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Asymptotic conditions for the use of linear ventilation models in the presence of buoyancy forces

  • Research Article
  • Indoor/Outdoor Airflow and Air Quality
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Low-dimensional discrete linear ventilation models have been studied by literature. In the present study, we investigate the validity and applicability of linear ventilation models for heavy-gas dispersion by employing Reynolds-averaged Navier-Stokes (RANS) simulations. A simple benchmark ventilation case is considered under isothermal condition. Considering large density differences from pollutant gas and fresh air, the effect of buoyancy force has been taken into account in turbulent production term to obtain correct diffusion behaviour. A low-Re k-ε model has been selected and the generalised gradient diffusion hypothesis is used for buoyancy source term. It is concluded that the flow equations decouple from the concentration equation when the ratio α of air mass-flow rate to pollutant mass-flow rate is larger than 105, which is 10 times higher than the range without density differences (α>104). The dependence of the coupling on Richardson number Ri is also studied. It is found that the higher the Richardson number, the larger the α should be to decouple equations.

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  • Awbi HB (2003). Ventilation of Buildings, 2nd edn. London: Spon Press.

    Google Scholar 

  • Cao S-J, Meyers J (2011). Evaluation of a discrete linear ventilation model for a range of indoor Reynolds numbers. In: Proceedings of ISHVAC, Shanghai, China, pp. 1052–1059.

    Google Scholar 

  • Cao S-J, Meyers J (2012). On the construction and use of linear low-dimensional ventilation models. Indoor Air, 22: 427–441.

    Article  Google Scholar 

  • Cao, S-J, Meyers J (2013). Influence of turbulent boundary conditions on RANS simulations of pollutant dispersion in mechanically ventilated enclosures with transitional slot Reynolds number. Building and Environment, 59: 397–407.

    Article  Google Scholar 

  • Chang KC, Hsieh WD, Chen CS (1995). Modified low-Reynolds-number turbulence model applicable to recirculating flow in pipe expansion. Journal of Fluids Engineering, 17: 417–423.

    Article  Google Scholar 

  • Chung W, Devaud CB (2008). Buoyancy-corrected k-ɛ models and large eddy simulation applied to a large axisymmetric helium plume. International Journal for Numerical Methods in Fluids, 58: 57–89.

    Article  MATH  Google Scholar 

  • Ricciardi L, Prévost C, Bouilloux L, Sestier-Carlin R (2008). Experimental and numerical study of heavy gas dispersion in a ventilated room. Journal of Hazardous Materials, 152: 493–505.

    Article  Google Scholar 

  • van Hooff T, Blocken B, Defraeye T, Carmeliet J, van Heijst GJF (2012). PIV measurements and analysis of transitional flow in a reduced-scale model: Ventilation by a free plane jet with Coanda effect. Building and Environment, 56: 301–313.

    Article  Google Scholar 

  • Worthy J, Sanderson V, Rubini P (2001). Comparison of modified k-ɛ turbulence models for buoyant plumes. Numerical Heat Transfer Part B: Fundamentals, 39: 151–165.

    Article  Google Scholar 

  • Yan Z, Holmstedt G (1999). A two-equation turbulence model and its application to a buoyant diffusion flame. International Journal of Heat and Mass Transfer, 42: 1305–1315.

    Article  MATH  Google Scholar 

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Correspondence to Shi-Jie Cao.

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Cao, SJ., Meyers, J. Asymptotic conditions for the use of linear ventilation models in the presence of buoyancy forces. Build. Simul. 7, 131–136 (2014).

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