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TWiki> CfdTm Web>TestCaseAddNew>TestCase057>TestCase057Res000 (2018-11-28, ConstantinosKatsamis)

TWiki> CfdTm Web>TestCaseAddNew>TestCase057>TestCase057Res000 (2018-11-28, ConstantinosKatsamis)

*Version:* 2.0-beta2

*Authors:* D. Sénéchal

Figure 1: Mesh used for the different computations.

- For all the computation cases, time averages are activated to compute the velocity average as the kinetic energy of the unresolved structures. this energy is added to the "unresolved" energy contained in the model.

At first, we can compare the head loss computed during the crossing bundle with the one theoretical given by [1]. We recall below the expression for the tubes bundle staggered. The head loss is expressed as following in the case where %$\tfrac{S_1}{d} \ge 1 $% and %$7 \le \tfrac{S_1 -d}{S_2 -d} \le 5.2$% (see the Figure 2 for the definitions of %$S_1$% and %$S_2$%):

Figure 2: Definition of the different quantities.

The %$Re^{-0.27}_{\mbox{\small\sc moy}}$% is defined as %$\displaystyle Re^{-0.27}_{\mbox{\small\sc moy}}=\tfrac{w_{\mbox{\small\sc moy}}d}{\nu}$% where %$w_{\mbox{\small\sc moy}} = w_0\tfrac{S_1}{S_1-d}$% with %$w_0$% the bundle upstream velocity.

The results obtained with the different computations are given below inside the following table 1. The head loss is estimated on all the domain (between 0 and 180 mm) and the central part (between 45 and 135 mm). The results are globally the same order of magnitude and underestimate the head loss. The head loss between 45 and 135 mm is not quite good predicted, but this result is compared with the Idel'Cick 's formula, which assumes that the velocity strictly longitudinal at the entrance of the bundle. It is not exactly the case between 0 and 180 mm and not at all between 45 and 135 mm. It should be noted that the method used to compute the head loss differs from the 1.3 version (the mean pressure is here averaged along a line, assuming a constant mesh surface along this line which does not seem to be the case for the 45-135mm sections), this explain the differences.

Model | version | 0 - 180 mm | 45 - 135 mm | Error [0-180] | Error [45 - 135] |
---|---|---|---|---|---|

Idel'Cik | 3910 | 2445 | 0 %$\%$% | 0%$\%$% | |

%$k-\varepsilon$% | [v.1.3.1] | 2905 | 1487 | -26 %$\%$% | -39%$\%$% |

%$k-\varepsilon~\mbox{\small \sc pl}$% | [v.1.3.1] | 2923 | 1837 | -25 %$\%$% | -25%$\%$% |

%$R_{ij}$% - %$\varepsilon~\mbox{\small \sc lrr}$% | [v.1.3.1] | 3432 | 1893 | -12%$\%$% | -22%$\%$% |

%$R_{ij}$% - %$\varepsilon~\mbox{\small \sc ssg}$% | [v.1.3.1] | 3613 | 1817 | -8%$\%$% | -26%$\%$% |

%$k-\omega$% | [v.1.3.1] | 2981 | 1664 | -24 %$\%$% | -32%$\%$% |

%$k-\varepsilon$% | [v.2.0-beta2] | 2869 | 721 | 26.6 %$\%$% | 70.5 %$\%$% |

%$k-\varepsilon~\mbox{\small \sc pl}$% | [v.2.0-beta2] | 2770 | 789 | -29.1 %$\%$% | -67.7 %$\%$% |

%$R_{ij}$% - %$\varepsilon~\mbox{\small \sc lrr}$% | [v.2.0-beta2] | 3370 | 976 | -13.8 %$\%$% | -60 %$\%$% |

%$R_{ij}$% - %$\varepsilon~\mbox{\small \sc ssg}$% | [v.2.0-beta2] | 3611 | 1070 | -7.6 %$\%$% | -56.2 %$\%$% |

%$k-\omega$% | [v.2.0-beta2] | 2779 | 760 | -28.9 %$\%$% | -68.9 %$\%$% |

The Figures 3 to 8 show the mean velocities (U, V) and the mean turbulent kinetic energy (k) profiles for different planes x=constant which are compared to the experimental measurements. The plane locations are marked on the Figure 1.

The Figures 9 to 11 show the mean velocity fields (in streamwise and spanwise directions) and the turbulent kinetic energy for the different models tested.

Figure 3: Mean streamwise velocity profiles in the spanwise direction for different abscissas and three different turbulent models with 2-transport equations

(%$iturb20$%: k-%$\varepsilon$% standard model, %$iturb21$%: k-%$\varepsilon-(\mbox{\sc lp})$% model with linear production and %$iturb60$%: k-%$\omega$% model).

Figure 4: Mean streamwise velocity profiles in the spanwise direction for different abscissas and two second order

turbulent models (%$iturb30$%: %$R_{ij} - \varepsilon$% standard model, %$iturb31$%: %$R_{ij} - \varepsilon-(\mbox{\sc ssg})$% model).

For the mean streamwise velocity profiles (cf. Figures 1 and 2), we observed that the results are all globally right and close to the previous computational results obtained with the 1.3.1 version. The k - %$\varepsilon$% seems to be very slightly better that the other models with two equations. But probably for bad reasons since this case combines both break points and narrowing/widening zones where the k - %$\varepsilon$% is known as being notoriously unsuited (as we can see with the turbulent kinetic energy figures).

Figure 5: Mean spanwise velocity profiles in the spanwise direction for different abscissas and three different turbulent models with 2-transport equations

(%$iturb20$%: k-%$\varepsilon$% standard model, %$iturb21$%: k-%$\varepsilon-(\mbox{\sc lp})$% model with linear production and %$iturb60$%: k-%$\omega$% model).

Figure 6: Mean streamwise velocity profiles in the spanwise direction for different abscissas and two second order

turbulent models (%$iturb30$%: %$R_{ij} - \varepsilon$% standard model, %$iturb31$%: %$R_{ij} - \varepsilon-(\mbox{\sc ssg})$% model).

The standard %$R_{ij}$% - %$\varepsilon$%- (%$\mbox{\small \sc lrr}$%) and (%$ \mbox{\small \sc ssg}$%) lead to similar results. And as regards the spanwise velocity, the results tend to also be similar, the profiles being in a better agreement with the experiment for the k - %$\varepsilon$% - (%$ \mbox{\small \sc lp}$%) and the %$R_{ij}$% - %$\varepsilon$%-(%$ \mbox{\small \sc ssg}$%).

Figure 7: Mean streamwise velocity profiles in the spanwise direction for different abscissas and three different turbulent models with 2-transport equations

(%$iturb20$%: k-%$\varepsilon$% standard model, %$iturb21$%: k-%$\varepsilon-(\mbox{\sc lp})$% model with linear production and %$iturb60$%: k-%$\omega$% model).

Figure 8: Mean streamwise velocity profiles in the spanwise direction for different abscissas and two second order

turbulent models (%$iturb30$%: %$R_{ij} - \varepsilon$% standard model, %$iturb31$%: %$R_{ij} - \varepsilon-(\mbox{\sc ssg})$% model).

Differences are observed with the mean turbulent kinetic energy curves. As usual the k -%$\varepsilon$% gives results which substantially overestimate the turbulence. For the other turbulent models of which the result is unsteady, we recall that we represent the sum of the average k%$_{\mbox{\small \sc moy}}$% of both the modelled turbulent kinetic energy and the energy of the resolved structures. This last contribution is in general largely predominant, as we can see on Figure 7, where k%$_{\mbox{\small \sc moy}}$% is also presented for the %$R_{ij}$% - %$\varepsilon$% model. It should also be noted that the results between version 1.3 and version 2.0 are, on some graphs, slightly different,

- The computations with a second order model, which will give a unsteady behaviour, have been realized with periodicity conditions on the lateral faces.
- The computations with a first order model have been run with symmetry conditions.

Figure 9: Mean streamwise and spanwise velocity fields and mean turbulent kinetic energy field for the k-%$\varepsilon$% (top) and k-%$\varepsilon-(\mbox{\sc lp})$% (bottom) models.

Figure 10: Mean streamwise and spanwise velocity fields and mean turbulent kinetic energy field for the %$R_{ij}-\varepsilon$% (top) and %$R_{ij}-\varepsilon-(\mbox{\sc ssg})$% (bottom) models.

Figure 11: Mean streamwise and spanwise velocity fields and mean turbulent kinetic energy field for the k-%$\omega$% model.

I | Attachment | Action | Size | Date | Who | Comment |
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cgns | fedora.cgns | manage | 1596.0 K | 2010-12-06 - 11:38 | JuanUribe | |

png | mesh.png | manage | 68.9 K | 2010-11-03 - 07:17 | DorotheeSenechal | mesh - 2D plane |

png | pdc.png | manage | 6.3 K | 2010-11-03 - 16:17 | DorotheeSenechal | head losses - definition |

png | results_K20_21_60_finish.png | manage | 17.4 K | 2010-11-03 - 10:27 | DorotheeSenechal | Mean turbulent kinetic energy profiles |

png | results_K30_31_finish.png | manage | 15.5 K | 2010-11-03 - 10:28 | DorotheeSenechal | Mean turbulent kinetic energy profiles |

png | results_U20_21_60_finish.png | manage | 14.7 K | 2010-11-03 - 10:23 | DorotheeSenechal | Mean streamwise velocity profiles |

png | results_U30_31_finish.png | manage | 14.6 K | 2010-11-03 - 08:26 | DorotheeSenechal | Mean streamwise velocity profiles |

png | results_V20_21_60_finish.png | manage | 19.4 K | 2010-11-03 - 10:21 | DorotheeSenechal | Mean spanwise velocity profiles |

png | results_V30_31_finish.png | manage | 14.5 K | 2010-11-03 - 10:22 | DorotheeSenechal | Mean spanwise velocity profiles |

jpg | visu3D_UVKmoy_iturb20.jpg | manage | 315.8 K | 2010-11-03 - 12:39 | DorotheeSenechal | mean velocity and turbulent kinetic energy fields |

jpg | visu3D_UVKmoy_iturb21.jpg | manage | 286.7 K | 2010-11-03 - 12:54 | DorotheeSenechal | mean velocity and turbulent kinetic energy fields |

jpg | visu3D_UVKmoy_iturb30.jpg | manage | 261.1 K | 2010-11-03 - 12:42 | DorotheeSenechal | mean velocity and turbulent kinetic energy fields |

jpg | visu3D_UVKmoy_iturb31.jpg | manage | 263.2 K | 2010-11-03 - 12:51 | DorotheeSenechal | mean velocity and turbulent kinetic energy fields |

jpg | visu3D_UVKmoy_iturb60.jpg | manage | 312.1 K | 2010-11-03 - 12:55 | DorotheeSenechal | mean velocity and turbulent kinetic energy fields |

Topic revision: r79 - 2018-11-28 - 22:01:27 - ConstantinosKatsamis

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