Numerical Investigation of a Double-Swirled Gas Turbine Model

Subscriber access provided by - Access paid by the | UCSB Libraries

Article

Numerical Investigation of a Double-Swirled Gas Turbine Model Combustor Using RANS Approach with Different Turbulence-Chemistry Interaction Models Amir Mardani, and Alireza Fazlollahi-Ghomshi Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b00452 • Publication Date (Web): 27 Jun 2016 Downloaded from http://pubs.acs.org on June 30, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Energy & Fuels is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Numerical Investigation of a Double-Swirled Gas Turbine Model Combustor Using RANS Approach with Different Turbulence-Chemistry Interaction Models Amir Mardani* and Alireza Fazlollahi-Ghomshi Department of Aerospace Engineering, Sharif University of Technology, Azadi St., Tehran, Iran *

Email Address: [email protected]; Tel: +98-2166164625

Abstract In this work, numerical investigation of a gas turbine model combustor (GTMC) was carried out using two different turbulence-chemistry interaction models: the EDC (Eddy Dissipation Concept) and TPDF (Transported Probability Density Function). GTMC with a good optical access for laser measurements provides a useful database for swirling CH /Air diffusion flames at atmospheric

pressure. Modeling was performed by solving RANS and RSM equations for a 2D axisymmetric computational domain accompanied with swirl and the combustion chamber was investigated for both reacting and non-reacting conditions. A detailed reduced mechanism of DRM22 (with 22 species and 104 reactions) was used to represent the chemical reactions. Comprehensive comparisons were done for the predictions and measurements of velocity, mixture fraction, temperature, and chemical species concentrations of H , O , OH, H O, CH , CO, and CO . Results

showed an acceptable accuracy of predictions by considering computational cost. That means that

the simplified 2D-axismmetric-swirl simulation has the ability to capture some important features and structure of combustion field in a double highly swirled chamber, like GTMC, with much lower CPU time in comparison with costly 3D modellings, although misses some details of flow field characteristics in comparison with more accurate LES approach. In terms of comparison between the turbulence-chemistry interaction models, TPDF led to a good prediction for major species and flame structure near the inlets while the EDC predicted more accurately downstream of the flow field. Keywords: gas turbine combustor; turbulent partially-premixed combustion; EDC; TPDF.

1. Introduction Recently many investigations are performed on gas turbines in order to achieve a lower pollutant formations and higher performance at a reduced fuel consumption [1, 2, 3, 4, 5]. The concept of highly swirling flame is introduced as a promising choice in practical combustion systems to provide small size and yet high energy conversion chambers with a reasonable mixing, ignition, and stability characteristics [1, 3, 6]. In this technology, highly swirling Injectors lead to wide range of operating conditions with an extended life time for gas turbine combustors [6 ,7]. Variation in swirl number in these systems leads to different topologies in flow structure which imposes difficulties in design and modeling of such of combustors [3, 4]. Numerical modeling of physical phenomena in these

ACS Paragon Plus Environment

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

chambers has been investigated in some studies to find a less complicated numerical method with reasonable calculation cost and time [5, 6, 7]. However, validation and optimization of these numerical simulations need accurate data from experiments such as a standard laboratory scale combustor with comprehensive measurements. The GTMC, as a laboratory test stand, is a good chamber with many complicated characteristics reported in real gas turbine combustion chambers. A rotary unstable processing vortex core (PVC) and vortex shedding near the injectors are important features of combustion with high swirl number [6, 7]. Simultaneously occurrence of vortex breakdown due to low pressure region inside the vortex and suction of flow toward the inlets have also made these combustion chambers more complicated [2, 3, 4, 5, 6, 8]. The GTMC has provided experimental reacting and non-reacting data for three operational conditions under partiallypremixed characteristics. Flame A of this setup with a specific power rate of 42.4 [ ] is related to aeronautical or modern aero-derivative industrial gas turbines [1]. This flame, which is a stable flame without blow off, lift off, flash back, and extinction [1 ,9], could be assumed as a suitable case for validation of numerical schemes and therefore was considered in the present work. First time GTMC was investigated numerically by Widenborn et al. [7, 10, 11] in 2008 by a 3D simulation. They examined the hybrid turbulence models of SAS (scale adaptive simulation), DES (detached eddy simulation) and RANS approach for modeling the non-reacting flow field and reported reasonable cost and performance of the SAS model for GTMC modeling. In another works in 2009 [6, 12, 13], they presented the results of the EDM/FRC model for modeling reactive flow field inside the chamber. In 2013 Ihme et al. [2] modeled the GTMC using the large eddy simulation approach and reported sensitivity of modeling to sub-grid scale turbulence models and finally recommended the Verman sub-grid model for GTMC. Benim et al [8] studied the performance of different turbulence models for GTMC and the effect of boundary conditions of predictions. Wankhede et al. [4] used the URANS and DES approach with FGM for 3D modeling of GTMC. They concluded that URANS yields acceptable results but at the same time misses some details of flow field characteristics in comparison with DES. In another work, Ihme et al [5] examined the application of LES method with FPV for modeling GTMC under combustion mode. Design and optimization of gas turbine combustion chambers are an iterative procedure which requires accurate and low cost numerical schemes. In most research studies in this field, a 3D approach has been considered to model GTMC. In present work, however, it was aimed to model the GTMC using a 2D computational domain in such a manner that the major features of reacting flow field would be captured in addition to distribution of major and minor species. Moreover, using different combustion-turbulence interaction models in conjunction with a detail chemical mechanism for modeling highly double swirled flames is not well studied until now. In this frame


Page 2 of 24

Page 3 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

work, the performances of two different turbulence-chemistry interaction models in simulation of GTMC were considered to be investigated. Indeed, the main objective of this paper was to successfully present a simplified and low cost modeling set of GTMC under reacting and non-reacting condition with a capability to capture the main characteristics of flow field. It should be worthy to mention as an example that Wankhede et al. [4] reported a 3D modeling of GTMC using URANS required 260 hours and DES simulation required 280 hours for computing four combustor flow throughtimes using 32 processes in parallel on a cluster using Intel Xeon E5-2600 processors and infiniband interconnect. As mentioned above choosing an appropriate combustion model for GTMC also was considered to follow in this work by performing a comparison between two combustion models of EDC and TPDF. The GTMC as a double high swirled chamber represents local dilution and preheating through itself. Assessment different combustion models under condition of preheating and dilution have been the main subjects of some reports in recent years. In 2013 Shabanian et al [14] used the EDC, Flamelet, and PDF transport models in combination with the K − ϵ turbulence

model and two different kinetic mechanisms of GRI-Mech 3.0 and POLIMI to numerically investigate the combustion of ethylene jet flames in diluted and heated oxidant stream conditions. The results of this study showed that the EDC model is found to overestimate the reactivity of the flame and under-predict flame liftoff height. The agreement between measurements and predictions of the

PDF transport and modified EDC models got generally better results than for the flamelet model. Although PDF modelling approach of Shabanian et al. resulted in good agreement with the apparent lift-off phenomenon but the computationally cheaper EDC model was not able to provide good predictions for such phenomena. In another work, Graça et al [15] simulated a reversed flow smallscale combustor using the realizable K − ϵ turbulence model and investigated the performance of

two different combustion models of the eddy dissipation concept and the composition PDF model. Results of this study showed that the two combustion models yield similar results, and predict a delayed combustion process. Elsewhere, a good agreement between the predictions and measurements of the temperature and molar fraction of the major species was found. They also reported the fast ignition and combustion close to the burner tip as the weakness of their

simulations and suggested the use of Large Eddy Simulation to overcome this problem. RANS simulation of the fuel jet in hot diluted co-flow using composite PDF combustion model, also showed good agreement between prediction and experimental measurements [16, 17, 18]. Christo et al. [19] also performed a comparison between the TPDF and EDC simulation for the CH4/H2 jet in hot diluted co-flow (i.e. known as JHC burner). That study showed that the TPDF model performs better results in the regions close to the burner, although moving downstream makes the results far from experimental data. According these reports and some other reports both mentioned combustion


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

models introduced some weakness and advantageous in terms of prediction of flame characteristics such lift off, temperature and minor and major species for condition of diluted and preheated combustion. Accompanying the complicated flow dynamics of GTMC resulted from inlet air swirling and in consequence local dilution and preheating may leads to a conclusion that the selection of suitable combustion model for such chambers could be also an open field of study. To achieve the main aim of present work, the GTMC geometry was translated to a 2D axisymmetric computational domain and modeled using the RANS approach including the prediction of the swirl velocity under cold condition. In addition to the non-reacting simulation, a reacting simulation was carried out with a reduced detail chemical mechanism of DRM22 [20] and using the EDC and TPDF models. Finally, the simulation results and measurements were compared to obtain an overall conclusion on the performance of each model for a complicated combustion chamber simulation.

2. Gas Turbine Model Combustor (GTMC) description GTMC was a laboratory combustion chamber which was established in DLR (The German Aerospace Center) to provide a comprehensive database for validation and improvement of numerical tools for

gas turbine combustor. This combustor is schematically shown in Figure 1. It included two co-axial air inlets which supply co-swirling and central swirling airs. The central air nozzle inlet had an inner diameter of 15 mm and annular nozzle had an inner diameter of 17 mm and outer diameter of 25 mm. Methane as fuel was injected in non-swirling mode through 72 channels (0.5*0.5 mm ) such as

a ring between air nozzles. Air flow in central air inlet was around 40% of all supplied air.

Combustion chamber figured in cubic style with a square cross section of 85*85 mm and a height of

114 mm. A cylindrical duct (diameter of 40 mm and length of 50 mm) which was connected to the main chamber by a conical plate was used as the chamber exhaust.

Three different flames of A, B, and C were tested in this chamber. In the present work, flame type A, whose characteristics are shown in Table 1, was considered for modeling. It can be understood from measurements and other reports on GTMC that flow field in the chamber would be fully turbulent and highly swirled [1, 9].

3. Numerical method description Experimental and 3D numerical investigation of the GTMC has shown that the flow field inside the combustion chamber could be approximately assumed axisymmetric [1, 4, 6, 7, 8, 9], although there are some asymmetries in the corners of chamber [2]. To simplify the computational domain, chamber was modeled as a 2D swirling flow in an axisymmetric domain. In this framework, methane nozzle inlet was assumed as an annular slit with width of 0.34 mm to preserve the mass flow rate of


Page 4 of 24

Page 5 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

fuel. Using a homemade pressure based implicit code, the governing equations consisting of the axisymmetric incompressible Favre-averaged form of continuity, momentum including for swirl velocity, energy, species conservation [21, 22] (i.e. RANS equations), and the Reynolds stress model equations (RSM) [23, 24], were solved by Patankar SIMPLE algorithm. The RSM closes the RANS equations by solving five transport equations in 2D flows for the Reynolds stresses, together with an equation for the dissipation rate while giving up the isotropic eddy-viscosity hypothesis. Since the RSM accounts for the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate in a more rigorous manner than one-equation and two-equation models, it has greater potential to give accurate predictions for complex flows [25]. The exact transport equations for the transport of

u , may be written as equation 1. In which D the Reynolds stresses, ρu , , Φ and ε represent

turbulent diffusion, pressure-strain and dissipation rate tensor, respectively. In this case turbulent

diffusion is modeled by the simplified gradient-diffusion model of Daly and Harlow [26] as equation 2 and turbulent viscosity is computed using equation 3 . The pressure-strain term is modeled according to linear pressure-strain assumption [27, 28, 29, 23]. The dissipation tensor, ε , is modeled as equation 4 where Y is an additional “dilatation dissipation” term according to the

model by Sarkar [30] in equation 5. The turbulent Mach number M% in this term is defined as equation 6 where a is the speed of sound described in equation 7. When the turbulence kinetic energy (k) is needed for modeling a specific term, it is obtained by taking the trace of the Reynolds

stress tensor as equation 8 and the scalar dissipation rate, ϵ, is computed with a model transport equation similar to that used in the standard k − ϵ model.

Regarding the species conservation equations, the transport equation for one of the species (the bulk species) was not solved and substituted by the equation relating all species (i.e. ∑)) *+,-,* Y = 1). This method helped to satisfy the total mass conservation. Here the N2 was the most abundant

species and was chosen as the bulk species. All the equations except the species conservation were discretized by second order Quick method (i.e. Quadratic Upstream Interpolation for Convective Kinetics [31]). The appropriate boundary conditions for velocity and turbulence profiles were set using 3D modeling of the inlets’ upstream. Results of the mentioned 3D modeling were averaged in the chamber inlet planes because the 3D effects of flow inside the upstream passage of the chamber should not be ignored. Figure 2 shows the computational domains, boundary conditions, and computational grids. Grid inside the chamber was generated in multi-block structure, using the hybrid methods in which structured and unstructured cells in the domain were filled by 95 and 5 percent, respectively. To capture the flow separation in chamber walls (Coandă effect [3]), a condition of Y 0 < 1 was met in injector walls. Two criteria were chosen for identifying the solution

convergence. The first was to ensure that the residuals of all variables drop below 103 . The second


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

was to ensure that some of all variables had been stabilized and were no longer changing with iterations. Chemical mechanism was represented by a reduced detail chemical mechanism of

DRM22, which consists of 22 species, plus Ar and N , for a total of 104 reversible reactions. This

mechanism has been used successfully for methane combustion under dilute condition by the authors in [32, 33].

The main challenges in modeling turbulent combustion are handling the mean rate of reaction and adequate representation of the chemistry in the model. In this study the capability of two classes of turbulence-chemistry interaction models for predicting the behavior of combustion in a gas turbine model combustor is assessed: volumetric reaction-based model of the Eddy-Dissipation-Concept (EDC [34]) and Transported Probability Density Function (TPDF). The Eddy dissipation concept (EDC) model has the advantage of incorporating detailed kinetics with a computational cost which is quite moderate compared to more advanced models such as the transported PDF method, especially if the In-Situ Adaptive Tabulation (ISAT) method [35] is used. However, this advantage comes at the cost of a less accurate description of turbulent-combustion interaction [36]. The EDC is an extension of the eddy-dissipation model to include detailed chemical mechanisms in turbulent flow assuming that the reaction takes place in the small turbulent structures, namely the fine scales. The length and volume fraction of the fine structures are modeled as ζ and ζ5 respectively which is described in

equation 9 [37] and when each structure is a Constant-Pressure-Reactor (CPR). Species are assumed to react in the fine structures over a time scale of τ using equation 10 [37] and according to

Arrhenius finite rate law and a detailed chemical mechanism where ν is kinematic viscosity, k is

turbulent kinetic energy, ε is turbulent dissipation rate, cζ = 2.1377 is the volume fraction constant, and cτ = 0.4082 is the time scale constant.

The composition PDF transport (TPDF) equation is an alternative to the Reynolds-averaging of the

species and energy equations [38]. Nevertheless, the TPDF model requires the modeling of the molecular mixing of species and heat which are usually the most significant source of errors in the TPDF approach [39]. The TPDF model allows simulating finite rate chemical kinetic effects in turbulent reacting flows as well as flame extinction and ignition [39]. This combustion model is computationally expensive, but the computational power currently available allows the use of such an approach for two-dimensional simulations. In this method, the highly-non-linear reaction term is completely closed and does not need any modeling. Here the composition PDF transport equation is derived from the Navier-Stokes equations. The PDF (i.e. P), which is considered to be proportional to the fraction of the time that the fluid spends at each species and temperature state, has N + 1 dimensions for the N species and temperature. From the PDF, any thermoechemical moment (e.g.

mean reaction rate or mean or RMS temperature) can be calculated. The TPDF equation is derived


Page 6 of 24

Page 7 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

from the Navier-Stokes equations as equation 11 [40]. In this equation P is the Favre joint PDF of composition, ρ is the mean density of the fluid, u is the Favre mean fluid velocity vector, SA is the

reaction rate for species k, ψ is the composition space vector, u" is the fluid velocity fluctuation vector, and J,A is the molecular diffusion flux vector. The generic notation < A|B > indicates the

conditional probability of event A, given the occurrence of event B. In this equation, unsteady rate of change of the PDF, the change of the PDF due to convection by the mean velocity field, and the change due to chemical reactions are closed while the PDF change due to scalar convection by turbulence (turbulent scalar flux) and molecular mixing/diffusion are unclosed and require modeling. The turbulent scalar flux term is modeled by the gradient-diffusion assumption which is delivered by equation 12 and the molecular mixing of heat and species are modeled by the Euclidean Minimum Spanning Tree (EMST) model [41]. Thermal radiation was found to have little effect on the result and yet impose expensive computational cost; therefore it was not considered in this research. In the species mass conservation equations, the diffusion velocities were determined using the first Fick’s law and the binary diffusion coefficients were found from molecular kinetic theory [42]. Moreover, the laminar viscosity and the thermal conductivity of each species were computed using the results of the kinetic theory of monatomic gases, which is written in terms of the Lennard-Jones parameters. To calculate the viscosity and conductivity of the mixture, the formula of Wilke was used [43]. The mixture’s specific heat capacity was computed as a mass fraction average of the pure species heat capacities, while the heat capacities of pure species were estimated using polynomials fitted through the thermodynamic standard databases of the used chemical mechanism.

4. Results and discussion 4.1. Non-reacting flow analysis As shown in Table 2, three cases for calculation were considered here to study the effect of the combustion and turbulence-chemistry interaction models on chamber flow field and also accuracy of GTMC predictions. At first a grid study was performed using two grids with 24370 and 97480 cells for reacting and nonreacting flow. Results showed the grid with 24370 cells worked as well as fine grids and its results were independent from grid resolution, although some local grid adaptation was done in the case of 24370 to improve the grid quality. Profiles of velocity components for reacting and non-reacting flow and temperature, mixture fraction, and mass fractions of CO from reacting flow modelling for two grids are compared with each other in Figure 3 and this figure illustrates the independency of results of the case with 24370 cells from grid resolution.


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Predicted mean path-lines for non-reacting flow field are presented in Figure 4. Three recirculation zones indicated that the flow field inside the GTMC was such complicated that needed very especial considerations in modelling. A strong inner recirculation zones (IRZ) along the axial centre line and two outer recirculation zones (ORZ) near the walls force the injected fuel to flow between IRZ and ORZ inside of shear layers. These mean there was a strong vortex breakdown inside of chamber and could be considered as a sign of good qualitative performance of selected models given the fact that this phenomenon has been already observed experimentally. It is worthy to note that an appropriate turbulence model plays a key role here in capturing the experimental observation through modelling. To follow the precise accuracy of modelling, axial, radial, and swirl components of velocity profiles are compared with experimental measurements in Figure 5. For three axial distances of 2.5, 20, and 90 mm from the inlet plane, radial profiles of velocity components are presented in these figures. It can be seen for axial distance of 2.5 mm that there was a good agreement between the measurements and predictions. At X = 2.5 mm maximum value of axial velocity inside of shear layer

was 35 m/s which was predicted reasonably. Negative values for radial velocity were related to the

ORZ region where Y > 17 mm. For X = 20 mm velocity profiles were flattened and ORZ region

exhibited a reduction in size. A more distancing along the axis led to disappearance of IRZ and ORZ regions. Although physical phenomena and their trends were captured, it seems that the higher dissipations in RANS in comparison with reality has led to an underprediction of axial and swirl velocities at downstream. It is worthy to mentioned that 3D modelling of GTMC surely would improve the accuracy of velocity field prediction as reported in [2, 7] but with much higher computational cost. 4.2. Reacting flow analysis In this section, combustion was also considered in the modeling using two different turbulencechemistry interaction models of the EDC and TPDF. The purpose of this study, in continuation, was to investigate the hot flow field within the chamber and get an insight on the performance of these two models in capturing some important features of combusting flow, when limitations of RANS method were considered in analyzing the results. In this way, first, predicted flow field by these two approaches (i.e. EDC and TPDF) will be investigated from velocity field point of view, and then, in the next section, more focus will be put on the predicted species and temperature field. 4.2.1. Discussion on velocity field Contours of velocity field for two cases of EDC and TPDF models are depicted in Figure 6 while black lines indicate the location of zero mean axial velocity (i.e. VL) = 0) and represent the IRZ

boundaries. In comparison with experimental findings, Figure 6 shows that the physical aspects of


Page 8 of 24

Page 9 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

flow field were captured with a qualitatively good accuracy. Negative velocity values and large velocity gradients inside of IRZ are result of a strong eddy break up which opens way to a suction flow toward the central air inlet. Moreover, it could be seen that the ORZ in the corner of the computational domain takes the same structure as that of non-reacting results. The modelling with the EDC predicted a larger IRZ region than the TPDF one. It should be say that velocity field and temperature field, resulted from combustion, have interaction with each other. Any weaknesses of combustion models regarding ignition and lift off leads to a stable reaction zone at higher heights and therefore may be known as a reason for different sizes of IRZ. To get a quantitative view on the accuracy of the results, isolines of zero axial velocity are also compared with the experimental data. Figure 6 also shows that there were some discrepancies between the predictions and the experiments for both modelling approaches. In terms of predictions of IRZ height on the axis of flame, the TPDF yielded more accurate results and had a prediction same as the measurements (i.e. 60 mm). On the other hand, the EDC model predicted the maximum height of IRZ (i.e. 73 mm) more accurately than the TPDF one while its overprediction for width was higher. That means that the IRZ size was larger in EDC prediction than both the TPDF modelling and experimental. Quantitative study of predicted velocity fields for hot condition is investigated in Figure 7. In this figure, axial, radial, and swirl components of velocity are compared with measurements at heights of 2.5, 20, and 90 mm from the nozzle. The minimum axial velocity at X = 20 mm were predicted around −20 m/s by two

models which was in agreement with experimental data although for X < 20 MM it was

underpredicted. In the profiles of axial velocity, the maximum velocities were related to the shear layers between the IRZ and ORZ while the minimum velocity in the axis of flame represents the region in which there was a reverse flow toward the central air inlet axis. In radial velocity profiles at X=2.5 mm, the region of outer side of the second positive maximum velocity and also inward

directed radial velocities (i.e. Y > 18 MM) were related to the ORZ; and the minimum positive radial

velocity, between two maximums, showed approximately the IRZ border. The swirl velocity profile, at X=2.5 mm, showed two maximum positive values in the region where swirl inlet air was flowed and a minimum value between them which was related to the region of non-swirl inlet fuel flow.

At 2.5 < N < 20 MM the velocity profiles trends did not change but they broadened by moving

away from the nozzle. That means that as we moved away from the chamber bottom the IRZ increased in size while the ORZ size in contradiction decreased. With enough moving toward the downstream, IRZ and ORZ disappeared and velocity profiles smoothed out. As a whole, axial maximum velocities were predicted satisfactory while their minimum were underpredicted in the upstream at X = 20 mm. Radial velocities were predicted well although there

were some overpredictions near the inlet plane. For swirl velocity profiles deviations were increased


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

at the downstream especially in relation with broadening the profiles. Both of the EDC and TPDF worked relatively similar in an away that, overly, predicted velocity field showed less sensitivity to them and both models produced reasonably accurate flow field structures. In comparison with cold flow field (i.e. figure 5), it seems that the accuracy of modelling is increased which may be due to higher dissipation and relaminarization of flow resulted from higher temperature and molecular viscosity. 4.2.2. Discussion on temperature and species field Investigation of combustion in GTMC was followed in this section using mixing level, temperature profiles, and species concentrations. Mixing could be measured by mixture fraction distribution and here was computed using Bilger’s formula [44]. Comparison between contours of mixture fraction in numerical and experimental data is shown in Figure 8 while global mixture fraction contours is also imposed to the figures. It can be seen that in the ORZ the mixture fraction was lower than its global

value. Moreover, in the IRZ results of TPDF model showed f > fP)Q) while for the EDC model

mixture fraction was around global mixture fraction (fP)Q) ) in comparison with the experimental

data. Furthermore, the contours of mixture fraction were predicted better by the TPDF than the EDC model in the IRZ and the EDC model suggested a more rapid mixing rather than the TPDF model. It was interesting that at large area of chamber the mixture fraction was around its global value which means the mixing was well performed in GTMC per our expectations. Moreover, gradually decrease in mixture fraction level by distancing from the flame showed that the GTMC worked approximately under partially premixed condition as could be seen especially in the contours of mixture fraction for

the TPDF case. To complete the discussions, the contours of temperature, CH , H O, O , and OH

were compared with experimental measurements in Figures 9 to 13. It can be seen that in general both models had an ability to introduce similar contours as experiments, although the resulted TPDF modeling contours for OH mass fraction and CH mole fraction were more accurate than the EDC

ones while in relation with the temperature and major species of H O and O the EDC model had

marginally a better performance especially in the IRZ. Maximum predicted temperature using the EDC model and TPDF were around 2056 K and 1839 K, respectively, while it was around 1800 K in measurements. The maximum temperatures for both cases of the EDC and TPDF have occurred in the IRZ and downstream of the central air inlet. Moreover, temperature decreased along the axis of chamber for EDC case while it was not true in the case of TPDF. On the other hand, the results of the EDC demonstrated a more uniform temperature field with a lower level in the most area of the chamber except the inner border of ORZ and upstream front side of the IRZ. One reason for these behaviors may be due to the weakness in mixing prediction as mentioned in the mixture fraction

contours. According to contours of OH and temperature it could be concluded that for the reaction


Page 10 of 24

Page 11 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

rates predictions there were an overestimation in the ORZ in results of both cases, although it is more severe for the EDC case. Furthermore, contours show that there was also an overestimation for H2O and temperature and an underestimation for O2 in the IRZ for the results of two cases with a higher in predictions of the TPDF. To have a more precise comparison between prediction and

measurements, the radial profiles of mixture fraction, temperature, H , CO, and CO at three

different heights were depicted in Figures 14-18. Mixture fraction profiles indicated that there was a good result of modeling for height above 20 mm but in distances lower than 20 mm, the mixing was overpredicted which led to rapid smoothing of mixture fraction profiles. Moreover, the results in graphs show a marginal better performance of TPDF in comparison with the EDC. Indeed, the increased deviation near the nozzle could be attributed to the effect of high unsteadiness of flow that the current modeling approaches in this paper were unable to capture. The later statement is in consistency with some other numerical and experimental reports on GTMC regarding the existence of unstable structures near the inlet plane and inside of shear layer. Weigand et al. [1] reported the instantaneous flow fields include strong turbulent fluctuations in the shear layer between the inflow and the IRZ where large u * (u * /u ,R >> 100%) values indicates that hear layer is not locally

stable. Also See et al. [5], by a LES modeling, showed the flame wrinkling at the lifted flame base in the nozzle-near region for GTMC. In a same manner as in mixing, temperature profiles showed less

discrepancy with measurements further away from the nozzle. At X = 5 mm the temperature at the

axis was overpredicted about 800 and 500 K by EDC and TPDF models, respectively. This may be due to the effects of unsteady flow and weakness of models in predicting the flame lift off or in other words rapid ignition which can be understood also from countors of OH and temperature in figures 9 and 13. Figures showed that in the region within shear layer, minimum temperature was affected by fuel inlet stream and predicted reasonably. Moreover, the increase in the size of the IRZ at far distances from nozzle led to the expansion of high temperature area which was captured successfully by both models. Finally, it seems that the TPDF worked with a higher performance than

the EDC model in prediction of reaction zone structure especially at the ORZ and upstream on the axis. This may be due to mixing predictions by the models.

In relation with species distribution, both models predicted CO more accurately at the downstream

compared to the upstream. Although, the results of TPDF near the nozzle was better than the EDC and it was in reverse at downstream. In relation with CO profiles, judgment was a little difficult to

make because although the maximum or minimum concentrations of CO were predicted more

accurately by the EDC model especially at downstream, somewhere the profile trends were calculated better in the TPDF. The profiles of H also had a behavior like CO profiles. It would be

worthy to notice that comparison between maximum of temperature and species profiles from


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

predictions and measurements revealed that deviations are lower for height of 15 and 30 mm than 5 mm. These deviations are in the range of 3%, 5%, 14%, and 18% for temperature, CO2, CO, and H2, respectively, at 15 and 30 mm while they are larger at 5 mm, in exception for H2. Some portion of the errors may be attributed to the physical phenomena related to the vortex shedding and core processing vortex near the inlets which could not be considered at a very precise style by 2D-Axiswirl modeling. Because of this the IRZ region has been captured like an apple shape instead of pear

shape which leads to thicker IRZ zone at 15 < N < 60 mm in comparison with measurements. On

other hand the prediction especially at near the injection plane was very sensitive to boundary conditions for velocity components and turbulence profiles. Although in this research it has been tried to set more accurate boundary conditions by 3D modeling of the inlets at upstream of chamber, they are not perfect yet. As a whole, it could be concluded the results of the EDC model was more reasonable at the downstream of the chamber in comparison with the upstream due to relatively weaker unsteadiness effects in the downstream field. In opposite side the TPDF model provided more precise prediction in the upstream than the downstream. Moreover, using the TPDF model showed some advantages in prediction of reaction zone structure. Furthermore current 2D axismmetric-swirl modeling presents some comparable accuracy in comparison with the other 3D modeling using URANS method [4] but it has a lower accuracy in comparison with 3D LES approach [2].

5. Conclusion In this paper, numerical modelling of an experimental gas turbine model combustor was done using the RANS method in a 2D axisymmetric-swirl computational domain. GTMC is a combustor with double swirl air inlets that utilizes methane as its fuel. Both cold and hot flow fields were simulated and a comprehensive comparison between the numerical and experimental results was presented for velocity, temperature, and some major and minor chemical species. Reacting modelling was performed using the chemical mechanism of DRM22 (with 22 species and 104 reactions) and two turbulence-chemistry interaction models of the EDC (Eddy Dissipation Concept) and TPDF (Transported Probability Density Function). Results indicated that both modelling approaches could almost capture the main flow field structures inside the chamber. Both models predicted the IRZ and ORZ satisfactory but in relation with temperature and chemical species there are some deviation in results comparing to the measurements. The EDC model worked more satisfactorily in the downstream of the chamber and predicted the maximums of temperature and major species (i.e. CO , O , H , and H O) more precisely compared to the TPDF. However, in the upstream and near of

air and fuel inlets the TPDF model showed a better performance in terms of predicting flame


Page 12 of 24

Page 13 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

structure and maximums of temperature and species concentrations. The present RANS modelling of high double swirled GTMC combustion chamber exhibited an acceptable accuracy by much lower numerical cost in comparison with the other 3D modellings based on URANS approach. For instance the modeling, in this work, by EDC model required 6 hours using an Intel(R) Core(TM) i7-4702MQ CPU 2.2GHz processors whereas there was reports on GTMC with 260 hours required for 3D URANS

simulation for computing four combustor flowthrough times using 32 processes in parallel on a cluster using Intel Xeon E5-2600 processors and infiniband interconnect. It should be noticed that modeling this combustion chamber showed a high sensitivity to grid resolution and quality especially on the wall at chamber base as well as peripheral walls at the upstream and also to the inlet boundary conditions for velocity and turbulence profiles. Authors think that any more precise study on inlet boundary conditions on fluid dynamic inside the chamber and also assessment of different tabulated chemistry models as combustion models would be worthy.

References [1] P. Weigand, W. Meier, X. R. Duan, W. Stricker, and M. Aigner, 'Investigations of Swirl Flames in a Gas Turbine Model Combustor: I. Flow Field, Structures, Temperature, and Species Distributions', Combustion and Flame, 144 (2006), 205-24. [2] Y.C. See, and M. Ihme, 'Large-Eddy Simulation of a Gas Turbine Model Combustor', in 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (American Institute of Aeronautics and Astronautics, 2013). [3] Y.C. See, and M. Ihme, 'Les Investigation of Flow Field Sensitivity in a Gas Turbine Model Combustor', in 52nd Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 2014). [4] M.J. Wankhede, F.A. Tap, P. Schapotschnikow, and W.J. Ramaekers, 'Numerical Study of Unsteady FlowField and Flame Dynamics in a Gas Turbine Model Combustor', in ASME Turbo Expo 2014: Turbine Technical Conference and Exposition (American Society of Mechanical Engineers, 2014), pp. V04AT04A050-V04AT04A50. [5] Y.C. See, and M. Ihme, 'Large Eddy Simulation of a Partially-Premixed Gas Turbine Model Combustor', Proceedings of the Combustion Institute, 35 (2015), 1225-34. [6] A. Widenhorn, B. Noll, and M. Aigner, 'Numerical Characterisation of a Gas Turbine Model Combustor Applying Scale-Adaptive Simulation', in ASME Turbo Expo 2009: Power for Land, Sea, and Air (American Society of Mechanical Engineers, 2009), pp. 11-23. [7] A. Widenhorn, B. Noll, and M. Aigner, 'Numerical Study of a Non-Reacting Turbulent Flow in a Gas-Turbine Model Combustor', in 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (American Institute of Aeronautics and Astronautics, 2009). [8] A. Benim, S. Iqbal, A. Nahavandi, W. Meier, A. Wiedermann, and F. Joos, 'Analysis of Turbulent Swirling Flow in an Isothermal Gas Turbine Combustor Model', in ASME Turbo Expo 2014: Turbine Technical Conference and Exposition (American Society of Mechanical Engineers, 2014), pp. V04AT04A001-V04AT04A01. [9] W. Meier, X.R. Duan, and P. Weigand, 'Investigations of Swirl Flames in a Gas Turbine Model Combustor: II. Turbulence–Chemistry Interactions', Combustion and Flame, 144 (2006), 225-36. [10] A. Widenhorn, B. Noll, M. Stöhr, and M. Aigner, 'Numerical Characterization of the Non-Reacting Flow in a Swirled Gas turbine Model Combustor', in High Performance Computing in Science and Engineering `07, ed. by Wolfgang E. Nagel, Dietmar Kröner and Michael Resch (Springer Berlin Heidelberg, 2008), pp. 431-44. [11] A. Widenhorn, B. Noll, M. Stöhr, and M. Aigner, 'Numerical Investigation of a Laboratory Combustor Applying Hybrid RANS-LES Methods', in Advances in Hybrid RANS-LES Modeling, ed. by Shia-Hui Peng and Werner Haase (Springer Berlin Heidelberg, 2008), pp. 152-61.


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

[12] A. Widenhorn, B. Noll, and M. Aigner, 'Numerical Characterization of the Reacting Flow in a Swirled Gasturbine Model Combustor', in High Performance Computing in Science and Engineering '08, ed. by WolfgangE Nagel, DietmarB Kröner and MichaelM Resch (Springer Berlin Heidelberg, 2009), pp. 365-80. [13] A. Widenhorn, B. Noll, and M. Aigner, 'Numerical Characterization of a Gas Turbine Model Combustor', in High Performance Computing in Science and Engineering '09, ed. by Wolfgang E. Nagel, Dietmar B. Kröner and Michael M. Resch (Springer Berlin Heidelberg, 2010), pp. 179-95. [14] S. R. Shabanian, P. R. Medwell, M. Rahimi, A. Frassoldati, and A. Cuoci, 'Kinetic and Fluid Dynamic Modeling of Ethylene Jet Flames in Diluted and Heated Oxidant Stream Combustion Conditions', Applied Thermal Engineering, 52 (2013), 538-5 [15] M. Graça, A. Duarte, P. J. Coelho, and M. Costa, 'Numerical Simulation of a Reversed Flow Small-Scale Combustor', Fuel Processing Technology, 107 (2013), 126-37. [16] A. R. Masri, R. Cao, S. B. Pope, and G. M. Goldin, 'Pdf Calculations of Turbulent Lifted Flames of H~ 2/N~ 2 Fuel Issuing into a Vitiated Co-Flow', Combustion Theory and Modelling, 8 (2004), 1-22. [17] R. Cabra, J. Y. Chen, R. W. Dibble, A. N. Karpetis, and R. S. Barlow, 'Lifted Methane–Air Jet Flames in a Vitiated Coflow', Combustion and Flame, 143 (2005), 491-506. [18] R. R. Cao, S. B. Pope, and A. R. Masri, 'Turbulent Lifted Flames in a Vitiated Coflow Investigated Using Joint Pdf Calculations', Combustion and flame, 142 (2005), 438-53. [19] F. Christo, and B.B. Dally, 'Application of Transport Pdf Approach for Modelling Mild Combustion' (DSTO, 2004).

[20] A. Kazakov, and M. Frenklach, 'Reduced Version of Gri-Mech 1.2. 22 Species (+ N2, Ar); 104 Reactions', (PennState: 1994), http://www.me.berkeley.edu/drm/. [21] K.K. Kuo, 'Principles of Combustion', John Wiley & Sons, Inc., the United States of America, 1986, page 430. [22] G.K. Batchelor, 'An Introduction to Fluid Dynamics', Cambridge Univ. Press, Cambridge, England, 1967 [23] B. E. Launder, 'Second-Moment Closure: Present… and Future?', International Journal of Heat and Fluid Flow, 10 (1989), 282-300. [24] B. E. Launder, G. Jr. Reece, and W. Rodi, 'Progress in the Development of a Reynolds-Stress Turbulence Closure', Journal of fluid mechanics, 68 (1975), 537-566. [25] M. Nallasamy, 'Turbulence Models and Their Applications to the Prediction of Internal Flows: A Review', Computers & Fluids, 15 (1987), 151-94. [26] B.J. Daly, and F.H. Harlow, 'Transport Equations in Turbulence', Physics of Fluids (1958-1988), 13 (1970), 263449.

[27] Gibson M.M. , and B.E. Launder, 'Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer', Journal of Fluid Mechanics, 86 (1978), 491-511.

[28] S. Fu, B.E. Launder, and M.A. Leschziner, 'Modelling Strongly Swirling Recirculating Jet Flow with ReynoldsStress Transport Closures', in 6th Symposium on Turbulent Shear Flows (1987), pp. 17-6.

[29] B.E. Launder, and B. Edward, 'Second-Moment Closure and Its Use in Modelling Turbulent Industrial Flows', International Journal for Numerical Methods in Fluids, 9 (1989), 963-85.

[30] S. Sarkar, and B. Lakshmanan, 'Application of a Reynolds Stress Turbulence Model to the Compressible Shear Layer', AIAA journal, 29 (1991), 743-49.

[31].B.P. Leonard, and S. Mokhtari, 'Ultra-Sharp Nonoscillatory Convection Schemes for High-Speed Steady Multidimensional Flow', (1990). [32] A. Mardani, S. Tabejamaat, and M. Ghamari, 'Numerical study of influence of molecular diffusion in the Mild combustion regime', Combustion Theory and Modelling, 14:5(2010), p.747 — 774. [33] A. Mardani, S. Tabejamaat and M. Baig Mohammadi, 'Numerical study of the effect of turbulence on rate of reactions in the MILD combustion regime', Combustion Theory and Modelling, 15:6 (2011), p.753-772 [34] B.F. Magnussen, 'On the Structure of Turbulence and a Generalized Eddy Dissipation Concept for Chemical Reaction in Turbulent Flow'. 19th AIAA Meeting, St. Louis, 1981. [35] S.B. Pope, 'Computationally Efficient Implementation of Combustion Chemistry Using in Situ Adaptive Tabulation', Combustion Theory and Modelling, 1 (1997), 41-63. [36] A. De, E. Oldenhof, P. Sathiah, and D. Roekaerts, 'Numerical Simulation of Delft-Jet-in-Hot-Coflow (Djhc) Flames Using the Eddy Dissipation Concept Model for Turbulence–Chemistry Interaction', Flow, Turbulence and Combustion, 87 (2011), 537-67.

[37] I.R. Gran and B.F. Magnussen, 'A numerical study of a bluff-body stabilized diffusion flame. part 2. influence of combustion modeling and finite-rate chemistry', Combustion Science and Technology (1996), pp.119:191.


Page 14 of 24

Page 15 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

[38] S. B. Pope, 'Pdf Methods for Turbulent Reactive Flows', Progress in Energy and Combustion Science, 11 (1985), 119-92. [39] S. R. Shabanian, P. R. Medwell, M. Rahimi, A. Frassoldati, and A. Cuoci, 'Kinetic and Fluid Dynamic Modeling of Ethylene Jet Flames in Diluted and Heated Oxidant Stream Combustion Conditions', Applied Thermal Engineering, 52 (2013), 538-5 [40] S. B. Pope, 'Pdf Methods for Turbulent Reactive Flows', Progress in Energy and Combustion Science, 11 (1985), 119-92.

[41] S. Subramaniam and S. B. Pope, 'A Mixing Model for Turbulent Reactive Flows Based on Euclidean Minimum Spanning Trees'. Combustion and Flame, 115 (1998), p.487-514. [42] J. Warnatz, U. Mass, R.W. Dibble, 'Combustion', springer,Germany,1996, Chapter 5 & pp. 186 [43] R.B. Bird, W.E. Stewart and E.N. Lightfoot, 'Transport Phenomena', John Wiley & Sons, Inc., second edition, 2002, pages 26, 276 & 659 [44] R.W. Bilger, S.H. Starner, and R.J. Kee, 'On Reduced Mechanisms for Methane/Air Combustion in Nonpremixed Flames', Combustion and Flame, 80 (1990), 135-49.


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 1- Characteristics of Flame A [1,9] CH P%V ΦP)Q) fP)Q)

Air

Flame A

sl/min g/min sl/min g/min 850

Page 16 of 24

1095

58.2

41.8

kW

34.9

0.65

TP)Q) X%-

0.037

K

1750

P%V , thermal power; ΦP)Q), equivalence ratio for the overall mixture; fP)Q) , mixture fraction for the overall mixture; TP)Q) X , adiabatic temperature for the overall mixture with inlet temperature T] = 295 K.

Case Number 1 2 3

Flame Type A A A

Table 2- Numerical test cases Turbulence Turbulence-Combustion model interaction model RSM RSM EDC RSM TPDF

u a ∂`ρu ∂`ρuA u u a ∂u ∂ ∂ ∂u u af − ρ gu u `u + = D, + dμ + u uA h + Φ − ϵ A ∂t ∂x A ∂x A ∂xA ∂x A ∂xA

D, =

u ∂ μ% ∂u g h ; σA = 0.82 ∂xA σA ∂xA

μ% = ρCk

k ; C = 0.09 ϵ k

(Equation 3) (Equation 4)

Y = 2ρϵM%

(Equation 5)

k a

(Equation 6)

a = oγRT 1 k= u u 2


νε ].v

ζ = cζ s

τ = cτ s

At


2 ϵ = δ mρϵ + Y ) 3 M% = n

Chemical mechanism DRM22 DRM22

u

; cζ = 2.1377

(Equation 9)

ν ].v u ; cτ = 0.4082 ε

(Equation 10)


Page 17 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

List of Tables Table 1- Characteristics of Flame A [1,9] Table 2- Numerical test cases List of figures Figure 1- Schematic drawing of the model combustor [1] Figure 2- a) 2D-Axisymmetric computational domain and applied boundary condition. b) 3D computational domain of annular swirler. c) 3D computational domain of central swirler

Figure 3- Grid sensitivity study for non-reacting (a-c) and reacting (d-i) flow at X = 5 mm

Figure 4- Streamline plot of the axial velocity colored by axial velocity

Figure 5- Comparison of computed and experimental velocity components for non-reacting flow field at three axial sections through GTMC Figure 6- Contours of axial velocity for the EDC and TPDF models. Black lines represent the location of zero axial velocity. Black points represent IRZ boundaries coming from experiments. Figure 7- Comparison of computed and experimental velocity components for EDC and TPDF models at three axial sections through GTMC. Figure 8- Distribution and comparison of computed and experimental mixture fraction for EDC and TPDF models. Figure 9- Distribution and comparison of computed and experimental Temperature for EDC and TPDF models.

Figure 10- Comparison of computed and experimental CH mole fraction for EDC and TPDF models.

Figure 11- Comparison of computed and experimental H O mole fraction for EDC and TPDF models. Figure 12- Comparison of computed and experimental O mole fraction for EDC and TPDF models.

Figure 13- Comparison of computed and experimental OH mass fraction for EDC and TPDF models.

Figure 14- Comparison of computed and experimental mixture fraction for EDC and TPDF models at three axial sections through GTMC. Figure 15- Comparison of computed and experimental Temperature for EDC and TPDF models at three axial sections through GTMC.

Figure 16- Comparison of computed and experimental H mass fraction for EDC and TPDF models at

three axial sections through GTMC.

Figure 17- Comparison of computed and experimental CO mass fraction for EDC and TPDF models at

three axial sections through GTMC.

Figure 18- Comparison of computed and experimental CO mass fraction for EDC and TPDF models at three axial sections through GTMC.


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1- Schematic drawing of the model combustor [1].

(a)

(b) (c) Figure 2- a) 2D-Axisymmetric computational domain and applied boundary condition. b) 3D computational domain of annular swirler. c) 3D computational domain of central swirler.

1


Page 18 of 24

Page 19 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

(a)

(b)

(c)

(d)

(e)

(f)

(g) (h) (i) Figure 3- Grid sensitivity study for non-reacting (a-c) and reacting (d-i) flow at

Figure 4- Streamline plot of the axial velocity colored by axial velocity

2


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 24

Figure 5- Comparison of computed and experimental velocity components for non-reacting flow field at three axial sections through GTMC.

Figure 6- Contours of axial velocity for the EDC and TPDF models. Black lines represent the location of zero axial velocity. Black points represent IRZ boundaries coming from experiments.

3


Page 21 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 7- Comparison of computed and experimental velocity components for EDC and TPDF models at three axial sections through GTMC.

4


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 8. Distribution and comparison of computed and experimental mixture fraction for EDC and TPDF models.

Figure 9. Distribution and comparison of computed and experimental Temperature for EDC and TPDF models.

Figure 10. Comparison of computed and experimental mole fraction for EDC and TPDF models.


Figure 13. Comparison of computed and experimental mass fraction for EDC and TPDF models.


5


Page 22 of 24

Page 23 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 14- Comparison of computed and experimental mixture fraction for EDC and TPDF models at three axial sections through GTMC.

Figure 15- Comparison of computed and experimental Temperature for EDC and TPDF models at three axial sections through GTMC.

Figure 16- Comparison of computed and experimental mass fraction for EDC and TPDF models at three axial sections through GTMC.


6


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


7


Page 24 of 24

Numerical Investigation of a Double-Swirled Gas Turbine Model

Recommend Documents