1 Introduction

Nitrogen oxides (NOx) and carbon monoxide (CO) are the most harmful emissions from the combustion of conventional fossil fuels, which have significant impacts on public health, the climate, and our fragile ecosystems [1]. Of the many alternate fuels proposed to reduce the emissions, biodiesel provides a compromise between performance and emissions as it releases fewer sulphur oxides, less carbon dioxide, and less soot while inherently having a low calorific value [2, 3]. Hence, biodiesel’s NOx and CO emissions have been one of the research interests as it is widely considered as a drop-in replacement for diesel engines [4].

Nitrogen oxides in combustion products include nitric oxide (NO), nitrous oxide (N2O), and nitrogen dioxide (NO2), which contribute to the formation of acid rain and smog in nature. It is reported that NOx formation was highly influenced by adiabatic flame temperature [5,6,7], where the increase in flame temperature due to fuel additives [8] and the introduction of the preheated fuel [9] caused an increase in NOx emissions. These studies further supported the primarily established Zeldovich [10] and Fenimore [11] mechanisms and reaction pathways.

Carbon monoxide is a colourless, odourless gas produced as a primary pollutant in incomplete combustion [11]. CO is a toxic gas that binds to red blood cells and inhibits oxygen uptake [1]. In conventional combustion systems, the production of CO is directly tied to the oxygen content in the oxidiser. The concentration of CO formation in combustion products could be a regulatory indicator to determine combustion efficiency [12]. Leaner fuel mixtures yield lower CO concentrations as CO itself plays a key role in hydrocarbon oxidation. In contrast, fuel-rich mixtures produce higher CO concentrations due to excess fuel in the mixture. CO is also a product of carbon dioxide dissociation at sufficiently high temperatures at near stoichiometric conditions [13]. In lab-scaled CO concentration measurement, diffusion flame of hydrocarbon fuels has been established because CO is produced in diffusion flames without the influence of the fuel-oxidiser mixture composition. It is noted that the CO production rate could be characterised and limited by the finite rate chemistry effects defined in a finite reactive region within the flame [14]. Two stages of CO reactions were observed: firstly, from the initiation of combustion, and secondly, the net destruction of CO via oxidation.

Several engine studies have reported a higher NOx concentration and a lower CO concentration in the combustion of biodiesel than that of pure diesel [15,16,17], which could be attributed to the oxygen content and degrees of unsaturation in the composition of biodiesel’s constituent fatty esters [18, 19]. Engine studies with biodiesel fuels showed a greater reduction in CO due to the fuel-borne oxygen being more effective than air-borne in achieving complete combustion [20]. The engine speed significantly impacted CO production, with in-chamber turbulence and residence times being the key factors [4]. In generator applications, biodiesel produced greater CO emissions than diesel at start-up but significantly less while in operation under load [21].

Several studies of biodiesel diffusion flame have been carried out with simplified surrogates [22,23,24], and none has specifically focused on palm biodiesel. Soot emission has also been the primary research focus [25,26,27]. For instance, Kholghy et al. [23] reported that CO formation was often treated as an essential intermediate reaction or by-product in soot chemistry with significant variance in reaction pathways depending on initial fuel compositions. Most palm biodiesel CO studies are often undertaken in engine environments, and a knowledge gap exists for diffusion flame studies. Several numerical studies have explored the impact of NOx formation. For instance, Ban-Weiss et al. [28] utilised Cantera and the GRI-MECH NOx sub-mechanism to evaluate the impact of biodiesel composition on NOx generation. They found that without rate-limiting reactions for each composition, 92% of NOx generated was through the thermal pathway. Kang et al. [29] also utilised the GRI-MECH NOx sub-mechanism in an experimental and numerical study of NOx and CO emissions of dimethyl ether/air jet diffusion flames. Lopez-Ruiz et al. [30] assessed the thermal NOx pathway of a laminar hydrogen-diffused flame. Lee et al. [31] investigated the soot and NOx emissions in laminar diffusion flames for methane, ethylene, ethane, propane, and n-butane. They found that increasing inlet velocity increased residence times, local temperatures and thus, NOx formation. The latter three studies [29,30,31] were conducted with ANSYS Fluent, and all numerical results agreed with experimental data. Feng et al. [32] experimentally and numerically investigated the formation of NOx in both laminar premixed and laminar diffusion flames for a wide range of biodiesel fuels. The lighter molecular weight fuels ranged from C2–C5, while the heavier molecular weight fuels ranged from C9–C12. In the diffusion flame, heavier fuels showed a positive correlation of increasing NOx mole fraction with increasing fuel mole fraction and carbon number. Comparison of the NOx emissions of fatty acid methyl esters (FAME), ethyl-esters, and n-alkane with similar molecular size revealed that the latter two fuels had a great peak NOx mole fraction. Compared to n-alkane fuel with the same carbon numbers, biodiesel showed a greater NOx mole fraction due to its double bonds (and thus unsaturation) in the fuel structure; however, the double bond position did not show any significant effect. It is noted that the thermal NOx pathway was predominant, where increasing fuel mole fractions yielded a power-law emission increment while a more linear increase via the prompt NOx pathway was observed [32]. Both N2O and NNH routes remained constant, suggesting that these pathways required the fuel species containing nitrogen. Because palm biodiesel specifically contains hydrocarbons in the range of C16–C18; hence, it is more chemically complex than the largest model biodiesel fuel (methyl undecanoate) in the study of Feng et al. [32].

To our knowledge, no study has been undertaken to determine both NOx and CO emissions in palm biodiesel laminar diffusion flames. All existing studies focus on CO emissions of engines and only soot specifically in diffusion flames. NOx emissions studies have been completed only for less complex biodiesel blends or its constituent methyl esters and not specifically for palm biodiesel of C16–C18 methyl-ester blends. As such, this study aims to examine the concentrations of NOx and CO emissions in laminar diffusion flame of biodiesel at different carbon flow rates and to compare the emissions with those of other hydrocarbon fuels such as n-heptane and iso-octane through numerical simulations with ANSYS Fluent 19.1. For the second objective, the fuels’ carbon flow rate was kept constant to compare the resultant emissions from the combustion of alkane fuels and fuel surrogates. The results could provide qualitative insights into NOx and CO emissions at the flamelet level.

2 Numerical model setup and methodology

2.1 Model geometry and boundary conditions

The numerical simulation was carried out using ANSYS Fluent 19.1 to investigate two-dimensional (2-D) axisymmetric laminar coflow diffusion flames of biodiesel, n-heptane, and iso-octane at atmospheric pressure. The numerical model used in this study is a development of our prior work [31], where the mesh was refined and adapted for the liquid fuels used in this study. Figure 1 illustrates the geometry of the modelled coflow burner, boundary conditions, and the mesh refinements used in the present study. The burner utilised in the experimental study [33] was used as a reference for this numerical model. Due to its symmetry about the centreline of the nozzle, the computational domain of the model contained half of the geometry only, as shown in Fig. 1a. A coordinate system was defined such that r represented the radial dimension and z represented the axial length along the centreline of the nozzle. The axisymmetric burner model had two inlets, one for coflow air and the other for diluted fuel, both of which were set as zero-gauge pressure. The burner walls were set with a non-slip adiabatic wall boundary condition and negligible heat loss to predict NOx and CO concentrations of various fuels and at different carbon flow rates. The exit of the computational domain was set as a pressure outlet with zero gradient boundary. The fuel nozzle had a length of 70 mm and a thickness of 1 mm, and stainless steel was selected for its material. This nozzle length was selected to establish a parabolic flow velocity at the nozzle exit [34]. A uniform coflow air of 10 cm/s was supplied through a coaxial nozzle with a radius of 46.5 mm and placed 10 mm below the central nozzle exit to minimise external disturbances. The axial height from the nozzle tip was selected to be 350 mm through an iterative process where observably stable laminar diffusion flames could be achieved inside the experimental setup [33].

Fig. 1
figure 1

Simulation geometry, a input parameters, b and c dimensions and mesh refinements

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2.2 Meshing, convergence study, and validation

Figure 1b presents a non-uniform, structured mesh adopted to discretise the computational domain in the present study. The mesh consisted of several refinement zones to increase the resolution of the meshes near the regions of interest, such as the regions where the flame was established, close to the nozzle, and downstream along the centreline of the nozzle. The mesh convergence strategy was applied to determine suitable mesh sizes with finer mesh at the flame region and coarser mesh further away from the flame, both in radial and axial directions. As a result of the mesh convergence study, a geometry with total mesh elements of 15,490 quadrilateral cells was used. As can be seen from Fig. 1b, the minimum mesh sizes were 0.5 mm axially and 0.08 mm radially from the nozzle wall. A bias factor of 2:1 was applied on the pressure outlet from the centreline to the wall boundary to achieve sufficient mesh density at the nozzle near the laminar diffusion flame. The outer wall with a bias factor of 1:2 was applied such that the mesh size expanded downstream towards the outlet. Compared to the results of a mesh of 32,100 elements, the selected mesh showed differences of 0.3% and 3.1% for the peak flame temperature in the axial and radial directions, respectively and differences of 1.8% and 0.9% for the peak NO and NO2, respectively.

To validate the simulated results, an experimental setup [33] that matched the conditions of the numerical simulation was used to measure the flame height of the biodiesel diffusion flame. It should be noted that the simulated flame height was defined as the position of the highest flame temperature along the centreline, while the experimental flame height was defined by the flame luminosity from the direct images. Figure 2 shows that both experimental and simulated flame heights increased with the carbon flow rate. The simulated flame heights were shorter than the experimental values due to the difference in the flame height definition; however, the difference was within the margin of experimental error.

Fig. 2
figure 2

Flame height validation for biodiesel diffusion flames

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2.3 Numerical setup and governing equations

In this study, a 2-D axisymmetric model represented a laminar reacting flow based on incompressible steady-state. Mass, energy, momentum, and species conservation equations were solved [35].

Mass conservation is governed by

$$\nabla \cdot (\rho \overrightarrow{u}) = 0$$
(1)

where ρ is density and \(\overrightarrow{u}\) is the velocity with \({u}_{z}\) axial velocity and \({u}_{r}\) radial velocity.

The momentum conservation is presented by

$$\nabla \cdot (\rho uu) = -\nabla p+ pg+ \nabla \cdot (\tau )$$
(2)

where g is the gravitational acceleration, p is the fluid pressure, and τ is the viscous stress tensor.

The energy conservation is presented by

$$\nabla \cdot \left[u(\rho E+p)\right] = \nabla \cdot (\tau .u) - \nabla \cdot q+{S}_{h}$$
(3)

where \({S}_{h}\) is the source term to account for the heat release from the combustion. The internal energy \(E\) is written as \(E=h-\frac{P}{\rho }+\frac{{u}^{2}}{2}\) with \(h\) representing the internal energy per unit mass. The local heat flux density \(\overrightarrow{q}\) is expressed as \(\overrightarrow{q}=-k\nabla T\) with k representing the thermal conductivity and \(\nabla T\) representing the temperature gradient.

The chemical species conservation is presented by

$$\nabla \cdot \left({\rho uY}_{i}\right)= -\nabla \cdot \left({J}_{i}\right)+{R}_{i}$$
(4)

where \({Y}_{i}\) represents the mass fraction of species i, \({\overrightarrow{J}}_{i}\) is the diffusion flux of species i, and \({R}_{i}\) is the net rate of production of species i by the chemical reaction.

The ideal gas simulation was achieved via the species transport chemistry model with volumetric reaction enabled and wall surface reactions disabled. Relaxation to the chemical equilibrium model was selected as the solver with the application of the ISAT table to reduce the computational load, wherein the ISAT error tolerance was set as 5E−5. The convective fluxes were discretised by adopting the second-order upwind scheme with the pressure-based coupled algorithm.

A uniform coflow air stream of 76.7% N2 and 23.3% O2 (by mass) was supplied perpendicularly to the coflow inlet. The ambient environment was set at 300 K. As the concentration of emissions and flame temperatures are dependent on nozzle heating [34, 36], the fuel input temperature was fixed at the vapourisation temperature of biodiesel (550 K) for all cases to ensure complete vapourisation of the fuel exiting at the nozzle. Convergence criteria for the simulation were set at 1E−4 for continuity and 1E−5 for energy, CO, and NOx mass fractions. Because liquid fuels were utilised in the study, nitrogen (N2) was used as a carrier gas. Jet velocity calculations had been made with the fuel mole fraction taken into consideration.

Since the present study aimed to calculate the NOx and CO concentrations in the combustion of three different liquid fuels, they had to be kept at the same carbon flow rate (g/h) to maintain the same amount of carbon in the fuel inlet of each simulation case. This method allowed a direct comparison of different fuels and their influences on the emissions generated in the flames, particularly NOx, CO, soot, and other unburnt hydrocarbons [37]. The jet velocity and fuel mole fraction of each case were calculated using parameters such as nozzle dimensions, fuel densities at the temperature of 550 K, and coflow air velocity. The composition of the biodiesel used in this study, as shown in Table 1, was obtained from gas chromatography-mass spectrometry (GC–MS) analysis of a commercially available biodiesel (EN14214, sourced from Mewah Oils Sdn. Bhd., Malaysia). Other chemical properties, such as fuel densities at elevated temperatures, were predicted from Cantera, an open-source chemical kinetics software for reacting laminar flows [38]. A preliminary experiment for biodiesel was conducted, and data for n-heptane and iso-octane from literature [39] were used to determine the appropriate carbon flow rate in the fuel stream. It is noted that the carbon flow rate of 17.2 g/h, denoted as the CF1 case, was selected as the baseline condition in which its flame could be established and stabilised within the computational domain.

Table 1 Chemical formulae and compositions of major components of biodiesel
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From the baseline condition, two sets of simulation were developed for two different objectives of the present study. The first objective was to evaluate the impact of the carbon flow rate (i.e., fuel mole fraction) in biodiesel by multiplying the carbon flow rate of the baseline condition (CF1 case) with 0.6 (CF0.6 case), 1.4 (CF1.4 case), and 1.8 (CF1.8 case). The input parameters for these cases are presented in Table 2. The second simulation set was developed to compare the emissions of the three selected fuels, i.e., n-heptane, iso-octane, and biodiesel. The input parameters for these cases are presented in Table 3. Apart from the 2-D simulation, sensitivity analysis and rate of production analysis were carried out in 1-D opposed diffusion flames using the OpenSMOKE++[40]. The initial conditions of the 1-D calculation, such as the fuel composition and temperature, were kept the same as the initial conditions in the actual 2-D cases [41].

Table 2 Input parameters for biodiesel simulations
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Table 3 Input parameters for selected fuels with composition content and fuel fraction
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2.4 Detailed gas-phase mechanisms

The three mechanisms used in this study are the biodiesel FAME (177 species, 2904 reactions) [42], n-heptane (188 species, 842 reactions) [39], and iso-octane (233 species, 959 reactions) [39] mechanisms. As neither of these mechanisms is able to model NOx formation, these mechanisms were merged with the NOx sub mechanism from GRI-Mech 3.0 [43] to compute NOx concentration. This method has been proven successful in several studies [31, 32, 44,45,46].

It is noted that the thermal oxidation reactions of nitrogen by-products (thermal NOx) and interaction reactions between hydrocarbon and nitrogen chemistry (prompt NOx) are the main pathways of NOx formation [32, 46, 47]. The NOx sub-mechanism in GRI-Mech 3.0 is detailed below:

  • The modified Zeldovich mechanism determines the thermal NO production pathway [10]. Oxidation of atmospheric nitrogen at high temperatures results in the formation of NO,

    $$\mathrm{O}+{\mathrm{N}}_{2}=\mathrm{N}+\mathrm{NO}$$
    (R1)
    $$\mathrm{N}+{\mathrm{O}}_{2}=\mathrm{O}+\mathrm{NO}$$
    (R2)
    $$\mathrm{OH}+\mathrm{N}=\mathrm{H}+\mathrm{NO}$$
    (R3)

  • Prompt NO reaction pathway plays a significant part in hydrocarbon combustion processes as CH radicals are constantly generated during the process [11],

    $${\mathrm{N}}_{2}+\mathrm{CH}=\mathrm{N}+\mathrm{HCN}$$
    (R4)
    $$\mathrm{N}+{\mathrm{O}}_{2}=\mathrm{O}+\mathrm{NO}$$
    (R5)
    $$\mathrm{HCN}+\mathrm{OH}=\mathrm{CN}+{\mathrm{H}}_{2}\mathrm{O}$$
    (R6)
    $$\mathrm{CN}+{\mathrm{O}}_{2}=\mathrm{NO}+\mathrm{CO}$$
    (R7)
    $$\mathrm{H}+\mathrm{HNO}={\mathrm{H}}_{2}+\mathrm{NO}$$
    (R8)
    $$\mathrm{HCCO}+\mathrm{NO}=\mathrm{CO}+\mathrm{HCNO}$$
    (R9)
    $${\mathrm{CH}}_{2}+\mathrm{NO}=\mathrm{H}+\mathrm{HCNO}$$
    (R10)

  • While the N2O mechanism is more prominent with compounds containing N and turbulent processes, this mechanism shows NO formation in the steps,

    $${\mathrm{N}}_{2}\mathrm{O}+\mathrm{O}=2\mathrm{NO}$$
    (R11)
    $${\mathrm{N}}_{2}\mathrm{O}+\mathrm{H}=\mathrm{NH}+\mathrm{NO}$$
    (R12)
    $${\mathrm{N}}_{2}\mathrm{O}+\mathrm{CO}=\mathrm{NO}+\mathrm{NCO}$$
    (R13)

  • NO is also generated through the NO2 mechanism in the following reversible reactions,

    $${\mathrm{HO}}_{2}+\mathrm{NO}=\mathrm{OH}+{\mathrm{NO}}_{2}$$
    (R14)
    $$\mathrm{O}+\mathrm{NO}+\mathrm{M}={\mathrm{NO}}_{2}+\mathrm{M}$$
    (R15)
    $${\mathrm{NO}}_{2}+\mathrm{O}={\mathrm{O}}_{2}+\mathrm{NO}$$
    (R16)
    $$\mathrm{H}+{\mathrm{NO}}_{2}=\mathrm{OH}+\mathrm{NO}$$
    (R17)
    $${\mathrm{NO}}_{2}+\mathrm{CN}=\mathrm{NCO}+\mathrm{NO}$$
    (R18)

For modelling of CO, each mechanism simulates the formation of CO in unique fuel-specific pathways, but the following reactions are primarily determined as the main steps of the oxidation process for hydrocarbon fuels,

$$\mathrm{CO}+{\mathrm{O}}_{2}={\mathrm{CO}}_{2}+\mathrm{O}$$
(R19)
$$\mathrm{O}+{\mathrm{H}}_{2}\mathrm{O}=\mathrm{OH}+\mathrm{OH}$$
(R20)
$$\mathrm{CO}+\mathrm{OH}={\mathrm{CO}}_{2}+\mathrm{H}$$
(R21)
$$\mathrm{H}+{\mathrm{O}}_{2}=\mathrm{OH}+\mathrm{O}$$
(R22)
$$\mathrm{HCO}+\mathrm{M}=\mathrm{CO}+\mathrm{H}+\mathrm{M}$$
(R23)
$$\mathrm{H}+\mathrm{HCCO}=\mathrm{CO}+{\mathrm{CH}}_{2}\left(s\right)$$
(R24)
$${\mathrm{C}}_{2}{\mathrm{H}}_{2}+\mathrm{O}=\mathrm{CO}+{\mathrm{CH}}_{2}$$
(R25)
$$\mathrm{HCO}+{\mathrm{H}}_{2}\mathrm{O}={\mathrm{H}}_{2}\mathrm{O}+\mathrm{CO}+\mathrm{H}$$
(R26)

3 Results and discussion

3.1 Palm biodiesel flame and emission characteristics

3.1.1 Flame height and temperature profile

Comparisons between the flame temperature profile of the baseline case, CF1, with those of the CF0.6, CF1.4, and CF1.8 cases, along with the colour map, are shown in Fig. 3. It is found that the maximum flame temperatures, Tpeak, are detected along the axisymmetric centreline of the nozzle for all the cases. It should be noted that the position of Tpeak is defined as the flame height in this study. It can be observed from Fig. 3 that the flame height increases with the increase in the carbon flow rate. Figure 4 shows that CF1.8 has the highest flame of 20.4 cm, followed by CF1.4 at 13.6 cm, CF1 at 8.48 cm, and CF0.6 at 6.23 cm. Besides that, the peak flame temperatures are observed to increase with the carbon flow rate, with CF1.8 (2375 K) having the highest Tpeak, followed by CF1.4 (2341 K), CF1(2300 K), and CF0.6 (2264 K). The greater entrainment rate of oxygen by the fuel stream at higher fuel flow rates results in an increased reaction rate, which is the cause of the observed increasing temperature and flame height trends [48].

Fig. 3
figure 3

Temperature contour of biodiesel diffusion flames with various carbon flow rates, a CF1 versus CF0.6, b CF1 versus CF1.4, c CF1 versus CF1.8

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Fig. 4
figure 4

Temperatures along the centreline of biodiesel diffusion flames with various carbon flow rates

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3.1.2 NOx formation

It has been reported that for the NOx released in the diffusion flame of hydrocarbon fuels, NO is the most prominent, followed by NO2 [32, 46, 49]. Because N2O is obtained at a peak mass fraction of 4E−7, which is significantly smaller than the mass fractions of NO and NO2, the present study focuses on determining the concentrations of NO and NO2 in the biodiesel diffusion flames. It has been found that the peak mass fractions of NO and NO2 for all carbon flow rates are located on the centreline of the flame but further downstream compared to the position of Tpeak, as can be seen in Fig. 5. With the change in the carbon flow rate, the trends of the NO and NO2 concentrations along the centreline are very similar to the trend of Tpeak. The peak NO mass fraction of CF1.8 is the highest, followed by that of CF1.4, CF1, and CF0.6, respectively. The peak NO mass fraction of CF1.8 is 5.3E−3, which is 11.51% greater than the baseline CF1 case and 3.92% higher than the CF1.4 case. Likewise, the CF1.8 case has the highest NO2 emission with a mass fraction of 7.11E−6, which is 6.19% and 2.66% greater than the CF1 case and CF1.4 case, respectively. When compared to the baseline, significant reductions of 7.57% in NO and 4.62% in NO2 are observed for CF0.6. These results are similar to the trend observed by Feng et al. [32], where NOx production proportionally increases with the fuel mole fraction increment.

Fig. 5
figure 5

a NO and b NO2 mass fractions along the centreline of biodiesel diffusion flames with various carbon flow rates

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The rate of reaction analysis in Fig. 6a for the base case CF1 presents the influence of the ten key reactions and their normalised contributions to the production/consumption of NO. Of these reactions, six reactions present the interactions between hydrocarbon and nitrogen compounds (prompt pathway), three reactions are for NO2 decomposition, and one reaction presents the thermal pathway. The greatest NO production is observed from R8 (prompt pathway) with hydrogenation of HNO, while R17 (NO2 pathway) and R3 (thermal pathway) are the second and third greatest production reactions. Minor contributions to NO production are observed with direct oxidation of nitrogen radicals and hydroxyl reaction of HNO (produced in the prompt reaction pathway). The prompt pathway is observed to have a greater contribution to NOx formation as the unsaturated FAME components of the fuel create a greater number of radicals in the fuel-rich zones [28]. The greatest consumption reaction, R9, is commonly associated with fuel/exhaust reburn-reactions, directly influencing HCN and thus, NO production through the prompt pathway [50]. The subsequent two consumption reactions, R14 and R15, are oxidation reactions that form NO2. In Fig. 6a, the last two consumption reactions generate cyano compounds that affect the prompt pathway.

Fig. 6
figure 6

a Normalised contributions to production/consumption of NO, b normalised reaction sensitivity coefficients for NO production/consumption in biodiesel diffusion flame (CF1 case)

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The sensitivity analysis in Fig. 6b provides an overview of the reactions that influence the production/consumption of NO. The overarching observation is the prevalence of three key species: cyano compounds (HCN, HCNO), hydroxyl, and hydrocarbon radicals. The generation of cyano compounds and consumption of CH directly link to the prompt route through the reaction R4, which has the greatest production sensitivity in Fig. 6b [6, 11, 32]. It should be noted that CH radical generation is an indicator of low-temperature pre-combustion reactions. Biodiesel could be defined as low-temperature combustion as it displays negative temperature coefficient behaviour (NTC), a decreased reaction sensitivity across low to intermediate temperature ranges [51]. It can be observed that the consumption of OH through numerous reactions directly influences all reaction pathways, especially those of thermal and NO2 generation. Therefore, the overall results from Fig. 6 imply that the primary pathway for NO generation in the biodiesel flame is the prompt NO pathway followed by thermal and NO2 decomposition. The greater availability of OH and hydrocarbon radicals at the flame front with higher temperatures could explain the increase in NO production with an increase in carbon flow rate [52]. Engine simulation studies for diesel and biodiesel have shown that increased HCN suppressed the thermal pathway [53]. It has also been formulated that in-situ engine NOx could be greater with biodiesel due to a significantly greater prompt pathway contribution because the adiabatic flame temperature required for the thermal pathway could not be reached in the engine flamelet [54]. Further discussion on the loci of key reactions will be presented in Sect. 3.2.2.

3.1.3 Carbon monoxide formation

Like NOx, the peaks CO mass fraction of biodiesel diffusion flames are also obtained on the centreline of the flame. As presented in Fig. 7, it clearly shows that the peak CO mass fraction increases with the carbon flow rate, where CF0.6 has the lowest and CF1.8 has the highest CO mass fraction. The peak CO mass fraction differences between CF0.6, CF1, and CF1.4 are found to be 6%, while a smaller difference of 4.35% exists between CF1.4 and CF1.8. In contrast to the peak NOx position, the peak CO is located further upstream compared to the position of Tpeak, indicating that CO is primarily produced in the incomplete combustion region. With the increase in carbon flow rate, more CO is produced because more fuel is available; hence, the reaction becomes comparatively more incomplete due to the higher fuel–air ratio.

Fig. 7
figure 7

CO mass fractions along the centreline of biodiesel diffusion flames with various carbon flow rates

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Figure 8a presents the key reactions to the production and consumption of CO. The primary consumption reaction is R21 which is the oxidation of CO by hydroxyl radicals. CO production is predominantly produced by formyl group oxidation reactions (R23, R26) and soot precursors of C2H2 and C4H4 oxidation. While these reactions produce CO, the sensitivity analysis reveals less influence outside of R21 itself and other reactions producing/consuming hydroxyl groups (OH, HO2). Therefore, the primary route for CO is rate limited by the consumption/production of said hydroxyl groups. As the fuel fraction and Tpeak increase, the available pool of hydroxyl groups increases; thus, the rate of CO consumption becomes greater by hydroxyl attack in the primary oxidation reaction CO + OH = CO2 + H [51]. Besides that, the third body collision reaction (R23) and the increases in both the alkene (CnH2n) and formyl (HCO) group concentrations (R23, R25, R26) also result in greater CO production.

Fig. 8
figure 8

a Normalised contributions to production/consumption of CO, b normalised reaction sensitivity coefficients for CO production/consumption in biodiesel diffusion flame (CF1 case)

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3.2 Comparison of biodiesel, N-heptane, and iso-octane diffusion flames

3.2.1 Flame height and temperature profile

Figure 9 shows the temperature profiles of the diffusion flames of biodiesel, n-heptane, and iso-octane with their input parameters described in Table 3. It is noted that all simulations were carried out at the same carbon flow rate of 17.2 g/h to compare the flame height, flame temperature, and NOx and CO emissions from the flames of the three liquid hydrocarbon fuels. The position of the peak flame temperature along the centreline is utilised to determine the flame height. As shown in Fig. 9a, biodiesel flame has a longer and narrower shape compared to n-heptane and iso-octane diffusion flames, which can be seen in Fig. 9b, c, respectively. This is because biodiesel has a higher flame speed, and thus, it requires more carrier gas (N2) to carry the same amount of carbon flow rate [55]. From the axial temperature profiles in Fig. 10, the flame heights of biodiesel, n-heptane, and iso-octane are 10, 9, and 9.3 cm, respectively. The differences in flame height can be explained by the application of Roper’s analysis for the prediction of flame height with a circular fuel port [56]. The flame length is defined as \({L}_{f}={Q}_{f}/\left({D}_{if}{Y}_{F,\mathrm{stoic}}\right)\), where \({Q}_{f}\) is the initial volumetric flow rate, \({D}_{if}\) is the diffusion coefficient of fuel and oxidiser, and \({Y}_{F,\mathrm{stoic}}\) is the stoichiometric mass fraction of fuel. Since the carbon flow rates of all fuels are the same (equal to 17.2 g/h), \({Y}_{F,\mathrm{stoic}}\) of the fuels are constrained. However, due to the variance of \({Q}_{f}\) and \({D}_{if}\), the flame heights are slightly different. In the case of n-heptane and iso-octane, \({Q}_{f}\) and \({D}_{if}\) are similar; hence, the flame heights of these two fuels are similar.

Fig. 9
figure 9

Temperature contour of diffusion flames at the carbon flow rate of 17.2 g/h, a biodiesel, b n-heptane, c iso-octane

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Fig. 10
figure 10

Temperatures along the centreline of diffusion flames at the carbon flow rate of 17.2 g/h

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The positions and maximum flame temperatures of the three tested fuels are listed in Table 4. It is observed that the differences in the Tpeak values across all the fuel cases are relatively small. For instance, n-heptane is the highest with a Tpeak of 2319 K, followed by iso-octane with a Tpeak of 2305 K, and lastly, biodiesel has a Tpeak of 2299 K. The qualitative difference in Tpeak is similar to the 0-D adiabatic flame temperature, Ta calculated in Cantera [38], whereby the Ta = [2339.4, 2340.9, 2341.4] K for the flames of biodiesel, iso-octane, and n-heptane, respectively. The difference in Ta between the alkane and FAME fuels is primarily due to the reduction in reaction enthalpy in FAMEs. The ester functional group is bound with a carboxylic group and already oxidised. In addition to not increasing the heat of combustion, the CO2 created from this carboxylic group also reduces the sensible heat of the product mixture [57]. The degree of unsaturation of FAMEs also affects Ta in which fuels with greater double bonds have higher Ta than saturated FAMEs of an equivalent number of carbon atoms [28]. Alkanes with 6–7 carbon atoms are predicted to have a Ta ≈ 2275 K compared to saturated FAME’s with 16–18 carbon atoms (Ta ≈ 2250 K) [57]. The composition of palm biodiesel used in this study contains a mixture of several unsaturated FAMEs and could cause small differences in Ta and Tpeak.

Table 4 Summary of the peak temperature, NO, and NO2 mass fractions with their positions (r-radial, z-axial)
Full size table

It should be noted that the positions of the Tpeak of the iso-octane and n-heptane diffusion flames are not on the centreline, which is not for the case of the biodiesel flame. The peak flame temperature positions of iso-octane and n-heptane flames are located towards the nozzle at a radial distance of 0.6 cm. The positions of these Tpeak could also be observed as spikes along the centreline at the axial distance of 5.8 cm, as can be seen in Fig. 10. The differences in Tpeak could be due to the greater lower heating value of n-heptane (48.44 MJ) compared to iso-octane (44.65 MJ) and biodiesel (37.52 MJ). It could also be due to the setting nozzle temperature (550 K) as it is higher than the vaporisation temperatures of n-heptane and iso-octane (371.5 K and 372.4 K, respectively); hence, it could increase the burned gas temperature of the flame [58]. Nevertheless, the Tpeak values between fuels differ by such small percentages; hence, further chemical analyses are required to evaluate the influence of temperature on both NOx and CO emissions.

3.2.2 NOx formation

Figure 11 presents the NO mass fraction contours of the diffusion flames of the three fuels. Compared to the flame height shown in Fig. 9, the NO mass fraction contours show that the peak NO concentration is located further downstream of the flame; however, the shapes of the NO contour distribution are like those of the flame temperature. Like Tpeak, the peak NO mass fractions of n-heptane and iso-octane are not located along the centreline of the diffusion flames. This is due to the greater flame temperature at the sides, leading to a greater NO formation at those positions [49]. The peak NO and NO2 mass fractions of the three diffusion flames and their positions have been summarised in Table 4. It is found that the n-heptane diffusion flame produces more NO and NO2 than the other two fuels. For instance, at the same flow rate, n-heptane produces the greatest NO with 2.1% greater than biodiesel and 4.2% greater than iso-octane. Likewise, n-heptane produces 2.6% and 5.1% greater NO2 than biodiesel and iso-octane, respectively. Figure 12 shows the NO and NO2 mass fractions along the centreline of the flames. Although the biodiesel flame is narrower, the maximum NOx mass fractions at the centreline are observed for all three fuels at almost the same location.

Fig. 11
figure 11

NO mass fraction contour of diffusion flames at the carbon flow rate of 17.2 g/h, a biodiesel, b n-heptane, (c) iso-octane

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Fig. 12
figure 12

a NO and b NO2 mass fractions along the centreline of diffusion flames at the carbon flow rate of 17.2 g/h

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Figure 13a, b present the key reactions in the production and consumption of NO in n-heptane and iso-octane, respectively. Both fuels exhibit the same key production reactions, which are R3, R8, and R17. All these reactions have greater contributions to NO production in n-heptane than in iso-octane. It is noted that the prompt pathway (R8) is dominant in both fuels; however, n-heptane shows a greater contribution from the thermal pathway reaction (R3) than the NO2 mechanism (R17), while iso-octane shows the opposite behaviour, with R17 greater than R3. Reactions for both n-heptane and iso-octane are nearly identical, where R9 is the predominant reaction, followed by R10, R14, and R15.

Fig. 13
figure 13

Normalised contributions to production/consumption of NO, a n-heptane, b iso-octane; normalised reaction sensitivity coefficients for NO production/consumption in diffusion flame of c n-heptane, d iso-octane

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Although the reactions that contribute to the production/consumption of NO in n-heptane and iso-octane are quite similar, the main pathways of these two fuels are significantly different, as shown in Fig. 13c, d. The primary sensitivity reactions for n-heptane in Fig. 13c are predominant by hydroxyl and hydroperoxyl radicals which influence the thermal and NO2 pathways. Meanwhile, iso-octane (Fig. 13d) has the primary sensitivity contribution from iso-octyl radicals emanating from the initial oxidation of the fuel. This implies that both fuels have a lower contribution from the prompt mechanism than biodiesel (Fig. 6). Unlike biodiesel, where the prompt initiation reaction (R4) is important (Fig. 6b), NO generated from R8 for n-heptane and iso-octane play an intermediate role in NO consumption and reformation through other reactions, as shown in Fig. 13c, d. The difference in the pathways comes from the relatively greater complexity of the iso-octane model. In the model validation study [39], both fuels are observed to have similar ignition properties, but the difference in molecular structure renders the mechanisms and reaction pathways to be significantly different. While both fuels exhibit the cool flame and NTC behaviour, n-heptane exhibits shorter ignition delays and greater reduction in sensitivities at lower temperatures. The differences in the initial pyrolysis reactions of n-heptane and iso-octane could potentially cause this behaviour [59]. The iso-octane mechanism includes 8 H-abstraction reactions for C7H18 pyrolysis into different iso-octyl radicals while the n-heptane model only has one pyrolysis reaction nC7H16 =  > CH3 + C2H5 + nC3H7 + nC4H9 + nC5H11 + nC7H15 [39]. The lowered sensitivity at low ignition temperatures for n-heptane would factor into removing other pyrolysis reactions during reduction as those do not impact the combustion process. Whereas the contribution of iso-octyl radicals, specifically C-H β-scission of iso-octane to form β-iso-octyl radicals, is a rate-determining reaction for the overall combustion process of iso-octane [60, 61]. Likewise, the influence of iso-octyl radicals is also observed in the NOx reaction sensitivity in Fig. 13d.

3.2.3 Carbon monoxide formation

Figure 14 presents the CO mass fraction contours of the diffusion flames of the three fuels. Compared to the flame temperature contours (Fig. 9), it can be observed that CO forms further upstream of high-temperature regions. In addition, no bias is observed towards high-temperature regions indicating that CO is completely converted into CO2, which is one of the main by-products of the combustion of hydrocarbon fuels. Figure 15 presents the CO mass fractions along the centreline of the three diffusion flames. In contrast to the peak NOx of n-heptane and iso-octane, which are located at the radial edge of their flames, the peak CO mass fractions are observed along the centreline of the diffusion flame of the two fuels. Biodiesel is observed to have the greatest CO mass fraction, while iso-octane produces 0.4% greater CO than n-heptane.

Fig. 14
figure 14

CO mass fraction contours of diffusion flames at the carbon flow rate of 17.2 g/h, a biodiesel, b n-heptane, c iso-octane

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Fig. 15
figure 15

CO mass fractions along the centreline of diffusion flames at the carbon flow rate of 17.2 g/h

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Figure 16a, b present the production/consumption reactions of n-heptane and iso-octane, respectively. The primary consumption reaction is the same as observed for biodiesel in Fig. 8a, CO + OH = CO2 + H (R21). The peak location of CO for all fuels is below the peak temperature region of the flame shown in Fig. 9. As stated, OH is produced at the high-temperature region, and thus CO is consumed further downstream of this point primarily through R21. Unlike biodiesel in Fig. 8a, R24 has a greater production contribution in both n-heptane and iso-octane flames. The production reactions are generally the same nature as biodiesel, with the predominance of formyl group oxidation reactions (R23, R24) and soot precursor alkene (C2H2) oxidation (R25). The cyclopropyne oxidation reaction does not appear for biodiesel but makes a minor contribution for the other two fuels. Except for the iso-octyl radical reactions (Fig. 16d), the sensitivity analysis for n-heptane (Fig. 16c) and iso-octane (Fig. 16d) exhibits similar functional reactions as those of biodiesel (Fig. 8b). Of note is the increased sensitivities of OH + HO2 = O2 + H2O and HOCH2O decomposition which increase the pathways available for hydroxyl formation and thus, CO consumption.

Fig. 16
figure 16

Normalised contributions to production/consumption of CO, a n-heptane, b iso-octane; normalised reaction sensitivity coefficients for CO production/consumption in diffusion flame of c n-heptane, d iso-octane

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4 Conclusion

A numerical simulation is carried out to examine the concentrations of NOx and CO emissions of biodiesel, n-heptane, and iso-octane laminar diffusion flames. The carbon flow rate is varied to study the NOx and CO emissions from biodiesel, while emissions from the three fuels are compared at a fixed carbon flow rate of 17.2 g/h. Qualitative and quantitative analyses of the formations of NOx and CO are conducted for each fuel. Experimental study to determine the emissions of biodiesel diffusion flame could be the next step in this research. In summary, the primary outcomes of this study are as follows:

  • Both NOx and CO emissions of biodiesel diffusion flame increase with an increase in carbon flow rate.

  • NO in biodiesel is primarily produced through the prompt pathway with significant thermal and NO2 decomposition pathway contributions.

  • At the same carbon flow rate, biodiesel diffusion flame is longer and narrower compared to those of n-heptane and iso-octane flames. The peak flame temperature of n-heptane is the highest, followed by iso-octane and biodiesel.

  • Among the three fuels, the greatest NOx production is observed in n-heptane flame, predominantly through the thermal pathway, while iso-octane produces the least NOx.

  • The concentration of CO is proportional to the carbon number of the fuels, with the greatest generation from biodiesel, 3.2% greater than iso-octane and n-heptane. The oxidisation reaction of CO, CO + OH = CO2 + H primarily controls the CO mass fraction.