Inverse Modeling of Indoor Instantaneous Airborne Contaminant Source Location and Releasing Time in Unsteady Airflow

Available online at www.sciencedirect.com

ScienceDirect

Available online at www.sciencedirect.com Procedia Engineering00 (2017) 000–000

ScienceDirect

www.elsevier.com/locate/procedia

Procedia Engineering 205 (2017) 2289–2296

10th International Symposium on Heating, Ventilation and Air Conditioning, ISHVAC2017, 1922 October 2017, Jinan, China

Inverse Modeling of Indoor Instantaneous Airborne Contaminant Source Location and Releasing Time in Unsteady Airflow Jiajia Chenga, Haidong Wanga, *, Sai Lua, Zhiqiang (John) Zhaib a a

School of Environment and Architecture, University of Shanghai for Science and Technology, 516 Jun Gong Road, Shanghai, 200093, China b bDepartment of Civil, Environmental and Architectural Engineering, University of Colorado Boulder, Colorado, USA 80309-0428

Abstract Identification of airborne pollutant source location in indoor environment is significant for the indoor environment and occupants safety. Previous studies focus on unsteady air flow condition were proved valid to identify the source location with the information of boundary condition and known pollutant releasing time based on the adjoint probability algorithm. However, since pollutant releasing time is possibly unknown, it is necessary to investigate the source location identification with unknown releasing time under unsteady airflow condition. This paper mainly focuses on the airborne pollutant source location identification under unsteady airflow with unknown pollutant releasing time, by employing adjoint probability-based inverse tracking method. Two cases studies using CFD tools with RANS model under unsteady airflow were conducted. It is proved that the adjoint probability-based inverse tracking method is cable of identifying the air pollutant source location under unsteady airflow with unknown releasing time. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. Peer-review committee of of the the 10th 10th International International Symposium Symposium on on Heating, Heating, Ventilation Ventilation and and Air Peer-review under under responsibility responsibility of of the the scientific scientific committee Conditioning. Air Conditioning. Keywords: Unsteady Airflow; Inverse Modeling; Adjoint Probability Method; Conditioned Adjoint Location and Time Probability (CALTP); Indoor Airborne Contamination

1. Introduction People spend most of their time indoors, therefore, indoor air quality (IAQ) leakage and diffusion of indoor pollutants will impose serious impact on the

is drawing increasing attention. The occupants. Many different methods

* Corresponding author. Tel.: 021-5527-5979. E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility ofthe scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning.

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning. 10.1016/j.proeng.2017.10.083

Jiajia Cheng et al. / Procedia Engineering 205 (2017) 2289–2296 Jiajia Cheng et al./ Procedia Engineering00 (2017) 000–000

2290 2

have been established to identify the source location in order to help building operators to remove or isolate such source. Those methods focus on identifying the source location and releasing time with limited sensor readings are all considered as the inverse problem. Such inverse problem can be categorized to three types: forward method [1,2,3], reverse method [4,5,6], and adjoint probability method [7]. Previous researches have been well studied in different conditions. QR and PR method were used to identify the location of gas [8] and particulates [9] in an enclosed cabin [10]. Tikhonov-based matrix inversion was complemented to determine the locations of multiple temporally released sources [11]. Adjoint probability algorithm was established to identify the pollutant source location [12,13]. Wang [14] expanded this algorithm to unsteady airflow conditions with unknown source releasing time. However, in the real scenarios, the pollutants release is a random occurrence. The pollutant source location and the releasing time are both unknown parameters. Therefore, it is necessary to take further steps to develop this method to identify the pollutant source location with unknown releasing time under such unsteady airflow conditions. This paper mainly focuses on the identification of the pollutant source location with unknown releasing time under unsteady airflow conditions. Using adjoint probability algorithm, both pollutant source location and releasing time can be predicted successfully. Two representative cases were studies to demonstrate and verify this method. 2. Methods The adjoint probability method was initially established by Neupauer and Wilson, and was used to predict the pollutant source in underwater. It was utilized to predict the air pollutant source, releasing time, and pollutant mass in an enclosed space. The inverse modeling is mainly focus on two aspects: the probabilities calculation of pollutant source and releasing time. The research of identifying the pollutant source location with known releasing time, conditioned adjoint location probability (CALP) had been sufficiently considered in previous studies. Based on these researches, conditioned adjoint location and time probability (CALTP) and conditioned adjoint time probability (CATP) were studied. Assume that a pollutant source was originated at location of x, mass of M0 and releasing time of τ . The adjoint probability represents the source location and releasing time probability density which was calculated by several sensor readings at two different conditions of x1 ,τ 1 , Cˆ1 and x2 ,τ 2 , Cˆ 2 respectively, which is expressed as

P ( M 0 , x,τ Cˆ1 , Cˆ 2 , x1 , x2 ,τ 1 ,τ 2 ) .The integral of the source mass domain M0 is the CALTP, which can be defined

as follow:

f x ,τ ( x,τ Cˆ1 , Cˆ 2 ,τ 1,τ 2 , x1 , x2 ) =  P( M 0 , x,τ Cˆ1 , Cˆ 2 ,τ 1 ,τ 2 , x1 , x2 )dM 0 M0

(1)

On the basis of equation 1, the integral of the CALTP over the area domain X is the CATP. CATP can be defined as follow:

fτ (τ Cˆ1 , Cˆ 2 ,τ 1,τ 2 , x1 , x2 ) =   P( M 0 , x,τ Cˆ1 , Cˆ 2 ,τ 1 ,τ 2 , x1 , x2 )dM 0 dx x M0

(2)

Calculating the pollutant transportation employs computational fluid dynamics (CFD) method. The general format of governing equation of CFD is :

∂Φ + ∇(V ⋅ φ ) − Γφ ∇ 2φ = Sφ ∂t

(3)

Where ϕ is a generic variable that can be used as different variables. For each ϕ, Γφ is the corresponding

diffusion coefficient, and

Sφ is source term. At the end of every time step, a series of air velocity field as

V j = (V j1 ,V j2 ,......V jn −1 ,V jn ) can be obtained through equation 3. The mass of the pollutant transportation and boundary conditions can be defined as:

Jiajia Cheng et al./ Procedia Engineering 00 (2017) 000–000 Jiajia Cheng et al. / Procedia Engineering 205 (2017) 2289–2296



22913

1 1 C 1 − C 0 ∂V j C ∂  ∂C 1  1 1 + = vc  + ( S c + q1C I − q0C ) Δt ∂x j ∂x j  ∂x j  2 2 ∂  ∂C 2  C 2 − C 1 ∂V j C 2 2 = + vc  + ( S c + q1C I − q0C ) ∂x j ∂x j  ∂x j  Δt

(4)

... n n ∂ C n − C n −1 ∂V j C = + ∂x j ∂x j Δt

 ∂C n  n n vc  + ( S c + q1C I − q0C )  ∂x j 

C ( x ,0 ) = C 0 ( x )

C i ( x, t ) = g1 (t ) on Γ1  ∂C i   ni = g 2 (t ) on Γ2 vc  ∂x j   i i ∂C i  V j C − vc  ni = g 3 (t ) on Γ3 ∂x j   i Where C is the concentration of the ith measurement, V j is the air velocity at xj direction of the nth time step under unsteady airflow conditions. vc is the effective turbulent diffusion coefficient of pollutant, q0 is the per unit i

volume flow of pollutant outflow, q1 is the per unit volume flow of pollutant inflow, C I is the volume concentration of the pollutant corresponding to ith time step, S c is all other forms of pollutant, therefore, S c 0

+ q1C Ii − q0C i is the

1

sum of all external sources. C is the initial concentration of each cell position, V j is the initial air velocity, g1, g2 and g3 are known mathematic functions of the boundary conditions of pollutant. Γ2 , Γ2 and Γ2 are the three types of boundaries, ni is the outward unit normal vector in the xth direction. Backward location probability function also be extended for a series for consecutive multiple airflow field under unsteady airflow conditions. *,1 n Ψ *,1 − Ψ *,0 ∂V j Ψ ∂  ∂Ψ *,1  ∂h *,1 + = vc  + (− q0 Ψ ) + Δτ ∂x j ∂x j  ∂x j  ∂C n −1 *, 2 Ψ *, 2 − Ψ *,1 ∂V j Ψ ∂ + = Δτ ∂x j ∂x j

 ∂Ψ *,2  ∂h *, 2 vc  + (− q0 Ψ ) + ∂ x ∂ C j   

... 1

Ψ *,n − Ψ *,n −1 ∂V j Ψ + Δτ ∂x j

*,1

=

∂ ∂x j

 ∂Ψ *,n  ∂h *,n vc  + ( − q0 Ψ ) + ∂ x ∂ C j   

Ψ * ( x,0) = Ψ *,0 ( x) = 0

Ψ * ( x,ι ) = 0 on Γ1  ∂Ψ *,i  + V jn +1−i Ψ *,i  ni = 0 on Γ2 vc  ∂x j   ∂Ψ *，i  vc  ni = 0 on Γ3 ∂ x  j  

(5)

Cheng al. / Procedia Engineering 205 000–000 (2017) 2289–2296 JiajiaJiajia Cheng et al./etProcedia Engineering00 (2017)

42292

∂h = δ ( x − xw ) ⋅ δ T ∂C Where Ψ

*, i

n

is the Standard adjoint location probability (SALP) of pollutant source calculated by V j through

V jn +1−i , τ is the backward time, xw is the point of the pollutant monitoring position, ∂h / ∂C is the additional term of the source, and releasing time

τ

δ (x)

is the impulse function. Since SALP is a function of pollutant source location x and

, it can be expressed as f x ( x;τ , xi ,τ i ) . Thus, CALTP and CATP can be obtained as: N

f x ,τ ( x,τ Cˆ1 , Cˆ 2 ;τ 1 ,τ 2 , x1, x2 ) =

 ∏ P(Cˆ M0

i =1 N

τ   ∏ P(Cˆ x M0

i =1

N

fτ (τ Cˆ1 , Cˆ 2 ;τ 1 ,τ 2 , x1, x2 ) =

  ∏ P(Cˆ M0 x

i =1 N

τ   ∏ P(Cˆ x M0

i =1

i

i

i

i

M 0 , x 0 ;τ , xi ,τ i ) f x ( x0 ;τ , xi ,τ i )dM 0

M 0 , x 0 ;τ , xi ,τ i ) f x ( x0 ;τ , xi ,τ i )dM 0 dxdτ

(6)

M 0 , x 0 ;τ , xi ,τ i ) f x ( x0 ;τ , xi ,τ i )dxdM 0 M 0 , x 0 ;τ , xi ,τ i ) f x ( x0 ;τ , xi ,τ i )dM 0 dxdτ

(7)

Where equation 6 is the expression of CALTP and equation 7 is CATP. Assuming the pollutant source location is given as x0, CATP can be converted to: N

fτ (τ Cˆ1 , Cˆ 2 ;τ 1 ,τ 2 , x1, x2 ) =

 ∏ P(Cˆ M0

i =1 N

τ  ∏ P(Cˆ M0

i =1

i

i

M 0 , x 0 ;τ , xi ,τ i ) f x ( x0 ;τ , xi ,τ i )dM 0 M 0 , x 0 ;τ , xi ,τ i ) f x ( x0 ;τ , xi ,τ i )dM 0 dτ

(8)

Concentration data in equation 7 and 8 can be obtained by the consecutive temporal readings from the same or different sensors. 3. Results To verify the reliability of the adjoint probability method under the unsteady airflow condition, two specific cases were utilized to demonstrate the application of this method in real scenarios. 3.1. Airborne Pollutants Diffusion in a Typical Office under unsteady Airflow Field A simplified typical office place was shown for identify the pollutant source and releasing time. The rectangular office is 10m long and 3m high. The inlet and the outlet were installed on the top of the left wall and the button of the right wall separately. The conditioned air was supplied at the velocity of 0.1m/s and the temperature of 20oC constantly. A 700W occupant, a 200W computer, an adiabatic table were set in the office space. A large window with incoming heat flux of 100W was set on the right wall. Two sensors were installed on the ceiling of the office to monitor the pollutant concentration in the whole area. CFD simulation was performed to replace the real experiment, and the simulation results can be perceived as the sensor readings at one spot. A forward CFD velocity field was first needed to obtain the pollutant dispersion condition which can be used as the sensor readings as the inputs of the inverse program. The inverse modeling prediction can then be verified against the inputs of the forward simulation. Coarse meshes of 0.33m*0,1m was used for better demonstrate the office model. The whole simulation process has ten time steps, and every step is five seconds. Standard k-e model was used to predict the turbulence effect.



Jiajia Cheng et al. / Procedia Engineering 205 (2017) 2289–2296 Jiajia Cheng et al./ Procedia Engineering 00 (2017) 000–000

sensor 2

22935

sensor 1 source

Fig. 1. Predicted airflow field and the concentration of pollutant by forward CFD simulation at (a) t=5s; ( b)t=15s; ( c)t=20s; ( d)t=25s.

The result of identify the pollutant source location was shown in figure 2. Figure 2 (a) was based on the current reading of sensor 1 and (b) was based on the current readings both of sensor 1 and sensor 2. As shown in the figure, the location of the pollutant source is not accurate enough at these two scenarios. Figure 2 (c) and (d) were based on the historical readings from sensor 1 and both of sensor 1 and sensor 2. Obviously, the locating results are the much more accurate.

Fig. 2. Predicted location and time probabilities for the office case with (a)one current reading of sensor 1; ( b)current readings of both sensor 1 and sensor 2; ( c)four historical readings of sensor 1; ( d) historical readings of both sensor 1 and sensor 2.

After that, we further study the problem of predicting the pollutant releasing time. Based on previous studies [15], any significant release from an instantaneous source can be detected due to the arrangement of sensor network. As soon as the sensor, which is near the source, detects the release, this moment will be assumed as the starting point of the whole sensor system and then use this time parameter as inputs to predict the pollutant source and spread time. In this numerical experiment, the actual spread time is five seconds. Four sensing scenarios are the same as Figure 2. After identifying the pollutant source location, the problem of predict the spread time can be perceived as the predicting the spreading time with the known pollutant source location. The predicted spread time probabilities for this office model were shown in figure 3. Based on the CATP curves of every scenario, it’s obviously that scenario 1 and scenario 2 with only current readings cannot give the right time prediction. This is understandable that the spread time is a temporal concept. Historical concentration

Jiajia Cheng et al. / Procedia Engineering 205 (2017) 2289–2296 Jiajia Cheng et al./ Procedia Engineering00 (2017) 000–000

2294 6

readings are effective to help improve the spread time. This was also verified that other two curves with historical sensor readings can successfully predict the actual spread time of five seconds. 100%

scenario1 scenario2 scenario3 scenario4

90% 80%

CATP (%)

70% 60% 50% 40% 30% 20% 10% 0%

5

10

15

20

25

time (s)

Fig. 3. Predicted releasing time probabilities (%) for the office case.

3.2. Pollutants diffusion in a subway station when train passes Subway station is a typical model of unsteady air flow. The alternation of train movements makes the airflow in the station disturbing. The subway station was shown as a specific case to demonstrate the application of adjoint probability algorithm with unknown pollutant source location and releasing time. As shown in figure 4, the 2D subway station model was 9m long and 3m wide. In this model, two inlets were set on one side wall with supply air velocity of 1 m/s. A pollutant source near the first inlets released instantaneously 100 unit pollutant at a random time. When the pollutants begin to release, a train of 1m ×1m with the velocity of 1m/s moved from left to right. After this train passes completely through the station, another train with the same velocity moved through this station from the opposite direction. In this model, two sensors were installed on the opposite wall of the supply air inlets. Figure 4 also showed the location of the pollutant source location and the sensors location. CFD simulation was first employed to obtain the airflow velocity field and the pollutant spread condition. Pollutant concentration at sensors’ location can be obtained by simulation and then as the inputs to identify the pollutant source location. In this 2D model, a coarse grid of 0.27m long and 0.1m wide was used. This unsteady process contained eight time steps and each time step was set as 2s. In simulation, the pollutant releasing time was set as 2s. K-e model was used for the turbulent modeling. Figure 5 shows the results of identification of pollutant source location using different input data. Figure 5 (a) utilizing two current readings of both sensor 1 and sensor 2, the result of locating is relatively poor, the CALTP distribution in domain area is scattered due to the imperfection of the current readings. And the predicted releasing time is also not precise enough. The predicted releasing time under this condition is four seconds, deviate from the actual releasing time of two seconds. Figure 5 (b) using three historical readings of sensor 1 as input and is much more concentrated than previous result. The predicted location is close to the real source location. The predicted releasing time is 2s, the same as the real releasing time. As shown in figure 5 (a), sensor 2 was set farther than sensor 1 to the source location, therefore, sensor 2 has poor monitor performance than sensor 1 due to its slower and smaller readings. Figure 5 (c) using three historical readings of sensor 2, the result of locating is not as precise as using the historical data of sensor 1. Although the locating result is not precise, the predicted releasing time is quite accurate. Figure 5 (d) using historical readings of both sensor 1 and sensor 2, and the result of locating is rather accurate. And the predicted releasing time is precise too. These different results indicate that with proper selection of sensors, the algorithm can identify the pollutant source location and the releasing time.



Jiajia Cheng et al./ Procedia Engineering 00 (2017) 000–000 Jiajia Cheng et al. / Procedia Engineering 205 (2017) 2289–2296

Sensor 1

7 2295

Sensor 2

Source

Fig. 4. Predicted airflow field and the concentration of pollutant by forward CFD simulation at (a)t=2s; ( b)t=6s; ( c)t=8s; ( d)t=12s; ( e)t=14s; (f) t=16s.

Fig. 5. Predicted location and time probabilities for the subway station case with (a)two current readings of both sensor 1 and sensor 2; (b)three historical readings of sensor 1; ( c)three historical readings of sensor 2; ( d) historical readings of both sensor 1 and sensor 2.

Through the analysis of office case and subway station case, although the different sensors and combined readings can cause different positioning, careful selected readings still can predict the location and the releasing time of the pollutants.

2296 8

Jiajia Cheng et al. / Procedia Engineering 205 (2017) 2289–2296 Jiajia Cheng et al./ Procedia Engineering00 (2017) 000–000

4. Conclusions This paper utilized the adjoint probability algorithm to establish a method to identify the pollutant source location and releasing time under unsteady airflow conditions. Two cases of office model and subway station model were verified to demonstrate that this method can accurately locate the pollutant source and predict the pollutant releasing time. However, through the comparison of different conditions, different readings from different sensors may cause large differences in locating results. Therefore, the placement of sensors deserves further investigation in future research. Acknowledgements This research is supported by National Science Foundation of China (51508326), and partially sponsored by Shanghai Pujiang Program (15PJ1406300) and Scientific Research Foundation for Returned Scholars, Ministry of Education of China. References [1] Alapati S., and Kabala Z. J. Recovering the release history of a groundwater contaminant using a non-linear least-squares method, Hydrological Processes. 14 (2000) 1003-1016. [2] Mahar P. S., and Datta B. Identification of pollution sources in transient groundwater systems, Water Resources Management. 14 (2000) 209227. [3] Mahar P. S., and Datta B. Optimal identification of ground-water pollution sources and parameter estimation, Journal of Water Resources Planning and Management. 127 (2001) 20-29. [4] Skaggs T. H., and Kabala Z. J. Recovering the history of a groundwater contaminant plume: method of quasi-reversibility, Water Resources Research. 31 (1995) 2669-2673. [5] Cornacchiulo D., Bagtzoglou A.C. and Atmadja J, 2002. Hydrologic inverse on using marching-jury backward beam equation and quasi reversibility methods, Proceedings of the 15th ASCE Engineering Mechanics Conference. New York City. [6] Liu X., and Zhai Z. Inverse modeling methods for indoor airborne pollutant tracking: literature review and fundamentals, Indoor Air. 17 (2007) 419-438. [7] Liu X., and Zhai Z. Protecting a whole building from critical indoor contamination with optimal sensor network design and source identification methods, Building and Environment. 44 (2009) 2276-2283. [8] Zhang T. F.,and Chen Q. Identification of contaminant sources in enclosed spaces by a single sensor, Indoor Air. 17 (2007) 439-449. [9] Li H. 2010. Identification of particulate contaminant sources in enclosed space with inverse CFD modeling. Ph.D. Thesis, Dalian University of Technology. [10] Yin S. 2011. Quantitatively identify unsteady gas pollutant release in indoor environment by inverse CFD modeling. Ph.D. Thesis, Dalian University of Technology. [11] Wei Y., Zhou H. B., Zhang T. F., and Wang S. G. Inverse identification of multiple temporal sources releasing the same tracer pollutant, Building and Environment. 118 (2017) 184-195. [12] Liu X., and Zhai Z. Location identification for indoor instantaneous point contaminant source by probability-based inver computational fluid dynamics modeling, Indoor Air, 18 (2008) 2-11. [13] Zhai Z., Liu X., Wang H., Li Y., and Liu J. Experimental verification of tracking algorithm for dynamically-releasing single indoor contaminant, Building Simulation. 5 (2012) 5-14. [14] Wang H., Lu S., Cheng J., and Zhai Z. Inverse modeling of indoor instantaneous airborne contaminant source location with adjoint probability-based method under dynamic airflow field, Building and Environment. 117 (2017) 178-190. [15] Liu X. 2008. Identification of indoor airborne contaminant sources with probability-based inverse modeling methods. Ph.D. Thesis, University of Colorado