1、2008 ASHRAE 259ABSTRACT Due to the fact that the advection-diffusion equation forconcentration is linear for steady-state flow fields, it is possibleto compute transient concentration responses with convolutioncalculations using response coefficients corresponding topulses of finite duration. It is
2、difficult to analytically obtainconcentration responses to pulse inputs in steady-state flowfields, however, dividing the flow field into cells and applyinga numerical fluid analysis code facilitates easy calculation ofresponse coefficients for each cell, which correspond tocontaminant pulses of fin
3、ite duration generated from an arbi-trary cell. In this study we establish a formulation of the tran-sient concentration calculation method, patterned on theresponse factor method, which is used widely in the field of air-conditioning load calculations. Based on this, we created acomputer program to
4、 calculate transient concentrations andcarried out simulations of indoor contaminant release scenar-ios resulting from hypothetical terrorist actions, etc. Here wepresent the calculation method as well as examples of the simu-lation, and report on the results of quantitative investigationsinto the e
5、ffectiveness of 100% outdoor air supply operation inthe event of a contaminant being released. INTRODUCTIONMultizone network model has been used for the networkanalysis of airflow inside the building. COMIS (Feustel, 1999)of multizone network model is commonly used in the airvolume design. Zonal mod
6、el divides a zone into sub-zones andallows thermal and concentration distribution in the zone toimprove the accuracy of the calculation results. The couplingmodel of multizone network model and zonal model wasdeveloped and used (Stewart and Ren, 2003). The coupling of multizone network model and CFD
7、 hasbeen proposed to substantially improve the accuracy (Shaelin,et al., 1993). The recent study of the coupling model ofmultizone and CFD reports the existence of a solution and itsuniqueness (Wang and Chen, 2007).The present paper proposes a method to calculate concen-tration distributions in zone
8、s with low computational load onPC, after several calculations of response factors by usingCFD have been done.We finally aim to predict transient concentration responsesof some points including an exhaust outlet arranged in 3D loca-tion in each room connected with a duct system. The transientconcent
9、ration transportation from a room with concentrationgenerated points to other rooms through a duct system withtime lag will be able to be calculated by using a 1D flownetwork system like COMIS etc. including the present method.In this paper, we present a calculation method for transientconcentration
10、 response in any points in a room and calculationexamples as results in the first stage of the study.The advection-diffusion equation for concentration insteady-state flow fields may be regarded as a linear partialdifferential equation (Appendix Note 1). Therefore, if weregard the flow field as a li
11、near system, the response of thesystem to disturbance (input) functions acting on it can beexpressed as the convolution integral between the input func-tion and the impulse response (Hino 1977). When analyzingflow fields, it is difficult to actually calculate the impulseresponse. Using the response
12、coefficients to a pulse of finiteduration instead of the impulse response, the response of thesystem can be calculated by computing the convolution of thesequence. In this case, the input disturbance is the functionapproximated by the finite pulse. A typical example of successMethod for Coupling Thr
13、ee-Dimensional Transient Pollutant Transport into One-Dimensional Transport Simulation Based on Concentration Response Factor Yoshihiro Ishida, DrEng Shinsuke Kato, DrEngYosihiro Ishida is a postdoctoral research fellow and Shinsuke Kato is a professor at the Institute of Industrial Science, The Uni
14、versity ofTokyo, Tokyo, Japan.NY-08-0322008, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 114, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digita
15、l form is not permitted without ASHRAEs prior written permission.260 ASHRAE Transactionsof this approach is the response factor method (SHASE 1972;Matsuo 1970; Stephenson et al. 1967; Mitalas et al. 1967;SHASE 2001) that is used widely in air-conditioning loadcalculations. In this study, the flow fi
16、eld is divided into cells (compu-tational grid), and the response coefficients to finite pulses ofcontamination are calculated for all necessary cells using anumerical fluid analysis code . After obtaining the time-series response coefficients foreach necessary cell in this way, the transient respon
17、ses for thenecessary cells in the flow field to the transient inputs are calcu-lated by the same convolution computations as used in theresponse factor method in air-conditioning load calculations.Normal air-conditioning systems recirculate roomairflow and outdoor airflow rate is 20 to 30% of their
18、totalcirculating airflow rate (Inoue 2000). Therefore, investiga-tions into return air systems are extremely important (Kato etal. 2000.; Ito et al. 2005). For this reason, in this study weestablished a formulation of the “concentration response coef-ficients method” to apply to indoor transient con
19、centrationcalculations in air-conditioning systems that use return air.When sarin gas, etc., is dispersed indoors, contaminantconcentrations rise higher in return air systems than in 100%outdoor air supply systems.If the method of this study is used, multiple concentrationresponse calculations can e
20、asily be performed for a constantair volume system for different proportions of recycled airflowat the time of contaminant release, using pre-calculatedresponse coefficients. There is no need to carry out numericalanalysis of airflow and concentration for each individual case. It is also possible to
21、 quantitatively compute, with the sameaccuracy as numerical analysis of airflow and concentration,the rate of decline of concentration when 100% outdoor airsupply starts to operate immediately after a contaminantrelease accident.It is a concentration calculation method that is useful forinvestigatin
22、g countermeasures against terrorism, etc., whichhave become quite realistic threats. This is because the inputdata can be readily created for these problems, calculationscan be done on a PC, and the transient calculations are of thesame accuracy as numerical analysis of airflow and concen-tration us
23、ing fluid analysis code. As will be mentioned below,the computational load for this calculation technique is farlower than that for numerical fluid simulations, so as long asa numerical simulation of the airflow and concentration iscarried out twice or so on a computational machine such as aworkstat
24、ion to calculate the response coefficients, as manycases as desired can then be calculated with a PC. We believethis method can be applied effectively to transient concentra-tion calculations for an indoor and other contaminant release.CALCULATION METHODCalculation AssumptionsThe assumptions are as
25、follows:1. The fully developed turbulence airflow is distributed inthe calculation region and can be solved using CFD. Theflow field is steady state.2. The principle of superposition is applied to theconcentration calculation in the region.3. Contaminant is passive and the airflow is not affected by
26、concentration.4. There is neither sorption nor desorption of contaminantsby the walls including windows, ceilings and floors.Outline of Numerical Analysis of Airflow and Concentration (Figure 1, Tables 1 and 2)Figure 1 shows the indoor contaminant release model,and Table 1 an outline of the model. T
27、he shape of the room isa regular square with an area of 5.5m by 5.5m, and a ceilingheight of 3.0m. The airflow is supplied through an inlet in theleft-hand wall with a center height of 2.55m, and is exhaustedthrough an outlet in the right-hand wall with a centre height of0.45m. The air-conditioning
28、model recycles air through thereturn duct immediately after it passes out of the outlet, and isset to return only a mass flow rate of G to the inlet, and thento mix this with a mass flow rate of (1- )G of outdoor air tosupply a total air mass flow rate of G. Here, is the ratio ofairflow (mass flow)
29、recycled. Figure 1 Indoor contaminant release model (constantsupply air volume, variable airflow recyclingrate, ).ASHRAE Transactions 261Numerical analysis of airflow by fluid analysis code wascarried out by dividing this room up into 11 segments (x-direc-tion) by 11 segments (y-direction) by 10 seg
30、ments (z-direc-tion) (Appendix Note 2). An outline of the computationalconditions is presented in Table 2. A generalized logarithmiclaw (constant E=9) was applied to the rooms internal wallsurfaces (Launder et al. 1974). We assumed isothermalairflows, and assumed there was neither sorption nor desor
31、p-tion of contaminants by the walls in the present study. We used a highly reliable commercial CFD code fornumerical analysis. The standard k- model is used in thecalculation. For airflow calculations we applied the steady-state analysis method using the SIMPLE method, and for thespatial difference
32、scheme we applied the MARS scheme(second-order accuracy) (van Leer 1979), and we carried outcomputations until we were able to attain a velocity distribu-tion that could be regarded as almost steady. After this, wefixed the velocity distribution and carried out transientconcentration calculations fo
33、r two cases using a CFD code. Inone case contaminant was generated from the contaminantgeneration point in the cell in the centre of the room inFigure 1, SC (2.75m, 2.75m, 0.15m), as a finite pulse takingthe form of a wave with the shape of an isosceles triangle (seethe thick-lined triangle in Figur
34、e 4a, to be discussed below)with its apex equating to the unit amount of 1 kg/s generated(hereafter referred to as cell release). In the other case, thecontaminant was supplied from the inlet as a triangular finitepulse (see the thick-lined triangle in Figure 4b, to be discussedbelow) with a concent
35、ration of 1 kg/kg at its apex (hereafterreferred to as inlet release). Output was in the form of timeseries responses of concentration at the inlet, outlet, and thepoints M1, M2, and M3 in Figure 1, and the response coeffi-cients were extracted from these. The apex value of the isosceles triangle ca
36、n be consideredto be 1kg/s of cell release, or 1kg/kg of inlet release (for calcu-lating the response coefficients), or it can be considered to bea dimensionless value equal to 1, made dimensionless by anappropriate characteristic amount of contaminant generationor supply concentration (for concentr
37、ation calculations, seeSection 2.2 and beyond). Definition of Unit Pulse Responses and Response Coefficients (Figures 1, 2, 3, 4, and 5)Figure 2 shows the concentration distribution as well asthe steady-state distribution of velocity vectors in 6000 steps(600s) after releasing an isosceles-triangle
38、wave of a contam-inant (Appendix Note 3) into a steady-state airflow distribu-tion from the contaminant generation point (cell) SC thatcontacts with the floor in the centre of the room. The concen-tration contours are presented without smoothing the concen-tration of each cell so that the space divi
39、sion and theconcentration of each cell can be seen. The transient responses of concentrations at the outlet,and points M1, M2, and M3 in Figure 1 are shown in Figure 3.The triangle drawn with a thick-line in Figure 3 is the timeseries of the amount of contaminant generated at the cell SCin Figure 1.
40、 Contaminant generation rate started at step 0increases linearly until peaking at unit value 1kg/kg at step3000 and then decreasing linearly to return to zero at step 6000and beyond. The half of the base of the triangle, or the intervalof the finite pulse, , is 300s = 5min.Table 1. Outline of Indoor
41、 Contaminant Release ModelTime of a Tidal Volume of the Room Time constant = 20.17minAir SupplyMass flow rate G = F = 1.225 kg/m3 0.075 m3/s = 0.09189 kg/sVolume flow rate F = 0.075 m3/sDensity of air = 1.225 kg/m3Room ShapeLength 5.5 (x-direction) m 5.5 (y) m 3.0 (z) mVo lu m e V = 90.75 m3Table 2.
42、 Outline of Numerical Airflow CalculationsDivision of Time Time increment = 0.1 sDivision of SpaceDivision number 11 (x-direction) 11 (y) 10 (z)Space interval = =0.5 m, = 0.3 mSupply/ExhaustVelocity Uin = Uout= 0.5 m/s,Turbulence intensity Iin0.1Wall BoundaryAirflow Generalized logarithmic law (cons
43、tant E=9)Concentration No sorption/desorption of contaminantPresent Method Pulse interval = 300 s = 5 mintx y zTT262 ASHRAE TransactionsIn this section we aim to clarify the unit relationships sowe consider the peak value of the isosceles triangle to be 1 kg/s. The accumulated value of the amount of
44、 contaminant gener-ated in the room, Q (the area of the isosceles triangle wave =time integration of contaminant generated), is represented asQ = 1 kg/s = 300.00 kg in Figure 4a. Figure 3 shows every100 steps up to 21,000 steps, though the time integration wasperformed with intervals of = 0.1 s up t
45、o 60,000 steps(6000 s). These responses will be called unit pulse responses,meaning they are the responses to unit pulses. The thick dashed line (Integration) in Figure 3 is thecumulative value (value of the time integration), Qnkg, of theamount of contaminant exhausted from the outlet. Figure 4 sho
46、ws the response raw values at 3000-step inter-vals, extracted directly at the same time step without statistictreatment from the results (Figure 3, unit pulse response) of thenumerical analysis of the concentration done by fluid analysiscode. These response (concentration) values will be calledconce
47、ntration response coefficients. The concentrationresponse coefficients lose the smoothness of the curves corre-sponding to the fine time intervals of the unit pulse responsesin Figure 3, however the values shown every 3000 steps are thesame values as the unit pulse responses that resulted from thenu
48、merical analysis done by the fluid analysis code. By usingthe concentration response coefficients, a calculation time ofa PC will decrease at about three thousandths part of that byusing unit pulse responses.When you perform the convolution calculations usingthese values, the calculated values at ea
49、ch step of theresponse coefficients (equivalent to each 3000 steps withfluid analysis code) possess the same accuracy as numericalanalysis of the concentration by fluid analysis code, withinthe bounds of the approximation of the time variation of thegenerated contaminant. Figure 4a is made up of the concentration values at 3000-step intervals (concentration response coefficients) for eachcalculation point, extracted from the curve (unit pulseresponse) corresponding to the point in Figure 3. The thickdashed line (Integration) in Figure 4a is the cumulative value,Qn,
