Markov Chain Model For Indoor Passive Contaminant Distribution Prediction

Indoor air quality affects the health and work efficiency of indoor occupants.Prediction of indoor contaminant distribution contributes to the inverse identification of contaminant sources,the optimization of air distribution,and the arrangement of air purifiers.All of these are effective measures to eliminate indoor pollutants in time and ensure indoor air quality.Passive contaminants with good airflow following,such as respiratory microdroplets exhaled by sick people,fine particles generated by combustion,and harmful gases released from furniture and building materials,can spread in a wider range,and eventually be inhaled by occupants,causing great harm.The topic of this study comes from a project within the University Innovation Research Group in Chongqing–Healthy Built Environment and Build Wisely(No.CXQT21004).It is hard for traditional contaminant distribution prediction models(including CFD model,multi-zone model,and zonal model)to achieve the balance between computational accuracy and speed.Therefore,researchers proposed several modified or improved models.The solving process of indoor contaminant distribution can be divided into two stages,i.e.,airflow field prediction and contaminant transport simulation.According to the stage of improvement,the novel methods can be divided into three categories:fast airflow field prediction methods,fast pollutant transport simulation methods,and data-driven prediction models.The fast airflow field prediction methods include fast fluid dynamics,lattice Boltzmann method,etc.The fast pollutant transport simulation methods include accessibility of contaminant sources,Markov chain model,etc.The data driven prediction models include low dimensional linear ventilation models,proper orthogonal decomposition,machine learning algorithms,etc.There are some disadvantages in the existing methods,such as poor accuracy in some specific areas,reliance on traditional models to solve the airflow field or contaminant transport,difficulty to deal with complex turbulence scenarios,rely on sample data solved by traditional models,etc.The Markov chain model has several advantages for indoor airborne contaminant transport simulations,including simple principle,sample data independence,coupling with a variety of mechanisms,etc.However,it also faces some problems,such as poor accuracy of prediction at some time and locations,difficult application in scenarios with continuous release of contaminant source,and dependence on airflow data solved by traditional method.This study has carried out theoretical research on the above deficiencies of the Markov chain model.The main work and innovative results obtained are as follows:(1)Through theoretical analysis and numerical simulation,the influence of the form of state transfer matrix in Markov chain model on contaminant distribution prediction was clarified.The state transfer matrix should be constructed as an approximate double stochastic matrix,but this kind of matrix can not be obtained due to the discrete characteristics of the airflow field data solved by numerical simulation methods and the accompanying interpolation calculation.The left stochastic matrix causes errors in the total amount of contaminant in the domain,while the error caused by the right stochastic matrix is reflected in the contaminant distribution.Through the case study,the prediction performance of these two kinds of state transfer matrices is investigated.The results show that the accuracy is higher when the left stochastic matrix is used.Compared with the right stochastic matrix,it can reduce the L~2-norm relative error by a maximum of 5.32%.(2)Through numerical simulation and case studies,the performance of Markov chain model with three state transfer matrix calculation methods was compared.The method with the highest accuracy,fastest calculation speed,and strongest robustness to time step was determined.The results show that in two cases,the three Markov chain models are accurate enough,and the average normalized root-mean-square error between the predicted and benchmark results is less than 20%.In the two-dimensional case,Markov chain model with set-theory approach is the most accurate,with an average error as low as 10%.In the three-dimensional case,the performances of Markov chain models with flux-based method and Lagrangian tracking method are similar,with an average error of 17%and 19%,respectively.Markov chain model with Lagrangian tracking has the fastest speed and the strongest robustness to time step size.(3)Aiming at the continuous release of indoor passive contaminant sources,a Markov chain model coupling with the concentration response factor method was proposed and established.Through numerical simulation and case studies,the accuracy of the proposed coupling model was proved.In the two-dimensional case,when the point,line,and area sources are constant,linear,exponential,and periodically released,the average L~2-norm relative error between the prediction results and benchmark results is distributed from 3.4%to 16.4%.In the three-dimensional case,when the point,line,area,and volume sources are constant,linear,exponential,and periodically released,the average L~2-norm relative error between the prediction results and benchmark results is distributed from 12.7%to 28.8%.Finally,suggestions for the selection of two key parameters(pulse type and time step size)in the coupling method were given.(4)Markov chain model for indoor passive contaminant distribution was proposed,in which the lattice Boltzmann method was used to fast predict the airflow field and the Markov chain model coupling with the concentration response factor method was used to fast predict the contaminant transport.Through numerical simulation and case study,it was proved that the proposed model can efficiently and accurately predict the contaminant distribution based on the known boundary conditions.In the studied case,the normalized root-mean-square error between the predicted and measured results is12%,which is lower than the Euler model and Langrangian model based on the large eddy simulation of the CFD method.The calculation speed of the proposed model is fast,which is 5.21 times that of the Euler model based on the large eddy simulation of the CFD method,and 52.6 times that of the Lagrangian model based on the large eddy simulation of the CFD method.Finally,the model was used to evaluate the influence of exhaust position on the performance of indoor contaminant removal when a laboratory is heated in winter.The results show that the exhaust should be arranged on the wall opposite to the air supply and its height may be lower than the air supply inlet,in terms of efficiently removing indoor contaminants and ensuring air quality in breathing zone.