Abstract
In order to provide realistic ventilation flow rates, it is of great importance to know indoor pollutant concentration field quickly and efficiently resulting from any type of indoor-pollutant-source distribution, further facilitating the design and control of indoor ventilation systems for practical application. This work introduces the development of reduced-order ventilation models for transient pollutant dispersion. In particular, we focus on transients resulting from a step change in pollutant source distributions. We further focus on the decay problem. A reduced-order ventilation model is the solution for this decay problem, which is derived from a large coupled system of Ordinary Differential Equations (ODEs) for concentration that can be cast in terms of a matrix exponential, that is accurately represented with only a few dominant eigenmodes. Using a 2D ventilation case, dominant eigenmodes with their physical relevance and pollutant concentration results are presented. We find that the first 4 eigenmodes are sufficient to predict the pollutant concentration decay for the current test case. We also find that the complex eigenmodes play an important role in the indoor recirculation processes.
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References
Boyce WE, DiPrima RC (1992). Elementary Differential Equations, 5th edn. New York: John Wiley & Sons.
Cao S-J, Meyers J (2012). On the construction and use of linear lowdimensional ventilation models. Indoor Air, 22: 427–441.
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.
Cao S-J, Meyers J (2014). Asymptotic conditions for the use of linear ventilation models in the presence of buoyancy forces. Building Simulation, 7: 131–136
Campos C, Roman JE, Romero E, Tomas A (2012). SLEPc Users Manual. Technical Report, DSIC-II/24/02 - Revision 3.3, Universitat Politècnica de València.
Chang KC, Hsieh WD, Chen CS (1995). A modified low-Reynoldsnumber turbulence model applicable to recirculating flow in pipe expansion. ASME: Journal of Fluids Engineering, 117: 417–423.
Emmerich SJ, Persily AK (2001). State-of-the-art review of CO2-based demand controlled ventilation technology and application. NISTIR 6729.
Ferziger JH, Peric M (2002). Computational Methods for Fluid Dynamics. London: Springer.
Gockenbach MS (2010). Partial Differential Equations: Analytical and Numerical Methods, 2nd edn. Philadelphia, USA: Society for Industrial and Applied Mathematics.
Hernandez V, Roman JE, Vidal V (2005). SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Transactions on Mathematical Software, 31: 351–362.
van Hooff T, Blocken B, van Heijst GJF (2013). On the suitability of steady RANS CFD for forced mixing ventilation at transitional slot Reynolds numbers. Indoor Air, 23: 236–249.
Ockendon J, Howison S, Lacey A, Movchan A (1999). Applied Partial Differential Equations. Oxford, UK: Oxford University Press.
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Cao, SJ., Meyers, J. Fast prediction of indoor pollutant dispersion based on reduced-order ventilation models. Build. Simul. 8, 415–420 (2015). https://doi.org/10.1007/s12273-015-0240-9
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DOI: https://doi.org/10.1007/s12273-015-0240-9