Three-Dimensional Simulations of Steady Perforated-Plate Stabilized

Jul 10, 2014 - velocity, hole−hole distance, and plate thermal conductivity on flame stability are examined. The flame stand-off distance increases ...
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Three-Dimensional Simulations of Steady Perforated-Plate Stabilized Propane−Air Premixed Flames E. V. Jithin, V. Ratna Kishore,* and Robin John Varghese Department of Mechanical Engineering, Amrita School of Engineering, Ettimadai Campus, Amrita Vishwa Vidyapeetham, Coimbatore 641112, India S Supporting Information *

ABSTRACT: A numerical investigation of steady laminar premixed propane−air flames is presented. A three-dimensional simulation has been performed to examine the impact of operating conditions on steady-state characteristics of a perforated burner flame. A numerical simulation has been carried out using a reduced propane−air reaction mechanism having 30 species and 192 reactions. The results are validated against the one-dimensional flat-flame result obtained using PREMIX. Effects of the equivalence ratio, inlet velocity, hole−hole distance, and plate thermal conductivity on flame stability are examined. The flame stand-off distance increases with the increase in the inlet velocity. As the equivalence ratio increases, the heat flux to the plate increases as the flame moves closer to the plate. When the plate is adiabatic, the conical flame rests on the plate. The flame stand-off distance increases as the plate thermal conductivity is increased. The flame moves downstream of the plate as the distance between the adjacent holes is increased. Parmentier et al.3 presented the modeling and simulation of the lamella burner. Two-dimensional (2D) numerical simulations were carried out to find the optimal combustion conditions for minimum COx and NOx emissions. Lammers et al.6 conducted a numerical study on flashback of laminar premixed flames in ceramic-foam surface burners. They calculated the range of burning velocities, which can lead to flashback. Guahk et al.9 experimentally investigated the flame-intrinsic

1. INTRODUCTION Flame stabilization is one of the most important criteria in the design of gas burners. Premixed flames formed in burners undergo stabilization problems, such as quenching, flashback, and blowoff. The dependence of laminar premixed flames upon physical processes, such as cooling by the burner wall, mixing of reactants with surrounding unburnt gases, flame stretch, flame curvature, etc., makes stabilization a complex phenomenon. A laminar premixed flame primarily occurs in small-scale burners, such as household burners, which use liquefied petroleum gas (LPG) as fuel. LPG is the most widely used conventional burner fuel in Asian countries.1 LPG is termed as a clean source of energy, owing to its complete burning and lesser CO2, NOx, and SOx emissions. One of the major constituents of LPG is propane (C3H8). Therefore, it is helpful to examine the flame stabilization characteristics of propane to predict the LPG flame characteristics. Perforated-plate burners are commonly used for industrial and household applications. Conical-shaped laminar premixed flames are formed downstream of the perforated burner plate in perforated-plate burners. Steady and dynamic properties of such premixed flames have been studied by several researchers. The properties studied include flame− acoustic wave and flame−wall interactions,2 steady flame stability,3,4 and flashback and lift-off.5−7 The effect of flame−wall and flame−acoustic wave interactions in combustion dynamics of premixed flames was analyzed by Ducruix et al.2 Experimental and numerical studies on the stabilization of the tube and slit burner were conducted by Mallens and de Goey.5 They investigated the critical velocity gradient, an important design criterion for avoiding flashback in burners, using a one-step model of methane−air combustion. Mallens et al.8 extended these studies for analyzing the M- and V-shaped flames formed on a double-slit burner. They concluded that the single-step reaction mechanism is insufficient for exact prediction of the flame structure. © 2014 American Chemical Society

Figure 1. Schematic diagram showing the computational domain. Received: September 21, 2013 Revised: July 9, 2014 Published: July 10, 2014 5415

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On the basis of the literature survey conducted, it was seen that most of the previous studies involved 2D numerical simulations of flames using a single-step or highly reduced chemical kinetic reaction mechanism. However, stabilization on a perforated plate is actually three-dimensional (3D) because of geometry and, thus, requires a 3D model to simulate more realistically. The majority of the flame stabilization analysis has been focused on methane−air mixtures. In the current work, 3D numerical simulations of steady laminar premixed propane−air flames stabilized downstream of a perforated-plate burner has been performed. The effect of operating parameters, such as mean inlet velocity and equivalence ratio of the mixture, on the steady flame characteristics has been investigated. The dependence of perforated-plate thermal properties and design upon the characteristics of stabilized flames has been analyzed. Simulations are performed at various plate thermal conductivities and various hole−hole distances for the perforated plate.

2. NUMERICAL FORMULATION 2.1. Numerical Model. A 3D model for laminar premixed flames is solved using commercial computational fluid dynamics (CFD) software Fluent. The governing equations in Cartesian coordinates are solved. They are given below.

∇(ρν )⃗ = 0

(1)

∇(ρνν⃗ )⃗ = −∇p + ∇(τ ̿ ) + ρg ⃗

(2)

The stress tensor is related to the strain rate by τ ̿ = μ[(∇ν⃗ + ∇ν⃗ ) − (2/3)δ∇ν⃗I)] T

∇(ν (⃗ ρE + p)) = ∇(k T∇T −

∑ hiji ) + Sh i

Figure 2. Computational grid used in the present work.

∇(ρvY ⃗ i ) = −∇ji ⃗ + R i

(3) (4)

where I is the unit tensor, kT is the thermal conductivity, ji = −ρDi,m∇Yi is the diffusion flux of species i, μ is the molecular viscosity, and Yi is the mass fraction of each species i. The velocity correction has been neglected in eq 4 because it is small. The multi-component diffusion has been found to be prominent only in H2−air mixtures when compared to methane−air mixtures10,11 and can be neglected. In the present work, propane fuel mixtures are studied, which are heavier than methane, and hence, multi-component diffusion can be neglected. A finite-rate laminar species model along with a stiff chemistry solver is employed for solving volumetric reactions. The heat conduction equation within the burner plate is solved to include the effect of the heat exchange between the gas mixture and perforated plate.12

Kelvin−Helmholtz (K−H) instability using inverted conical flames. They concluded that, in addition to buoyancy-driven K−H instability, the flame-intrinsic K−H instability causes flame flickering. Two-dimensional numerical analyses of laminar premixed perforated-plate-stabilized methane−air flame were performed by Altay et al.4 They examined the impact of various operating conditions and perforated-plate design conditions on flame stabilizations, using a reduced chemical kinetic mechanism for methane−air combustion. Kedia and Ghoniem7 investigated flame stabilization and the variant conditions leading to blowoff in methane−air combustion with the help of a detailed chemical kinetics mechanism. They concluded that flame-based curvature has a strong dependence upon blowoff.

ρs Cs

∂T = ∇(k∇T ) ∂t

(5)

Figure 3. Heat flux to the top surface of the plate for ϕ = 0.8, k = 115 W m−1 K−1, and Uin = 2 m/s. 5416

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Figure 4. Heat flux along horizontal and radial directions on the top surface of the plate at ϕ = 0.8, Uin = 2 m/s, k = 115 W m−1 K−1, and P = 2 mm. The chemical kinetics mechanism employed in the present work is a reduced propane−air reaction mechanism having 30 species and 192 reactions based on the Qin et al.13 reaction mechanism. The chemical reaction mechanism is imported in CHEMKIN format along with thermodynamic and transport property databases (see the Supporting Information). Mixture-averaged formulation is used for calculation of thermodynamic and transport properties in the present simulations. The parabolic inlet velocity is given as a user-defined function. Species mole fractions are specified at the inlet. Cold-flow simulation is carried out up to a reasonable convergence limit. The fuel−oxidizer mixture is ignited by patching a region near the burner exit with a high temperature (2400 K). The convergence limit is set to 10−6 for all of the equations. The 3D geometrical model was created and meshed using commercial meshing software, GAMBIT. The computational domain, specifying the boundary conditions, is shown in Figure 1. A burner plate has a thickness of 10 mm and symmetrically distributed holes of 1 mm in diameter, and the length of the domain is 25 mm. The domain is meshed with 243 000 cells. A computational grid used in the present work is shown in Figure 2. 2.2. Boundary Conditions. (1) Velocity inlet: the air−fuel mixture enters from the bottom side of the hole. The flow velocity at the inlet is based on laminar fully developed flow assumption. (2) The inlet temperature of the mixture is atmospheric temperature, Tu = 300 K. The heat conduction between the perforated plate and the gas mixture has been considered. (3) A pressure is prescribed at the exit to be ambient pressure, P = Pamb = 101 325 Pa. (4) Symmetry boundary conditions are imposed on all of the vertical sides of the domain.

a higher value along the radial line compared to that along the horizontal line. This happens because of the influence of adjacent flames. The local heat flux on the top of the plate obtained in 2D simulation is also shown in the same figure. The figure shows that there is a huge difference in heat flux for the case of 2D and 3D simulations. The heat of reaction contours along with velocity vectors at two different planes are shown in Figure 5, viz., a vertical symmetry plane

3. NUMERICAL SOLUTION 3.1. Relevance of 3D Simulation. Generally, the flame stabilizes downstream of a burner by transferring heat to the burner plate. Figure 3 shows the contours of heat flux to the burner plate obtained for a propane−air mixture at ϕ = 0.8 and Uin = 2 m/s [the heat flux contour for the entire plate (see Figure 3) is obtained by mirroring the simulation result]. The heat capacity of the plate, Cs, is 871 J kg−1 K−1, and the thermal conductivity of the plate, k, is 115 W m−1 K−1. The result shows that the maximum heat transfer occurs at the central portion of the plate, where the four adjacent flames meet. A 2D axisymmetric model is insufficient to predict the properties where four adjacent flames meet. Because maximum heat is transferred to the plate in this region, it is important to perform a 3D simulation to resolve the region of maximum heat flux to the plate. Figure 4 shows the local heat flux calculated along a horizontal line and a radial line (45° line passing through the center) on the top surface of the plate. From the graph, it is clearly understood that heat flux shows

Figure 5. Heat of reaction contours along with velocity vectors (a) along the symmetric plane in the x direction, (b) along the vertical plane passing through the radial line, and (c) for 2D simulation. along the x direction (plane a) and a vertical plane passing through the radial line (plane b). Flame anchors at a shorter distance from the burner plate in plane b compared to that in plane a, which is due to a smaller stagnant zone. This enables higher convective heat transfer to the plate for the former. The recirculation zone in plane a is more compared to 5417

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Figure 6. Comparison of 3D simulation results to PREMIX.

Figure 7. Comparison of the temperature and OH mole fraction profiles of coarse, first- and second-level adaptations. that in plane b. Figure 5c shows the heat of reaction along with velocity vectors for 2D simulation. The heat of reaction obtained in 2D is different from that in 3D for the same bounadry conditions. These comparisons yield that the axisymmetric approximation for the perforated plate burner is inadequate and urges the need for 3D numerical computations. 3.2. Validation of the Numerical Model. To validate the reacting module of the numerical model, 3D simulation has been performed on a porous plug burner to stabilize a flat flame. The porous plug was a cube with sides of 1 mm. The domain was extended transverse up to 6 mm. The porosity of the porous plug is 0.57. Symmetry boundary conditions were given on all four sides. The temperature and OH and CO mole fractions along a line in the z direction were compared to onedimensional (1D) PREMIX code results. In both of the cases, the same propane−air reaction mechanism was used. Figure 6a shows the flame temperature, and Figure 6b shows OH and CO mole fractions obtained in both of the cases. From Figure 6a, it can be seen that the maximum and minimum temperatures obtained in both of the cases agree well. The gradients of temperature profiles of both 3D and 1D simulations in the flame region are also in complete agreement. OH and CO mole fractions obtained in 3D simulation compare well to that obtained in 1D PREMIX simulation, as seen in Figure 6b. The gradients of these species mole fractions also follow the same trend as the flame temperature profiles. Panel a and b of Figure 6 exhibit the accuracy of the reacting module used in the present work. 3.3. Grid Independence. The coarse initial grid consists of 243 000 cells. The initial grid sizes along x and y directions are 0.02 mm, while the

Figure 8. Flame heights and stand-off distances at different propane air− mixture inlet velocities, for ϕ = 0.8, k = 115 W m−1 K−1, and P = 2 mm. cell size along the z direction is 0.04 mm. Once the flame was stabilized, the flame region in the domain is adapted on the basis of the gradient of the net reaction rate of C3H8. After the first level adaptation, the total number of cells is above 4 × 105 for all of the cases. To test the grid convergence numerical simulation with the average inlet velocity of 5418

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Figure 9. Contours of the heat of reaction for Uin = 0.5, 1.5, 2.5, and 3.5 m/s, at ϕ = 0.8, k = 115 W m−1 K−1, and P = 2 mm. 3.5 m/s and ϕ = 0.8 was again refined in a manner similar to that stated above. The number of cells for this second level of adaptation was about 2 × 105. The temperature and OH mole fraction profiles in the flame region of the different adapted results are compared in Figure 7. The coarse, fine, and very fine meshes have 10, 20, and 40 cells in the flame region, respectively. From the temperature profile shown in Figure 7, it is clear that the first- and second-level adaptations are in good agreement. The OH mole fraction profiles also follow a similar trend. Hence, all of the simulation results presented in the present work used the mesh that was obtained after the first level of adaptation.

Table 1. Flame Consumption Speeds along the Center Line, Sc,0, and along the Edge of the Domain, Sc,k, for the Case of ϕ = 0.8, k = 115 W m−1 K−1, and P = 2 mm

4. RESULTS AND DISCUSSION 4.1. Effect of the Mean Inlet Velocity. Simulations were performed with inlet velocities varying from 0.5 to 3.5 m/s while keeping all other parameters constant, with ϕ = 0.8 and k =115 W m−1 K−1. Figure 9 shows the heat of reaction and velocity vectors along a symmetric plane at Uin = 0.5, 1.5, 2.5, and 3.5 m/s. The symmetric plane shown in the figure is a small region near the flame. The variation in the flame height with the inlet velocity is clearly visible in this figure. Flame heights are numerically calculated as the vertical distance from the top surface of the burner plate to the location of the peak value of the heat of reaction along the vertical line passing through the origin (center line). The distance between the flame base and plate top surface is known as the flame stand-off distance. The flame base is located at the point where T ≈ 0.8Tad,7 along the vertical line through the points (x = 0.001, y = 0, z = 0) and (x = 0.001, y = 0, z = 0.025). Figure 8 shows the calculated values of flame heights and stand-off distances as a function of the mean inlet velocity. It

inlet velocity (m/s)

Sc,0 (cm/s)

Sc,k (cm/s)

0.5 1 1.5 2 2.5 3 3.5

18.3 28.2 32.6 43.7 45.3 59.0 60.3

15.3 21.8 23.4 23.5 24.6 22.6 24.0

can be seen that the flame height increases with an increase in the inlet velocity, and this is because the flame cone angle decreases with the increase in the inlet velocity. The flame is negatively curved at the tip and positively curved at the base. As the inlet velocity increases, the flame base curvature and the flame tip curvature increase. The flame becomes stabilized at higher velocities as a result of the increase in the flame base curvature. The velocity vectors in Figure 9 show a recirculation zone near the burner plate. The flame base becomes stabilized above this recirculation zone. As the inlet velocity increases, the recirculation zone grows and the flame stabilizes at a higher distance from the plate. Figure 10 shows the OH mole fraction contours for various inlet velocities. OH is one of the important intermediate species, which plays an important role in propane combustion. The peak value of the OH mole fraction is obtained near the flame tip. The Lewis number based on fuel diffusivity for the C3H8−air mixture at ϕ = 0.8 is 1.82.14 The OH mole fraction is minimum at the 5419

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Figure 10. Contours of OH mole fractions for Uin = 0.5, 1.5, 2.5, and 3 m/s, at ϕ = 0.8, k = 115 W m−1 K−1, and P = 2 mm.

Figure 11. Local surface heat flux along the radial line on the top surface of the plate at different propane air−mixture inlet velocities, for ϕ = 0.8, k = 115 W m−1 K−1, and P = 2 mm.

Figure 12. Local surface heat flux along the radial line on the plate top surface at different equivalence ratios of the propane−air mixture for Uin = 2 m/s, k = 115 W m−1 K−1, and P = 2 mm.

flame base because of the positive stretch and the loss of heat to the plate. The OH mole fraction is peaking at the flame tip because of the negative flame stretch rate, which strengthens the flame with Le > 1.14 The diffusion thickness of OH is found to be smaller at the flame tip than the flame base because of the simultaneous stretch rate and preferential diffusion effect. The flame consumption speed (Sc) is calculated along the center line (x = 0, y = 0) and along the edge of the domain ... (x = 0.001, y = 0.001) using the relation Sc = ((∫ ∞ −∞q /Cp dy)/ (ρu(Tb − Tu))).4

Table 1 shows the flame consumption speeds along the center line, Sc,0, and along the edge of the domain, Sc,k, for different inlet velocities, and it can be seen that Sc,0 > Sc,k. Sc,0 increases with the increase in the inlet velocity. This is mainly due to the increase in the curvature stretch and preferential diffusion effect. In Figure 11, the local surface heat flux to the plate along the radial line on the top surface of the plate, for different mean inlet velocities, is shown. Because the flame stabilizes at a higher distance from the plate, the local surface heat flux to the plate 5420

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symmetric plane of the domain. The conical flame having a negatively curved tip and positively curved base was obtained downstream of the burner plate. Observing the velocity vectors, a recirculation zone can be seen near the top surface of the burner plate. The flame base is stabilized just above the recirculation zone. For ϕ = 0.8, a strong recirculation zone is formed, which causes a higher flame stand-off distance. As the equivalence ratio is increased, the recirculation zone decreases and, therefore, the flame base comes closer to the burner plate. The local surface heat flux along the radial line on the top surface of the plate, for various equivalence ratios, is shown in Figure 12. As expected, the heat flux to the plate decreases when the flame stand-off distance increases. The flame height decreases with the increase in the equivalence ratio, because the laminar burning velocity increases as ϕ increases, for the case of lean mixtures (ϕ < 1). Figure 13 shows the flame heights at different equivalence ratios. The flame heights at ϕ = 1 and 1.2 are almost similar, and this is because the laminar burning velocities for these equivalence ratios are almost the same. 4.3. Effect of the Distance between the Adjacent Holes. To investigate the effect of the perforated-plate design parameter on stabilized flame characteristics, simulations were performed by varying the distance between the adjacent holes (P). Three different spacing were used as 1.5, 2, and 3 mm, keeping all other parameters constant (ϕ = 0.8, Uin = 2 m/s, and k = 115 W m−1 K−1). In Figure 15, the heat of reaction contours along with velocity vectors on a symmetric plane are shown for three different hole− hole distances. When P = 1.5 mm, the flame stabilizes near the plate. The flame stand-off distance increases as P increases, as a result of the increase in the recirculation zone, as shown in Figure 15. The conical flame rests just above the recirculation zone. Figure 17 show the heat flux contours at different hole−hole distances. The heat flux

decreases with the increase in the inlet velocity. Still, a higher heat flux at Uin = 3.5 m/s is obtained in comparison to that at Uin = 2.5 m/s. This may be due to the fact that the rate of convective heat transfer in the recirculation zone increases with Uin. 4.2. Effect of the Equivalence Ratio. Flame stability is studied for lean and rich mixtures by performing simulations at various equivalence ratios, ϕ = 0.8, 0.9, 1, and 1.2, with Uin = 2 m/s and k = 115 W m−1 K−1. Figure 14 shows the heat of reaction contours and velocity vectors at different equivalence ratios along a

Figure 13. Flame heights at different equivalence ratios of the propane− air mixture for Uin = 2 m/s, k = 115 W m−1 K−1, and P = 2 mm.

Figure 14. Heat of reaction contours and velocity vectors for ϕ = 0.8, 0.9, 1, and 1.2, for Uin = 2 m/s, k = 115 W m−1 K−1, and P = 2 mm. 5421

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Figure 15. Contours of the heat of reaction and velocity vectors for P = 1.5, 2, and 3 mm, at Uin = 2 m/s, ϕ = 0.8, and k = 115 W m−1 K−1.

Figure 16. Local surface heat flux from the gas to the top surface of the plate along the radial line for pitch = 1.5, 2, and 3 mm, for ϕ = 0.8, Uin = 2 m/s, and k = 115 W m−1 K−1.

contours on the top surface look similar, but the magnitude of the heat fluxes at the center decreases with increase in pitch, which can be explained on the basis of results shown in Figure 16. The heat flux to the top surface of the plate along the radial line is shown in Figure 16, for different hole−hole distances. Heat flux to the plate is at a maximum when P = 1.5 mm, because the flame base is near the plate in this case. When P = 3 mm, the heat flux to the plate is at a minimum, because the flame stabilizes at a higher distance from the plate. In Table 2, the total heat-transfer rate calculated on the top surface of the plate for different hole−hole distances is shown. Even though the local surface heat flux to the plate decreases with the

Figure 17. Local surface heat flux from the gas to the top surface of the plate for P = 1.5, 2, and 3 mm, for ϕ = 0.8, Uin = 2 m/s, and k = 115 W m−1 K−1.

increase in P, the overall heat-transfer rate to the top surface of the burner increases. This contributes to the increase in the flame 5422

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Table 2. Heat-Transfer Rate to the Top Surface of the Plate at Different Hole−Hole Distances, for ϕ = 0.8, Uin = 2 m/s, and k = 115 W m−1 K−1 distance between the adjacent holes (mm) heat-transfer rate (W)

1.5 0.024

2 0.050

3 0.119

Table 3. Flame Consumption Speeds along the Center Line, Sc,0, and along the Edge of the Domain, Sc,k, for Different Hole−Hole Distances distance between adjacent holes (mm)

Sc,0 (cm/s)

Sc,k (cm/s)

1.5 2 3

64.9 43.7 32.9

42.4 23.6 4.4

4.4. Effect of the Thermal Conductivity of the Plate. Simulations were performed to understand the effect of the thermal conductivity, viz., k = 0 (adiabatic), 0.1, 1.5, and 115 W m−1 K−1 (keeping other parameters constant at ϕ = 0.8, Uin = 2 m/s, and P = 2 mm). The heat of reaction contours on a symmetric plane at various thermal conductivities is shown in Figure 19. In the adiabatic plate (k = 0), the flame rests on the top surface of the plate. The velocity vector makes it clear that there is no recirculation zone developed when k = 0, which verifies that there will be no standoff distance. Also, heat is not transferred from gas to the plate at this condition. When heat is allowed to transfer from gas to plate, the flame becomes positively curved at the base. When the thermal conductivity of the plate is increased, the flame stand-off distance increases because of the heat loss to the plate, but upon further increase from k = 10 W m−1 K−1, the increase in the stand-off distance is negligible. The flame base

Figure 18. Flame height and stand-off distances for P = 1.5, 2, and 3 mm, at Uin = 2 m/s, ϕ = 0.8, and k = 115 W m−1 K−1.

stand-off distance with the increase in P. The overall heat-transfer rate considered here is the integral quantity (∫ dQ dA), i.e., the rate of heat transferred to the unit area of the top surface of the burner. The calculated values of flame heights and flame stand-off distances are shown in Figure 18. As explained earlier, the flame height and stand-off distance increase with the increase in the hole−hole distance. Table 3 shows the flame consumption speeds along the center line, Sc,0, and along the edge of the domain, Sc,k, for different hole−hole distances. The value of Sc,k decreases as P increases and reaches a very low value at P = 3 mm because of the increase in the stretch rate.

Figure 19. Heat of reaction contours for k = 0, 0.1, 1.5, and 115 W m−1 K−1 at ϕ = 0.8 and Uin = 2 m/s. 5423

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The results show that the flame moves downstream of the plate with an increase in inlet velocity. The flame height and stand-off distance increase with the increase in the inlet velocity. Flame height variation is clearly identified in heat of reaction contours. The flame stand-off distance is visible in OH mole fraction contours. For the propane flame, the flame height and stand-off distance decrease with the increase in the equivalence ratio for lean mixtures, reach a minimum value near the stoichiometric ratio, and then increase with the increase in the equivalence ratio for rich mixtures. The local surface heat flux to the plate increases as the flame stand-off distance decreases. As the distance between adjacent holes is increased, the flame height and stand-off distance increase. Because of this increase in stand-off distance with the increase in the distance between adjacent holes, the local surface heat flux to the burner plate decreases.

curvature increases with the increase in thermal conductivity of the plate. The thickness of the flame reduces when the plate is made conductive, which indicates that a stronger flame is obtained when the plate is adiabatic. In Figure 20, the heat flux

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ASSOCIATED CONTENT

S Supporting Information *

Chemical reaction mechanisms imported in CHEMKIN format along with thermodynamic and transport properties. This material is available free of charge via the Internet at http:// pubs.acs.org.

Figure 20. Local surface heat flux from the gas to the top surface of the plate for k = 0.1, 1.5, and 115 W m−1 K−1.

■

along the radial line on the plate top surface for different values of k is shown. The heat flux decreases as the thermal conductivity increases. At k = 0.1 W m−1 K−1, there is a mismatch in the heat flux curve. Because it is nearly adiabatic conditions, thermal resistance is high in this case, as a result of which there is no temperature gradient. In Figure 21, the top surface temperature

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Muthukumar, P.; Shyamkumar, P. Development of novel porous radiant burners for LPG cooking applications. Fuel 2013, 112, 562−566. (2) Ducruix, S.; Schuller, T.; Durox, D.; Candel, S. Combustion dynamics and instabilities: Elementary coupling and driving mechanisms. J. Propul. Power 2003, 19 (5), 722−734. (3) Parmentier, S.; Braack, M.; Riedel, U.; Warnatz, J. Modeling of combustion in a lamella burner. Combust. Sci. Technol. 2003, 175 (1), 185−206. (4) Altay, H. M.; Kedia, K. S.; Speth, R. L.; Ghoniem, A. F. Twodimensional simulations of steady perforated-plate stabilized premixed flames. Combust. Theory Modell. 2010, 14 (1), 125−154. (5) Mallens, R.; De Goey, L. Flash-back of laminar premixed methane/ air flames on slit and tube burners. Combust. Sci. Technol. 1998, 136 (1− 6), 41−54. (6) Lammers, F.; De Goey, L. A numerical study of flash back of laminar premixed flames in ceramic-foam surface burners. Combust. Flame 2003, 133 (1), 47−61. (7) Kedia, K. S.; Ghoniem, A. F. Mechanisms of stabilization and blowoff of a premixed flame downstream of a heat-conducting perforated plate. Combust. Flame 2012, 159 (3), 1055−1069. (8) Mallens, R.; Loijenga, B.; De Goey, L.; Sonnemansb, P. Numerical and experimental study of lean M- and V-shaped flames. Combust. Sci. Technol. 1997, 122 (1−6), 331−344. (9) Guahk, Y. T.; Lee, D. K.; Oh, K. C.; Shin, H. D. Flame-intrinsic Kelvin−Helmholtz instability of flickering premixed flames. Energy Fuels 2009, 23 (8), 3875−3884. (10) Bongers, H.; De Goey, L. P. H. The effect of simplified transport modeling on the burning velocity of laminar premixed flames. Combust. Sci. Technol. 2003, 175 (10), 1915−1928. (11) Ern, A.; Giovangigli, V. Thermal diffusion effects in hydrogen−air and methane−air flames. Combust. Theory Modell. 1998, 2 (4), 349− 372.

Figure 21. Perforated-plate top surface temperatures for k = 1.5 and 115 W m−1 K−1.

of the plate along the radial line is shown. The plate top surface temperature decreases with the increase in the thermal conductivity as a result of the lower heat flux to the plate.

5. CONCLUSION In this paper, the characteristic of propane−air flames has been presented on the basis of the 3D numerical simulation of a perforated-plate burner. A reduced propane reaction mechanism having 30 species and 192 reactions was used for the simulation. The 3D result is validated against the results of PREMIX. Propane burner flame analysis is performed for various inlet velocities, equivalence ratios, and hole−hole distances. 5424

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(12) ANSYS, Inc. Fluent 6.3.26 User’s Guide; ANSYS, Inc.: Canonsburg, PA, 2005. (13) Qin, Z.; Lissianski, V. V.; Yang, H.; Gardiner, W. C.; Davis, S. G.; Wang, H. Combustion chemistry of propane: A case study of detailed reaction mechanism optimization. Proc. Combust. Inst. 2000, 28 (2), 1663−1669. (14) Mizomoto, M.; Yoshida, H. Effects of Lewis number on the burning intensity of Bunsen flames. Combust. Flame 1987, 70 (1), 47− 60.

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