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One-dimensional numerical study on pressure wave–flame interaction and flame acceleration under engine-relevant conditions
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 5 ) 1 e1 0
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One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions Haiqiao Wei*, Yibao Shang, Ceyuan Chen, Dongzhi Gao, Dengquan Feng State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China
article info
abstract
Article history:
Knock is considered as a major challenge when increasing thermal efficiency of internal
Received 25 December 2014
combustion engine. In this study, two possible causes of engine knock: flame acceleration
Received in revised form
and auto-ignition, are studied using one-dimensional simulation under engine-relevant
3 February 2015
conditions. Chemical source term is modeled using Arrhenius expression with detailed
Accepted 8 February 2015
chemical mechanism of hydrogen oxidation. Interaction between pressure wave and flame
Available online xxx
during propagation of flame front is investigated. It is observed that propagation and reflection of pressure wave in cylinder might trigger DeflagrationeDetonation Transition
Keywords:
(DDT), which leads to extremely high pressure oscillation. Pressure wave initialized by
Pressure wave
auto-ignition flame is also a reason leading to detonation by enhancing main flame front.
Knock
Chemical kinetics study is also carried out to analyze chemical process during auto-
Deflagrationedetonation transition
ignition. Pressure wave is considered to play an important role in the initiation of direct
Auto-ignition
detonation due to accumulation of intermediate radicals under higher pressure. Ignition
Hydrogen
delays under varying conditions are calculated according to the effects of pressure wave induction. As a result, gradient of ignition delays is observed, which might be a possible cause of detonation initialization. Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Increasing compression ratio as well as inlet air supercharging is a common method to increase the thermal efficiency of internal combustion Spark Ignition (SI) reciprocating engines. However, compression ratio of engine is limited by the occurrence of abnormal combustion such as knock and preignition. Engine knock, characterized by pressure oscillation and “pinging” sound in cylinder, causes undesirable engine performance and even damages engine cylinder. It is
commonly believed that knock is caused by end gas autoignition after spark plug ignition [1]. Some researchers also propose that flame propagation and acceleration in cylinder are also the reasons that lead to knock [2]. Despite these two different points of view, experiments showed that pressure profiles measured at different locations differ from each other during the same knocking cycle [3,4], which indicates the existence of propagation, interaction and reflection of pressure waves inside combustion chamber. Hydrogen, with low density, wide flammability limits and low minimum ignition
* Corresponding author. Tel./fax: þ86 022 27402609. E-mail address: [email protected] (H. Wei). http://dx.doi.org/10.1016/j.ijhydene.2015.02.034 0360-3199/Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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energy, suffers knocking problem as well as gasoline when utilized in hydrogen-fueled internal combustion engine [5]. During flame propagation, heat generated from flame front will raise local temperature quickly thus driving hot gas compressing cooler surroundings. Usually, a pressure wave is formed before flame front and travels away from it at the speed of sound. However, in some extreme conditions, flame front accelerates to supersonic, thus driving pressure wave propagating at the same speed as flame front. In turn, the pressure wave heats unburned gas before flame front, which will maintain flame propagation speed. This coupling between flame front and pressure wave leads to DeflagrationeDetonation Transition (DDT) phenomenon. The pressure peak of a detonation that could reach dozens of megapascal, corresponds to the magnitude of peak cylinder pressure during severe abnormal combustion. Previous works focusing on flame propagation and interaction between pressure wave and flame can be divided into two main aspects: the initialization of reaction wave and its transition during propagation. The different regimes of flame front initialized by non-uniform initial conditions were first studied by Zeldovich using a one-step chemical model [6]. He discovered that spontaneous reaction wave can propagate through a reactive material along a spatial gradient of variables such as temperature and species concentration that could influence ignition delay. Considering an area with temperature gradient along x-axis, auto-ignition will first occur at the location which has the highest temperature T(x)max, and the spontaneous reaction wave then propagates along the gradient with the speed usp:
usp ¼
vtig 1 vtig vT 1 ¼ vx vT vx
where tig is ignition delay as a function of initial temperature gained from experiment or chemical kinetics calculation. According to their relationships with ChapmaneJouguet speed and sound speed, different values of usp indicate the initialization of different regimes of spontaneous reaction wave, such as detonation, deflagration and homogenous explosion. This theory was studied by many researchers using detailed chemistry and was extended to the research on abnormal combustion in engines [7e9]. As for transition during propagation, DDT process is mainly considered. Khokhlov et al. [10e12] numerically studied shockeflame interactions in reactive mixture. They found that flame generates and enhances shock waves, which in turn creates turbulence in flames, thus promoting the formation of hot spots, causing auto-ignition and DDT. Similar effects of pressure wave on flame were also observed by Molkov et al. [13]. They modeled hydrogen-air deflagration in a long tunnel, where initial pressure wave develops into a shock due to reflection by obstacles. There are also multi-dimension CFD simulations investigating engine knock, with different focuses and methods such as heat transfer and pressure oscillation [14,15]. Since engine cylinder is a closed narrow space, pressure wave would be reflected by cylinder walls several times during combustion. Therefore, the heating effect of pressure wave, the interactions between unburned gas and pressure wave,
and the acceleration of flame influenced by pressure wave have to be considered when studying engine knock. As is mentioned, previous works mainly focus on the initialization of different auto-ignition forms or the DDT process during flame propagation. Very few researchers establish a connection between the propagation of pressure wave and the transition of flame front under engine-relevant condition. This work aims to maintain the understanding of engine knock by considering auto-ignition and DDT process during combustion. Numerical simulation is carried out in a 75 mm one-dimensional domain, which has the similar radial length of combustion chamber. Two possible forms of combustion leading to knock are investigated: acceleration of flame and end gas auto-ignition under the effect of pressure wave. DDT process induced by pressure waveeflame interaction along with high amplitude pressure oscillation are observed and analyzed. In addition, chemical kinetics study under varying conditions due to induction of pressure wave is carried out, giving a better understanding of chemical process during auto-ignition.
Numerical details Specifications of problem Since the location and the moment of knock onset are mainly determined by inhomogeneity of temperature and concentration of gas mixture that result in different ignition delays, the knock is a stochastic phenomenon, which has to be studied with simplification and assumption. In this study, combustion chamber at Top Dead Center (TDC) is simplified to a 75 mm one-dimensional domain. Adiabatic boundaries are assumed to rule out heat loss to the walls. Study on mesh convergence is performed within several empirical cell sizes, at last a cell size of 0.05 mm is chosen in consideration of both the ability to capture flow discontinuity and the reduction of computational cost. Fig. 1 shows two hypotheses of flame acceleration. If the mixture is ignited at left end and propagates to the right, pressure wave that travels faster than flame front will gradually raise the temperature of whole unburned mixture during its propagation and reflection between left and right walls. As the flame speed as well as mixture reactivity increases, the propagating flame will finally transited into a detonation if some critical conditions are reached. The other hypothesis is similar to the former one but includes end gas auto-ignition. Mixture is ignited near the middle of the domain, thus forming pressure waves towards both ends that cause pressure wave-induced auto-ignition at left end. Pressure wave initialized by auto-ignited flame then propagates to the right and interacts with main flame front, leading to detonation. In fact, the occurrence of auto-ignition does not necessarily cause severe pressure oscillation, indicating that some certain critical conditions have to be reached. Since auto-ignition happens in hot spots, different temperature gradients will be formed depending on turbulence, initial thermodynamic status and heat transfer with cylinder wall and so on, thus causing different levels of knock, which is consistent with gradient theory studied by many researchers. Ignition is achieved by patching a 2 mm-thick hot zone with
Please cite this article in press as: Wei H, et al., One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions, International Journal of Hydrogen Energy (2015), http://dx.doi.org/ 10.1016/j.ijhydene.2015.02.034
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Fig. 1 e Two hypotheses of flame acceleration: (a) flame acceleration without auto-ignition; (b) flame acceleration enhanced by auto-ignition.
the temperature of 2000 K. In auto-ignition case, a hot zone is also introduced into end gas area in consideration of promoting auto-ignition of end gas within a sufficiently short period. All mentioned above will be shown in detail within following sections.
CFD modeling The mixture is assumed to be compressible ideal gas, whose state is: p¼
E¼
r RT M X
Yi h i þ
2
v 2
where R denotes universal gas constant, M the molar weight of mixture, e the energy per unit mass, Yi the mass fraction, hi the sensible enthalpy and v the velocity. Subscript i indicates the ith species. The specific heat and enthalpy of the species are considered as functions of temperature and are calculated by polynomial fits using NASA chemical equilibrium code [16]. The governing equations of mass, momentum, energy and species transport are solved simultaneously while equations for other scalars are solved afterward: vr þ V$ðr! vÞ ¼ 0 vt vðr! vÞ þ V$ðr! v! v Þ ¼ Vp þ V$ðtÞ vt 2 y vI t ¼ m V! v þ V! v V$! 3 / / X vðreÞ þ V$ v ðre þ pÞ ¼ V$ keff VT þ Sh hi Ji þ t$v vt vðrYi Þ ! þ V$ðr! v Yi Þ ¼ V$ J i þ Ri vt where t denotes the stress tensor, m the dynamic viscosity, I ! the unit tensor, keff the effective conductivity, J i the diffusion flux, Sh the heat source and Ri the net production rate. Superscript y means a transposed matrix. Since calculation is
performed in a one-dimensional domain, the absence of compression stroke, the simplicity of computational domain and the high intensity of reaction make turbulence only neglectable effects on flow and reaction, thus no turbulence model is employed. In fact, the discrepancy between RANSmodeled turbulent flow and laminar flow in this calculation is barely observable according to our earlier comparisons, in which the pressure and temperature fluctuations in laminar flow are slightly higher. Chemical source terms are calculated using Arrhenius expression and ignoring the effect of turbulent fluctuations. The net production rate Ri can be expressed as: Ri ¼ Mw;i
NR X
b i;r R
r¼1
0 1 N 00 Y
h0j;r þh00j;r 0 b @ A kf ;r R i;r ¼ G yi;r yi;r Cj;r j¼1
kf ;r ¼ Ar Tbr eEr =RT where Mw,i ¼ molecular weight of species i b i;r ¼ Arrhenius molar rate of creation/destruction of speR cies i in reaction r G ¼ net effect of third bodies on the reaction rate Cj,r ¼ molar concentration of species j in reaction r h0j;r ¼ rate exponent of reactant species j in reaction r 00 hj;r ¼ rate exponent of product species j in reaction r kf,r ¼ forward rate constant of reaction r Ar ¼ pre-exponential factor br ¼ temperature exponent Er ¼ activation energy for the reaction R ¼ universal gas constant compared with Eddy-Dissipation Concept (EDC) model [17] employed in our previous work [18], this model is more appropriate for predicting low temperature auto-ignition and supersonic flames. Hydrogen, known as a renewable clean energy carrier, is utilized as fuel of SI engine where abnormal combustion also occurs as that fueled by gasoline. In addition, the combustion
Please cite this article in press as: Wei H, et al., One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions, International Journal of Hydrogen Energy (2015), http://dx.doi.org/ 10.1016/j.ijhydene.2015.02.034
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characteristics, such as laminar flame speed, flame instability and chemical kinetics of hydrogen are well investigated, which provides a knowledge background for the study of hydrogen combustion [19e21]. Besides, the simplicity and reliability of hydrogen oxidation mechanism makes it a practical tool for numerical research on combustion phenomenon. Among numerous mechanisms available [22e24], Conaire et al.'s [22] mechanism that consists of 9 Marcus O species and 21 reactions was validated with experimental data over wide ranges of temperature, pressure and equivalent ratio and is chosen here for reaction modeling. The entire CFD simulation is carried out using commercial CFD package ANSYS Fluent, while one-dimensional domain is achieved by limiting y-axis direction of two-dimension mesh to a single fine grid. Third-order MUSCL scheme is employed for spatial discretization as it improves spatial accuracy by reducing numerical diffusion. In order to maintain the stability and accuracy while reaction and flow is intensively coupled, a time step of 1e-8s is selected for second-order implicit time integration. In addition to CFD modeling, chemical kinetics study is carried out to have a better understanding of chemical process during end gas auto-ignition. Ignition delays and variations of species during pressure wave-end gas interaction are calculated using CHEMKIN-PRO [25]. Unlike ignition process under approximately uniform condition, a pressure profile extracted from CFD modeling is imported to simulate the varying pressure conditions caused by pressure wave incidence and reflection.
Fig. 2 e Variations of temperature and pressure at TDC vs. compression ratio.
Result and discussion
temperature T ¼ 323 K and initial pressure P ¼ 1 atm are also shown in Fig. 2, assuming adiabatic compression. As can be seen, there exists temperature difference between Szwaja's prediction and CHEMKIN calculation. This difference is expected to be caused by difference values of inlet temperature and pressure and equivalence ratio, which is not clarified in detail by Szwaja et al. Nevertheless, both predictions exhibit approximately linear relation between temperature and compression ratio. Considering the above calculation results, two conditions at TDC are chosen: (1) T0 ¼ 750 K, P0 ¼ 20 bar; (2) T0 ¼ 860 K, P0 ¼ 34 bar, which correspond to compression ratios of about 9 and 13, respectively.
Determination of initial condition
Flame evolution without auto-ignition
Hydrogen-fueled engine is usually operated under compression ratio ranging from 6 to 14 due to the limitation of wide knocking region [26]. Temperature before spark discharge and flame front formation plays a crucial role during the following main flame propagation. Higher compression ratio means higher temperature and pressure at TDC and meanwhile leads to stronger turbulence and inhomogeneity in combustion chamber, which enhances knocking tendency and intensity. Temperature before spark charge is approximately considered the same as that at TDC and is therefore determined by compression ratio, thermodynamics property of gas mixture, inlet condition and heat loss during compression. Determination of temperature vs. compression ratio by Szwaja et al. [27] based on polytropic process is shown in Fig. 2. The polytropic index was determined experimentally in advance on the basis of pressure-volume interaction at each compression ratio. Temperature at intake valve closure was determined with the aid of equation of state for ideal gas. The known variables were as follows: pressure, volume and the mass of hydrogeneair mixture. It can be observed that temperature increases linearly with the increase of compression ratio. Aiming to get knowledge of temperature and pressure under clarified inlet condition, closed internal combustion engine simulator in CHEMKIN is employed. The calculated conditions at TDC of stoichiometric hydrogen/air mixture with initial
This section discusses the situation that flame accelerates into detonation without the occurrence of auto-ignition, which is shown in Fig. 1a. Calculation results of initial condition (2) T0 ¼ 860 K, P0 ¼ 34 bar is analyzed first. Stoichiometric premixed hydrogen/air mixture is ignited by patching a 2 mm-thick hot zone of 2000 K on the left end. The evolution of pressure wave, including pressure wave propagation, reflection and interaction with flame are shown in sequence. Fig. 3a shows the evolution of pressure wave and flame front after ignition. It can be observed that the propagation speed of flame front is about 284.6 m/s, while that of pressure wave is about 857.8 m/s, which is higher than sound speed in unburned mixture usp ¼ 680.8 m/s, thus forming a shock wave. It has to be stated that ignition energy has considerable effect on initially formed flame and pressure wave. Usually, flame speed is observed to be higher at early stage (radius of flame rf < 5 mm) as affected by ignition energy, which will decrease to a slower steady propagation speed until cellular instability occurs [20]. Meanwhile, the peak value of pressure wave decreases during propagation as pressure wave moves away from flame front and couldn't gain energy from it. On the contrary, the energy in pressure wave dissipates into unburned mixture due to its compression effect and increases the temperature by about 130 K. The raised temperature diminishes to 105 K as peak value of pressure wave decreases
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Fig. 4 e Evolutions of pressure wave and flame front during DDT. Dotted lines represent temperature profiles and solid lines represent pressure profiles. From left to right: Time sequences are 407 ms, 408 ms and 409 ms respectively.
Fig. 3 e Evolutions of pressure and temperature profiles. Dotted lines represent temperature profiles and solid lines represent pressure profiles. (a) After ignition. From left to right: time sequences are 10 ms, 15 ms, 20 ms and 25 ms, respectively. (b) Before and after first reflection by right end wall. From left to right: Time sequences are 100 ms, 95 ms, 90 ms and 87 ms, respectively.
trigger DDT. An interesting phenomenon is observed and shown in Fig. 4. When flame front propagates to the location x ¼ 57.3 mm, a “tiny pressure wave” with an amplitude of about 5.5 bar that increases local temperature by about 70 K, catches up with flame front and triggers the DDT. Tracing this tiny pressure wave, it can be found that this pressure wave first occurs due to reflection of pressure wave by flame front, which then propagates and catches up with the flame front at that moment afterwards. Acute chemical reactions proceed on flame front, forming a strong supersonic shock wave with a peak value of 305 bar. Finally, a detonation wave with flame front and a coupled pressure wave, is formed at location x ¼ 59.8 mm. Heat release on flame front is so fierce that it also forms a pressure wave propagating to the left, but with a much smaller peak value. The formed detonation wave has much higher peak pressure and temperature than normal deflagration, which will cause mechanical damage and
and is stabilized at about 51 bar. It can also be observed that pressure undergoes an increase at the location of flame front along propagation direction due to compression effect of hot burnt mixture, which is consistent with the conclusion that flame front supplies energy to pressure wave, thereby maintaining its peak value. The pressure wave propagates to the right and is reflected by the right wall, which is shown in Fig. 3b. It is obvious that the temperature after pressure wave reflection is further increased but still not enough to trigger auto-ignition within several microseconds. As combustion proceeds, pressure wave is reflected several times by right and left walls. When pressure wave propagates towards opposite direction of flame front and passes through it, stagnation of flame front can be observed, which is expected to be caused by backflow of gas mixture after the passage of pressure wave. Each time pressure wave sweeps through unburned mixture, it heats unburned mixture up a little, eventually attaining it a critical condition that would
Fig. 5 e Variations of pressure and temperature vs. time at the location x ¼ 59.8 mm where detonation is formed. Dotted line represents temperature profile and solid line represents pressure profile.
Please cite this article in press as: Wei H, et al., One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions, International Journal of Hydrogen Energy (2015), http://dx.doi.org/ 10.1016/j.ijhydene.2015.02.034
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thermal erosion of combustion chamber. Fig. 5 shows the variation of pressure and temperature at the location x ¼ 59.8 mm where detonation is formed. It can be observed that main pressure wave (pressure wave generated by main flame front) has passed through this location five times, among which the second and the fourth peak on pressure profile are caused by reflected pressure wave. Despite pressure rises caused by main pressure wave, small pressure oscillations on pressure profile also exist as shown in Fig. 5, which are caused by a series of pressure wave reflected by flame front such as tiny pressure wave mentioned before and different propagation speed between them. Variation of overall heat release rate is shown in Fig. 6. Oscillation of heat release rate can be observed because the production and the diffusion of heat produced by reaction are kinetic processes, both physically and chemically, for which reason combustion is not absolutely stable. Among obvious oscillations of the profile, two relatively smooth sections indicates the stagnation of flame front caused by pressure wave induction. Heat release during these periods is slow but turns out to have higher amplitude after flame front keeping on moving, indicating the enhancement of combustion by pressure wave. Due to DDT, flame front rapidly finishes sweeping over the remaining unburned mixture at 416 ms. In comparison, simulation with initial condition (1) T0 ¼ 750 K, P0 ¼ 20 bar does not encounter DDT till flame propagates through the while domain, which is not shown here. It can be concluded that initial temperature T0 ¼ 750 K leads to relatively low reactivity of unburned mixture, thus restraining the occurrence of DDT and engine knock. However, heat release rate also increases each time after flame front stagnation, which has the same tendency as that with initial condition (2).
Flame evolution with end gas auto-ignition As it is considered as a major cause of engine knock, autoignition of end gas is investigated in this section. Initial condition (1) is chosen since it has lower reactivity and is unlikely to develop into detonation itself, which keeps the focus on the effect of auto-ignition. A hot zone of 2000 K is patched
Fig. 6 e Variation of overall heat release rate vs. time in computational domain.
between x ¼ 20 mm and x ¼ 22 mm to simulate spark-ignition. According to engine experiments carried out by Downs and Theobald [28], surface temperature could reach up to 1180 K in normal combustion and to 1500 K when pre-ignition occurred. As ignition delay is extremely sensitive to temperature, a temperature rise of 200 K might decrease ignition delay by 1e2 orders of magnitudes. Taking these into consideration, a 2mm thick hot zone with temperature of Te is introduced into the left end of computational domain. The results of two different Te are shown here, representing two typical situations: auto-ignition before and after pressure wave induction. The inducing pressure wave is formed by main flame front, so it remains the same amplitude and speed in the two cases.
Hot zone with Te ¼ 1300 K In this case, Te is sufficiently high that hot zone auto-ignites before main pressure wave arrives. Then the main pressure wave is reflected by left end wall and catches up with the autoignited flame front to the right. The interaction between main pressure wave and auto-ignited flame front is shown in Fig. 7. At 31 ms, pressure wave catches up with the flame front and splits into two peaks. The left one is due to the reflection by flame front while the right one due to the enhancement by flame front. Although the flame front is sped up by pressure wave while in turn the amplitude of main pressure wave is strengthened by flame front, the auto-ignited flame front fails to develop into a detonation. It is similar with what can be observed in Fig. 5, that the main pressure wave passes through flame front with its same direction three times but does not trigger DDT. This phenomenon indicates that DDT can only be triggered when some critical conditions are reached. For example, a sufficiently high temperature and pressure of unburned mixture which ensures high reactivity, a pressure wave with high amplitude that would ignite mixture ahead of flame front, the unnoticeable accumulation of intermediate species such as HO2 or the disturbance of flame front due to turbulence and obstacle. Despite the fact
Fig. 7 e Evolutions of temperature and pressure profiles during interaction between reflected main pressure wave and auto-ignited flame front. Dotted lines represent temperature profiles and solid lines represent pressure profiles. From left to right: time sequences are 31 ms, 32 ms and 33 ms, respectively.
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that auto-ignited flame front fails to develop into a detonation, the pressure wave formed by it catches up with the main flame front that propagates to the right and triggers DDT. This evolution is consistent with that shown in Fig. 1b and is similar to that shown in Fig. 4, which is not shown here.
Hot zone with Te ¼ 1125 K Fig. 8 shows the evolution of pressure and temperature profiles after pressure wave induction at 27 ms. Auto-ignition occurs at 46 ms, before which moment the temperature and pressure in hot zone increase to 1276 K and 27 bar, respectively, due to the induction and reflection of main pressure wave. The auto-ignited flame front directly develops into a detonation with a peak value of 175 bar. It is interesting that a higher Te ¼ 1300 K does not trigger direct detonation as in this case. The major difference between the two cases seems to be the pressure. As pressure increases, collisions between species become more frequent, thus promoting reactions. On the other hand, the p-T diagram of explosion limits of stoichiometric hydrogeneoxygen mixture [29] indicates complicated chemical kinetics during chain initiating and chain branching process, although data are only available in low pressure range. To further understand the chemistry involved in two cases, CHEMKIN-PRO is employed for chemical kinetic study. Temperature sensitivity analysis is carried out during homogeneous auto-ignition under constant pressure. Fig. 9 shows the normalized temperature sensitivity coefficients of three dominant reactions: R1: H þ O2 ¼ O þ OH; R9: H þ O2 (þM) ¼ HO2 þ (M); R11: HO2 þ H ¼ OH þ OH, with initial conditions (3) T0 ¼ 1275 K, P0 ¼ 20 bar and (4) T0 ¼ 1275 K, P0 ¼ 27 bar, respectively. The positive value of a reaction indicates that increasing the rate of this reaction leads to a higher temperature as well as heat release. It can be observed that absolute peak value of temperature sensitivity with initial condition (4) is much larger than that with condition (3). A higher sensitivity means that these reactions contribute more to temperature when combustion proceeds, which in some ways reflects the intensity of reaction. Furthermore, R9
Fig. 8 e Evolutions of pressure and temperature profiles after pressure wave induction. Dotted lines represent temperature profiles and solid lines represent pressure profiles. From left to right: time sequences are 45 ms, 46 ms, 47 ms and 48 ms, respectively.
Fig. 9 e Normalized sensitivity coefficients of three dominant reactions with different initial conditions. (a) T0 ¼ 1275 K, P0 ¼ 20 bar; (b) T0 ¼ 1275 K, P0 ¼ 27 bar.
becomes more important and produces more HO2 as pressure increases. Being relatively inactive, HO2 will survive longer during collisions and plays an important role in the following reactions. Fig. 10 shows the variations of mole fraction of intermediate radicals HO2 and H during these two auto-ignition process. The ignition delay under initial condition (4) is slightly longer than that under initial condition (3), while the HO2 in (4) begins to accumulate to a considerable quantity at early stage. The long surviving HO2 generates active radicals such as O, H, and OH that promotes chain propagation reactions: R1: H þ O2 ¼ O þ OH; R2: O þ H2 ¼ H þ OH; R3: OH þ H2 ¼ H þ H2O, which in turn generates more active radicals and introduces more fuel and oxygen. This selfpromoting behavior finally leads to intensive heat release and, in some conditions, (4) for instance, initializes a detonation. It can be observed that HO2 accumulates more under 27 bar, while H has a lower value compared with that under 20 bar. More accumulated HO2 ensures faster production and consumption of active radicals, which is the reason why mole fraction of H is slightly lower under 27 bar.
Please cite this article in press as: Wei H, et al., One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions, International Journal of Hydrogen Energy (2015), http://dx.doi.org/ 10.1016/j.ijhydene.2015.02.034
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Fig. 10 e Variations of intermediate radicals during autoignition.
Ignition delay influenced by pressure wave Although temperature field of end gas is determined mainly by heat transfer with cylinder wall, valve and spark plug, gas flow in cylinder and so on, pressure wave has to be taken into consideration since its induction and reflection causes temperature variation. Since different locations in end gas are impacted by pressure wave at different time, the variations of temperature would also be different, which might leads to different ignition delays. Therefore, unlike most ignition delays calculated under constant initial conditions, ignition delays under varying pressure and temperature are investigated here. Aiming to gain the pressure and temperature close to the actual situation, CFD simulation performed in Sec. Hot zone with Te ¼ 1125 K where end gas initial condition is T0 ¼ 1125 K, P0 ¼ 20 bar is referenced. Variations of pressure at different location are extracted and shown in Fig. 11a. It can be seen that locations other than x ¼ 0 mm undergoes two pressure rise, between which is the time interval that pressure is reflected by the wall and passes through again. CHEMKIN is employed to calculate ignition delays while pressure profiles are imported according to data extracted from hot zone. To stabilize the calculation, pressure profiles are simplified to polylines instead, which are shown in Fig. 11b. Since mixture will auto-ignite before 50 ms and ignition delays at different locations share nearly the same pressure profile after 43 ms, it's acceptable to remain pressure constant at 27.5 bar after 43 ms. Ignition delay is defined as the period between initial moment and the moment when initial temperature increases by 400 K. Fig. 12 shows calculated ignition delays at different locations. Ignition delay is observed to increase as the location moves away from the left end. The reason seems to be clear: pressure at x ¼ 0 mm undergoes only one sharp rise and increases to and remains the highest among other locations, the time integral of temperature is therefore higher, which is the dominant factor of ignition delay. The increase of ignition delay along the right hand direction might be a reason for direct formation of detonation.
Fig. 11 e Variations of pressure at different locations in end gas. (a) Pressure profiles extracted from CFD simulation. (b) Simplified pressure polylines imported in CHEMKIN.
Fig. 12 e Calculated ignition delays at different locations.
Please cite this article in press as: Wei H, et al., One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions, International Journal of Hydrogen Energy (2015), http://dx.doi.org/ 10.1016/j.ijhydene.2015.02.034
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However, as chemical kinetics is a complicated process affected by every detail, several other factors have to be considered as the specification of case investigated changes. Despite the differences in initial pressure and temperature, pressure profiles of different locations might also have different peak value and the interval between two pressure rises, according to the intensity of inducing pressure and the length of hot zone. Furthermore, if the fuel implemented has Negative Temperature Coefficient (NTC) behavior such as nheptane and iso-octane, the prediction of auto-ignition modes [9] will be more complicated. Further investigations have to be carried out in future works.
Conclusions In this study, two possible causes of engine knock: flame acceleration and auto-ignition, are studied using onedimensional simulation under engine-relevant conditions. Chemical source term is modeled using Arrhenius expression with detailed chemical mechanism of hydrogen oxidation. Chemical kinetic study is performed to further understand the detailed process during auto-ignition. Ignition delays under varying conditions since the effect of pressure wave are calculated by importing pressure profiles extracted from CFD simulation into CHEMKIN. Propagation and reflection of pressure wave in engine might cause DDT. Propagations of pressure wave generated by main flame front under engine-relevant conditions are investigated. The main pressure wave passes through flame front several times and causes either stagnation or acceleration of flame front. At one moment, a tiny pressure wave, which is reflected by flame front, catches up with the flame front and triggers DDT. However, no DDT is observed under low compression ratio, which indicates the key role of initial temperature. Heat release rate is observed to increase due to the passage of pressure wave through flame front. Pressure wave-induced auto-ignition might lead to direct formation of detonation. Two hot zones with different temperature are investigated, among which the one with higher temperature auto-ignites without detonation while the one with lower temperature auto-ignites and develops into detonation due to the induction of pressure wave. Even though auto-ignition does not forms detonation, the pressure wave it generates might still enhance combustion and lead to DDT. Pressure is considered to be the main cause for the difference, since higher pressure enhances the accumulation of HO2, thus leading to more intensive chain reactions during autoignition. Ignition delay is influenced by varying pressure and temperature due to the induction and reflection of pressure wave. The calculation result shows that ignition delay near the end wall is lower due to higher temperature integral compared with that further away. This leads to the formation of the increase of ignition delay along the right hand direction, which is proposed to be the possible cause for detonation formation. However, gradient of ignition delay might be affected by complicated factors according to the intensity of inducing pressure wave, the length of hot zone and the characteristics of different fuels.
9
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 51476114 and 51176138). Prof. Zheng Chen in Peking University and Prof. Zhuyin Ren in Tsinghua University are also appreciated for providing helpful advice and guidance.
references
[1] Livengood JC, Wu PC. Correlation of autoignition phenomena in internal combustion engines and rapid compression machines. Sym Int Combust 1955;5(1):347e56. Elsevier. [2] Curry S. A three-dimensional study of flame propagation in a spark ignition engine. No. 630487. SAE Technical Paper. 1963. [3] Chun KM, Heywood JB. Characterization of knock in a sparkignition engine. SAE Technical Paper. 1989. p. 890156. € schl M, Sattelmayer T. Influence of temperature [4] Po inhomogeneities on knocking combustion. Combust Flame 2008;153(4):562e73. [5] White CM, Steeper RR, Lutz AE. The hydrogen-fueled internal combustion engine: a technical review. Int J Hydrogen Energy 2006;31(10):1292e305. [6] Zeldovich YB. Regime classification of an exothermic reaction with nonuniform initial conditions. Combust Flame 1980;39(2):211e4. [7] Gu XJ, Emerson DR, Bradley D. Modes of reaction front propagation from hot spots. Combust Flame 2003;133(1):63e74. [8] Liberman MA, Kiverin AD, Ivanov MF. Regimes of chemical reaction waves initiated by nonuniform initial conditions for detailed chemical reaction models. Phys Rev E 2012;85(5):056312. [9] Peng D, Zheng C, Shiyi C, Yiguang J. Numerical experiments on reaction front propagation in n-heptane/air mixture with temperature gradient. Proc Combust Inst 2014;35(3):3045e52. [10] Oran ES, Gamezo VN. Origins of the deflagration-todetonation transition in gas-phase combustion. Combust Flame 2007;148(1):4e47. [11] Khokhlov AM, Oran ES. Numerical simulation of detonation initiation in a flame brush: the role of hot spots. Combust Flame 1999;119(4):400e16. [12] Khokhlov AM, Oran ES, Thomas GO. Numerical simulation of deflagration-to-detonation transition: the role of shockeflame interactions in turbulent flames. Combust Flame 1999;117(1):323e39. [13] Molkov V, Verbecke F, Makarov D. LES of hydrogen-air deflagrations in a 78.5-m tunnel. Combust Sci Technol 2008;180(5):796e808. [14] Wang Z, Wang Y, Reitz RD. Pressure oscillation and chemical kinetics coupling during knock processes in gasoline engine combustion. Energy & Fuels 2012;26(12):7107e19. [15] Rakopoulos CD, Kosmadakis GM, Pariotis EG. Critical evaluation of current heat transfer models used in CFD incylinder engine simulations and establishment of a comprehensive wall-function formulation. Appl Energy 2010;87(5):1612e30. [16] Gordon S, McBride J. NASA report SP-27. NASA Lewis Research Center; 1971. [17] Magnussen BF. On the structure of turbulence and a generalized eddy dissipation concept for chemical reaction in turbulent flow. In: 19th AIAA aerospace meeting, St. Louis, USA; 1981.
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[18] Wei H, Shang Y, Chen C, Gao D, Feng D. A numerical study on pressure wave-induced end gas auto-ignition near top dead center of a downsized spark ignition engine. Int J Hydrogen Energy 2014;39(36):21265e74. [19] Hu E, Huang Z, He J, Miao H. Experimental and numerical study on laminar burning velocities and flame instabilities of hydrogeneair mixtures at elevated pressures and temperatures. Int J Hydrogen Energy 2009;34(20):8741e55. [20] Sun ZY, Liu FS, Bao XC, Liu XH. Research on cellular instabilities in outwardly propagating spherical hydrogen-air flames. Int J Hydrogen Energy 2012;37(9):7889e99. [21] Liu Y, Pei P. Asymptotic analysis on autoignition and explosion limits of hydrogeneoxygen mixtures in homogeneous systems. Int J Hydrogen Energy 2006;31(5):639e47. Conaire M, Curran HJ, Simmie JM, Pitz WJ, Westbrook CK. A [22] O comprehensive modeling study of hydrogen oxidation. Int J Chem Kinet 2004;36(11):603e22.
[23] Li J, Zhao ZW, Kazakov A, Dryer FL. An updated comprehensive kinetic model of hydrogen combustion. Int J Chem Kinet 2004;36(10):566e75. [24] Saxena P, Williams FA. Testing a small detailed chemicalkinetic mechanism for the combustion of hydrogen and carbon monoxide. Combust Flame 2006;145(1):316e23. [25] Design R. Chemkin-Pro 15101. San Diego, CA: Reaction Design; 2010. [26] Li H, Karim GA. Knock in spark ignition hydrogen engines. Int J Hydrogen Energy 2004;29(8):859e65. [27] Szwaja S, Naber JD. Dual nature of hydrogen combustion knock. Int J Hydrogen Energy 2013;38(28):12489e96. [28] Downs D, Theobald FB. The effect of fuel characteristics and engine operating conditions on pre-ignition. Proc Inst Mech Eng Automob Div 1963;178(1):89e108. [29] Law CK. Combustion physics. Cambridge University Press; 2006.
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Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions Haiqiao Wei*, Yibao Shang, Ceyuan Chen, Dongzhi Gao, Dengquan Feng State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China
article info
abstract
Article history:
Knock is considered as a major challenge when increasing thermal efficiency of internal
Received 25 December 2014
combustion engine. In this study, two possible causes of engine knock: flame acceleration
Received in revised form
and auto-ignition, are studied using one-dimensional simulation under engine-relevant
3 February 2015
conditions. Chemical source term is modeled using Arrhenius expression with detailed
Accepted 8 February 2015
chemical mechanism of hydrogen oxidation. Interaction between pressure wave and flame
Available online xxx
during propagation of flame front is investigated. It is observed that propagation and reflection of pressure wave in cylinder might trigger DeflagrationeDetonation Transition
Keywords:
(DDT), which leads to extremely high pressure oscillation. Pressure wave initialized by
Pressure wave
auto-ignition flame is also a reason leading to detonation by enhancing main flame front.
Knock
Chemical kinetics study is also carried out to analyze chemical process during auto-
Deflagrationedetonation transition
ignition. Pressure wave is considered to play an important role in the initiation of direct
Auto-ignition
detonation due to accumulation of intermediate radicals under higher pressure. Ignition
Hydrogen
delays under varying conditions are calculated according to the effects of pressure wave induction. As a result, gradient of ignition delays is observed, which might be a possible cause of detonation initialization. Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Increasing compression ratio as well as inlet air supercharging is a common method to increase the thermal efficiency of internal combustion Spark Ignition (SI) reciprocating engines. However, compression ratio of engine is limited by the occurrence of abnormal combustion such as knock and preignition. Engine knock, characterized by pressure oscillation and “pinging” sound in cylinder, causes undesirable engine performance and even damages engine cylinder. It is
commonly believed that knock is caused by end gas autoignition after spark plug ignition [1]. Some researchers also propose that flame propagation and acceleration in cylinder are also the reasons that lead to knock [2]. Despite these two different points of view, experiments showed that pressure profiles measured at different locations differ from each other during the same knocking cycle [3,4], which indicates the existence of propagation, interaction and reflection of pressure waves inside combustion chamber. Hydrogen, with low density, wide flammability limits and low minimum ignition
* Corresponding author. Tel./fax: þ86 022 27402609. E-mail address: [email protected] (H. Wei). http://dx.doi.org/10.1016/j.ijhydene.2015.02.034 0360-3199/Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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energy, suffers knocking problem as well as gasoline when utilized in hydrogen-fueled internal combustion engine [5]. During flame propagation, heat generated from flame front will raise local temperature quickly thus driving hot gas compressing cooler surroundings. Usually, a pressure wave is formed before flame front and travels away from it at the speed of sound. However, in some extreme conditions, flame front accelerates to supersonic, thus driving pressure wave propagating at the same speed as flame front. In turn, the pressure wave heats unburned gas before flame front, which will maintain flame propagation speed. This coupling between flame front and pressure wave leads to DeflagrationeDetonation Transition (DDT) phenomenon. The pressure peak of a detonation that could reach dozens of megapascal, corresponds to the magnitude of peak cylinder pressure during severe abnormal combustion. Previous works focusing on flame propagation and interaction between pressure wave and flame can be divided into two main aspects: the initialization of reaction wave and its transition during propagation. The different regimes of flame front initialized by non-uniform initial conditions were first studied by Zeldovich using a one-step chemical model [6]. He discovered that spontaneous reaction wave can propagate through a reactive material along a spatial gradient of variables such as temperature and species concentration that could influence ignition delay. Considering an area with temperature gradient along x-axis, auto-ignition will first occur at the location which has the highest temperature T(x)max, and the spontaneous reaction wave then propagates along the gradient with the speed usp:
usp ¼
vtig 1 vtig vT 1 ¼ vx vT vx
where tig is ignition delay as a function of initial temperature gained from experiment or chemical kinetics calculation. According to their relationships with ChapmaneJouguet speed and sound speed, different values of usp indicate the initialization of different regimes of spontaneous reaction wave, such as detonation, deflagration and homogenous explosion. This theory was studied by many researchers using detailed chemistry and was extended to the research on abnormal combustion in engines [7e9]. As for transition during propagation, DDT process is mainly considered. Khokhlov et al. [10e12] numerically studied shockeflame interactions in reactive mixture. They found that flame generates and enhances shock waves, which in turn creates turbulence in flames, thus promoting the formation of hot spots, causing auto-ignition and DDT. Similar effects of pressure wave on flame were also observed by Molkov et al. [13]. They modeled hydrogen-air deflagration in a long tunnel, where initial pressure wave develops into a shock due to reflection by obstacles. There are also multi-dimension CFD simulations investigating engine knock, with different focuses and methods such as heat transfer and pressure oscillation [14,15]. Since engine cylinder is a closed narrow space, pressure wave would be reflected by cylinder walls several times during combustion. Therefore, the heating effect of pressure wave, the interactions between unburned gas and pressure wave,
and the acceleration of flame influenced by pressure wave have to be considered when studying engine knock. As is mentioned, previous works mainly focus on the initialization of different auto-ignition forms or the DDT process during flame propagation. Very few researchers establish a connection between the propagation of pressure wave and the transition of flame front under engine-relevant condition. This work aims to maintain the understanding of engine knock by considering auto-ignition and DDT process during combustion. Numerical simulation is carried out in a 75 mm one-dimensional domain, which has the similar radial length of combustion chamber. Two possible forms of combustion leading to knock are investigated: acceleration of flame and end gas auto-ignition under the effect of pressure wave. DDT process induced by pressure waveeflame interaction along with high amplitude pressure oscillation are observed and analyzed. In addition, chemical kinetics study under varying conditions due to induction of pressure wave is carried out, giving a better understanding of chemical process during auto-ignition.
Numerical details Specifications of problem Since the location and the moment of knock onset are mainly determined by inhomogeneity of temperature and concentration of gas mixture that result in different ignition delays, the knock is a stochastic phenomenon, which has to be studied with simplification and assumption. In this study, combustion chamber at Top Dead Center (TDC) is simplified to a 75 mm one-dimensional domain. Adiabatic boundaries are assumed to rule out heat loss to the walls. Study on mesh convergence is performed within several empirical cell sizes, at last a cell size of 0.05 mm is chosen in consideration of both the ability to capture flow discontinuity and the reduction of computational cost. Fig. 1 shows two hypotheses of flame acceleration. If the mixture is ignited at left end and propagates to the right, pressure wave that travels faster than flame front will gradually raise the temperature of whole unburned mixture during its propagation and reflection between left and right walls. As the flame speed as well as mixture reactivity increases, the propagating flame will finally transited into a detonation if some critical conditions are reached. The other hypothesis is similar to the former one but includes end gas auto-ignition. Mixture is ignited near the middle of the domain, thus forming pressure waves towards both ends that cause pressure wave-induced auto-ignition at left end. Pressure wave initialized by auto-ignited flame then propagates to the right and interacts with main flame front, leading to detonation. In fact, the occurrence of auto-ignition does not necessarily cause severe pressure oscillation, indicating that some certain critical conditions have to be reached. Since auto-ignition happens in hot spots, different temperature gradients will be formed depending on turbulence, initial thermodynamic status and heat transfer with cylinder wall and so on, thus causing different levels of knock, which is consistent with gradient theory studied by many researchers. Ignition is achieved by patching a 2 mm-thick hot zone with
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Fig. 1 e Two hypotheses of flame acceleration: (a) flame acceleration without auto-ignition; (b) flame acceleration enhanced by auto-ignition.
the temperature of 2000 K. In auto-ignition case, a hot zone is also introduced into end gas area in consideration of promoting auto-ignition of end gas within a sufficiently short period. All mentioned above will be shown in detail within following sections.
CFD modeling The mixture is assumed to be compressible ideal gas, whose state is: p¼
E¼
r RT M X
Yi h i þ
2
v 2
where R denotes universal gas constant, M the molar weight of mixture, e the energy per unit mass, Yi the mass fraction, hi the sensible enthalpy and v the velocity. Subscript i indicates the ith species. The specific heat and enthalpy of the species are considered as functions of temperature and are calculated by polynomial fits using NASA chemical equilibrium code [16]. The governing equations of mass, momentum, energy and species transport are solved simultaneously while equations for other scalars are solved afterward: vr þ V$ðr! vÞ ¼ 0 vt vðr! vÞ þ V$ðr! v! v Þ ¼ Vp þ V$ðtÞ vt 2 y vI t ¼ m V! v þ V! v V$! 3 / / X vðreÞ þ V$ v ðre þ pÞ ¼ V$ keff VT þ Sh hi Ji þ t$v vt vðrYi Þ ! þ V$ðr! v Yi Þ ¼ V$ J i þ Ri vt where t denotes the stress tensor, m the dynamic viscosity, I ! the unit tensor, keff the effective conductivity, J i the diffusion flux, Sh the heat source and Ri the net production rate. Superscript y means a transposed matrix. Since calculation is
performed in a one-dimensional domain, the absence of compression stroke, the simplicity of computational domain and the high intensity of reaction make turbulence only neglectable effects on flow and reaction, thus no turbulence model is employed. In fact, the discrepancy between RANSmodeled turbulent flow and laminar flow in this calculation is barely observable according to our earlier comparisons, in which the pressure and temperature fluctuations in laminar flow are slightly higher. Chemical source terms are calculated using Arrhenius expression and ignoring the effect of turbulent fluctuations. The net production rate Ri can be expressed as: Ri ¼ Mw;i
NR X
b i;r R
r¼1
0 1 N 00 Y
h0j;r þh00j;r 0 b @ A kf ;r R i;r ¼ G yi;r yi;r Cj;r j¼1
kf ;r ¼ Ar Tbr eEr =RT where Mw,i ¼ molecular weight of species i b i;r ¼ Arrhenius molar rate of creation/destruction of speR cies i in reaction r G ¼ net effect of third bodies on the reaction rate Cj,r ¼ molar concentration of species j in reaction r h0j;r ¼ rate exponent of reactant species j in reaction r 00 hj;r ¼ rate exponent of product species j in reaction r kf,r ¼ forward rate constant of reaction r Ar ¼ pre-exponential factor br ¼ temperature exponent Er ¼ activation energy for the reaction R ¼ universal gas constant compared with Eddy-Dissipation Concept (EDC) model [17] employed in our previous work [18], this model is more appropriate for predicting low temperature auto-ignition and supersonic flames. Hydrogen, known as a renewable clean energy carrier, is utilized as fuel of SI engine where abnormal combustion also occurs as that fueled by gasoline. In addition, the combustion
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characteristics, such as laminar flame speed, flame instability and chemical kinetics of hydrogen are well investigated, which provides a knowledge background for the study of hydrogen combustion [19e21]. Besides, the simplicity and reliability of hydrogen oxidation mechanism makes it a practical tool for numerical research on combustion phenomenon. Among numerous mechanisms available [22e24], Conaire et al.'s [22] mechanism that consists of 9 Marcus O species and 21 reactions was validated with experimental data over wide ranges of temperature, pressure and equivalent ratio and is chosen here for reaction modeling. The entire CFD simulation is carried out using commercial CFD package ANSYS Fluent, while one-dimensional domain is achieved by limiting y-axis direction of two-dimension mesh to a single fine grid. Third-order MUSCL scheme is employed for spatial discretization as it improves spatial accuracy by reducing numerical diffusion. In order to maintain the stability and accuracy while reaction and flow is intensively coupled, a time step of 1e-8s is selected for second-order implicit time integration. In addition to CFD modeling, chemical kinetics study is carried out to have a better understanding of chemical process during end gas auto-ignition. Ignition delays and variations of species during pressure wave-end gas interaction are calculated using CHEMKIN-PRO [25]. Unlike ignition process under approximately uniform condition, a pressure profile extracted from CFD modeling is imported to simulate the varying pressure conditions caused by pressure wave incidence and reflection.
Fig. 2 e Variations of temperature and pressure at TDC vs. compression ratio.
Result and discussion
temperature T ¼ 323 K and initial pressure P ¼ 1 atm are also shown in Fig. 2, assuming adiabatic compression. As can be seen, there exists temperature difference between Szwaja's prediction and CHEMKIN calculation. This difference is expected to be caused by difference values of inlet temperature and pressure and equivalence ratio, which is not clarified in detail by Szwaja et al. Nevertheless, both predictions exhibit approximately linear relation between temperature and compression ratio. Considering the above calculation results, two conditions at TDC are chosen: (1) T0 ¼ 750 K, P0 ¼ 20 bar; (2) T0 ¼ 860 K, P0 ¼ 34 bar, which correspond to compression ratios of about 9 and 13, respectively.
Determination of initial condition
Flame evolution without auto-ignition
Hydrogen-fueled engine is usually operated under compression ratio ranging from 6 to 14 due to the limitation of wide knocking region [26]. Temperature before spark discharge and flame front formation plays a crucial role during the following main flame propagation. Higher compression ratio means higher temperature and pressure at TDC and meanwhile leads to stronger turbulence and inhomogeneity in combustion chamber, which enhances knocking tendency and intensity. Temperature before spark charge is approximately considered the same as that at TDC and is therefore determined by compression ratio, thermodynamics property of gas mixture, inlet condition and heat loss during compression. Determination of temperature vs. compression ratio by Szwaja et al. [27] based on polytropic process is shown in Fig. 2. The polytropic index was determined experimentally in advance on the basis of pressure-volume interaction at each compression ratio. Temperature at intake valve closure was determined with the aid of equation of state for ideal gas. The known variables were as follows: pressure, volume and the mass of hydrogeneair mixture. It can be observed that temperature increases linearly with the increase of compression ratio. Aiming to get knowledge of temperature and pressure under clarified inlet condition, closed internal combustion engine simulator in CHEMKIN is employed. The calculated conditions at TDC of stoichiometric hydrogen/air mixture with initial
This section discusses the situation that flame accelerates into detonation without the occurrence of auto-ignition, which is shown in Fig. 1a. Calculation results of initial condition (2) T0 ¼ 860 K, P0 ¼ 34 bar is analyzed first. Stoichiometric premixed hydrogen/air mixture is ignited by patching a 2 mm-thick hot zone of 2000 K on the left end. The evolution of pressure wave, including pressure wave propagation, reflection and interaction with flame are shown in sequence. Fig. 3a shows the evolution of pressure wave and flame front after ignition. It can be observed that the propagation speed of flame front is about 284.6 m/s, while that of pressure wave is about 857.8 m/s, which is higher than sound speed in unburned mixture usp ¼ 680.8 m/s, thus forming a shock wave. It has to be stated that ignition energy has considerable effect on initially formed flame and pressure wave. Usually, flame speed is observed to be higher at early stage (radius of flame rf < 5 mm) as affected by ignition energy, which will decrease to a slower steady propagation speed until cellular instability occurs [20]. Meanwhile, the peak value of pressure wave decreases during propagation as pressure wave moves away from flame front and couldn't gain energy from it. On the contrary, the energy in pressure wave dissipates into unburned mixture due to its compression effect and increases the temperature by about 130 K. The raised temperature diminishes to 105 K as peak value of pressure wave decreases
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Fig. 4 e Evolutions of pressure wave and flame front during DDT. Dotted lines represent temperature profiles and solid lines represent pressure profiles. From left to right: Time sequences are 407 ms, 408 ms and 409 ms respectively.
Fig. 3 e Evolutions of pressure and temperature profiles. Dotted lines represent temperature profiles and solid lines represent pressure profiles. (a) After ignition. From left to right: time sequences are 10 ms, 15 ms, 20 ms and 25 ms, respectively. (b) Before and after first reflection by right end wall. From left to right: Time sequences are 100 ms, 95 ms, 90 ms and 87 ms, respectively.
trigger DDT. An interesting phenomenon is observed and shown in Fig. 4. When flame front propagates to the location x ¼ 57.3 mm, a “tiny pressure wave” with an amplitude of about 5.5 bar that increases local temperature by about 70 K, catches up with flame front and triggers the DDT. Tracing this tiny pressure wave, it can be found that this pressure wave first occurs due to reflection of pressure wave by flame front, which then propagates and catches up with the flame front at that moment afterwards. Acute chemical reactions proceed on flame front, forming a strong supersonic shock wave with a peak value of 305 bar. Finally, a detonation wave with flame front and a coupled pressure wave, is formed at location x ¼ 59.8 mm. Heat release on flame front is so fierce that it also forms a pressure wave propagating to the left, but with a much smaller peak value. The formed detonation wave has much higher peak pressure and temperature than normal deflagration, which will cause mechanical damage and
and is stabilized at about 51 bar. It can also be observed that pressure undergoes an increase at the location of flame front along propagation direction due to compression effect of hot burnt mixture, which is consistent with the conclusion that flame front supplies energy to pressure wave, thereby maintaining its peak value. The pressure wave propagates to the right and is reflected by the right wall, which is shown in Fig. 3b. It is obvious that the temperature after pressure wave reflection is further increased but still not enough to trigger auto-ignition within several microseconds. As combustion proceeds, pressure wave is reflected several times by right and left walls. When pressure wave propagates towards opposite direction of flame front and passes through it, stagnation of flame front can be observed, which is expected to be caused by backflow of gas mixture after the passage of pressure wave. Each time pressure wave sweeps through unburned mixture, it heats unburned mixture up a little, eventually attaining it a critical condition that would
Fig. 5 e Variations of pressure and temperature vs. time at the location x ¼ 59.8 mm where detonation is formed. Dotted line represents temperature profile and solid line represents pressure profile.
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thermal erosion of combustion chamber. Fig. 5 shows the variation of pressure and temperature at the location x ¼ 59.8 mm where detonation is formed. It can be observed that main pressure wave (pressure wave generated by main flame front) has passed through this location five times, among which the second and the fourth peak on pressure profile are caused by reflected pressure wave. Despite pressure rises caused by main pressure wave, small pressure oscillations on pressure profile also exist as shown in Fig. 5, which are caused by a series of pressure wave reflected by flame front such as tiny pressure wave mentioned before and different propagation speed between them. Variation of overall heat release rate is shown in Fig. 6. Oscillation of heat release rate can be observed because the production and the diffusion of heat produced by reaction are kinetic processes, both physically and chemically, for which reason combustion is not absolutely stable. Among obvious oscillations of the profile, two relatively smooth sections indicates the stagnation of flame front caused by pressure wave induction. Heat release during these periods is slow but turns out to have higher amplitude after flame front keeping on moving, indicating the enhancement of combustion by pressure wave. Due to DDT, flame front rapidly finishes sweeping over the remaining unburned mixture at 416 ms. In comparison, simulation with initial condition (1) T0 ¼ 750 K, P0 ¼ 20 bar does not encounter DDT till flame propagates through the while domain, which is not shown here. It can be concluded that initial temperature T0 ¼ 750 K leads to relatively low reactivity of unburned mixture, thus restraining the occurrence of DDT and engine knock. However, heat release rate also increases each time after flame front stagnation, which has the same tendency as that with initial condition (2).
Flame evolution with end gas auto-ignition As it is considered as a major cause of engine knock, autoignition of end gas is investigated in this section. Initial condition (1) is chosen since it has lower reactivity and is unlikely to develop into detonation itself, which keeps the focus on the effect of auto-ignition. A hot zone of 2000 K is patched
Fig. 6 e Variation of overall heat release rate vs. time in computational domain.
between x ¼ 20 mm and x ¼ 22 mm to simulate spark-ignition. According to engine experiments carried out by Downs and Theobald [28], surface temperature could reach up to 1180 K in normal combustion and to 1500 K when pre-ignition occurred. As ignition delay is extremely sensitive to temperature, a temperature rise of 200 K might decrease ignition delay by 1e2 orders of magnitudes. Taking these into consideration, a 2mm thick hot zone with temperature of Te is introduced into the left end of computational domain. The results of two different Te are shown here, representing two typical situations: auto-ignition before and after pressure wave induction. The inducing pressure wave is formed by main flame front, so it remains the same amplitude and speed in the two cases.
Hot zone with Te ¼ 1300 K In this case, Te is sufficiently high that hot zone auto-ignites before main pressure wave arrives. Then the main pressure wave is reflected by left end wall and catches up with the autoignited flame front to the right. The interaction between main pressure wave and auto-ignited flame front is shown in Fig. 7. At 31 ms, pressure wave catches up with the flame front and splits into two peaks. The left one is due to the reflection by flame front while the right one due to the enhancement by flame front. Although the flame front is sped up by pressure wave while in turn the amplitude of main pressure wave is strengthened by flame front, the auto-ignited flame front fails to develop into a detonation. It is similar with what can be observed in Fig. 5, that the main pressure wave passes through flame front with its same direction three times but does not trigger DDT. This phenomenon indicates that DDT can only be triggered when some critical conditions are reached. For example, a sufficiently high temperature and pressure of unburned mixture which ensures high reactivity, a pressure wave with high amplitude that would ignite mixture ahead of flame front, the unnoticeable accumulation of intermediate species such as HO2 or the disturbance of flame front due to turbulence and obstacle. Despite the fact
Fig. 7 e Evolutions of temperature and pressure profiles during interaction between reflected main pressure wave and auto-ignited flame front. Dotted lines represent temperature profiles and solid lines represent pressure profiles. From left to right: time sequences are 31 ms, 32 ms and 33 ms, respectively.
Please cite this article in press as: Wei H, et al., One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions, International Journal of Hydrogen Energy (2015), http://dx.doi.org/ 10.1016/j.ijhydene.2015.02.034
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that auto-ignited flame front fails to develop into a detonation, the pressure wave formed by it catches up with the main flame front that propagates to the right and triggers DDT. This evolution is consistent with that shown in Fig. 1b and is similar to that shown in Fig. 4, which is not shown here.
Hot zone with Te ¼ 1125 K Fig. 8 shows the evolution of pressure and temperature profiles after pressure wave induction at 27 ms. Auto-ignition occurs at 46 ms, before which moment the temperature and pressure in hot zone increase to 1276 K and 27 bar, respectively, due to the induction and reflection of main pressure wave. The auto-ignited flame front directly develops into a detonation with a peak value of 175 bar. It is interesting that a higher Te ¼ 1300 K does not trigger direct detonation as in this case. The major difference between the two cases seems to be the pressure. As pressure increases, collisions between species become more frequent, thus promoting reactions. On the other hand, the p-T diagram of explosion limits of stoichiometric hydrogeneoxygen mixture [29] indicates complicated chemical kinetics during chain initiating and chain branching process, although data are only available in low pressure range. To further understand the chemistry involved in two cases, CHEMKIN-PRO is employed for chemical kinetic study. Temperature sensitivity analysis is carried out during homogeneous auto-ignition under constant pressure. Fig. 9 shows the normalized temperature sensitivity coefficients of three dominant reactions: R1: H þ O2 ¼ O þ OH; R9: H þ O2 (þM) ¼ HO2 þ (M); R11: HO2 þ H ¼ OH þ OH, with initial conditions (3) T0 ¼ 1275 K, P0 ¼ 20 bar and (4) T0 ¼ 1275 K, P0 ¼ 27 bar, respectively. The positive value of a reaction indicates that increasing the rate of this reaction leads to a higher temperature as well as heat release. It can be observed that absolute peak value of temperature sensitivity with initial condition (4) is much larger than that with condition (3). A higher sensitivity means that these reactions contribute more to temperature when combustion proceeds, which in some ways reflects the intensity of reaction. Furthermore, R9
Fig. 8 e Evolutions of pressure and temperature profiles after pressure wave induction. Dotted lines represent temperature profiles and solid lines represent pressure profiles. From left to right: time sequences are 45 ms, 46 ms, 47 ms and 48 ms, respectively.
Fig. 9 e Normalized sensitivity coefficients of three dominant reactions with different initial conditions. (a) T0 ¼ 1275 K, P0 ¼ 20 bar; (b) T0 ¼ 1275 K, P0 ¼ 27 bar.
becomes more important and produces more HO2 as pressure increases. Being relatively inactive, HO2 will survive longer during collisions and plays an important role in the following reactions. Fig. 10 shows the variations of mole fraction of intermediate radicals HO2 and H during these two auto-ignition process. The ignition delay under initial condition (4) is slightly longer than that under initial condition (3), while the HO2 in (4) begins to accumulate to a considerable quantity at early stage. The long surviving HO2 generates active radicals such as O, H, and OH that promotes chain propagation reactions: R1: H þ O2 ¼ O þ OH; R2: O þ H2 ¼ H þ OH; R3: OH þ H2 ¼ H þ H2O, which in turn generates more active radicals and introduces more fuel and oxygen. This selfpromoting behavior finally leads to intensive heat release and, in some conditions, (4) for instance, initializes a detonation. It can be observed that HO2 accumulates more under 27 bar, while H has a lower value compared with that under 20 bar. More accumulated HO2 ensures faster production and consumption of active radicals, which is the reason why mole fraction of H is slightly lower under 27 bar.
Please cite this article in press as: Wei H, et al., One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions, International Journal of Hydrogen Energy (2015), http://dx.doi.org/ 10.1016/j.ijhydene.2015.02.034
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Fig. 10 e Variations of intermediate radicals during autoignition.
Ignition delay influenced by pressure wave Although temperature field of end gas is determined mainly by heat transfer with cylinder wall, valve and spark plug, gas flow in cylinder and so on, pressure wave has to be taken into consideration since its induction and reflection causes temperature variation. Since different locations in end gas are impacted by pressure wave at different time, the variations of temperature would also be different, which might leads to different ignition delays. Therefore, unlike most ignition delays calculated under constant initial conditions, ignition delays under varying pressure and temperature are investigated here. Aiming to gain the pressure and temperature close to the actual situation, CFD simulation performed in Sec. Hot zone with Te ¼ 1125 K where end gas initial condition is T0 ¼ 1125 K, P0 ¼ 20 bar is referenced. Variations of pressure at different location are extracted and shown in Fig. 11a. It can be seen that locations other than x ¼ 0 mm undergoes two pressure rise, between which is the time interval that pressure is reflected by the wall and passes through again. CHEMKIN is employed to calculate ignition delays while pressure profiles are imported according to data extracted from hot zone. To stabilize the calculation, pressure profiles are simplified to polylines instead, which are shown in Fig. 11b. Since mixture will auto-ignite before 50 ms and ignition delays at different locations share nearly the same pressure profile after 43 ms, it's acceptable to remain pressure constant at 27.5 bar after 43 ms. Ignition delay is defined as the period between initial moment and the moment when initial temperature increases by 400 K. Fig. 12 shows calculated ignition delays at different locations. Ignition delay is observed to increase as the location moves away from the left end. The reason seems to be clear: pressure at x ¼ 0 mm undergoes only one sharp rise and increases to and remains the highest among other locations, the time integral of temperature is therefore higher, which is the dominant factor of ignition delay. The increase of ignition delay along the right hand direction might be a reason for direct formation of detonation.
Fig. 11 e Variations of pressure at different locations in end gas. (a) Pressure profiles extracted from CFD simulation. (b) Simplified pressure polylines imported in CHEMKIN.
Fig. 12 e Calculated ignition delays at different locations.
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However, as chemical kinetics is a complicated process affected by every detail, several other factors have to be considered as the specification of case investigated changes. Despite the differences in initial pressure and temperature, pressure profiles of different locations might also have different peak value and the interval between two pressure rises, according to the intensity of inducing pressure and the length of hot zone. Furthermore, if the fuel implemented has Negative Temperature Coefficient (NTC) behavior such as nheptane and iso-octane, the prediction of auto-ignition modes [9] will be more complicated. Further investigations have to be carried out in future works.
Conclusions In this study, two possible causes of engine knock: flame acceleration and auto-ignition, are studied using onedimensional simulation under engine-relevant conditions. Chemical source term is modeled using Arrhenius expression with detailed chemical mechanism of hydrogen oxidation. Chemical kinetic study is performed to further understand the detailed process during auto-ignition. Ignition delays under varying conditions since the effect of pressure wave are calculated by importing pressure profiles extracted from CFD simulation into CHEMKIN. Propagation and reflection of pressure wave in engine might cause DDT. Propagations of pressure wave generated by main flame front under engine-relevant conditions are investigated. The main pressure wave passes through flame front several times and causes either stagnation or acceleration of flame front. At one moment, a tiny pressure wave, which is reflected by flame front, catches up with the flame front and triggers DDT. However, no DDT is observed under low compression ratio, which indicates the key role of initial temperature. Heat release rate is observed to increase due to the passage of pressure wave through flame front. Pressure wave-induced auto-ignition might lead to direct formation of detonation. Two hot zones with different temperature are investigated, among which the one with higher temperature auto-ignites without detonation while the one with lower temperature auto-ignites and develops into detonation due to the induction of pressure wave. Even though auto-ignition does not forms detonation, the pressure wave it generates might still enhance combustion and lead to DDT. Pressure is considered to be the main cause for the difference, since higher pressure enhances the accumulation of HO2, thus leading to more intensive chain reactions during autoignition. Ignition delay is influenced by varying pressure and temperature due to the induction and reflection of pressure wave. The calculation result shows that ignition delay near the end wall is lower due to higher temperature integral compared with that further away. This leads to the formation of the increase of ignition delay along the right hand direction, which is proposed to be the possible cause for detonation formation. However, gradient of ignition delay might be affected by complicated factors according to the intensity of inducing pressure wave, the length of hot zone and the characteristics of different fuels.
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Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 51476114 and 51176138). Prof. Zheng Chen in Peking University and Prof. Zhuyin Ren in Tsinghua University are also appreciated for providing helpful advice and guidance.
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Please cite this article in press as: Wei H, et al., One-dimensional numerical study on pressure waveeflame interaction and flame acceleration under engine-relevant conditions, International Journal of Hydrogen Energy (2015), http://dx.doi.org/ 10.1016/j.ijhydene.2015.02.034