Experimental and computational study of a lifted, non-premixed turbulent free jet flame

Fuel 86 (2007) 793–806 www.fuelfirst.com

Experimental and computational study of a lifted, non-premixed turbulent free jet flame T. Mahmud b

a,*

, S.K. Sangha a, M. Costa b, A. Santos

b

a School of Process, Environmental and Materials Engineering, The University of Leeds, Leeds LS2 9JT, UK Mechanical Engineering Department, Instituto Superior Te´cnico/Technical University of Lisbon, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal

Received 23 February 2006; received in revised form 17 August 2006; accepted 22 August 2006 Available online 2 October 2006

Abstract The results of an experimental and modelling study of a lifted, non-premixed methane turbulent free jet flame issuing into still air are presented. Detailed in-flame measurements, including the gas temperature, oxygen and NO concentration distributions, are made. In a parallel computational study, a radiative mixedness–reactedness flamelet combustion model is employed to simulate the experimental flame. A comprehensive radiation heat transfer model based on the discrete transfer method of solution of the radiative transport equation, together with the wide-band model for gas absorption coefficients, was used. The NO formation and emission was also calculated using a post-processing approach. Validation of the numerical results against the experimental data shows generally good quality combustion predictions in the near burner region. However, predictive difficulties are encountered in the downstream region, particularly for the oxygen concentration. The NO predictions reveal discrepancies when compared with measurements in the fuel rich part of the flame. The in-flame experimental data, with the aid of the predictions, has provided an enhanced understanding of combustion and NO characteristics of the lifted, non-premixed turbulent free jet flame.  2006 Elsevier Ltd. All rights reserved. Keywords: Lifted turbulent flame; Flamelet modelling; Radiation modelling

1. Introduction Many of the burners employed in practical combustion systems are based on non-premixed combustion and designed in such a way that rapid initial mixing of fuel and air streams occur. No flame can exist at aerodynamic strain rates above a critical value due to quenching effects. However, further downstream of the burner nozzle the strain rates reduce to a value where ignition can take place resulting in a stable, but lifted flame. There is evidence from the planar imaging and Rayleigh scattering measurements [1–3] and direct numerical simulations [4], as quoted in Ref. [5], that extensive straining results in the flame quenching and that appreciable premixing of the fuel and *

Corresponding author. Tel.: +44 (0) 113 343 2431; fax: +44 (0) 113 343 2405. E-mail address: [email protected] (T. Mahmud). 0016-2361/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2006.08.030

air streams occurs upstream of the flame stabilisation point. There have been a number of investigations (e.g., Refs. [6–13]) into the mechanisms of stabilisation of lifted, non-premixed turbulent jet flames. These studies have provided diverse and conflicting explanations for this phenomenon (see review in Ref. [14]). Domingo et al. [15] have argued, based on recent experimental studies [16–18], that the propagation of partially premixed flames at the leading edge of a lifted flame plays an important role in flame stabilisation. The presence of triple flames has been suggested [16,17] as a basis for the stabilization of turbulent lifted flames. More recently, Joedicke et al. [19] have identified via Rayleigh scattering, LIPF/LIF and PIV the existence of triple flame structure in the proximity of the stabilisation point in turbulent lifted flames. In many previous studies, measurements were restricted to the flame lift-off heights, defined as the distance from the burner nozzle to the location where the flame is stabilised, as a function of the fuel

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Nomenclature A area of a computational cell surface c mixture fraction cmax rich flammability limit cmin lean flammability limit Cp,mix specific heat at constant pressure Ce1 and Ce2 constants in the e-equation D burner tube diameter h sensible enthalpy I radiation intensity k turbulence kinetic energy K Karlovitz stretch factor l mixing length Le Lewis number P pressure ql laminar heat release rate qr heat loss due to radiation qt mean turbulent heat release rate r radial distance from the jet axis Re Reynolds number s distance travelled by a ray within a cell T gas temperature ui velocity u0 rms velocity ul unstretched laminar burning velocity wi reaction rate of species i

injection velocity and burner nozzle diameter. However, in a few studies [20–24], data on gas temperature and species concentration distributions has been collected, which is suitable for a detailed validation of combustion models for such flames. The mathematical modelling of lifted, non-premixed turbulent flames is challenging because of the diversity of theories accounting for the mechanisms of flame stabilisation. Stretched laminar flamelet models, based on either diffusion [8,9,23,25] or premixed [5,26,27] flamelets, embedded in Reynolds-average Navier–Stokes (RANS) modelling have been applied to simulate hydrocarbon flames. The triple flamelet structure has been introduced into modelling partially premixed combustion in turbulent lifted hydrocarbon flames using RANS [28] and LES [15] approaches. Masri et al. [24] have used a transported probability density function (PDF) approach to model lifted H2/N2 flames. Recently, calculation of the turbulent lifted hydrogen flame of [22] has been performed by Kim and Mastorakos [29] using a first-order CMC method. In many of these studies, only the predicted flame lift-off heights were compared against measurements. It is important to note that in the flamelet modelling approach the assumption of adiabatic combustion is frequently invoked, which can lead to the overprediction of flame temperatures. This restricts the applicability of the

Greek symbols laminar flame thickness dl e turbulence kinetic energy dissipation rate /i mass concentration of species i j gas absorption coefficient h reaction progress variable X representative direction of a ray q density r Stefan–Boltzman constant k Taylor microscale of turbulence Superscript Favre fluctuating quantity

00

Subscripts i, j coordinate directions in inlet Overbars  Reynolds-averaged quantity ,  Favre-averaged quantity

model to situations with negligible radiation heat losses. The heat loss due to thermal radiation has been overlooked in many previous numerical studies of attached (e.g., Refs. [30–33]) as well as lifted [5,8,9,25,26,28] non-premixed turbulent flames using various laminar flamelet models. When radiation was considered [34–36], simplified assumptions were made in order to account for the heat loss by prescribing a local heat loss fraction into the flamelet profiles without calculating thermal radiation by solving a radiative transport equation. In some previous studies, the effect of radiation heat loss has been taken into account via a detailed treatment of the radiation–flamelet interaction coupled with thermal radiation modelling. However, a relatively simple approach based on the optically thin flame assumption has frequently been employed for the calculation of radiation heat transfer. This approach has been implemented in flamelet models for calculations of attached [37–41] and lifted [27] turbulent jet flames. However, some of these studies [38,40] have also used comprehensive radiation models, and have shown that the optically thin flame approximation tends to overpredict the heat loss causing underpredictions of temperature due to the fact that this approach does not account for the absorption of radiation. Therefore, a thermal radiation model, which accounts for both the absorbing and emitting medium is required in order to accurately calculate heat

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losses. Relatively few numerical studies [38,40,42] of attached flames only using a flamelet model together with a comprehensive treatment of radiation have been reported in the literature. This paper reports an integrated experimental and numerical modelling investigation into a lifted, free turbulent non-premixed methane jet flame issuing from a vertical straight tube into the quiescent air at atmospheric pressure and temperature. Detailed in-flame measurements of chemical species, including nitric oxide (NO), concentration and mean gas temperatures were carried out. The flame lift-off height and the visible length of the flame were also measured. The experimental data has been analysed with the aid of the predictions of flame properties obtained using an in-house CFD code based on a radiative mixedness– reactedness flamelet combustion model [26,27] coupled with the optically thin flame model for thermal radiation. In the present study, a comprehensive radiation model, namely the discrete transfer method (DTM) of Lockwood and Shah [43], has been incorporated into the code to simulate radiation heat transfer and the results have been compared with the predictions obtained using the optically thin flame approximation used in the original code [27]. The predicted gas temperature and oxygen concentration fields have been used to calculate NO formation in the flame. NO predictions are obtained using the well-known Zeldovich mechanism [44] for thermal-NO and the kinetic rate expression of De Soete [45] for the formation of promptNO. The effect of turbulence–chemistry interactions on NO formation rates is represented by a single variable beta PDF. Predictions are compared with the measured mean gas temperature and oxygen concentration, and also with the in-flame NO concentration. Finally, a study of the flame lift-off height and flame length is presented, where the predicted lift-off height and length of the flame are compared with experimental data. The work reported in this paper advances our modelling capability [27] of radiating, lifted turbulent flames via integration of an advanced radiation heat transfer model for absorbing and emitting medium, and by further detailed validation of the predictions against a more comprehensive data set, including NO concentration, amassed by the collaborating research group at the Instituto Superior Te´cnico, Lisbon. The present study also paves the way for the application of the simulator to practical-scale turbulent flames where thermal radiation is the dominant mode of heat transfer from the flame. 2. The experimental facility and data collection Measurements were carried out using the experimental facilities in the combustion laboratory at Instituto Superior Te´cnico, Lisbon. Fig. 1 shows a schematic of the experimental set-up. The burner was a straight vertical tube with an internal diameter of 5 mm through which the fuel (99.5% methane) was injected into still air. The fuel injection velocity was 46.4 m/s with a corresponding Reynolds

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number of 14,402. The fuel flow rate was controlled using valves and pressure regulators, and a calibrated flow meter was used to measure the flow rate. A fine mesh wire screen, which was constructed of moveable 1 m · 2.4 m panels, surrounded the flame in order to minimise the room disturbances. Detailed in-flame measurements of mean gas temperature, major species and NO concentration distributions as well as flame lift-off height and flame length were carried out. Local mean gas temperature measurements from the flame region were obtained using fine wire (25 lm) uncoated thermocouples of platinum/platinum:13% rhodium. The hot junction was installed and supported on 350 lm wires of the same material as that of the junction. The 350 lm diameter wires were located in a twin-bore alumina sheath with an external diameter of 4 mm and placed inside a stainless steel tube. As flame stabilisation on the temperature probe was not observed, interference effects were unlikely to have been important and, hence, no effort was made to quantify them. The uncertainty due to radiation heat transfer was estimated to be less than 5% by considering the heat transfer by convection and radiation between the thermocouple bead and the surroundings. Measurement errors associated with the use of uncoated thermocouples are much lower than those resulting from radiation losses. Given the small errors, less than 5%, in gas temperature due to radiation losses, it is expected that uncertainties due to catalytic effects would be marginal. The sampling of combustion gases from the flame region for the measurement of local mean major species and NOx concentrations was achieved using an aerodynamic quench quartz probe. The probe was 300 mm long and 6 mm in outer diameter. The tip of the probe was narrowed down to an orifice diameter of 1 mm over a final length of 16 mm. The analytical instrumentation included a magnetic pressure analyzer for O2 measurements and a chemiluminescent analyzer for NOx measurements. The major sources of uncertainty in the concentration measurements in the flame region were associated with the quenching of chemical reactions and aerodynamic disturbances of the flow. Through the rapid expansion near the probe tip, the quenching of the chemical reactions was aerodynamically achieved. No attempt was made to quantify the probe flow disturbances. On average, the repeatability of the gas species concentration data was within 10%. The thermocouple and the sample probes were mounted on a 3-D computer controlled traverse mechanism, which allowed for axial and radial movements. The analog outputs of the analysers and of the thermocouple were transmitted via A/D boards to a computer where the signals were processed and the mean values calculated. Finally, to determine the lift-off height and the length of the flame, direct flame photography was used, where five still photographs were taken with a relatively long exposure time of 5 s because of the flame oscillations. With the aid of an image processing software, both the lift-off height and the flame length were measured and averaged.

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a

L f (Flame length)

(Lift-off hh (Lift -of height)

D Burner tube

Fuel

b

Fig. 1. Schematic of (a) a lifted jet flame and (b) experimental set-up.

A detailed description of the experimental set-up and measurement techniques as well as associated uncertainties may be found elsewhere [46]. 3. The mathematical model An existing computer code [27,47] at Leeds, originally developed by Bradley and co-workers [26,48] using the adiabatic mixedness–reactedness strained flamelet combustion model, was adapted in this study. The calculation procedure is based on the solution of the Favre-averaged conser-

vation equations for mass, momentum, thermal-energy and chemical species. The turbulent transport of momentum is handled by the standard k–e model and the transport of mass and energy is modelled using a gradient transport approach [49]. The original adiabatic flamelet combustion model has been successfully applied to predict the flame lift-off heights and blow-off limits of turbulent non-premixed flames [5,26]. In our previous study [27], this model was extended to incorporate the effect of radiation heat transfer using the concept of enthalpy defect [50]. Radiation was modelled based on the optically thin flame assumption.

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3.1. Thermo-fluids model A brief description of the governing equations for the analysis of turbulent reacting flows is presented here. These equations are expressed in Cartesian tensor notation as follows. Overall mass conservation equation: o ð q~ uj Þ ¼ 0 oxj Momentum conservation:    o o oP  u00i u00j  ð q~ ui ~ uj Þ ¼  q oxj oxj oxi

ð1Þ

ð2Þ

 and P are the unweighted mean mixture density where q and pressure; ui is the instantaneous velocity in the xi coordinate direction;  or  represents a Favre mean quantity and 00 denotes a corresponding fluctuating quantity. Thermal energy conservation:    o o ~  u00i h00 þ  ð q~ ui hÞ ¼  qr ð3Þ q qt   oxj oxj where ~ h and h00 are the mean and fluctuating parts of sensible enthalpy, respectively;  qt is the source term representing the mean turbulent volumetric heat release rate due to combustion, and qr the volumetric heat loss due to radiation. The sensible enthalpy, ~ h, is defined as ~ h¼

Z

T~

C p;mix ð Te Þd Te

ð4Þ

T ref

where Cp,mix is the constant pressure specific heat of the mixture and Tref is a reference temperature. Species conservation:    o o ~  u00j /00i þ w i ð q~ uj /i Þ ¼  ð5Þ q oxj oxj ~ i and /00 are the mean and fluctuating mass concenwhere / i u00j /00i is the turbulent mass flux and w i trations of species i, q is the source term representing the mean reaction rates. In common with many previous numerical studies of turbulent jet flames, the turbulent momentum fluxes,   u00i u00j , are obtained using the k–e turbulence model with q the standard values of the model constants [49], and the    u00i h00 and q  u00j /00i , using a gradient transport scalar fluxes, q approach [49] with a constant turbulent Schmidt and Pra i in Eqs. (3) and (5) ndtl number. The source terms,  qt and w are prescribed via the radiative mixedness–reactedness flamelet combustion model and  qr in Eq. (3) via the DTM, as described below. 3.2. Combustion model Details of the original adiabatic mixedness–reactedness flamelet combustion model [5,26] and its extension to

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incorporate radiation effects [27] may be found in the references cited. Bradley and co-workers proposed a model for lifted, turbulent non-premixed flames based on strained laminar premixed, rather than diffusion, flamelets, which uses a mixture fraction, c (mixedness), to quantify the degree of premixing before reaction occurs and a progress variable, h (reactedness), to quantify the completeness of combustion. This approach is valid for sufficiently high jet velocities where the product of Karlovitz stretch factor, K = (u 0 /k) Æ (dl/ul), and the Lewis number, Le, is greater than 7 [5,51]. The adiabatic flamelet model was extended by Ma et al. [27] to incorporate the effect of radiation heat transfer using the concept of enthalpy defect [50]. The enthalpy defect is defined as the difference between the actual (non-adiabatic) enthalpy, ~h, and the adiabatic enthalpy of a flame. The enthalpy defect is caused by the radiation heat loss (qr), which is then imposed on the flamelets as an additional parameter. In the context of this combustion modelling approach, the laminar volumetric heat release rate can be expressed as ql = ql(c, h, qr). The turbulent mean value of ql is obtained using the joint PDF of c, h and qr: Z cmax Z 1 Z qr; max qt ¼ P b ðcÞ ql ðc; h; qr Þpðc; h; qr Þ dqr dh dc cmin

0

0

ð6Þ where h = [T  Tu]/[Tm(c)  Tu], Tu the unburnt gas temperature, Tm(c) the maximum temperature of the particular pre-mixture characterised by c; cmax (= 0.08) and cmin (= 0.028) are the rich and lean flammability limits of the mixture corresponding to equivalence ratios of 1.5 and 0.5, respectively (outside which there is no chemical reaction [51]); and Pb(c) is the probability that the stretch rate can sustain a flamelet. By assuming statistical independence between c, h and qr, and neglecting the effect of qr fluctuations [50], the joint PDF can be expressed as pðc; h; qr Þ ¼ pðcÞpðhÞdðqr  qr Þ

ð7Þ

where p(c) and p(h) are represented by a beta-function, and dðqr  qr Þ is a delta-function. This joint PDF treatment is consistent with the assumptions made in the original mixedness–reactedness flamelet model [26], and that in Ref. [37]. The turbulent mean heat release rate is given by Z cmax Z 1 qt ¼ P b ðcÞ ql ðc; h; qr ÞpðcÞpðhÞdh dc ð8Þ cmin

0

The beta-function PDF’s of p(c) and p(h) were determined  from their Favre mean values, ~c and ~h, and variances, c002 and h002 , which were obtained by solving their own modelled transport equations [26,48]. A similar approach was adopted to account for the effect of radiation heat transfer on the mean reaction rates. The laminar heat release rate, ql(c, h, qr), and reaction rate, wi,l(c, h, qr), data was generated from extensive calculations of one-dimensional premixed methane–air flames

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with a detailed chemical mechanism using the CHEMKIN code [52]. The GRI reaction mechanism 2.11 [53] involving 49 species and 279 reaction steps was employed. For the generation of a non-adiabatic flamelet data library, the CHEMKIN code was modified by introducing a source term, qr, into the energy conservation equation to account for radiation heat loss. A large volume of laminar heat release data was generated for qr 2 (0, qr,max), where qr,max is the maximum radiation heat loss, and for each value of qr for c 2 (cmin, cmax). The computed values of ql(c, h, qr) and wi,l(c, h, qr) were curve fitted against h for each value of qr and c. 3.3. Thermal radiation model The DTM [43] of solution of the radiative transport equation in an emitting/absorbing and scattering medium has been widely used in conjunction with fast chemistry based equilibrium combustion models, such as the conserved scalar with a presumed PDF and eddy-dissipation [54] combustion models, in a variety of combustors (see reviews in Refs. [55,56]). This approach is computationally expedient, which provides enhanced level of accuracy without paying a penalty in terms of computing resources, easy to apply to complex geometries and to any coordinate systems. The radiative transport equation for non-scattering combustion products can be expressed as dI jrT 4 ¼ jI þ ds p

ð9Þ

where I is the radiation intensity and s is the distance in the direction X, j is the absorption coefficient of the participating medium, and r is the Stefan–Boltzmann constant. The transport equation describes the change in intensity of a ray passing through an absorbing and emitting medium at temperature T. Scattering due to the presence of soot particles has been neglected. The amount of soot formed in laboratory-scale methane flames at atmospheric pressure is generally small [57] and hence the soot modelling element, in line with previous thermal radiation simulations in turbulent jet flames (e.g. [38,40,42]), has been omitted from the present calculation. A brief outline of the solution procedure of Eq. (9) is given here, for details see Ref. [43]. In the DTM, the computational domain is divided into a number of control volumes (or cells) defined by the computational grid used for solving the thermo-fluids conservation equations through which representative rays are traced from the centre of a cell on one boundary to that on another boundary. The gas temperature and absorption coefficient of the medium within each cell are taken as constant. The intensity distribution for a ray along its path can be calculated from the following recurrence formula obtained by integration of Eq. (9): I nþ1 ¼

rT 4 ð1  ejds Þ þ I n ejds p

ð10Þ

where In and In+1 are the intensity of the ray at the entrance and exit of a cell, respectively, and ds is the distance travelled by the ray within the cell. The net gain or loss of energy in a cell by radiation is the source term, qr , in Eq. (3) and is given by X qr ¼ ½I nþ1  I n X  dA dX ð11Þ all rays

where A is the area of the cell surface from which the radiation beam emerges. For the free jet flame considered here, the computational boundaries were assumed to be at ambient conditions with emissivity of 1.0. In this study, the data for the absorption coefficients of the radiating species, CH4, CO2, H2O and CO, provided by Tien [58] using the wide-band model was used in the calculations. 3.4. NO model The NO concentration is calculated using a post-processing NO model [59], coupled with the CFD combustion code. The two main sources of the production of NO in a methane flame are the thermal-NO, where the oxidation of atmospheric nitrogen in the high temperature region is accounted for, and the prompt-NO [60], where reactions between hydrocarbon free radicals such as CH and atmospheric nitrogen under fuel rich conditions are considered. In this study, NO formation is modelled outside the flamelet structures. The formation of thermal-NO is modelled via the Zeldovich mechanism [44] with the inclusion of the reverse reactions. The oxygen atom (O) concentration needed to determine the rate of formation is calculated by assuming partial equilibrium between O and O2. The rate constants are taken from Baulch et al. [61]. For the prompt mechanism, a global rate expression proposed by De Soete [45] for the combustion of hydrocarbon fuels is used. A Favre-averaged conservation equation (similar to Eq. (5)) is solved in order to obtain the concentration distribution of NO. The source term represents the net rate of formation of NO. The mean reaction rates are obtained, taking into account the effect of temperature fluctuations, using a single variable PDF with a beta-function. A post-processing approach has been employed in order to solve the NO conservation equation using the predicted velocity, temperature and major species concentration fields, which were obtained from the thermo-fluids and combustion models. 3.5. Method of solution The Favre-averaged conservation equations, written in cylindrical coordinates, were discretised by integrating over control volumes covering one half of the computational domain. The convection terms were approximated by a third-order accurate, non-diffusive, boundednesspreserving discretisation scheme [62], while the diffusion terms were approximated using central differencing. The discretised equations were solved by a variant [62] of the

T. Mahmud et al. / Fuel 86 (2007) 793–806

SIMPLE algorithm [63] using the ‘Penta-Diagonal-MatrixAlgorithm’. 4. Computational details Calculations were carried out on a staggered, twodimensional, non-uniform mesh containing 107 (axial) · 127 (radial) grid lines. A higher grid density in the region near the burner exit and the jet axis was used. Test calculations with different mesh sizes (59 · 75 and 140 · 180) showed that the selected mesh containing 107 · 127 grid lines was sufficiently fine to produce acceptable grid independent solutions. The location of the outflow boundary was far away from the region of interest, and was placed at a distance of 388D from the burner exit. The entrainment boundaries were located parallel to the flame jet axis, at 129D from the axis and perpendicular to the axis at the burner exit plane. The usual entrainment and outflow boundary conditions were employed at these locations. The input data for the calculations was obtained from the experiment, where available. In the absence of measurements, the axial velocity at the burner exit was estimated from the measured fuel mass flow rate. A uniform axial velocity distribution at the inlet was employed and the radial velocity was taken as zero. The inlet turbulence kinetic energy, ~k in , was estimated by assuming 6% turbulence intensity corresponding to fully developed turbulent pipe flow. The inlet value of the turbulence kinetic energy dissipation rate was determined from ~ein ¼ ~k 1:5 in =l, with the mixing length, l, taken as 0.33 times the radius of the burner tube. The inlet parameters and the k–e turbulence model constants in the present calculation were specified based on the outcome of an extensive sensitivity study [27] carried out on lifted jet flames of similar configuration. The sensitivity of the predictions to the shape of the inlet axial velocity profile and turbulence levels was examined for lifted flames [20,21] produced by burners of 7.74 and 8 mm inside diameters for Re = 15,000–30,000. The uniform inlet velocity profile was replaced by a one-seventh power law profile and the inlet turbulence level was varied between 5% and 10%. The predicted flow fields and the resulting flames were relatively insensitive to these changes. Calculations were also performed by varying the turbulence model constant Ce1 within the range 1.44–1.60 and Ce2 within 1.87–1.92 to examine the effects of the jet spreading rate on the predictions. The results obtained with the original values of the constants (i.e., Ce1 = 1.44 and Ce2 = 1.92) provided the best overall agreement with measurements. 5. Discussion of experimental and predicted results 5.1. Flame characteristics Fig. 2 shows comparisons between the predicted radial profiles of mean gas temperature obtained using both the

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DTM and the optically thin flame assumption for radiation heat transfer calculations and the measured profiles at various stations along the length of the flame. The quantity of data collected in the close proximity of the burner was somewhat limited compared with those in the main flame region. The measured temperature distribution at the first station, x = 0.2 m (x/D = 40), in the near burner region, indicates that combustion has already occurred. It can be seen at this station that the temperature distributions predicted using both methods of radiation heat transfer calculations are in good agreement with the measurement and therefore correctly predicts the onset of combustion. Further downstream, at stations x = 0.30 and 0.40 m (x/D = 60 and 80), temperatures in the fuel rich region around the axis of the jet flame are underpredicted revealing the presence of a central non-reacting core. However, the predictions obtained using the DTM, which accounts for both emission and absorption of radiation, are in better agreement with the measurement compared with those obtained using the optically thin flame approximation. This is because the latter approach does not account for the absorption of radiation from the enveloping flame and hence predicts lower levels of gas temperature at and about the jet axis. Also, at station x = 0.3 m, the off-axis peak temperatures and their radial locations are overestimated by both methods of radiation calculation. Further down the length of the flame, at stations x = 0.5, 0.6 and 0.7 m (x/D = 100, 120 and 140), both sets of predictions are in general agreement with measurements, but the optically thin flame model underpredicts the temperature around the axis at x = 0.5 m. However, in the outer region of the flame, r > 0.04 m, the temperature predictions obtained using the DTM are higher compared with those obtained using the optically thin flame model. The reason for these differences can be attributed to the fact that the optically thin flame approximation only accounts for emission without absorption resulting in the overprediction of heat loss due to radiation, and therefore underpredicts the temperature level. Similar predictive trends were also reported in previous radiation modelling of attached non-premixed turbulent jet flames [38,40]. In the region near the outer edge of the jet, r > 0.07 m, the predictions using the DTM are in better agreement with measurements compared with those obtained with the optically thin flame assumption. To ascertain the effect of soot on the predicted gas temperature, radiation calculations were performed by taking into account the contribution of soot into the absorption coefficient of the medium on an approximate basis as suggested in Ref. [64]. The predicted temperatures were little different by this action. Fig. 3 shows the predicted radial profiles of oxygen concentration using both the DTM and the optically thin flame assumption together with measurements at the same stations along the axial distance. As can be seen in this figure, the predicted oxygen concentrations using these two radiation heat transfer calculation methods reveal similar differences, as observed in the predicted temperature profiles

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x = 0.2 m x = 0.2 m

2500 2000

2000

1500

1500

1000

1000

500

500

0

0.00

Temperature (K)

2500

0.04

0.08

0 0.00

0.12

x = 0.3 m

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1500

1500

1000

1000

500

500

2500

0.08

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xx = 0.6 m = 0.6m

0 0.04

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0.00

2500

x = 0.4m

2000

2000

1500

1500

1000

1000

500

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0 0.00

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x = 0.3m

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xx = 0.5m 0.5 m

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0 0.00

0.04

0.0 8

0.12

x = 0.7 m

x = 0.7m

0.04

0.08

0.12

Radial Distance (m)

Fig. 2. Comparison between the predicted radial profiles of the mean gas temperature and measurements. (s) measurements, (- - -) optically thin flame model, (—) DTM.

shown in Fig. 2. Here again, it can be seen that in the near burner region at station x = 0.2 m, the predicted oxygen concentration distributions are in good agreement with the measurement suggesting that the onset of combustion is correctly predicted using the radiative mixedness–reactedness flamelet combustion model. The good predictions of thermochemical properties in the near burner region are in line with our earlier predictions [27] of lifted flames studied experimentally by [20,21]. Although some recent studies (e.g., Refs. [16,17,19]) have suggested the presence of a triple flame at the leading edge of the lifted flame as a basis for flame stabilization, the underlying mechanisms of this phenomenon still remain unclear in spite of extensive investigations. The mixedness–reactedness flamelet model based on stretched premixed flamelets has successfully predicted the general structure of turbulent lifted flames [5,26,27], which confirms the validity of the assumption [6,12] of premixed flame propagation at the turbulent burning velocity at the base of the lifted flame. At downstream stations, x = 0.3 and 0.4 m, the off-axis troughs in the predicted oxygen concentration profiles located in the region 0.02 < r < 0.04 m show virtually zero oxygen concentration compared with the experimental data. These low levels of oxygen are located in the same

regions where the temperature peaks are located, as shown in Fig. 2, and correspond to the overprediction of gas temperature. Further downstream, at stations x = 0.5, 0.6 and 0.7 m, the predicted oxygen concentration profiles at and about the jet flame axis using both methods of radiation calculations reveal that virtually all the oxygen is consumed. Discrepancies observed between the predicted and measured oxygen concentrations are also reflected in the predictions of other major species concentrations, which are not shown here. In recent calculations of piloted turbulent non-premixed methane–air flames with local extinctions, studied experimentally by Barlow and Frank [65], using a CMC method [66] and a combined flamelet/CMC approach [67] have also revealed discrepancies in the fuel rich part of the flames. The underprediction of the oxygen concentration in the present study may be attributed in part to the underestimation of the rate of entrainment of surrounding air by the fuel jet. The k–e turbulence model is known to be deficient for predicting jet entrainment and spreading rate. Within the framework of RANS modelling, a second moment closure for turbulence would be expected to alleviate such deficiencies. But, previous numerical studies [68–73] revealed little superiority of Reynold-stress closures over the k–e model in predicting the

T. Mahmud et al. / Fuel 86 (2007) 793–806

x = 0.2 m

25 20

20

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10

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5

0 0.00

0.04

0.08

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25

20

15

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x = 0.4m

20

0 0.00

0.12

x = 0.6m

x = 0.4 m 25

0.08

x = 0.6 m 25

x = 0.3m

20

0 0.00

801

0.12

Radial Distance (m)

0 0.00

x = 0.7m

0.04

0.08

0.12

Radial Distance (m)

Fig. 3. Comparison between the predicted radial profiles of the oxygen concentration distribution and measurement. (s) measurements, (- - -) optically thin flame model, (—) DTM.

decay and spreading rates of turbulent reacting and nonreacting free round jets. The values of the model constants had to be adjusted on an ad hoc basis to match the experimental data. It is worth noting that the RANS modelling approach is unable to capture the details of the instantaneous vortex structures and their influence on local flame extinction, as revealed by the simultaneous measurements of flow and CH/OH radical fields using PIV and PLIF in lifted turbulent flames by Watson et al. [18]. This limitation can be overcome with the LES approach. 5.2. Flame structure Fig. 4a–d shows the predicted structure of the flame using the DTM in terms of contours of mean heat release rate, temperature, mixture fraction and mean strain rate (u 0 /k). The contour of heat release at a rate of 5 · 106 W/m3 is taken as the flame front boundary, as suggested in previous studies [5,26,27]. A mean heat release rate, within the range of 3 · 106–1 · 107 W/m3, has been used in a number of previous studies [5,26,27,48,51,67,74] to determine the flame lift-off height and the length. This approach has its basis in that the flame visibility is due largely to the emissions from C2 and CH radicals, which are well correlated with the heat release rate [5,67,75].

These figures reveal the overall structure of the predicted flame where, in accordance with the experimental observation, the flame is lifted. The predicted flame structure and lift-off heights using both methods of radiation calculation are very similar. Upstream of the leading edge of the flame, x 6 0.051 m (x/D = 10.2), see Fig. 4a, a rich non-flammable mixture exists and the strain rates, as shown in Fig. 4d, are high enough to quench even premixed flamelets. It should be noted that to quench a methane–air laminar diffusion flame a strain rate as low as 360 s1 is required, whereas a stoichiometric laminar premixed flame can survive relatively high strain rates up to 2200 s1 [5]. As can be seen in Fig. 4a and b, the flame envelops a low temperature central non-reacting core around the jet axis, where the mixture is rich although the strain rates have relaxed with the decay of the jet velocity. The length of this cold central core, which extends up to a distance of 0.47 m (x/D = 94), dictates the location of ignition at the jet axis. Downstream of this location, the mixture is now flammable and as a result the combustion zone has spread up to the jet axis. The predicted contour of the mean heat release rate of 5 · 106 W/m3 suggests that the flame lift-off height is 0.051 m (x/D = 10.2) and the flame length is 1.09 m (x/D = 218) away from the nozzle exit, as depicted schematically in

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Fig. 4. Predicted flame structure: (a) heat release rate distribution, (b) temperature distribution, (c) mixture fraction distribution, (d) strain rate distribution.

Fig. 1a. The experimentally determined lift-off height, which is 0.127 m (x/D = 25.4), is higher than the predicted value; however, the predicted flame length is in better agreement with the experimentally observed visible flame length of 0.96 m (x/D = 192). It is obvious that the level of agreement between the predicted and measured flame lengths and lift-off heights will depend on the values of the heat release rate taken as the onset of combustion. The lift-off height obtained from the present prediction agrees well with that given by the correlation of Bradley et al. [5], which is 0.08 m (x/D = 16). It should be noted that the optically thin flame radiation model predicts very similar lift-off height and flame length.

5.3. In-flame NO formation The predicted NO concentration distribution obtained using the aerodynamic and combustion results produced from the radiative flamelet model together with the DTM for radiation heat transfer is shown in Fig. 5. The predicted rates of NO formation reveal that the length of the reaction zone is shorter than that of the combustion zone, as shown in Fig. 4a, presumably as a result of the underprediction of the oxygen concentration around the flame axis for x > 0.4 m. Fig. 6 shows comparisons between the predicted and measured radial profiles of NO concentration. As can be seen, the predicted NO concentration profiles are in

T. Mahmud et al. / Fuel 86 (2007) 793–806

803

Radial distance (m)

(ppm) ABOVE

0.15

22

20 - 22 15 - 20 10 - 15

6 - 10

0.00 0.00

0.25

0.50

0.75

1.00

1.25

1-

1.50

6

Axial distance (m)

Fig. 5. Predicted NO concentration distribution.

x = 0.2 m

50 40

40

30

30

20

20

10

10

0 0.00

0.04

0.08

0.12

x = 0.3 m

50

NO (ppm)

50

x = 0.2m

0 0.00

50

x = 0.3m

40

40

30

30

20

20

10

10

0 0.00

0.04

0.08

0.12

x = 0.4 m

50

0 0.00

50

x = 0.4m

40

40

30

30

20

20

10

10

0 0.00

0.04

0.08

0.12

Radial Distance (m)

0 0.00

x = 0.5 m

x = 0.5m

0.04

0.08

0.12

x = 0.6 m

x = 0.6m

0.04

0.08

0.12

x = 0.7 m x = 0.7m

0.04

0.08

0.12

Radial Distance (m)

Fig. 6. Comparison between the predicted radial profiles of NO concentration and measurement. (s) Measurements, (- - -) optically thin flame model, (—) DTM.

qualitative agreement with the measured trends in the near burner (at x = 0.2 m) and far downstream locations (x = 0.6 and 0.7 m). However, in the region 0.3 6 x 6 0.5 m, the measured NO concentrations are low in the fuel rich area at and about the jet flame axis and the concentration peaks are located away from the axis near the flame front. This trend is not reproduced in the predictions. The NO concentrations are overpredicted in the fuel rich part of the flame with concentration peaks located at the jet axis, indicating that the NO formation zone has spread towards the axis. It should be noted that in the fuel rich area of the flame NO is reduced via the reburn reactions: CHi + NO ! HCN + Hi1O and HCCO + NO ! HCNO + CO [76]. The NO reburn mechanism is not accounted for in

the present calculation resulting in the overprediction of NO concentration in the fuel rich part of the flame. Inadequacy of the present treatment of the interaction between turbulence and NO chemistry has also contributed towards the overall discrepancy between the predictions and measurements. As mentioned above, the formation of thermal and prompt-NO was modelled outside the flamelets via the well-known Zeldovich mechanism [44] and De Soete rate expression [45]. As an alternative approach, the O concentration needed in the calculation of thermal-NO can be obtained from the flamelet data instead of assuming partial equilibrium between O and O2, and the prompt-NO modelled within the flamelet structures using a detailed reaction mechanism. However, previous studies have revealed that

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the flamelet [77–79] and CMC [66] approaches have difficulties in reproducing experimental NO data. 6. Concluding remarks Detailed experimental data has been collected for a lifted, turbulent non-premixed methane–air free jet flame issuing into still air. The complementary computational input has further enhanced the value of the work, where the predictions have been validated against the experimental flame data. The radiative mixedness–reactedness flamelet combustion model is capable of simulating, with useful precision, the mean gas temperatures, species concentrations and the structure of a turbulent lifted flame. Comparisons between the predictions obtained using the DTM and the optically thin flame radiation model and the experimental data show that in the near burner region the temperature predictions are very similar and are in good agreement with measurements. Further downstream, the heat loss due to radiation becomes significant. In this region, the predictions obtained using the optically thin flame assumption overpredicted the heat loss due to radiation and hence, the temperature is underpredicted at and about the axis and at the outer edge of the flame. However, the DTM predictions are in better agreement with the experimental data in this region due to the fact that it accounts for both emission and absorption of radiation. The good prediction of temperature is mirrored by the similarly good prediction of oxygen in the near burner region, but the predictive difficulties exist in the downstream region. The flame lift-off height was also obtained from the prediction and compared with the experimental measurement and that calculated using a correlation [5], where the prediction is in better agreement with the value obtained using the correlation compared with the experimental data. These findings are in agreement with our previous investigation [27]. The predicted flame length is in good agreement with that measured. A further study was carried out where the NO formation in the flame was predicted using the aerodynamic/combustion data produced using the mixedness–reactedness flamelet model for combustion together with the DTM for radiation. The NO concentration predictions were in qualitative agreement with the experimental data close to the burner exit and far downstream, however, in the intervening region the predicted trends deviate from those measured. In this region, the peaks in the predicted NO profiles were located at the jet axis whereas the experimental peaks occurred away from the axis near the flame front. Acknowledgements The experimental work reported here was carried out within the framework of a project (POCTI/EME/37410/ 2001) funded by Fundac¸a˜o para a Cieˆncia e a Tecnologia, Portugal. The modelling work was supported via a student-

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