Accelerating the Lagrangian Method for Modeling Transient Particle Transport in Indoor Environments

Abstract

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.

Comparing the Markov Chain Model with the Eulerian and Lagrangian Models for Indoor Transient Particle Transport Simulations

“…To reduce the necessary particle number and increase the speed of calculation, Chen et al (2015b) have proposed a combined Lagrangian and superimposition method. Instead of injecting particles in each time step, as in the pure Lagrangian method, the combined Lagrangian and superimposition method injects particles only in one time step.…”

“…For cases of person-to-person particle transport, the target zone can be defined as the breathing zone, whose volume is about 0.027 m 3 (OSHA 2014). N target * is the necessary particle number in the target zone, which can be set at 30 (Student 1908;Chen et al 2015b). The parameter t is the time constant of the room:…”

“…The necessary particle number in the combined Lagrangian and superimposition method can be estimated by (Chen et al 2015b)…”

“…Statistically speaking, a large number of particles are needed in the calculations in order to ensure accuracy. For a case in which particles are emitted through an inlet or by an indoor source, the necessary particle number in the Lagrangian model can be estimated by (Chen et al 2015b)…”

“…where t s is the particle source duration; V room is the volume of the room; a is a coefficient that depends on the tolerance of error, which can be set at 1% (Chen et al 2015b); and V target is the volume of the target zone. For cases of person-to-person particle transport, the target zone can be defined as the breathing zone, whose volume is about 0.027 m 3 (OSHA 2014).…”