAC, a speed-up factor of hundreds to thousands for chemistry calculations has been achieved in a simple 2D HCCI simulation [28]. However, ISAT–DAC with extreme high speed up factor is only achieved so far for simple configurations and close-tohomogeneity conditions. Its performance is still unclear for challenging simulations with complex configurations and significant composition inhomogeneity. In recent study [29], Gianluca et al. carried out a heavy-duty diesel engine simulation with the ISAT– DAC similar to that proposed by Contino et al. [28]. It was found that an overall speed-up factor of only 1.2 was achieved compared to direct integration (DI) due to the significant composition inhomogeneity in the simulation, although a detailed analysis of the influence of the temperature and compositions inhomogeneity on the chemistry calculation acceleration is not provided. The object of this work is to investigate the performance of the ISAT–DAC method for practical engine simulations with significant temperature inhomogeneity, which is the case even for HCCI engine due to wall heat loss. To do so, the ISAT–DAC method has been implemented into a three-dimensional flow solver to simulate a homogenous charged compression ignition (HCCI) engine with a primary reference fuel (PRF). A detailed analysis has been

187

performed to investigate the acceleration characteristics of DAC and ISAT at different combustion stages. The study further quantifies the effect of composition inhomogeneity on the computation efficiency. As an outline of the paper, the acceleration methods DAC, ISAT, ISAT–DAC and the computational model are reviewed in Section 2. In Section 3, the performance of the ISAT–DAC in HCCI engine simulations is analyzed. Conclusions are in Section 4. 2. Model description For a gas-phase reacting mixture consisting of ns chemical species participating in nk elementary reactions, its thermo-chemical state is described by the pressure P, temperature T, mixture sensible enthalpy hs and the ns-sized vector Y of species mass fractions. In reaction sub-steps of the simulations with an operator splitting scheme [30,31], the compositions U  {Y, hs, Ps} of each cell is governed by a set of nonlinear stiff ordinary differential equations:

dU ¼ SðUÞ; dt

ð1Þ

where S is the rate of change due to chemical reactions. Note that this source term has contributions from all the nk reactions in the mechanism. 2.1. Combined method implemented into CFD The DAC approach accelerates the time-integration of Eq. (1) through the use of locally (spatially and temporally) valid reduced mechanisms, which is obtained using the direct relation graph (DRG) method [22]. The DRG method eliminates the species that do not significantly affect the reaction rates of the major species based on a threshold, eDAC , for the truncation of weak species couplings. Details on the DAC method can be found in Refs. [13,20]. Note that the starting species need to be provided at each combustion step. In the present study, 6 species including three maximum mass fractions and three fixed species like CO, NO and HO2 are selected as starting species for each given local composition based on the past studies [9,14]. For the ISAT, from the initial condition U0 at time t0, Eq. (1) is integrated for a time Dt to obtain U(t0 + Dt). For fixed Dt, the reaction is mapping RðU0 Þ ¼ Uðt0 þ DtÞ. In practice, the typical combustion system involves dozens of chemical species and the stiffness of Eq. (1) is very strong, direct integration (DI) is a computational intensive process and requires significant computational resources. However, ISAT uses the ODE solver DDASAC to integrate Eq. (1) and stores the relevant information in a binary tree, with each termination node representing a record consisting of the tabulation points, the reaction mapping f, and the mapping gradient matrix A. Thus, for a given query composition xq close to a tabulated point x, from the tabulated quantities at x, a linear approximation to fl,n can be obtained with a small error tolerance eISAT as

f

l;n

n

¼ f þ An ðxq  xn Þ;

ð2Þ

The detailed explanation can be found in Ref. [13]. In this work, the combined use of ISAT and DAC, denoted as ISAT–DAC is implemented into the multi-dimensional CFD code KIVA3V [32] and the reaction sub-step of a CFD simulation is shown in Fig. 1. The composition, /  fY; hs ; Pg involving the entire reaction species in a detailed chemical kinetic mechanism is solved in CFD solver. For the reaction sub-step in CFD the species mass fractions are used to describe species variations and enthalpy is used to evaluate the energy or temperature variation. Besides, the local pressure is a known parameter. For the reaction substep with ISAT–DAC, the composition /(Dt) is determined based

188

L. Zhou, H. Wei / Fuel 171 (2016) 186–194

Fig. 1. Schematic of KIVA- ISAT–DAC employed in the reaction sub-step.

on the starting composition /(0) at adiabatic and isobaric conditions. An ISAT table stores a pair of values of /(0) and /(Dt) to be re-used in future integration steps [13]. For ISAT–DAC, the calculation procedure follows as below: Firstly, Given the initial composition /(0), from the searchinitiating species, DRG reduction is performed to obtain a skeletal mechanism that is valid for the local thermochemical conditions. Then the initial composition is decomposed as  ð/r ; /u Þ, with /r being the mass fractions of the retained species together with mixture sensible enthalpy hs, and /u being the mass fractions of the unimportant species. Secondly, the simplified ODEs for the species retained in the skeletal mechanism are integrated for a time step to obtain the full composition with the unimportant species being approximated to be frozen, the equations are solved as follows:

( d/r

dt d/u dt

¼ Sr ð/r ; /u Þ

ð3Þ

¼0

The ISAT–DAC method inherited the advantages from both ISAT and DAC to solve combustion problems with complex chemistry efficiently: the number of expensive direct ODE integrations is reduced by tabulating and reusing the solutions, and the required direct integrations are expedited by the local DRG reduction. 2.2. Numerical models and conditions The computational efficiency and performance of dynamic adaptive chemistry (DAC) and tabulation strategies are investigated in a HCCI engine fuelled with a primary reference fuel.

ISAT–DAC used in this work follows that of Ren et al. [13]. The engine operation conditions are listed in Table 1. The numerical scheme is based on the Arbitrary Lagrangian–Eulerian method with the finite volume method. For the continuum phase in URANS, a RNG k-e turbulence model is used with default model parameters C_l = 0.085, C_e1 = 1.42, C_e2 = 1.68, C_es = 1.50, Pr_k = 1.39, and Pr_e = 1.396. The heat transfer model of Han and Reitz [33] with standard parameters is employed to describe wall heat loss. The well-stirred combustion model consisting of a PRF reduced mechanism of 41 species and 124 reactions [2] and a NOx submechanism of 4 species and 13 reactions [34] is employed to describe the combustion and emission processes. Threedimensional simulations with a grid of approximately 0.1M cells (see Fig. 2) start at the intake valve close crank angle 108 °CA before TDC (BTDC) and end at 30 °CA after TDC (ATDC). In this work, the combustion calculation is activated after the temperature of the computation cell is larger than 650 K. The time step varies from 1.0  108 s to 1.0  106 s, depending on physicochemical time scales and the CFL number in the simulations. 3. Results and discussions Until now, there are few works applying the combined method ISAT–DAC to study a realistic HCCI engine and investigate the effect of temperature inhomogeneity on the computational efficiency. In the present study, firstly the convergence of ISAT–DAC with different error tolerances is discussed. Then a comparison of computational efficiencies using the DAC, ISAT and ISAT–DAC in

Table 1 Specifications of simulated engines. Fuel

Engine type

Bore  stroke (mm)

Compression ratio

Equivalence ratio

Swirl number

Engine speed (r/min)

Simulated Ti (K)

Ref.

PRF70

HCCI

86  86

14

0.2785

1.8

1200

524

[32]

189

L. Zhou, H. Wei / Fuel 171 (2016) 186–194

obtain same pressure variation following crank angle compared with that using DI with full mechanism. However, both DAC and ISAT–DAC fail to accurately predict the pressure evolution and have a little deviation from the experiment data with eDAC ¼ 0:01. It shows that the large error tolerance eDAC ¼ 0:1 postpones the auto-ignition timing. The present results are dominantly controlled by the DAC error tolerance when the ISAT error tolerance is set to be eISAT ¼ 104 . The obvious difference using different DAC error tolerances on combustion process can be observed in Fig. 4b. The evolution of heat release rate with the two error tolerances eDAC ¼ 0:01 and eDAC ¼ 0:001 are well in agreement with that using full mechanism. The methods with eDAC ¼ 0:1 fail to predict the timing of heat release rate reaching its peak value. In addition, the peak value of heat release rate predicted by the methods with error tolerance eDAC ¼ 0:001 is closer to that with full mechanism due to more retained important reactions. Table 2 summarizes the speed-up factor using different DAC error tolerances for DAC and ISTA–DAC. It can be seen that the increased percentage of speed-up factor using ISAT–DAC is improved by about 20% from 2.67 with eDAC ¼ 0:001 to 3.2 with eDAC ¼ 0:01, with a 0.2 °CA delay of the auto-ignition timing. Fig. 5 shows the mass evolutions of n-heptane, octane mass and CO. Obviously, the profiles with eDAC ¼ 0:1 are different from other profiles with eDAC ¼ 0:01 and eDAC ¼ 0:001, specially for the evolution of CO. Note that the evolution of CO is similar to the evolution of heat release rate as shown in Fig. 4. The production of CO is postponed with a maximum error about 1 °CA using only DAC with eDAC ¼ 0:1, about 0.0005 °CA using only DAC with eDAC ¼ 0:001 and about 0.07 °CA using ISAT–DAC with eDAC ¼ 0:001. For the mass of heptane and octane, the overall variation trends are similar. However, in the descending process of the evolution of octane mass, the octane profile is a little steeper than that of heptane due to their different burning features. Furthermore, the local amplified images as shown in Fig. 5 demonstrate the performances of using ISAT, DAC and ISAT–DAC methods with different error tolerances more clearly. Generally, ISAT–DAC inherits the advantages of ISAT and DAC to achieve the high-efficiency and accuracy simulation results. The fuel consumption predicted by DAC with eDAC ¼ 0:001 is very close to that by full mechanism. Fig. 6 further shows the evolution of the retained species distribution as a function of temperature at several crank angles. It can be seen that the distribution of the retained important species has significantly differences at the different temperatures with varied crank angles. The retained important species strongly rely on the

Fig. 2. Computational grids for HCCI engine simulation. Three-dimensional, 93174 cells for PRF70 HCCI combustion simulation.

the combustion process is presented by the profiles of transient computational time. Finally, the effect of temperature inhomogeneity on computational efficiency is demonstrated. 3.1. Convergence characteristics of ISAT–DAC Fig. 3 shows the evolutions of mean pressure and heat release rate versus crank angle obtained by employing ISAT–DAC with different ISAT error tolerances. It is observed that the results obtained by ISAT–DAC with ISAT error tolerances of

eISAT ¼ 10

5

eISAT ¼ 104 and

present a very good agreement with results obtained by DI with the full mechanism and experiment data. ISAT–DAC with ISAT error tolerance eISAT ¼ 2  104 fails to predict the mean pressure and heat release rate. That is because that increasing ISAT error tolerance means the increase of the numbers of computational cell using the ISAT table to interpolate the species variation, which can lead to the inaccurate prediction due to the big difference of thermodynamic parameters in different computational cells. Overall, the ISAT error tolerance eISAT = 104 is set as the default value in this work. Fig. 4 shows the profiles of the pressure and heat release rate with different DAC error tolerances for DAC and ISAT–DAC compared with experiment data and the results obtained by DI with full mechanism. It can be seen from Fig. 4a that DAC and ISAT– DAC with the error tolerances eDAC ¼ 0:01 and eDAC ¼ 0:001 can

100

6

80 Heat Release Rate (J/CA)

Pressure (MPa)

5

4

3 ISAT-DAC(εISAT =2.0E-4) 2

ISAT-DAC(εISAT =1.0E-4) ISAT-DAC(εISAT =1.0E-5) Full

1

Experiment

0

-10

0

10

ISAT-DAC(εISAT =2.0E-4)

60

ISAT-DAC(εISAT =1.0E-4) ISAT-DAC(εISAT =1.0E-5) Full

40

Experiment

20

20

0

-10

0

10

Crank angle (degree)

Crank angle (degree)

(a) Pressure

(b) Heat release rate

Fig. 3. Pressure (a) and heat release rate (b) profiles with different ISAT error threshold values for ISAT–DAC with

20

eDAC ¼ 0:001.

190

L. Zhou, H. Wei / Fuel 171 (2016) 186–194

6

Heat Release Rate (J/CA)

5

Pressure (MPa)

DAC(εDAC =0.1)

100

4 3 DAC(εDAC =0.1) DAC(εDAC =0.001) ISAT-DAC(εDAC =0.001) ISAT-DAC(εDAC =0.01) ISAT-DAC(εDAC =0.1) Full Experiment

2 1 0 -30

-20

-10

0

10

20

DAC(εDAC =0.001) ISAT-DAC(εDAC =0.001) ISAT-DAC(εDAC =0.01) ISAT-DAC(εDAC =0.1)

80

Full Experiment

60

40

20

0 -20

30

-10

0

10

20

Crank angle (degree)

Crank angle (degree)

(a) Pressure

(b) Heat release rate

Fig. 4. Pressure (a) and heat release rate (b) profiles with different DAC threshold value for DAC and ISAT–DAC.

Table 2 The speed-up factors with different DAC threshold value for DAC and ISTA–DAC. Method

DAC

Speed-up

1.2

eDAC ¼ 0:001

DAC

eDAC ¼ 0:1

ISTA–DAC

1.55

0.002

eDAC ¼ 0:1

ISTA–DAC

3.4

eDAC ¼ 0:01

ISTA–DAC

3.2

2.67

0.00432

0.006

0.00163

0.00431 0.00162 0.0043

0.00161

0.0015

0.00429

Octane mass (g)

n-Heptane mass (g)

0.005

0.0016 0.00159

0.001 DAC(εDAC=0.001) ISAT-DAC(εDAC=0.001) ISAT-DAC(εDAC=0.01)

0.004

0.00427

0.003

0.001

Full

-30

ISAT-DAC(εDAC=0.01) ISAT-DAC(εDAC=0.1) ISAT

ISAT

0

DAC(εDAC=0.001) ISAT-DAC(εDAC=0.001)

0.002

ISAT-DAC(εDAC=0.1)

0.0005

0.00428

0

Full

0

30

-30

0

Crank angle (degree)

Crank angle (degree)

(a) n-Heptane

(b) Octane

20000 DAC(εDAC=0.001) ISAT-DAC(εDAC=0.001) ISAT-DAC(εDAC=0.01) ISAT-DAC(εDAC=0.1) ISAT Full

CO (ppm)

15000

10000

5000

0 -30

-20

-10

0

10

20

30

40

Crank angle (degree)

(c) CO Fig. 5. Profiles of n-heptane, Octane and CO versus crank angle with DAC, ISAT and ISAT–DAC.

eDAC ¼ 0:001

Full 1

191

L. Zhou, H. Wei / Fuel 171 (2016) 186–194

Fig. 6. Retained species distribution in overall computational domain against temperature at different crank angles with

Fig. 7a presents the pressure profiles against crank angle using only DAC, ISAT and ISAT–DAC, compared with experiment data and the results using DI with full mechanism. In this work, the error tolerances with DAC eDAC ¼ 0:001 and with ISAT eDAC ¼ 0:0001 for the combustion simulations are set as default values. It can be seen that the average pressure profiles with DAC, ISAT and ISAT–DAC agree with that using DI with full mechanism, which are also similar to the experiment data. The above results prove that the coupled approach has the ability to accurately predict the combustion process compared with the results obtained using DI with full mechanism. Table 3 compares the speed-up factors achieved by DAC, ISAT and ISAT–DAC with same error tolerance. The speed-up factor is calculated based on the entire simulation time, rather than the chemistry computational time. From the results, it can be seen that ISAT–DAC performs the highest-efficiency, although the chemistry mechanism is a reduced mechanisms with a small scale of species and reactions. Fig. 7b presents the performance and computational acceleration mechanism of DAC, ISAT and ISAT–DAC compared with full mechanism by transient computational time. It can be seen that the most computation time costs at the low temperature combustion stage for the full mechanism case. The result with DAC also has similar trend at low temperature combustion stage due to the most species retained as shown in Fig. 6. However, DAC can effectively reduce computational cost at high temperature combustion stage

Pressure (MPa)

5

4

3

2 DAC ISAT ISAT-DAC Full

1

Experiment

0 -30

-20

-10

0

10

20

30

Crank angle (degree)

(a) Pressure 90

600

Full DAC ISAT ISAT-DAC T-variance

60

500 high temperature and inhomogenerity 400 area

300

30

200

T variance (K)

3.2. Computational efficiency

6

Transient Computation Cost (min/CA)

combustion states. As the piston moves up, temperature and pressure increase gradually and low temperature oxidation reaction occurs. Consequently, more species are retained by the DRG reduction method. As shown in Fig. 4b, the main combustion stage is from 10 °CA BTDC to TDC, and the retained species are almost the same as the entire species in the mechanism. Fig. 6 also demonstrates that at low temperature combustion stage from around 650 K to 1000 K, combustion process requires all species included in the mechanism to join the reaction to calculate the auto ignition process and heat release accurately. Note that the low temperature combustion process plays a very important role in the whole combustion process and it needs more species and reactions, which agrees with the foundation studies in Refs. [2,35]. At the post-combustion stage, most species and reactions reach chemical equilibrium and the numbers of the retained important species start reducing. Moreover, it is observed that the retained important species with different numbers distribute widely in the entire computational domain, which also explain the thermo-chemistry parameters become inhomogeneity in combustion chamber.

eDAC ¼ 0:001.

100

0 -60

0 -40

-20

0

20

Crank Angle (degree)

(b) Computational efficiency Fig. 7. The overall evolution of Pressure versus crank angle (a) and quantify the computational efficiency versus crank angle (b) using DAC, ISAT, and ISAT–DAC with eISAT ¼ 104 and eDAC ¼ 0:001 compared with Full mechanism.

Table 3 The speed-up factors with DAC, ISAT and ISAT–DAC. Method

DAC

ISAT

ISAT–DAC

Full

Speed-up

1.2

2.3

2.67

1

and post-combustion stage due to the fact that the significant reduction in the mechanism size by DAC is obtained. On the contrary, ISAT has very high computational efficiency and the

192

L. Zhou, H. Wei / Fuel 171 (2016) 186–194

Fig. 8. Distribution of compositions in CO-OH-T subspace, colored by the mixture fraction of n-heptane at 5 °CA TDC for Full case and ISAT–DAC case with eDAC ¼ 0:001 and eISAT ¼ 104 .

transient speed-up factor reaching about more than 100 at low temperature combustion stage when the tabulated entries can be effectively reused. Such high speed-up factor is in agreement with previous study on the homogeneity condition [28]. However, the efficiency of ISAT method becomes very low after the beginning of the fast heat release at around 10 °CA BTDC. The computation time with ISAT becomes close to that with full mechanism due to temperature inhomogeneity resulting in that the storage of ISAT table becomes full as shown in Fig. 7b that will be discussed later. Thus, the poor performance of ISAT at this stage urgently requires to be improved. When ISAT–DAC is employed, it takes advantages of both DAC and ISAT at different combustion stages and significantly reduce the computational cost. That is, ISAT plays an important role at the low temperature stage but the acceleration of DAC is not obvious, while at high temperature stage DAC obviously domains the acceleration of chemistry calculation. Fig. 8 shows the projection of compositions in the emission CO, crucial radical OH and temperature T subspace at 5 °CA TDC. It obviously demonstrates the distribution of compositions in the entire computational domain. The scatter dots are colored by mixture fraction of fuel n-heptane. As shown in Fig. 8, the present

ISAT–DAC does not significantly influence the manifold in the composition space compared with the results using DI with full mechanism. 3.3. Effect of temperature inhomogeneity Fig. 9 shows contour plots of temperature, fuel species and emissions at different crank angles. At crank angle 10 °CA BTDC, the combustion intensity is weak, but the temperature at the boundary of the combustion chamber is obviously below the other areas due to wall heat loss. However, the distribution of temperature is still relatively homogeneous at this time. It can be seen that from the 5 °CA BTDC to 10 °CA ATDC the temperature increases fast, meanwhile the distribution of temperature becomes more inhomogeneous. In addition, it is found that the distribution of NOx strongly depends on the distribution of temperature. Much higher NOx concentration appears at the center of combustion chamber. The figure also indicates the temperature inhomogeneity near the wall has significant effect on the CO concentration as highest CO concentration is near the combustion chamber wall due to the insufficient combustion process. Therefore, for the

Fig. 9. Contour of temperature distribution, NOx and CO species distribution at four crank angles for full mechanism case.

L. Zhou, H. Wei / Fuel 171 (2016) 186–194

present HCCI case the emissions strongly rely on the temperature distribution, particularly in the regime near the combustion chamber wall. In order to demonstrate the evolution of temperature inhomogeneity against crank angle quantitatively, the inhomogeneity variance equation is used in this study. The equation can be found at below:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 Xn  S¼ XI  X i¼1 n1

ð4Þ

S represents the inhomogeneity rate (or temperature variance), n is the overall computational cells, and Xi is the temperature in the i th cell, X is the average temperature. Fig. 10 presents the mean pressure evolutions and overall computation time predicted by ISAT–DAC with and without the wall heat loss compared with that using DI with the full mechanism. As shown in Fig. 10a, it indicates that the proper modelling of wall heat loss is critical to capture the right combustion phasing for HCCI case. Without heat loss model, the ignition timing is significantly advanced. The predicted pressures using ISAT–DAC with

eISAT ¼ 104 and eDAC ¼ 0:001 are in good agreement with experiment data, and have only very tiny difference. Actually, the errors induced by ISAT–DAC are much smaller than that by heat loss model in this work. Fig. 10b shows that for the case without wall heat loss, ISAT–DAC can further improve computation efficiency

6

5

Pressure (MPa)

4

3

2 ISAT-DAC ISAT-DAC-no wall heat loss Full Full-no wall heat loss Experiment

1

0 -30

-20

-10

0

10

20

30

Crank angle (degree)

(a) Pressure

2000

Full Full-no wall heat loss ISAT-DAC ISAT-DAC-no wall heat loss T-variance T-variance-no wall heat loss

800

600

1500 400 1000

T-variance (K)

Overall Computation Cost (min)

2500

200 500

0 -100

0 -50

193

and the overall speed-up factor can achieve more than 5. From Fig. 10a, it can be seen that the combustion without wall heat loss is stronger than that with wall heat loss. Thus, the overall computational time for the case without wall heat loss is larger than that with wall heat loss in terms of using the full mechanism. However, the conclusion for ISAT–DAC is very different. It is found that the computation time obtained by ISAT–DAC without wall heat loss is smaller than that obtained by ISAT–DAC with wall heat loss. Through the comparison of temperature variance variations, it can be seen that the temperature inhomogeneity due to the wall heat loss increases obviously at around TDC, which leads to higher computational cost. It is also noteworthy that the speed-up factor reaches around 100-fold before the rapid increase of temperature invariance. After that, the computational efficiency becomes very low. Therefore, the overall computation efficiency is significantly weakened. 4. Conclusions In this work, a coupled method of DAC and ISAT has been successfully implemented into a 3-D CFD code for the efficient simulations of a realistic HCCI engine with a reduced PRF mechanism. A detailed analysis reveals that ISAT–DAC effectively reduces the computational cost by taking advantage of the respective acceleration characteristics of DAC and ISAT at different combustion stages. In this work, the overall speed-up factor can achieve about 3 with the temperature inhomogeneity. Firstly, the performance of ISAT–DAC with different error tolerances is investigated. Compared with the evolutions of the mean pressure, heat release and compositions versus the crank angle, ISAT–DAC with eDAC ¼ 0:001 and

eISAT ¼ 104 can perform accurate results, which are in well agreement with experiment data and simulation results obtained by DI with full mechanism. Then the computational efficiency is studied in detail. In ISAT– DAC, ISAT plays a dominant role in controlling the computational efficiency in the low temperature region, as a speedup factor up to 100 is achieved due to the fact that the tabulated entries can effectively be reused. Furthermore, DAC can effectively reduce the size of the needed ODE integrations by freezing a significant number of unimportant species and reactions at high temperature combustion stage and post-combustion stage. The study further quantifies the effect of temperature inhomogeneity on the computation efficiency in detailed chemistry calculations in the realistic engine simulations. The computational efficiency becomes very low due to the rapid increase of temperature inhomogeneity induced by wall heat loss. Therefore, the overall computation efficiency is significantly weakened. It is also worth mentioning that challenges still exist in applying both ISAT–DAC and separated ISAT and DAC, for practical nonpremixed combustion engine, especially the diesel engine with complex local thermodynamic parameters. In addition, based on the present work, the error tolerance has a significant influence on the computation efficiency and accuracy. In addition, in order to further effectively reduce the computational time for practical engineering applications whatever the method of DAC, ISAT or the coupled ISAT–DAC, the error tolerance should be dynamically determined depending on local thermodynamic parameters, such as temperature, pressure and fuel components. Our future work is to improve the present ISAT–DAC and apply it to much more complex configurations.

0

Crank Angle (degree)

(b) Overall time Fig. 10. The mean pressure (a) and overall computation time (b) variations against crank angle with ISAT–DAC with eISAT ¼ 1:0e  4 and eDAC ¼ 0:001 and full mechanism with and without heat loss compared with experiment data.

Acknowledgments The work is supported by the National Natural Science Foundation of China (Grant No. 51476114).The authors gratefully thanks Dr. Liu Yaodong for providing the engine model in this paper.

194

L. Zhou, H. Wei / Fuel 171 (2016) 186–194

References [1] Ra Y, Reitz RD. A combustion model for IC engine combustion simulations with multi-component fuels. Combust Flame 2011;158(1):69–90. [2] Liu Y-D, Jia M, Xie M-Z, Pang B. Enhancement on a skeletal kinetic model for primary reference fuel oxidation by using a semidecoupling methodology. Energy Fuels 2012;26(12):7069–83. [3] Ra Y, Reitz RD. A reduced chemical kinetic model for IC engine combustion simulations with primary reference fuels. Combust Flame 2008;155 (4):713–38. [4] Curran H, Pitz W, Westbrook C, Callahan G, Dryer F. Oxidation of automotive primary reference fuels at elevated pressures. Proc Combust Inst 1998;27 (1):379–87. [5] Luong MB, Luo Z, Lu T, Chung SH, Yoo CS. Direct numerical simulations of the ignition of lean primary reference fuel/air mixtures with temperature inhomogeneities. Combust Flame 2013;160(10):2038–47. [6] Tsurushima T. A new skeletal PRF kinetic model for HCCI combustion. Proc Combust Inst 2009;32(2):2835–41. [7] Saisirirat P, Togbé C, Chanchaona S, Foucher F, Mounaim-Rousselle C, Dagaut P. Auto-ignition and combustion characteristics in HCCI and JSR using 1-butanol/ n-heptane and ethanol/n-heptane blends. Proc Combust Inst 2011;33 (2):3007–14. [8] Liu Y-D, Jia M, Xie M-Z, Pang B. Development of a new skeletal chemical kinetic model of toluene reference fuel with application to gasoline surrogate fuels for computational fluid dynamics engine simulation. Energy Fuels 2013;27 (8):4899–909. [9] Shi Y, Liang L, Ge H-W, Reitz RD. Acceleration of the chemistry solver for modeling DI engine combustion using dynamic adaptive chemistry (DAC) schemes. Combust Theor Model 2010;14(1):69–89. [10] Zhou L, Lu Z, Ren Z, Lu T, Luo K. Numerical analysis of ignition and flame stabilization in an n-heptane spray flame. Int J Heat Mass Transfer 2015;88:565–71. [11] Goldin G, Ren Z, Zahirovic S. A cell agglomeration algorithm for accelerating detailed chemistry in CFD. Combust Theor Model 2009;13(4):721–39. [12] Oluwole OO, Ren Z, Petre C, Goldin G. Decoupled species and reaction reduction: an error-controlled method for dynamic adaptive chemistry simulations. Combust Flame 2015;162(5):1934–43. [13] Ren Z, Liu Y, Lu T, Lu L, Oluwole OO, Goldin GM. The use of dynamic adaptive chemistry and tabulation in reactive flow simulations. Combust Flame 2014;161(1):127–37. [14] Liang L, Stevens JG, Raman S, Farrell JT. The use of dynamic adaptive chemistry in combustion simulation of gasoline surrogate fuels. Combust Flame 2009;156(7):1493–502. [15] Lu L, Lantz SR, Ren Z, Pope SB. Computationally efficient implementation of combustion chemistry in parallel PDF calculations. J Comput Phys 2009;228 (15):5490–525. [16] Lu L, Pope SB. An improved algorithm for in situ adaptive tabulation. J Comput Phys 2009;228(2):361–86.

[17] Jia M, Xie M, Peng Z. Implementation and Improvement of ISAT in HCCI multidimensional modeling with detailed chemical kinetics. SAE technical paper, 2008-01-0978; 2008. [18] Curtis NJ, Niemeyer KE, Sung C-J. An automated target species selection method for dynamic adaptive chemistry simulations. Combust Flame 2015;162(4):1358–74. [19] Gou X, Chen Z, Sun W, Ju Y. A dynamic adaptive chemistry scheme with error control for combustion modeling with a large detailed mechanism. Combust Flame 2013;160(2):225–31. [20] Liang L, Stevens JG, Farrell JT. A dynamic adaptive chemistry scheme for reactive flow computations. Proc Combust Inst 2009;32(1):527–34. [21] Yang H, Ren Z, Lu T, Goldin GM. Dynamic adaptive chemistry for turbulent flame simulations. Combust Theor Model 2013;17(1):167–83. [22] Lu T, Law CK. A directed relation graph method for mechanism reduction. Proc Combust Inst 2005;30(1):1333–41. [23] Lu T, Law CK. Linear time reduction of large kinetic mechanisms with directed relation graph: n-heptane and iso-octane. Combust Flame 2006;144(1):24–36. [24] Sankaran R, Hawkes ER, Chen JH, Lu T, Law CK. Structure of a spatially developing turbulent lean methane–air Bunsen flame. Proc Combust Inst 2007;31(1):1291–8. [25] Zheng X, Lu T, Law C. Experimental counterflow ignition temperatures and reaction mechanisms of 1,3-butadiene. Proc Combust Inst 2007;31(1):367–75. [26] Sun W, Chen Z, Gou X, Ju Y. A path flux analysis method for the reduction of detailed chemical kinetic mechanisms. Combust Flame 2010;157 (7):1298–307. [27] Pope SB. Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust Theor Model 1997;1(1):41–63. [28] Contino F, Jeanmart H, Lucchini T, D’Errico G. Coupling of in situ adaptive tabulation and dynamic adaptive chemistry: an effective method for solving combustion in engine simulations. Proc Combust Inst 2011;33(2):3057–64. [29] D’Errico G, Lucchini T, Onorati A, Hardy G. Computational fluid dynamics modeling of combustion in heavy-duty diesel engines. Int J Engine Res 2015;16(1):112–24. [30] Pope SB, Ren Z. Efficient implementation of chemistry in computational combustion. Flow, Turbul Combust 2009;82(4):437–53. [31] Ren Z, Xu C, Lu T, Singer MA. Dynamic adaptive chemistry with operator splitting schemes for reactive flow simulations. J Comput Phys 2014;263:19–36. [32] Alamos L. KIVA-3V: A block-structured Kiva program for engines with vertical or canted values. LA-18818-MS; 1997. [33] Han Z, Reitz RD. A temperature wall function formulation for variable-density turbulent flows with application to engine convective heat transfer modeling. Int J Heat Mass Transfer 1997;40(3):613–25. [34] Li Y, Jia M, Liu Y, Xie M. Numerical study on the combustion and emission characteristics of a methanol/diesel reactivity controlled compression ignition (RCCI) engine. Appl Energy 2013;106:184–97. [35] Chang Y, Jia M, Liu Y, Li Y, Xie M. Development of a new skeletal mechanism for n-decane oxidation under engine-relevant conditions based on a decoupling methodology. Combust Flame 2013;160(8):1315–32.