Paper # 070LT-0096 Topic: Turbulent Flames 8 th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-22, 2013 Evaluation of Numerical Turbulent Combustion Models Using Flame Speed Measurements from a Recently Developed Fan- Stirred Explosion Vessel Sankaranarayanan Ravi, Anibal Morones, and Eric Petersen Department of Mechanical Engineering, Texas A&M University, 3123 TAMU, College Station, Texas- 77843 Computational combustion codes rely on turbulent combustion models (or correlations) for providing flame speed estimates. This method necessitates the need to evaluate the predictive capabilities of these correlations against experimentally measured data. Global displacement speeds were measured in a recently developed fan-stirred, cylindrical flame speed vessel using high-speed schlieren imaging. Measurements were conducted in homogeneous and isotropic turbulent conditions at an average RMS turbulent intensity of 1.5 m/s and at an integral length scale of 27 mm. Methane and a representative synthetic gas or syngas blend containing : by volume of hydrogen and carbon monoxide, all diluted in air, were studied. A wide range of equivalence ratios was covered, and the flame speeds were estimated when the flame radius was equal to the integral length scale. Turbulent flame speeds were computed using four widely used numerical models: (1) Zimont turbulent burning velocity model (1988); (2) Kerstein pair-exchange model (1988); (3) the coherent flame speed model (1993); and, (4) the distributed reaction zone model (1995). The Kerstein model and the Zimont model agreed well with the experimental measurements. Also, S T /S L was higher for syngas than methane for the same u /S L, which is indicative of the preferential diffusion effect of hydrogen in increasing the flame surface area by distorting it. 1. Introduction Gas turbine combustion processes are challenging to model due to the chemistry and fluid dynamic (turbulent flow) interactions. As a result, computational combustion codes use widely validated correlations or combustion models to provide the much needed turbulent flame speed estimates. Damköhler (Peters, 1999) postulated that the increased burning rates under turbulent conditions were due to an increase in the local flame surface area by the turbulent eddies, and he proposed a simple expression for turbulent flame speed. Since then, several experimental investigations have identified different regimes of turbulent flame propagation. However, a universally accepted correlation that can model all these regimes is still under development. Nevertheless, turbulent combustion models have been developed for common fuels of interest such as methane and hydrogen, and they have been validated with experimental measurements over a wide range of conditions. The primary objective of this study was to assess the most promising burning velocity correlations from the literature with recent measurements from the authors laboratory. Fuels that are of interest to gas turbine designers, namely, methane (primary constituent of natural gas) and syngas (: H 2 :CO by volume) were studied in this work and are organized in the paper as follows. First, the various regimes of turbulent combustion are introduced, followed by a brief background literature review on the existing turbulent combustion models. The experimental apparatus and the post processing procedure are then discussed in detail. Results from flame speed experiments are presented and are compared with the model predictions. 2. Regimes of Turbulent Combustion Unlike laminar flames, turbulent flame propagation can be classified into several regimes. The Borghi diagram (Borghi, 1985) demarcates the different regimes based on both flame properties such as the laminar flame speed (S L ) and the
flame thickness (, as well as the turbulent field parameters, namely, the turbulent intensity (u ) and the integral length scale (L). Non-dimensional numbers- Reynolds, Karlovitz, and Damköhler--form the boundaries of each regime (Eqs. (1) - (3)). Two regimes, namely, the thin reaction zone and the corrugated flamelet regime were studied in the present investigation. Flame images corresponding to these regimes are shown in the Borghi diagram in Fig. 1. The sphericity of the growing flame ball decreases as the turbulence intensity is increased due to increased turbulent straining (as a result of moving from corrugated flamelet to thin reaction zone). Turbulent Reynolds Number: ( ) ( ) (1) Damköhler Number: ( ) ( ) (2) Karlovitz Number: ( ) ( ) (3) Where the laminar flame thickness,, is given by, ( ) ( ) (4) and, Mixture-averaged specific heat (unburned): (5) Where, X i is the mole fraction of i th species Mixture thermal conductivity (unburned): (( ) (6) 10 3 Methane - Syngas Da =1 Thin Reaction Zone 10 2 Distributed Reactions u'/s L 10 1 Re L = 1 Ka = 1 10 0 Laminar Corrugated Flamelet u' = S L Wrinkled Flamelet 10-1 10-1 10 0 10 1 10 2 10 3 10 4 Figure 1. Turbulent combustion regime diagram (Borghi diagram). The morphologies of the flames (image insets) are distinctly different from one regime to the other. Measurements from the present study are shown as symbols. L/ L 2
3. Turbulent Combustion Models- Background Literature Lipatnikov and Chomiak (2002) analyzed experimental data from different facilities and have established six criteria or trends that have to be satisfied by turbulent flame speed models. These criteria are summarized below: a. Turbulence intensity (u - Turbulent flame speed (S T ) shows a nonlinear relation with intensity levels. A linear increase in the weak intensity regime (u < S L ) is observed, followed by a power law increase in the moderately turbulent conditions up to maximum, S T,max, when u = u m. This threshold intensity associated with the maximum S T is highly dependent on the Lewis number of the mixture. In the high intensity turbulence regime (u > u m ), a decrease in the flame speed is observed and is referred to as the bending effect. b. Integral length scale (L)- There is no consensus on the influence of turbulence length scale on S T. The ratio of integral length scale and laminar flame thickness (L/ ) has a positive exponent ranging between 0.15 and 0.25, as determined by processing the existing spherical flame speed database. However, facilities using gridgenerated turbulence mechanisms have reported that with an increase in L, the burning velocities increased or decreased based on the ratio of u /S L. As a result, correlations developed using data from a burner-type apparatus may not predict the observed trends of length scale influence as measured in fan-stirred, spherical flame bombs. c. Laminar flame speed (S L )- both S T and ds T /du increase with S L and scale with an exponent q ~ 0.5-0.8 ( ) d. Molecular heat diffusivity ( )- S T decreases with. e. Pressure- Unlike the laminar flame speed, S T increases with pressure. But the pressure dependency of S T is controlled through S L for most correlations. This trend is contradictory to what is observed experimentally. f. Damköhler and Karlovitz (Ka) Numbers- (S T /u ) scales as Da 0.2-0.5 and (1/Ka) 0.2-0.4. Four numerical models, namely, (1) Zimont burning velocity model (Lipatnikov and Chomiak, 2002) (Eq. (7)); (2) Kerstein pair-exchange model (Kerstein, 1988) (Eq. (8)); (3) coherent flame speed model (Duclos and Veynante, 1993) (Eq. (9)); and (4) Distributed reaction zone (DRZ) model (Ronney, 1995) (Eq. (10)) are evaluated here against experimental measurements. These models were chosen due to better agreement of the model predictions with the experimental data (Lipatnikov and Chomiak, 2002; Liu et al., 2012). Zimont burning velocity model: (7) Kerstein pair-exchange model: (8) Coherent flame speed model: [ ( )] (9) The model constants are adjusted for a particular fuel. 4. Definition Dependency of Turbulent Flame Speed DRZ Model: ( (10) The definition dependency of turbulent flame speed has been discussed extensively in the literature. Global displacement speeds or turbulent flame speeds are commonly measured using schlieren imaging inside a fan-stirred vessel. Global consumption speeds or mass rate of burning can be obtained from pressure transducer measurements. The two definitions differ by the value of the reaction progress variable,, of the measurement surfaces. Recently, Bradley et al. (2011) derived a relationship (Eq. (11)) that can be used to estimate the turbulent burning velocities at different measurement surfaces. The ratios of radii relative to the schlieren radius and the corresponding burning velocities ratios are shown in Table 1. 3
( ) (11) Table 1. Radii and burning velocities ratios of different measurement surfaces with respect to the schlieren surface as measured by Bradley et al. (2011). 5. Apparatus Description and Flame Image Analysis Measurement Technique OH PLIF 0.05 0.9 0.81 Schlieren 0.1 1 1 Equal Volume Method 0.34 1.22 1.49 Equal Area Method 0.4 1.27 1.61 Mean Flame (Cone angle method) 0.5 1.34 1.8 Pressure Trace/ Mass rate of burning 0.6 1.4 1.96 The turbulent flame speed vessel is made of aircraft-grade aluminum (Al 7075) with an internal diameter of 305 mm and an internal length of 355 mm. Optical-quality quartz windows at the two ends of the vessel enable visual tracking of the expanding flame up to a maximum diameter of 127 mm under constant-pressure conditions. The spark-ignited flame is imaged using a z-type schlieren setup used in combination with a high-speed camera (Photron Fastcam SA 1.1). The temperature inside the vessel is monitored using a k-type thermocouple, and typical initial temperatures are 296 ± 3 K. Four fans are installed symmetrically around the central circumference of the vessel to generate turbulence during the experiment. The fans are radial impellers with three backward-curved blades which direct the flow towards the vessel wall. They are made of aluminum (Al 6061-T6) with an outer diameter of 76.2 mm and a blade pitch angle of 20. These fans are fitted on steel shafts (A2 tool steel) that are polished to an extremely fine surface finish. Shaft sealing is provided by means of PTFE lip seals. High-speed bearings for the shafts are stacked inside cartridge housings that are directly mounted onto the vessel. Each fan is turned by a 2.25-HP router motor whose rotational speeds can be varied between 8,000 and 24,000 rpm. The impeller shafts are connected to the motor shafts by means of flexible couplings which can compensate for minor shaft misalignments. Figure 2 shows the actual experimental apparatus along with the 3D computer model. An average RMS turbulent intensity, u = 1.5 m/s with negligible mean flow (< 0.1 u ), was measured at the lowest fan speeds with an integral length scale of 27 mm. Additionally, the turbulent flow field exhibited two features: (1) homogeneity or spatial uniformity; and, (2) isotropy or directional equality of the velocity components in the two orthogonal directions at the center of the vessel. Both the homogeneity and isotropy ratios varied between 0.9 and 1.1 (ideal value being 1), thus providing stationary (no mean flow) and uniform perturbations (also called homogeneous and isotropic turbulence, HIT) during flame growth. Sample images from a typical turbulent flame speed experiment are shown in Fig. 3. The images are analyzed using a MATLAB code that was developed in house. The program tracks the flame boundary and estimates the area within the turbulent flame kernel for each frame, as shown in Fig. 3d. The enclosed area is then used to compute the radius of a circle with an equivalent area. This radius is defined as the schlieren radius, r sch. To determine the global displacement speed, the instantaneous turbulent flame speed, S F, is first computed through Eq. (12) using a central difference technique. The global displacement speed (S T,0.1 ) is then estimated by multiplying S F with the density ratio of the burned to unburnt gases (continuity) following Eq. (13). A polynomial regression-based smoothing filter (Savitzky-Golay) is used when computing the derivative in Eq. (12). This filter has been successfully applied to laminar flame speed measurements using high-frequency dynamic pressure traces without the loss of experimental trend (Dahoe, 2005). For the current application, the derivative errors can be attributed to the unequal flame propagation rates in the different directions. As a result, the flame may become more wrinkled as opposed to growing monotonically in the imaging plane, which results in noisy derivatives 4
A B Figure 2. Fan-stirred flame speed vessel. (a) 3D solid works model (b) photograph of the facility. The four fans at the central circumference generate homogeneous and isotropic turbulence at the vessel center.. ( ( (12) ( ( (13) Figure 3. (a-c) Sample images from a typical turbulent flame speed experiment. (d) Image processing technique used to estimate the flame radius by computing the enclosed area within the kernel boundary (shown in blue). 6. Results and Discussion Turbulent flame speeds of methane and syngas mixtures over a wide range of equivalence ratios are shown in Fig. 4. The numerical model predictions at these conditions are also plotted. The flame propagation rates from the various models are converted to global displacement speeds using Eq. (11) to enable comparison with the measured data. The model constants are provided in Table 2. The Kerstein pair-exchange and the Zimont models follow the experimental data closely for both fuels. Additionally, the model constants do not vary significantly for both fuels. The coherent flame speed model, though, is insensitive to changes in equivalence ratio and agrees satisfactorily with the measurements for both fuels. in Eq. (9) was computed using the procedure outlined in Duclos and Veynante (1993). The DRZ model under predicts the flame speeds under lean conditions and over predicts for the fuel-rich cases for methane. However, the model fails to capture the flame speeds for syngas. 5
S T,0.1 S T,0.1 S T,0.1 S T,0.1 75 Methane/Air A Turbulent 100 Methane/Air B 75 Curve Fit 25 Laminar TAMU Data Kerstein Model (A= 0.06) Zimont Model (A= 0.32) DRZ CFM (C=1,C 1 = 0.5,C 2 =0.6) 25 0.7 0.8 0.9 1.0 1.1 1.2 0.7 0.8 0.9 1.0 1.1 1.2 200 : H 2 /CO + Air C 2 : H 2 /CO+Air D 1 Turbulent 200 100 Curve Fit 1 Laminar 100 TAMU Data Kerstein Model (A= 0.09) Zimont Model (A= 0.47) DRZ Model (A= 0.08) CFM (C=1.5,C 1 = 0.3,C 2 =0.3) 0.5 0.6 0.7 0.8 0.9 1.0 0.5 0.6 0.7 0.8 0.9 1.0 Figure 4. Global displacement speeds of methane (Ravi et al., 2013) and syngas mixtures at various equivalence ratios. (A, C) Turbulence has increased the flame speeds at all conditions. The corresponding laminar flame speeds are included for reference. (B, D) Turbulent combustion model predictions. Good agreement is seen amongst the experimental data, the Kerstein pair-exchange model and the Zimont burning velocity model for both fuels. Table 2. Turbulent combustion model constants for the two fuels. CFM Kerstein Zimont DRZ C C 1 C 2 Methane 0.06 0.32 0.08 1 0.5 0.6 Syngas 0.09 0.47 0.08 1.5 0.3 0.3 To assess the effect of u on the S T,0.1, the turbulent flame speeds are plotted as a function of the intensity levels (both normalized by the laminar flame speed) in Fig. 5. For a given value of u /S L, S T /S L is higher for syngas than methane. This amplification can be attributed to the increased flame surface distortion due to preferential diffusion of hydrogen (Kwon et al. 1991). Distortion increases the flame surface area, and hence, the burning velocities are higher. 6
5 Methane - Syngas 4 S T,0.1 / S L 3 2 Figure 5. Normalized global displacement speeds as a function of normalized intensity for methane and syngas. The flame speed increase is higher for syngas than methane due to higher flame surface distortion effected by the preferential diffusion of hydrogen. 7. Conclusion Global displacement speeds of methane and a : blend (by volume) of H 2 :CO were measured in a recently developed, fan-stirred, constant-volume flame speed vessel. A wide range of equivalence ratios that are relevant to practical applications such as gas turbine combustion were studied. The turbulent flame propagation rates were estimated using high-speed schlieren photography whose flame surfaces are characterized with a reaction progress variable, = 0.1. Four widely used numerical combustion models were validated with measurements from this study. The Kerstein pair exchange model and the Zimont burning velocity model agreed well with the experimental data. Additionally, it was shown that S T /S L was higher for syngas than methane for the same value of u /S L, which is indicative of the strong preferential diffusion effect of hydrogen in distorting the flame surface thereby increasing the turbulent propagation rates. Extension of these results to higher intensity levels and to higher-hydrogen-content fuels is proposed as a part of future work. Acknowledgements This work is funded in part by the National Energy Technology Laboratory of the US Department of Energy through the UTSR grant No. DE-FE0004679. Anibal Morones is supported by CONANCYT of Mexico and CIDESI. References 1 0 2 4 6 8 10 12 u' / S L Borghi, R., On the Structure and Morphology of Turbulent Premixed Flames, Recent Advances in the Aerospace Science, Plenum, New York, 1985, p. 117-138. Bradley, D., Lawes, M., Mansour, M. S., Combust. Sci. 158 (2011) 123-138. Dahoe, A. E., J Loss Prevent. Proc. 18 (2005) 152-166. Duclos, J. M., Veynante, D., Combust. Flame. 95 (1993) 101-117. Kerstein, A. R., Proc. Combust. Inst. 21 (1988) 1281-1289. Lipatnikov, A. N., Chomiak, J., Prog. Energy Combust. Sci. 28 (2002) 1-74. Liu, C. C., Shy, S. S., Peng, M. W., Chiu, C. C., Dong, Y. C., Combust. Flame. 159 (2012) 2608-2619. Peters, N., J. Fluid Mech. 384 (1999) 107-132. Ravi, S., Morones, A., Petersen, E.L., AIAA Paper 2013-1184. Ronney, P. D., in: Buckmaster, J. D., Takeno, T., (Eds.), Modeling in Combustion Science, Lecture Notes in Physics, Springer-Verlag, Berlin, 1995, p. 3-20. Wu, M. S., Kwon, S., Driscoll, J. F., Faeth, G. M., Combust. Sci. Tech. 78 (1991) 69-96. 7