Abstract

Autoignition of an n-heptane/air mixture was simulated in nonuniform temperature environments of a rapid compression machine (RCM) and shock-tube (ST) with and without the presence of a cold-spot. The simulations were performed to investigate how the presence of a cold-spot and the cold boundary layer of the chamber wall may affect the ignition delay of the hydrocarbon mixture with negative temperature coefficient (NTC) behavior. The simulations were performed using three models: (1) three-dimensional (3D) computational fluid dynamics (CFD) model, (2) zero-dimensional (0D) homogenous batch reactor model by including the heat transfer model, and (3) 0D adiabatic homogenous batch reactor model. A detailed n-heptane mechanism was reduced in this work and used for 3D combustion modeling. A cold-spot critical radius of 7 mm was determined, which affects the ignition delay by more than 9%. In addition, two combustion modes were observed in the combustion chamber with a nonuniform temperature environment. With the first combustion mode, combustion starts at the high gas temperature region of the combustion chamber and quickly propagates toward the periphery of the chamber. In this combustion mode, the location of the maximum concentration of hydroxyl radical and the maximum temperature are the same. With the second combustion mode, the combustion starts at the periphery of the chamber, where the temperature is lower than the center of the chamber due to heat transfer to the cold chamber wall. The location of maximum concentration of the hydroxyl radical and maximum temperature is different with this combustion mode. The two observed combustion modes are due to the NTC behavior of the n-heptane mixture. The 0D homogenous batch reactor model (with and without heat transfer models) failed to mimic the ignition delay accurately when the second combustion mode was present. In addition, a propagating combustion has been observed in the simulation which is in agreement with some of the optical autoignition diagnostics of these hydrocarbons. This propagating combustion leads to a gradual pressure rise during autoignition, rather than a sharp pressure rise. The results of this work show that 0D homogenous batch reactor models are unable to simulate autoignition of mixtures with NTC behavior.

1 Background

Hydrocarbon mixtures that present negative temperature coefficient (NTC) combustion behavior may exhibit unique autoignition characteristics if thermal inhomogeneity exists within the combustion chamber. Theoretically, autoignition of these mixtures in the NTC regime may initially occur in lower temperature regions, such as e.g., the boundary layer near the wall and piston, instead of the hot core gas in the center of the chamber. Thermal nonuniformity within the combustion chamber from both hot- and cold-spots have been reported previously in the literature, which is briefly reviewed in the following paragraphs.

Zeldovich [1] was the first one to study the effect of the nonhomogeneity of a mixture on combustion. The author studied different modes of propagating flame/combustion due to nonuniform reactivity and proposed classification for combustion propagation in a reacting mixture. Gu et al. [2] used a zero-dimensional (0D) model to study the effect of hot-spots on combustion initiation. A mixture of hydrogen, carbon monoxide, and air was used at the high pressure of 5.06 MPa and a range of temperatures from 830 K to 1400 K, conditions close to those seen during engine operation. The authors used three different radii for the hot-spot and altered the temperature difference between the center of the hot-spot (the hottest point) and the environment. In addition, they investigated to see if the hot-spot may cause a propagating detonation. Two modes of propagating flame and autoignition due to the presence of the hot-spot were identified. However, detonation wave propagation was not observed at the studied conditions. Dai et al. [3] used a computational fluid dynamics (CFD) model to study the effect of temperature inhomogeneity in reaction front propagation. The authors used a one-dimensional planar configuration with an n-heptane/air mixture at initial temperatures within and below the NTC regime. They found that the initial temperature gradient has a strong impact on the autoignition modes. Supersonic autoignition deflagration, detonation, shock-detonation, and shock deflagration were observed with the numerical model. Combustion due to the cold-spot was compared with that of a hot-spot and similar autoignition modes were observed. The authors concluded that cold-spots and hot-spots may generate knock in engines. Bradley [4] studied engine knock initiated by hot-spots using a numerical model. Critical radius of the hot-spot was computed using thermal explosion theory. Two different modes of autoignition were observed; in the first mode, deflagration was observed and a pressure wave attenuated as it propagated into the unburned charge. With the second mode (detonation mode) pressure coupling with chemical reactions occurred. Zhao et al. [5] studied two-stage autoignition and combustion mode evolution in boundary layer flows above a cold flat plate. The authors used two-dimensional numerical simulations to investigate the autoignition of hot mixture flows on a cold plate. They concluded that the first-stage ignition delay is not affected by the cold boundary layer but the total ignition delay was affected when the main ignition occurs within the boundary layer. Javed et al. [6] studied the effect of localized ignition on the ignition delay using a shock tube. n-heptane and n-hexane ignition delays (up to 32 ms) were measured over a wide range of temperatures (650–1250 K) at a pressure of approximately 1.5 atm. They found significant discrepancies in the measured ignition delays versus modeled ignition delays using a homogenous batch reactor model at the intermediate temperature range from 700 K to 1100 K. They related this behavior to localized ignition kernels. They used a CFD model with a hot-spot in the center of the model to mimic this behavior, but no evidence of this behavior was provided using optical diagnostics. Rudloff et al. [7] used a detailed kinetic mechanism and a two-zone model to analyze the flame propagation mode at a wide range of engine operating conditions. They showed that pre-ignition does not trigger violent autoignition. They also concluded that pre-ignition may lead to either deflagration or detonation.

There are very few systematic investigations to show if combustion caused by a cold-spot may happen in a practical combustion system, at what conditions, and to what extent it may affect the accuracy of experimental measurements and simulations. The focus of this work is to answer these questions using 0-dimensional and three-dimensional CFD models of rapid compression machine and shock tube. The simulations were performed using an n-heptane/air mixture at a temperature range from 650 K to 940 K. This temperature range is within the NTC regime for the fuel mixture, and a nonuniform temperature field will affect the combustion of this mixture directly. The effect of cold-spots on combustion initiation is explored first with the models, which evaluate a critical radius of these spots. Next, the effect of the cold boundary near the chamber wall on combustion initiation is explored.

2 Methodology

2.1 Mechanism Reduction.

The detailed n-heptane mechanism (version 3.1, developed by Lawrence Livermore National Laboratory) [8] with 654 species and 2827 reactions was reduced to 140 species and 602 reactions. The mechanism reduction includes several repetitions of DRG, DRGEP, FSSA, sensitivity, and optimization methodologies. The details of these mechanism reduction methodologies can be found elsewhere, such as Refs. [912]. The mechanism reduction was performed using Chemkin-PRO/Workbench [13] using four nodes with 24 cpus per node (Intel Xeon CPU 4670, 2.9 GHz), which took approximately 15 days. The mechanism reduction was performed by allowing maximum 10% absolute error between the ignition delays of the detailed mechanism and the reduced mechanism. The mechanism reduction was performed at the temperature range of 625–1200 K, pressure range of 3–10 bar, 79% and 84% inert content, and an equivalence ratio of 1. The comparison between the ignition delays of the reduced and detailed mechanisms is shown in Fig. 1. The reduced and detailed mechanisms’ modeled ignition delays match excellently at the target conditions. The n-heptane mixture (n-C7H16/air) at an equivalence ratio of 1.0 and initial pressure of 3 bar was used for combustion modeling in this paper.

Fig. 1
The modeled ignition delays of the detailed and reduced mechanisms of n-heptane and air mixture at the equivalence ratio of 1.0 and at the two pressures of 3 and 10 bar
Fig. 1
The modeled ignition delays of the detailed and reduced mechanisms of n-heptane and air mixture at the equivalence ratio of 1.0 and at the two pressures of 3 and 10 bar
Close modal

2.2 Three-Dimensional Computational Fluid Dynamic Model.

The CFD package Converge [14] was used for the three-dimensional (3D) modeling of the rapid compression machine (RCM) and shock-tube (ST). The numerical simulation subroutines are similar to the works of Refs. [1519]. The RCM has a cylindrical combustion chamber with a 2 in. bore, and 0.9271 in. length (at end of compression) and its stroke is 10 in. The model is based on the device in the authors’ laboratory; further details about the apparatus can be found in previous works, e.g., Refs. [2022]. The RCM simulation includes the compression and post-compression processes and was developed using a nitrogen mixture. A schematic of the RCM model and the pressure trace of the model with the inert mixture are shown in Fig. 2. The RCM piston has a crevice to provide a uniform temperature field and species concentration inside the chamber as explained in Ref. [23]. For modeling the ST, a cylindrical constant volume chamber with radius of 1.96 in. and length of 1.96 in. was used. The temperature of the ST chamber wall was assumed to be same as the RCM wall at the different conditions to investigate the effect of the flow pattern inside the RCM chamber.

Fig. 2
(a) The RCM model and (b) the simulated gas pressure of the nonreactive mixture. The end of compression is at 0 ms, with an approximate compression time of 30 ms.
Fig. 2
(a) The RCM model and (b) the simulated gas pressure of the nonreactive mixture. The end of compression is at 0 ms, with an approximate compression time of 30 ms.
Close modal

For 3D CFD modeling, pressure–velocity coupling is accomplished using the pressure implicit with splitting of operators method of Issa [24]. The spatial domains are discretized using the implicit second-order central difference schemes. The first-order implicit method was used for temporal discretization. The Redlich–Kwong equation of state [6] was used in the gas phase. Turbulent Prandtl and Schmidt numbers are assumed to be 0.9 and 0.78, respectively. These values were taken from a previous work [25]. The turbulence chemistry interaction was not modeled in this work regardless of its importance. The standard renormalization group (RNG) k–ε Reynolds-averaged Navier–Stokes turbulence model was used for the simulations. Combustion chemistry was solved by directly integrating the reaction equations.

The simulation was performed using parallel computing. Each simulation utilized three nodes with 12 cpus per node (Intel × 5670, 2.9 GHz) and a 10e connection between nodes to model the various cases. Each reacting and nonreacting simulation took approximately 264 and 48 h, respectively.

2.3 Cold-Spot Model.

The effect of a cold-sport on the autoignition of a hydrocarbon mixture with NTC behavior was modeled by placing a cold sink in the hot reacting mixture of the 3D model. The cold-spot is placed in the center of the ST geometry and its initial temperature is 752 K, lower than the initial ST gas temperature of 850 K. As shown in Fig. 1, the n-heptane/air mixture shows the shortest and longest ignition delays at approximately 752 K and 850 K, respectively. The cold-spot is spherical in shape with a radius ranging from 5 to 10 mm. Its temperature is not fixed and can change gradually due to heat transfer to (or from) the hot gas or chemical reactions which proceed during the simulation.

2.4 Zero-Dimensional Computational Fluid Dynamic Model.

Traditionally, RCMs and STs are modeled using a 0D homogenous batch reactor, mainly due to its simplicity. This type of modeling is computational fast and inexpensive. The homogenous batch reactor model of Chemkin-Pro [13] was used for the 0D simulations. In 0D modeling, only the energy equation is solved, and there is assumed to be no flow or turbulence. The accuracy of the model can be increased by including the heat transfer of the combustion system, which is developed using empirical data (e.g., Ref. [26]) or using the 3D simulation of a non-reacting mixture within the modeled combustion device, as it is performed in this work. The nonreactive (or inert) mixture pressure and heat capacity ratio of the 3D RCM model were used to develop a temporal volume profile through application of the isentropic equation. This profile was used in the 0D simulations to model the heat transfer.

3 Results and Discussions

In order to understand how a cold-spot can initiate combustion, a ST simulation was run initially. The simulation was performed at an initial gas pressure of 3 bar, initial gas temperature of 850 K, initial cold-spot temperature of 752 K, and cold-spot radius of 10 mm. The temperatures were selected to have the longest (at 850 K) and shortest (at 752 K) ignition delays in the NTC region for this mixture, as previously shown in Fig. 1. Zero-dimensional homogenous batch reactor simulations were performed at the two gas temperatures for comparison purpose. Theses simulations were run adiabatically. The pressure rises associated with combustion for the different simulations of cold-spot and two homogenous environments with temperatures of 752 K and 850 K are shown in Fig. 3. The simulated ignition delay (defined as the time from the start of initiation to when the pressure reaches its maximum value) using the adiabatic homogenous batch reactor model with an initial gas temperature of 752 K is shorter than the model with the initial gas temperature of 850 K. The 3D case with a single cold-spot in the center of the chamber has an ignition delay between the two 0D model’s ignition delay. Indeed, the 0D models appear to serve as limits for the 3D case. For the cold-spot model, the pressure begins to rise at approximately 60 ms and takes approximately 5 ms to reach 8 bar. However, the 0D models only require a few microseconds to reach the same pressure of 8 bar. To understand this gradual pressure rise due to the presence of the cold-spot, the time-resolved contours of the hydroxyl concentration and gas temperature of the 3D model are plotted and shown in Fig. 4. As shown in the figure, the combustion starts from the location of the cold-spot and propagates throughout the chamber, which approximately takes 5 ms to accomplish. The combustion behavior is more similar to flame propagation than mixture autoignition, when there is a quick pressure rise. An average propagation speed is on the order of 10 m/s, which is much smaller than the detonation speed. The hydroxyl production begins in the location of the cold-spot and occurs in the first few milliseconds of the simulation. The concentration is negligible elsewhere in the chamber at the same time. The initial shape of the cold-spot is spherical but it becomes more like a diamond shape during combustion propagation due to the unsymmetrical chamber wall effect (the chamber diameter is larger than its length).

Fig. 3
The pressure rises at the initial gas pressure of 3 bar. In the cold-spot model, the initial gas and cold-spot temperatures were 850 K and 752 K, respectively. The homogenous temperature models were performed using 0D adiabatic simulations. The cold-spot is a sphere with a radius of 10 mm.
Fig. 3
The pressure rises at the initial gas pressure of 3 bar. In the cold-spot model, the initial gas and cold-spot temperatures were 850 K and 752 K, respectively. The homogenous temperature models were performed using 0D adiabatic simulations. The cold-spot is a sphere with a radius of 10 mm.
Close modal
Fig. 4
The hydroxyl mass fraction and temperature (with unit of Kelvin) contours histories at the initial gas pressure of 3 bar. The timings of the pictures from left to right are 0.5, 2, 50, 60, 62, and 65 ms.
Fig. 4
The hydroxyl mass fraction and temperature (with unit of Kelvin) contours histories at the initial gas pressure of 3 bar. The timings of the pictures from left to right are 0.5, 2, 50, 60, 62, and 65 ms.
Close modal

The effect of the cold-spot size on the ignition delay was also studied and is shown in Fig. 5. Cold-spots with a radius of 6 mm (and smaller) do not affect the ignition delay noticeably. However, at a cold-spot radius of 7 mm, the ignition delay decreases by approximately 9%, and at radius of 10 mm it decreases by approximately 25%.

Fig. 5
The combustion pressure histories of the cold-spot with various source sizes. The radii of the sources are shown in the figure. The pressure rises of the 0D simulations with uniform temperatures of 752 K and 850 K are also shown in the figure for reference.
Fig. 5
The combustion pressure histories of the cold-spot with various source sizes. The radii of the sources are shown in the figure. The pressure rises of the 0D simulations with uniform temperatures of 752 K and 850 K are also shown in the figure for reference.
Close modal

Since a cold-spot in the center of the model produced a significant effect on the ignition delay, the next step was to see if a cold chamber wall could produce a similar effect on the autoignition. Initially, the wall temperature and the gas temperature are assumed to be the same, which is representative of a heated RCM (such as the one in the authors’ Lab). As the piston compresses the gas mixture in the RCM, the gas temperature increases at a different rate than the wall temperature. The wall temperature and final gas temperature and pressure at the end of compression determined by the RCM model were used as the initial condition for the ST model. Simulations of the 0D homogenous batch reactor model were also performed at the same condition; however, the heat transfer model was developed from the noncombustible mixture in the 3D RCM model or 3D ST model.

As an example, the gas pressure histories at the gas and wall temperatures of 850 K and 423 K using the 3D ST model and 0D homogenous batch reactor model are shown in Fig. 6. The simulated pressure histories of the two models are quite different. To understand the reason behind this discrepancy, the time-resolved hydroxyl concentration contours of the 3D ST model are shown in Fig. 7. The hydroxyl production occurs along the periphery of the chamber, which is at the lower gas temperature. Temperature begins to increase from the sides of the chamber and propagates toward the center of the chamber. Thus, it can be concluded that combustion is initiated within the thermal boundary layer, which varies in temperature between 423 and 850 K. Clearly, the 0D homogenous batch reactor model cannot mimic these complex physics, even when including a heat transfer model. This is an important conclusion, since historically the 0D homogenous batch reactor model (with or without a heat transfer model) has been used for kinetic model development and validation, e.g., Ref. [27].

Fig. 6
The gas pressure at the initial gas temperature of 850 K and the wall temperature of 423 K. The 0D homogenous batch reactor model includes a heat transfer model.
Fig. 6
The gas pressure at the initial gas temperature of 850 K and the wall temperature of 423 K. The 0D homogenous batch reactor model includes a heat transfer model.
Close modal
Fig. 7
The hydroxyl mass fraction and temperature (with unit of Kelvin) contours at the initial gas temperature and wall temperature of 850 K and 423 K. The timings of the pictures from left to right are 20, 50, 61, 71, 81, 83, 84, and 85 ms. The simulation was performed using the ST model.
Fig. 7
The hydroxyl mass fraction and temperature (with unit of Kelvin) contours at the initial gas temperature and wall temperature of 850 K and 423 K. The timings of the pictures from left to right are 20, 50, 61, 71, 81, 83, 84, and 85 ms. The simulation was performed using the ST model.
Close modal

A comparison of the gas pressure histories for all models (3D RCM, 3D ST, 0D homogeneous batch reactor) using the reacting mixture are shown in Fig. 8. The RCM model compression time (shown as before time zero in Fig. 8) is also shown in the figure; however, the end of compression conditions are the same as the prior initial conditions with a gas pressure of 3 bar, gas temperature of 850 K, and a wall temperature of 423 K. The 0D homogenous batch reactor model’s ignition delay is longer than the 3D RCM and ST models. As discussed before and shown in Fig. 7, the longer ignition delay of the 0D model with respect to the 3D models is due to the inability of the 0D model to mimic the effect of the cold boundary layer, which begins the combustion initiation of a hydrocarbon mixture with NTC behavior. Due to a small heat release during the compression of the RCM model at the studied condition, the pressure at the end of the compression is slightly higher than the inert mixture pressure, as shown in Fig. 8. In addition, due to heat release during the post-compression period, the RCM pressure with the reactive mixture is slightly higher (depending on initial condition) than the noncombustible mixture pressure. The 3D RCM ignition delay (72.4 ms) is shorter than 3D ST ignition delay (84 ms). In addition, as shown in the right side of Fig. 8, the pressure rise is more gradual in the RCM than the ST, and the slope in increasing (shown by blue lines in Fig. 8). These two observations could be due to the more complex flow motion inside the chamber of the RCM with respect to the quiescent flow (absolute zero velocity) of the ST model. In addition, the gradual pressure rise inside the RCM (as shown on the right side of Fig. 8) is due to the flame-like combustion propagation as shown in Fig. 9. The flame-like combustion propagation in the RCM is slower than the one in the ST, as shown in Fig. 8.

Fig. 8
The gas pressure at the gas temperature (RCM end of compression temperature) of 850 K and the wall temperature of 423 K. The 0D homogenous batch reactor model of the RCM and ST includes the heat transfer model, developed by using noncombustible mixture at the RCM and ST conditions.
Fig. 8
The gas pressure at the gas temperature (RCM end of compression temperature) of 850 K and the wall temperature of 423 K. The 0D homogenous batch reactor model of the RCM and ST includes the heat transfer model, developed by using noncombustible mixture at the RCM and ST conditions.
Close modal
Fig. 9
Temperature (with unit of Kelvin) and hydroxyl mass fraction at using the 3D RCM model. The gas temperature and wall temperature are 850 K and 423 K. The timing of the images from left to right are 70.1, 71.1, 72.1, and 73.1 ms. Half of the chamber is shown and the temperature unit is Kelvin.
Fig. 9
Temperature (with unit of Kelvin) and hydroxyl mass fraction at using the 3D RCM model. The gas temperature and wall temperature are 850 K and 423 K. The timing of the images from left to right are 70.1, 71.1, 72.1, and 73.1 ms. Half of the chamber is shown and the temperature unit is Kelvin.
Close modal

The time-resolved carbon monoxide concentration using the 3D RCM model and 0D RCM homogenous batch reactor model are shown in Fig. 10. The 3D RCM carbon monoxide concentration was calculated using two methods, by using the concentration of the carbon monoxide in the whole chamber and using its concentration on several planes passing the center of the chamber (as schematically shown in the left side of Fig. 2). Regardless of the method of calculation, the 3D RCM carbon monoxide concentration at the end of combustion (i.e., when its concentration reaches a steady value or freezes) is less than the 0D homogenous batch reactor model.

Fig. 10
Carbon monoxide concentration using the 3D RCM model and 0D RCM homogenous batch reactor model. The gas temperature at the end of compression is 850 K and the wall temperature is 423 K.
Fig. 10
Carbon monoxide concentration using the 3D RCM model and 0D RCM homogenous batch reactor model. The gas temperature at the end of compression is 850 K and the wall temperature is 423 K.
Close modal

The gas pressure histories at the gas temperature of 794.6 K and wall temperature of 390 K using the different models are shown in Fig. 11. At this condition, ignition delay is shorter than the previously investigated condition (gas temperature of 850 K). The pressure rise using the 3D and 0D ST models match excellently. However, the ignition delay of the 0D RCM model is longer than 3D RCM model. Furthermore, the ignition delay of the 3D RCM model is shorter than the 3D ST model. The first-stage heat release timing is the same between 3D and 0D models, but it is longer using the ST model than RCM model.

Fig. 11
The gas pressure at the initial gas temperature of 794.6 K and the wall temperature of 390 K. The 0D homogenous batch reactor model of the RCM and ST includes the heat transfer model.
Fig. 11
The gas pressure at the initial gas temperature of 794.6 K and the wall temperature of 390 K. The 0D homogenous batch reactor model of the RCM and ST includes the heat transfer model.
Close modal

The temperature and hydroxyl concentration contours at different timings using the ST model are shown in Fig. 12. The locations of the maximum temperature and maximum hydroxyl concentration are the same, which was opposite to the results at the gas temperature of 850 K, as discussed before. The combustion starts from the center of the chamber with a hot gas temperature region and propagates toward the colder temperature region in the periphery of the chamber as shown in Fig. 12. The 3D RCM model temperature and hydroxyl concentration contours at different timings are shown in Fig. 13. The hydroxyl concentration is higher around the periphery of the chamber and halfway between the wall and the center of the piston. Due to the crevice design of the piston, the high temperature region is at approximately the same location (halfway between the wall and the center of the piston). Only half of the piston is shown in Fig. 13 due to the symmetry, as demonstrated in Fig. 14. The high concentration of hydroxyl at the periphery of the chamber is due to the NTC behavior of the hydrocarbon mixture at the studied temperature. The hydroxyl concentrations within the 3D RCM model at several temperatures are shown in Fig. 15. Only at very low temperatures does the location of maximum hydroxyl concentration occur where the temperature is maximum (at the center of the half-chamber). By increasing the overall gas temperature, the hydroxyl maximum moves toward the top and periphery of the chamber, where the temperature is lower due to the colder wall temperature.

Fig. 12
The hydroxyl mass fraction and temperature contours. The initial gas and wall temperatures are 794.6 K and 390 K. The timings of the pictures from left to right are 5, 10, 20, 30, 40, 45, 50, and 52 ms. The simulation was performed using 3D ST model.
Fig. 12
The hydroxyl mass fraction and temperature contours. The initial gas and wall temperatures are 794.6 K and 390 K. The timings of the pictures from left to right are 5, 10, 20, 30, 40, 45, 50, and 52 ms. The simulation was performed using 3D ST model.
Close modal
Fig. 13
The hydroxyl mass fraction and temperature (with unit of Kelvin) contours. The initial gas and wall temperatures are 794.6 K and 390 K. The timings of the pictures from left to right are approximately 21, 26, 30, and 34 ms. The simulation was performed using 3D RCM model.
Fig. 13
The hydroxyl mass fraction and temperature (with unit of Kelvin) contours. The initial gas and wall temperatures are 794.6 K and 390 K. The timings of the pictures from left to right are approximately 21, 26, 30, and 34 ms. The simulation was performed using 3D RCM model.
Close modal
Fig. 14
The temperature contour plot at 34 ms using 3D RCM model
Fig. 14
The temperature contour plot at 34 ms using 3D RCM model
Close modal
Fig. 15
The hydroxyl concentration plot at different gas temperatures and at the timing close to the ignition delay. The end of compression temperature (Tc), wall temperature (Tw), image timing (t), and the ignition delay (τ) from left to right are (1) Tc = 657 K, Tw = 310 K, t = 42 ms, τ = 46.28 ms, (2) Tc = 692 K, Tw = 330 K, t = 16.38 ms, τ = 14.58 ms, (3) Tc = 726.97 K, Tw = 350 K, t = 13.98 ms, τ = 15.98 ms, (4) Tc = 761 K, Tw = 370 K, t = 22.18 ms, τ = 23.68 ms, and (5) Tc = 794 K, Tw = 390 K, t = 33.18 ms, τ = 35.08 ms.
Fig. 15
The hydroxyl concentration plot at different gas temperatures and at the timing close to the ignition delay. The end of compression temperature (Tc), wall temperature (Tw), image timing (t), and the ignition delay (τ) from left to right are (1) Tc = 657 K, Tw = 310 K, t = 42 ms, τ = 46.28 ms, (2) Tc = 692 K, Tw = 330 K, t = 16.38 ms, τ = 14.58 ms, (3) Tc = 726.97 K, Tw = 350 K, t = 13.98 ms, τ = 15.98 ms, (4) Tc = 761 K, Tw = 370 K, t = 22.18 ms, τ = 23.68 ms, and (5) Tc = 794 K, Tw = 390 K, t = 33.18 ms, τ = 35.08 ms.
Close modal

The overall ignition delays for the various models at wide range of temperatures are shown in Fig. 16. The 0D RCM model (with the heat transfer model) shows a longer ignition delay with respect to the other models. Generally, the adiabatic 0D homogenous batch reactor model’s ignition delays are closer to those of the 3D RCM model. In addition, the simulated ignition delays using the 3D ST and 3D RCM models are close to each other which shows the flow pattern inside an RCM with a creviced piston design has minor effects on the overall ignition delay. Furthermore, the results of this work shows the 0D homogenous batch reactor model is not enough to simulate combustion of a hydrocarbon mixture with NTC behavior.

Fig. 16
Modeled ignition delay of n-heptane/air at equivalence ratio of one pressure of 3 bar
Fig. 16
Modeled ignition delay of n-heptane/air at equivalence ratio of one pressure of 3 bar
Close modal

4 Summary

The autoignition of n-heptane mixture (n-heptane/air) with NTC behavior was modeled at a gas pressure of 3 bar and in an environment with temperature inhomogeneity. The detailed mechanism model of n-heptane was reduced at wide range of temperature and pressure conditions and the final reduced model was used for the 3D combustion modeling. CFD models with different complexities and computational costs were used to predict the gas pressure and ignition delays at different conditions. The performance and computational cost of the different models were discussed briefly. Initially, the effect of a cold-spot inhomogeneity was studied by modeling a spherical cold-spot with various radii in the center of a hot reactive environment. The critical radius of the cold-spot to initiate the combustion in the hot environment was determined. Additionally, the effect of the cold thermal boundary layer on the chamber wall at a wide range of gas temperatures was modeled within an RCM and ST environments. It was shown that the 0D homogenous batch reactor model is not able to mimic the complex combustion of a hydrocarbon mixture with NTC behavior at some of the studied conditions, and detailed 3D CFD modeling is necessary. Two combustion modes of deflagration (propagating combustion or flame) and autoignition were observed at the studied conditions. For the deflagration mode, the combustion starts from the cold chamber wall and propagates slowly toward the core of the hot reacting mixture. This mode was observed especially within the RCM model. In this combustion mode, the locations of the maximum hydroxyl radical concentration and the maximum temperature are different. For the autoignition mode, the combustion starts and propagates from the hot gas at the center of the model and propagates toward the cold boundary of the chamber wall quickly. The simulated ignition delays using 3D and 0D models were approximately the same when autoignition was observed. However, significant differences in the ignition delay times were observed for the deflagration mode, when the combustion starts at the periphery of the chamber. The pressure rise is more gradual in the deflagration mode than the autoignition mode. The results of this work suggest a 3D CFD model of the combustion system is needed for the development of chemical kinetic mechanisms of hydrocarbons with NTC behavior, at least at the studied conditions.

Acknowledgment

This research was sponsored partially by Grant No. W56HZV-21-C-0041.

Conflict of Interest

There are no conflicts of interest.

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