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Chen, C., Liu, W., Lin, C.-H., Chen, Q. (2015). Comparing the Markov chain model with the Eulerian and Lagrangian models for indoor transient particle transport simulations. Aerosol Science and Technology, 49, 857-871. (Particle dispersion, Infectious particle, Building/Aircraft cabin)

Correctly predicting transient particle transport in indoor environments is crucial to improving the design of ventilation systems and reducing the risk of acquiring airborne infectious diseases. Recently, a new model was developed on the basis of Markov chain frame for quickly predicting transient particle transport indoors. To evaluate this Markov chain model, this study compared it with the traditional Eulerian and Lagrangian models in terms of performance, computing cost, and robustness. Four cases of particle transport, three of which included experimental data, were used for this comparison. The Markov chain model was able to predict transient particle transport indoors with similar accuracy to the Eulerian and Lagrangian models. Furthermore, when the same time step size (Courant number ≤ 1) and grid number were used for all three models, the Markov chain model had the highest calculation speed. The Eulerian model was faster than the Lagrangian model unless a super-fine grid was used. This investigation developed empirical equations for evaluating the three models in terms of computing cost. In addition, the Markov chain model was found to be sensitive to the time step size when the Courant number is larger than 1, whereas the Eulerian and Lagrangian models were not. 

Chen, C., Liu, W., Lin, C.-H., Chen, Q. (2015). A Markov chain model for predicting transient particle transport in enclosed environments. Building and Environment, 90, 30-36. (Particle dispersion, Infectious particle, Building) 

Obtaining information about particle dispersion in a room is crucial in reducing the risk of infectious disease transmission among occupants. This study developed a Markov chain model for quickly obtaining the information on the basis of a steady-state flow field calculated by computational fluid dynamics. When solving the particle transport equations, the Markov chain model does not require iterations in each time step, and thus it can significantly reduce the computing cost. This study used two sets of experimental data for transient particle transport to validate the model. In general, the trends in the particle concentration distributions predicted by the Markov chain model agreed reasonably well with the experimental data. This investigation also applied the model to the calculation of person-to-person particle transport in a ventilated room. The Markov chain model produced similar results to those of the Lagrangian and Eulerian models, while the speed of calculation increased by 8.0 and 6.3 times, respectively, in comparison to the latter two models. 

Chen, C., Liu, W., Lin, C.-H., Chen, Q. (2015). Accelerating the Lagrangian method for modeling transient particle transport in indoor environments. Aerosol Science and Technology, 49, 351-361. (Particle dispersion, Infectious particle, Building)

Computational fluid dynamics (CFD) with the Lagrangian method has been widely used in predicting transient particle transport in indoor environments. The Lagrangian method calculates the trajectories of individual particles on the basis of Newton’s law. Statistically speaking, a large number of particles are needed in the calculations in order to ensure accuracy. Traditionally, modelers have conducted an independence test in order to find a reasonable value for this particle number. However, the unguided process of an independence test can be highly time-consuming when no simple method is available for estimating the necessary particle number. Therefore, this investigation developed a method for estimating the necessary particle number in the Lagrangian method. Furthermore, the computing cost of the Lagrangian method is positively associated with the particle number. If this number is too large, the computing cost may not be affordable. Thus, this study proposed the superimposition and time-averaging methods to reduce the necessary particle number. This investigation designed multiple cases to verify the proposed methods. The verification results show that the estimation method can provide the necessary particle number with a reasonable magnitude. Moreover, the superimposition method can reduce the necessary particle number when the particle source duration is relatively long. On the other hand, the time-averaging method can reduce the necessary particle number by up to 30 times. When compared with experimental data, predictions of transient particle transport in indoor environments by the combined Lagrangian, superimposition, and time-averaging method with the estimated particle number are reasonably accurate.

2014 Particle