Constructing Markov matrices for real-time transient contaminant transport analysis for indoor environments

Modeling transient particle transport in transient indoor airflow by fast fluid dynamics with the Markov chain method

It is crucial to accurately and efficiently predict transient particle transport in indoor environments to improve air distribution design and reduce health risks. For steady-state indoor airflow, fast fluid dynamics (FFD) + Markov chain model increased the calculation speed by around seven times compared to computational fluid dynamics (CFD) + Eulerian model and CFD + Lagrangian model, while achieving the same level of accuracy. However, the indoor airflow could be transient, if there were human behaviors involved like coughing or sneezing and air was supplied periodically. Therefore, this study developed an FFD + Markov chain model solver for predicting transient particle transport in transient indoor airflow. This investigation used two cases, transient particle transport in a ventilated two-zone chamber and a chamber with periodic air supplies, for validation. Case 1 had experimental data for validation and the results showed that the predicted particle concentration by FFD + Markov chain model matched well with the experimental data. Besides, it had similar accuracy as the CFD + Eulerian model. In the second case, the prediction by large eddy simulation (LES) was used for validating the FFD. The simulated particle concentrations by the Markov chain model and the Eulerian model were similar. The simulated particle concentrations by the Markov chain model and the Eulerian model were similar. The computational time of the FFD + Markov chain model was 7.8 times less than that of the CFD + Eulerian model.

Modeling transient particle transport by fast fluid dynamics with the Markov chain method

Fast simulation tools for the prediction of transient particle transport are critical in designing the air distribution indoors to reduce the exposure to indoor particles and associated health risks. This investigation proposed a combined fast fluid dynamics (FFD) and Markov chain model for fast predicting transient particle transport indoors. The solver for FFD-Markov-chain model was programmed in OpenFOAM, an open-source CFD toolbox. This study used two cases from the literature to validate the developed model and found well agreement between the transient particle concentrations predicted by the FFD-Markov-chain model and the experimental data. This investigation further compared the FFD-Markov-chain model with the CFD-Eulerian model and CFD-Lagrangian model in terms of accuracy and efficiency. The accuracy of the FFD-Markov-chain model was similar to that of the other two models. For the two studied cases, the FFD-Markovchain model was 4.7 and 6.8 times faster, respectively, than the CFD-Eulerian model, and it was 137.4 and 53.3 times faster than the CFD-Lagrangian model in predicting the steady-state airflow and transient particle transport. Therefore, the FFD-Markov-chain model is able to greatly reduce the computing cost for predicting transient particle transport in indoor environments.

A Risk Assessment Approach for Evaluating the Impact of Toxic Contaminants Released Indoors by Considering Various Emergency Ventilation and Evacuation Strategies

The release of toxic airborne contaminants resulting from terrorist attacks on buildings can lead to disastrous consequences. To evaluate and reduce the effects of these emergencies, various methods and models have been developed in the past few years. Such work has provided effective tools for the building management system to do risk assessment of the contaminated areas. Although risk analysis methods to describe the contaminant dispersion scenarios made significant progress, these approaches did not generally consider the releasing scenario occurring in the ventilation system and the effect of human behavior during the developing process of an emergency event. Emergency strategies chosen by the decisionmaker are not always associated with the early-warning system, such as the sensor monitoring network and the source identification system inside the building. This study aims to provide a risk assessment model considering both the variation of contaminant concentration and occupant distribution after the release of toxic agents to obtain the exposure risk for people indoors. The contaminant dispersion is simulated using computational fluid dynamics. The evacuation process for people is modeled using Pathfinder, and the exposure risk for occupants under various emergency strategies is calculated using the efficiency factor of the contaminant source. The results of the exposure risk for 40 basic cases are discussed, and the optimal ventilation mode for these specific cases is recommended. Next, the impact of the variation of human behavior, contaminant detection time needed by sensors, and source identification time needed by inverse modeling on the exposure risk for people indoor is studied. The uncertainty and reproducibility of the numerical simulations are emphatically discussed in the Supporting Information.

A methodology for optimal placement of sensors in enclosed environments: A dynamical systems approach

Air quality has been an important issue in public health for many years. Sensing the level and distributions of impurities help in the control of building systems and mitigate long term health risks. Rapid detection of infectious diseases in large public areas like airports and train stations may help limit exposure and aid in reducing the spread of the disease. Complete coverage by sensors to account for any release scenario of chemical or biological warfare agents may provide the opportunity to develop isolation and evacuation plans that mitigate the impact of the attack. All these scenarios involve strategic placement of sensors to promptly detect and rapidly respond. This paper presents a data driven sensor placement algorithm based on a dynamical systems approach. The approach utilizes the finite dimensional Perron-Frobenius (PF) concept. The PF operator (or the Markov matrix) is used to construct an observability gramian that naturally incorporates sensor accuracy, location constraints, and sensing constraints. The algorithm determines the response times, sensor coverage maps, and the number of sensors needed. The utility of the procedure is illustrated using four examples: a literature example of the flow field inside an aircraft cabin and three air flow fields in different geometries. The effect of the constraints on the response times for different sensor placement scenarios is investigated. Knowledge of the response time and coverage of the multiple sensors aides in the design of mechanical systems and response mechanisms. The methodology provides a simple process for place sensors in a building, analyze the sensor coverage maps and response time necessary during extreme events, as well as evaluate indoor air quality. The theory established in this paper also allows for future work in topics related to construction of classical estimator problems for the sensors, real-time contaminant transport, and development of agent dispersion, contaminant isolation/removal, and evacuation strategies.