Isothermal 2D zonal air volume model Victor Norrefeldt, Thierry Nouidui, Christoph van Treeck, Gunnar Grün Fraunhofer Institute for Building Physics – Valley, Germany

Goal of zonal models quick estimation of airflow patterns quick estimation of local distributions of heat moisture contaminants …

Idea of zonal modeling single-zone multi-zone CFD zonal

Principles of zonal modeling Subdivision of a room into zones (volumes) Volume model: Mass Conservation Conservation of thermal energy Other particle / contaminant conservations possible (moisture, CO2, VOC, …) Flow Model Links two volume models Calculates mass flow rate from pressure difference

State of art Volume 1 p1 Volume 2 p2 Flow Link many volumes → room Cd approximately 0.83 (Jiru and Haghighat, 2006, Wurtz et al., 1999)

Basic Zonal Model

Basic Zonal Model Source Sink

Application examples of Zonal Models Prediction of temperature stratification in an experimental atrium in Kanagawa, Japan (Heiselberg et al., 1998) Calculation of refrigeration load of an ice-rink in Canada (Daoud et al., 2007) Modeling of a ventilated double-skin façade (Jiru et al., 2008)

Inifinte gradient at zero Difficulty with state-of-the-art zonal model: Small pressure differences Current solution: Linearization (Boukhris et al., 2009) New solution: Calculate acceleration of air flow Inifinte gradient at zero

Difficulty with state-of-the-art zonal model: Dissipation of airflow velocity in volumes Current solution: Jet- or plume correlations for regions with driving air flows (e.g. Wurtz et al., 2006) New solution: Air flow velocity as a property in volumes

Difficulty with state-of-the-art zonal model: Number of zones influences the total pressure drop Current solution: None found New solution: Size of a zone taken into account u0 4 pressure drops 2 pressure drops

Formulation of the new zonal model Forces on flow path → acceleration of air flow Use of apparent µ → losses Steady State → acceleration = 0, velocity = constant Pressure Impluse Gravitation Viscous losses

Application example: Nielsen-Room

Zoning

Comparison of results (µ = 0.001) + Maximal velocity + Recirculation point - Recirculating air flow

Comparison of results (µ = 0.001) Maximal velocity + Recirculation point - Recirculating air flow

Conclusion New formulation of zonal models Incorporated impulse conservation Quick prediction of air flow pattern in rooms Next steps Extension to non-isothermal cases Validation with own measurements

References Jiru, T.E. and Haghighat, F., 2006. A new generation of zonal models. ASHRAE Transactions. Vol. 112. Part 2. pp 163-174 Heiselberg, P., Murakami, S., Roulet, C.-A. 1998. Ventilation of large spaces in buildings, Analysis and prediction techniques. IEA Annex 26 Daoud, A., Galanis, N., Bellache, O. 2008. Calculation of refrigeration loads by convection, radiation and condensation in ice rinks using a transient 3D zonal model. Applied Thermal Engineering. Vol. 28. pp 1782-1790 Jiru, E., Haghighat, F. 2008. Modeling ventilated double skin façade—A zonal approach. Energy and Buildings. Vol. 40. pp 1567-1576 Wurtz, E., Mora, L., Inard, C. 2006. An equation-based simulation environment to investigate fast building simulation, Building and Environment. Vol. 40. pp 1571-1583 Boukhris, Y, Gharbi, L, and Ghrab-Morcos, N. 2009. Modeling coupled heat transfer and air flow in a partitioned building with a zonal model: application to the winter thermal comfort. Building Simulation. Vol. 2. pp 67-74 Nielsen, P.V. 1990. Specification of a two-dimensional test case. International Energy Agency. Energy conservation in buildings and community systems, Annex 20: Air flow patterns within buildings.

Thank you for your attention Questions? in discussion or to victor.norrefeldt@ibp.fraunhofer.de