EVALUATION OF FOUR TURBULENCE MODELS IN THE INTERACTION OF MULTI BURNERS SWIRLING FLOWS

Transcription

1 EVALUATION OF FOUR TURBULENCE MODELS IN THE INTERACTION OF MULTI BURNERS SWIRLING FLOWS A Aroussi, S Kucukgokoglan, S.J.Pickering, M.Menacer School of Mechanical, Materials, Manufacturing Engineering and Management University of Nottingham, University Park, Nottingham, NG7 2RD, UK Keywords: CFD, Turbulent Modeling, Swirling Flow, Burner, Furnace, RST Model Abstract Predictions of the turbulent isothermal swirling flows, from four adjacent coal burners enclosed in a furnace type geometry have been carried out using the commercial Computational Fluid Dynamics (CFD) code FLUENT version 5.1. This paper describes the performance of four different turbulence models in terms of accuracy and economy of computation. The numerical models being used are the standard k-ε, the RST k-ε, the RNG k-ε, and the realizable k-ε. The latter model is a new model and is untried in this type of application and needs to be compared with well-established models as well as validated against experimental data. The grid for the enclosed furnace-type geometry of the rig was created using the GAMBIT V package in this study. The Cartesian co-ordinate system is used to set up the geometry of the computational region the four-burner/furnace model, and Body-Fitted Co-ordinates to generate the grid. The predictions of the four burners case, on a three-dimensional axisymmetric mesh; show that the near burner region is accurately predicted by increasing the mesh density. In full furnace simulation a fine mesh has been used within the near burner region to eliminate mesh dependency. The standard, RST and RNG k-ε are well-established models in predicting turbulent isothermal swirling flows that have been compared successfully to experimental results in previous work (S.J.Tarr, 1997). The results obtained from the 3D CFD models are presented as velocity vector and magnitude of axial, radial and tangential velocities. Comprehensive comparisons of the four models show that good agreement is achieved with a high mesh resolution. In general, the velocity profiles, contours and flow patterns of the realizable k-ε, model are in good agreement with the standard, RST and RNG k-ε models, indicating that the general flow-field within the furnace has been predicted accurately. In addition, Velocity magnitude histograms have been used for a global 3Dvelocity comparison of the four numerical models. The histograms indicate a very good agreement between the methods in general. It can be concluded that the mixing of swirling burner flows issued from typical isothermal scale models of burner geometries can be predicted well by using the standard, RST, Realizable and RNG k-ε turbulence model, together with a fine computational mesh. The quantified accuracies and uncertainties will be given in the full paper. 1

2 Introduction Many scientists and environmental engineers have been concerned with the reduction of pollutant emissions, in particular NOx within the field of coal-fired boiler technology. Methods of reducing NOx within coal flames include air staging, where the burner inlet flows are separated into two or more co-axial annular jets, and re-burn where fuel and then over-fire air are introduced at separate locations from the burner; in the upper part of the boiler furnace (Wendt J O.L., 1995). Burner technology is relatively advanced, where burners are generally designed and optimized in large combustion test rigs to reduce pollutant emissions. Nevertheless, It is often found that performance deteriorates when the burners are fitted on site in the multiple burner banks contained within large power station furnaces. Experiments on full-scale furnaces present difficulties, not only because of their sheer size, but also because of the high temperatures within the flames. A lack of experimental data also adds uncertainty when building physical isothermal models representative of real furnaces. Furthermore, full-furnace simulations using Computational Fluid Dynamics (CFD) modeling is one possible solution to the problem, however, there are always uncertainties with these models due to turbulence model closure assumptions and numerical diffusion. The lack of experimental data also means that predictions cannot always be validated. In addition to that, the simulation of a full-scale furnace using CFD is computationally uneconomical. Therefore small-scale burner/furnace model has been simulated for this study. Both the single air phase and the two-phase air/coal are simulated. The performance of four different turbulence models in isothermal swirling flows, from four adjacent coal burners enclosed in furnace type geometry, using the commercial CFD code FLUENT version 5.1, have been predicted. The numerical models being used are the standard k-ε, RST k-ε, RNG k-ε, and realizable k-ε. 2.0 Numerical models The main features of turbulence are the random fluctuations of fluid velocity over space and time. These random fluctuations occur over very small distances (as small as 0.1mm in air) in space and time compared to the overall domain. In order for a turbulent flow to be modeled accurately the computational mesh spacing must be smaller than the smallest element of turbulent motion (eddy) but cover the entire control volume. The computations will have to be unsteady using a time-step smaller than that of the fastest eddy. This leads to an impossibly large number of grid nodes. The calculations required are beyond the capabilities of current computing technology. As engineers are not usually interested in the fluctuating components of flow a statistical approach is taken. This is achieved by averaging over a time scale that is large compared with the turbulent motion. This results in equations that describe the flow in terms of the mean velocities and pressures. However, these equations contain unknowns representing the Reynolds stresses and transport of mean momentum, thus, additional equations are needed to solve for all the parameters. This is described as "turbulence modeling". This solves the Navier-Stokes equations, the continuity equation and some additional differential equations. The number of these additional equations increases with the complexity of the model (Fluent 5, 1998). 2

3 Basically, turbulence models incorporated with the governing equations are used to determine the Reynolds Stresses. In FLUENT, these are four turbulence modeling options; the standard k-ε, the RNG k-ε, and the realizable k-ε models, used in this study. The k-ε model focuses on the mechanisms that affect the turbulent kinetic energy. The standard k-ε model in FLUENT falls within this class of turbulence model and has become the workhorse of practical engineering flow calculations in the time since it was proposed by (Launder,B.N., 1972). Robustness, economy, and reasonable accuracy for a wide range of turbulent flows explain its popularity in industrial flow and heat transfer simulations. It is a semi-empirical model, and the derivation of the model equations relies on phenomenological considerations and empiricism. As the strengths and weaknesses of the standard k-e model have become known, improvements have been made to the model to enhance its performance. Two of these variants are available in FLUENT: the RNG k-ε model (Yakhot,A.,1986) and the realizable k-ε model (Shih, T.-H, 1995) In the Re-Normalization Group (RNG) k-ε model, the theory is employed to set up the turbulence transport equations for the turbulent kinetic energy k and the eddy dissipation rate ε (Yakhot,A.,1986). The RNG k-ε model was derived using a rigorous statistical technique (called re-normalization group theory). It is similar in form to the standard k-ε model, but includes the effect of swirl on turbulence; therefore enhancing accuracy for swirling flows. The realizable k-ε model differs from the standard k-ε model in two ways: the realizable k-ε includes new formulation for the turbulent viscosity and a new transport equation for the dissipation rate, ε, is derived from an exact equation for the transport of the mean square vorticity fluctuation. The realizable k-ε model satisfies certain mathematical constraints on the Reynolds stresses, consistent with the physics of the turbulent flows. Neither the RNG k-ε model or standard k-ε model is realizable (Fluent 5,1998). Assessment of turbulence modeling for engineering prediction of swirling Vortices in the near burner zone were reported (Weber, 1990). The RNG, the standard and the realizable k-ε models were used for the assessment of single burner and two counter rotating burner swirling flows (Aroussi A. et.al, 2000 and Kucukgokoglan, S. et.al. 2000). 3.0 Computational Program The commercial CFD code FLUENT version 5.1 was used for predictions of the flow-field within burner/furnace systems. The Cartesian co-ordinate system is selected to set up the geometry of the computational region for the single burner model, and the curvilinear Body-Fitted Coordinates to generate the grid, i.e. the matrix of the points of interest in the computational region. The geometries and grid (Figure 1) of all the computational regions considered in this study were set up with GAMBIT V The strategy of grid generation within the computational region and density of the grid play an important role in the prediction accuracy (Lin, S., 1995). The grid is non-uniform, with high density in area of high gradient and low density in area of low gradient, so that minimal computational effort is required whilst gaining sufficient accuracy. In order to obtain a grid-independent solution, the grid should be refined until the solution no longer varies with additional grid refinement. In this study, cells size of the grids for the 3

4 computational regions have been used for the four turbulence models. The dimensions of the model rig is 1.2m * 0.8m * 0.75m. The symmetrical boundary condition is specified on the symmetrical planes. At the inlet of the computational region, the boundary condition is based on the experimental set-up. Figure 1a: Grid for four burners enclosed in furnace Table 1.Boundary Conditions 4 Figure 1b: Schematic Drawing of the Burner (dimensions in mm) The flow rate at the primary inlet was supplied with a water mass-flow of 15 l/m; at the secondary inlet was supplied with three times this quantity giving an overall mass-flow through the burner of 45 l/min for this study. The flow is discharged from the burner into the stationary water of the water tank (figure 1b). Theoretically, zero gradient condition can be given at the outlet boundary. These boundary conditions can be expressed as follows: Inlet, outlet and wall boundary conditions. Some assumptions about boundary conditions that are not directly measured had to be made. These are: Velocity components and turbulence quantities at the primary and secondary inlets are constant, that is flat-profiled across the inlet The angle of the flow at the secondary inlet is equal to the vane angle, that is, 40º Turbulence intensity at the burner inlet is 5-10%. A summary of flow boundary conditions, based on a water temperature of 20ºC, is given in Table 1. Boundary Density of water kg/m³ Axial Velocity u(m/s) Radial Velocity v (m/s) Primary Inlet Primary Inlet Primary Inlet Primary Inlet Tangential Velocity w (m/s) Secondary Inlet Secondary Inlet Secondary Inlet Secondary Inlet

5 RESULTS AND DISCUSSION The axial and tangential velocity profiles from the results have been extracted as velocity vectors, velocity magnitudes, axial, and tangential velocity values. The histogram method has been used as mean of comparison between the different models. It is a practical and useful tool for quantitative comparisons. The histograms of the velocities are obtained from the overall 3D model of the rig. Thus, global comparisons are possible. Velocity Vectors: The velocity vector maps for the three models have been obtained in front of the burner at 3 mm away (The burner diameter is 50mm). A close look at areas A, B, C and D in the velocity vector maps for the three different models, show similar patterns of velocity vectors all around the swirling burner flows. In addition, the scale of vectors, for the three models, is very similar (1% difference for maximum values). Although, the velocity vector profiles for the three-turbulence models are very similar (figure 2-5), a more qualitative and quantitative method for comparison is needed. For this purpose, the histograms for the velocity vectors, velocity magnitudes, axial velocities and tangential velocity have been used. Velocity Magnitude: The histograms represent all the velocity vectors (figures 6-9) in the 3D model. These show that 56% of low velocity vectors range between 0 to 0.18 m/s for all models. From 0.18 m/s to 1.65 m/s, the four turbulence models have very similar predictions for all velocity magnitudes. However, differences in the amount of velocity magnitudes start to appear between 1.65 to 1.85 m/s. 0.1% of vectors where obtained from the RST against around 1% for the other three models. This becomes a significant variation in the models for high velocities. This shows that the RST model gives slightly different predictions in the high velocity magnitude range compared to the standard k-ε, the RNG and realizable k-ε models. In general, 96% of the overall velocity magnitudes were similarly predicted for the four models, which show a very good agreement between the models. Axial Velocity The histograms of axial velocities (U), from the three models, (figures 10-13) in the 3D model show that a large number of low velocity vectors (68%) ranging from 0 to 0.25 m/s while RST model 62%. From 0.25 to 0.5m/s, the four turbulence models predicted almost equal number of velocity magnitudes. Also, below 0.5 m/s and above 0.5 m/s four models show same results. In terms of axial velocities, the four models predict equal number of velocity vectors. Tangential Velocity From figures 14-17, the histograms show that a large number of (up to 66%) of tangential velocity vectors (W) range from 0.9 m/s to 0.3 m/s for the four models. For tangential velocities below 0.9 m/s and above 0.3 m/s, the four turbulence models show the same results. These illustrate very well that the three turbulence models are in a very good agreement as far as the tangential velocities are concerned. 5

6 A B A B C D C D Figure 2: Velocity Vectors from standard k-ε Model Figure 3: Velocity Vectors from realizable k-ε Model A B A B C D C D Figure 4: Velocity Vectors from RST model. Figure 5: Velocity Vectors from RNG model % % Figure 6: Velocity Magnitude Histogram from standard k-ε Model Figure 7: Velocity Magnitude Histogram from realizable k-ε Model 6

7 Figure 8: Velocity Magnitude Histogram from RST model. Figure 9: Velocity Magnitude Histogram from RNG K- ε Model Figure 10. Axial Velocity Histogram from standard k-ε Model Figure 11. Axial Velocity Histogram from realizable k- ε Model Figure 12: Axial Velocity Histogram from RST model. Figure 13: Axial Velocity Histogram from RNG k-ε Model 7

8 Figure 14. Tangential Velocity Histogram from standard k-ε Model Figure 15. Tangential Velocity Histogram from realizable k-ε Model Figure 16: Tangential Velocity Histogram from RST model. Figure 17: Tangential Velocity Histogram from RNG k-ε Model CONCLUSIONS In conclusion, the mixing of swirling burner flows issued from typical isothermal scale models of burner geometries can be predicted well by using the standard k-ε, the RST, Realizable k-ε and RNG k-ε turbulence model, together with a fine computational mesh The results obtained from the 3D CFD models are presented as velocity magnitudes, and velocity magnitude histograms. When simulating coal combustion, it is important to consider the modeling of the near-burner region. Flame ignition generally occurs within one and a half diameters of the burner exit, and within this region a substantial amount of the overall NOx is produced (Wendt, 1995). Furthermore, in low NOx burner flows a large recirculation zone generally occurs downstream of the burner exit, which re-circulates, hot volatile gases and combustion products. Correct prediction of the near-burner field is therefore critical if realistic predictions of emissions are a requirement. The evidence from the present predictions suggests that this can only be achieved if the flow is resolved sufficiently within this region. 8

9 Therefore the results obtained at 3mm from the burner exit are shown in Figures 2-5. A close comparison of the three models shows that good agreement is achieved with a high mesh resolution. In addition, velocity magnitude histograms have been used for a global 3D-velocity comparison of the four numerical models. The histograms (figure 6-9) indicate a very good agreement between the methods. In general, the velocity magnitudes flow patterns (figure 2-5) and histograms of the realizable k- ε model are very similar to the RST model, and in a good agreement with the RNG k-ε model, and standard k-ε model indicating that the general flow-field within the furnace has been predicted accurately. Although the realizable k-ε models show similar velocity histograms; in terms of economy of computation; the realizable k-ε is better than the standard k-ε model, the RST and the RNG k-ε because it converged after 1404 iterations while the standard k-ε model, the RST and the RNG k-ε converged after 11876, 3208 and 2874 iterations respectively. The RST model needs more computational time than the other three models. Finally it can be concluded that the realizable k-ε model is as good as the standard k-ε model, the RST and the RNG k-ε models for the swirling multiple burner flows. In terms of economy of computation the realizable k-ε model is better that the other three models. REFERENCES Wendt J. O. L., 1995, Mechanisms Governing the Formation and Destruction of NOx...., Combust. Sci. and Tech., Vol. 108, pp S.J.Tarr, 1997,The Mathematical Modeling Multiple Swirling Burner Flow. PhD Thesis, University of Nottingham, Launder, B.N. and Spalding, D. B. 1972, Lectures in Mathematical Models of Turbulence. Academic Press, London, England. Yakhot,A. and Orszag, S. 1986, Renormalisation Group Analysis of Turbulence: I.Basic Theory. Journal of Scientific Computing, 1(1):1-51 Shih, T.-H., Liou,W.W., Shabbir,A., and Zhu,J. 1995, A new k-ε Eddy-Viscosity Model for High Reynolds Number Turbulent Flow-Model Development and Validation. Computers Fluids, 24(3): , Aroussi A, Kucukgokoglan S, Menacer M, Pickering S.J., 2000, Numerical Simulation Of A Single Burner Flow 9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh. S Kucukgokoglan, A Aroussi, M Menacer, S.J Pickering 2000, Evaluation of three turbulence models on swirling flows from two counter-rotating burners in a furnace. 4th EUROMECH Fluid Mechanic Conference, Eindhoven University of Technology, The Netherlands Weber, Visser and Boysan, 1990 Assessment of Turbulence Modeling for Engineering Prediction of Swirling Vortices in the Near Burner Zone, Int. J. Heat and Fluid Flow, Vol. 22, No. 3. Fluent 5 Users Guide, Vol.2. July 1998 Lin, S. and Griffith, A.J.; 1995, CFD simulation of cooling air flows within shrouded finned heater/cooler systems used on barrel extruders; Proceedings of the Joint ASME/JSME Fluid Engineering Annual Conference, Hilton Head Island, South Carolina, USA. 9