Main flow characteristics in a lean premixed swirl stabilized gas turbine combustor Numerical computations

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1 AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH 213, Science Huβ, ISSN: X, doi:1.5251/ajsir Main flow characteristics in a lean premixed swirl stabilized gas turbine combustor Numerical computations H. M. AbdelGayed*, W. A. Abdelghaffar, K. El Shorbagy Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, Egypt *Corresponding author; Mobile Phone: , Hekhalil@gmail.com ABSTRACT Main swirling flow characteristics are numerically investigated in a typical lean premixed swirl stabilized combustor. The combustor under investigation has been reported previously in the literature for experimentally determining both the combustion instabilities frequency and amplitude with no reference to the detailed flow dynamics inside. It is described in details in the present work. Both realizable K- epsilon and Detached eddy simulation (DES) turbulence models have been used to investigate the flow characteristics inside the combustor. The resultant governing equations have been solved by means of couple pressure based finite volume methodology. ANSYS-Fluent 12 commercial package has been used in the study. Using realizable K-epsilon, a central recirculation zone which is necessary for flame stabilization and efficient combustion has been shown. Also a corner recirculation zone has been detected due to flow separation near combustor dump plane. Using DES, Worm like small scale coherent turbulent structures have been noticed over the vortex break down region followed by a large scale, full length, columnar precessing vortex core along the pipe center line in consistent to previous findings. Results of the current moderate swirl case (S=.45) have been qualitatively compared with an experimental high swirl case (S=.6) to determine the effect of swirl on flow characteristics. The high swirl experimental case of S=.6 resulted in wider central recirculation zone, shorter corner recirculation zone, faster flow reattachment to the wall and slower decay of tangential velocity in comparison of current moderate swirl case of S=.45. However, further numerical and experimental investigations need to be done in order to gain more insight of the flow dynamics inside the combustor. Keywords: Swirling flow, lean premixed combustion, realizable k-epsilon, DES, ANSYS fluent. INTRODUCTION The stricter legislations implied on emissions of internal combustion engines, especially gas turbines, have been the driving force behind the increasing interest in stable and efficient combustion (Boyce, 26). One of the most common means of stabilizing flames is to provide a swirler upstream the combustor dump plane. The swirl component imparted by the swirler on the incoming mixture (in case of premixed combustion) results in the creation of a central recirculation zone immediately downstream the combustor dump plane. This recirculation zone is directly responsible for entrainment, recirculation, and mixing of fresh reactants with hot products to ensure continuous and stable combustion. Moreover, due to swirling, the axial component of flow velocity is reduced which prevents the flame from being convected downstream the combustor and anchors it, hence provide enough time for complete combustion (Le Febvre, 1999). The spreading of the flow at the beginning and while moving downstream along the axial direction of the combustor is mainly because of the centrifugal force imparted on the flow (Eldrainy et al, 29). This centrifugal force results also in an area of low pressure at the centerline of the combustor. At a certain point and when the centrifugal force starts to decay because of viscous effects the low pressure zone causes the vortex to gradually collapse while moving further downstream until it finally vanished in a process known as '' vortex break down'' (Huang et al, 29). Several experimental investigations have been conducted in the last decade to address the main characteristics of swirling flows (Huang et al, 29). Marliani et al. (23) experimentally investigated the evolution characteristics of swirl flow in a pipe for moderately high-reynolds numbers and over a wide range of swirl numbers. A dominant effect of swirl with a solid body rotation along the center line has been showed

2 Am. J. Sci. Ind. Res., 213, 4(1): in their study. Also, Ahmed (1998) measured the flow characteristics of a confined, isothermal, swirling flow field in an axisymmetric sudden expansion research combustor. It was shown that swirl reduces the size of the corner recirculation region in comparison to noswirl case. Moreover, it creates a central toroidal recirculation region along the axis of the combustor. In addition to experimental studies performed, Unsteady Reynolds-averaged Navier Stokes (URANS) models have been widely used in numerical computations of swirling flows over the past decades (Xia et al., 1998; Chen et al., 1999; Jakirlic et al., 22; Gupta et al., 27; Wegner et al., 24). However, significant challenges still remain in predicting accurately unsteady flow features and turbulence statistics, and in particular the accurate resolution of the energy contained in the coherent motion of the precessing vortex core (Xia et al., 1998; Chen et al., 1999; Jakirlic et al., 22; Gupta et al., 27; Wegner et al., 24). Recently, large eddy simulation (LES) has been introduced as a particular suitable approach to investigate the generation and evolution of coherent structures in turbulent swirling flows (Schluter et al., 24; Wang et al., 24; Garcıa et al., 26), but most of such simulations still focus on confined flows at moderate Reynolds numbers or unconfined swirling flows. Detached-eddy simulation (DES) is a promising hybrid RANS/LES strategy capable of simulating internal flows dominated by large scale detached eddies at practical Reynolds number. The method aims at entrusting the boundary layer to RANS while the detached eddies in separated regions are resolved using LES. DES thus attempts to capitalize on the strengths of RANS and LES; the RANS region of a DES comprises the entire boundary layer with the remainder of the flow been treated in the LES mode using a subgrid-scale model. DES predictions of massively separated flows, for which the technique was originally designed, are typically superior to those achieved using RANS models, especially in terms of the threedimensional and time-dependent features of the flow (Frohlich et al., 28; Spalart, 29). Using (DES), Paik et al. (21) investigated turbulent swirling flow through an abrupt axisymmetric expansion at both moderate and high Reynolds numbers. Comparison of the computed solutions with the experimental measurements of Dellenback et al. (1988) showed that the DES approach was able to capture the main characteristics of the flow with good accuracy. In this paper, the main non- reacting flow characteristics in a typical lean premixed swirl stabilized combustor, that was experimentally studied by Hyung Ju Lee (29) will be reported. This will be done numerically using both realizable K-epsilon turbulence model and detached eddy simulation technique. The aim of this paper, however, is to: a. First: investigate the main non-reacting swirling flow characteristics inside the combustor, which will provide a suitable ground for studies of flame vortex interaction, as one of the main combustion instability mechanisms inside the combustor. b. Second: demonstrate the capabilities of the detached eddy simulation technique (DES) in capturing the details of the flow versus the URANS models like realizable K-epsilon model. The experimental set-up of Hyung Ju Lee (29) is first described, and then numerical methods are revisited followed by discussion of various computational details. Subsequently, the computed results are presented, including grid and domain sensitivity studies. Comparisons of the two models used and analysis of the flow physics are conducted. Finally, major findings and conclusions are summarized. Physical and Numerical Formulation: The model combustor used in the present work has been used by Hyung Ju Lee (29). Fig. 1 shows a schematic drawing and a photograph of the variable-fuel injector, variable-length combustor (PSU combustor). The combustor consists of a mixing section and a combustor section. The mixing section contains a movable fuel injector and a 3 axial swirler with eight flat vanes as shown in Fig. 2. The combustor section consists of an optically-accessible quartz section followed by a variable length steel section shown in Fig. 3. All combustor details can be found in Hyung Ju Lee (29). The case considered here is the premixed one of Hyung study. In this case the fuel and air are assumed to be perfectly mixed far upstream the choked inlet. As a result, no perturbations in the mixture equivalence ratio are considered. 124

3 Am. J. Sci. Ind. Res., 213, 4(1): Fig. 1: (a) Schematic drawing, and (b) photograph, of PSU combustor (Hyung Ju Lee, 29) Fig. 2: Schematic drawing of the mixing section (Hyung Ju Lee, 29) Fig. 3: Schematic drawing of the prolonged section (Hyung Ju Lee, 29) 125

4 Am. J. Sci. Ind. Res., 213, 4(1): Fig. 4 shows a schematic drawing of the flow domain used in the fig. 4 shows a schematic drawing of the flow domain used in the present study. In this case, the perfectly mixed methane/air mixture (Φ =.65) enters the domain from the inlet section with an inlet velocity of 1 m/s and temperature of 2 ᵒC. The flow goes through the premixed section in the axial direction before it is being swirled via a 3ᵒ axial swirler with eight flat fins, which is located 76 mm upstream the combustor dump plane. The flow is first investigated using unsteady Reynolds averaged Navier-Stokes equations (URANS) with the realizable K-epsilon turbulence model being used for the closure problem. After that, detached eddy simulation technique (DES) is used to investigate the details of the flow and to demonstrate its capabilities against URANS models. (a) Premixed Section Combustor Section Prolonged Section (b) (c) Fig. 4: (a) Schematic of the flow domain and the three dimensional orientation, (b) A 3D screen shot of the discretized computational domain of a quarter section of the combustor, (c) A 3D screen shot of the discretized computational domain of a complete combustor as shown in ANSYS

5 Am. J. Sci. Ind. Res., 213, 4(1): Unsteady Reynolds averaged Navier Stokes Approach ( ) ( ) [( ) ] (4) The unsteady Reynolds averaged continuity and momentum Navier Stokes equations in the compressible form are given as: ( ) (1) ( ) ( ) [ ( ( ) ( ) [( ) ] Where [ ] (5) )] ( ) (2) Where is the density of the fluid, is the time, and is a mean component of velocity in the direction, is the pressure, is the dynamic viscosity, and is a fluctuating component of velocity. Repeated indices indicate summation from one to two. The term expresses the Reynolds stresses which are modeled using Boussinesq hypothesis (Hinz, 1975; Versteeg and Malalasekera, 1995) to relate the Reynolds stresses to the mean velocity gradients: ( ) ( ) (3) Where is the turbulent kinetic energy, as defined by, and is the Kroneker delta. An advantage of the Boussinesq approach is the relatively low computational cost associated with the computation of the turbulent viscosity. A disadvantage is that it assumes is an isotropic scalar quantity, which is not always the case. The Realizable -epsilon model is an example of twoequation models that use the Boussinesq hypothesis. The term realizable means that the model satisfies certain mathematical constraints on the Reynolds stresses, consistent with the physics of turbulent flows. It is based on the work of Shih et al (1995) and differs from other k-epsilon models in two ways: a. The realizable k-epsilon model contains a new formulation for the turbulent viscosity. b. A new transport equation for the dissipation rate,, has been derived from an exact equation for the transport of the mean-square vorticity fluctuation. In these equations, represents the generation of turbulence kinetic energy due to the mean velocity gradients, is the generation of turbulence kinetic energy due to buoyancy, and represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. and are constants. and are the turbulent Prandtl numbers for and, respectively. and are any other defined source terms. Detached Eddy Simulation Technique (DES) Detached-eddy simulation (DES), proposed by Spalart et al (1997) is a promising hybrid RANS/LES strategy capable of simulating internal flows dominated by large scale detached eddies at practical Reynolds numbers. The method aims at entrusting the boundary layer to RANS while the detached eddies in separated regions are resolved using LES. DES thus attempts to capitalize on the strengths of RANS and LES; the RANS region of a DES comprises the entire boundary layer with the remainder of the flow been treated in the LES mode using a subgrid-scale model. The used form of DES is based on the Realizable K-epsilon two-equation eddy viscosity model which was described in the previous section (ANSYS Fluent, 29). This DES model is similar to the realizable k-epsilon model with the exception of the dissipation term in the k equation. In the DES model, the Realizable K-epsilon RANS dissipation term is modified such that: ( ) The transport equations for both and are shown below (Shih et al, 1995): 127

6 Am. J. Sci. Ind. Res., 213, 4(1): Where is a calibration constant used in the DES model and has a value of.61 and is the maximum local grid spacing ( x, y, z). To alleviate the well-known shortcoming of the standard DES, namely that of grid-induced modeled stress depletion (MSD) leading to premature laminarlike flow separation, an extension of the DES model has been employed, delayed DES (DDES) to ensure that a URANS layer is always present near the wall, regardless of the local grid spacing (Spalart et al, 26). Note, however, that the grid spacing parallel to the wall in most regions, in the present case even on the finest mesh, are large enough to do not suffer from the grid induced modeled stress depletion. The detailed description of both the Realizable k epsilon model and DES technique can be found in Pope (2), and Fluent User s Guide (29). Computational Details: Simulations were performed using the ANSYS Fluent 12.1 CFD software. The prescribed compressible form of governing equations has been solved by means of coupled pressure based finite volume methodology. In the coupled pressure-based solver, Fluent solves the governing equations of pressure-based continuity, momentum, and energy transport equations simultaneously (i.e., coupled together). The governing equations for the additional scalars are solved afterward and sequentially (i.e., segregated from one another and from the coupled set). Ideal gas law has been used for density. A second order upwind scheme was used for the momentum, turbulence kinetic energy, turbulence dissipation rate, and the energy equations. Convergence criteria were set to three orders of magnitude reduction for continuity equation and fifth order of magnitude for all other equations. All simulations have been run on a desktop computer with an Intel core I7 CPU (3.2 GHz, 16 GB RAM). Boundary Conditions: Velocity inlet of 1 m/s was set at the inlet boundary (choked inlet), while the pressure outlet condition (Gauge pressure was set to zero) was set at the outlet boundary for all calculations. No-slip and adiabatic conditions have been set at all the combustor walls. The adiabatic condition has been used since non-reacting flow is simulated, hence, the wall temperature will reach the inlet flow temperature at steady state. For the grid independent study and the URANS calculations, only a quarter section of the combustor is used for calculations, (see Fig. 4.b) due to the enormous computational cost. In this case periodic boundary conditions have been used in the azimuthal direction. Grid and Time Independent Studies: One of the main objectives of this study is that it provides a suitable ground for a study of the reacting case in which the effect of the swirling flow characteristics (determined in the current work) on the flame evolution can be investigated. In this prospect, the present case is considered as a highly unsteady problem in which the effect of the time step size on the flow evolution should be demonstrated. Therefore, the grid independent study is divided into two steps separated by a time refinement procedure. In the first step, an initial time step of 1 µs is used based on both the physics of the problem (estimated to be suitable for capturing the combustion instabilities in Hyung Ju Lee (29)) and the stability of the solution. Five different grids have been tried with spatial step reduction ratio of 25 %. Comparisons of axial velocity both radial and axial distributions have been conducted while the flow reached the steady state. Using the most suitable grid resolution (44349 cells) from this step, time step is then refined from 1 µs to 1 µs which is considered small enough to capture the inherent turbulent transients of flow characteristics and has CFL number of less than one in all domain. Finally, the grid is refined one more time using the new time step of 1 µs and following the same procedure of the first grid refinement study till convergence is reached. As mentioned before, convergence criteria were set to three orders of magnitude for continuity equation and fifth order of magnitude for all other equations. At this stage, a spatial cell size of (.85 mm) and a time step of (1 µs) has been decided to be used in the present calculations (This combination gives an estimated CFL number of nearly one in the whole domain). The final grid resolution is of cells using the quarter domain shown in Fig. 4.b, and cells using the full domain shown in Fig. 4.c. It is noteworthy to mention that the authors have been stricted to use a uniform structured grid everywhere in the domain to ensure minimal discretization errors and to avoid slower convergence resulted by high aspect ratio cells. 128

7 Am. J. Sci. Ind. Res., 213, 4(1): RESULTS AND DISCUSSION The normalized axial and tangential velocity distributions are qualitatively compared with published experimental data of Dellenback et al (1988) higher swirl case due to shortage of published experimental velocity measurements for the current case. The effect of swirl number on both combustors flow characteristics is explained. Fig.5 shows the combustor investigated by Dellenback et al (1988) which has three main differences from the current combustor. First, is the smaller expansion ratio of the dump plane compared to the current case (The expansion ratio in Dellenback case is 2 while in the present case is 2.89). Second, is the higher degree of swirl of Dellenback case (S=.6) than in the current case (S=.45). Finally, unlike the current case, the combustor is entirely open at the end which allows a fully developed zero-gradient convective outflow condition. Fig. 5: The combustor tested experimentally by Dellenback et al. (1988), (S=.6) Fig. 6 shows the two main recirculation zones inside the combustor through the calculated negative axial velocity contours using the realizable K-epsilon model. Fig. 6: Calculated negative axial velocity contours at steady state (Realizable K-epsilon). Fig. 7A-H demonstrates the calculated normalized axial velocity distribution over combustor radius at several axial locations using realizable k-epsilon model (Axial locations are indicated in Fig.6). Lines of A, B, C, D, E, F, G, and H represent L/D = 1/4, 1/2, 3/4, 1, 3/2, 2, 3 and 4 respectively. Results are qualitatively compared with the available experimental results of the high swirl case (S=.6) reported by Dellenback et al (1988) to determine the effect of swirl number on the flow characteristics. Fig. 7A-H indicates that two main recirculation zones can be recognized downstream. The first zone is the corner recirculation zone (CRZ) which appears due to flow separation behind the combustor dump plane and then starts to decay while moving further downstream the combustor until it completely vanish at L/D = 3 because of the flow re-attachment to the combustor wall. In the current higher expansion ratio case (D/d = 2.89), and as demonstrated in Figs. 7A- H, the corner recirculation zone exists from r/r =.45 till the combustor wall. In Dellenback case (lower expansion ratio of D/d = 2) the corner recirculation zone exists from r/r =.65. Also, it is observed that the flow reattaches to the wall at some distance further downstream (L/D = 3) in the current case, compared to Dellenback case. This is apparently due to the lower swirl number in the current case (.45) which makes the corner recirculation zone longer compared with the high swirl case of Dellenback. The other recirculation zone is the central toroidal recirculation zone due to the action of the centrifugal force imparted by the swirling motion of the flow. This first expands while moving downstream the combustor until it reaches its maximum at L/D = 3. A sudden vortex collapse then happens because of the adverse pressure gradient and the central toroidal 129

8 Am. J. Sci. Ind. Res., 213, 4(1): recirculation zone completely disappears at L/D = 4. This could be primarily due to the well-known phenomenon of vortex break down. Comparisons with Dellenback high swirl case show a wider central recirculation zone in Dellenback's. This can be attributed to the higher swirl number in Dellenback case. Also, it is noticed that the maximum axial velocity in both cases are shifted to the wall while moving downstream, which is consistent with this type of swirling flow. However, the experimental data of Dellenback show that the maximum velocity is closer to the wall than in the current case, possibly due to the wider recirculation zone in Dellenback high swirl case. Finally, the axial velocity component decays while moving downstream the combustor in both cases. This can be mainly attributed to axial momentum diffusion in the radial direction and viscous effects. Figs. 8A-H shows the URANS computed tangential velocity distribution along the combustor radius, at the same axial locations (L/D = 1/4 to 4). From L/D = 1/4 to 1, Rankin vortex is observed with the forced vortex region which extends to r/r =.35, followed by a free vortex region that extends from r/r =.35 to.5. Then the wall stabilization effect is seen to take place. This Rankin structure remains while moving downstream but decays until L/D = 2 where the flow distribution begins to become relatively flat which is a characteristic of constant angle swirler (Paik et al.21). The tangential velocity decays while moving down stream because of the viscous effects and the decaying of centrifugal force imparted by the swirl motion. Comparison with experimental data reported by Dellenback et al (1988) shows good agreement except for L/D=1/4 to 3/4 where poor agreement near the wall is apparent. This may be attributed to the limited capabilities of the realizable K-epsilon model near the wall where the turbulence dissipation rate due to wall viscous effects is apparent as shown in Shamami and Birouk (28). Figs 8.G, H starts from L/D = 3 to 4 shows faster tangential component decay in the present moderate swirl case (S=.45) than in the experimental high swirl case of Dellenback which seems to be a result of weaker swirl (smaller swirl number) in the current case (A ) L/D=1/ (B) L/D=1/ r/ R.6 (A) L/D=1/ (B) L/D=1/

9 Am. J. Sci. Ind. Res., 213, 4(1): (C) L/D=3/ (C) L/D=3/ (D) L/D= (E) L/D=3/ r/ R.6 (D) L/D= (E) L/D=3/

10 Am. J. Sci. Ind. Res., 213, 4(1): (F) L/D= (F) L/D=2 -.3 r/ R (G) L/D= (G) L/D= r/ R (H) L/D=4 Fig.7.A-H: Steady state normalized axial velocity distribution at various axial locations, ( Current moderate swirl case (S=.45) (Realizable k- epsilon), Experimental Dellenback high swirl case (S=.6) [Dellenback et al (1988)]) (H) L/D=4 Fig.8.A-H: Steady state normalized tangential velocity distribution at various axial locations, ( Current moderate swirl case (S=.45) (Realizable k-epsilon), Experimental Dellenback high swirl case (S=.6) [Dellenback et al (1988)]). 132

11 Am. J. Sci. Ind. Res., 213, 4(1): Fig. 9 demonstrates a 3D visualization of swirling motion utilizing q-criterion for the realizable K-epsilon case. It is obvious that the model fails to capture the detailed flow structures, although it demonstrates an average shape of the main swirling flow. Also, it is shown the pressure loss across the swirler due to swirling motion in the premixed section and in vortex core. Fig. 9: Vortex breakdown visualized by instantaneous iso-surface of q-criterion (q= ) at steady state (Realizable K- epsilon) colored by pressure. Using detached eddy simulation, several flow features have been visited. Figs. 1 a, b show a comparison between the vortical flow structures in the present moderate swirl case against the low and high swirl cases reported by Paik et al. (21) as seen in Fig. 1c. In the present case, Fig 1.a demonstrates the coherent small-scale worm-like vortical structures which occupy the entire domain downstream the sudden expansion. These structures are visualized by employing the q-criterion used in Paik et al. (21). After the vortex break down region, the flow pattern is noticed to be more organized and characterized by a large scale, full length, columnar vortex along the pipe center line similar to the one observed by Paik et al. (21) in his high swirl case. This combination of both wormlike small scale structures and large scale, columnar vortex pipe distinguish the present moderate critical swirl case. Also, as seen in Fig 1.b, the pressure is noticed to be lower in the vortex core region which is mainly due to swirling motion and centrifugal force imparted on the flow. In addition, Fig.11 shows the distracted flow pattern in the vortex breakdown region, and the recovery of the organized swirl shape of the flow, after this region, and in the rest of the domain. Flow visualization have been achieved using instantaneous axial velocity stream lines which gives similar results as those observed in Paik et al. (21). Finally, Fig. 12 demonstrates both vortex rolling up at the tip of the center body and vortex shedding, which provide the basis of the main mechanism of combustion instability in the reacting case, as experimentally investigated in Hyung Ju Lee (29). 133

12 Am. J. Sci. Ind. Res., 213, 4(1): Fig. 1.a, b: 3D vortical structures visualized by instantaneous isosurface of q-criterion (q=.1) at (.65 s) very close to steady state (DES) (S=.45). Fig. 1.c: 3D vortical structures visualized by instantaneous iso-surface of q-criterion for low and high swirl numbers (S=.17, S=.74), from Paik et al. (21) Fig. 11: 3D flow pattern visualized by axial velocity stream lines at (.65 s) very close to steady state (DES) 134

13 Am. J. Sci. Ind. Res., 213, 4(1): Fig. 12: Vortex rolling up and shedding visualized by iso-vorticity magnitude at (.65 s) very close to steady state (DES) CONCLUSIONS Main swirling flow characteristics have been numerically studied in a typical lean premixed swirl stabilized combustor. The combustor under investigation has been reported previously in the literature and described in details in the present work. The main findings have been summarized in the following points. URANS Realizable K-epsilon model has been able to capture both central toroidal and corner recirculation zones successfully. High swirl (as shown in the experimental case of Dellenback of S=.6) results in wider central recirculation zone, shorter corner recirculation zone, faster flow reattachment to the wall and slower decay of tangential velocity in comparison of current moderate swirl case of S=.45. K-epsilon URANS model has failed to determine the detailed flow structures which is important in studies of combustion like vortex shedding and precessing vortex core. In comparison with Dellenback high swirl experimental data, the performance of K- epsilon URANS model is seen to be poor near the wall while it seems to perform well elsewhere. This is apparently due to the inaccuracy of K-epsilon to predict turbulence dissipation rate near the wall. Detached eddy simulation (DES) has been used to investigate this detailed flow structures with success. Worm like small scale coherent turbulent structures have been noticed over the vortex break down region followed by a large scale, full length, columnar vortex along the pipe center line in consistent to previous findings of Paik et al (21). Finally, detached eddy simulation is considered a promising tool in wall bounded flow calculations since it requires less computational cost than LES in such cases, especially at high Reynolds numbers. However, due to limited computer resources, some aspects like comparing the velocity profiles with the ones obtained using realizable K-epsilon and also determining the precession frequency have not been covered as they depend on running the DES simulation for sufficient and long time to obtain a meaningful averaged turbulent statistics. So, a further numerical and experimental investigations need to be done in order to gain more insight of the flow dynamics inside this combustor. REFERENCES ANSYS Fluent 12.1 Users Guide, ANSYS Inc., 29. Chen J.C., Lin C.A., Computations of strongly swirling flows with second moment closures. Methods Fluids 3, (1999) Dellenback P.A., Metzger D.E., Neitzel G.P., Measurements in turbulent swirling flow through an abrupt axisymmetric expansion, AIAA J., 26 (6) (1988) Eldrainy Y. A., Saqr K. M., Aly S. H, Jaafar M.N, CFD insight of the flow dynamics in a novel swirler for gas turbine combustors, International Communications in Heat and Mass Transfer 36 (29)

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