On the construction and use of linear low-dimensional ventilation models

Abstract

The construction of fast reliable low-dimensional models is important for monitoring and control of ventilation applications. We employ a discrete Green's function approach to derive a linear low-dimensional ventilation model directly from the governing equations for indoor ventilation (i.e., the Navier-Stokes equations supplemented with a transport equation for indoor-pollutant concentration). It is shown that the flow equations decouple from the concentration equation when the ratio α of air-mass-flow rate to pollutant-mass-flow rate increases to infinity. A low-dimensional discrete representation of the Green's function of the concentration equation can then be constructed, based on either numerical simulations or experiments. This serves as a linear model that allows for the reconstruction of concentration fields resulting from any type of pollutant-source distribution. We employ a suite of Reynolds-averaged Navier-Stokes (RANS) simulations to illustrate the methodology. We focus on a simple benchmark ventilation case under constant-density conditions. Discrete linear ventilation models for the concentration are then derived and compared with coupled RANS simulations. An analysis of errors in the discrete linear model is presented: dependence of the error on the (low-dimensional) resolution in the discrete model is quantified, and errors introduced by too low values of α are also investigated. The paper introduces the derivation and construction of linear low-dimensional ventilation models, which allow reconstructing concentration fields resulting from any type of indoor-pollutant-source distribution. Once constructed, these ventilation models are very efficient to estimate indoor contaminant concentration distributions, compared to direct CFD simulation approaches. Therefore, these models can facilitate monitoring and control of ventilation systems, to remove indoor contaminants.