Experimental and theoretical study on radiative heat transfer characteristics of dimethyl ether jet diffusion flame

Fuel 158 (2015) 684–696

Contents lists available at ScienceDirect

Fuel journal homepage: www.elsevier.com/locate/fuel

Experimental and theoretical study on radiative heat transfer characteristics of dimethyl ether jet diffusion flame Yinhu Kang a,b,c,⇑, Quanhai Wang b,⇑, Xiaofeng Lu b, Xuanyu Ji d, Hu Wang b, Qiang Guo b, Ye Chen b, Jin Yan b, Jinliang Zhou b a

School of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400045, China Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education of China, Chongqing 400044, China Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment, Ministry of Education, Chongqing University, Chongqing 400045, China d College of Mechanical and Power Engineering, Chongqing University of Science & Technology, Chongqing 401331, China b c

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 New correlations for DME flame

width with high accuracy were developed.  Correlations for radiation fraction of DME/air jet diffusion flame were derived.  Method to calculate radiative heat flux outside the DME jet flames was suggested.  Radiative flux in the near-field of small-scale flames was self-similar.

a r t i c l e

i n f o

Article history: Received 25 January 2015 Received in revised form 3 June 2015 Accepted 4 June 2015 Available online 13 June 2015 Keywords: Dimethyl ether Jet diffusion flame Thermal radiation Flame length Radiation fraction

a b s t r a c t The radiative heat transfer characteristics of the dimethyl ether (DME)/air jet diffusion flame (JDF) were experimentally and theoretically studied in this paper. A series of fuel nozzle diameters (df), fuel jet velocities (uf), and air co-flow velocities (uco) were investigated for their influences on the thermal radiation behavior individually. The results showed that the DME jet diffusion flame length was independent of uco, but the flame width decreased exponentially with the increase in uco. Besides, new correlations for the DME jet diffusion flame width were developed in this paper. In the laminar regime, the radiation fraction (vR) was nearly constant with the increase in fuel jet Reynolds number (Ref). In the transitional regime, it increased with Ref. In the turbulent regime, it began to decrease gradually with Ref. Additionally, vR increased gradually with the increase in df. As uco was increased, vR decreased because of the reductions in flame width and volume. Empirical correlations between vR and the operational parameters, including df, Ref, and uco, were developed in this paper to predict the radiative heat flux (RHF) at any position and incident angle outside the DME JDF, in conjunction with the weighted multi-point source model (WMP model). Besides, at any cylindrical surface around the flame, the RHF peaked at about x = 0.7 Lf. At a smaller radius, the axial RHF profile was characterized by larger axial gradients and higher global values. Additionally, the RHF distribution in the near-field (x/Lf < 2, R/Lf < 2) of small-scale flames was self-similar. Based on this behavior, a simplified method for predicting the local RHF was proposed. While with respect to the large-scale flames or far-field (x/Lf > 2 or R/Lf > 2) of the

⇑ Corresponding authors at: School of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400045, China (Y. Kang). Tel./fax: +86 023 65102475. E-mail addresses: [email protected] (Y. Kang), [email protected] (Q. Wang). http://dx.doi.org/10.1016/j.fuel.2015.06.015 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.

Y. Kang et al. / Fuel 158 (2015) 684–696

685

small-scale ones, self-similarity of the local RHF distribution was invalid. In such cases, the RHF was suggested to be calculated by the WMP model with the atmospheric transmissivity. Ó 2015 Elsevier Ltd. All rights reserved.

Nomenclature

Abbreviations DME dimethyl ether, CH3OCH3 FLA flammability limits in air JDF jet diffusion flame LHV lower heating value LNG liquefied natural gas LPG liquefied petroleum gas RHF radiative heat flux WMP weighted multi-point source model Latin symbols C⁄ normalized radiative heat flux, dimensionless Csoot soot concentration, mol m3 df fuel nozzle diameter, m df⁄ momentum diameter of the fuel jet, m DHi height of the ith cylinder element, m Dhc heat of combustion for the fuel, kJ kg1 Kp the Planck-mean absorption coefficient, m1 Lf visible flame length, m Lf⁄ dimensionless flame length, dimensionless M total number of measuring points on the cylinder surface, dimensionless _F m mass flow rate of fuel, kg s1 N total number of point sources of the flame, dimensionless psa saturation pressure at 25 °C, MPa radiative heat transfer rate from the flame to the Q_ rad surroundings, kW q radiative heat flux outside the flame, kW m2 qi measured radiative flux on the ith cylinder element, kW m2 qv,soot volumetric heat dissipation rate of soot, kW m3 R radius of the cylinder surface around the flame, m Ref fuel jet Reynolds number, dimensionless r radial coordinate, m rva latent heat of vaporization, kJ kg1

1. Introduction Dimethyl ether (DME, CH3OCH3) is one of the most promising alternative fuels emerging in the past few decades, and it has the potential of substituting for the liquefied petroleum gas (LPG), diesel fuel, and liquefied natural gas (LNG) [1,2]. It can be manufactured from various traditional energy sources in large amounts, such as coal, natural gas, and biomass etc., or exists as a byproduct of the chemical industry. Many superiorities of DME have been reported in the literature, in terms of availability, economics, acceptability, combustion and ignition performances, clean property, and national security which make DME the most promising competitor among the alternative fuel candidates (e.g. hydrogen, methanol, ethanol, and biofuels) [2]. DME has been successfully used in the internal-combustion engines [3,4], gas turbines [5,6], and household cooking [7]. More recently, DME was also introduced into the fields of industrial boiler [8–12] and kiln furnace. Economical and clean properties of

S Scf SL,max T Tad Tau T0 uco uf Vf Wf Wf⁄ wj x Yf,st

distance from the point source to the receiver, m Schmidt number of fuel, dimensionless maximum laminar flame speed, cm s1 flame temperature, K adiabatic flame temperature of the stoichiometric premixture, K auto-ignition temperature, K ambient temperature, K air co-flow velocity, m s1 fuel jet velocity, m s1 visible flame volume, m3 visible flame width, m dimensionless flame width, dimensionless weighting factor for the jth point source, dimensionless axial coordinate, m fuel mass fraction in the stoichiometric premixture, dimensionless

Greek symbols vR radiation fraction, dimensionless u angle between the receiver normal and the connection line from receiver to the point source, sr j absorption coefficient, m1 lf molecular viscosity of fuel at 25°C, Pa s qf fuel density, kg m3 q1 density of air co-flow, kg m3 sG global residence time, s ss atmospheric transmissivity over the distance S, dimensionless, m1 Superscripts meas measured data SPS single point source model using distance S WMP weighted multi-point source model ⁄ dimensionless

DME in them were also reported. The fundamental combustion characteristics of DME, in terms of ignition [13,14], laminar flame speed [15], and chemical kinetic mechanism [13,16] etc., were extensively studied in the literature. However, the radiative heat transfer characteristics of the DME jet diffusion flames (JDFs) were not studied as thoroughly, which limited the development of DME-fired combustion systems considerably. Although Mogi et al. [17,18] tested the thermal radiation hazardous of DME, the experimental fuel was liquefied DME released at high pressures, which was rather different from that in the industrial boilers. Hence, to design the gaseous DME-fired industrial boilers or kiln furnaces appropriately, the radiative heat transfer characteristics of the gaseous DME JDF should be studied systematically. In general, thermal radiation is the dominated heat transfer mechanism in the boiler furnace. Hence, the knowledge of flame radiation behavior is a crucial prerequisite for proper design and operation of the boilers and gas burners.

686

Y. Kang et al. / Fuel 158 (2015) 684–696

The radiative intensity of flame depends on various factors, including the fuel type, flame temperature, species composition, residence time, flame shape and dimensions, fuel jet Reynolds number, and air co-flow velocity, etc. The flame radiation characteristics of the traditional fuels were extensively studied in the literature [19–23]. In this paper, the thermal radiation characteristics of the DME/air JDF were experimentally and theoretically studied. The radiative heat flux (RHF) distribution outside the DME JDF, flame radiation fraction (vR), as well as the effects of fuel nozzle diameter (df), fuel jet Reynolds number (Ref), and air co-flow velocity (uco) on the radiative heat transfer behavior, were investigated by experiments. Based on these results, empirical correlations for vR with respect to the operational parameters including df, Ref, and uco were developed in this paper. Finally, a method to predict RHF outside the DME JDF was proposed. The concept of radiation fraction (vR) was frequently employed to characterize thermal radiation behavior of the flame in the literature [21,23]. It evaluates the ratio of radiative heat transfer rate from the flame to the surroundings (Q_ rad ) to the overall heat _ F Dhc ), as defined in formula (1) below. released by the flame (m

Q_

vR ¼ _ rad mF Dhc

ð1Þ

_ F is the fuel mass flow rate; Dhc is heat of combustion of where m the fuel. Additionally, the present results can also provide the basic safety data for risk assessment of DME. Since the fires caused by accidental release of high-pressure DME are physically similar to the JDFs, the empirical correlations developed in this paper can also be used to estimate the safety distance of DME vessels.

2. Experimental section 2.1. Experimental apparatus The experiments were conducted on a coaxial jet burner, which is schematically shown in Fig. 1. In the coaxial jet burner, an annular tube (internal diameter 100 mm) was used to generate the air co-flow. A fuel nozzle was concentrically installed with the outer annular tube. During the experiments, the gaseous DME issuing from the inner fuel nozzle was injected into the air co-flow stream. Additionally, a glass bead layer (100 mm in thickness) and a honeycomb screen (50 mm in thickness) were located inside the annular tube to generate a uniformly-distributed air co-flow velocity. Additionally, a series of fuel nozzles with an equal external diameter (12.00 mm) but different internal diameters (df = 1.12, 1.98, 3.30, 4.20, and 6.11 mm) were used to investigate the dependence of flame thermal radiation behavior on df systematically. During the measurements, the tips of the fuel nozzles protruded 25 mm above the rim of the annular tube, as shown in Fig. 1. A compressor and an air tank were used to generate and supply compressed air for the experiments. During the measurements, the vent pipes on the air tank and header were opened to maintain the air pressure and flow rate stable, by discharging a fraction of air to the atmospheres. The volumetric flow rates of fuel and air were controlled by a series of regulators, and were measured by a few LZB type rotameters (precision accuracy ±2.5%). 2.2. Experimental methodology and operational parameters The operational parameters for the experiments are listed in Table 1. Cases 1–49 were operated at a constant uco (uco = 3.0 m/s) but different df (df = 1.12, 1.98, 3.30, 4.20, and 6.11 mm) to investigate the effect of df on the flame radiation behavior. Cases 12–20

Fig. 1. Schematic diagrams of the experimental system (a) and coaxial jet burner (b).

687

Y. Kang et al. / Fuel 158 (2015) 684–696 Table 1 Operational parameters for the experiments a. Case

df (mm)

uf (m/s)

Ref

_ F Dhc (kW) m

uco (m/s)

Case

df (mm)

uf (m/s)

Ref

_ F Dhc (kW) m

uco (m/s)

1 2 3 4 5 6 7 8 9 10 11 12 A 13 14 B 15 16 17 C 18 19 D 20 21 22 23 24 25 26 27 28 E 29 30 31 32 33 34 35 36 37 F 38

1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 3.30 3.30 3.30 3.30 3.30 3.30 3.30 3.30 3.30 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20

2 6 10 14 18 22 26 30 34 39 44.1 2 4 6 8 12 16 20 24 26 2 4 6 8 10 12 14 16 18 0.7 2 3 4 6 8 10 12 14

459 1377 2294 3212 4130 5047 5965 6883 7801 8948 10118 811 1622 2434 3245 4867 6490 8112 9734 10545 1352 2704 4056 5408 6760 8112 9464 10816 12168 602 1721 2582 3441 5162 6883 8604 10324 12045

0.12 0.35 0.58 0.82 1.05 1.28 1.51 1.75 1.98 2.27 2.57 0.36 0.73 1.09 1.46 2.18 2.91 3.64 4.37 4.73 1.01 2.02 3.03 4.04 5.06 6.07 7.08 8.09 9.10 0.57 1.64 2.46 3.28 4.91 6.55 8.19 9.83 11.46

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 G 56 57 58 59 60 61 62 63 64 H 65 66 67 68 69 70 71 72 73 74 75 76

4.20 6.11 6.11 6.11 6.11 6.11 6.11 6.11 6.11 6.11 6.11 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98

16 0.7 2 3 4 6 8 10 12 14 16 2 4 6 8 12 16 20 24 26 2 4 6 8 12 16 20 24 26 2 4 6 8 12 16 20 24 26

13766 933 2503 3999 5006 7510 10013 12516 15019 17523 20026 811 1622 2434 3245 4867 6490 8112 9734 10545 811 1622 2434 3245 4867 6490 8112 9734 10545 811 1622 2434 3245 4867 6490 8112 9734 10545

13.10 1.21 3.47 5.21 6.93 10.40 13.86 17.33 20.80 24.26 27.73 0.36 0.73 1.09 1.46 2.18 2.91 3.64 4.37 4.73 0.36 0.73 1.09 1.46 2.18 2.91 3.64 4.37 4.73 0.36 0.73 1.09 1.46 2.18 2.91 3.64 4.37 4.73

3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7

a The cases labled by A–H were selected for temperature measurements, and those labled by C and E–H were selected for discussing the RHF distribution behavior outside the flame.

Table 2 Properties of the experimental fuel DME. Fuel

Purity (vol.%)

qf (kg/m3)

lf (lPas)

DME

99.71

1.881

9.12

b

psa (MPa)

Tau (K)

0.61a,b

508

a,b

Tad (K) 2293

FLA (vol.%)

b

3.4–18.6

a,b

SL,max (cm s1) 50

b

rva (kJ kg1)

LHV (MJ kg1)

467

28.8

b

qf: gaseous fuel density at 25 °C; lf: molecular viscosity of fuel at 25 °C; psa: saturation pressure at 25 °C; Tau: auto-ignition temperature; Tad: adiabatic flame temperature; FLA: flammability limits in the air; SL,max: maximum laminar flame speed; rva: latent heat of vaporization; LHV: lower heating value. a Data reproduced from Ref. [5]. b Data reproduced from Ref. [10].

and 50–76 were conducted on the fuel nozzle with internal diameter df = 1.98 mm but at various uco (uco = 1.0, 3.0, 5.0, and 7.0 m/s), to investigate the effect of uco on the flame radiation behavior. At given df and uco, uf was increased gradually to investigate its effect on the flame radiation behavior. DME with purity 99.71 vol.% was used for the experiments. Properties of DME are specified in Table 2. During the experiments, each case was obtained by regulating the openings of the needle valves for fuel and air respectively to achieve the designed velocities. Then when the flame reached the thermal/chemical equilibrium state (usually in 2 min after ignition), a JTR09A type radiative flux meter (measuring range 0–10 kW/m2, precision accuracy ±3.95%) was employed to measure the axial RHF profiles at four cylindrical surfaces around the flame (R = 0.25, 0.5, 1.0, and 1.5 Lf, where Lf is the visible flame length), within the axial range x = 0–2 Lf. As illustrated in Fig. 1, during the measurements, the normal to the radiative flux meter was perpendicular to the flame axis. Besides, a vertical ruler was located beside the flame to

determine its visible flame length (Lf) and width (Wf), respectively. The definitions of Lf and Wf are schematically shown in Fig. 1. During the experiments, a digital camera was utilized to record the flame image sequences at a frame rate 30 Hz. Then, Lf and Wf were defined as the average values of the overall instantaneous flame lengths and widths recorded in a sufficiently long imaging interval (usually in 2 min), respectively. Q_ rad is equal to the integral of RHF along the axial direction on a cylindrical surface around the flame, which can be approximately estimated using the measured RHF data on the cylinder, as shown in formula (2).

Q_ rad ¼

Z

1

x¼0

2pR  qðxÞdx 

M X 2pR  DHi  qi :

ð2Þ

i¼1

where R is the radius of the cylindrical surface around the flame. M is the total number of measuring points on this cylinder, based on which the cylinder is divided into M elements along the flame

688

Y. Kang et al. / Fuel 158 (2015) 684–696

height. DHi is the height for the ith element, and qi is the measured RHF on the ith elemental surface. Then the practical vR can be calculated by substituting Q_ rad to formula (1). In the present tests, for each flame case, the axial RHF profiles at four radii (R = 0.25, 0.5, 1.0, and 1.5 Lf) were measured. Theoretically, Q_ rad passing through each cylindrical surface should be equal. Hence, the measured RHFes at R = 0.25 Lf were used to calculate the practical vR of the flame, according to formulas (1) and (2). Additionally, the cases labled by A–H in Table 1 were selected for temperature measurements. The radial temperature profiles at three normalized axial positions (x/Lf = 0.2, 0.5, and 0.8) were measured using several unshielded K type (measuring range 40 to 1150 °C, precision accuracy ±0.4%) and B type (measuring range 600–1800 °C, precision accuracy ±0.25%) thermocouples. All of the measured temperature data were corrected using the approach proposed by Roberts et al. [24] to reduce the measuring error resulting from heat dissipation from thermocouples to the cool surrounding. The three normalized axial positions (x/Lf = 0.2, 0.5, and 0.8) are typical representations for the near-burner, mid-flame, and fur-burner regions. Hence, the present measurements could characterize the global temperature levels inside the DME JDFs.

the receiver to the point source, as shown in Fig. 2a. ss is the atmospheric transmissivity over the distance S at the prevailing atmospheric condition. It depends on the atmospheric temperature and humidity [25], and decreases with S exponentially [26]. The relevant studies [27] showed that when S < 3 m, ss  1.0, such that ss can be removed from formula (3). In the near-field (x/Lf < 2, R/Lf < 2) of small-scale flames (Lf < 1.5 m), S < 3 m was satisfied basically. Hence, removal of ss from the formulas it appears did not reduce the prediction accuracy. The superscript SPS designates that the incident radiation is evaluated based on the SP model and distance S. In the literature, numerous researchers utilized the SP model, along with a measured incident RHF in the far-field (x/Lf > 2 or R/Lf > 2), to determine the practical vR, i.e.:

qmeas 4pS2 vSPS R ¼ _ mF Dhc sS cosu

ð4Þ

It is worth noting that the SP model is valid only in the far-field (x/Lf > 2 or R/Lf > 2); in the near-field (x/Lf < 2, R/Lf < 2), its prediction accuracy will reduce. This issue was explored by Sivathanu et al. [28] who measured the axial RHF distribution at R = 0.5 Lf, as shown in Fig. 2b. In their study, first, Q_ rad was calculated by integrating the measured RHFes along the axial direction, according to formula (2). Then, the practical vR was determined by substituting Q_ rad to formula (1). Second, the RHF at R = 0.5 Lf and x = 0.5 Lf was

2.3. Point source radiation models

calculated using the practical vR, according to formula (5) below.

2.3.1. Single-point source model (SP model) The SP model is frequently used to predict the RHF in the far-field (x/Lf > 2 or R/Lf > 2) of the flame. It assumes that the flame shape and dimensions have insignificant effect on the RHF outside the flame, which is a good approximation for the far-field. While in the near-field (x/Lf < 2, R/Lf < 2), the prediction accuracy of the SP model will reduce. As illustrated in Fig. 2a, for the SP model, the whole flame is represented by a single point source located at half-length along the flame axis. Then the incident radiation at a receiver which is located S far away from the point source (shown in Fig. 2a) can be expressed as:

qSPS ¼

v m_ F Dhc sS qSPS ¼ R cos u 4pS2

where S is the distance from the point source to the receiver, u is the angle between the receiver normal and the connection line from

ð5Þ

Then, according to formula (6), the measured RHFes at R = 0.5 Lf were normalized by qSPS, obtaining the corresponding normalized RHFes (C⁄). Sivathanu et al. [28] found that the C⁄ curves for different fuels collapsed onto a single curve, indicating that the RHF distribution outside the flame was self-similar. Additionally, the C⁄ curves peaked at about x/Lf = 0.5–0.7, with the peak value of about 0.85. All of the C⁄ values at R = 0.5 Lf were lower than 1.0, implying that the prediction accuracy of the SP model reduced in the near-field (x/Lf < 2, R/Lf < 2).

C ¼ ð3Þ

vR m_ F Dhc 4pR2

qmeas qSPS

ð6Þ

Based on this behavior, Sivathanu et al. [28] proposed another method for calculating vR, i.e. substituting the measured RHF at R = 0.5 Lf, x  0.5 Lf and C⁄ = 0.85–0.90 to formula (7).

Fig. 2. Schematic diagrams for the SP model (a and b) and the WMP model (c), respectively.

689

Y. Kang et al. / Fuel 158 (2015) 684–696

qmeas 4pR2 vSPS R ¼ _ mF Dhc C 

ð7Þ

N N X X _ F Dhc sSj wj vR m ! qj ¼ cos uj 4pS2j j¼1 j¼1

ð11Þ

j¼1

2.3.2. Weighted multi-point source model (WMP model) Compared with the SP model, the WMP model developed by Hankinson and Lowesmith [27] can not only calculate RHF in the far-field (x/Lf > 2 or R/Lf > 2), but also predict that in the near-field (x/Lf < 2, R/Lf < 2) accurately. Fig. 2c schematically shows the principle of the WMP model. The whole flame is divided into several segments along the flame height, and each segment is represented by a point source located on the flame axis. Thus for a receiver outside the flame, each point source contributes a fractional RHF to the overall incident RHF, and each fractional RHF can be estimated using the SP model (formula (3)). Then the overall incident RHF onto the receiver (qWMP) is the vector sum of the RHF from each individual point source, as expressed in formula (8).

qWMP ¼

N X wj ¼ 1

ð8Þ

In formula (8), N is the total number of point sources of the flame. wj is the weighting factor for the jth point source, which is estimated by formulas 9–11. The sum of all wj is equal to 1.0. It is analyzed that in the near-field, the WMP model can consider the effect of flame shape and dimensions on the incident radiation. While in the far-field, importances of flame shape and dimensions become insignificant, such that the WMP model reduces to the SP model. In the WMP model, the flame length must be known a priori to determine the locations of the point sources. In the Section 3 part, empirical correlations for DME flame length and width with high accuracies will be addressed. Additionally, prediction accuracy of the WMP model also depends on the values of wj considerably. Based on the measurements of Cook et al. [29], Hankinson and Lowesmith [27] proposed the following formulas to estimate wj.

In the above formulas, N is the total number of point sources. In general, a value above 20 is required for N to guarantee that the predicted incident radiation is independent of N. Fig. 3 shows the comparison between the WMP-predicted axial RHF profiles at R = 0.25, 0.5, 1.0, and 1.5 Lf of flame case A in Table 1 using N = 20 and those using N = 50. It is shown that the predicted results using N = 20 coincided very well with those using N = 50. Hence, in this paper, N = 20. It can guarantee that the predicted results are independent of N adequately. As formulas (9) and (10) show, wj increases linearly from point 1 to n, reaching the maximum at points n and n + 1 (wn = wn+1). Then, it decreases linearly from point n + 1 to N. At the point N, wN = w1 is satisfied. As reported by Hankinson and Lowesmith [27], the predicted results using n = 0.75 N coincided with the measurements of Sivathanu et al. [28] and Cook et al. [29] fairly well. Besides, Yang and Blasiak [30] conducted a study on the entrainment characteristics of the turbulent JDFs. The flame entrainment rate, which was defined as the ratio of high-temperature mass flow rate across the cross-section at a given axial position to the initial fuel jet mass flow rate, can evaluate the local radiative intensity basically. It was reported that the flame entrainment rate increased linearly in the axial range x = 0–0.7 Lf, and then decreased nearly linearly in the range x = 0.7–1.0 Lf, peaking at about x = 0.7 Lf. The axial position x = 0.7 Lf for the maximum flame entrainment rate reported by Yang and Blasiak [30] is approximate to x = 0.75 Lf for the maximum wj suggested by Hankinson and Lowesmith [27]. Additionally, both the flame entrainment rate and wj varied linearly with x. This can also validate the accuracy of formulas (9)– (11). In the present study, the WMP model was also used to predict RHF outside the flame. On the basis of WMP model, Hankinson and Lowesmith [27] proposed another method to determine vR, i.e. substituting a measured RHF qmeas to formula (12).

vR ¼ qmeas

N X j¼1

W j ¼ jw1

ðj ¼ 1; 2; . . . ; nÞ

 wj ¼ n 

 n1  ½j  ðn þ 1Þ w1 N  ðn þ 1Þ

ðj ¼ n þ 1; n þ 2; . . . ; NÞ

4pS2j _ F Dhc sSj cos uj wj m

ð12Þ

ð9Þ 3. Results and discussion 3.1. Flame length and width

ð10Þ

Fig. 3. The comparison between the WMP-predicted axial RHF profiles at R = 0.25, 0.5, 1.0, and 1.5 Lf for flame case C using N = 20 and those using N = 50.

For the convenience of presentation in the later section, the flame length and width behaviors of the DME JDF are primarily discussed, since they directly determine the residence time of high-temperature gases in the flame zone which can affect vR profoundly. In this part, the effects of uf and uco on DME flame length and width are particularly addressed. Flame length and width behaviors of the DME JDFs at uco = 2 m/s were experimentally and theoretically studied in one of our previous publications [10]. It was reported that the dimensionless flame length (L⁄f defined in formula (15)) and width (W⁄f defined in formula (21)) were correlated with Ref intrinsically. Specifically, under the laminar condition, L⁄f increased linearly with the increase in Ref. While under the transitional and turbulent conditions, L⁄f kept constant with the increase in Ref, as shown in Fig. 4a. With regard to the flame width behavior, W⁄f kept constant at the laminar or turbulent condition. It increased quickly with the increase in Ref in the transitional regime, as shown in Fig. 4b. More detailed discussion in this aspect is available in the Ref. [10]. As Fig. 4a shows, the measured L⁄f at different uf and uco converged together, verifying that the normalization method for L⁄f (formula (15)) was reasonable, and more importantly, the impact

690

Y. Kang et al. / Fuel 158 (2015) 684–696

Fig. 4. The dimensionless flame length L⁄f (a) and width W⁄f (b) versus Ref at different df and uco. The discrete points are the measured data, and the lines are the fitting curves.

of uco on L⁄f was unimportant. Hence, the previously-published flame length correlations in Ref. [10] (formulas (13) and (14)) can also be applicable to the present flames at various uco adequately, as shown in Fig. 4a.

Lf ¼ 5:564



 Ref ðRef 6 4500Þ 1000

Lf ¼ 22:86 ðRef > 4500Þ Lf ¼

Lf Y f ;st  df

ð13Þ ð14Þ ð15Þ

sffiffiffiffiffiffiffi  df

¼ df

qf q1

ð16Þ

where Yf,st is fuel mass fraction in the stoichiometric premixture. d*f is momentum diameter of the fuel jet. qf and q1 are densities for fuel and air co-flow, respectively. Ref = 4500 designates the lower limit of the transitional range. The above L⁄f correlations are valid for the laminar, transitional, and turbulent DME/air JDFs at uco = 1–7 m/s. As verified in the Ref. [10], the above L⁄f correlations had a higher accuracy versus the Delichatsios correlation [31], which was most frequently used in the literature.

As shown in Fig. 4b, the measured W⁄f at different df converged together, but those measured at different uco did not collapse onto a single curve. This indicates that W⁄f was influenced by uco significantly. Additionally, Fig. 4b also demonstrates that at a given uco, both the laminar and turbulent W⁄f kept constant, irrelevant with df and Ref. To investigate the effect of uco on W⁄f quantitatively, the averages of the measured laminar and turbulent W⁄f at constant df (df = 1.98 mm) but various uco (uco = 1, 3, 5, and 7 m/s) were calculated and are displayed in Fig. 5, respectively. It indicates that W⁄f of the turbulent flame was about twice that of the laminar one. In Ref. [10], it was attributed to variation of the fuel Schmidt number (Scf) in the transitional regime. Fig. 5 also shows that W⁄f decreased with uco exponentially, regardless of the fluid regime. When uco was above 5 m/s, the curves became flat, indicating that the effect of uco on W⁄f became insignificant gradually. Given the fact that the ) and exponents 0.325 and -0.32 for the laminar (W⁄f = 1.2 u0:325 co turbulent (W⁄f = 2.4 u0:32 ) fitting curves are approximately equal, co it was assumed that W⁄f was proportional to u0:32 , regardless of co the fluid regime, i.e.:

W f  u0:32 co W⁄f

The correlations at uco = 2 m/s (denoted as developed in our previous study [10], i.e.:

ð17Þ W⁄f (uco

= 2)) were

691

Y. Kang et al. / Fuel 158 (2015) 684–696

Due to the high oxygen content (35 wt.%) and absence of C-C bonds in DME molecular structure, reduced soot concentrations in the DME JDFs versus the traditional fuels, such as methane and propane, were confirmed in the literature [10,33–35]. Hayashida et al. [33] reported that the laser-induced incandescence intensity of soot in the DME JDF was much lower than those of methane and propane. Yoon et al. [34] and Song et al. [35] reported that soot concentrations in the methane and propane diffusion flames could be reduced evidently by DME addition. In one of our previous publications [10], it was also observed that the DME JDF emitted less soot than the LPG JDF, especially than the methane JDF. Hence, the dependence of vR of the DME JDF on soot concentration is fairly low. vR of the DME JDF depends on flame temperature and volume particularly. The volumetric heat dissipation rate of soot (qv,soot) is proportional to soot concentration (Csoot), flame volume (Vf), and Fig. 5. The averages of the measured laminar and turbulent W⁄f versus uco (df = 1.98 mm).

W f ¼ 0:98 ðRef 6 4500Þ

ð18Þ

    Ref þ 0:051 ð4500 < Ref < 6500Þ W f ¼ 0:254 1000

ð19Þ

W f ¼ 1:96 ðRef P 6500Þ

ð20Þ

W f ¼

W f Y f ;st  df

ð21Þ

where Wf is the visible flame width; Ref = 4500 and 6500 designate the lower and upper limits of the transitional range, respectively. Then, W⁄f at various uco can be readily obtained on the basis of W⁄f (uco = 2), just by multiply it by u0:32 =20:32 (equal to 1.2 co 0:32 uco ), i.e.:

W f ¼ 0:98 1:2 u0:32 co

ðRef 6 4500Þ

h

i Ref W f ¼ 0:254 1000 þ 0:051 1:2 u0:32 co

ð22Þ

ð23Þ

ð4500 < Ref < 6500Þ W f ¼ 1:96 1:2 u0:32 co

ðRef P 6500Þ

ðT 5  T 50 Þ, as shown in formula (25) below [10].

qv ;soot  C soot V f ðT 5  T 50 Þ

ð25Þ

where T and T0 are the flame temperature and ambient temperature, respectively. Variations of uf and uco may change Csoot, Vf, and T, and change qv,soot further. Since qv,soot is proportional to Csoot, which is fairly low in the DME JDF, the effect of Csoot on qv,soot of the DME JDF is low. qv,soot particularly depends on Vf and T, especially on T since it is approximately proportional to T5. As a result, in the present study, dependence of qv,soot on soot was analyzed based on discussing the Vf and T behaviors. Due to the complex configuration of JDF, it is fairly difficult to derive an exact analytic solution for vR. For simplicity, Turns and Myhr [36] suggested that the practical flame could be equivalent to an optically-thin homogenous flame with volume (Vf), uniform temperature Tad (adiabatic flame temperature for the stoichiometric premixture), and the Planck-mean absorption coefficient (Kp). Thus, Q_ rad could be assumed proportional to the radiative heat emitted by the equivalent optically-thin flame, as shown below [37]. It evaluates the comprehensive thermal dissipation rate of heat emission and absorption of the high-temperature species.

Q_ rad  K p V f T 4ad

ð26Þ

Then, vR is:

ð24Þ

As shown in Fig. 4b, correlations 22–24 agreed with the measured results fairly well. W⁄f decreased with the increase in uco, which is consistent with the findings reported by Lawn [32]. This phenomenon was ascribed to the intensified air-to-fuel entrainment by convection with the increase in uco, which made the stoichiometry contour move inwardly. As a result, the W⁄f was reduced. The above W⁄f correlations (formulas (22)–(24) are valid for the laminar, transitional, and turbulent DME/air JDFs at uco = 1–7 m/s. 3.2. Flame radiation fraction vR

vR depends on various factors, including the fuel type, flame temperature, uf, and uco etc. In general, the fuel with a higher C/H mole ratio has a higher vR due to the increased concentration of soot particles inside the flame. For a given type of fuel, vR increases at higher uf because of the enlargement of flame volume. On the contrary, vR usually decreases with the increase in uco. The reason is that first, the increase in uco can reduce the flame width and volume, which further leads to decrease in the flame residence time. Second, the increase in uco can reduce the soot concentration by intensifying the air-to-fuel convective entrainment.

vR ¼ Q_ rad =m_ F Dhc  K p qad W 2f Lf T 4ad =m_ F Dhc

ð27Þ 2

_ F  qf df uf, it Given that Lf and Wf are proportional to df, m yields:

vR  K p T 4ad ðqad =qf Þ  ðdf =uf Þ

ð28Þ

Thereafter, Turns and Myhr [36] introduced the concept of global residence time sG, as shown in formula (29).

sG ¼ ðqad W 2f Lf Y f ;st Þ=ð3qf d2f uf Þ

ð29Þ

where qf is the fuel density; qad is the density for adiabatic burnout products of the stoichiometric premixture. Additionally, after plotting vR versus log10(sGKpT 4ad ), Molina et al. [38] found that the measured vR of different fuels collapsed onto a single line. On the basis of this behavior, Molina et al. [38] suggested a correlation for vR which was expressed as a linear function of log10(sGKpT 4ad ), like that in formula (33). The theories and correlations proposed by Turns and Myhr [36] and Molina et al. [38] predicted the flame radiation behavior fairly well in the literature. Hence, they are also used for the current analysis. Formula (29) indicates that sG is proportional to Vf (Vf  Wf2Lf). Considering the dependence of flame dimensions on Ref, the

692

Y. Kang et al. / Fuel 158 (2015) 684–696

Additionally, as shown in Fig. 7, in the laminar regime, the measured gas temperatures inside the DME JDF kept nearly unchanged with the increase in Ref. This can be explained using the concept of specific surface area (c) of the flame. It is defined as the ratio of the overall surface area of the flame to its volume, as expressed in formula (31). A flame with higher c has larger surface area per unit volume, and thus, has higher thermal dissipation rate by heat conduction and convection.

c¼

Fig. 6. The measured vR versus Ref at different df and uco.

variation of vR versus Ref, as shown in Fig. 6, is primarily discussed herein. 3.2.1. Effect of Ref on vR As mentioned previously, Lf and Wf are correlated with the fluid regime intrinsically [10]. As illustrated in Fig. 6, the fluid regime can be classified as laminar, laminar-turbulent transitional, and fully-turbulent regimes. As Fig. 6 shows, at given df and uco, in the laminar regime, vR kept nearly constant. In the transitional regime, it increased evidently, reaching the maximum at the end of the transitional stage. In the fully-turbulent regime, vR began to decrease gradually with the increase in Ref. The above phenomena will be discussed in the following section. (I) Laminar regime As formulas (13) and (22) show, in the laminar regime, Wf  df, Lf  df Ref = qf uf df2/lf. Applying them to formula (29), it yields:

sG  qad Y f ;st d2f =lf

ð30Þ

pW f  L f  W 1 f pW 2f  Lf =6

ð31Þ

In the laminar regime, since Wf kept constant, c of the flame, as well as the resultant heat dissipation rate by conduction and convection, also kept constant. As a result, the flame temperatures and resultant vR kept nearly constant with the increase in Ref in the laminar regime. Additionally, at given uco, in the laminar regime, with the increase in uf, the velocity excess uf–uco increased. It will enhance the air entrainment and reduce soot concentration inside the flame. As presented previously, vR kept nearly constant in the laminar regime. Hence, in the laminar regime, the effect of soot concentration on vR was fairly low. (II) Transitional regime As formulas (14) and (23) show, in the transitional regime, Lf  df, Wf increased with Ref (Ref = qf uf df/lf) linearly. Substituting them to formula (29), it can be inferred that sG increased with the increase in Ref. As a result, vR increased accordingly. Additionally, in the transitional regime, with the increase in Ref, Wf increased quickly, and thus c decreased accordingly (formula (31)). Hence, the flame temperatures (as shown in Fig. 8) and resultant vR increased. Moreover, in the transitional regime, air entrainment will be enhanced and soot formation will be depressed with the increase in uf, which tends to decrease the thermal radiation. Hence, the increase of vR in the transitional regime was due to the increases in flame volume and temperature.

The absence of uf in formula (30) implies that in the laminar regime, vR is irrelevant with Ref. In other words, in the laminar _ F (m _ F  df2 uf), the ratio of regime, since Vf is proportional to m _ F Dhc (i.e. vR) remained nearly constant. Q_ rad to m

Formulas (14) and (24) show that in the turbulent regime, Wf  df, Lf  df. Applying them to formula (29), it yields:

Fig. 7. Comparison of the measured radial temperature profiles between cases A and B in Table 1. Cases A (Ref = 1622) and B (Ref = 3245) are two laminar flames operated at equal df (df = 1.98 mm) and uco (uco = 3 m/s).

Fig. 8. Comparison of the measured radial temperature profiles between cases B (Ref = 3245) and C (Ref = 8112) in Table 1. Cases B and C were operated at equal df (df = 1.98 mm) and uco (uco = 3 m/s).

(III) Turbulent regime

Y. Kang et al. / Fuel 158 (2015) 684–696

sG  qad Y f ;st df =qf uf

693

ð32Þ

As shown above, sG is inversely proportional to uf. Therefore, vR decreased with Ref in the turbulent regime. In other words, in the turbulent regime, with the increase in uf, since the heat release _ F Dhc ) increased, but the flame volume as well as the of flame (m resultant radiative heat transfer rate (Q_ rad ) maintained basically unchanged, thus vR of the DME JDF decreased. Additionally, the increase in uf will enhance the air entrainment and reduce soot concentration inside the DME JDF, which will also lead to decrease of vR. However since the soot concentration inside the DME JDF is fairly low because of the high oxygen content (35 wt.%) and absence of C–C bonds in DME molecular structure, this part of contribution was rather unimportant. Fig. 9 shows the comparison of temperature profiles between cases C and D which are two typical turbulent DME JDFs. It demonstrates that the turbulent DME JDF at larger Ref had higher flame temperatures, which was favorable to increase vR. The increase of flame temperatures with the increase in Ref in the turbulent regime may be because of the enhanced air entrainment and combustion intensity. Consequently, it was concluded that in the turbulent regime, the decrease of vR of the DME JDF with the increase in Ref was caused by the unchanged flame volume, rather than the increased flame temperatures.

Fig. 10. Comparison of the measured radial temperature profiles between cases E and F in Table 1. Cases E (Ref = 12168) and F (Ref = 12045) were operated at nearly equal Ref and uco (uco = 3 m/s), but different df.

3.2.2. Effect of df on vR As illustrated in Fig. 6, the flames formed on the fuel nozzle with larger df had higher levels of vR globally. The reason is that first, as demonstrated by formulas (30) and (32), sG increased with the increase in df. As a consequence, vR increased accordingly. Second, as formula (31) indicates, at a larger df, c of the flame decreased. Thus, heat dissipation rate of the flame by conduction and convection decreased, and flame temperatures increased, as shown in Fig. 10. As a result, vR increased.

3.2.3. Effect of uco on vR It can also be seen from Fig. 6 that with the increase in uco, the values of vR decreased globally. This is because the increase in uco resulted in reduced Wf (Fig. 5) and Vf, which further led to decreases in sG and vR. This was even more evident for smaller uco, at which its effect on vR was more significant. When uco was above 5 m/s, its effect on vR became fairly weak. Additionally, the reduced Wf led to increases in c and heat dissipation rate by

Fig. 11. Comparison of the measured radial temperature profiles between cases G and H in Table 1. Cases G and H were operated at equal df (df = 1.98 mm) and Ref (Ref = 8112), but different uco.

conduction and convection. Hence, the flame temperatures (as shown in Fig. 11) and resultant vR decreased. Additionally, the velocity excess uf–uco decreased with the increase in uco, which will decrease the air entrainment and increase soot concentrations inside the flame as well as the thermal radiation. Thus, the decrease of vR with the increase in uco was due to the decreases in flame volume and temperature. Finally, the measured vR at various df and uco versus sGKp T 4ad are plotted in Fig. 12. In this part, the horizontal coordinate is expressed in a logarithmic scale. Kp was estimated using the thermal equilibrium composition data of the stoichiometric premixture, based on the method available in Ref. [37]. For DME, Kp = 0.552. As shown in Fig. 12, the measured vR for each case regressed onto a single line basically. Therefore, the following empirical correlation was developed.

vR ¼ 0:0348log10 ðsG K p T 4ad Þ  0:3263

Fig. 9. Comparison of the measured radial temperature profiles between cases C and D in Table 1. Cases C (Ref = 8112) and D (Ref = 10545) are two turbulent flames operated at equal df (df = 1.98 mm) and uco (uco = 3 m/s).

ð33Þ

Substituting the expressions for Lf (formulas (13) and (14)) and Wf (formulas 22–24) to formula (29), and then applying the resultant sG to formula (33), new correlations for vR of the DME/air JDF can be readily obtained. They are expressed as functions of the operational parameters including Ref, df (unit in m), and uco (unit

694

Y. Kang et al. / Fuel 158 (2015) 684–696

Fig. 12. The measured radiation fraction vR versus sG KpT 4ad at different df and uco.

in m/s), as shown below. During the derivation process, qf df2uf = df lf (qf df uf /lf) = df lf Ref is applied; and qad, qf, Yf,st, and lf for DME are replaced by their specific values, respectively. 2 vR ¼ 0:0348log10 ðu0:64  df Þ þ 0:2753 ðRef 6 4500Þ co

vR

ð34Þ

( ) ½0:254ðRef =1000Þ þ 0:0512 0:64 2 ¼ 0:0348log10  uco  df ðRef =1000Þ þ 0:2942 ð4500 < Ref < 6500Þ 1

vR ¼ 0:0348log10 ½ðRef =1000Þ

2  u0:64  df  þ 0:3129 co

ð35Þ

ðRef P 6500Þ ð36Þ

Formulas 34–36 are valid for the DME/air JDFs at uco = 1–7 m/s, regardless of the fluid regime.

3.3. RHF distribution behavior outside the flame 3.3.1. Validation of the WMP model prediction In this section, the flame case C in Table 1 is taken as an example to validate the WMP model by comparing it with the measured results, and additionally, to discuss the RHF distribution behavior outside the flame. For the flame case C, its Q_ rad can be calculated according to formula (2), using the measured RHFes at R = 0.25 Lf. Then applying Q_ rad to formula (1), the practical vR can be readily obtained. Using the practical vR and WMP model (formula (8)), the incident RHF at arbitrary location and incident angle can be predicted. Fig. 13 shows the measured and WMP-predicted axial profiles of RHF at R = 0.25, 0.5, 1.0, and 1.5 Lf for case C. Fig. 13 demonstrates that using the practical vR, the WMP model could predict the RHF distribution outside the flame fairly well. Furthermore, it can also be seen from Fig. 13 that, on each cylindrical surface outside the flame, with the increase in x, the local RHF increased at first, and then decreased gradually, peaking at about x/Lf = 0.7. On the inner cylindrical surface, the RHF curve was featured by larger axial gradients and higher global values. While on the outer cylindrical surface, the RHF was distributed more uniformly; and its value was reduced globally. At R = 1.5 Lf, the axial RHF profile was approximate to a homogenous distribution along the axial direction.

Fig. 13. Comparison between the measured and WMP-predicted incident RHFes at the radii R = 0.25, 0.5, 1.0, and 1.5 Lf for the flame case C in Table 1.

3.3.2. Self-similarity of the RHF distribution in the near-field (x/Lf < 2, R/Lf < 2) of small-scale flames (Lf < 1.5 m) In the later section, the self-similarity behavior of the RHF distribution in the near-field (x/Lf < 2, R/Lf < 2) of small-scale flames (Lf < 1.5 m) will be discussed by theoretical analysis. Given the vR, substituting it to formula (5), it yields the incident RHF perpendicular to the flame axis at the position of x = 0.5 Lf and arbitrary R. Additionally, the RHF at arbitrary axial position on this cylindrical surface can be predicted using the WMP model (denoted as qWMP). Replacing qmeas with qWMP and substituting it to formula (6), the C⁄ is obtained.

C  ðxÞ ¼

N X wj sSj cos uj qWMP 2 ¼ 4 p R qSPS 4pS2j j¼1

ð37Þ

_ F Dhc in formula (37) indicates that C⁄ is The absence of vR m independent of vR, it just depends on the local position. Additionally, normalizing R and Sj in formula (37) with Lf, it yields:

C  ðx=Lf Þ ¼

N X wj sSj cos uj qWMP ¼ 4pðR=Lf Þ2  2 SPS q j¼1 4pðSj =Lf Þ

ð38Þ

For the small-scale flames (Lf < 1.5 m) involved herein, in the near-field (x/Lf < 2, R/Lf < 2), it can be assumed that sSj = 1.0. Moreover, wj and uj at the same normalized position (R/Lf and Sj/Lf) should be equal. Therefore, the C⁄ curves for the small-scale flames with distinct dimensions should be exactly identical, demonstrating that the RHF profile in the near-field of small-scale jet flames is self-similar. 3.3.3. Normalized RHF outside the flame The measured axial C⁄ profiles at R = 0.25, 0.5, 1.0, and 1.5 Lf for the cases C and E–H in Table 1 are shown in Fig. 14. Additionally, the WMP-predicted C⁄ curves at R = 0.25, 0.5, 0.75, 1.0, 1.5, and 2.0 Lf are also added to Fig. 14. As Fig. 14 shows, the measured data kept within high consistency with the WMP-predicted curves, indicating that the RHF distributions outside the current flames were surely self-similar. Besides, C⁄ increased gradually with the increase in R. Theoretically, C⁄ should be always smaller than 1.0; When R = 1, C⁄ tends to 1.0. It is worth noting that with respect to the large-scale flames (Lf > 1.5 m) with distinct dimensions, although wj and uj at the same normalized position (R/Lf and Sj/Lf) are identical, the atmospheric transmissivity sSj is no longer equal. Specifically, as the

Y. Kang et al. / Fuel 158 (2015) 684–696

695

The combination of vR and WMP model can predict the RHF at any position and incident angle outside the DME JDF accurately. (4) At any cylindrical surface around the DME JDF, the RHF peaked at about x = 0.7 Lf. At smaller radius, the axial RHF profile was characterized by larger axial gradients and higher global values. While at larger radius, the axial gradient of the RHF curve decreased, and the local RHF was reduced globally. (5) In the near-field (x/Lf < 2, R/Lf < 2) of small-scale flames (Lf < 1.5 m), the RHF distribution was self-similar. Based on this behavior, a simplified method to predict the local RHF was proposed in this paper. While for the large-scale flames as well as far-field of the small-scale ones, self-similarity of the local RHF distribution was not satisfied. In such cases, the RHF was suggested to be predicted using the WMP model with the sSj. Acknowledgments Fig. 14. The measured and WMP-predicted C⁄(x/Lf) profiles at the radii R = 0.25, 0.5, 0.75, 1.0, 1.5, and 2.0 Lf for the flame cases C and E–H, respectively. The discrete points designate the measured data and the curves designate the predicted results.

Beer’s Law (formula (39)) [25] shows, the radiative intensity decays exponentially along the line of sight, such that sSj for the large-scale flames decreases significantly and is no longer equal to 1.0. As a result, for the large-scale flames, self-similarity of the RHF distribution is not satisfied. For the same reason, it is also invalid in the far-field (x/Lf > 2 or R/Lf > 2) of small-scale flames (Lf < 1.5 m).

sSj ¼ ejSj ¼ ejðSj =Lf ÞLf

ð39Þ

where j is the absorption coefficient [25]. In summary, for the engineering applications, formulas 34–36 can be primarily employed to estimate vR of the DME JDF. Then the RHF at arbitrary position and incident angle outside the flame can be predicted using the WMP model (formulas 8–11). Besides, for the small-scale flame (Lf < 1.5 m), the RHF in its near-field (x/Lf < 2, R/Lf < 2) can also be calculated by a simplified method. Specifically, first, qSPS is calculated by substituting the vR estimated by formulas 34–36 into formula (5). Second, C⁄ in the near-field can be estimated by performing an interpolation algorithm in Fig. 14. Third, the product of qSPS and C⁄ is just the desired RHF. 4. Conclusions In this paper, an experimental and theoretical study was conducted to investigate the radiative heat transfer characteristics of the DME/air JDFs. The main findings include: (1) The effect of uco on Lf was unimportant. Wf decreased expo). Additionally, nentially with the increase in uco (W f  u0:32 co new empirical correlations for W⁄f of the DME JDF (formulas 22–24) were developed. (2) In the laminar regime, vR kept nearly constant with the increase in Ref. In the transitional regime, vR increased evidently with Ref. In the turbulent regime, it decreased gradually with Ref. At larger df, the level of vR increased. At higher uco, vR decreased due to the reductions in Wf and Vf. (3) vR correlated with log10(sGKp T 4ad ) in a linear function (formula (33)), based on which the empirical correlations for vR with respect to the operational parameters including df, Ref, and uco (formulas 34–36) were developed presently.

The present research was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA07030100), Sichuan Special Project of Transformation of Scientific and Technological Achievements (Plan No. 2012GC0046), Chongqing Science and Technology Commission Research Project (Grant No. cstc2014jcyjA90011), and Scientific Research Fund of Chongqing University of Science and Technology (Grant Nos. ck2014B09 and ck2015Z22). References [1] Arcoumanis C, Bae C, Crookes R, Kinoshita E. The potential of di-methyl ether (DME) as an alternative fuel for compression-ignition engines: a review. Fuel 2008;87:1014–30. [2] Park SH, Lee CS. Combustion performance and emission reduction characteristics of automotive DME engine system. Prog Energ Combust 2013;39:147–68. [3] Lee S, Oh S, Choi Y, Kang K. Effect of n-Butane and propane on performance and emission characteristics of an SI engine operated with DME-blended LPG fuel. Fuel 2011;90:1674–80. [4] Jang J, Lee Y, Cho C, Woo Y, Bae C. Improvement of DME HCCI engine combustion by direct injection and EGR. Fuel 2013;113:617–24. [5] Lee MC, Yoon Y. Development of a gas turbine fuel nozzle for DME and a design method thereof. Fuel 2012;102:823–30. [6] Lee MC, Seo SB, Chung JH, Joo YJ, Ahn DH. Industrial gas turbine combustion performance test of DME to use as an alternative fuel for power generation. Fuel 2009;88:657–62. [7] Marchionna M, Patrini R, Sanfilippo D, Migliavacca G. Fundamental investigations on di-methyl ether (DME) as LPG substitute or make-up for domestic uses. Fuel Process Technol 2008;89:1255–61. [8] Kang YH, Lu XF, Wang QH, Ji XY, Miao SS, Luo XuJ, et al. Experimental and modeling study on the flame structure and reaction zone size of dimethyl ether/air premixed flame in an industrial boiler furnace. Energy Fuels 2013;27:7054–66. [9] Kang YH, Lu XF, Wang QH, Ji XY, Miao SS, Zong C, et al. An experimental and modeling study of NOx and CO emission behaviors of dimethyl ether (DME) in a boiler furnace. Fuel Process Technol 2014;122:129–40. [10] Kang YH, Wang QH, Lu XF, Ji XY, Miao SS, Wang H, et al. Experimental and theoretical study on the flow, mixing, and combustion characteristics of dimethyl ether, methane, and LPG jet diffusion flames. Fuel Process Technol 2015;129:98–112. [11] Kang YH, Lu XF, Wang QH, Gan L, Ji XY, Wang H, et al. Effect of H2 addition on combustion characteristics of dimethyl ether jet diffusion flame. Energ Convers Manage 2015;89:735–48. [12] Kang YH, Wang QH, Lu XF, Wan H, Ji XY, Wang H, et al. Experimental and numerical study on NOx and CO emission characteristics of dimethyl ether/air jet diffusion flame. Appl Energ 2015;149:204–24. [13] Zheng XL, Lu TF, Law CK, Westbrook CK, Curran HJ. Experimental and computational study of nonpremixed ignition of dimethyl ether in counterflow. P Combust Inst 2005;30:1101–9. [14] Deng SL, Zhao P, Zhu DL, Law CK. NTC-affected ignition and low-temperature flames in nonpremixed DME/air counterflow. Combust Flame 2014;161:1993–7. [15] Huang ZH, Wang Q, Yu JR, Zhang Y, Zeng K, Miao HY, et al. Measurement of laminar burning velocity of dimethyl ether–air premixed mixtures. Fuel 2007;86:2360–6.

696

Y. Kang et al. / Fuel 158 (2015) 684–696

[16] Zhao ZW, Chaos M, Kazakov A, Dryer FL. Thermal decomposition reaction and a comprehensive kinetic model of dimethyl ether. Int J Chem Kinet 2008;40:1–18. [17] Mogi T, Shiina H, Wada Y, Dobashi R. Experimental study on the hazards of the jet diffusion flame of liquefied dimethyl ether. Fuel 2011;90:2508–13. [18] Mogi T, Shiina H, Wada Y, Dobashi R. Investigation of the properties of the accidental release and explosion of liquefied dimethyl ether at a filling station. J Loss Prevent Proc 2013;26:32–7. [19] Kim M, Oh J, Yoon Y. Flame length scaling in a non-premixed turbulent diluted hydrogen jet with coaxial air. Fuel 2011;90:2624–9. [20] Yin CG, Rosendahl LA, Kær SK. Chemistry and radiation in oxy-fuel combustion: a computational fluid dynamics modeling study. Fuel 2011;90:2519–29. [21] Hu LH, Wang Q, Delichatsios M, Lu SX, Tang F. Flame radiation fraction behaviors of sooty buoyant turbulent jet diffusion flames in reduced- and normal atmospheric pressures and a global correlation with Reynolds number. Fuel 2014;116:781–6. [22] Kozanoglu B, Zárate L, Gómez-Mares M, Casal J. Convective heat transfer around vertical jet fires: an experimental study. J Hazard Mater 2011;197:104–8. [23] Gómez-Mares M, Muñoz M, Casal J. Radiant heat from propane jet fires. Exp Therm Fluid Sci 2010;34:232–9. [24] Roberts IL, Coney JER, Gibbs BM. Estimation of radiation losses from sheathed thermocouples. Appl Therm Eng 2011;31:2262–70. [25] Kondratyev KY. Radiative heat exchange in the atmosphere. New York: Pergamon Press; 1965. [26] Modest MF. Radiative heat transfer. Academic Press; 2003. [27] Hankinson G, Lowesmith B. A consideration of methods of determining the radiative characteristics of jet fires. Combust Flame 2012;159:1165–77.

[28] Sivathanu YR, Gore JP. Total radiative heat loss in jet flames from single point radiative flux measurements. Combust Flame 1993;94:265–70. [29] Cook DK, Fairweather M, Hammonds J, et al. Size and radiative characteristics of natural gas flares. Part 2–empirical model. Chem Eng Res Des 1987;65:310–7. [30] Yang W, Blasiak W. Flame entrainments induced by a turbulent reacting jet using high-temperature and oxygen-deficient oxidizers. Energ Fuel 2005;19:1473–83. [31] Delichatsios MA. Transition from momentum to buoyancy-controlled turbulent jet diffusion flames and flame height relationships. Combust Flame 1993;92:349–64. [32] Lawn CJ. Lifted flames on fuel jets in co-flowing air. Prog Energ Combust 2009;35:1–30. [33] Hayashida K, Mogi T, Amagai K, Arai M. Growth characteristics of polycyclic aromatic hydrocarbons in dimethyl ether diffusion flame. Fuel 2011;90:493–8. [34] Yoon SS, Anh DH, Chung SH. Synergistic effect of mixing dimethyl ether with methane, ethane, propane, and ethylene fuels on polycyclic aromatic hydrocarbon and soot formation. Combust Flame 2008;154:368–77. [35] Song KH, Nag P, Litzinger TA, Haworth DC. Effects of oxygenated additives on aromatic species in fuel-rich, premixed ethane combustion: a modeling study. Combust Flame 2003;135:341–9. [36] Turns SR, Myhr FH. Oxides of nitrogen emissions from turbulent jet flames: Part I-Fuel effects and flame radiation. Combust Flame 1991;87:319–35. [37] TNF workshop. International workshop on measurement and computation of turbulent nonpremixed flames. http://www.sandia.gov/TNF/radiation.html/; 2001. [38] Molina A, Schefer RW, Houf WG. Radiative fraction and optical thickness in large-scale hydrogen-jet fires. P Combust Inst 2007;31:2565–72.