# Evaluation AC2-07

## Contents

**Confined double annular jet**

**Application Challenge 2-07** © copyright ERCOFTAC 2004

**Comparison of Test data and CFD**

**Introduction**

Turbulence kinetic energy, axial and radial velocity profiles are calculated with the five different quoted turbulence models. The numerical results are compared with the empirical test data in 18 different vertical cross-sections of the combustion chamber. In this report, only comparison of test data and CFD will be done in sections 2, 4 and 7. Figure 22 and Table 10 give the locations of these sections, whereby the position is oriented in the direction of the flow.

Section | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

Position [mm] | 5 | 10 | 15 | 20 | 25 | 30 | 40 | 50 | 60 |

Section | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

Position [mm] | 70 | 80 | 90 | 100 | 120 | 150 | 180 | 210 | 240 |

Table 10: Longitudinal position of the sections.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Figure 22: Measuring sections

In the next paragraphs, the axial, radial and turbulence kinetic energy of the different turbulence models (Baldwin-Lomax, Spalart Allmaras, Chien, Launder Sharma and Yang Shih) are viewed and compared with the empirical results. The turbulence kinetic energy k is estimated as described in paragraph 3.1 “Computational domain and boundary conditions”.

But first, the grid sensibility will be studied. The numerical calculation will be done with the k-ε turbulence model of Yang-Shih. This model is chosen because these numerical results estimate the empirical data better than all other quoted models.

Finally, the assessment parameters, defined as in the paragraph “Description” will be compared with all numerical results of the difference turbulence models. It are the specific position points of the several toroidal vortices, a stagnation point and stagnation lines, recirculation and high turbulence intensity in the mixing regions as shown in Figure 2. “Streamlines of the flow, and designations of specific position points”

**Study of Grid Sensitivity**

Before starting with the final calculation for the comparison of CFD results with empirical data, the sensibility of the grid is studied. Two different grids were modeled. In Table 11, the total points for each grid and their grid levels are written. The different of the two grids are the number of grid points in the region with high density of circulation. Outside this zone of number of points are not changed.

Numerical calculations were done for all grid levels of the first grid (Grid level 000, Grid level 111, Grid level 222 and Grid level 333) and only for the finest grid level of grid 2 (Grid2level000). The numerical results of the axial, radial and turbulence kinetic energy profiles are compared with the experimental data and plotted in the following figures (Fig. 23 to 28). The k-ε turbulence model of Yang-Shih was chosen, because this model estimates better the empirical data than all other quoted models.

Name of Grid | Grid | Grid Level | Number of Points |
---|---|---|---|

Grid2level000 | 2 | 000 | 407.330 |

Gridlevel000 | 1 | 000 | 204.034 |

Gridlevel111 | 1 | 110 | 51.330 |

Gridlevel222 | 1 | 220 | 12.994 |

Gridlevel333 | 1 | 330 | 3.330 |

Table 11: Total numbers of points of different grid levels.

Figure 23: Axial velocity in section 3 Figure 24: Axial velocity in section 6

Figure 25: Radial velocity in section 3 Figure 26: Radial velocity in section 6

Figure 27: Turbulent kinetic energy in section 3 Figure 28: Turbulent kinetic energy in section 6

**Comparison of Turbulence models with Experimental Data (Mean Axial Velocity)**

Figure 29: Axial velocity in section 2. Figure 30: Axial velocity in section 2.

(Baldwin-Lomax and Spalart Allmaras) (Chien, Launder Sharma and Yang Shih)

Figure 31: Axial velocity in section 4. Figure 32: Axial velocity in section 4.

(Baldwin-Lomax and Spalart Allmaras) (Chien, Launder Sharma and Yang Shih)

Figure 33: Axial velocity in section 7. Figure 34: Axial velocity in section 7.

(Baldwin-Lomax and Spalart Allmaras) (Chien, Launder Sharma and Yang Shih)

**Comparison of Turbulence models with Experimental Data (Mean Radial Velocity)**

Figure 35: Radial velocity in section 2. Figure 36: Radial velocity in section 2.

(Baldwin-Lomax and Spalart Allmaras) (Chien, Launder Sharma and Yang Shih)

Figure 37: Radial velocity in section 4. Figure 38: Radial velocity in section 4.

(Baldwin-Lomax and Spalart Allmaras) (Chien, Launder Sharma and Yang Shih)

Figure 39: Radial velocity in section 7. Figure 40: Radial velocity in section 7.

(Baldwin-Lomax and Spalart Allmaras) (Chien, Launder Sharma and Yang Shih)

**Comparison of Turbulence models with Experimental Data (Turbulent Kinetic Energy)**

Figure 41: Turbulent kinetic energy in section 2. Figure 42: Turbulent kinetic energy in section 5.

(Chien, Launder Sharma and Yang Shih) (Chien, Launder Sharma and Yang Shih)

Figure 43: Turbulent kinetic energy in section 7. Figure 44: Turbulent kinetic energy in section 10.

(Chien, Launder Sharma and Yang Shih) (Chien, Launder Sharma and Yang Shih)

**Comparison Position of DOAP's of the different Turbulence models with Empirical Data**

The positions of the DOAP’s of the different turbulence models are localized by the results of the corresponding stream-function contours calculated from the numerical turbulence models.

Description | Experimental | Baldwin - Lowmax | Spalart - Allmaras | Chien | Launder Sharma | Yang Shih |
---|---|---|---|---|---|---|

A | (0.0, 1.0) | (0.0, 0.92) | (0.0, 0.87) | (0.00, 1.01) | (0.00, 1.17) | (0.00, 1.00) |

B | (0.44, 0.52) | (0.42, 0.34) | (0.42, 0.31) | (0.35, 0.36) | (0.42, 0.50) | (0.42, 0.42) |

C | (0.75, 0.32) | (0.74, 0.20) | (0.02, 0.27) | (0.71, 0.24) | (0.75, 0.37) | (0.73, 0.25) |

D | (0.71, 0.20) | (0.70, 0.10) | (0.70, 0.10) | (0.68, 0.06) | (0.72, 0.20) | (0.70, 0.11) |

E | (0.81, 0.21) | (0.02, 0.10) | (0.83, 0.11) | (0.83, 0.10) | (0.82, 0.23) | (0.83, 0.10) |

Table 12: Position of the DOAPs

**Conclusions**

Evaluating the calculations of the axial (see Figures 23 and 24), radial (Figures 25 and 26) and turbulence kinetic energy (Figures 27 and 28) of all grid levels of grid 1, and the finest level of grid 2 together with the empirical data, we conclude that the calculation with the finest level of grid 1 (number of grid points is 204.034) is accurate enough for comparing the numerical results of all quoted turbulence models.

The structures of the numerical axial, radial velocities and turbulent kinetic energy profiles, calculated with the algebraic (Baldwin-Lomax) model, the one-equation (Launder Sharma) model and different k-ε turbulence models (Chien, Spalart Allmaras and Yang Shih) represent the experimental data. Quantitatively, the different k-ε turbulence models, and especially the turbulence model of Yang Shih, give good numerical results that are representative with the empirical data (see plots 29 until 44).

The yellow mark in Table 12 indicates the best agreement of the DOAP’s with the empirical data. Hereby the k-ε turbulence model of Launder Sharma is the best.

Other k-ε and non-linear turbulence models have to be checked with these complex turbulent flows in the combustion chamber.

**References**

Becker, H. A., 1961, *Concentration fluctuation in ducted jet-mixing*, Sc. D. Thesis in Chem. Engg., MIT, Cambridge, Mass.

Becker, H. A., Hottel, H. C., and Williams, G. C., 1963, *“Mixing and flow in ducted turbulent jets”, Ninth Symposium on Combustion*, Academic Press, pp. 7-20.

Beér, J. M., and Chigier, N. A., 1983, *Combustion Aerodynamics*, Robert E. Krieger Publi. Comp., Malabar.

Guruz, A. G., et al., 1975, “Aerodynamics of a confined burning jet”, Comb. Sci. Tech., 9, p. 103.

Craya, A. and Curtet, R., 1955, “Sur l’évolution d’un jet en espace confiné”, C. R. Acad. Sci., Paris, 241, p. 621.

Curtet, R., 1958, “Confined jets and recirculation phenomena with cold air”, *Combustion and Flame*, 2, p. 383.

Escudier, M. P. and Keller, J. J., 1985, “Recirculation in Swirling Flow: A Manifestation of Vortex Breakdown”, AIAA Journal, 23, p. 111.

Hazarika, B. K., D. Vucinic, F. Schmitt, Ch. Hirsch, 2001, "Analysis of toroidal vortex unsteadiness and turbulence in a confined double annular jet", *39th Aerospace Sciences Meeting&Exhibit*, AIAA paper 2001-0146, Reno, Nevada, Januray 2001.

Schmitt F. and Ch. Hirsch, 2000, "Experimental study of the constitutive equation for an axisymmetric complex turbulent flow", Z. *angew. Math. Mech.,* 80, 11/12, 815-825, 2000.

Schmitt, F., B. K. Hazarika and Ch. Hirsch, 2001, "LDV measurements of the flow field in the nozzle region of a confined double annular burner". *Journal of Fluid Engineering,* Vol. 23, June 2001.

Schmitt, F., Ch. Hirsch and B. K. Hazarika, 2001, "LDA measurements in the nozzle region of a confined double annular burner : statistical analysis and model evaluation", *Lisboa 2000 : 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics*, Libon, Portugal, July 2000 ; in press in the special issue of Estudos de Engenharia Civil, 2001.

Schmitt, F., Ch. Hirsch, 2001, "Direct experimental assessment of the nonlinear constitutive equation for a complex flow", *39th Aerospace Sciences Meeting&Exhibit*, AIAA paper 2001-0881, Reno, Nevada, Januray 2001.

Thring, M. W. and Newby, M. P., 1953, “Combustion length of enclosed turbulent jet flames”, *Fourth Symposium on Combustion*, Williams and Wilkins, pp. 789-796.

Zhu, J., and Shih, T.-H., 1994, “Computation of confined coflow jets with three turbulence models”, *Int. J. Numerical Meth. Fluids*, 19, p. 939.

© copyright ERCOFTAC 2004

Contributors: Charles Hirsch; Francois G. Schmitt - Vrije Universiteit Brussel

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