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TWiki> CfdTm Web>TestCase005 (2011-02-10, StefanoRolfo)

TWiki> CfdTm Web>TestCase005 (2011-02-10, StefanoRolfo)

*Type: Numerical*

*Status*:

Schematic of ascending flow | Schematic of descending flow: |
---|---|

- Low-Reynolds RANS models are compared to DNS and LES data for profiles, and a number of experiments showing Nusselt versus heat/buoyancy loading.
- Nusselt Number versus Buoyancy:

- What it shows: In the heated & upward flow case the near wall layer is accelerated by buoyancy. This shifts the high velocity gradient region closer to the wall and as a result turbulence production is restrained by wall proximity, and eventually the flow relaminarises. It is a very good test of whether models correctly account for interaction between the actual turbulence length-scale (size of large eddies), and the non-local influence of a solid wall. The V2F , Lien & Leschziner, and Launder & Sharma models perform well. The k-omega, and SST models miss the relaminarisation. There is some similarity with accelerating boundary layers (see TaniaKlein 1st year report in this Twiki), as there is no direct effect of buoyancy on the turbulence.

* Key results: Some models (e.g. k-omega SST) miss the relaminarisation
* Velocity: = = Temperature: = = Kinetic energy:

- Heated-PipeShort_KNOO_Addad_Laurence.ppt: More graphs in ppt file (2.3 Mb)

- Steady state
- %$Re = 2650$% (based on radius) %$\Rightarrow Re_\tau=180$%
- GRashof number %$Gr=\frac{g \beta q_w R^4}{\lambda \nu^2}$%
- Constant properties with the exception of the density (isobaric):
- %$ \rho = \frac {\rho_0} {1+\beta(T-T_0)} $% where %$ \rho_0 = 1.205 $%, %$ \beta =0 .00343 $% and %$ T_0 = 293 $%
- %$\mu = 18.1 \cdot 10^{-6}$%
- %$\nu = \mu/\rho_0$%
- %$c_p = 1006$%
- %$Pr = 0.71$%

- Five different heat transfer regimes are considered:
- %$ \frac {Gr} {Re^2} = 0 \Rightarrow$% "force convection"
- %$ \frac {Gr} {Re^2} = 0.063 \Rightarrow$% "force/mixed convection"
- %$ \frac {Gr} {Re^2} = 0.087 \Rightarrow$% "re-laminarization"
- %$ \frac {Gr} {Re^2} = 0.241 to 0.400 \Rightarrow$% "recovery"

- The flow is fully developed. Periodicity in the stream-wise direction can be used
- The flow pattern is axial-symmetric. For RANS it is possible to use just one cell in the ortho-radial direction
- The RANS mesh for RANS (See CONVERT in results section)
- Radial direction:
- n cells: 120
- distribution: geometric progression with expansion factor equal to 0.99, $y^+\; \backslash leq\; 0.3$

- Streamwise direction (z): periodicity, with a momentum source term to drive the flow

- Pressure Drop

%BEGINLATEX{label="bal_mom"}%

\begin{equation*}p S_{inlet}-(p+dp)S_{outlet}=\tau_wS_{lat} \end{equation*}

%ENDLATEX%

%BEGINLATEX{label="pres_drop"}% \begin{equation*} S_{inlet}=S_{outlet}=S \Rightarrow dp=-\tau_w \frac {S_{lat}} {S} = -\tau_w \frac {P dz} {S} \end{equation*} %ENDLATEX% %BEGINLATEX{label="beta"}% \begin{equation*} \beta= \frac {dp} {dz} = -(\frac {2\tau_w} {R})_{\mbox{for\,pipe}} \end{equation*} %ENDLATEX% the term %$\beta$% has to be added into the '''explicit''' part of the source term into the z direction, with a positive sign.

- Mass flow rate

Also for the energy equation a source term is required. If we consider the element of figure-1 and we apply the first principle of thermodynamic from the point of view of an external observer moving with the fluid and we also consider constant density we can write: %BEGINLATEX{label="1_princ_termo"}% \begin{equation*} dE=dQ \end{equation*} %ENDLATEX% and from this equation it is possible to compute the variation of the bulk temperature between inlet and outlet as: %BEGINLATEX{label="Delta_T"}% \begin{equation*} T_{b_{outlet}}- T_{b_{inlet}}=\frac {\dot{q}S_{wall}} {\dot{m}c_p} \end{equation*} %ENDLATEX% Then the source term for the transport equation of the temperature is the following: %BEGINLATEX{label="source_term"}% \begin{equation*} s_T=-\rho W \sigma \end{equation*} %ENDLATEX% where %$ \sigma=\frac {dT} {dz} = \frac {\dot{q}S_{wall}} {\dot{m}c_pdz}$%

- You et al 2003;
**"Direct numerical simulation of heated vertical air flows in fully developed turbulent mixed convection"**; International Journal of Heat and Mass Transfer, Volume 46, Issue 9, April 2003, Pages 1613-1627. Download - Keshmiri A., Addad Y., Cotton M.A., Laurence D. and Billard F., 2008;
**"Refined Eddy Viscosity Schemes and LES. for Ascending Mixed Convection Flows"**To appear in the Proc. of Computational Heat Transfer (CHT08) Symp., Marakkech, Morroco, 11-16 May 2008 Download - Keshmiri A., Cotton M.A., Addad Y., Rolfo S. and Billard F., 2008,;
**"RANS and LES Investigations of Vertical Flows in Passages of Gas-Cooled Nuclear Reactors"**To appear in the Proc. of ASME 16th Int. Conf. on Nuclear Engineering (ICONE16), Orlando, Florida, 11-15 May 2008, Vol. ICONE16-48372 Download - Keshmiri A. and Cotton M.A., 2008,;
**"Turbulent Mixed Convection Flows Computed Using Low-Reynolds-Number and Strain Parameter Eddy Viscosity Schemes"**; Proc. of 7th Int. ERCOFTAC Symp. on Engineering Turbulence Modelling and Measurements (ETMM7), Vol. 1, pp.274-279, Limassol, Cyprus, 4th-6th June 2008.Download - W.S. Kim, S. He and J.D. Jackson, 2008;
**"Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection"**; International Journal of Heat and Mass Transfer, Volume 51, Issues 5-6, , March 2008, Pages 1293-1312. download doi ijheatmasstransfer.2007.12.002

Code | Version | Author | Restrictions |
---|---|---|---|

CONVERT |
[[CfdTm.TestCase005Res001][]] |
Amir Keshmiri | Main.None |

CONVERT |
[[CfdTm.TestCase005Res002][]] |
Amir Keshmiri | Main.None |

CONVERT |
[[CfdTm.TestCase005Res003][]] |
Amir Keshmiri | Main.None |

reference DNS |
[[CfdTm.TestCase005Res004][]] |
You et al [2003] | Main.None |

STAR-CD, fine LES |
[[CfdTm.TestCase005Res005][]] |
Yacine Addad | Main.None |

Code_Saturne |
[[CfdTm.TestCase005Res006][]] |
Flavien Billard | Main.None |

STAR-CD, k-eps |
[[CfdTm.TestCase005Res007][]] |
Stefano Rolfo | Main.None |

STAR-CD, SST |
[[CfdTm.TestCase005Res008][]] |
Stefano Rolfo | Main.None |

Number of topics: 8

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I | Attachment | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|

ppt | Heated-PipeShort_KNOO_Addad_Laurence.ppt | manage | 2396.0 K | 2008-11-23 - 13:57 | UnknownUser | More graphs in ppt file |

JPG | ICONE16-Nu.JPG | manage | 137.4 K | 2009-02-12 - 17:22 | UnknownUser | |

png | slide0012_image032.png | manage | 50.3 K | 2008-11-23 - 12:50 | UnknownUser | Velocity |

png | slide0012_image033.png | manage | 51.5 K | 2008-11-23 - 12:51 | UnknownUser | Temperature |

png | slide0012_image034.png | manage | 65.8 K | 2008-11-23 - 12:53 | UnknownUser | Kinetic energy |

Topic revision: r49 - 2011-02-10 - 09:08:09 - StefanoRolfo

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