A Markov chain model for predicting transient particle transport in enclosed environments

Enhancing the effectiveness of bioaerosol disinfection in indoor environments by optimizing far-UVC lamp locations based on Markov chain model

Far-ultraviolet C (far-UVC) light is an effective and safe disinfection method for bioaerosol control in occupied indoor environments. The installation location of a far-UVC lamp strongly influences the spatial distribution of far-UVC irradiance, and thus the effectiveness of bioaerosol disinfection. To assist the design process, this study developed a fast prediction approach based on the Markov chain model for optimizing the installation locations of far-UVC lamps in order to enhance the disinfection effectiveness for indoor bioaerosol control. Experiments were conducted in an environmental chamber to validate the proposed simulation-based optimization approach. The results show that the proposed method can correctly predict the disinfection efficiency when compared with experimental data, and optimizing the installation location of the far-UVC lamp increased the disinfection efficiency by 54 % compared with the worst location. As an application, the validated method was then used to design the installation location of a far-UVC lamp in a real conference room. The results show that installing the far-UVC lamp in the optimal location can increase the disinfection efficiency by 48 % compared with the worst installation location. Therefore, optimizing the far-UVC lamp location using the proposed Markov chain model can enhance the effectiveness of bioaerosol disinfection in indoor environments.

Evaluation of intervention measures in reducing the driver's exposure to respiratory particles in a taxi with infected passengers

In the fifth wave of the COVID-19 epidemic in Hong Kong in early 2022, the large number of infected persons caused a shortage of ambulances and transportation vehicles operated by the government. To solve the problem, taxi drivers were recruited to transport infected persons to hospitals in their taxis. However, many of the drivers were infected after they began to participate in the plan. To tackle this issue, the present study numerically evaluated the effectiveness of several intervention measures in reducing the infection risk for taxi drivers. First, experiments were conducted inside a car to validate the large-eddy simulation (LES)-Lagrangian model for simulation of particle transport in a car. The validated model was then applied to calculate the particle dispersion and deposition in a Hong Kong taxi with intervention measures that included opening windows, installing partitions, and using a far-UVC lamp. The results show that opening the windows can significantly reduce the driver's total exposure by 97.4 %. Installing partitions and using a far-UVC lamp can further reduce the infection risk of driver by 55.9 % and 32.1 %, respectively. The results of this study can be used to support the implementation of effective intervention measures to protect taxi drivers from infection.

Transmission characteristics of respiratory droplets aerosol in indoor environment: an experimental study

Transmission of droplets has been recognized as an important form of infection for the respiratory diseases. This study investigated the distribution of human respiratory droplets and assessed the effects of air change rate and generated velocity on droplet transmission using an active agent in an enclosed chamber (46 m³). Results revealed that the higher the air change rate was, the fewer viable droplets were detected in the range of <3.3 μm with ventilation; an increased air change rate can increase the attenuation of droplet aerosol. Without ventilation, the viable droplet size was observed to mainly distribute greater than 3.3 μm, which occupied up 87.5% of the total number. When the generated velocity was increased to 20 m/s, 29.38% of the viable droplets were detected at the position of 2.0 m. The findings are excepted to be useful for developing the technology of reducing droplet propagation and providing data verification for simulation research.

Cross-Regional Dynamic Transfer Characteristics of Liquid Oil Contamination Induced by Random Contact in Machining Workshops in Shanghai, China

In industrial sites, the movement and contact behaviors of workers are random, but their frequency and statistical characteristics can be determined. Particularly in machining workshops, metalworking fluids (MWFs) cause liquid oil contamination on the processed workpieces, and the contamination spreads to the entire workshop given the random contact of workers or the handling of workpieces. This study proposes a contact transmission model based on the Markov chain to quantify oil contamination transfer. First, the transfer efficiency between the glove and the workpiece, which is regarded as a key model parameter in this research, was determined through experiments. The model was used to characterize and predict the spread of oil contamination across different regions, including production and assembly areas. Specifically, the oil contamination concentrations on workbench surfaces in seven locations of a machining workshop in Shanghai GKN HUAYU Driveline Systems Co., Ltd. (SDS) were measured on-site. Findings showed that the model could feasibly depict the transfer process of oil contamination across different surfaces. Then, the variation law of oil contamination concentration on the workbench surfaces over time was analyzed, the oil contamination distribution map of the entire workshop plane was drawn, and the effectiveness of two cleaning measures to reduce oil contamination concentrations was compared. The proposed contact transmission model offers a basis for identifying highly polluted surfaces in machining workshops and controlling the spread of liquid oil contamination.

Predicting indoor particle dispersion under dynamic ventilation modes with high-order Markov chain model

Mechanical and natural ventilations are effective measures to remove indoor airborne contaminants, thereby creating improved indoor air quality (IAQ). Among various simulation techniques, Markov chain model is a relatively new and efficient method in predicting indoor airborne pollutants. The existing Markov chain model (for indoor airborne pollutants) is basically assumed as first-order, which however is difficult to deal with airborne particles with non-negligible inertial. In this study, a novel weight-factor-based high-order (second-order and third-order) Markov chain model is developed to simulate particle dispersion and deposition indoors under fixed and dynamic ventilation modes. Flow fields under various ventilation modes are solved by computational fluid dynamics (CFD) tools in advance, and then the basic first-order Markov chain model is implemented and validated by both simulation results and experimental data from literature. Furthermore, different groups of weight factors are tested to estimate appropriate weight factors for both second-order and third-order Markov chain models. Finally, the calculation process is properly designed and controlled, so that the proposed high-order (second-order) Markov chain model can be used to perform particle-phase simulation under consecutively changed ventilation modes. Results indicate that the proposed second-order model does well in predicting particle dispersion and deposition under fixed ventilation mode as well as consecutively changed ventilation modes. Compared with traditional first-order Markov chain model, the proposed high-order model performs with more reasonable accuracy but without significant computing cost increment. The most suitable weight factors of the simulation case in this study are found to be (λ₁ = 0.7, λ₂ = 0.3, λ₃ = 0) for second-order Markov chain model, and (λ₁ = 0.8, λ₂ = 0.1, λ₃ = 0.1) for third-order Markov chain model in terms of reducing errors in particle deposition and escape prediction. With the improvements of the efficiency of state transfer matrix construction and flow field data acquisition/processing, the proposed high-order Markov chain model is expected to provide an alternative choice for fast prediction of indoor airborne particulate (as well as gaseous) pollutants under transient flows.

Evolution of pressure drop across electrospun nanofiber filters clogged by solid particles and its influence on indoor particulate air pollution control

Because of the relatively low pressure drop and high particle removal efficiency, nanofiber filter media can be potentially used for indoor particulate air pollution control. However, the influence of particle loading on the long-term performance of nanofiber filters in indoor particle control has not been well studied. This study first experimentally investigated the relationship between the pressure drop and solid particle loading mass for 42 nanofiber filter samples under various face velocities. The results show that the air resistance coefficient increased with the solid particle loading mass for the nanofiber filter media. Furthermore, the air resistance coefficient was positively associated with the face velocity, as a higher air velocity tended to make the particle cake tighter with higher resistance. Based on the experimental data, a semi-empirical equation was developed for predicting the pressure drop under different particle loading masses and face velocities. The developed semi-empirical model was then used to assess the long-term performance of an air cleaner equipped with nanofiber filter media in indoor PM_2.5 control. The case study demonstrated that an air cleaner equipped with nanofiber filter media could effectively control indoor PM_2.5, but the lifetime of the nanofiber filter was shorter than that of traditional HEPA filters.

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.

Estimating the nationwide transmission risk of measles in US schools and impacts of vaccination and supplemental infection control strategies

BACKGROUND

The spread of airborne infectious diseases such as measles is a critical public health concern. The U.S. was certified measles-free in 2000, but the number of measles cases has increased in recent years breaking the record of the nationwide annual number of cases since 1992. Although the characteristics of schools have made them one of the most vulnerable environments during infection outbreaks, the transmission risk of measles among students is not completely understood. We aimed to evaluate how three factors influence measles transmission in schools: personal (vaccination), social (compartmentalizing), and building systems (ventilation, purification, and filtration).

METHODS

We used a combination of a newly developed multi-zone transient Wells-Riley approach, a nationwide representative School Building Archetype (SBA) model, and a Monte-Carlo simulation to estimate measles risk among U.S. students. We compared our risk results with the range of reported transmission rates of measles in school outbreaks to validate the risk model. We also investigated the effectiveness of vaccination and ten supplemental infection control scenarios for reducing the risk of measles transmission among students.

RESULTS

Our best nationwide estimate of measles transmission risk in U.S. schools were 3.5 and 32% among all (both unvaccinated and immunized) and unvaccinated students, respectively. The results showed the transmission risk of measles among unvaccinated students is > 70 times higher than properly immunized ones. We also demonstrated that the transmission risk of measles in primary schools (assuming teacher self-contained classrooms) is less than secondary schools (assuming departmentalized systems). For building-level interventions, schools with ductless-with-air-filter and ductless-without-air-filter systems have the lowest and highest transmission risks of measles, respectively. Finally, our simulation showed that infection control strategies could cut the average number of infected cases among all students in half when a combination of advanced air filtration, ventilation, and purification was adopted in the modeled schools.

CONCLUSIONS

Our results highlight the primary importance of vaccination for reducing the risk of measles transmission among students. Yet, additional and significant risk reduction can be achieved through compartmentalizing students and enhancing building ventilation and filtration systems.

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 simple method for differentiating direct and indirect exposure to exhaled contaminants in mechanically ventilated rooms

Many airborne infectious diseases can be transmitted via exhaled contaminants transported in the air. Direct exposure occurs when the exhaled jet from the infected person directly enters the breathing zone of the target person. Indirect exposure occurs when the contaminants disperse in the room and are inhaled by the target person. This paper presents a simple method for differentiating the direct and indirect exposure to exhaled contaminants in mechanically ventilated rooms. Experimental data for 191 cases were collected from the literature. After analyzing the data, a simple method was developed to differentiate direct and indirect exposure in mixing and displacement ventilated rooms. The proposed method correctly differentiated direct and indirect exposure for 120 out of the 133 mixing ventilation cases and 47 out of the 58 displacement ventilation cases. Therefore, the proposed method is suitable for use at the early design stage to quickly assess whether there will be direct exposure to exhaled contaminants in a mechanically ventilated room.

Investigating the impact of gaspers on cabin air quality in commercial airliners with a hybrid turbulence model

It is not clear whether turning on the gaspers in the cabins of commercial airliners actually improves the air quality. To answer this question, this study first developed a hybrid turbulence model which was suitable for predicting the air distribution in an aircraft cabin with gaspers turned on. Next, the investigation validated the model using two sets of experimental data from a cabin mockup and an actual airplane. This study then used the validated model to systematically investigate the impact of gaspers on cabin air quality in a seven-row section of the fully-occupied, economy-class cabin of Boeing 767 and 737 airplanes. The CFD calculations formed a database consisting of 9660 data points that provide information about SARS infection risk. It was found that the distribution of opened gaspers can influence the infection risk for passengers. Even though the gasper supplies clean air, it is possible for it to have a negative impact on the passengers' health. Statistically speaking, the overall effect of turning on the gaspers on the mean infection risk for the general population was neutral.

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.

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

Predicting the movement of contaminants in the indoor environment has applications in tracking airborne infectious disease, ventilation of gaseous contaminants, and the isolation of spaces during biological attacks. Markov matrices provide a convenient way to perform contaminant transport analysis. However, no standardized method exists for calculating these matrices. A methodology based on set theory is developed for calculating contaminant transport in real-time utilizing Markov matrices from CFD flow data (or discrete flow field data). The methodology provides a rigorous yet simple strategy for determining the number and size of the Markov states, the time step associated with the Markov matrix, and calculation of individual entries of the Markov matrix. The procedure is benchmarked against scalar transport of validated airflow fields in enclosed and ventilated spaces. The approach can be applied to any general airflow field, and is shown to calculate contaminant transport over 3000 times faster than solving the corresponding scalar transport partial differential equation. This near real-time methodology allows for the development of more robust sensing and control procedures of critical care environments (clean rooms and hospital wards), small enclosed spaces (like airplane cabins) and high traffic public areas (train stations and airports).