Interactions of hydrogen flames with walls: Influence of wall temperature, pressure, equivalence ratio, and diluents

International Journal of Hydrogen Energy 32 (2007) 2094 – 2104 www.elsevier.com/locate/ijhydene

Interactions of hydrogen flames with walls: Influence of wall temperature, pressure, equivalence ratio, and diluents R. Owston ∗ , V. Magi1 , J. Abraham School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA Received 6 June 2006; received in revised form 24 July 2006; accepted 24 July 2006 Available online 2 October 2006

Abstract The thermal and chemical effects of one-dimensional, premixed hydrogen flames quenching against a single surface are studied numerically using a detailed chemical mechanism. The results for stoichiometric H2 .O2 flames impinging on a 750 K inert wall agree qualitatively with prior published results. Other wall boundary conditions studied include an adiabatic wall and isothermal walls with temperatures ranging from 298 to 1200 K. Chemical pathway analysis of the detailed hydrogen mechanism reveals the growing importance of radical recombination reactions near the inert walls for increasing wall temperature. Implementation of a H, O, and OH radical sink at the surface of a 750 K isothermal wall results in significantly lower heat generation near the surface. Investigations of various gas properties include changes to equivalence ratio (0.7–2.0), chamber pressure (1 and 2 bar), and inert gas (N2 ) addition. 䉷 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Flame–wall interaction; Head-on impingement; Quenching; Single surface

1. Introduction Near-wall flame impingement has been the focus of numerous studies due to interest in determining quenching distances in boundary layers, improving efficiency in engines, and reducing emissions from combustion applications. Information on quenching distances can be quite important since elevated temperatures near the walls of a combustion chamber degrade components, decreasing their lifespan. Heat transfer has a significant impact on the efficiency of an engine, lowering the usable work when heat transfer rates to the chamber walls are high. Finally, the effect of wall temperature on unburned hydrocarbon emissions from the quench layer has been the topic of several investigations [1–3]. Flame–wall interaction studies employing premixed hydrocarbon fuels have explored the near-wall laminar quenching effects on heat transfer and product concentrations for different

∗ Corresponding author. Tel.: +1 765 494 1505; fax: +1 765 494 0530.

E-mail address: [email protected] (R. Owston). 1 Permanent address: Department of Environmental Engineering and

Physics, University of Basilicata, Potenza 85100, Italy.

parameters. Such parameters include wall temperature (Tw ), equivalence ratio (), chamber pressure, and surface reactivity [1–13]. Popp [4] found using direct numerical simulation (DNS) that the peak heat release rate of propane/air flames occurs directly at the surface for isothermal wall temperatures above 400 K. Sotton et al. [5] determined that the wall heat flux increases non-linearly with increasing chamber pressure for methane flames. Hasse et al. [1], using iso-octane flames, and Owston [3], using n-heptane flames, have numerically observed the increase of wall heat flux for increasing surface temperature (300 K < Tw < 600 K) seen also by Popp et al. [6,7] using propane flames. The experimental trends in heat flux observed by Ezekoye et al. [8] and Connelly et al. [9,10], employing methane and propane flames, disagree with the numerical trends above. Popp [4] theorized that this was due in part to heat losses in the experiments other than those to the wall. Additionally, he showed that failing to include surface chemistry effects in numerical studies could produce significant errors when wall temperatures are high. The fact that only a few experimental datasets currently exist for comparison to numerical work further complicates matters. The participation of the surface in determining the outcome of flame–wall quenching is interesting and has attracted prior

0360-3199/$ - see front matter 䉷 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2006.07.030

R. Owston et al. / International Journal of Hydrogen Energy 32 (2007) 2094 – 2104

attention. The addition of a H2 –O2 surface mechanism has been shown to decrease the heat release rate adjacent to a wall for propane/air flames [4]. Popp suggested this might be due to a decline in the rates of the highly exothermic recombination reactions occurring there. With the implementation of a surface mechanism, these reactions must compete for the radicals which are being depleted by the wall surface chemistry. This work focuses on hydrogen rather than hydrocarbon flame impingement as most quenching studies do. Hydrogen is currently recognized as a promising fuel for future mainstream engine and turbine operation. Emission benefits, using optimized operating conditions, include elimination of soot, unburned hydrocarbons, and greenhouse gases. Additionally, the use of lean H2 –air mixtures has been shown to control the release of nitrogen oxides (NOx ). Aside from pollutant reductions, hydrogen is also recognized as an important fuel because of its ability to be derived from various sources, many of which are renewable. This will become increasingly important as fossil fuel supplies become exhausted. While the economic and environmental benefits to using hydrogen fuel have already been stated, the computational modeling of hydrogen flames presents unique challenges due to their fast flame propagation speeds and small flame thicknesses. These properties require simulations with very high resolution, both temporally and spatially. Only a limited number of quenching studies have been completed employing hydrogen fuel. In the work of Dabireau et al. [11] a one-dimensional, premixed stoichiometric H2 –O2 flame impinged on a 750 K isothermal, inert wall. Heat release rates peaked directly at the wall, similar to the propane flames interacting with hot walls reported by Popp [4]. The effect of surface chemistry on H2 –air flames quenched in a stagnation-point configuration was investigated by Aghalayam et al. [12] and Vlachos [13], who found that the addition of surface chemistry (acting as a radical sink) served to inhibit ignition. In this work, heat transfer and kinetic properties of onedimensional hydrogen flames impinging on a wall in a head-on configuration are studied. First, due to a lack of experimental results, the validation case is compared to the computational results of Dabireau et al. [11], which models the same physical problem. Prior works in the literature reviewed above, investigating the influence of hydrogen flame interaction with a single surface, have focused on a limited set of parameters. In practical applications, these parameters can take a wide range of values. It is, therefore, interesting to determine if the behavior of the interacting flame changes as parameters are changed. For example, when the wall temperature is increased, how does the heat release rate and heat flux behavior change? This same question is asked about changes in pressure, equivalence ratio, diluent addition, and surface chemistry incorporation. Such information could be useful in determining which materials should be used for combustion chamber walls and what level of cooling, if any, needs to be provided to the engine in order to achieve optimum efficiency. Moreover, knowing the effects of variations in equivalence ratio has obvious applications with regards to determining the optimum values needed for efficiency and

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reduction in emissions. Since most combustion applications use air to react with fuel, as opposed to pure oxygen, the study of diluent addition is relevant. Additionally, this topic may also relate to the behavior of flames in the presence of exhaust gas recirculation. Finally, the effect of adding a radical sink at the wall is especially relevant to near-wall flame behavior at elevated surface temperature or with a highly reactive wall material. In the next section, the computational setup is discussed. Results and discussion follow in Section 3. The paper closes in Section 4 with summary and conclusions. 2. Computational setup A multi-dimensional code, REC, employed for prior studies in a variety of configurations [3,14–17] is modified to the one-dimensional configuration shown in Fig. 1. The boundary at the right is open and the flame propagates towards the wall on the left. Mixture-averaged diffusion coefficients are used for the species diffusion model. The flame is identified by the point where the temperature profile reaches 1500 K. This definition has been successfully employed in past quenching studies [1–3,18]. Modifications to the code were made to allow initial profile inputs for temperature, pressure, and species mole fractions from the program PREMIX, which is part of the CHEMKIN program [19,20]. The flame profile was initiated sufficiently far from the wall such that the flame achieved a quasi-steady state before interacting with the wall. Initial velocities are set to zero within the domain. Two zones of meshing are used in the domain. In the first zone the mesh is uniform with cell sizes of 2 m. The grid of the second zone is stretched in the post-flame region to allow for faster computation. The time step was allowed to vary between 1.0 × 10−9 and 1.0 × 10−5 ms. Flame speeds in the region of free propagation were compared to values computed with PREMIX to assure adequate resolution of the flame. The PREMIX and REC values were found to agree to within 5% for all the mixture compositions presented in this work. Ambient temperature of the unburned gas mixture remains at 750 K for all test cases, which is physically similar to chamber temperatures experienced by spark-ignition engines. Atmospheric pressure conditions are employed. The detailed nine-species, 20-step chemical kinetic mechanism used in the computations is shown in Table 1. However, a mechanism developed by Miller et al. [22] was also employed in order to compare results for the stoichiometric H2 –O2 flame interacting with a 750 K

2 μm - 182 μm cells Zone 2

2 μm cells Zone 1 0.15 cm

Fig. 1. Computational domain setup.

2.0 cm

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R. Owston et al. / International Journal of Hydrogen Energy 32 (2007) 2094 – 2104

Table 1 Chemical kinetic scheme [21] Reaction

A



1. H + O2 + M = HO2 + M H2 O enhanced by 1.860E + 01 H2 enhanced by 2.860E + 00 2. H + H + M = H2 + M 3. H + H + H2 = H2 + H2 4. H + H + H2 O = H2 + H2 O 5. H + OH + M = H2 O + M H2 O enhanced by 5.000E + 00 6. H + O + M = OH + M H2 O enhanced by 5.000E + 00 7. O + O + M = O2 + M 8. H2 O2 + M = OH + OH + M 9. H2 + O2 = 2OH 10. OH + H2 = H2 O + H 11. O + OH = O2 + H 12. O + H2 = OH + H 13. OH + HO2 = H2 O + O2 14. H + HO2 = 2OH 15. O + HO2 = O2 + OH 16. 2OH = O + H2 O 17. H + HO2 = H2 + O2 18. HO2 + HO2 = H2 O2 + O2 19. H2 O2 + H = HO2 + H2 20. H2 O2 + OH = H2 O + HO2

3.61E + 17

−0.7

Table 2 Adiabatic flame temperatures and free flame-speeds for the indicated mixture conditions

Ea

Fuel/oxidizer



Pressure (bar)

Tb (K)a

SL (cm/s)b

H2 /O2 H2 /O2 H2 /O2 H2 /O2 H2 /Air H2 /Air

1.0 1.0 0.7 2.0 1.0 0.4

1 2 1 1 1 1

3133 3232 3090 2945 2599 1815

3300 3750 3200 3100 1250 640

0.0

1.00E + 18 9.20E + 16 6.00E + 19 1.60E + 22

−1.0 −0.6 −1.2 −2.0

0.0 0.0 0.0 0.0

6.20E + 16

−0.6

0.0

1.89E + 13 1.30E + 17 1.70E + 13 1.17E + 09 3.61E + 14 5.06E + 04 7.50E + 12 1.40E + 14 1.40E + 13 6.00E + 08 1.25E + 13 2.00E + 12 1.60E + 12 1.00E + 13

0.0 0.0 0.0 1.3 −0.5 2.7 0.0 0.0 0.0 1.3 0.0 0.0 0.0 0.0

−1788.0 45500.0 47780.0 3626.0 0.0 6290.0 0.0 1073.0 1073.0 0.0 0.0 0.0 3800.0 1800.0

Forward reaction rate coefficients are calculated as kf = AT  exp(−Ea /RT ); units are A: mole cm s K and E: cal/mol.

a Computed b Calculated

by PREMIX. from REC simulations.

at the unburned gas temperature, Tu . SL is the freely propagating flame speed. Note that flame speeds approximated from the REC simulations are shown in Table 2, along with the adiabatic flame temperature of the mixture. Non-dimensional time is taken to be t t∗ = , (3) tF where t is the physical time from the beginning of the computation and tF is the characteristic residence time in the flame, given by tF =

 . SL

(4)

inert surface with the results presented by Dabireau et al. [11]. A comparison of these results is discussed in the next section.

Non-dimensionalization of temperature is accomplished through the following equation:

3. Results and discussion

T∗ =

3.1. Validation study The comparison study discussed here simulates the same physical problem as that studied by Dabireau et al. [11], wherein a one-dimensional, premixed stoichiometric H2 –O2 flame impinges against a 750 K isothermal, inert surface. For the purpose of this comparison, the same nondimensional variables employed by Dabireau et al. are used here. These are the non-dimensional distance x ∗ , time t ∗ , temperature T ∗ , and heat release rate  ˙ ∗. The non-dimensional distance from the wall is given by x∗ =

x , 

(1)

where x is the physical distance from the wall and  is the characteristic flame thickness, reported to be 12 m by Dabireau et al. The value of  has been analytically computed and confirmed for this work using the following equation: u = ,  u cp S L

(2)

where u is the conductivity of the unburned gas, u is the density of the unburned gas, and cp is the specific heat of the gas. Here cp is assumed to have a constant value, computed

T − Tu . Tb − T u

(5)

Here Tu is the unburned gas temperature, set to 750 K, and Tb is the burned gas temperature, taken to be the adiabatic flame temperature. As indicated in Table 2, the adiabatic flame temperature of this mixture has been computed by PREMIX to be 3133 K. Finally, the heat release rate is non-dimensionalized through the following equation:  ˙∗ =

 ˙

, (ql◦ /)

(6)

where  ˙ represents the spatially varying heat release rate, and ql◦ is the laminar flame power, given by ql◦ = u YF,u SL H .

(7)

YF,u and H are the mass fraction of fuel in the unburned mixture and the heat produced by the flame, respectively. The product of these is computed as [7] YF,u H = cp (T2 − T1 ) = cp (Tb − Tu ).

(8)

Transient profiles of reduced temperature are provided in Fig. 2. Good qualitative agreement is found between Fig. 2 and the results presented by Dabireau et al. In both cases the flame is initially (t ∗ = 8.3/t = 0.003 ms and t ∗ = 25.0/t = 0.009 ms) allowed to freely propagate towards the wall. As the flame

R. Owston et al. / International Journal of Hydrogen Energy 32 (2007) 2094 – 2104

begins to feel the influence of the wall (t ∗ = 41.7/t = 0.015 ms and t ∗ =66.7/t =0.024 ms) its thickness decreases significantly and the temperature gradient at the wall gets steeper. When the flame is thinnest the flame ceases to propagate forward and is quenched. After quenching, the flame (as denoted by the 1500 K point) begins to retreat from the wall with a corresponding decrease in wall temperature gradient. Mass fraction profiles of H2 , O2 , HO2 , H2 O2 , O, H, and OH have been examined [3] and found to possess trends in agreement with those of Dabireau et al. [11]. Fig. 3 displays the transient profiles of the non-dimensional heat release rate. As in the work of Dabireau et al., the heat release peaks directly at the wall shortly before quenching. Fig. 3(b) provides a closer look at the region of the domain adjoining the isothermal surface. Good qualitative agreement is seen between these results and those provided by the comparison study. Recall from Section 2 that Dabireau et al. used an 18-step H2 –O2 mechanism, whereas in this work the 20step reaction mechanism in Table 1 is employed. However, it was verified that running the validation case simulation using the 18-step mechanism yielded the same qualitative results as those with the 20-step mechanism [3].

Reduced Temperature

1

t*=125.0 t*=66.7

0.8

t*=8.3 t*=25.0

0.6 t*=41.7 0.4 0.2 0 0

50

100 x*

150

200

Fig. 2. Non-dimensional transient temperature profiles for validation of H2 –O2 case with 750 K isothermal wall.

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The maximum wall heat flux and heat release rate of this work are found to occur at t ∗ = 44.4 (t = 0.016 ms). Note that the numerical time values can be different based on the initial starting location of the flame. For the purposes of this work all flames were initialized at the same location from the wall. Reaction rates fall near the wall after t ∗ = 44.4 (t = 0.016 ms), with corresponding decreases in heat flux and the heat release rate. At approximately t ∗ = 47.8 (t = 0.0172 ms) the flame “quenches”, halting its progress towards the wall. Based on the definition that the flame is located at 1500 K, it is seen that the flame recedes from the wall after quenching. It is of interest to study the reaction pathways, which contribute to the maximum heat release rates at the wall. Thus, a breakdown of the various reactions at t ∗ = 44.4 (t = 0.016 ms) in the cell adjacent to the wall (x ∗ = 0.083/x = 1 m) is provided. The top five heat contributing reactions are R1, R14, R5, R4, and R11, listed in descending order of heat generation and shown in their direction of progression in Table 1. R5, R4, and R11 are clearly chain-terminating, while R1 is chain-propagating. R14 may be considered to be chainbranching since two OH radicals are produced by the reaction of H and the relatively stable HO2 radical. R1, R5, and R4 are ternary recombination reactions, which have zero activation energy required for progression. Therefore, because their reaction rates are affected less by temperature, it is expected that they would become more significant in the cooler region near the wall. The heat release rate chemistry at x ∗ = 0.25 (x = 3 m) shows the same five reactions have the largest contribution to the overall heat release rate. However, the magnitudes of the heat release rates associated with the reactions are reduced by about 43% from those of the near-wall cell (x ∗ = 0.083/x = 1 m). The chemical analysis of the free-flame region, as opposed to the near-wall area, is now discussed. Recall that the peak value of the heat release rate in the free flame was much smaller than that obtained at the wall just before quenching. At t ∗ = 25.0 (t = 0.009 ms) the flame has a peak heat release rate

0.3

0.25 t*=41.7

t*=41.7

t*=66.7 Heat Release*

Heat Release*

t*=25.0 t*=41.7 t*=66.7 t*=125.0

0.25

0.2 0.15 0.1 t*=25.0

t*=8.3

0.05

0.2 0.15 t*=66.7 0.1

t*=125.0

0.05

t*=125.0 0

0 20

(a)

40

60 x*

80

2

100

(b)

t*=25.0

4

6

8

10

x*

Fig. 3. Non-dimensional transient heat release rate profiles for validation of H2 –O2 flames near a 750 K isothermal wall: (a) 0 < x ∗ < 100, (b) 0 < x ∗ < 10.

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R. Owston et al. / International Journal of Hydrogen Energy 32 (2007) 2094 – 2104 7000

7000 6000

5000

Flame Speed (cm/s)

Flame Speed (cm/s)

6000

4000 3000 2000 1000 0

4000 3000 2000 1000 0

0

0.005

0.01

0.015

0.02

0.025

0.03

0

0.005

0.01

0.015

0.02

0.025

0.03

-1000

-1000

(a)

5000

Time (ms)

(b)

Time (ms)

Fig. 4. Flame speed: (a) adiabatic and (b) isothermal walls.

of about  ˙ ∗ = 0.0484 ( ˙ = 1.5 × 1011 W/m3 ) at x ∗ = 21.2(x = 0.0254 cm) from the wall, while at t ∗ = 44.4 (t = 0.016 ms) the ˙ = 1.8 × 1012 W/m3 ) in the heat release rate was  ˙ ∗ = 0.582 ( cell adjacent to the wall. This order of magnitude difference can be explained by comparing the elementary reactions of importance in the free-flame region with those x ∗ = 0.083 (x = 1 m) from the wall, where the peak heat release rate occurs. A breakdown of the total heat release rate in the free flame by each contributing reaction reveals that the three main heat-producing reactions are R10, R1, and R14, listed in descending order. Note that they progress in the forward direction as shown in Table 1. R1 and R14 were also shown to be major heat producers at the wall during quenching. However, unlike the heat release at the wall, the free flame shows R11, progressing in the reverse direction, to be a heat absorbing reaction of significant magnitude. This reaction is the same one (progressing forwards) that was the fifth largest heat producer at the wall. Whereas recombination reactions that consume radicals are favored by the low-temperature chemistry near the wall, chainbranching reactions (like R11 operating in reverse) are more prevalent in the high-temperature free-flame zone.

3.2. Effects of wall temperature Simulations involving variations in isothermal wall temperature, as well as a computation using an adiabatic wall, are presented in this section. First, the differences in the interaction of a stoichiometric H2 –O2 flame with an adiabatic versus a 750 K isothermal wall are reviewed. The temperature gradient at an adiabatic wall is zero at all times by definition. Thus, the temperature of the wall rises as the flame approaches this boundary. It is important to note, therefore, that in using a definition of flame position of 1500 K the flame impinging on the adiabatic wall never quenches but interacts directly with the wall. The near-wall flame speed behaves quite differently for the two cases. Fig. 4 shows the flame speed development as the

two boundary conditions begin to affect the behavior of their respective flames. At the adiabatic wall in Fig. 4(a) the flame increases its speed as it draws closer to the surface. Since the gas ahead of the flame is being heated due to the presence of the wall this is not surprising. As there is no heat loss to the wall, the flame speed continues to increase until the wall itself reaches a temperature of 1500 K. In Fig. 4(b) confirmation of the wall heat loss decreasing the flame speed is provided. Initially the speed remains that of a freely propagating flame. As the influence of the wall is felt, the flame speed increases due to a rise in the temperature of the gas preceding the flame. This is similar to the case of the adiabatic wall. Then, at approximately 0.0144 ms, the heat loss to the 750 K wall begins to take over and the flame speed drops rapidly. The flame is eventually quenched at about 0.0172 ms. Fig. 5 shows the heat release rate profiles of the two cases. Near the adiabatic wall there is no heat generation spike, unlike the case of the isothermal wall. Instead, as the flame enters the zone of influence of the wall, the heat release rate decreases with increasing proximity to the surface. The behavioral differences are due to high-temperature chemistry taking place near the adiabatic wall while low-temperature chemistry is prevalent near the 750 K isothermal wall. This is supported by looking at a breakdown of the chemical reactions contributing to the heat release near the wall in both cases. An interesting difference to note between the two simulations is that R11, progressing in the reverse direction, absorbs a significant amount of heat at the adiabatic wall, whereas operating in the forward direction near the cool isothermal wall it is a heat producer. This is similar to the chemistry in the free-flame. R11 consumes two radicals for every one produced. Thus, it is chain-terminating in its forward direction. Chain-branching usually occurs at high temperatures, whereas recombination reactions occur in lowtemperature regions. Hence the near-wall behavior of this reaction makes sense in light of the temperature regimes of the two cases being considered. Examining now the development of the mass fraction profiles of the radical species H, O, and OH, it is seen that the two cases

R. Owston et al. / International Journal of Hydrogen Energy 32 (2007) 2094 – 2104 t=0.004

t=0.008

t=0.012

t=0.015

t=0.016 t=0.02

t=0.017 2.0E+12

Heat Release Rate (W/m3)

Heat Release Rate (W/m3)

1.6E+11

1.2E+11

8.0E+10

4.0E+10

0.0E+00

t=0.004 t=0.008 t=0.012 t=0.015 t=0.016 t=0.02 t=0.05

1.6E+12

1.2E+12

8.0E+11

4.0E+11

0.0E+00

0

(a)

2099

0.01

0.02 0.03 Distance (cm)

0.04

0

0.05

0.01

0.02

0.03

0.04

0.05

Distance (cm)

(b)

Fig. 5. Heat release rate profiles: (a) adiabatic and (b) isothermal walls; t is time in ms.

2.5E+07 298 K 2.0E+07 Wall Heat Flux (W/m2)

are identical in the freely propagating region of the flame. As the influence of the wall is felt, however, the trends in the species concentrations near the adiabatic and 750 K isothermal walls become different. At the adiabatic wall the mass fractions of the radicals build up near the surface. However, there is depletion of the H, O, and OH species near the cool isothermal wall. From our examination earlier of the chemistry occurring at the two walls, this result is not surprising. It is expected that recombination reactions will become dominant in low-temperature chemistry near the isothermal wall, thereby lowering radical concentrations. However, it was seen that chain-branching reactions, like R11 (reverse direction), become important near the adiabatic wall because of the higher temperatures there. The effect of changing the temperature of the isothermal wall is now assessed. Five studies ranging from 298 to 1200 K were carried out to gauge the results of both increased and decreased wall temperature from that of the 750 K validation study discussed in Section 3.1. Other simulations with higher wall temperatures were also performed. These revealed auto-ignition occurring near the wall. However, the current discussion is limited to studies of a quasisteady flame approaching the wall without an ignition event preceding it. Fig. 6 shows the wall heat flux variation over time for the range of temperatures used. Notice that heat fluxes during the initial period before the flame begins interaction with the surface are negative for wall temperatures below 750 K. This is because the heat diffuses to the surface from the unburned gas before the propagating flame reaches the zone of influence of the wall. The peak value of heat flux is found to be highest for the lowest wall temperature and lowest for the highest wall temperature. Due to the fast flame speeds associated with hydrogen/oxygen combustion, the heat diffusion to/from the wall does not have time to penetrate a significant distance into the

500 K

1.5E+07 750 K

298 K 500 K 750 K 1000 K 1200 K

1.0E+07 1000 K 5.0E+06 1200 K 0.0E+00 0

0.01

0.02

0.03

0.04

0.05

-5.0E+06 Time (ms)

Fig. 6. Transient wall heat flux, 298–1200 K isothermal wall boundary conditions.

domain. Thus, with Tu near the surface remaining largely unchanged over a range of Tw , the flame approaches very close to the wall and leads to higher temperature gradients for lower wall temperatures. Recall that the adiabatic flame temperature is a constant, and thus is not the cause of the evident variation in heat flux. Heat release rates are shown in Fig. 7 for three isothermal wall temperatures. The peak values for all the cases occur directly at the wall at the same time as those of maximum heat flux, as shown in Fig. 6. As the wall temperature is decreased the peak heat release rate at the wall increases. Since the same reaction mechanism is used for all cases, this confirms that the low-temperature chemistry of the near-wall region is responsible for the heat release spike at the surface. Recall that this phenomenon was not seen for the hot adiabatic wall where quenching did not occur.

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R. Owston et al. / International Journal of Hydrogen Energy 32 (2007) 2094 – 2104

5.0E+12

2.0E+12

4.0E+12

t=0.016

t=0.018

Heat Release Rate (W/m3)

Heat Release Rate (W/m3)

t=0.0168

t=0.015 t=0.0168 t=0.018 t=0.05

3.0E+12

2.0E+12 t=0.05 1.0E+12

t=0.015

0.0E+00

t=0.015 t=0.016 t=0.02 t=0.05

1.6E+12 t=0.02 1.2E+12

8.0E+11

t=0.05 t=0.015

4.0E+11

0.0E+00 0

0.002

0.004

0.006

0.008

0.01

Distance (cm)

(a)

6.0E+11 Heat Release Rate (W/m3)

0.002

0

0.004

t=0.0152

5.0E+11

0.006

0.008

0.01

Distance (cm)

(b)

t=0.012 t=0.014 t=0.0152 t=0.016 t=0.02 t=0.05

t=0.016

4.0E+11 t=0.02 3.0E+11

t=0.014

t=0.05 2.0E+11 1.0E+11 0.0E+00 0

(c)

0.002 t=0.012

0.004 0.006 Distance (cm)

0.008

0.01

Fig. 7. Heat release rate profiles for three isothermal wall temperatures: (a) 298 K, (b) 750 K, (c) 1200 K.

3.3. Equivalence ratio effects 1.6E+07 Wall Heat Flux (W/m2)

The isothermal wall remains at a constant temperature of 750 K for all cases in this section. Note that the characteristics of the free flame become different when the equivalence ratio is varied. First, as shown in Table 2, the combustion temperature is lowered as the equivalence ratio increases (=2.0) or decreases ( = 0.7) from stoichiometric proportions. Alterations in the flame thickness and speed are also evident. Note that of the three cases considered, the highest flame speed is obtained for  = 1.0. The transient heat flux to the wall is given in Fig. 8 for the three cases. Observe that the simulation with  = 1.0 peaks earliest with the highest value. The case with  = 2.0 peaks last, but with the second highest value. Finally, the smallest peak is found for  = 0.7, which occurs between the times of  = 1.0 and 2.0. There is only about a 3% difference in the peaks between  = 0.7 and 2.0. However, there is a 12.4% difference between  = 0.7 and 1.0. A comparison of the spatial profiles of the heat release rates, reported also in Ref. [3], reveals that the three cases all have spikes occurring near the wall. The largest peak, 1.8 × 1012 W/m3 , occurs at 0.016 ms for the case of  = 1.0.

1.2E+07 ϕ 0.7 1.0 2.0

8.0E+06

4.0E+06

0.0E+00 0

0.01

0.02 0.03 Time (ms)

0.04

0.05

Fig. 8. Transient wall heat flux for premixed H2 –O2 flames with various equivalence ratios.

The second largest is 1.62 × 1012 W/m3 for  = 0.7, occurring at 0.017 ms. At 0.018 ms the peak for  = 2.0 occurs, measuring 1.24 × 1012 W/m3 . This variation in peak magnitudes is thought to be primarily due to chemical effects resulting from

R. Owston et al. / International Journal of Hydrogen Energy 32 (2007) 2094 – 2104

2101

3.0E+06 H2-Air, ϕ=1.0, Tw=750 K

1.6E+07 Wall Heat Flux (W/m2)

Wall Heat Flux (W/m2)

2.5E+06

1.2E+07 H2/O2 H2/Air 8.0E+06

4.0E+06

2.0E+06 H2-Air, ϕ=0.4, Tw=400 K 1.5E+06 1.0E+06 5.0E+05

0.0E+00 0

0.02

0.04 0.06 Time (ms)

0.08

0.1

0.0E+00 0

0.05

0.1

0.15

0.2

Time (ms)

Fig. 9. Transient wall heat flux of stoichiometric H2 –air and H2 –O2 flames on 750 K wall.

using different mixture compositions for each equivalence ratio. The  = 1.0 case has a stoichiometric composition which allows for complete combustion of the reactants with no dilution effect. Thus, the combustion temperature of the flame is higher and the heat release spike is largest. With  = 0.7, the combustion temperature is slightly lower than the  = 1.0 case. Note that since the flame is lean there is an excess of highly reactive O, and OH radicals near the wall. Thus, it is not surprising that reactions R11, R15, and R16 become increasingly important to heat production. At  = 2.0 the combustion temperature is the lowest of the three cases because the rich flame has less oxidizer available to mix with the excess fuel in the domain. R4 is found to be the largest heat-producing reaction near the wall. The importance of this ternary recombination reaction is not unexpected. For  = 2.0 there is more hydrogen available from breakdown of the fuel to advance the progress of this reaction. 3.4. Inert gas addition Since most hydrogen combustion applications use air to react with the fuel, the topic of inert gas addition to premixed hydrogen flames is of interest. First, a stoichiometric mixture composition of hydrogen and oxygen is compared to a mixture having the same quantity of hydrogen and oxygen, but with the diluent species nitrogen added in proportions commonly used for air, H2 + 0.5(O2 + 3.76N2 ) → Products.

(9)

The wall is held at 750 K. Fig. 9 displays the wall heat flux for the two cases as they progress in time. The fact that there are lower combustion temperatures for the H2 –air computation due to dilution partially accounts for the nearly 84% drop in peak heat flux from the case which contained no inert. With higher temperatures, we would expect the temperature gradient to be higher for the H2 –O2 computation. A larger temperature gradient alone would act to increase the heat flux at the wall assuming the conductivity of the gas near the wall remained constant. However, it was found

Fig. 10. Transient wall heat flux for H2 –air flames of equivalence ratios 1.0 and 0.4 impinging on 750 K and 400 K walls, respectively.

that the thermal conductivity of the H2 –O2 case is nearly 47% higher than that of the H2 –air simulatio. This further acts to increase the heat flux at the wall. The heat release rate profiles show that, as expected, the peak value near the wall is higher for the case with no dilution, by approximately 93% [3]. In both cases the top four heat-producing reactions are R1, R14, R5, and R4, listed in descending order and progressing in the forward direction. However, per unit volume of gas in the domain, there is less reactive species when a diluent is added. Consequently, the reaction rates drop for the computation with inert gas. This explains the lower heat release rates as compared to the case with no diluent addition. Note that for the high combustion temperatures of the two cases, nitrogen would not remain completely unreactive in practice. However, for the present study this is assumed in order to gauge the effect of adding a purely inert species. Most current work on hydrogen internal combustion engines focuses on lean-burning in order to control NOx emissions by lowering the combustion temperatures. Therefore, we will now focus on a H2 –air mixture with an equivalence ratio of 0.4 impinging on a 400 K wall (typical of lean-burn engines). This simulation will be compared to that of the stoichiometric H2 –air flame impinging on a 750 K wall discussed previously. The adiabatic flame temperature of the  = 0.4 simulation is 1815 K and its flame thickness is greater than that of the =1.0 case. Thus, its quenching distance is larger, and its free-flame speed much lower, as indicated in Table 2. Fig. 10 shows the behavior of the transient wall heat flux of the two cases. The value of the  = 0.4 case initially falls due to the fact that Tw is smaller than the unburned temperature of the gas. However, there is no sharp peak in wall heat flux near quenching as was seen in the  = 1.0 case. The maximum value of the  = 1.0 wall heat flux is over four times greater than that of the  = 0.4 case. The heat release rate of the =0.4 computation shows similar trends to that of the =1.0 case. Near the time of quenching, the heat release rate at the wall achieves higher values than are seen in the free flame. However, the maximum value attained at the

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5.0E+07

Wall Heat Flux (W/m2)

4.0E+07 P=1 bar P=2 bar

3.0E+07

2.0E+07

1.0E+07

0.0E+00 0

0.005

0.01

0.015 0.02 Time (ms)

0.025

0.03

Fig. 11. Transient wall heat flux for pressures at 1 and 2 bar.

wall is about an order of magnitude lower for the  = 0.4 case compared to the  = 1.0 case. Whereas the top four reactions contributing to the heat generation in the  = 1.0 case were R1, R14, R5, and R4, the reactions for the  = 0.4 case are R1, R8, R14, and R13, listed in descending order. Note that R8 proceeds in the reverse direction from that indicated. R5 and R4, key reactions in the  = 1.0 case, require more hydrogen and so are not able to maintain the same progression rates in the case with less fuel ( = 0.4). 3.5. Chamber pressure effects Combustion in a spark-ignition engine takes place somewhere in the range of 20 to 60 bar [23], and the thickness of a H2 –O2 flame decreases with increasing pressure. A decrease in flame thickness requires a finer computational grid in order to resolve the flame. Therefore, it was unfeasible to carry out simulations at 20–60 bar, in the context of this work, since this would require a significantly longer computational time. Instead, the results of doubling the combustion chamber pressure are compared to those of the case discussed in Section 3.1 at 1 bar, keeping the initial conditions, other than chamber pressure and density, the same as that of the validation study. The grid resolution is doubled for this simulation. Even though the conditions employed here do not reflect actual engine operation pressures, it is interesting to see what trends develop for increased chamber pressure. From this we can attempt to extrapolate the near-wall flame behavior to engine conditions. Attention is first given to the behavioral differences of wall heat flux in the two studies. Fig. 11 shows that the peak heat flux next to the wall at 2 bar is much higher (168% larger) than 1 bar. The temperature gradient at the wall, and consequently the heat flux, is higher there because of the smaller quenching distance. Recall from Section 1 that Sotton et al. [5], using stoichiometric methane/air flames impinging on the walls of a constant volume combustion chamber, found that wall heat flux increased non-linearly over a pressure rise from 0.05 to 1.7 MPa. Furthermore, quenching distances were seen to

decrease over the same pressure rise. These experimental trends for CH4 –air flames agree well with those found here using H2 –O2 flames over a pressure range of 1 to 2 bar. It has been observed that the maximum heat generation occurs adjacent to the wall for both the cases under consideration. The spike in the near-wall cell at the time of maximum heat flux is almost six times higher for the 2 bar case. Additionally, the free-flame heat release rate peaks are approximately six times greater for this simulation. A breakdown of the chemical reactions occurring at the wall for the two cases found that the same reactions are important for heat generation in both computations. The top five heat-producing reactions were R1, R14, R5, and R4, listed in descending order. However, the magnitude of the heat release rates of the reactions at 2 bar was far larger than that at 1 bar. Thus, it appears that the heat generation disparity at the wall is simply due to the reaction rates being much faster at higher pressures. In conclusion, we would expect the heat flux and heat generation at the wall of an engine operating between 20 and 60 bar to be higher than the values reported here for computations with chamber pressures of 1 and 2 bar. However, note that the results from this section have employed stoichiometric H2 –O2 flames, whereas practical hydrogen engines would utilize H2 –air mixtures with equivalence ratios of around  = 0.4. Therefore, the quenching distances and flame thicknesses would be larger than those reported here, causing the computational requirements for flame–wall interaction studies to be less daunting. Additionally, the peak heat release rates would be decreased. Sotton et al. [5] states that there are no experimental methods that allow direct measurement of quenching distances at high pressures, i.e. at engine conditions. Thus, it is important to be able to predict these values through numerical modeling. 3.6. Radical recombination boundary In this section, the effect of near-wall radical concentrations on reaction rates is assessed. In the near-wall cell, the mass fractions of the radicals H, O, and OH are set to zero and their values are added to the mass fraction of water. This simulates a reactive wall with a sticking coefficient of unity for the indicated radicals in the cell adjoining the wall. These radicals are then assumed to undergo recombinative desorption to gaseous water according to the reaction xH∗ + yO∗ + zOH∗ → (x + y + z)H2 O, where surface species are denoted by ∗. Note that this reaction does not artificially add heat to the domain. The coefficients x, y, and z represent the mass fractions of the adsorbed species. It is clear that the ratio of oxygen and hydrogen elements will not be conserved using this approach. However, the primary motivation of this study is to observe the changes that might arise due to wall recombination. Thus, the formation of more/less water than that necessary to conserve mass is deemed inconsequential. From the study of Section 3.1 using an inert boundary condition, it was seen that of the reactions significant to heat generation/absorption near the wall, H2 O is used as a reactant

R. Owston et al. / International Journal of Hydrogen Energy 32 (2007) 2094 – 2104

Heat Release Rate (W/m3)

1.6E+11 t=0.008 t=0.012 t=0.015 t=0.016 t=0.017 t=0.02 t=0.05

1.2E+11

8.0E+10

4.0E+10

0.0E+00 0

0.01

0.02 0.03 Distance (cm)

0.04

0.05

Fig. 12. Heat release rate profiles with recombination boundary condition.

only in R4. Here it acts only as a third body for the recombination of atomic hydrogen, with its concentration remaining constant. In any case, since the addition of the recombination boundary removes the H radical from the cell adjacent to the wall, the progression rate of this reaction will be significantly reduced. This work attempts to simulate a full surface kinetic mechanism, such as that employed by Popp [4]. However, a simpler model than employing a full chemical surface mechanism is desired because of limitations on computational resources, hence the use of the recombination wall. A comparison of the wall heat flux of the cases having inert and recombination walls reveals that the flux of the case with the recombination wall remains lower over the entire time of the computation. The peak value of heat flux of the inert wall is more than double that of the recombination wall. Fig. 12 depicts the heat release rate profile of the simulation with the recombination boundary as it progresses in time. Note that the heat release rates do not peak near the wall as in the case of the inert wall (see Fig. 5b). Instead, the heat release begins to decrease with increasing proximity to the wall. Note that the heat release is nearly four orders of magnitude lower next to the wall than in the free flame. This is thought to be because of reductions in the reaction rates occurring near the wall due to radical depletion. This idea is supported by the work of Egolfopoulos et al. [24] who found that the destruction of atomic hydrogen at the boundary surface in a CH4 –air stagnation-point flame caused the chemical activity near a high-temperature wall to decrease drastically. Dabireau et al. [11] stated that 750 K would be classified as a “hot” wall with regards to increased heat release rate behavior near a surface. Recall that this is the wall temperature used for the two cases compared in this section. From the chemical analysis of the inert wall in the nearwall cell at 0.016 ms, we saw that the top five heat-producing reactions were R1, R14, R5, and R4. Since all of these were shown to progress in the forward direction, it is apparent they all consume radicals that are unavailable next to the recombination wall. Thus, it is not surprising that the high heat release peak observed at the inert wall is absent from the recombination case. The only reaction of any significance to heat production

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in the cell adjacent to the recombination boundary was R18, which has an activation energy of zero in the mechanism and requires none of the depleted radicals to proceed. This reaction produces four orders of magnitude less heat than the highest heat generating reaction next to the inert wall, R1. It is observed that at 7 m from the wall at 0.016 ms the same top three reactions are the major heat producers in both the case with the inert and recombination boundary conditions. These reactions are R1, R14, and R10, progressing in the forward direction. The rates of progress of the reactions are much less in the case of the recombination boundary though, due to H, O, and OH radical depletion. Note that R5 and R4, which are nearly as large producers as R10 in the inert wall case, do not produce a significant amount of heat in the case with the recombination boundary. This is most likely because they require two of the depleted radicals in order to proceed instead of one as with R1, R14, and R10. Since temperatures are too low near the wall to form radicals, diffusion of H, O, and OH from nearby cells acts to reduce the slope of the concentration gradient at the wall. Thus, with constant H, O, and OH destruction at the wall and the same production in the free-flame region as for the inert wall case, the amount of radicals is depleted throughout the near-wall region near the recombination boundary. This acts to reduce the rates of progress of reactions requiring these radicals throughout the near-wall region, leading to the trend of overall decreasing heat release rates with increasing proximity to the surface. 4. Summary and conclusions In this work premixed hydrogen flames impinging on walls have been analyzed. Investigations into the influence of adiabatic and isothermal walls, equivalence ratios and chamber pressure, as well as dilution of the reactant species, are carried out. Finally, the consequences of creating a radical sink at the wall have been addressed. It was observed that the heat release rate spiked at the isothermal wall as a result of low-temperature reactions. On the other hand, at the adiabatic wall the heat release rate near the surface did not rise to levels exceeding those of the free flame. In fact, the chemical reaction rates slowed with increasing proximity to the wall as the fuel was consumed. Low-temperature chemistry was not a dominant factor as it was in the case of the isothermal wall. Near the 750 K isothermal all the radicals H, O, and OH underwent significant depletion due to the recombination reactions prevalent there. However, near the adiabatic wall this considerable decrease in concentration levels was not observed. This analysis of surface effects on heat release rates occurring near a wall can assist in improving the efficiency of a combustion device, as well as providing a foundation for nearwall emission predictions. Examination of the influence of wall temperature on flame properties showed that the peak heat flux to the wall decreased with increasing wall temperature over the range of temperatures examined (298 K < Tw < 1200 K). This has important ramifications for engines, where high heat fluxes to surfaces can cause serious degradation to mechanical components. Additionally,

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it was found that the heat release rate peak at the wall decreased in magnitude for increasing wall temperatures. Changes in the equivalence ratio () of the H2 –O2 mixture showed that the peak value of wall heat flux is obtained for  = 1, while the fluxes of  = 2 and 0.7 were approximately the same. Using a stratified charge in an engine, therefore, the peak heat flux of near-wall regions having moderately lean and rich mixtures are expected to be of similar magnitude. Using a stoichiometric H2 –air flame as opposed to H2 –O2 caused decreased reaction rates both in the free flame and near the wall. Consequently, the wall heat flux and the peak heat release rate at the surface were significantly smaller with the addition of inert nitrogen to the mixture. Employing a lean-burn ( = 0.4) flame interacting with a 400 K wall, the maximum heat release rate was shown to be approximately an order of magnitude lower than with the stoichiometric H2 –air flames impinging on a 750 K wall. Additionally, the peak wall heat flux was four times smaller for the lean-burn computation. Increasing the chamber pressure by a factor of two was shown to cause the peak heat flux at the wall to rise by 168% and the heat release rate at the wall to spike to a value almost six times greater than that attained with a pressure of 1 bar. The same reactions were shown to be important to heat generation at both pressures. However, the reaction rates were much higher for a chamber pressure of 2 bar. It is thought that this trend of increasing reaction rates with increasing pressure will continue to manifest in the range of engine operating conditions. The spike in heat release rate at the wall of the 750 K, inert wall case was attributed to low-temperature induced radical recombination reactions. Thus, it was of interest to study the effect of removing radicals at the wall in order to gauge the role that surface kinetics might play in reducing high heat release rates near reactive walls. It was found that this caused the peak wall heat flux to decrease to less than half that of the inert wall case. The heat release rate declined from its free-flame values as the flame interacted with the wall. The fact that the near-wall heat release rate trend using a recombination boundary is opposite to that seen in the inert wall case emphasizes the importance of radical concentration to the elevated heat generation of the inert wall. Thus, the degree of reactivity in the exposed surfaces must be considered when selecting materials in the design of efficient combustion chambers. Acknowledgments Computational resources for this research were provided by the Department of Environmental Engineering and Physics at the University of Basilicata, Italy. Financial support from the Department of Defense, the National Science Foundation, and the Indiana 21st Century Fund and ArvinMeritor Corporation is gratefully acknowledged. References [1] Hasse C, Bollig M, Peters N, Dwyer HA. Quenching of laminar isooctane flames at cold walls. Combust Flame 2000;122:117–29.

[2] Kiehne TM, Matthews RD, Wilson DE. The significance of intermediate hydrocarbons during wall quench of propane flames. Proc Combust Inst 1986;21:481–9. [3] Owston R. Wall interactions of premixed laminar flames. MSME thesis, Purdue University; 2006. [4] Popp P. Simulation of homogeneous/heterogeneous reaction mechanisms, heat transfer, and pollutant formation during flame–wall interaction. PhD thesis, Institut National Polytechnique de Toulouse; 1996. [5] Sotton J, Boust B, Labuda SA, Bellenoue M. Head-on quenching of transient laminar flame: heat flux and quenching distance measurements. Combust Sci Technol 2005;177:1305–22. [6] Popp P, Smooke M, Baum M. Heterogeneous/homogeneous reaction and transport coupling during flame–wall interaction. Proc Combust Inst 1996;26:2693–700. [7] Popp P, Baum M. Analysis of wall heat fluxes, reaction mechanisms, and unburnt hydrocarbons during the head-on quenching of a laminar methane flame. Combust Flame 1997;108:327–48. [8] Ezekoye O, Greif R, Sawyer RF. Increased surface temperature effects on wall heat transfer during unsteady flame quenching. Proc Combust Inst 1992;24:1465–72. [9] Connelly L, Ogasawara T, Lee D, Greif R, Sawyer RF. Fall meeting 1993, The Combustion Institute/Western States Section, Stanford, CA; Paper WSCI 93-077; 1993. [10] Connelly L, Greif R, Sawyer RF, Lee D. Fall meeting 1992, The Combustion Institute/Western States Section, Berkeley, CA; Paper WSCI 92-109; 1992. [11] Dabireau F, Cuenot B, Vermorel O, Poinsot T. Interaction of flames of H2 + O2 with inert walls. Combust Flame 2003;135:123–33. [12] Aghalayam P, Bui P-A, Vlachos DG. The role of radical wall quenching in flame stability and wall heat flux: hydrogen–air mixtures. Combust Theory Modelling 1998;2:515–30. [13] Vlachos DG. Homogeneous–heterogeneous oxidation reactions over platinum and inert surfaces. Chem Eng Sci 1996;51:2429–38. [14] Magi V. REC-87: a new 3-D code for flows, sprays and combustion in reciprocating and rotary engines. Princeton University: Mechanical and Aerospace Engineering Report No. 1793; 1987. [15] Gopalakrishnan V, Abraham J. An investigation of ignition behavior in diesel sprays. Proc Combust Inst 2002;29:641–6. [16] Gopalakrishnan V, Abraham J. Computed NO and soot distribution in turbulent transient jets under diesel conditions. Combust Sci Technol 2004;176:603–41. [17] Song L. Modeling combusting diesel jets—the wall regime. PhD thesis, Purdue University; 2003. [18] Westbrook CK, Adamczyk AA, Lavoie GA. A numerical study of laminar flame wall quenching. Combust Flame 1981;40:81–99. [19] Kee RJ, Rupley FM, Miller JA. Chemkin-II: a Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics. SAND89-8009, Sandia National Laboratories; 1989. [20] Kee RJ, Grcar JF, Smooke M, Miller J. PREMIX: a Fortran program for modeling steady laminar one-dimensional flames. SAND85-8240, Sandia National Laboratories; 1986. [21] Lutz AE, Kee RJ, Grcar JF, Rupley FM. OPPDIF: a FORTRAN program for computing opposed flow diffusion flames. SAND96-8243, Sandia National Laboratories; 1997. [22] Miller JA, Mitchell RE, Smooke M, Kee RJ. Toward a comprehensive chemical kinetic mechanism for the oxidation of acetylene: comparison of model predictions with results from flame and shock tube experiments. Proc Combust Inst 1982;19:181–96. [23] Heywood J. Internal combustion engine fundamentals. New York: McGraw-Hill Inc.; 1988. [24] Egolfopoulos FN, Zhang H, Zhang Z. Wall effects on the propagation and extinction of steady, strained, laminar premixed flames. Combust Flame 1997;109:237–52.