CFD modelling of cyclohexane auto-ignition in an RCM

Fuel 96 (2012) 192–203

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CFD modelling of cyclohexane auto-ignition in an RCM John F. Griffiths a, Renzo Piazzesi b, Elena M. Sazhina b,⇑, Sergei S. Sazhin b, Pierre-Alexandre Glaude c, Morgan R. Heikal b,1 a

School of Chemistry, University of Leeds, Leeds LS2 9JT, UK Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Computing, Engineering and Mathematics, Faculty of Science and Engineering, University of Brighton, Brighton BN2 4GJ, UK c Laboratoire Réactions et Génie des Procédés, CNRS, Université de Lorraine, ENSIC, 1, rue Grandville, BP 451, 54001 Nancy Cedex, France b

a r t i c l e

i n f o

Article history: Received 19 March 2011 Received in revised form 9 December 2011 Accepted 29 December 2011 Available online 14 January 2012 Keywords: Kinetic modelling Auto-ignition Rapid compression machine Computational Fluid Dynamics Cyclohexane

a b s t r a c t The kinetic modelling of cyclohexane auto-ignition in a rapid compression machine is addressed, based on the comprehensive kinetic mechanism, comprising 499 species and 2323 reactions, then reduced to 56 species involved in 196 reactions and 50 species involved in 143 reactions. The purpose is to explore the merits of reduced kinetic models that can be incorporated into Computational Fluid Dynamic codes for the numerical investigation of the performance of fuels in engines, with specific reference to Homogeneous Charge Compression Ignition (HCCI) or Controlled Auto-Ignition (CAI). Calculations of ignition delay, using the SPRINT zero-dimensional code assuming adiabatic reaction, have been performed for the stoichiometric mixture of cyclohexane in air, comprising C6H12 + 9O2 + 33.86N2, at an initial pressure of 0.48 bar, yielding compressed gas pressures of 7.2–9.7 bar over the compressed gas temperature range 650–925 K. There is reasonable agreement between the predicted delays of each scheme over the whole range of compressed gas temperatures. The common feature for alkane fuels, of negative temperature dependent ignition delays in an intermediate range, is predicted. However, the agreement with experimental measurements, especially in the negative temperature dependent region, is not very satisfactory. Non-adiabatic reaction as a cause of the discrepancy is addressed, initially via simple tests using SPRINT. The reduced mechanism comprising 50 species has then been implemented into the multidimensional CFD code FLUENT, which is the maximum number of species that can be incorporated in this code. The predictions of FLUENT are in excellent agreement with those from SPRINT under closed, constant volume adiabatic conditions. When non-adiabaticity at the wall is assumed, the FLUENT calculations show how temperature gradients evolve, leading to spatial differences in the rates of development of reaction. In particular, reaction is able to evolve more rapidly in the boundary layer region at compressed gas temperatures that correspond to the region of negative temperature dependence of ignition delay, so causing a reduction in the overall ignition delay relative to that predicted under adiabatic conditions. Ignition itself is initiated in the boundary layer under these circumstances. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.

1. Introduction Cyclohexane constitutes an important surrogate compound for the use of cycloalkanes in transportation fuels. Cycloalkanes are a major constituent in automotive fuels, with up to 3% in petrol, from 15% to 70% in kerosene and 35% in diesel [1]. The potential for auto-ignition hazards of cyclohexane and closely related substances in chemical process industries is also of some concern [2]. As contributions to understanding the kinetics, engine-related experimental studies of ignition have been performed in a rapid ⇑ Corresponding author. E-mail address: [email protected] (E.M. Sazhina). Present address: Department of Mechanical Engineering, Universiti of Teknologies PETRONAS, Bandar Sri Iskandar, 31750 Tronoh, Perak Darul Ridzuan, Malaysia. 1

compression machine over the compressed gas temperature range 670–870 K [3] and kinetic studies have been performed in a perfectly stirred, isothermal reactor at 807 and 1050 K [4]. Numerical modelling of detailed chemistry has followed from these studies [5,6,16]. Characteristics leading to soot formation have also been studied in flames of cyclohexane [7] and its substituted derivatives. The purpose of the present paper is to explore the merits and success of reduced kinetic models that are amenable for incorporation into Computational Fluid Dynamic (CFD) codes for the numerical investigation of the performance of fuels in engines, with specific reference to Homogeneous Charge Compression Ignition (HCCI) or Controlled Auto-Ignition (CAI). Since one of the major interests in the development of combustion rests with the ignition delay in HCCI engines, the main emphasis here is on the prediction of the time to ignition over a range of compressed gas temperatures

0016-2361/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2011.12.059

J.F. Griffiths et al. / Fuel 96 (2012) 192–203

and pressures. In this study we first compare predictions of ignition delay over a range of conditions using kinetic schemes for cyclohexane combustion of decreasing complexity. We then apply the simplest of these schemes in tests involving a CFD code. Most available commercial CFD packages have been designed to model fluid flow and heat/mass transfer in relatively complex geometries, but relatively simple combustion processes. In the case of ANSYSÒ FLUENTÒ (hereafter referred to as FLUENT) relatively complex chemistry can be incorporated using user-defined functions and subroutines. This is why we have chosen this package. We believe that the results obtained in our paper open the way of using FLUENT to take into account the conventional fluid dynamics and heat/mass transfer in relatively in complex geometries, while taking into account the effects of relatively complex combustion processes. As a first step to compare zero dimensional calculations and CFD simulations with adiabatic boundaries, and to avoid discrepancies in the compression stage, simulations have been performed considering the domain as a steady closed vessel at the ‘‘top dead centre’’ (tdc) using a CFD package coupled to a reactive chemical mechanism. This is an important prelude to simulations involving complex flow fields for heat and mass transport because it is essential to be confident that a multidimensional code is able to reproduce the results of a dedicated chemical kinetic analysis in a quantitative way, when the numerical complexity of a multidimensional flow is mitigated by the closed vessel assumption. The experiments that form the basis of the study were performed in a rapid compression machine at Lille [3]. Following the introduction of the experiments to which the numerical results relate, we describe the kinetic models investigated and the numerical background. Results predicted by the zero-dimensional SPRINT code and multidimensional FLUENT code are then presented that pertain to the varying stages of evolution of gas temperature and pressure. Finally, the main results of the paper are summarized.

2. The Lille rapid compression machine The rapid compression machine at Lille, in which studies of cyclohexane auto-ignition have been made, has been described many times previously [8,9]. It is a single shot system in which a piston is driven pneumatically by high pressure air to compress the charge in a cylinder. There is a mechanical connecting device which is designed to control the piston speed and to lock it in the final position at tdc. The compression stroke is 200 mm, into a cylindrical chamber of 50 mm diameter, giving a clearance at tdc of 20 mm. The compression ratio is 9.2. The design of the machine enables the initial pressure in the chamber to be varied up to 0.5 bar, giving compressed gas pressures of up to 14 bar, over a range of temperatures 650–900 K (i.e. compressed gas densities of up to 170 mol m3). The compressed gas temperature is varied by changing the proportions of a nitrogen/argon/CO2 mixture, as non-reactive diluents, in order to control c (=cp/cv). Experiments were performed on cyclohexane in a stoichiometric mixture in ‘‘air’’ (u = 1). In the nature of the mechanical system the compression stroke (60 ms) is somewhat longer than in most rapid compression machines, which may have some disadvantage in the potential for heat loss during the compression stroke. Also, with a relatively low piston speed (0.33 m s1), with highly reactive compositions reaction may begin before the piston has reached the end of its travel, although no reaction products could be detected at the end of the compression period in the experiment described in [9]. However, the lower piston speed has an advantage that the reduced speed of compression induces appreciably less gas motion than that following a more

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rapid compression stroke. In particular, when a flat piston head is used, there is far less scope to induce a roll-up vortex and the complex temperature field that evolves at the end of compression [10]. As a consequence of the more benign nature of the compression, the Lille research group have interpreted the behaviour of the compressed gas to be governed by the temperature in an adiabatic core throughout the post compression interval [9]. However, there can be some ambiguity regarding this interpretation, because a slow compression creates less fluid motion than that from a fast compression and, consequently, also a thicker boundary layer.

3. Comprehensive chemical mechanisms and model reduction methods Except in the simplest circumstances, the reduction of comprehensive kinetic models that are applied to combustion problems is necessary because the detail and complexity of the models (incorporating hundreds of chemical species and thousands of reactions) makes their computational application too inefficient, or even not viable, when the complementary physical processes such as heat and mass transfer or gas motion are also embodied in the simulations. The computational time taken to obtain a numerical solution from a mechanism of given size is typically / N2, where N is the number of species, or / n, where n is the number of reactions. To reduce the numbers of reaction species and reactions without losing the quantitative capability to predict the required information, formal mathematical methods are required and, where practicable, to be incorporated in automated programs in a format that is widely applicable. The most commonly used format to represent the mechanism includes thermodynamic data in the form of 14 NASA polynomial coefficients for each chemical species and a list of reactions and associated Arrhenius parameters. Mechanisms are in a standard CHEMKIN format [11]. Within this environment, models retain mass balance and compatibility with any CHEMKIN based software. The evaluation and validation of the reduction process is normally made in a zero-dimensional environment (e.g. a spatially uniform chemical reactor). This enables gas motion, either intentionally induced or arising from natural convection in practical circumstances, to be disregarded and (if appropriate) for heat transport from the system to be characterised by a Newtonian heat transfer coefficient. The reduced mechanisms must be validated at the various stages of reduction and this is done through comparison to output predictions obtained from the comprehensive mechanism. The precision with which quantitative agreement between the reduced and full models is established becomes a determinant of the extent of the reduction that can be achieved. This is controlled by tests at different thresholds. The overall target becomes a balance between computational efficiency and accuracy of reproduction of the output of the model. The foundation for kinetic model reduction is ‘‘local sensitivity analysis’’, in which the effect of making small changes in parameters or variables on the magnitude of other variables of the system is investigated. The effect of perturbations successively applied to each variable (e.g. how changes of concentration of each species affects rates of product generation) can be quantified and ranked in importance, such that thresholds can then be applied to decide which species (or reactions) can be discarded [12]. Schemes of varying size can be easily developed depending on the required accuracy of the final application. There is a range of software available, such as KINALC [13], which is based on the CHEMKIN family of numerical codes [11,14]. Further reduction may be achieved by the exploitation of the range of time scales present in the system via the application of

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the Quasi Steady State Approximation (QSSA) combined with reaction lumping [12,13]. The QSSA method is employed in mechanism reduction to identify species which react on a very short time scale and locally equilibrate with respect to species whose concentrations vary on a slower timescale – so leading to an assumption of ‘‘instantaneous equilibration’’. The concentration of these quasisteady state (QSS) species can then be determined (to good approximation) from a local algebraic expression rather than a differential equation. The algebraic expression is derived by setting the QSS species rate of production to zero. Substantial computational savings can be made when the QSS species is removed via reaction lumping [15], in which intermediates are eliminated by changing a set of reactions to a single reaction involving only reactants going to products. The rate constants of the lumped reactions will be algebraic combinations of other rate parameters and intermediate species concentrations and are derived subsequent to the application of QSSA. The resulting scheme does not then comply with CHEMKIN formulations since the reaction rates are no longer in the ‘‘Arrhenius’’ form. However, mass balance is retained in the scheme and simple subroutines describing the chemical rate equations could be automatically developed to restore compatibility. The savings, in terms of the number of species eliminated, make this a worthwhile procedure. If the concentrations of any of the QSS species are required, they can be regenerated using the appropriate algebraic expressions, although usually only the major products and temperature are required from the simulation. In the present case, the comprehensive kinetic mechanism for cyclohexane combustion was generated automatically using EXGAS [16], so circumventing the laborious and error prone procedure of manual construction. The initial scheme comprised 499 species in 1025 reversible reactions and 1298 irreversible reactions (2323 reactions in total). The comprehensive cyclohexane kinetic scheme was reduced using timescale-based techniques, as described above, via a 104 species and 541 irreversible reaction scheme, to a reduced mechanism comprising 68 necessary species in 493 irreversible reactions. Then, using principal component analysis, the number of reactions was successfully reduced in a mechanism comprising 68 necessary species and 238 irreversible reactions [17]. The reduction process was implemented at initial temperatures around 700 K in order to encapsulate the kinetic detail that evolves throughout the entire temperature range to full ignition. Further reductions of the scheme were also made by applying a QSSA analysis, which yielded a mechanism comprising 45 species in 323 irreversible reactions [17] and, eventually, 35 species in 238 reactions. However, as noted above, there are issues for the implementation of mechanisms that include QSSA species within a CFD code unless each of the complex algebraic equations for QSSA species that are embedded in the kinetic data set were interpreted as functional forms represented by a set of ‘‘Arrhenius’’ parameters. In order to avoid this inherent requirement for application of a QSSA scheme, the necessary further reduction of the number of species was implemented from the 68 species scheme (i.e. prior to the application of QSSA) by a combination of systematic sensitivity analysis, yielding 56 species in 196 reactions, followed by the empirical elimination of minor, intermediate species that were involved only in a single pair of formation/removal reactions. The resulting scheme, used in the present work, comprised 50 species involved in 143 irreversible reactions. The motivation for adopting this final stage of mechanism reduction is that we have used FLUENT for multidimensional modelling of the auto-ignition processes in an RCM. This code has a limit of 50 species for the species transport model, with mass balance being retained in the scheme. Throughout the development and prior to implementation, each

mechanism was routinely manipulated with MECHMOD [18], which is a very useful module that verifies that no errors have been created in mass balance or formatting in the binary code and creates the mechanism with specified units for the data set. MECHMOD also enables the derivation of reverse reaction rate data from thermodynamic parameters. The program can be accessed through [18] and is self explanatory. 4. Calculations: zero-dimensional SPRINT code Results of calculations are presented here, based on the comprehensive and reduced chemical mechanisms as described in Section 3, using the SPRINT code [19]. The simulations were set up to simulate the conditions of the RCM at Lille (see Section 2), assuming adiabatic conditions throughout. 4.1. Description of the code SPRINT solves the coupled differential equations describing the rate of change of concentration of each chemical species and energy conservation. The chemical rate of change of concentration is given by:

d½ci  X ¼ v ij Rj ; dt j

ð1Þ

where ci is the concentration of species i, vij is the stoichiometric coefficient of the species i in the reaction j and Rj is the jth reaction rate. Reactant temperature is calculated as the ‘‘(i + 1)th’’ species through the species heat capacities. For reaction in a closed vessel the energy conservation is described by:

ðC v qÞ

dT X UA ¼ ðT  T a Þ; DU oj Rj  dt V j

ð2Þ

where Cv is heat capacity at constant volume, DU oj is the internal energy of reaction j, V the volume, A the reactor surface area, U is the heat transfer coefficient Ta is the ambient temperature, q is density. Where appropriate, the heat loss rate is calculated on the basis of Newtonian cooling through the walls. U is set to zero for an adiabatic calculation. Inflow and outflow mass and energy terms are added for CSTR applications. The outputs of the code can be selected as temperature, pressure and species profiles, or heat release and reaction rates. For the simulation of reaction in a rapid compression machine, the energy equation includes supplementary terms to represent an ideal adiabatic compression based on a prescribed piston speed, stroke and compression ratio. Since the zero dimensional calculation required only to achieve the appropriate compressed gas temperature and pressure, the compression was derived from an empirical, fixed value input of c rather than via a full calculation based on the temperature dependent heat capacities of the reactant mixture. Appropriate heat capacities were fully utilised in the thermokinetic calculations. Eq. (2) is coupled to the simulation of the compression stroke via the increasing gas temperature T, gas density and heat capacities of the individual components, so that the prediction of reaction throughout this process is enabled. For circumstances in which reaction was assumed to be nonadiabatic, heat loss during the post-compression interval could be simulated through Newtonian heat transfer incorporating time dependent, exponential decay terms. This formulation was adopted because the experimental pressure decay of non-reactive gases, once the piston has stopped, always shows a highly non-linear, rate of decay in the early, post-compression interval (Dt < 10 ms), as a result of the decaying gas motion set up by the moving piston.

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4.2. Results of the SPRINT simulations

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The assessment of the performance of any reduced scheme relates to its response relative to that of the comprehensive scheme from which it is derived. Nevertheless, it is useful and instructive to include comparisons with related experimental results, if available. The predicted total delay from the Nancy comprehensive mechanism [16], the results of our own calculation, using the same mechanism and the experimental results from the Lille Rapid Compression Machine (RCM) are compared in Fig. 1. Both modelling results are based on the assumption that the process is adiabatic. The compressed gas temperature (Tc) is used as a reference temperature. The results of our calculations and those by the Nancy group [16] are in excellent accord (Fig. 1). This is an important foundation, given that different numerical codes have been used for the simulations. However, the numerical results differ considerably from the experimental data, in particular throughout the range of the negative temperature dependent (or Negative Temperature Coefficient, NTC) regime, which could be attributed to the limitations of zero-dimensional calculations coupled to the assumption of adiabatic conditions (see Sections 5.2 and 6). The initial composition was taken as a stoichiometric mixture of cyclohexane in air, comprising C6H12 + 9O2 + 33.86N2, over the compressed gas temperature range 650–925 K, yielding compressed gas pressures of 7.2–9.7 bar, consistent with the experimental results [3]. Predicted total ignition delays, using the Leeds derived reduced kinetic models and the results from the comprehensive model are shown in Fig. 2. As noted in Section 3, the reduced schemes that were studied were 56 species in 196 reactions and 50 species in 143 reactions. The results show that the qualitative structure of the complex dependence of the ignition delay on compressed gas temperature is captured. However, both the temperature range in which the NTC for the ignition delay exists and the minimum predicted delay is decreased when the reduced schemes are applied. Fortuitously, the results seem to be more consistent with the experimental results but there is no significance to be inferred from that. The relevant connection is that between the predictions from the reduced mechanisms and the comprehensive scheme. The predicted ignition delays at the lowest and the highest compressed

120

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tign / ms

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750

800

850

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Tc / K Fig. 1. A comparison of experimentally measured and numerically predicted total ignition delay (tign) during cyclohexane combustion in an RCM at u = 1 over the range of compressed gas temperature (Tc) from 650 to 925 K. The compressed gas pressure was in the range 7.2–9.8 bar. Experimental results are shown as closed triangles [3]. Numerical results are based on the comprehensive kinetic mechanism generated by EXGAS [16]. Calculations from Nancy are shown as open triangles. Calculations using SPRINT are shown as open circles.

tign / ms

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650

700

750

800

850

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Tc / K Fig. 2. Predicted ignition delay as a function of compressed gas temperature. Open circles refer to the comprehensive scheme, as in Fig. 1. Closed circles refer to 56 species and 196 reactions. Open squares refer to 50 species and 143 reactions.

gas temperatures are in excellent agreement. Compression to temperatures higher than 900 K is required in HCCI combustion, so the agreement in the high temperature region is especially important. Comparisons between the predictions from the comprehensive and reduced cyclohexane models at reactant temperatures as low as 530 K are discussed in [17]. Typical temperature–time and pressure–time curves, calculated using the 50 species reduced kinetic model, are shown in Fig. 3. The selected conditions give approximately the same ignition delay in the three regions of the tign vs Tc curve (Fig. 2). The conditions chosen are: (i) the low compression temperature (positive temperature dependent) regime, Tc = 703 K, (ii) the intermediate compression temperature (negative temperature dependent) regime, Tc = 753 K, and (iii) the high compression temperature (positive temperature dependent) regime, Tc = 873 K. The three curves showing the evolution of temperature (Fig. 3a) exemplify the key thermokinetic distinctions in the development of alkane auto-ignition when reaction is initiated at different temperatures. The high temperature combustion (Tc = 873 K) is a single stage process. The low and intermediate temperature regimes give rise to two stage ignition development, the quantitative distinction between these being that at the lowest compressed gas temperature (Tc = 703 K), the first stage has a very much longer development than that at the intermediate compressed gas temperature (Tc = 753 K). However, a consequence of the evolution from the lowest temperature illustrated (Tc = 703 K) is that the first stage chemistry culminates at a higher temperature than that which develops during reaction from 753 K. The roles for the development of the second stage of reaction are then reversed; at the intermediate compressed gas temperature the interval for the second stage reaction is rather longer at Tc = 753 K than at Tc = 703 K. This is not solely attributed to the temperature reached in the first stage but it also involves important differences in the composition of intermediate reaction products, with particular emphasis on hydrogen peroxide. As has been recognised from the 1960s [20], the intermediate stage of development of auto-ignition (i.e. through the approximate temperature range 800–1000 K) is controlled to a great extent by the decomposition of hydrogen peroxide formed as an intermediate. The subtle interaction between the amount of hydrogen peroxide present and the prevailing temperature that determines when the second stage of two stage ignition develops has been discussed elsewhere [21,22]. As in this work, the rate data for the dissociation of hydrogen peroxide that are used in virtually all kinetic model-

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Fig. 4. The simulation of the effect of heat loss by Newtonian cooling for reactions in the negative temperature dependent region, at Tc = 759 K. The solid line refers to adiabatic reaction. The broken line refers to non-adiabatic reaction with a characteristic Newtonian cooling time of 500 ms throughout the post-compression interval.

14 12

p / bar

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t / ms Fig. 3. (a) Temperature–time simulations at different compressed gas temperatures under adiabatic conditions, based on the 50 species scheme. The solid line refers to Tc = 703 K; the dashed line refers to Tc = 751 K; the dotted line refers to Tc = 873 K. The simulated compression ends at 60 ms. (b) Pressure–time simulations for the conditions as in (a).

ling of hydrocarbon combustion are those derived from the (reverse step) recombination of OH radicals, which are then combined with a theoretical determination of the temperature dependence and the equilibrium constant [23,24]. For the forward reaction, where M represents any species in the system,

H2 O2 ðþMÞ ! 2OHðþMÞ:

ð3Þ 14

(24406/T)

1

This procedure yields k = 3.00  10 exp s , in the high pressure limit. Based on these data, the half-life for hydrogen peroxide is predicted to be about 1.4 ms at 900 K and less than 0.1 ms at 1000 K. Although not shown explicitly in Fig. 3a, it may be inferred that, as the compressed gas temperature is raised throughout the NTC region, the first stage duration decreases and the second stage duration increases, but to a greater extent than the diminution of the first stage duration, so giving the overall increase of ignition delay throughout the NTC range. The onset of single stage ignition coincides with the peak of the NTC range, at which point the low temperature, first stage chemistry has ceased to take place. The transition from two-stage to single stage ignition, coincident with the maximum ignition delay of the NTC range, has been verified experimentally during the combustion of other hydrocarbons following rapid compression [25]. One of the subtleties that can arise as a result of the negative temperature dependence of reaction rate is illustrated in Fig. 4. The conditions are for a compressed gas temperature of 759 K

using the 50 species reduced kinetic model. In both cases the compression is regarded to be adiabatic. However, the post compression period is assumed also to be adiabatic in one case, whereas, for illustrative purposes, in the other a characteristic time constant of 500 ms for Newtonian heat loss from the moment the piston stops is assumed. (This represents the time required for the temperature difference between the reactants and the chamber walls to decay to e1 of its initial value.) In the region of negative temperature dependence, the effect of heat loss is to decrease the gas temperature in the immediately post compression interval, when the initial rate of heat release is very low. Although lengthening the first stage induction time, this fall in temperature enhances the reaction rate during the first stage activity which leads to a higher gas temperature at the end of the first stage and the commensurate increase in second stage reactivity (Fig. 4). The extent to which an overall decrease in the ignition delay has been brought about in this example shows how heat losses, which must occur in reality (if only in the boundary regions of the combustion chamber in an RCM), may account for the discrepancy between the adiabatic numerical simulations and the experimental results shown in Fig. 1. The effects of variation of post-compression heat loss rates were observed experimentally in rapid compression studies of n-butane combustion [26]. A shift in the compressed gas temperature range in which the NTC of reaction rate occurred was also revealed. Although, in reality, there may well be an ‘‘adiabatic core’’ in the combustion chamber after the end of compression, heat loss to the walls is inevitable on timescales of tens of milliseconds, which must create cooler boundary regions. In consequence, where an overall NTC of reaction rate prevails, the full ignition can start from the boundary regions as a result of a decreasing ignition delay, as was predicted numerically [27] and, subsequently, confirmed experimentally [28]. This is part of the reason why simulation of auto-ignition using CFD packages that can predict the spatio-temporal variations as reaction develops is important. Results predicted by one of these packages, FLUENT, are presented and discussed in Section 5. The prediction of reaction at higher reactant pressures in a rapid compression machine somewhat closer to those that would prevail in an HCCI engine, based on the 50 species reduced model, are explored in Fig. 5. The simulations are related to the operating conditions of the Lille RCM, with a 60 ms compression, so that any

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a cylinder with a moving piston) it is essential to ensure that the reactivity is sufficiently low for reaction to not be induced prior to the moment when the piston stops. The conditions selected for results reported in Section 5 satisfy this condition.

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5. Calculations: CFD FLUENT code 60

5.1. Comparisons with the zero-dimensional code under adiabatic conditions

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Tc / K Fig. 5. The ignition delay calculated as a function of compressed gas temperature for compressed gas pressures in the range 7.2–9.7 bar (open squares), as in Fig. 2, and 22.0–29.7 bar (closed squares).

0.025

C6H12

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0.015

0.010

Mole Fraction

0.020

T

800 End of compression

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t / ms Fig. 6. The simulated temperature and mole fraction of reactant (C6 H12) profiles that evolve during reaction following compression to 925 K. from an initial pressure of 1 bar.

reaction that may take place during this relatively slow compression stroke may be taken into account. Adiabatic conditions are assumed. The much reduced ignition delays, compared with those shown in Fig. 2, reflect the overall pressure dependence of the combustion process, and show that the sensitivity of the kinetics to pressure is most significant in the temperature range above 750 K, where the overall negative temperature dependence starts to intervene. When the ignition delay is very short there is the possibility for reaction to begin during the compression stroke, as has been observed experimentally [25]. Consequently, simplified numerical investigations based on closed constant volume conditions, including those based on FLUENT (see Section 5), cannot take into account the contribution of chemical reactions during the compression stage. To explore the extent to which reaction may be initiated during the final stage of compression, the molecular concentration of fuel vapour and gas temperature in the system were calculated at the most reactive conditions shown in Fig. 5 (Tc = 924 K, pc = 30.3 bar, for which ti = 4 ms). As shown in Fig. 6, almost 5% of the reactant has been consumed before the piston has come to rest. This confirms that if comparisons are to be between predicted ignition delays under closed volume conditions and experiments in an RCM (or calculations related to combustion in

Although the results predicted by the zero-dimensional SPRINT code show the correct qualitative behaviour with respect to temperature–time records over a range of conditions and also with respect to the existence of the NTC region, the applicability of this code for quantitative analysis of these processes is always limited by the inability to allow for spatial variations in temperature and species concentrations that result from heat and mass transport. This is the domain of Computational Fluid Dynamics (CFD) codes, including FLUENT as a representative code. In this section, results of CFD calculations using FLUENT, based on the reduced 50 species mechanism, are presented. Mass fractions of each species are predicted solving conservation equations for each species. The chemical source terms are computed using three-parameter Arrhenius expressions of the form (ATnexp(E/ RT) ). A direct stiff solver has been employed to solve the highly non-linear and coupled chemical equations. The segregated solver has been used with second order implicit transient formulation, SIMPLE algorithm for pressure–velocity coupling, standard scheme for pressure and second order upwind spatial discretization for density, momentum, energy and species. As discussed above, the SPRINT zero-dimensional calculations incorporated an empirical approach to simulation of the effect of heat capacities during the compression stroke in the Lille RCM. This simplification allowed the observed compressed gas temperature and pressure to be reached at the end of compression by choosing an appropriate value of c, without the need to modify other initial conditions. However, artificial and non-physical values of c cannot be used in FLUENT. As a first step to a comparison of outputs from the various computational approaches, the simulations were restricted to a closed, constant volume, adiabatic reactor. This procedure ignores possible contributions of chemical reactions during the compression stroke, but by selecting reactant pressures of less than 10 bar this can be justified under present circumstances. Also, by adopting a closed adiabatic reactor, the CFD code can be applied in its simplest possible mode, insofar that, although there is a grid structure, there is no heat or mass transport between cells invoked in the simulations. This opens the way to direct comparison of SPRINT and FLUENT results. A wide temperature range has been investigated (from 670 K to 910 K) at various compressed gas pressures over the 7.2 to 9.8 bar range for the stoichiometric mixture of C6H12 in air, with mole fractions of C6H12, O2 and N2 equal to 0.0228, 0.2052 and 0.772 respectively. The cylindrical combustion chamber of the Lille RCM has been approximated as an axisymmetric 2-D chamber with adiabatic walls. Grid and time step sensitivity studies have been performed. Numerical tests of the temporal evolutions of pressure, temperature and species, and the ignition delay showed that these remained unchanged when the number of cells exceeded 2300 and the time step was reduced below 5  105 s. Hence, these threshold values were chosen for the FLUENT calculations. The plots of temperature versus time for the initial temperatures in the range 670–910 K and pressures in the range 7.20– 9.75 bar, as calculated by FLUENT and SPRINT, are shown in Fig. 7. As can be seen from this figure, the FLUENT solutions capture very well the two stage ignition characteristics, typical

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for cyclohexane auto-ignition, and predict total ignition delays that are very close to those obtained using the SPRINT code. The slight discrepancies can be related to a higher temperature predicted by the CFD calculation at the end of the first stage ignition promoting a slightly faster second stage. Temperature traces predicted by both codes for the initial temperatures 813 K and 910 K are practically indistinguishable. In contrast to the previous figures, in Fig. 7 and all subsequent figures, time is measured from the end of the compression phase. The calculations, similar to those shown in Fig. 7, have been performed for additional initial temperatures and pressures in the range of initial temperatures from 670 K to 910 K. In all cases the agreement between FLUENT and SPRINT predictions was satisfactory. Based on these results, the total ignition delays predicted by FLUENT and SPRINT were obtained and compared with Lille experimental data (Fig. 8). As follows from this figure, the delays predicted by FLUENT and SPRINT are close, with the largest deviation between them not exceeding about 6%. The results of both calculations agree qualitatively with experimental data, since the effect of the NTC region is adequately reproduced. However, we can see noticeable differences between the predicted and measured values of the total ignition delays up to and beyond the peak of the NTC, as is also seen in Fig. 1.

5.2. Non-adiabatic conditions The most obvious shortcoming of the numerical experiments with FLUENT, as described in 5.1, is that they are based on the assumption that the processes in the RCM are adiabatic. Even with scope for species and heat transport within the numerical treatment, the predicted temperature distribution inside the RCM must remain spatially uniform. This condition is relaxed for FLUENT calculations once heat loss through the chamber wall, cylinder head and piston crown is allowed. To assess how heat loss modifies the spatial response, FLUENT calculations have been performed using the same initial compressed gas conditions as in 5.1, but with a constant negative heat flux through the walls imposed, via an empirical parameter. Spatial variations in temperature (and concentration) are then able to evolve through diffusion. We recognise that this approach has a number of limitations. We have made no attempt to calculate the processes before top

850

900

950

Fig. 8. Experimentally measured and predicted total ignition delay (tign) during cyclohexane combustion in an RCM at u = 1 over the range of compressed gas temperature (Tc) from 670 to 910 K. The compressed gas pressure was in the range 7.2–9.8 bar. Experimental results are shown as closed triangles [3]. Numerical results are based on the reduced 50 species kinetic mechanism. Calculations using SPRINT are shown as open squares. Calculations using FLUENT are shown as open circles.

13

12

11

p / bar

Fig. 7. Comparisons between the temperature versus time profiles under adiabatic conditions for the range of initial temperatures 670–910 K. Solid lines represent the 0-D calculations using SPRINT. Broken lines represent the 2-D calculations using FLUENT. The results from SPRINT are represented with t = 0 corresponding to the end of compression. The results from FLUENT are based on a closed, constant volume at initial temperature and pressure of reactants corresponding to the compressed gas conditions predicted by SPRINT.

800

Tc / K

t / ms

10

9

8

7 0

10

20

30

40

t / ms Fig. 9. Pressure–time traces predicted for the initial temperature 702 K at 7.48 bar in a closed, constant volume using FLUENT, under adiabatic (dashed line) and nonadiabatic (solid line) conditions with a heat flux through the wall and the piston equal to 10 kW m2. Time points, related to Fig. 10, are marked at 38 and 41 ms.

dead centre (tdc), did not take into account the existence of the thermal boundary layer at the start of our calculations or time variations of the heat flux through the walls, taking into account complex processes inside the walls of the RCM. Our aim, however, is not to perform the simulation of the processes in the RCM taking into account as many details as possible, but to try to identify the main reason for the deviation between the predictions of a zero-dimensional code, which is widely used in combustion simulations and engineering applications, and the experimental data. Pressure traces in which predictions from the adiabatic model and the non-adiabatic model are compared in Fig. 9 for the initial temperature 702 K and pressure 7.48 bar, with heat fluxes through the wall and the piston equal to 10 kW m2. The distribution of temperature at three time points is shown in Fig. 10. The cooling through the cylinder walls and the piston leads to the decrease in gas temperature in the regions close to the cold surfaces; this temperature remains lower than that in the core throughout the whole process. The hot ignition is initiated within the core of the

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Fig. 10. The distribution of temperature in a 2-D axisymmetric section of a closed constant volume, corresponding to the non-adiabatic case as shown in Fig. 9 for three time points. The ‘‘piston crown’’, at ‘‘tdc’’ in the RCM, is on the left hand side. The lower edge represents the axis of symmetry. The right hand wall is considered to be adiabatic.

13

12

11 p /bar

chamber (Fig. 10). As shown in Fig. 9, the overall ignition delay is dominated by the first stage of two-stage ignition, from which there is a negligible rate of heat release. The decreasing gas density within the very substantial, adiabatic core volume, resulting from the (spatially non-uniform) cooling in the boundary layer, is the cause of the increase in the overall ignition delay. The overall reaction rate is affected through both its temperature and pressure dependence, as a result of the (virtually adiabatic) fall in gas density. The pressure traces for the initial temperature equal to 762 K and pressure equal to 8.14 bar, with heat fluxes through the wall and the piston equal to 14 kW m2 are shown in Fig. 11. As in Fig. 9, heat loss through the walls leads to an overall decrease in pressure inside the chamber. However, in this case there is a conspicuous decrease of the ignition delay relative to that predicted for the adiabatic process, which is dominated by an acceleration of the second stage of the combustion process. As shown in Fig. 12, in this case the ignition starts near the walls of the chamber where the temperature has fallen as a result of heat transfer to the cold walls. This complex response is attributed to the effect of the negative temperature dependent kinetics under non-isothermal conditions, as has been also demonstrated recently in the context of n-heptane combustion [29]. Superficially, the first stage of the ignition delay seems not to have been affected (Fig. 11) but, in reality, the effect of the decreasing pressure has been compensated by the enhanced reaction rate as a result of the falling temperature in the boundary regions. The results shown in Figs. 13 and 14, at an initial temperature of 813 K and pressure of 8.44 bar, with a heat flux through the wall and piston equal to 16 kW m2, reflect a change in qualitative response with respect to adiabatic reaction. The increased heat flux

10

9

8

7

0

10

20

30

40

50

60

t /ms Fig. 11. Pressure–time traces predicted for the initial temperature 762 K at 8.14 bar in a closed, constant volume using FLUENT, under adiabatic (dashed line) and nonadiabatic (solid line) conditions with a heat flux through the wall and the piston equal to 14 kW m2. Time points, related to Fig. 12, are marked at 16, 19,25 and 28.5 ms.

reflects the increased gas temperature. The initial temperature of 813 K is sufficiently high that single stage ignition develops under adiabatic conditions. However, this initial temperature is only marginally above the peak of the NTC (Fig. 8), such that cooling within the boundary layer under non-adiabatic conditions is sufficient to induce ‘‘first stage’’ chemistry, which precipitates two-stage ignition leading to a considerably shorter ignition delay. A subtle

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Fig. 12. The distribution of temperature in a 2-D axisymmetric section of a closed constant volume, corresponding to the non-adiabatic case as shown in Fig. 11 for six time points. The cross-section details are as for Fig. 10.

interaction between heat release and heat loss rates should be noted: the outcome would be different if there was a sufficient heat release rate in the initial stage of reaction to compensate for the cooling induced by heat loss to the walls. At a still higher initial temperature and pressure, 910 K and 9.75 bar, with heat fluxes through the wall and the piston equal to 20 kW m2, single stage auto-ignition is initiated in the core of the chamber under non-adiabatic conditions (Figs. 15 and 16). The initial temperature (910 K) is considerably higher than that of the NTC range so that the cooling in the boundary region is not sufficient to enable the NTC region to be entered during the timescale of evolution of ignition. The ignition delays in the whole range of initial temperatures, predicted by FLUENT (using adiabatic and non-adiabatic models), Sprint and measured experimentally, are shown in Fig. 17. As follows from this figure, even on this most simple basis for the

interpretation of heat transfer, the predictions under non-adiabatic conditions show much better agreement with experimental data than those predicted under adiabatic calculations.

6. Discussion and conclusions Based on a comprehensive scheme for cyclohexane combustion generated by EXGAS [16], comprising 499 species and 2323 reactions, a reduced mechanism comprising 68 species and 238 irreversible reactions has been obtained previously [17]. This mechanism was further simplified to 56 species involved in 196 reactions and 50 species involved in 143 reactions. The comprehensive scheme and the three reduced mechanisms were implemented into the SPRINT zero-dimensional code. Calculation were performed for the conditions of the Lille Rapid Compression

J.F. Griffiths et al. / Fuel 96 (2012) 192–203

13

12

p / bar

11 10

9

8

7 0

20

40

60

80

100

t / ms Fig. 13. Pressure–time traces predicted for the initial temperature 813 K at 8.44 bar in a closed, constant volume using FLUENT, under adiabatic (dashed line) and nonadiabatic (solid line) conditions with a heat flux through the wall and the piston equal to 16 kW m2. Time points, related to Fig. 14, are marked at 37 and 45 ms.

Machine (RCM), in which the initial composition was taken as a stoichiometric mixture of cyclohexane in air, comprising C6H12 + 9O2 + 33.86N2, at an initial pressure of 0.48 bar, yielding compressed gas pressures of 7.2–9.7 bar over the compressed gas temperature range 650–925 K. The total ignition delays predicted by each of the schemes were compared with those from the comprehensive scheme. The reduced mechanism comprising 50 species was implemented into the two-dimensional CFD code

201

FLUENT. This is the maximum number of species allowed in this code. The FLUENT calculations were started at tdc, such that any contribution from chemical activity during the compression process has been ignored. However, their negligible contribution, under the conditions adopted in this work, is supported by an assessment of the contribution of these reactions using SPRINT. The predictions of FLUENT and SPRINT codes are in very good agreement under adiabatic conditions, which has given us confidence in a sound basis on which FLUENT may be exploited in more complex applications. The development of auto-ignition of hydrocarbons and, in particular, the duration of the ignition delay is governed by the evolving kinetics and heat release. Adiabatic conditions confer the simplest physical environment for this development and yet, as is confirmed here, the complexities of the kinetics and heat release over the temperature range 650–900 K are such that the ignition delay passes through a minimum and a maximum, i.e. in the ‘‘negative temperature dependent’’ (or NTC) range. The response of the underlying chemical kinetics is governed entirely by the containment of the released heat within the system. In non-adiabatic conditions, in zero-dimensional calculations represented by Newtonian heat transfer at the walls for the simulation of combustion in an RCM, cooling occurs simultaneously throughout the reacting gas so as to maintain a spatially uniform temperature. In their zero-dimensional calculations of RCM combustion, Mittal et al. [29,30] have used an elegant procedure to represent heat transport to the walls, in which the cooling is simulated empirically from an ‘adiabatic volume expansion’ within the reacting gas. However, there are still quantitative discrepancies of up to 30% in the zero-dimensional calculation with respect to the CFD predictions of ignition delay during n-heptane combustion [29].

Fig. 14. The distribution of temperature in a 2-D axisymmetric section of a closed constant volume, corresponding to the non-adiabatic case as shown in Fig. 13 for four time points. The cross-section details are as for Fig. 10.

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13

p / bar

12

11

10

9

0

5

10

15

20

25

t / ms Fig. 15. Pressure–time traces predicted for the initial temperature 910 K at 9.75 bar in a closed, constant volume using FLUENT, under adiabatic (dashed line) and nonadiabatic (solid line) conditions with a heat flux through the wall and the piston equal to 20 kW m2. Time points, related to Fig. 16, are marked at 22.5 and 23.5 ms.

The temporal and spatial evolution can be captured in quantitative detail only in the application of CFD, whereby heat and mass transport is represented as appropriate for the system under investigation [25]. The initial calculations presented here, using FLUENT, take a very simple form in which reaction evolves in a closed, constant volume with the initial condition set at the temperature and pressure at tdc of the RCM stroke. Non-adiabatic conditions are

encapsulated through Newtonian heat transfer to the cold walls of the RCM chamber, so that temperature gradients are allowed to evolve in the boundary regions. There is no gas movement at the quiescent initial conditions, so only thermal diffusion takes place. In all of the pressure records (Figs. 9, 11, 13 and 15) the gas cooling near the walls leads to an initial fall in gas pressure throughout the entire domain of the combustion chamber. The dependence of the overall reaction rate on the concentration of the reactants would naturally cause a slowdown as a result of the uniform change in gas density. But the thermal history exerts a stronger influence, so what happens next depends not only on the spatial variation in the rate and extent of cooling but also whether or not there is a positive or negative temperature dependence of the overall reaction rate. The entire history of the evolution of the thermokinetic process determines the ultimate outcome in both the temporal and spatial structure of the auto-ignition. Consequently, when and where the final stage of combustion is reached is strongly controlled by the initial kinetic development. In Figs. 9 and 15, the development in the adiabatic core is the dominant influence. In Figs. 11 and 13, the development in the boundary region is the dominant influence. When the chemical reaction rate is dominated by a positive temperature dependence of reaction rate then the activity in the core gas drives the ignition. Thus, for the initial gas temperatures of 702 K and 910 K, under non-adiabatic conditions the initial pressure decrease affects the reaction rate throughout the entire domain sufficiently for the early stage of reaction to be retarded, even in the ‘‘adiabatic’’ core gas, leading to an increase of the total ignition delay relative to the prediction for adiabatic reaction

Fig. 16. The distribution of temperature in a 2-D axisymmetric section of a closed constant volume, corresponding to the non-adiabatic case as shown in Fig. 15 for three time points. The cross-section details are as for Fig. 10.

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References

120

[1] McEnally CS, Pfefferle LD. Fuel decomposition and hydrocarbon growth processes for substituted cyclohexanes and for alkenes in nonpremixed flames. Proc Combust Inst 2005;30:1425–32. [2] Snee TJ, Griffiths JF. Criteria for spontaneous ignition in exothermic, autocatalytic reactions: chain branching and self-heating in the oxidation of cyclohexane in closed vessels. Combust Flame 1989;75:381–95. [3] Lemaire O, Ribaucour M, Carlier M, Minetti R. The production of benzene in the low-temperature oxidation of cyclohexane, cyclohexene, and cyclohexa-1,3diene. Combust Flame 2001;127:1971–80. [4] El Bakali A, Braun-Unkhoff M, Dagaut P, Frank PM, Cathonnet M. Detailed kinetic reaction mechanism for cyclohexane oxidation at pressure up to ten atmospheres. Proc Combust Inst 2000;28:1631–8. [5] Sirjean B, Buda F, Hakka H, Glaude PA, Fournet R, Warth V, et al. The autoignition of cyclopentane and cyclohexane in a shock tube. Proc Combust Inst 2007;31:277–84. [6] Silke EJ, Pitz WJ, Westbrook CK, Ribaucour M. Detailed chemical kinetic modeling of cyclohexane oxidation. J Phys Chem 2007;A111:3761–75. [7] Law ME, Westmoreland PR, Cool TA, Wang J, Hansen N, Taatjes CA, et al. Benzene precursors and formation routes in a stoichiometric cyclohexane flame. Proc Combust Inst 2007;31:565–73. [8] Ribaucour M, Minetti R, Carlier M, Sochet LR. Autoinflammation à haute pression, conception, réalisation et test d’une machine à compression rapide. J Chim Phys 1992;89:2127–52. [9] Minetti R, Carlier M, Ribaucour M, Thersen E, Sochet LR. A rapid compression machine investigation of oxidation and auto-ignition of n-heptane: measurements and modeling. Combust Flame 1995;102:298–309. [10] Clarkson J, Griffiths JF, MacNamara JP, Whitaker BJ. Temperature fields during the development of combustion in a rapid compression machine. Combust Flame 2001;125:1162–75. [11] Kee RJ, Rupley FM, Meeks E, Miller JA. CHEMKIN: a software package for the analysis of gas-phase chemical and plasma kinetics. Reaction Design Inc.; 2000. [12] Turanyi T. Reduction of large reaction mechanisms. New J Chem 1990;14:795–803. [13] Turányi T. Applications of sensitivity analysis to combustion chemistry. Reliab Eng Syst Safe 1997;57:41–8. [14] Westbrook CK, Mizobuchi Y, Poinsot TJ, Smith PJ, Warnatz J. Computational combustion. Proc Combust Inst 2005;30:125–75. [15] Whitehouse LE, Tomlin AS, Pilling MJ. Systematic reduction of complex tropospheric chemical mechanisms. Part I: Sensitivity and time-scale analyses. Atmos Chem Phys 2004;4:2025–56. [16] Buda F, Heyberger B, Fournet R, Glaude PA, Warth W, Battin-Leclerc F. Modeling of the gas-phase oxidation of cyclohexane. Energy Fuel 2006;20:1450–9. [17] Hughes KJ, Fairweather M, Griffiths JF, Porter R, Tomlin AS. The application of the QSSA via reaction lumping for the reduction of complex hydrocarbon oxidation mechanisms. Proc Comb Inst 2009;32:543–51. [18] http://garfield.chem.elte.hu/Combustion/mechmod.htm. [19] Berzins M, Furzeland RM. A user’s manual for SPRINT. Shell Research Ltd., TNER; 1985. p. 85058. [20] Bradley JN, Jones GA, Skirrow G, Tipper CFH. A mass-spectroscopic study of stabilized low-temperature flames of aldehydes. Proc Combust Inst 1965;10:139–44. [21] Griffiths JF, Hughes KJ, Porter R. The role and rate of hydrogen peroxide decomposition during hydrocarbon two-stage autoignition. Proc Combust Inst 2009;30:1083–91. [22] Griffiths JF, Scott SK. Thermokinetic interaction: fundamentals of spontaneous ignition and cool flames. Prog Energy Combust Sci 1987;13:161–97. [23] Baulch DL, Cobos CJ, Cox RA, Frank P, Hayman G, Just Th, et al. Evaluated kinetic data for combustion modeling. J Phys Chem Ref Data 1994;23(I):847–1033. [24] Brouwer L, Cobos CJ, Troe J, Dubal H-R, Crim FF. Specific rate constants k(E, J) and product state distributions in simple bond fission reactions. II: Application to HOOH ? OH + OH. J Chem Phys 1987;86:6171–82. [25] Griffiths JF, Halford-Maw P, Rose DJ. Fundamental features of hydrocarbon autoignition in a rapid compression machine. Combust Flame 1993;95:291–306. [26] Franck J, Griffiths JF, Nimmo W. The control of spontaneous ignition in a rapid compression machine. Proc Combust Inst 1986;21:447–54. [27] Griffiths JF, Jaio Q, Schreiber M, Meyer J, Knoche KF. Development of thermokinetic models for autoignition in a CFD code: experimental validation and application of the results to rapid compression studies. Proc Combust Inst 1992;24:1809–15. [28] Griffiths JF, Whitaker BJ. Thermokinetic interactions leading to knock during homogeneous charge compression ignition. Combust Flame 2002;131:386–99. [29] Mittal G, Raju MP, Sung C-J. CFD modeling of two-stage ignition in a rapid compression machine: assessment of zero-dimensional approach. Combust Flame 2010;157:1316–24. [30] Mittal G, Raju MP, Sung C-J. Computational fluid dynamics modeling of hydrogen ignition in a rapid compression machine. Combust Flame 2008;155:417–28.

100

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80 60 40 20 0 650

700

750

800

850

900

950

Tc / K Fig. 17. Experimentally measured and predicted total ignition delay (tign) during cyclohexane combustion in an RCM at u = 1 over the range of compressed gas temperature (Tc) from 670 to 910 K. The compressed gas pressure was in the range 7.2–9.8 bar. Experimental results are shown as closed triangles [3]. Numerical results are based on the reduced 50 species kinetic mechanism. Calculations using FLUENT in adiabatic conditions are shown as open inverted triangles. Calculations using FLUENT in non-adiabatic conditions, as defined in Fig. 10, are shown as crosses.

(Figs. 9 and 15). It is conspicuous also in Fig. 17 that, at an initial temperature of 670 K, the predicted ignition delay is increased from 80.5 ms in the adiabatic calculation using FLUENT to 88.7 ms, when there is a heat transfer flux of 10 kW m2 at the combustion chamber surfaces. This result implies that the core gas is not maintained at the adiabatic temperature throughout exceptionally long ignition delays, as has been assumed elsewhere [9]. When the negative temperature dependent kinetics dominate, the cooling in the boundary layer region begins to accelerate the reaction there, generating higher concentrations of reactive (i.e. chain branching) intermediates. Consequently, there is a partitioning of the reactant composition, with the ‘‘activated’’ mixture being confined to the boundary layer region, not only causing the full ignition to be induced there (Figs. 12 and 14) but also decreasing the overall ignition delay (Figs. 11 and 13) relative to that under adiabatic conditions. The initial ‘‘tdc’’ condition, adopted here, ensures that no additional complexity develops as a result of gas motion created by a moving piston [27,30]. This is the simplest quantitative basis on which the temporal and spatial interaction between heat transport and complex chemical kinetics can be evaluated. The complexities introduced by the interaction between heat loss and the existence of a temperature range in which there is an overall kinetic negative temperature dependence yield ignition delays predicted by the non-adiabatic model in a CFD code are in rather better agreement with experimental data compared with the predictions of the zerodimensional model. This improvement in quantitative agreement is a significant contribution to the validation of the reduced kinetic model, and the comprehensive model for cyclohexane combustion from which it was derived, and endorses the need for a CFD foundation to the quantitative application of kinetic models for the prediction of the performance of practical combustion systems. Acknowledgment The authors are grateful to EPSRC (Projects EP/F058276/1 and EP/F058837/1) for the financial support.