Pressure Oscillation and Chemical Kinetics Coupling during Knock

Article pubs.acs.org/EF

Pressure Oscillation and Chemical Kinetics Coupling during Knock Processes in Gasoline Engine Combustion Zhi Wang,† Yue Wang,‡ and Rolf D. Reitz*,‡ †

State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, 100084, China Engine Research Center, University of WisconsinMadison, Madison, Wisconsin, 53706, United States

‡

ABSTRACT: Knock in a single-cylinder spark ignition (SI) optical engine was modeled and investigated using an improved version of the KIVA code with a G-equation combustion model, together with a reduced chemical kinetics model and an enhanced wall heat transfer model. The ERC PRF mechanism (47 species, 132 reactions) was adopted to model the end gas autoignition in front of the flame front and the postoxidation process behind the flame front in the burned zone. An improved wall heat transfer model was developed that accounts for pressure oscillations and near wall chemical heat release. The model describes end gas autoignition and the spatial distribution of intermediate combustion radicals, as well as the characteristics of the pressure wave oscillation during spark-ignition engine combustion. The predicted data agree well with available experimental results from an optical engine. The simulated results further indicate that the local in-cylinder pressure is extremely uneven during the knocking process. The pressure oscillations couple with chemical reactions simultaneously and interactively and lead to significantly enhanced heat transfer. The acoustic characteristics of SI engine knock are basically consistent with the “drum mode”, and the oscillating energy is mainly focused in the first resonance mode.

■

INTRODUCTION The knocking phenomenon has been an inherent problem of internal combustion (IC) engines from their inception.1 It is the main obstacle toward increasing the compression ratio to improve the thermal efficiency of spark ignition (SI) engines. In recent decades, engine knock has been studied intensively not only with focus on energy savings, but also due to the fact that rapid progress in combustion diagnostics and chemical kinetics make it possible to improve the understanding of this complicated combustion process. For combustion diagnostics, Ebina et al.2 detected the knock locations in-cylinder based on multipoint pressure measurement and obtained the pressure wave characteristics. Merola and Vaglieco et al.3,4 analyzed the flame propagation and low-temperature reactions in a research SI (spark ignition) engine using spectroscopic measurements, and they found that the occurrence of the HCO radical in the end gas denoted the start of knocking phenomena. For knock prediction, a first knock model introduced was the Livengood−Wu integral method,5 which computes ignition delay using a global reaction. Heywood1 proposed a zero-dimensional two-zone method that considers a burned and an unburned zone during gasoline engine knock. Using the two-zone method with the Golovichev PRF mechanism, Noda et al.6 predicted the possibility of engine knock at different operating conditions. However, a zero-dimensional model can only capture the ignition delay event prior to autoignition. In fact, knock is a spatiotemporal combustion phenomenon. Recent researchers have utilized multidimensional numerical simulations to analyze knocking.7−10 Liang et al.15 simulated knocking cases in a gasoline direct injection SI engine using the KIVA code incorporating a reduced reaction mechanism (22 species, 42 reactions). The calculated results predicted knock intensity under different spark timing and injection strategies. © 2012 American Chemical Society

As can be seen, the trend of engine knock modeling research is from zero-dimensional to three-dimensional models, with single-step reaction models being replaced by complex chemical kinetics. Although there have been considerable investigations in the engine knocking area, IC engine knock is still at an early stage of understanding. It is generally accepted that knock is associated with autoignition in the end gas, but the detailed mechanism from autoignition to pressure oscillations and pressure wave effects on the chemical kinetics are still unclear. To more deeply understand the physical−chemical mechanism during knocking combustion and the deflagrative flame structure, complex chemical kinetics and pressure wave propagation phenomena, as well as their interactions, must be considered. The present study investigates pressure wave and intermediate species interactions during knocking combustion using a G-equation flame propagation model with a reduced chemistry mechanism that includes aldehydes such as CH2O and radical species, such as HCO to indicate autoignition. The computational fluid dynamics (CFD) predictions are analyzed together with the cylinder pressure and combustion visualizations to understand their dynamic interactions.

1. EXPERIMENTAL METHOD The engine modeled in this study is an optically accessible, singlecylinder, port-fuel injection, naturally aspirated spark ignition engine investigated by Vaglieco et al.3 of the Istituto Motori-CNR. The specifications are given in Table 1, and a schematic diagram of the engine is presented in Figure 1. A detailed description of the engine can be found in ref 3. Optical access is gained through an extended piston and a flat piston crown. The fuel used in the engine experiment was primary reference fuel PRF (iso-octane and n-heptane), and the engine was operated under stoichiometric conditions. Received: September 9, 2012 Revised: November 4, 2012 Published: November 6, 2012 7107

dx.doi.org/10.1021/ef301472g | Energy Fuels 2012, 26, 7107−7119

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the CHEMKIN-II library.15 The ERC PRF mechanism16 with 47 species and 142 reactions, which involves low C number species, hydrogen oxidation, and NOx formation, was used in the chemical calculations. Therefore, the autoignition due to preflame reactions and pollutant formation due to postoxidation can be calculated. Moreover, a pressure wave-determined numerical time step criterion was taken into account to capture the pressure oscillation due to autoignition. Since pressure oscillation and chemical heat release near the wall may enhance heat transfer during knocking combustion, an improved wall heat transfer model was developed and implemented in the current model. The simulations were performed using the KIVA-3V, release 2 code. The DMC (discrete multi-component) model17 and the RNG k−ε turbulence model18 were used in this study. 2.1. Combustion Models. (1) Ignition Kernel Model. The growth of the ignition kernel was tracked by using the DPIK model by Fan, Tan, and Reitz.19,20 Here, the flame front position is marked by Lagrangian particles with a spherical growth rate

Table 1. CNR Gasoline Engine Parameters bore stroke connect rod stroke type valves number displacement compression ratio engine speed load fuel mixture

79.0 mm 81.3 mm 143 mm 4 4 0.399 L 10:1 1000 r/min wide open throttle PRF(iC8H18, nC7H16) stoichiometric

The recorded images contained spectral information along the rows of the ICCD detector and spatial information along the columns. Two narrow-band (10 nm) interference filters were optically matched with the UV lens. The center wavelengths of the filters corresponded to the emission wavelengths of radical species (OH, 310 nm; HCO, 330 nm). Details of the optical diagnostics can also be found in ref 3. Model predictions of the combustion processes and flame structures were compared with the measured pressure traces and active radical locations (OH, HCO).

ρ drker = u (Splasma + ST) dt ρker

2. MODEL DETAILS In SI engine combustion the deflagrative flame can be viewed as an ensemble of thin reaction-diffusion layers, called flamelets.11 The advantage of the flamelet concept is that the calculation of the chemical reaction and turbulent flow can be decoupled. Figure 2 shows schematic diagrams of the models for spark ignition engine combustion in this study. To track the deflagrative flame front evolution, a field equation of the scalar G is used,12 where the flame front is represented by level-set surface G = 0. This interface divides the flow field into an unburned region, G < 0, and a burned gas region, G > 0. Tan et al.13 successfully introduced the G-equation combustion model into the KIVA-3v code.14 In the current model, the mixture within the mean flame brush is calculated assuming thermodynamic equilibrium using an element-potential method (EPM). Outside the flame brush, including in the burned zone behind the flame and the unburned zone ahead of the flame, the computational cells are regarded as well-stirred reactors in which the chemical source term in the governing conservation equations is calculated using

(1)

where rker is the kernel radius, and Splasma is the plasma velocity.13 The transition from the kernel model to the turbulent G-equation combustion model follows the criterion: rk ≥ cm1SI = cm10.16

k3/2 ε

(2)

where cm1 is a model constant, and S I is the turbulence integral length scale. Here, k is the turbulence kinetic energy, and ε is the dissipation rate obtained from the RNG turbulence model. (2) G-Equation Combustion Model for Turbulent Flame Propagation. The G-equation suitable for KIVA implementation is13 ρ̅ ∂G̃ ∼ ) ·∇G̃ = u ST0|∇G̃ | − DTκ |̃ ∇G̃ | + (u ⃗ − u vertex ⃗ ∂t ρb̅

(3)

where G is the level set scalar function, u is the velocity of the fluid, ρb is the density of the burned mixture, and ρu is the density of the unburned mixture.

Figure 1. Schematic diagram of optical apparatus for (a) spectroscopic, (b) digital imaging, and (c) the combustion chamber field of view.3 7108


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Figure 2. Schematic diagrams of advanced combustion model for SI combustion.

Also, κ̃ is the Favre mean flame front curvature defined as12 ⎛ ∇G̃ ⎞ κ̃ = ∇·⎜ ⎟ ⎝ |∇G̃ | ⎠

(3) Viscous dissipation and enthalpy diffusion are neglected. (4) Heat transfer from the walls is only due to convection; radiation is not considered. (5) The ideal gas law is assumed as thermodynamic property relations. With these assumptions, the energy equation becomes

(4)

To account for the laminar to turbulent evolution of the spark kernel flame, the modified turbulent flame speed correlation is written as10,15 ST0 SL0

∂qη

⎧ ⎫ 2 ⎡⎛ ⎤1/2 ⎪ ⎪ a4b32 SI a4b32 SI ⎞ 2 u′SI ⎥ ⎢ ⎬ ⎟ + a4b3 0 = 1 + IP⎨− + ⎜ SL SF ⎥⎦ ⎪ ⎪ 2b1 SF ⎢⎣⎝ 2b1 SF ⎠ ⎩ ⎭

∂η

1 ∂p + Qc γ − 1 ∂t

(7)

in which qη is the rate of heat transfer in the normal-to-wall direction “η”, γ is the ratio of specific heats, and Qc is the heat release rate due to chemical reactions. The ideal gas law has been used to relate thermodynamic properties of the gaseous mixture:

(5)

S0T and S0L are unstretched laminar and turbulent flame speeds. The term IP, called a progress variable in the present study, takes the form15 1/2 ⎡ t − t 0 ⎞⎤ ⎛ ⎟ IP = ⎢1 − exp⎜ −cm2 ⎥ ⎝ ⎣ τ ⎠⎦

=−

I= (6)

p ρ(γ − 1)

(8)

The first term on the right-hand-side of eq 7 accounts for the pressure oscillation associated with a change of local thermal energy. As noted before, pressure oscillation is induced by the propagation and reflection of pressure waves when engine knocking occurs. The second term accounts for the chemical heat release when the flame propagates to the wall, when an oil-film burns (e.g., pool fire in piston bowl for stratified direct injection combustion), or when autoignition near a wall occurs. In practical CFD simulations, it is of interest to examine eq 7 within the first CFD cells that are adjacent to the wall boundaries. Integrating eq 7 from the wall (η = 0) to the other face of the wall cell (η = y) gives

S I and S F are the turbulence integral length scale and the laminar flame thickness, respectively. The terms a4, b1, and b3 are constants from turbulence models, experimental data, or DNS studies.11 2.2. Improved Wall Heat Transfer Model. In order to study the effects of pressure oscillation on the wall heat transfer, the conservation of thermal energy based on the first Law of Thermodynamics is considered. The current analysis uses the near-wall boundary layer assumptions, which state (1) Flow velocity in the streamwise direction (“ξ”) is much larger than the velocities in the normal direction “η”. (2) Flow field is fully developed in the streamwise direction. Variations and gradients of the flow field variables are only considered in the normal direction.

qη|η= y = qw + Hy 7109

(9)


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In which qw is the rate of heat transfer from the wall. The turbulent heat transfer rate at η = y is modeled with a diffusion analogy: ⎛μ μ ⎞ dT + t⎟ qη|η= y = −c p⎜ Prt ⎠ dη ⎝ Pr

(10)

y

with Pr and Prt being the Prandtl numbers for laminar and turbulent heat transfer, respectively. In eq 9 we have also denoted: 1 ∂p + Qc γ − 1 ∂t

H=−

(11)

Introducing the following dimensionless variables, νt ; ν

ν+ =

y+ =

u*y u*η = ; ν ν

H+ =

Hv qw u* (12)

Figure 3. Pressure traces with different time steps.

In which u* is the friction velocity, eq 9 can be rearranged as −

ρcpu* qw

dT =

1 + H +y+ 1 Pr

+

ν+ Prt

dy

last until EVO (exhaust valve open). (The time step of 1 ×10−7 s leads to slightly higher pressures before knock due to the mesh dependence of the DPIK ignition model.) It is of interest to discuss the numerical issues associated with modeling knocking combustion. To capture the pressure wave in a numerical simulation, it should take no less than one time step for a sonic wave to be transmitted across a computational cell. With

+

(13) 21

According to Han’s integration method, adopting Kays’ correlation22 about Prandtl number and Peclet number, Yakhot’s relation23 between the turbulent Prandtl number and Reynolds number, eq 11 is integrated from 0 to y+ and yields ρcpu*T ln(T /Tw ) qw

c=

= 2.1ln(y+ ) + 2.1H +y+ + 33.4H + + 2.5

(18)

where l is the computational cell size. Thus, the criteria of the time step is

Finally, the new formulation which considers wall heat flux with pressure gradients and near-wall chemical heat release is given as

dt < l / c

(19)

Here γ is the adiabatic index, R is the gas constant (287.05 J/(kg K)), and T is the gas temperature in kelvin. For a stoichiometric gasoline engine combustion case, γ ∼ 1.3 for the mixture, T is assumed to be 2500 K for the burned mixture, and the computational cell size, l = 3 mm. Thus, c ∼ 973 m/s, and thus, dt should be less than about 3 μs. The bore of the CNR engine is 79 mm, and the average grid size in the numerical mesh is around 3 mm. Therefore, assuming c = 1000 m/s and a time step of 1 ×10−6 s, it takes approximately 79 time steps for a sonic wave to be transmitted across the cylinder. For each cell, the results indicated about 3 time steps are needed to resolve the chemical kinetics. Therefore, the pressure effect on the chemical reactions is considered in the numerical method. Thus, it is concluded that a numerical time step of 1 ×10−6 is suitable to resolve the transmission of sonic waves and to track even low Mach number supersonic waves across the cylinder. 2.4. FFT Analysis for Pressure Wave. A discrete Fourier transform is a process that converts a signal in the time domain into its counterpart in the frequency domain. In order to understand the vibration mode during the knocking process, the details of the frequency spectrum of the pressu re oscillations were investigated using a fast Fourier transform (FFT). The objective was to determine the quantitative contribution of pressure oscillation in SI knocking combustion.

⎡ ν qw = ⎢ρcpu*T ln(T /Tw) + (2.1y+ + 33.4) u* ⎣

(15)

In the computations, the time derivative ∂p/∂t is evaluated by an explicit finite difference in each computational cell: ∂p pn − pn − 1 ≈ ∂t Δt

(17)

Δx = c·Δt = l

(14)

⎛ ⎞⎤ 1 ∂p + Q c⎟⎥2.1/[ln(y+ ) + 2.5] ⎜− ⎝ γ − 1 ∂t ⎠⎦

γRT

(16)

where superscripts n and n − 1 denote the current and the previous time steps, respectively. 2.3. Numerical Solution of Pressure Wave. To validate the capability of capturing the pressure wave phenomena, different time steps were adopted in knock calculations. The simulations were run and parallelized using the Message-Passing Interface (MPI) mode. The calculation time was about 2, 8, and 16 h at 1 ×10−5, 1 ×10−6, and 1 ×10−7 time steps, respectively, for each case using 8 CPUs. Figure 3 shows a comparison of the local pressure evolution near the cylinder wall with different time steps. It can be seen that with a time step of 1 ×10−5 s (about 0.6 °CA at 1000 rev/ min) the pressure oscillation only can be resolved during the initial stage of knock at around 9 °CA aTDC. However, with time steps of 1 ×10−6 s and 1 ×10−7 s, the pressure oscillations

N−1

Fn =

∑ xie−j2πn/Ni i=0

7110

(20)


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8.2 °CA aTDC while the experimental result is 12 °CA aTDC. It is thought that this discrepancy is related to the fuel’s autoignition sensitivity to the uncertain boundary conditions and to cycle-to-cycle variations in the gasoline engine. The experimental data in Figure 5b is a typical cylinder pressure trace from the 50 engine cycles at knock operation. 3.2. Ignition Radical Species Distributions. Figure 6 gives the experimental and calculated results of intermediate species distributions in the combustion field at the time of occurrence of knock with the engine fueled with PRF90 and at spark timing of 13 °CA bTDC. It can be seen that a high concentration of OH radicals had been formed in the center of the cylinder at the time of initial knock. This high concentration of OH indicates that the central burned zone has reached the postoxidation stage where NOx is formed. A high concentration of HCO radicals is seen to surround the OH radicals on the intake side of the engine. The presence of HCO indicates end gas autoignition is about to take place. Figure 7 gives comparisons of experimental and calculated results of ignition radical history in the combustion chamber during knock fuelled with PRF90. After the spark time the OH and HCO species concentrations increase gradually. When knock occurs, HCO decreases rapidly and OH decreases gradually. Both the experimental and simulated data indicate the same tendency of the ignition radicals. Note that the model does not distinguish between OH and HCO and excited state OH* and HCO* species that are monitored in chemiluminescence experiments. However, the locations of these species are also indicators of knock precursors.

where xi are the data points in the time domain, n is the index of the transformed components in the frequency domain, and N is the number of points. As discussed above, to obtain high quality pressure data for the FFT analysis, a 1 ×10−6 time step was selected for each knocking case, and the sample rate was 1000 kHz. With the transformed data, the amplitude and power density can be computed by the FFT library as amplitude =

Re2 + Im 2 n

power density =

Re2 + Im 2 n2

(21)

(22)

3. COMPARISON OF EXPERIMENTAL DATA AND CALCULATED RESULTS 3.1. Model Validation. Figure 4 displays the experimental data of cylinder pressure for 50 continuous engine cycles under

4. THEORETICAL ANALYSIS OF KNOCK PROCESS 4.1. Local Pressure at Different Positions. Since the diameter of the intake valve is larger than that of the exhaust valve, the spark plug position is closer to the cylinder center with a 1 mm eccentricity toward the exhaust side. In the simulations, three digital pressure sensors (MP0, MP1, MP2) were set in the cylinder: the first is at the center, and the second and third are near the liner wall on the intake side and exhaust side, as shown in Figure 8a. Figure 8b gives the comparison of pressure traces at the center (MP0), near the wall (MP1, MP2), and the averaged incylinder pressure. It can be seen that the amplitude of pressure oscillation near the wall is much higher (for MP1 and MP2, maximum Δp = 1.5 MPa) than that of the center (for MP0, maximum Δp = 1.0 MPa). This can be explained by the fact that the pressure wave amplitude is doubled when a wave is reflected at a wall. Pressure traces of MP1 have similar behavior in amplitude with MP2, while the phase is different due to pressure wave propagation. 4.2. Pressure Wave and Chemical Kinetics Coupling. Figure 9 shows pressure, temperature, and critical species at two autoignition timings during the knocking process. The high amplitude of the pressure reveals the oscillations, while high temperatures and high OH concentrations show the burned zone. High CO shows the incomplete burned zone, while high HCO shows the autoignition spots. NOx emissions are produced at the center of the cylinder in the flame. As mentioned before, the first autoignition spots occur at 8.2 °CA aTDC between the outer rim of the flame front and the cylinder wall on the intake side (as in the HCO radical indicated area in Figure 6b). After the first autoignition, the pressure wave propagates to both the left and right simultaneously. The second autoignition spots occur at 8.6 °CA

Figure 4. Measured cylinder pressure traces and averaged heat release rate under knocking operation in ref 3.

knocking operation with PRF90 fuel at 13 °CA bTDC spark timing. The pressure oscillation can be observed in every engine cycle, as shown by the thin lines. The cyan thick line indicates the average cylinder pressure trace. It is smooth but with an apparent two-stage heat release. To validate the CFD model, parametric calculations were carried out based on the experimental cases, but with different ignition timings and different fuels. The standard model constants cm1 = 2.0 in eq 2 and cm2 = 2.0 in eq 6 were used in all simulated cases for the in-cylinder process in this engine. The initial temperature is 780 K and initial pressure is 1.36 MPa at −15 °CA bTDC according to a 1D engine simulation. Figure 5a shows a comparison of the simulated and experimental cylinder pressures fueled with PRF100 fuel at different spark timings. It can be seen that the combustion characteristics are well captured when the spark timing is retarded from 13° to 3 °CA bTDC. Figure 5b shows the simulated and experimental cylinder pressures at a spark timing of 13 °CA bTDC fuelled with PRF100 and PRF90, respectively. Both the experimental data and the simulated results using PRF90 presented knocking behavior, i.e., pressure oscillations that occur at the end of the main combustion period, and the model reflects the fuel’s ignition properties, since the PRF100 fuel does not exhibit appreciable knock. However, the calculated initial time of knocking is 7111


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Figure 5. Measured3 and predicted cylinder pressure at various spark timings with different fuels.

present at the measurement points. The initial autoignition is mainly dominated by the reactions,

aTDC near the intake wall (as in the HCO radical indicated area in Figure 9). After the second autoignition, the pressure wave amplitude is enhanced by 0.4 MPa. This pressure wave propagates toward the right and is first reflected by the right wall on the exhaust side at 9.3 °CA aTDC (as in the HCO radical and temperature indicated areas in Figure 9), and a nearly 1.0 MPa enhanced pressure amplitude indicates the occurrence of a third autoignition near the right wall on the exhaust side. The third autoignition reinforces the pressure wave energy and enhances the pressure amplitude on the exhaust side. The heat release coupling with these pressure waves will be discussed next. Figure 10 gives a detailed analysis of the pressure wave coupling with chemical kinetics during the knock process. It can be seen that the pressure oscillation has a close correlation with the ignition species and the local heat release. The CO and CH2O species increase gradually until OH radicals are suddenly

CH 2O + OH = HCO + H 2O

(R1)

HCO + OH = CO + H 2O

(R2)

CO + OH = CO2 + H

(R3)

When both CH2O and OH are accumulated to high concentrations, reaction R1 consumes CH2O and produces HCO, then HCO disappears rapidly by OH attack and is converted to CO and H2O. Therefore, occurrence of HCO indicates the start of knock and CO is the main product at this stage. Compared to HCO, CO oxidation (R3) is relatively slow. When OH sharply increases at autoignition positions, R3 is a main heat release reaction, as shown in the HRR curve in Figure 10. 7112


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Figure 6. Predicted intermediate species distribution at time of engine knock with PRF90 fuel.

For MP1. The first autoignition spot occurs near the wall (intake side) at 8.6 °CA. At this measurement point (MP1), [CO] reaches its peak (incomplete combustion) and a slight heat release can be seen from the HRR curve. A 0.4 MPa pressure rise (Δp) can be seen from the local pressure fluctuation (p′ curve). After 0.01 ms, the pressure wave propagates and is reflected by the left wall to MP1 again. [OH] reaches its peak (at 8.74 °CA) and rapid local heat release (HRR) leads to a 0.9 MPa pressure rise (Δp) at MP1. For MP2. The pressure wave with 0.9 MPa amplitude propagates from the left side to the right side (exhaust wall) at nearly 9.2 °CA with the same amplitude, as shown in Figure 10b (n = 1000 rev/min, sonic wave transmission across the 79 mm cylinder takes about 0.5 °CA, so 8.74 °CA + 0.5 °CA ≅ 9.2 °CA). A Δp of 0.9 MPa can also be seen at MP2 (from p′ the purple curve). Similar behavior as for MP1 is seen. The pressure wave peak (0.9 MPa) leads to a small quantity of heat release at MP2 and then the pressure wave trough suppresses the heat release. After a very short time (0.01 ms, at 9.34 °CA),

Figure 7. Measured3 and predicted ignition radicals during knocking process. 7113


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Figure 8. Predicted cylinder pressure at different positions.

distribution in the combustion chamber at 10 °CA aTDC is displayed in Figure 11a. It can be seen that the pressure in the combustion field is extremely uneven during the knock process. The local peak pressure in the cylinder reaches 7.3 MPa during the knocking process, while the average cylinder pressure at 9.3 °CA aTDC is only about 5.5 MPa. This reflects the fact that the pressure waves propagate and impinge on the cylinder wall, and the wave is reflected with double its amplitude at walls. This impingement is also a main reason for possible damage to engine components in knocking combustion. The pressure signal was band-pass filtered from 2.0 to 20.0 kHz, and an FFT analysis was performed on the calculated pressure results. The frequency spectra obtained from knocking conditions are displayed in Figure 11b. The largest peak in the spectra occurs at 7.2 kHz. Since the clearance height is much smaller than the cylinder diameter in the engine at TDC, the gas resonance mode can be analyzed using Draper’s “drum” modes shown in Figure 12.24 The resonant frequency can be written as c fm , n = αm , n s (23) πB

the rapidly completed heat release is in the same phase as the second pressure peak and reinforces the wave energy. This enhancement leads to a 1.7 MPa pressure rise (Δp) for the second pressure wave peak. A 1.7 MPa pressure amplitude is the maximum pressure fluctuation in the cylinder. This pressure wave propagates, reflects in a radial resonant mode, and attenuates gradually until exhaust valve closure (EVC). Moreover, the variations of the CO and OH species density histories follow the pressure fluctuations. In order to analyze the coupling between pressure and heat release in combustion systems, the “Rayleigh criterion”26 was used to evaluate the knock process, where RI =

∫ p′(t )q′(t ) dt

RI is the Rayleigh index, p′ is the pressure fluctuation, and q′ is the heat release rate. If RI > 0, the heat release oscillations are in phase with the pressure oscillations and the magnitude of the thermo-acoustic instability is maximized. From Figure 10, it can be seen that the heat release peak is in phase with the pressure wave peak, and the Rayleigh index is positive and maximized at 8.74 °CA for MP1 and at 9.34 °CA for MP2. The duration of positive RI is short (about 0.1 °CA). Even a short period with RI > 0 can excite the combustion wave near the wall. This leads to high frequency pressure oscillations in the high temperature gas near the wall. Since the unburned mixture is distributed near the wall in SI engines, the interaction of pressure waves and chemical reaction usually occurs near the wall in knocking combustion. Compared to compression ignition (CI) engines, CI combustion typically has larger amplitude pressure oscillations than SI engines. However, the pressure waves in diesel engines or homogeneous charge compression ignition (HCCI) engines typically do not result in engine damage due to the lower maximum temperatures and absence of unburned rich mixture near the wall to promote thermo-acoustic coupling. 4.3. Acoustic Characteristics of Pressure Oscillations. The end gas autoignition process initializes a pressure discontinuity. This causes pressure waves that propagate and reflect at the walls, leading to pressure oscillations. Both the pressure oscillation and chemical reaction processes occur simultaneously during the knocking process. This is seen by comparing the HCO distribution history and the accumulated heat release curve, as shown in Figure 10. The 3D pressure

where the subscripts m and n denote the radial and circumferential mode numbers. αm,n is the corresponding wavenumber (determined by Bessel’s equation), cs is the sound speed, and B is the cylinder bore. The calculated first six frequencies are listed in Table 2. From the calculated results for the CNR single cylinder optical engine shown in Figure 11c, the knocking oscillation is mainly from the first resonant mode and the oscillating energy is focused at 7.2 kHz. Although some resonances also occur at 12.0, 15.0, and 16.4 kHz, their amplitudes are much smaller than that of the first resonant mode. 4.4. Heat Transfer during the Knock Process. Figure 13 presents the predicted total fuel energy and the total wall heat transfer for a knocking and a nonknocking case. The engine is fuelled with PRF100 and PRF90 with the same spark timing of 13 °CA bTDC (as in Figure 3). As before, it can be seen that nonknocking operation is achieved when the engine is fuelled with the higher RON fuel, PRF100, while, heavy engine knock occurs with PRF90. From the accumulated heat transfer curve it can be seen that heat losses to the walls increase significantly when knock occurs. The improved wall heat transfer model predicted more heat transfer than that of the original heat 7114


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Figure 9. Two representative timings of autoignition in the midplane of the cylinder during the knocking process (spark timing = 13 °CA bTDC).

oscillations and near wall chemical heat release due to autoignition. The total heat transfer during the combustion period is 332 J, which is about 40% of the total fuel energy, while

transfer model without consideration of pressure gradient and heat release. With the present improved wall heat transfer model, the heat transfer is further enhanced by the pressure 7115


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Figure 10. Local pressure waves, heat release rates, and Rayleigh index at the measurement point.

model with microsecond-level time-steps in the computations. (2) The in-cylinder local pressure is extremely uneven during the engine knocking process. The pressure oscillations and chemical reactions occur simultaneously and interactively. Sequential autoignition occurs at multiple locations in the chamber during the pressure wave propagation. The local heat release provides energy to the pressure wave, as predicted by the Rayleigh criterion, and elevates the local pressure amplitude and enhances the pressure oscillations. The oscillating characteristics of the pressure wave are consistent with Draper’s “drum mode”, and the oscillation energy is mainly focused on the first radial resonant mode. (3) The interaction of a pressure wave and chemical reaction usually occurs near the wall in SI knock combustion. A short positive Rayleigh index excites the combustion wave near the wall during the initial stage of SI knock. This leads to a high frequency pressure oscillation in the high temperature gas near the wall. (4) A new wall heat transfer model was derived and implemented. The model takes the oscillating flow field into account using a pressure gradient correction. In addition, an energy source term was introduced to reflect chemical heat release from near-wall reactions. The model is suitable for modeling wall heat transfer with oscillating flows and wall fires, like engine knock and pool fire conditions.

for the nonknocking case with PRF 100, the heat transfer during the combustion period is only 10% of the total fuel energy. To further explain the mechanism of autoignition induced in the oscillating flow, Figure 14 shows details of the oscillating flow during the knocking process at 10 and 10.2 °CA aTDC, respectively. The maximum local burned gas velocity in the combustion chamber is 144 m/s, while it is only ∼10 m/s during the nonknocking case. The oscillating flows can enhance the convective heat transfer greatly, as Dec et al. reported.25 Therefore, the heavy knocking pressure amplitude can not only damage the engine components but also enhance heat transfer. The present results indicate that the pressure oscillation term in eq 15 has the largest effect on the predicted wall heat transfer. As a result, the knocking pressure oscillations significantly reduce the engine’s thermal efficiency.

5. CONCLUDING REMARKS The effects of coupled pressure oscillations and chemical kinetics were explored in this study of pressure wave behavior and its effect on intermediate species distributions during knocking combustion in an optical spark ignition engine. The following conclusions can be drawn: (1) The end gas autoignition, intermediate combustion species, and pressure oscillation can be described well using the present G-equation combustion model, together with the present reduced chemical kinetics 7116


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Figure 11. Pressure patterns and frequency spectra during the knocking process.

Figure 12. First six resonance modes from eq 23.

Table 2. First Six Resonant Frequencies resonant mode

f10

f 20

f 01

f 30

f40

f11

Analytical Value (kHz)

7.2

12.0

15.0

16.4

20.8

26.3

Figure 13. Comparison of total cumulative energy release and wall heat transfer with/without knock.

The energy loss via heat transfer during the combustion period is predicted to be nearly 40% of total fuel energy

(5) Compared to the nonknocking case, engine knock significantly enhances the heat transfer to the walls. 7117


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Figure 14. Autoignition induced oscillating flows (unit: cm/s) in the midplane of the cylinder during the knocking period. Model) for SI Engines and Its Application to Knocking Prediction; Society of Automotive Engineers: Warrendale, PA, 2005; SAE technical paper, 2005-01-0199. (9) Yang, X.; Ohashi, T.; Takabayashi, T. Knock Phenomena Modeling with G-Equation Model and Detailed Chemistry for Butane Fueled SI Engine. Proceedings of 43rd Symposium (Japanese) on Combustion, Tokyo, Japan, Dec. 5−7, 2005; pp 218−219. (10) Long, L.; Reitz, R. D.; Claudia O. I. Modeling Knock in SparkIgnition Engines Using a G-Equation Combustion Model Incorporating Detailed Chemical Kinetics; Society of Automotive Engineers: Warrendale, PA, 2007; SAE technical paper, 2007-01-0165. (11) Peters, N. Laminar Diffusion Flamelet Modes in Non-premixed turbulent Combustion. Prog. Energy Combust. Sci. 1984, 10, 319−339. (12) Peters, N. Turbulent Combustion; Cambridge University Press: Cambridge, UK, 2000. (13) Tan, Z.; Reitz, R. D. An ignition and combustion model based on the level-set method for spark ignition engine multidimensional modeling. Combust. Flame 2006, 145, 1−15. (14) Amsden, A. A. KIVA Program with Block-Structured Mesh for Computer Geometries; Los Alamos National Lab Report: Los Alamos, NM, 1993; LA-12503-MS. (15) Liang, L.; Reitz, R. D. Spark Ignition Engine Combustion Modeling Using a Level Set Method with Detailed Chemistry; Society of Automotive Engineers: Warrendale, PA, 2006; SAE technical paper, 2006-01-0243. (16) Ra, Y.; Reitz, R. D. A reduced chemical kinetic model for IC engine combustion simulations with primary reference fuels. Combust. Flame 2008, 155, 713−738. (17) Ra, Y.; Reitz, R. D. A vaporization model for discrete multicomponent fuel sprays. Int. J. Multiphase Flow. 2009, 35, 101−117. (18) Han, Z.; Reitz, R. D. Turbulence Modeling of Internal Combustion Engines Using RNG k-ε Models. Combust. Sci. Technol. 1995, 106, 267−295. (19) Fan, L.; Reitz, R. D. Development of Ignition and Combustion Model for Spark-Ignition Engines; Society of Automotive Engineers: Warrendale, PA, 2000; SAE technical paper, 2000-01-2809. (20) Tan, Z.; Kong S.-C.; Reitz, R. D. Modeling Premixed and Direct Injection SI Engine Combustion Using a Level Set G-Equation Model, Society of Automotive Engineers: Warrendale, PA; SAE Int. J. Fuels Lubr. 2003, 112 (Section 4), 1298−1309. (21) Han, Z.; Reitz, R. D. A temperature wall function formulation for variable-density turbulent flow with application to engine convective heat transfer modeling. Int. J. Heat Mass Transfer 1997, 40 (3), 613−625. (22) Kays, W. M. Turbulent Prandtl number − where are we? ASME J. Heat Transfer 1994, 116, 284. (23) Yakhot, V.; Orszag, S. A. Renormalization group analysis of turbulence. I. Basic theory. J. Sci. Comput. 1986, 1, 3. (24) Draper, C. S. Pressure Waves Accompanying Detonation in Engines. J. Aeronaut. Sci. 1938, 5, 219.

under heavy knocking conditions and is nearly 4 times the heat transfer under the nonknocking condition. (6) Heavy knock pressure amplitude not only may lead to damage of engine components but also enhances wall heat transfer due to the increased convective heat transfer associated with the pressure oscillation-induced flows. This significantly reduces engine thermal efficiency.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge the financial support provided by the National Science Foundation of China under Grant No. 51036004 and the scholarship provided by China Scholarship Council (CSC). The authors are also thankful for support from CEI, Inc., for the use of EnSight software for the in-cylinder visualization and gratefully appreciate the experimental data provided by Prof. Bianca Vaglieco of the Istituto Motori-CNR, Naples, Italy.

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REFERENCES

(1) Heywood, J. B. Internal combustion engine fundamentals; New York: McGraw-Hill; 1988. (2) Ebina, M. The Detection of Knock Location by Multipoint Pressure Measurement. Trans. JSAE 2008, 39 (6), 83−88. (3) Merola, S. S.; Vaglieco, B. M. Knock investigation by flame and radical species detection in spark ignition engine for different fuels. Energy Convers. Manage. 2007, 48, 2897−2910. (4) Sementa, P.; Vaglieco, B. M.; Catapano, F. Thermodynamic and optical characterizations of a high performance GDI engine operating in homogeneous and stratified charge mixture conditions fueled with gasoline and bio-ethanol. Fuel 2012, 96, 204−219. (5) Livengood, J. C.; Wu, P. C. Correlation of Autoignition Phenomena in Internal Combustion Engines and Rapid Compression Machines. Proceedings of the Combustion Institute, 1955; Vol. 5, pp 347−356. (6) Noda, T.; Hasegawa, K.; Kubo, M. Development of Transient Knock Prediction Technique by Using a Zero-Dimensional Knocking Simulation with Chemical Kinetics; Society of Automotive Engineers: Warrendale, PA, 2004; SAE technical paper, 2004-01-0618. (7) Liberman, M. A.; Ivanov, M. F.; Peil, O. E. Numerical modeling of the propagating flame and knock occurrence in spark-ignition engines. Combust. Sci. Technol. 2004, 177 (1), 151−182. (8) Teraji, A.; Tsuda, T.; Noda, T.; Kubo, M.; Itoh, T. Development of a Novel Flame Propagation Model (UCFM: Universal Coherent Flamelet 7118


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(25) Dec, J. E.; Keller, J. O.; Arpaci, V. S. Heat transfer enhancement in the oscillating turbulent flow of a pulse combustor tail pipe. Int. J. Heat Mass Transfer 1992, 35 (9), 2311−2325. (26) Nicoud, F.; Poinsot, T. Thermoacoustic instabilities: Should the Rayleigh criterion be extended to include entropy changes? Combust. Flame 2005, 142, 153−159.

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Pressure Oscillation and Chemical Kinetics Coupling during Knock

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