Effect of Pressure Oscillations on Flashback Characteristics in a

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Effect of Pressure Oscillations on Flashback Characteristics in a Turbulent Channel Flow Tomoaki Kitano, Takafumi Tsuji, Ryoichi Kurose,* and Satoru Komori Department of Mechanical Engineering and Science, and Advanced Research Institute of Fluid Science and Engineering, Kyoto University, Kyoto daigaku-Katsura, Nishikyo-ku, Kyoto 615-8540, Japan ABSTRACT: A flashback phenomenon is reproduced by a direct numerical simulation (DNS) of a premixed hydrogen−air flame in a turbulent channel flow, and effects of the pressure oscillation, is caused by a virtual combustion instability on the flashback characteristics, are investigated. In addition, the interaction between the flashback flame structure and the turbulent flow structure is examined in detail. For the hydrogen−air reaction, a chemical reaction model, which considers 9 chemical species and 20 reactions, is employed. The results show that the pressure oscillation strongly affects the flashback characteristics, such as the flashback speed and heat flux on the wall, and is at risk for increasing the flashback speed, because the acceleration of the flashback speed by the pressure oscillation is greater than the deceleration of it. Independent of the pressure oscillation, the turbulent eddies passing through the flame tend to be suppressed and vanish by the acceleration of the streamwise flow caused by thermal expansion. However, other turbulent eddies are generated again in a form of longitudinal eddies behind the flame only at the cusps and center of the channel where the upper and lower flames meet, because of the strong fluid shear owing to the thermal expansion.

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INTRODUCTION At present, fossil fuels are burned in combustors, such as powergenerating turbines and airplane engines. In using these combustors, however, the drain of the fossil fuel and the environmental influence caused by emissions of carbon dioxide (CO2) and nitrogen oxide (NOx) are concerned. Therefore, the research and development of the hydrogen (H2)-fueled combustors, which aim to have a lower environmental impact and higher energy efficiency, have been carried out in recent years.1,2 Hydrogen is mainly produced by the steam reforming method, the partial oxidation method, and the self-heating reforming method from natural gas or coal,3 but in later years, alternative methods using biomass instead of natural gas and coal have been investigated4 and paid attention to as fuel solving energy and environmental problems. Hydrogen combustion is stable across a wide fuel concentration range and is easily ignited because of its wide flammable range and high burning velocity. These characteristics, however, give hydrogen a risk of flashback, which is a transient upstream propagation of a flame, and therefore make it difficult to develop the hydrogen combustor. Flashback has been studied by experiments and numerical simulations.5,6,7,8,9 Mayer et al.6 performed experiments of flashback in a swirl burner using CH4, CH4/H2 mixtures, and pure H2, and they investigated the conditions, such as fuel components and equivalence ratios, in which the flashback occurs. Eichler et al.7 also performed experiments of flashback in wall boundary layers and investigated the flame structures. However, it is difficult to measure a number of physical characteristics simultaneously, and detailed mechanisms of flashback, such as the relationship between flame and turbulence, have not been sufficiently investigated. Similarly, the computational cost of numerical simulations considering detailed chemical reactions are very high, and therefore, the underlying mechanism is still not well examined numerically either. Recently, Gruber et al.8 © XXXX American Chemical Society

performed a three-dimensional direct numerical simulation (DNS) of the flashback. They discussed the flame structure in detail and investigated the effect of ambient pressure on flashback speed. In addition, they proposed a mean flame shape model using the DNS results.9 However, because the ambient pressure was static, the effect of the pressure oscillation often caused by combustion instability,10,11 which sometime induces the flashback, was not considered. Also, they did not discuss the interaction of the flashback flame structure with the turbulent flow structure in the channel flow very much. In this study, the effect of pressure oscillation, which is caused by a virtual combustion instability on the flashback characteristics of a premixed hydrogen−air flame in a turbulent channel flow, is investigated by DNS. In addition, the detailed interaction of the flashback flame structure with the turbulent flow structure is examined in detail.

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NUMERICAL SIMULATION

The governing equations are conservation equations of mass, momentum, enthalpy, and chemical species. The governing equations are following conservation equations of mass, momentum, enthalpy, and chemical species

∂ρ + ∇(ρu) = 0 ∂t

(1)

∂ρu + ∇(ρuu) = −∇P + ∇σ ∂t

(2)

Received: July 24, 2015 Revised: September 18, 2015

A

DOI: 10.1021/acs.energyfuels.5b01687 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 1. Computational grid and conditions.

∂ρh + ∇(ρhu) = ∇[ρDh(∇h − ∂t

performed for three cases: case 1, without pressure oscillation using fine grids; case 2, without pressure oscillation using coarse grids; and case 3, with pressure oscillation (given by a sine wave from the outlet side) using coarse grids. The intensity of the pressure oscillation is 1.5 kPa (1.5% of the average pressure). This magnitude is chosen based on that caused by combustion instability in a real combustor,15 and the sine wave is given as a fundamental wave, which is generally used in previous studies of combustion instability.16 The grid resolutions of the flashback region for case 1 are 50 μm in the x, y, and z directions (Δx+, Δy+, and Δz+ = 0.6), while those for cases 2 and 3 are 100 μm in the x and z directions (Δx+ and Δz+ = 1.2) and 50−100 μm from the wall to the center of the channel in the y direction (Δy+ = 0.6−1.2). The wall-unit lengths in the flashback region in the x, y, and z directions are approximately 1240 × 240 × 360 for all cases. For the turbulence generation region, the grid resolution in the x direction is 700 μm (Δx+ = 8.4) for all cases. The total number of grid cells for case 1 is approximately 0.4 billion, and that for cases 2 and 3 is approximately 0.1 billion. The time resolution for case 1 is approximately 4.5 × 10−8, and that for cases 2 and 3 is approximately 9 × 10−8 s. The chemical reactions are calculated using the multitimescale (MTS) method17 in every time step with a minimum time resolution of 1 × 10−9 s for all cases. The spatial derivatives of the momentum equation are approximated by a fourth-order accurate central difference scheme. For the convection terms of energy and mass fractions of chemical species, a quadratic upstream interpolation for convective kinematics (QUICK) scheme is employed. A second-order accurate central difference scheme is used for the other terms. The fractional-step method for compressible flows is used as the computational algorithm,10−19,20 and a third-order explicit Runge−Kutta method is used for the timeadvancement computation of the convection terms. The simulations are performed using the thermal flow analysis code, an in-house code “FK3”.18,19 The CPU time for case 1 is about 5.3 million h (520 h on the wall-clock time) on the K computer (Fujitsu SPARC64TM VIIIfx processor, 10 240 cores).

∑ (hk∇Yk)) − ρ ∑ hkYkVk] k

k

(3)

+ σ ∇u

∂ρYk + ∇(ρYku) = −∇(ρYkVk) + Scomb, k ∂t

(4)

where ρ is the density, u is the velocity, P is the pressure, h is the enthalpy, Yk is the mass fraction of species k, Dh is the diffusion coefficient of enthalpy, σ is the stress tensor, Vk is the diffusion velocity of species k, and Scomb,k is the source term as a result of combustion, which is calculated by a detailed chemical reaction model proposed by Miller and Bowman, which considers 9 chemical species and 20 reactions.12 Figure 1a shows the computational grid. The domain consists of two regions of “channel flow region” and “buffer region”. The flashback phenomenon is reproduced in the “channel flow region”, and the “buffer region” is introduced to remove effects of outlet boundary conditions on the flashback phenomenon. As the inlet boundary of the “channel flow region” and outlet boundary condition of the “buffer region”, the Navier−Stokes characteristic boundary condition (NSCBC)13 is used. Figure 1b shows the computational conditions of the “channel flow region”. To reproduce a realistic flashback flame in a fully developed wall-bounded turbulent flow, two computations using two computational domains are combined in this region. In the upstream computational domain for one computation, a fully developed wallbounded turbulent flow is generated by imposing a periodic boundary condition in the x direction. In the downstream computational domain for the other computation, on the other hand, the flashback phenomenon in the fully developed wall-bounded turbulent flow is simulated by giving the outflow characteristics of the upstream computational domain as the inflow characteristics. The no-slip isothermal (750 K) boundary condition is applied in the y direction, and the periodic boundary condition is applied in the z direction. The flame is ignited at the y−z plane at the downstream end of the flashback region by imposing an artificial reaction 100 ms after the initiation of turbulent production. The Reynolds number based on the channel width and the mean streamwise velocity is approximately 3500, and that based on the channel half width and the friction velocity is approximately 120. The initial gas temperature, pressure, and equivalence ratio are 750 K, 0.1 MPa, and 1.5, respectively. The laminar burning velocity in this condition is estimated to be 14.0 m/s.14 All of these flow conditions are set to close to those of the previous work by Gruber et al.8 Table 1 shows the computational conditions. In this study, computations are

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RESULTS AND DISCUSSION Effect of the Pressure Oscillation. Figure 2 shows the instantaneous distributions of isosurfaces of temperature at 1200 K and second invariant of velocity gradient tensor and streamwise flow velocity on the x−z plane at y+ = 2.5, Uwall, for case 2. It is observed that the flame surface is wrinkled by the streak structure in the wall turbulent flow, and flame bulge and cusp have formed. This feature of the flashback was also observed in the previous study.8 It was confirmed that the approaching value of the flashback speed for case 2 (coarse grids) agreed well with those for case 1 (fine grids) and the previous study8 (see Figure 3 described below). Therefore, the discussion below is conducted with the results for cases 2 and 3 (coarse grids) to save the computational cost. Here, the flashback speed is defined by the propagation speed of the flame at

Table 1. Computational Conditions case

number of computational grids

pressure oscillation

1 2 3

0.4 billion 0.1 billion 0.1 billion

1.5%, 1000 Hz B


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y+ = 2.5. This value is calculated by detecting the spanwise (z direction) mean position of the isosurface of the gas temperature (1200 K) at y+ = 2.5 in each time step. Figure 3 shows the time variations of pressure, P, central streamwise flow velocity, UC, and flashback speed evaluated at y+ = 2.5, SFB, for case 3, mean flashback speeds, SF̅ B, for cases 1−3, and heat release rate, Q, and mean heat release rate, Q̅ , for cases 2 and 3. In this figure, the time variation of the flame speed at an upper location of y+ = 20, Sy+20, for case 3 is also shown. Here, the flame speed is defined by the propagation speed of the flame at y+ = 20. This value is calculated by detecting the spanwise (z direction) mean position of the isosurface of the gas temperature (1200 K) at y+ = 20 in each time step. The heat release rate is the global value of the whole domain. Mean values are calculated by taking an average over 1 cycle of pressure oscillation (1.0 ms) at each time step (e.g., the

Figure 2. Instantaneous distributions of isosurfaces of the temperature at 1200 K and second invariant of velocity gradient tensor and streamwise flow velocity on the x−z plane at y+ = 2.5, Uwall (t = 1.75 ms, case 2).

Figure 3. Time variations of pressure, P, central streamwise flow velocity, UC, and flashback speed, SFB, for case 3, mean flashback speeds, S̅FB, for cases 1−3, and heat release rate, Q, and mean heat release rate, Q̅ , for cases 2 and 3.

Figure 4. Time variation of instantaneous temperature distribution on the x−y plane at z = 15 mm at t = t1−t12 in Figure 3 (case 3). C


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Energy & Fuels value at t = 1.0 ms is calculated by taking the average from t = 0.5−1.5 ms, and the value at t = 1.1 ms is calculated by taking the average from t = 0.6−1.6 ms). P and UC are the values at the center of the inlet plane of the flashback region. It is found that the pressure oscillation generates the oscillations of UC, SFB, and Q and tends to increase SF̅ B and Q̅ . This increase in S̅FB is due to the fact that, in the region close to the wall at y+ = 2.5, SFB is easily accelerated by the rise in the pressure but

largely unaffected by the subsequent fall in the pressure. This phenomenon is explained as follows. In the flashback deceleration period (t = t1−t6), SFB is clearly higher than Sy+20. This is due to the fact that the increase of Uwall caused by the drop in the pressure is smaller than that of UC. This is because the change of the velocity near the wall is suppressed by the viscous friction drag, and therefore, SFB in the flashback deceleration period is unaffected by UC. In the flashback acceleration period (t = t7−t12), in contrast, the difference between SFB and Sy+20 is smaller than that in the flashback deceleration period (t = t1−t6), although Sy+20 is a little higher than SFB. This is because the flame close to the wall is accelerated by the heat diffused from the flame much more accelerated in the upper region. The above analysis of the deceleration period is supported by Figure 4, which shows the time variation of instantaneous temperature distribution on the x−y plane. As shown by red circle markers, the flame top away from the wall at t = t1−t2 comes to touch the wall at t = t3−t4 as the pressure decreases. Figure 5 shows the comparison of the time variation of instantaneous heat flux, q, on the x−y pane at z = 15 mm at t = 1.00, 1.25, and 1.50 ms between cases 2 and 3. The heat flux is defined as

q = −λ Figure 5. Time variation of instantaneous heat flux, q, on the x−y plane at z = 15 mm at t = 1.00, 1.25, and 1.50 ms (cases 2 and 3).

∂T ∂y

wall

(5)

where λ is the thermal conductivity. The temperature gradient at the wall is obtained using the values of the cells at the wall and their immediate neighbors in the vertical (y) direction. Independent of the time, q dramatically increases toward the flame front, where it reaches the maximum value and then gradually decreases toward the downstream end. Furthermore, in comparison to case 2, the maximum value of q at the flame front tends to markedly oscillate in time for case 3. To clarify the interaction between q and pressure oscillations, the time variation of the heat flux averaged along the flame front indicating the peak heat flux, qflame, for cases 2 and 3 is compared in Figure 6. In the figure, the mean heat flux at the flame front, qf̅ lame, calculated by the same method with mean flashback speed in Figure 3 is also shown. It is evident that qflame for case 3 is strongly affected by the pressure oscillation, but qf̅ lame is almost the same as that of case 2. The comparison of Figures 3 and 6 shows that the maximum value of qflame coincides with maximums of pressure and flashback speed, SFB (see at t = 1.5 ms in Figure 3 and t = t10 in Figure 4). This is considered to be due to the fact that, at this time, the flame temperature close

Figure 6. Time variations of heat flux at the flame front, qflame, and mean heat flux at the flame front, qf̅ lame (cases 2 and 3).

Figure 7. Instantaneous distributions of isosurfaces of the temperature at 1200 K and second invariant of velocity gradient tensor in side and bottom views (t = 1.75 ms, case 2). D


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Energy & Fuels to the wall is increased by the heat diffused from the flame in the upper region, as described above. Interaction of the Flashback Flame Structure with the Turbulent Flow Structure. Figure 7 shows the instantaneous distributions of isosurfaces of the temperature at 1200 K and secondary invariant of velocity gradient tensor in side and

bottom views at t = 1.75 ms for case 2. Here, in the bottom view, the isosurfaces of the temperature close to the wall are removed to show more clearly the secondary invariant of the velocity gradient tensor. The instantaneous distributions of streamlines (black line) and isolines of temperature at 1200 K

Figure 8. Instantaneous distributions of streamlines (black line) and isolines of the temperature at 1200 K (red line) (t = 1.75 ms, case 2).

Figure 9. Distribution of magnitude of the turbulent production term (the third term on the right-hand side in eq 6) on the x−y plane at z = 21 mm (t = 1.75 ms, case 2). Black lines indicate the isolines of the averaged temperature at 1200 K.

Figure 11. Distributions of Favre-averaged velocities in the x, y, and z directions on the x−y plane at z = 21 mm (t = 1.75 ms, case 2). Black lines indicate the isolines of the averaged temperature at 1200 K.

Figure 10. Distributions of magnitudes of each term in the turbulent production term on the x−y plane at z = 21 mm (t = 1.75 ms, case 2). Black lines indicate the isolines of the averaged temperature at 1200 K. E


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Energy & Fuels (red line) on the x−y plane at z = 21 mm, the y−z plane at x = 26 mm, and the x−z plane at y = 4.5 mm at the same time as Figure 7 are shown in Figure 8. The x−y plane is located at the top of a bulge. In front of the flame surfaces in the unburned region, the turbulent eddies and streamlines are observed to be bent along the flame surfaces. This is attributed to the fact that the thermal expansion in the flame induces a flow toward the center of the channel. Furthermore, it is found that, whereas most of the turbulent eddies are suppressed and vanished behind the flame as reported in previous studies for the turbulent premixed flame,21,22 other turbulent eddies are generated again in a form of longitudinal eddies behind the flame only at the cusps and center of the channel where the upper and lower flames meet. To clarify the mechanism, the

following transport equation for the turbulent kinetic energy is introduced:23 ∂u ̃ ∂p 2 ∂ρ ̅ K̃ ∂ 1 ∂ = − ρ ̅ uj̃ K̃ − uk″ − ρ ̅ u″j u͠ k″ k − ρ ̅ u″j u͠ k″ ∂xj ∂t ∂xj ∂xk 2 ∂xj + uk″ −

∂σkj ∂xj

(6)

∼

where and indicate the Reynolds- and Favre-averaged values, respectively, and ″ indicates the variation from the Favreaveraged value. K is the turbulent kinetic energy given by K=

∑ j

1 2 uj″̃ 2

(7)

The third term on the right-hand side ∂u ̃ ∂u ̃ ∂v ̃ ∂w̃ − ρ ̅ v″u͠ ″ − ρ ̅ w″͠ u″ k ̇ = −ρ ̅ u″j u͠ k″ k =−ρ ̅ u″u͠ ″ ∂xj ∂x ∂x ∂x − ρ ̅ u″͠v″

∂v ̃ ∂w̃ ∂u ̃ − ρ ̅ v″v͠ ″ − ρ ̅ w″͠ v″ ∂y ∂y ∂y

͠ ″ ∂u ̃ − ρ ̅ v″w͠ ″ ∂v ̃ − ρ ̅ w″w ͠ ″ ∂w̃ − ρ ̅ u″w ∂z ∂z ∂z (8)

Figure 12. Distribution of magnitude of the turbulent production term (the third term on the right-hand side in eq 6) on the x−z plane at y = 4.5 mm (t = 1.75 ms, case 2). Black lines indicate the isolines of the averaged temperature at 1200 K.

represents the turbulent production term. Figure 9 shows the distribution of magnitude of the turbulent production term on the x−y plane at z = 21 mm, and Figure 10

Figure 13. Distributions of magnitudes of each term in the turbulent production terms on the x−z plane at y = 4.5 mm (t = 1.75 ms, case 2). Black lines indicate the isolines of the averaged temperature at 1200 K. F


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indicates that the combustion instability, which often generates large pressure oscillations in combustors, increases the risk of flashback. (2) Independent of the pressure oscillation, the turbulent eddies passing through the flame tend to be suppressed and vanish as a result of the acceleration of the streamwise flow caused by thermal expansion. However, other turbulent eddies are generated again in the form of longitudinal eddies behind the flame only at the cusps and center of the channel where the upper and lower flames meet, because of the strong fluid shear owing to the thermal expansion.

shows the distributions of magnitudes of each term in the turbulent production term on the same x−y plane. Here, the black lines indicate the isolines of the averaged temperature at 1200 K. The Favre- and Reynolds-averaged terms are calculated by taking the time average for 0.2 ms and space average for 1 mm in spanwise (z) direction at each position. The turbulent production is negative in the wide region behind the flame but is locally positive at the center of the channel where the upper and lower flames meet (see circle A in Figure 9). These negative and positive regions appear to correspond, respectively, to the regions where the turbulent eddies are suppressed and generated in Figure 7a. Furthermore, it is clear that the negative and positive turbulent productions are attributed to the ∂u ∂u variations of the −ρ ̅ u″u͠ ″ ∂x ̃ and −ρ ̅ u″͠v″ ∂y ̃ in k,̇ respectively.

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AUTHOR INFORMATION

Corresponding Author

*Telephone/Fax: +81-75-383-3610. E-mail: kurose@mech. kyoto-u.ac.jp.

Figure 11, which shows the distributions of Favre-averaged velocities in the x, y, and z directions, suggests that the acceleration of the streamwise velocity owing to the thermal expansion is extremely remarkable. Therefore, it is considered that the negative and positive values for k̇ are attributed to the remarkable acceleration of the streamwise velocity (i.e., the increase in ∂ũ/∂x) and the strong fluid shear on the x−y plane caused by this accelerated streamwise velocity (i.e., the increase in the absolute value of −ρ ̅ u″͠v″), respectively. On the other hand, the generation of the turbulent eddies behind the cusps are similarly explained by the distributions of magnitudes of the turbulent production term and each term in the turbulent production term on the x−z plane at y = 4.5 mm in Figures 12 and 13. Here, the black lines indicate the isolines of the averaged temperature at 1200 K. The comparison to Figure 7b illustrates that the locations of the generated turbulent eddies behind the cusps roughly ∂u correspond to those of the high values of the −ρ ̅ u″͠v″ ∂y ̃ in k̇

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the “Strategic Programs for Innovative Research (SPIRE)Field No. 4: Industrial Innovations” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) using the K computer at RIKEN Advanced Institute for Computational Science (Project hp130018).

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REFERENCES

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(see circle B in Figure 13), suggesting that, similar to the turbulent eddies generated behind the flame at the center of the channel where the upper and lower flames meet, the turbulent eddies behind the flame at the cusps are generated by the strong fluid shear on the x−y plane caused by the thermal expansion. In summary, the suppression and regeneration of turbulent eddies are due to the acceleration of the streamwise flow and the strong fluid shear owing to the thermal expansion, respectively. This interaction of the flashback flame structure with the turbulent flow structure was also observed for the case with the pressure oscillation (case 3).

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CONCLUSION In this study, a flashback phenomenon was reproduced by DNS of a premixed hydrogen−air flame in a turbulent channel flow and effects of pressure oscillation, which was caused by a virtual combustion instability on the flashback characteristics, were investigated. In addition, the interaction between the flashback flame structure and the turbulent flow structure was examined in detail. For the hydrogen−air reaction, a chemical reaction model, which considered 9 chemical species and 20 reactions, was employed. The main results obtained in this study can be summarized as follows: (1) The pressure oscillation strongly affects the flashback characteristics, such as the flashback speed and heat transfer on the wall, and increases the mean flashback speed because the acceleration of the flashback speed as a result of the pressure oscillation is greater than its deceleration. This fact G


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Energy & Fuels (19) Kitano, T.; Nishio, J.; Kurose, R.; Komori, S. Fuel 2014, 136, 219−225. (20) Moureau, V.; Bérat, C.; Pitsch, H. J. Comput. Phys. 2007, 226, 1256−1270. (21) Tanahashi, M.; Fujimura, M.; Miyauchi, T. Proc. Combust. Inst. 2000, 28, 529−535. (22) Yenerdag, B.; Fukushima, N.; Shimura, M.; Tanahashi, M.; Miyauchi, T. Proc. Combust. Inst. 2015, 35, 1277−1285. (23) Swaminathan, N.; Bray, K. N. C. Turbulent Premixed Flames; Cambridge University Press: Cambridge, U.K., 2011.

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Effect of Pressure Oscillations on Flashback Characteristics in a

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