Numerical Modelling of Transport Phenomena in a Diesel Spray “Stabilized Cool Flame” Reactor

Numerical modelling of transport phenomena in a diesel spray “stabilized cool flame” reactor D. I. Kolaitis and M. A. Founti* Heterogeneous Mixtures and Combustion Systems, Thermal Engineering Department, School of Mechanical Engineering, National Technical University of Athens, Heroon Polytechniou 9, Polytechnioupoli Zografou, 15780 Athens, Greece *Corresponding author: Tel.: +30-210-7723605, Fax: +30-210-7723527, e-mail: [email protected]

Abstract The paper focuses on the numerical simulation of diesel oil droplet evaporation in a “stabilized cool flame” environment. For this purpose, a dedicated model is formulated, correlating cool flame induced heat release with local temperature and fuel concentration values. The developed model is capable of adequately describing the main physico-chemical phenomena involved in the process and is deduced using both experimental data and chemical kinetic simulations. The model is implemented in an in-house developed twophase CFD code and predictions are compared with available experimental data, achieving very good levels of agreement. Parametric studies examining the effects of temperature and fuel concentration variations on the thermal behaviour of the system are also conducted. Nomenclature A model constants B model constants CD drag coefficient Dp droplet diameter Hu fuel’s lower heating value air mass flow rate m a  fu m fuel mass flow rate

[m] [J kg-1] [kg s-1] [kg s-1]

Mp p Q r Rep T tres  u Vp λ

droplet mass pressure volumetric heat release rate radial distance droplet Reynolds number temperature residence time velocity vector droplet volume lambda factor, λ ≡ ( m a / m fu ) / ( m a / m fu )st

[kg] [Pa] [W m-3] [m]

ρ

density

[kg m-3]

[K] [s] [m s-1] [m3]

Subscripts CF cool flame e experimental value G gas phase in inlet out outlet p droplet st stoichiometric -1This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

Keywords Cool flames, CFD, droplet evaporation, n-heptane oxidation 1. Introduction Liquid fuel sprays are utilized in a large variety of combustion systems, such as furnaces, boilers, Diesel or gasoline direct injection engines and stationary or aviation gas turbines. With the aim of increasing the available fuel surface area subjected to the hot gas environment and thus accelerate the respective evaporation and combustion rates, liquid fuels are injected into the combustion chamber through an atomizing nozzle, generating a large number of droplets. In conventional systems, the droplets, moving in the hightemperature gaseous environment, are evaporated and burnt in a partially sequential process, during which autoignition phenomena play an important role. Droplet autoignition depends on a multitude of processes, both physical and chemical in nature, such as atomization, evaporation and turbulent mixing on one hand and free radical generation and exothermic heat release activity on the other. One of the most important ignition rate-controlling parameters, which is also capable of raising problems associated with enhanced formation of pollutants, is mixture preparation. Thus, for the air-fuel vapour mixture inside the combustion chamber, high levels of homogeneity are usually required. Towards this end, a novel approach, based on the temporal and spatial separation of the two main phenomena, namely evaporation and combustion, has been proposed by Lucka and Koehne (1999), with the aim of achieving better mixing conditions. A promising way to accomplish this is to take advantage of the Stabilized Cool Flame (SCF) phenomenon, during the fuel evaporation stage. “Cool flame evaporation” results in a highly homogeneous, heated (though without being ignited) mixture, thus allowing the use of premixed combustion technologies. The latter are known to exhibit a wide range of advantages regarding the respective environmental impact, such as reduction in emissions of soot, NOx, CO and unburned hydrocarbons (Glassman, 1996). The utilization of the “cool flame evaporation” process may have additional advantageous side effects, owed to the resulting shorter droplet evaporation times; for instance, the total length of the “evaporation device” may be reduced, a feature that can be of paramount importance in certain applications, such as in Lean Premixed Prevaporized (LPP) combustors for aviation gas turbines. Moreover, the products of low temperature partial oxidation cool flame reactions are suggested to play an important role in the reforming of fuels into hydrogen-rich gas. Current research (Naidja et al., 2003, Hartmann et al., 2003) has shown that investigations on SCF are promising to pave the way for several beneficial industrial applications including generation of hydrogen for fuel cell systems. The present work was motivated by the requirement to investigate the impact of the major occurring physical and chemical phenomena on the thermal behaviour of an SCF evaporation device, designed to operate at atmospheric pressure. Such a device can find direct application in industrial furnaces and household boilers. Analytical information regarding cool flame heat release characteristics is acquired, by means of numerically simulating an atmospheric pressure, diesel spray SCF reactor, using an in-house developed two-phase Computational Fluid Dynamics (CFD) code. A novel “cool flame heat release” model is developed, based on physico-chemical reasoning coupled with experimental data. The proposed model is implemented in the two-phase CFD code and is validated by comparing predictions to experimental data obtained from an actual SCF reactor. Predictions are also proved to be supportive of the reactor’s design optimization process, by identifying specific flow regimes where intense cool flame activity takes place, since the -2This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

phenomenon is hard to be detected, as it is nearly invisible to the naked eye (Sheinson & Williams, 1973). 2. Cool Flames Low-temperature oxidation of hydrocarbon fuels exhibits a very rich variety of nonisothermal phenomena, such as cool flames, single-, two- and multiple-stage ignitions (Griffiths, 1995). The cool flame phenomenon is essentially a low temperature oxidation process during which the fuel is partially oxidized but not burnt. In systems where alkane fuels reside, either partially or fully mixed in an oxidizing atmosphere, in the temperature range of 500-800K, chemical activity is observed resulting in a two-stage ignition process during which the conventional “hot” ignition is preceded by a self-quenching pressure and temperature pulse known as “cool flame”. During cool flame reactions occurrence, fuel molecules essentially break down and recombine to produce a variety of stable and unstable chemical compounds including alcohols, acids, peroxides, aldehydes and carbon monoxide (Griffiths, 1995, Naidja et al., 2003). These reactions are generally exothermal in nature, producing modest amounts of heat, owing to the breaking and reforming of the fuel’s chemical bonds. Cool flames are also associated with the appearance of a faint pale bluish light, attributed to the chemiluminescence of excited formaldehyde, occurring preferentially under fuel-rich conditions (Sheinson & Williams, 1973). During the autoignition process, the operating kinetic mechanisms change continuously according to the temperature level of the air-fuel mixture. It is possible to define low and high temperature mechanisms, in which different oxidising schemes are effective. Cool flames manifest themselves in the temperature range where transition between low- and high-temperature mechanisms occurs and are dominated by exothermic degenerately branched chain reactions involving one or more important long-lived intermediates (Harrison and Cairnie, 1988). In the temperature transitional region, competition between termination and branching reactions is observed, since the former exhibit higher activation energies than the latter (Lignola and Reverchon, 1987). As a result, a Negative Temperature Coefficient (NTC) of the reaction rate emerges, i.e. the overall reaction rate decreases with increasing temperature. By exploiting the NTC phenomenon as a chemical “barrier” for autoignition to occur (Gray and Felton, 1984), it is possible to “stabilize” the cool flame reactions in an open flowing system when heat losses at the system’s boundaries are balanced by heat generation owed to the exothermal chemical activity. In this case, the thermo-chemical system converges to a stationery state since thermal runaway that would eventually lead to “hot” ignition (two-stage ignition) is prevented. According to Lucka and Koehne (1999), when SCF are confined in open flowing systems, the air-fuel mixture’s temperature increases and stabilizes at the raised level, which is, however, lower than the fuel’s autoignition temperature. During this process, only 2-10% of the fuel mass, and therefore of the respective available thermal energy attributed to the fuel’s heating value, is “consumed”. Experimental evidence from Steinbach (2002) suggest that the occurrence of atmospheric pressure diesel oil SCF is favoured under fuel-rich conditions in the temperature range of 550-800K. The utilization of SCF in a dedicated “liquid fuel evaporation” device, results in the enhancement of liquid fuel spray evaporation rate, producing a well mixed, heated and residue-free air-fuel vapour mixture. This mixture can be either subsequently burnt, utilizing premixed combustion technologies, or reformed into hydrogen-rich gas for use in fuel cells. Although research on the utilization of SCF as a liquid fuel-reforming step is still at an initial stage (Hartmann et al., 2003), it is a very -3This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

promising technique that could potentially lead to the widespread use of diesel fuel as a feedstock for fuel cell technology. There are numerous reports in the literature describing the fundamental origins of cool flame reactions by presenting a phenomenological approach, primarily based on experimental observations (Griffiths, 1995, Aggarwal, 1998, Pekalski et al., 2002). Attention to cool flames has been mainly driven by the fact that they are associated with “knocking” phenomena in spark ignition internal combustion engines, therefore most of the respective studies deal with the high-temperature, high-pressure conditions prevailing inside the engine cylinder (Aggarwal, 1998). However, there is a scarcity of information regarding nonigniting SCF, both in terms of extensive experimental investigation and of numerical modelling of the respective phenomena, especially in the frame of a CFD code. Visual observations of cool flames stabilized in flow reactors have been reported by Bradley et al. (1966) and Williams and Sheinson (1973) that examined acetaldehyde and n-butane, respectively. Ballinger and Ryason (1971), using a flat flame burner, observed SCF for nbutane, n-pentane and n-heptane. Morley (1988), investigating one-dimensional n-heptane SCF at atmospheric pressure conditions, observed that the temperature achieved by the mixture downstream the SCF was almost independent of the initial temperature, as a subsequence of the competition between chain branching and chain termination reactions. In the paper of Cavanagh et al. (1990), a detailed kinetic mechanism is used to simulate acetaldehyde oxidation in a CSTR where SCF behaviour was observed. 3. “Cool Flame” Model Development To successfully simulate the droplet evaporation process in an SCF environment, a dedicated model, capable of estimating the additional amount of heat release associated with exothermic chemical activity, is needed. The model should be able to adequately describe the occurring physical and chemical phenomena, covering a broad range of operational parameter values. It is widely accepted that modelling of the low-temperature oxidation of hydrocarbons is the foundation to the thermo-kinetic processes of autoignition (Griffiths, 1995). In order to effectively simulate the autoignition behaviour of conventional fuels, several characteristics such as two-stage ignition and NTC phenomena need to be modelled. Hence, cool flames are usually seen as a merely “transitional stage” that leads to ignition and are not confronted “per se” during hydrocarbon autoignition behaviour predictions. This kind of simulations are normally performed using either detailed or reduced chemical kinetic mechanisms (Griffiths, 1995, Aggarwal, 1998) and they frequently regard the vigorous, hightemperature, high-pressure in-cylinder internal combustion engine environment, being consequently “tuned” for such conditions. As a result, there is a lack of reduced chemical kinetic mechanisms capable of reproducing cool flame behaviour in low-temperature, lowpressure conditions, such as those encountered in the reactor under consideration (Kolaitis and Founti, 2003a). Incorporating detailed chemical kinetic mechanisms into multidimensional, two-phase CFD computational approaches to account for non-igniting SCF is currently not a straightforward procedure due to their excessive computational requirements and due to lack of relevant experimental data for the intermediate species concentrations, necessary to serve as validating means (Montgomery et al., 2002). The scope of the present work was to acquire a more in-depth comprehension of the heat release phenomena under SCF conditions and to investigate how these phenomena affect the evaporation characteristics of a diesel spray. Bearing that in mind, it was decided to opt for an algebraic model, which at the same time could serve as a “basis” for further development. As a first step, a simple, low computational cost model was developed, -4This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

capable of predicting the additional amount of heat owed to the cool flame reactions, with an acceptable level of accuracy. The developed model can be used to improve the predictive capabilities of two-phase droplet evaporation CFD codes, especially regarding heat and mass transfer rates. 3.1 Heat Release Correlation Utilizing a wealth of experimental data, obtained by measurements conducted in an experimental SCF reactor (Steinbach, 2002), a polynomial equation, correlating the heat release rate due to the exothermal reactions to the local temperature of the mixture, was derived. The available data regarded temperature measurements along the reactor for atmospheric pressure conditions, at various inlet temperature levels, but for a specific global fuel concentration value (λe = 1.27). In order to calculate the amount of heat released per unit volume due to cool flame reactions, a plug-flow reactor analysis was employed, taking into account the mixture’s thermal losses towards the reactor’s wall, while the contribution of the fuel’s latent heat of evaporation has been carefully eliminated. A curve-fitting procedure was applied to the experimental data points, yielding a polynomial equation which correlates the volumetric heat release rate (Qe) with the mean local mixture temperature (T) - Eq. (1). The corresponding correlation constants (Ai) vary between two different temperature level ranges (namely 598-733K and 733-830K); their respective values are given in Table 1. Q e T  

5

AT

i

(1)

i

i 0

Table 1. Model constants for Equations (1) – (2) Temperature Range [K] A0 A1 A2 A3 A4 A5 B0 B1 B2

598 – 733

733 - 830

+ 3.5835462x1010 + 1.3380906x108 – 2.7328904x108 – 5.0541130x105 5 + 8.3222840x10 + 6.3590903x102 – 1.2650643x103 – 2.6643670x10-1 -1 + 9.5998219x10 -4 – 2.9094685x10 0.47154 1.37276 – 0.76665

A comparison between the developed polynomial correlation (continuous line) and available experimental data (open symbols) is presented in Fig. 1. At temperatures lower than 600K, no chemical activity is observed. The curve depicts the characteristics of a typical SCF: after an abrupt increase in the heat release rate standing up to approximately 670K, there emerges an NTC region lasting up to 730K. Cool flame behaviour is inextricably linked to the NTC. Since the developed correlation emanates from actual experimental data, it is inherently capable of capturing and reproducing the very important NTC region. At temperatures higher than 730K, lower heat release rates are observed; however chemical reactions do not cease to exist. The available SCF experimental data, regard conditions that do not lead to autoignition since they extend up to 830K, which is the temperature upper limit where the developed correlation is valid. For atmospheric pressure conditions, -5This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

autoignition phenomena are expected to occur at temperatures above this limit, a case which could not be considered in the present work because of the aforementioned experimental restrictions.

Figure 1. Heat release rate per unit volume versus temperature in an atmospheric pressure, “stabilized cool flame” reactor, utilizing diesel oil (λ = 1.27). 3.2 Fuel Concentration Correction It is well documented (Lignola and Reverchon, 1987, Griffiths, 1995, Dagaut et al., 1995) that the main operational parameters affecting cool flame characteristics are pressure, temperature and fuel concentration. The effects of local variations of temperature and fuel concentration (expressed via the lambda factor) on the thermal behaviour of the system have been modelled since the current study focuses on the analysis of SCF at atmospheric pressure conditions and no data were available for different pressure levels. The above derived polynomial expression - Eq. (1) - correlates the cool flame induced heat release rate with the mixture’s temperature for the case of a globally constant lambda factor (λe = 1.27). As a result, an extra “fuel concentration correction factor” is needed in order to consider the influence of this additional parameter. Literature suggests that the overall cool flame reaction rates intensify when the fuel’s total concentration is increased (Dagaut et al., 1995). However, these observations are of a strictly qualitative nature and no consistent correlations are available in order to quantify this phenomenon. Hence, with the aim of incorporating the effects of fuel concentration variation, a chemical kinetic mechanism approach has been adopted. At present, there are no chemical kinetic schemes available for “real” diesel oil fuel, which is essentially a mixture consisting of a plethora of components. For the current modelling approach, it was assumed that the chemical and physical properties of diesel oil can be sufficiently well described by n-heptane, a single-component “model” fuel, commonly used as “simulant” for diesel oil. This can be regarded to be a valid assumption, especially for autoignition modelling purposes, since n-heptane’s cetane number (CN = 56) is very similar to that of diesel oil (CN = 50) (Tao et al., 2000, Montgomery et al., 2002). There exists a broad body of literature dealing with autoignition modelling of n-heptane and a range of chemical kinetic mechanisms, of varying degree of complexity (i.e. number -6This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

of reacting species), is currently available (Griffiths et al., 1995, Simmie, 2003). However, most of the available studies focus on the prediction of ignition delay times and there is a serious lack in the literature with respect to the modelling of the SCF phenomenon, i.e. cases that do not lead to ignition. In general, the chemical mechanism for the autoignition behaviour of hydrocarbons is quite complex and different types of chemical reactions are important in different temperature regions. At high temperatures (usually above 800K) alkyl radicals quickly decompose and hydrogen atom chemistry is important, while at temperatures lower than 625K (Peters et al., 2002), “degenerate chain branching” is observed, characterized by chain branching precursors that decompose as temperature increases above 700K leading to the well-known NTC behaviour (Schnaubelt et al., 2000). The focus of this work was on the thermal behaviour of SCF that emerge in the NTC region, thus only chemical kinetic mechanisms that incorporate both low- and intermediate-temperature oxidation phenomena could be taken into account. A comparative study (Kolaitis and Founti, 2003a), assessing the performance of four nheptane oxidation, chemical kinetic mechanisms in low and medium pressure Jet-Stirred Flow and Plug-Flow Reactors, revealed that the semi-detailed kinetic mechanism of the Chalmers University (Tao et al., 2000), involving 290 reactions and 57 species, exhibited the best thermo-chemical performance. This mechanism is practically a reduced version of the detailed kinetic scheme of Curran et al. (1998), consisting of 2446 reactions and 544 species. The mechanism of Chalmers has been selected to be used for the formulation of a “correction factor” for Eq. (1), to account for local variations of fuel concentration, by solving the conservation equations of energy and chemical species for an air/n-heptane mixture fed Perfectly Stirred Reactor (PSR). A PSR is practically a constant volume flow reactor in which the feed is instantaneously, continuously and rigorously mixed with the reacting fluid, thus achieving spatially uniform conditions of temperature, pressure and composition throughout the entire reactor volume. The mathematical model of a PSR consists of differential equations, the number of which depends on the number of chemical species involved in the kinetic mechanism implemented, for the mass, energy and species conservation. By numerically solving the resultant particularly “stiff” system of ordinary differential equations, using a modified version of the LSODE code (Hindmarsh, 1980), the thermo-chemical conditions at the reactor’s outlet have been estimated. In order to validate the predictive capabilities of the selected chemical kinetic scheme, the constant lambda factor case (λe = 1.27), for which experimental data were available, has been at first simulated using the PSR assumption. In Fig. 1, the temperature dependence of the experimentally derived heat release rate (open symbols) is compared to simulation results (dashed line). A good agreement between experiments and predictions is observed up to 730K. The kinetic mechanism of Chalmers is able to effectively follow the general experimental trends, not only in a qualitative, but also in a quantitative manner. Even the characteristic NTC region is sufficiently predicted with minor discrepancies. Experimental data (Fig. 1) suggest that at the high-temperature limit of the NTC region (T > 730K), a modest exothermic heat release activity is still observed with an increasing trend. This feature is not well captured by the predictions, which indicate that heat production practically ceases at T > 780K. The observed divergence from the measured data may be attributed to a variety of reasons, such as the adoption of n-heptane as a “simulant” fuel of the diesel oil actually used in the reactor or certain limitations inherent to the utilized kinetic mechanism (Kolaitis and Founti, 2003a). However, overall good agreement with experiments confirms that the selected kinetic scheme is capable of well describing the -7This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

main phenomena observed during low-temperature alkane oxidation, thus rendering it capable of yielding reliable predictions for the SCF reactor modelling. Following this, a parametric study has been performed to quantify the effects on total cool flame heat release rates due to fuel concentration variations. In particular, a series of PSR simulations has been conducted, by assuming constant inlet temperature conditions but varying inlet lambda factor values. The studied operational parameter, namely fuel concentration, was varied within a range covering the typical values expected in SCF reactors (the examined lambda factor values ranged from 0.2 to 1.4). For the fixed temperature at the PSR inlet, a constant value of 640K was chosen. This represents a typical temperature level where, under atmospheric pressure conditions, cool flame reactions become extremely important, thus dominating the thermo-chemical behaviour of the system (see Fig. 1). The residence time of the mixture inside the PSR was considered to be equal to 0.1s, corresponding to the mean gaseous phase residence time in the experimental SCF reactor (Steinbach, 2002).

Figure 2. Calculated heat release rate normalized with respective experimentally determined values for various global lambda factor conditions (T = 640K, tres = 0.1s). In order to formulate a convenient “fuel concentration correction factor”, the values of the predicted heat release rates using the Chalmers chemical kinetic mechanism (QCF) were “normalized” by the respective value for λe = 1.27 (Qe) that was determined via the temperature measurements. The variation of the “normalized” heat release rates (open symbols) with respect to inlet lambda factor values is depicted in Fig. 2, which essentially visualizes the effect of the initial fuel concentration variation on the thermal behaviour of the system. It is evident that predicted heat release rate values increasingly deviate from the respective value corresponding to the experimental conditions (dashed line) with decreasing lambda factor (i.e. increasing fuel concentration values), indicating that heat release is enhanced at fuel-rich conditions, an observation consistent with similar remarks in the literature (Dagaut et al., 1995, Aggarwal, 1998, Steinbach, 2002). The additional continuous line appearing in Fig. 2, corresponds to a correlation that ensued from the implementation of a data-fitting process. A “classic” exponential decay was found to be capable of reproducing very well (R2 = 0.999) the values obtained by the numerical -8This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

experiments. The exponential decay correlation, Eq. (2), represents the required “correction factor”; the values of the corresponding constants (Bi) are given in Table 1. Eq. (2) enables the calculation of the local heat release rate (QCF) as a function of both T and λ parameters, since it correlates the temperature-dependent experimentally obtained values (Qe) with the local fuel concentration. Thus, a combination of physical and chemical description of the cool flame heat release phenomena is achieved, by utilizing information from both experimental and theoretical results.

Q CF T , λ  B λ  B0  B1 e 2 Q e T 

(2)

4. Two-Phase Flow Numerical Modelling The CFD code used to model the two-phase flow field inside the SCF reactor is a modified version of the 2PHASE code developed in the Laboratory of Heterogeneous Mixtures and Combustion Systems of NTUA. The code is based on a Eulerian-Lagrangian computational formulation for the continuous and dispersed phases respectively. It has been previously validated in a number of test cases (Klipfel et al., 1998, Founti and Klipfel, 1998, Kolaitis and Founti, 2003b) regarding gas-particle, liquid-particle and gas-liquid flows, yielding satisfactory quantitative predictions compared to experimental data. 4.1 Continuous Phase The continuous phase is treated as a steady, incompressible and turbulent flow and is computed by solving the Reynolds-averaged Navier-Stokes equations. The resulting system of equations is solved via a finite volume method based on a staggered grid arrangement, using the SIMPLE algorithm and a hybrid differencing discretization scheme (Patankar, 1980). Turbulence quantities are modelled using a modified version of the k-ε turbulence model (Sung et al., 1990). In this model, the constants C μ and C2 of the standard k-ε model are modified, in order to take into account the radius of curvature of the flow. The model has proved to yield better prediction accuracy than the standard k-ε model in recirculating flows with abrupt area changes (Founti and Klipfel, 1998). Standard wall functions are used for the near-wall boundary conditions. 4.2 Dispersed Phase A Lagrangian treatment is adopted for the dispersed phase, where a large number of droplet “parcels”, each one representing a number of real droplets with the same properties (velocity, diameter and temperature), are traced through the flow-field. Each parcel’s trajectory is calculated by solving the instantaneous droplet motion equations in a three-dimensional Cartesian frame of coordinates (in order to avoid the singularity that droplet radial position may assume by applying cylindrical coordinates), with the use of a 4th order Runge-Kutta method. The general form of the droplet motion equation is introduced in Eq. (3), where the following forces are taken into account:  Drag force, where the drag coefficient of the evaporating droplets (CD) is calculated using the well-known Schiller and Naumann correlation (Crowe et al., 1998) - Eq. (4).  Gravitational force.  Pressure gradient force.

-9This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

Mp

 du p dt

CD 

     ρ   3 ρG M p C D uG  u p  uG  u p  M p g  1  G   pVp  ρ  4 Dp p  

(3)



(4)

=

24 0.687 1  0.15Re p Re p



The large density ratio (ρp / ρG) between the droplets and the gas indicates that the effects of the added mass, shear lift and the Basset history forces are negligible and can be neglected (Faeth, 1983, Crowe et al., 1998, Sommerfeld, 1998). Droplet turbulent dispersion is modelled using a Lagrangian Stochastic Separated Flow (SSF) model by sampling random Gaussian gas velocity fluctuations and accounting for the crossing trajectories and eddy life time effects (Gosman and Ioannides, 1983). The gas and the liquid phase are coupled by calculating source/sink terms for the interfacial mass, momentum, species concentration, thermal and turbulent energy exchange (two-way coupling), following a modified version of the PSI-cell approach (Crowe et al., 1977). In order to improve the accuracy of the droplet mass flow rate predictions near the symmetry axis, a “drift correction” term across the transverse direction is applied to the turbulent dispersion model (Sommerfeld, 1998). 4.3 Droplet Evaporation Following various comparative studies (Miller et al., 1998, Kolaitis and Founti, 2003b), the evaporation model of Bellan and Harstad (1987), was chosen to be implemented in the CFD code. This model is based on the Langmuir-Knudsen law and is essentially a modified version of the “classic” Spalding (1953) evaporation model, taking into consideration the non-equilibrium phenomena that may appear in the gas/droplet interface. The original Bellan and Harstad model incorporated a finite liquid conductivity model that assumed a non-uniform temperature profile across the droplet radius. However, the “infinite conductivity” assumption is used here, since as literature reports suggest (Miller et al., 1998, Berlemont et al., 1991), no significant improvements can be expected from the implementation of the “finite conduction” model. In an actual spray environment, the droplet has a non-zero slip velocity with respect to the air stream surrounding it, and therefore the gas-phase heat and mass boundary layers emerge. Gas-phase convection influences the droplet evaporation process in a two-fold manner: not only does it increase the heat- and mass-transfer rates between the phases, but it also generates liquid circulation inside the droplet with a consequent increase of the liquid-phase transfer rates. There is a variety of semi-empirical correlations available in the literature for the convective correction of both heat and mass transfer equations. Nevertheless, for the low/moderate evaporation rates as those encountered in atmospheric pressure reactors, no significant differences are observed among predictions utilizing various correlations (Kolaitis and Founti, 2003b). Thus, the well-known Ranz and Marshall (1952) correlations are used. Surface blowing results in the thickening of both heat and mass boundary layers, thus impeding transport phenomena near the droplet surface. The outward-streaming vapour leaving the droplet surface must be heated in the thermal boundary layer until it reaches the ambient temperature at the edge of it. The energy absorbed by this superheating process is being subtracted from the thermal energy that can reach the liquid surface, thus the heat transfer rate is further hindered. In order to take into account the aforementioned phenomena, a modified value of the Nusselt number is used (Miller et al., 1998, Kolaitis and - 10 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

Founti, 2003b), based on an analytic expression that has been deduced from the solution of the gas-field equations near the droplet surface utilizing the quasi-steady flow assumption (Bird et al., 1960). The fuel vapour and the gas phase species properties are determined using the well-known “1/3-rule” (Yuen and Chen, 1976), whereas the standard ideal gas additive rules and the Wilke mixing rule (Reid et al., 1987) are used for the calculation of the gas-vapour mixture properties near the droplet surface. Droplet evaporation phenomena are taken into account by implementing the mass and energy balance equations for the droplet in the two-phase CFD code. For every Lagrangian time-step, these equations are solved and the temporary local droplet diameter and temperature values are updated, while at the same time and for the specific computational cell that the droplet resides, heat “sink” and mass “source” terms are calculated and stored, in order to be used in the subsequent two-way coupling iteration. In addition, the developed “cool flame model” is implemented in the CFD code by utilizing Eqs. (1) and (2) in order to estimate the values of the cool flame induced heat release rate per unit volume (QCF) for every computational cell. The respective heat “source” terms are determined by using the corresponding “local” cell values for both temperature (T) and lambda factor (λ). These additional heat “source” terms are added to the heat “sink” terms, calculated in the preceding Lagrangian iteration and associated with droplet evaporation, before they are introduced into the gas-phase energy transport equation. 5. Simulated Test Case Description 5.1 Experimental “Stabilized Cool Flame” Reactor For the validation of the developed cool flame computational model, a series of experimental datasets from an atmospheric pressure, tubular, SCF reactor operated at the EST Lab. of RWTH-Aachen (Steinbach, 2002) has been used. The reactor is essentially a metal pipe 1.0m long, with an internal diameter of 0.1m (Fig. 3). The insulated cylindrical pipe wall embodies heating elements used to achieve homogeneous thermal boundary conditions along the reactor. The device is equipped with eleven retractable 1mm thick NiCrNi thermocouples, allowing measurement of local temperatures in both axial and radial directions. Local heat release rates are obtained on the basis of a differential heat balance approach that calculates local temperature gradients and accounts for wall heat losses. After an initial pre-heating stage, air is supplied to the reactor through a perforated disk, used to control the flow turbulence level and homogenize the general fluid-flow characteristics. A water-cooled, 60 deg. hollow cone, Simplex atomizer, fixed upstream, at the centre of the perforated disk, is utilized to inject diesel oil into the reactor. The liquid droplets are evaporated, the process being assisted by heat release due to cool flame reactions, resulting in a homogeneous air-fuel vapour mixture issuing at the downstream end of the device. The main features of the temperature distribution inside the reactor, as determined by experimental observations, are as follows (see Fig. 5, open symbols): immediately downstream the fuel injection plane there is a sudden drop in the temperature, due to the evaporation of the fuel droplets. However, further downstream, an increase in the mean temperature of the order of 50-150K is observed reaching a nearly constant value at an axial distance of approximately 0.3m without, however, the mixture being actually ignited and burnt. This temperature rise is attributed to the exothermal cool flame reactions. The additional amount of heat released represents roughly 2% of the available thermal energy due to the fuel’s heating value and it enhances the evaporation process, resulting in the shortening of the total evaporation time. - 11 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

Figure 3. General layout of the tubular diesel spray “stabilized cool flame” reactor. 5.2 Computational Details In order to numerically simulate the flow and thermal field in the above-described tubular reactor, a non-uniform, cylindrically axisymmetric, rectangular grid has been used, measuring 94*35 nodes in the axial and radial direction, respectively. The grid was refined close to the nozzle tip in order to improve local flow resolution. The simulation results obtained with this grid did not deviate more than 2% when compared to those obtained by using a 143*52 nodes grid arrangement, thus ensuring grid independence. Air entered the simulation region, having a uniform velocity profile, corresponding to the experimentally determined mass flow rate value of 3.58*10–3 kg/s. In every simulated test case, both the inlet air and the insulated boundary wall temperatures were assumed to be equal, a condition well corresponding to the actual experimental practice. Diesel oil fuel droplets, assumed to be spherical, were considered to be injected by the nozzle from 10 discrete starting locations. A total number of 30 000 droplet “parcels” were launched and tracked throughout the flow-field, for 20 two-way coupling iteration cycles which were sufficient for full convergence of all the two-phase flow variables. The total liquid phase mass flux, as measured in the experiments, was 2.211*10-4 kg/s, yielding a mean mass loading of 6.2% and a global lambda factor value of λe = 1.27. Both initial droplet velocity and size distribution at the nozzle injection plane have been obtained by interpolating experimental measurements available for a Simplex pressure atomizer, similar to the one used in the considered reactor (Sommerfeld and Qiu, 1998). The water-cooled nozzle temperature was kept constant at 120oC; droplets were considered to be injected having the same temperature. 6. Results and Discussion 6.1 “Standard” Test Case The “standard” experimental test case, for which the inlet air temperature was set at 623K, has been considered first, since for this case more extensive measurements were available. At this temperature level, it has been experimentally observed that the reactor exhibits a very steady behaviour; a remark that can be further corroborated by looking at Fig. 1, where it is clear that cool flame exothermal activity is expected to be quite vigorous. Fig. 4 compares predicted values with the respective experimental data of the spatial evolution of the gaseous mixture temperature field inside the reactor. Initially, simulations have been conducted without taking into consideration cool flame reactions. This case - 12 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

pertains to conditions where evaporation is only “physically” controlled and no “chemical” phenomena are modelled. The respective predictions are presented in Fig. 4 (dotted line), where it becomes evident that by assuming a purely “physical” evaporation mode the temperature field inside the reactor cannot be adequately described. Although the initial drop in the mixture’s temperature is properly captured, predictions further downstream completely fail to follow the experimental data. Since, in this case, thermal energy is only transferred from the air to the droplets, air-phase temperature predictions are invariably lower than the respective inlet value of 623K. The observed significant discrepancies demonstrate the necessity of using a “cool flame model” in order to improve the simulation of the phenomenon.

Figure 4. “Standard” test case: Comparison of predictions of gas phase temperature with experimental data, along the axial direction for four different radial positions. A clear improvement over the preceding simulation is achieved when the developed polynomial correlation, Eq. (1), is implemented (Fig. 4, dashed line). By accounting for the heat release due to cool flame reactions, one of the main features of the experimental data, i.e. the increase of the downstream temperature at levels above the inlet value of 623K, is well reproduced. Predictions regarding the initial temperature decrease, due to the droplet latent heat of evaporation, remain practically unaltered. Such a behaviour is expected, since the modelled homogeneous cool flame reactions are considered to occur in the gas-phase only, thus the model is “activated” in regions where significant amounts of fuel vapour are present, i.e. downstream the droplet evaporation region. Nevertheless, the mixture’s temperature increase rate is under-predicted, resulting in lower temperatures at the reactor’s outlet, when compared to the experimentally obtained values. The considerable improvement in agreement between measured data and predictions utilizing the developed “fuel concentration correction”, Eq. (2), suggests that the proposed dependence of the cool flame heat release rate on both temperature and fuel concentration represents a very reasonable assumption. As can be seen in Fig. 4 (continuous line), the predicted temperature values lie quite near the experimental data, thus being able to accurately describe the establishment of a downstream steady-state temperature of approximately 760K. In this case, the CFD code’s predictive capabilities are noticeably improved, especially regarding the temperature increase rate. The observed improvement with Eq. (2) is due to the more detailed description of the effect of the actual local fuel - 13 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

vapour concentration distribution on the predicted heat release. Although there appear some slight discrepancies regarding the upstream droplet evaporation region in the case of r = 0.03m, overall agreement is quite satisfactory, confirming that the developed model is capable of capturing reasonably well the experimentally determined general trends of the temperature field inside the reactor. 6.2 Variation of the inlet temperature In order to validate the applicability of the developed model in a variety of flow conditions, two additional test cases have been considered. In these cases, all flow parameters have been kept the same, including the total lambda factor value λe = 1.27, except from the inlet air (and the reactor wall) temperature that was raised to 673K and 723K, respectively. For these test cases though, measurements were available only for the device’s symmetry axis (Steinbach, 2002). Fig. 5 presents experimental values of the axial temperature profiles along the reactor’s centre-line, together with the relevant computational predictions for the two test cases considered; results for the “standard” test case (Tin = 623K) are also shown. In general, when no “cool flame model” is utilized, CFD predictions are completely incapable of matching the experimental data. Predictions assuming a purely “physical” evaporation mode result in outlet temperatures significantly lower than their respective inlet values, whereas experimental data suggest that the temperature at the reactor’s outlet is higher than the respective inlet temperature by 50150K. In fact, the comparison of these predictions with the available measurements represents a vivid illustration of the potential advantages that the utilization of the SCF phenomenon may have in the form of droplet evaporation rate enhancement.

Figure 5. Comparison of predictions with experimental data for the gas phase temperature along the symmetry axis. Variation of inlet air temperature. By utilizing the polynomial correlation, Eq. (1), predictions are improved, although the mixture’s heating-up rate is constantly under-predicted, failing to reproduce at its full extend the observed temperature increase. However, when the proposed “correction factor”, Eq. (2), is implemented, predictions exhibit a very good agreement with measurements, following the experimental trends much closer than the previous approach. Nevertheless, when the inlet temperature is increased, a slight deterioration in the quality - 14 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

of the predictions is noticed. The observed discrepancies appearing immediately downstream the droplet injection plane may be attributed to a variety of parameters ranging from inaccuracies in the assumed boundary and inlet conditions to errors associated with the intrusive measurement technique used during the experiments, since all measurement locations near the injection nozzle were prone to errors due to the possible existence of liquid droplets in their vicinity (Steinbach, 2002). The aforementioned validation tests have shown that the performance of the developed computational tool is encouraging, yielding results within a satisfactory level of accuracy. Cool flame-induced heat release characteristics and their impact on droplet evaporation rates are adequately described, enabling the investigation of the thermal behaviour of a SCF reactor, hence assisting the design optimization procedure. However, there are still challenges associated with a need for more detailed experimental data sets, regarding flow variables other than temperature, in order to serve as validating means. Considerable effort is still required for the accurate prediction of the two-phase flow field inside the reactor, as well as for the validation of the developed model over a variety of operational parameter values. An alternative approach, utilizing a reduced chemical kinetic mechanism in the frame of a look-up table formulation is under way, with the aim of implementing more “chemical” reasoning in the experimental foundation of the current modelling effort.

Figure 6. Parametric variation of gas phase temperature along the symmetry axis for various air inlet temperatures. A parametric study has been performed, using the developed “correction factor” - Eq. (2), to investigate the influence of the inlet temperature on the reactor’s thermal behaviour. The global lambda factor was kept constant (λe = 1.27) whereas the air inlet temperature was varied between 623K and 723K; these values correspond to the boundaries of intense cool flame activity for atmospheric pressure conditions (Fig. 1). The axial temperature profiles along the device’s symmetry axis, for various inlet temperatures, are depicted in Fig. 6. Close to the spray injection plane an abrupt temperature drop is calculated, associated with droplet evaporation. Further downstream, temperatures start rising again due to the initialisation of cool flame exothermal reactions. In this region a significant dependence on inlet air temperature is observed. However, one cannot fail to observe that - 15 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

despite the large inlet temperature variation (Tin = 623-723K), temperature levels at the downstream end of the reactor (Tout = 745-765K) remain practically constant and independent of the inlet temperature. The trend is in agreement with experimental evidence suggesting that, for a given pressure level, a limiting value exists which may be regarded as the “equilibrium” temperature for the SCF oxidative reactions (Lucka and Koehne, 1999, Steinbach, 2002). As a result, in the current geometrical configuration, it would be a waste of energy to preheat the inlet air above 623K (see Figs. 4 and 5). 6.3 Variation of the lambda factor Aiming to explore the impact of fuel concentration on the heat and mass transfer phenomena occurring inside the reactor, a series of numerical experiments, utilizing the developed model, Eq. (2), has been conducted. Inlet and boundary conditions were kept identical with the “standard” test case, except from the injected liquid mass flow rate value that was modified, resulting in the variation of the reactor’s total lambda factor in the range of 0.8 to 1.4. In Fig. 7, predictions for the gas phase temperature along the reactor’s symmetry axis are presented.

Figure 7. Parametric variation of gas phase temperature along the symmetry axis for various lambda factors. All temperature profiles exhibit essentially the same general behaviour, demonstrating a gradual increase downstream the location of the initial abrupt temperature drop. However, differences in the absolute temperature values are observed among the various lambda factor predictions. For lambda factor values close to stoichiometric (λ = 0.9-1.27), temperature differences due to fuel concentration variations remain small. On the contrary, when the mixture becomes moderately fuel-rich (λ = 0.8), the predicted outlet temperature is almost 100Κ higher compared to the “standard” test case (λe = 1.27), whereas at fuel-lean conditions (λ = 1.4), the observed behaviour is exactly the opposite, and the predicted outlet temperature is lower than the respective “stoichiometric” value by approximately 50Κ. In addition, in the case of λ = 0.8, the mixture does not reach a steady-state temperature before exiting the reactor. These remarks are consistent with similar observations found in the literature (Dagaut et al., 1995, Aggarwal, 1998), suggesting that - 16 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

cool flame reactivity is favoured in fuel-rich conditions; a remark that is further supported by the form of the heat release rate curve in Fig. 2. The variation of the total fuel thermal energy conversion with respect to the inlet air temperature and the global lambda factor value is presented in Fig. 8. Thermal energy conversion represents the percentage of the available energy, associated with the fuel’s  fu Hu), which is being “consumed” during the cool flame exothermal heating value ( m activity. This amount of energy is eventually utilized in order to raise the mixture’s temperature, thus enhancing the evaporation process, and is calculated by summing the local values of the cool flame heat release terms (QCF) in all computational cells.

Figure 8. Calculated total fuel thermal energy conversion. (a) Variation of inlet air temperature (λe = 1.27), (b) Variation of lambda factor (Tin = 623K). For the case of varying inlet air temperature, the total lambda factor inside the reactor was kept equal to the respective value of the “standard” test case (λe = 1.27). Inlet temperatures were allowed to vary between 623K and 723K, since, as shown in Fig. 1, cool flame reactions are mainly active in this range. As can be seen in Fig. 8 (dashed line), a monotonically decreasing trend is observed, suggesting that cool flame reactivity declines with increasing temperature. This finding is in accordance with the negative slope of the heat release curve in Fig. 1, since the examined temperature region is dominated by the NTC behaviour. When inlet air temperature is kept constant (Tin = 623K) and total lambda factor is increased, thermal energy conversion is decreasing, as depicted in Fig. 8 (continuous line). However, total heat release rates are almost constant for a wide range of lambda factor values (λ = 0.9-1.2), an observation consistent with the axial temperature profile trends, shown in Fig. 7. Higher fuel “conversion” values (of the order of 2.5%) can be achieved when strongly sub-stoichiometric conditions prevail (λ < 0.7). In terms of global energy conservation, a simple heat balance analysis reveals that SCF can lead to significant savings in the energy needed to preheat and maintain the mixture at elevated temperatures. This can be exploited with appropriate design modifications of the reactor, in order to use part of the cool flame induced heat for inlet air preheating and enhancement of the droplet evaporation rate. - 17 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

7. Concluding Remarks A novel method to evaporate liquid fuels yielding a heated air-vapour mixture, that can be subsequently either burnt, using premixed combustion methodologies, or used to produce a hydrogen-rich gas for fuel cell applications, is to utilize the “stabilized cool flame” phenomenon. With the aim of numerically investigating the thermal behaviour of an atmospheric pressure, diesel spray, non-igniting cool flame reactor, a two-phase CFD code has been employed. To adequately describe the main physico-chemical phenomena emerging in the region of intense cool flame activity, a dedicated model has been developed and implemented into the CFD code. The model, correlating cool flame induced heat release with temperature, has been deduced by analyzing experimental data available for a tubular reactor. Furthermore, in order to take into account the effects that fuel concentration variations have on the observed thermal energy conversion, a “correction factor” has been introduced by using a semi-detailed n-heptane oxidation kinetic mechanism, involving 57 species and 290 reactions. Good levels of agreement have been observed during the validation procedure, i.e. comparing numerical predictions with available experimental data, thus indicating that the developed model is able to capture reasonably well the major characteristic features of the flow inside a cool flame reactor. A parametric study, varying the two main influencing parameters, i.e. temperature and fuel concentration, has revealed the prevailing features regarding the thermal behaviour of the system. NTC behaviour, which constitutes the main distinguishing feature of cool flame reactions, has been well described, by predicting a decreasing trend in heat release with increasing temperature. Moreover, predictions agreed well with reports in the literature suggesting that cool flame reactivity is enhanced at fuel-rich conditions. The proposed modelling approach, while requires limited computational resources, yields quite reasonable results that can be reliably used to support the design optimization process of SCF reactors. Acknowledgements The work has been financially supported by the E.C. in the frame of an EU-project (Contract No. ENK6-CT-2000-00317). The authors would like to thank Dr.-Ing. K. Lucka and Dr.-Ing. N. Steinbach (EST-RWTH Aachen) for providing the cool flame reactor experimental datasets. The fruitful discussions with Prof. J.F. Griffiths (University of Leeds) on the topic of chemical kinetics are gratefully acknowledged. References Aggarwal, S. K. (1998) A Review of Spray Ignition Phenomena: Present Status and Future Research. Prog. Energy Comb. Sci., 24, 565-600. Ballinger, P.R. and Ryason, P.R. (1970) Isolated Stable Cool Flames of Hydrocarbons, Proc. Combust. Instit., 13, 271-277. Bellan, J. and Harstad, K. (1987) Analysis of the convective evaporation of nondilute clusters of drops. Int. J. Heat Mass Transfer, 30, 125-136. Berlemont, M.S. Grancher, G. and Gouesbet, G. (1991) On the Lagrangian simulation of turbulence influence on droplet evaporation. Int. J. Heat Mass Transfer,34, 2805-2812. Bird, R.B., Steward, W.E. and Lightfoot, E.N. (1960) Transport Phenomena, Wiley, New York, pp. 636-684. Bradley, J.N., Jones, G.A., Skirrow, G. and Tipper, C.H.F. (1966) Stabilized Low Temperature Cool Flames of Acetaldehyde and Propionaldehyde – A Mass Spectrometric Study. Combust. Flame, 10, 259-266. - 18 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

Cavanagh, J., Cox, R.A. and Olson, G. (1990) Computer Modeling of Cool Flames and Ignition of Acetaldehyde. Combust. Flame, 82, 15-39. Crowe, C.T., Sharma, M.P. and Stock, D.E. (1977) The particle-source-in-cell (PSI-cell) model for gas-droplet flows. J. Fluids Eng., 99, 325-332. Crowe, C., Sommerfeld, M. and Tsuji, Y. (1988) Multiphase Flows with Droplets and Particles, CRC Press, Boca Raton, pp. 57-112. Curran, H.J., Gaffuri, P., Pitz, W.J. and Westbrook, C.K. (1998) A Comprehensive Modeling Study of n-Heptane Oxidation. Combust. Flame, 114, 149-177. Dagaut, P., Reuillon, M. and Cathonnet, M. (1995) Experimental Study of the Oxidation of nHeptane in a Jet Stirred Reactor from Low to High Temperature and Pressures up to 40 Atm. Combust. Flame, 101, 132-140. Faeth, G.M. (1983) Evaporation and combustion of sprays. Prog. Energy Comb. Sci., 9, 1-76. Founti, M. and Klipfel, A. (1998) Experimental and Computational Investigations of Nearly Dense Two-Phase Sudden Expansion Flows. Exp. Thermal and Fluid Science, 17, 27-36. Glassman, I. (1996) Combustion, 3rd Edition, Academic Press, San Diego, pp. 351-433. Gosman, A.D. and Ioannides, E. (1983) Aspects of computer simulation of liquid fueled combustor. Journal of Energy, 7, 482-490. Gray, B.G. and Felton, P.G. (1974) Low-Temperature Oxidation in a Stirred-Flow Reactor-I. Propane. Combust. Flame, 23, 295-304. Griffiths, J.F. (1995) Reduced Kinetic Models and their Application to Practical Combustion Systems. Prog. Energy Comb. Sci., 21, 25-107. Harrison, A.J. and Cairnie, L.R. (1988) The Development and Experimental Validation of a Mathematical Model for Predicting Hot-Surface Autoignition Hazards Using Complex Chemistry. Combust. Flame, 71, 1-21. Hartmann, L., Lucka, K. and Koehne, H. (2003) Mixture preparation by cool flames for diesel-reforming technologies. Journal of Power Sources, 118, 286-297. Hindmarsh, A.C. (1980) LSODE and LSODI, Two Initial Value Differential Equation Solvers. ACM SIGNUM Newsletter, 15, 4. Klipfel, A. Founti, M., Zaehringer, K., Martin, J.P. and Petit, J.P. (1998) Numerical simulation and experimental validation of the turbulent combustion and perlite expansion processes in an industrial perlite expansion furnace. Flow, Turb. and Comb., 60, 283-300. Kolaitis, D. and Founti, M. (2003a) Assessment of Reduced Mechanisms for Low Temperature-Pressure Oxidation of n-Heptane. In Beretta, F. and Bouhafid, A. (Eds.) Proc. 3rd Mediterranean Combustion Symposium, The Combustion Institute, Marrakech, Morocco, pp. 838-848. Kolaitis, D. and Founti, M. (2003b) Scrutinizing Evaporation Models for Computational Modelling of Turbulent Sprays. In Cavaliere, A. (Ed.) Proc. 9th International Conference on Liquid Atomization and Spray Systems (ICLASS 2003), Sorrento, Italy, Paper 2-18. Lignola, P.G. and Reverchon, E. (1987) Cool Flames. Prog. Energy Comb. Sci., 13, 75-96. Lucka, K. and Koehne, H. (1999) Usage of cold flames for the evaporation of liquid fuels. In Carvalho, M.G. and Lockwood, F.C. (Eds.) Proc. 5th International Conference On Clean Air Technology, Lisbon, Portugal, pp. 207-213. Miller, R.S., Harstad, K. and Bellan, J. (1998) Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations. Int. J. Multiphase Flow, 24, 1025-1055. Montgomery, C.J., Cremer, M.A., Chen, J.Y., Westbrook, C.K. and Maurice, L.Q. (2002) Reduced Chemical Kinetic Mechanisms for Hydrocarbon Fuels. Journal of Propulsion and Power, 18, 192-198. - 19 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580

Morley, C. (1988) Photolytic Perturbation Method to Investigate the Kinetics of Hydrocarbon Oxidation Near 800K, Proc. Combust. Instit., 22, 911-918. Naidja, A., Krishna, C.R., Butcher, T. and Mahajan, D. (2003) Cool flame partial oxidation and its role in combustion and reforming of fuels for fuel cell systems. Prog. Energy Comb. Sci., 29, 155-191. Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Co., New York, pp. 79-138. Pekalski, A.A., Zevenbergen, J.F., Pasman, H.J., Lemkowitz, S.M., Dahoe, A.E. and Scarlett, B. (2002) The relation of cool flames and auto-ignition phenomena to process safety at elevated pressure and temperature. J. Hazardous Materials, 93, 93-105. Peters, N., Paczko, G., Seiser, R. and Seshadri, K. (2002) Temperature Cross-Over and NonThermal Runaway at Two-Stage Ignition of n-Heptane. Combust. Flame, 128, 38-59. Ranz, W.E. and Marshall, W.R. (1952) Evaporation from drops: I. Chem. Engng. Prog., 48, 141-146. Reid, R.C., Prausnitz, J.M., Poling, B.E. (1987) The Properties of Gases and Liquids, 4th Edition, McGraw-Hill, Singapore, pp. 404-417. Schnaubelt, S., Moriue, O., Coordes, T., Eigenbrod, C. and Rath, H.J. (2000) Detailed Numerical Simulations of the Multi-Stage Self-Ignition Process of n-Heptane Isolated Droplets and Their Verification by Comparison with Microgravity Experiments, Proc. Combust. Instit., 28, 953-960. Sheinson, R.S. and Williams, F.W. (1973) Chemiluminescence Spectra from Cool and Blue Flames: Electronically Excited Formaldehyde. Combust. Flame, 21, 221-230. Simmie, J.M. (2003) Detailed chemical kinetic models for the combustion of hydrocarbon fuels. Prog. Energy Combust. Sci., 29, 599-634. Sommerfeld, M. (1998) Analysis of isothermal and evaporating turbulent sprays by phaseDoppler anemometry and numerical calculations. Int. J. Heat Fluid Flow, 19, 173-186. Sommerfeld, M. and Qiu, H.H. (1998) Experimental studies of spray evaporation in turbulent flow. Int. J. Heat Fluid Flow, 19, 10-22. Spalding, D.B. (1954) The Combustion of Liquid Fuels, Proc. Combust. Instit., 4, 847-864. Steinbach, N. (2002) Untersuchungen zum Zündverhalten von Heizöl EL-Luft-Gemischen unter atmosphärischem Druck, Ph.D. Thesis, RWTH-Aachen, Germany. Sung, H.J., Jang, H.C. and Cho, C.H. (1990) Curvature-dependent two-equation model for recirculating flows. In Rodi, W. and Ganic, G. (Eds.), Engineering Turbulence Modelling and Experiments, Elsevier Science Publishing Co., pp. 33-42. Tao, F., Golovitchev, V.I. and Chomiak, J. (2000) Self-Ignition and Early Combustion Process of n-Heptane Sprays Under Diluted Air Conditions: Numerical Studies Based on Detailed Chemistry. SAE Proceedings, 2000-01-2931. Williams, F.W. and Sheinson, R.S. (1973) Manipulation of Cool and Blue Flames in the Winged Vertical Tube Reactor. Combust. Sci. Technol., 7, 85-92. Yuen, M.C. and Chen, L.W. (1976) On drag of evaporating liquid droplets. Combust. Sci. Technol., 14, 147-154.

- 20 This is an Accepted Manuscript of an article published by Taylor & Francis Group in "Combustion, Science and Technology " on 25/01/2007, available online: http://dx.doi.org/ 10.1080/00102200500296580