IMPLEMENTATION OF AREA, VOLUME AND LINE SOURCES

Transcription

1 December 01 ADMS 5 P503I1 IMPEMENTATION OF AREA, VOUME AND INE SOURCES The Met. Office (D J Thomon) and CERC 1. INTRODUCTION ADMS model line ource, and area and volume ource with conve polgon bae area. The algorithm treat all three ource tpe in a imilar wa, but the ource geometrie mut be defined in the following wa b the uer: (i) (ii) (iii) line ource - poition of the end point of the line (X 1, Y 1 ) and (X, Y ), Z the height of the ource and the width of the line. ine ource are aumed to be horiontal (the height of the end point the ame) and mut have width greater than 0.001m, ee Figure 1. area ource - (X n, Y n ), n1,,3 are the location of the vertice of the conve polgon defining the bae area of the ource and Z the height of the ource. It i aumed that the bae area of an area or volume ource lie in a horiontal plane. The bae area ma have from 3 to 50 vertice. volume ource - (X n, Y n ), n1,,3 are the location of the vertice defining the bae cro-ection of the volume ource a for the area ource. V i the vertical etent (depth) of the volume ource and the ource height Z i 0.5 V above the bae i.e. Z i the mid-height of the ource, ee Figure. The calculation cheme ued in ADMS for line, area and volume ource i outlined in Section, below, and decribed in more detail in Section 3 and 4. Section 5 decribe the treatment of plume rie. Calculation in low wind condition are decribed in Section 6. Page 1 of 11

2 (X, Y, Z) Y Z X (X 1, Y 1, Z) Figure 1 Definition of a line ource Z Y X (X 3, Y 3, Z V ) V mid-height of ource (Z) (X 1, Y 1, Z V ) (X, Y, Z V ) Figure Definition of a volume ource Page of 11

3 Page 3 of 11. OUTINE OF SCHEME Note that the epreion ued in ADMS for calculating concentration from a point ource i a follow. Taking coordinate centred on a point ource at (0, 0, Z ), with in the downwind direction, the concentration C i given b ( ) ( ) reflection term. ep ep,, U Q C π (1) where and are the plume pread parameter in the crowind and vertical direction in metre repectivel, U i the wind peed in m and Q i in ma unit. For line, area and volume ource, the concentration i calculated a follow. The ource i decompoed into a number of ource element, the decompoition being a function of the receptor location. The difference in treamwie ditance between ource element and each receptor i contrained not to var too rapidl, ubject to the maimum number of ource element. The concentration i then calculated b umming the contribution from each element. In the cae of a line or area ource, the contribution from each element i approimated b a crowind line ource of finite length. The epreion for the concentration, ( ) C,,, from a finite crowind line ource of length i given b equation (). The ource trength, Q, i in ma unitm. ( ) reflection term ep ),, ( U Q C π () Similarl, for a volume ource, the contribution from each element i approimated b a crowind vertical lice of finite length and height. The epreion for the concentration ( ) C,, from a crowind vertical lice of length and height V i given b equation (3). The ource trength Q i in ma unitm. ( ) reflection term 4,, V V U Q C (3) The tep in the calculation are: For each meteorological condition: (i) Calculate the near-field preading rate at the mean plume height, 10, from the lateral

4 pread 10 m downwind from a point ource i.e. 10 ( m, 10 m)10. Thi calculation will include plume rie if the ource ha non-ero plume rie characteritic. Then for each output point: (ii) Remove redundant part of the ource that cannot poibl contribute to the calculated concentration, baed on the preading rate 10, ee 3.1 (iii) Decompoe the ource into ource element, ee 3. (iv) Replace each of thee ource element with a cro-wind line ource of equivalent ource trength, ee 3.3 (v) Calculate the concentration b umming over the ource element uing equation (). Thee tep are decribed in more detail in Section 3. Figure 3 Domain of influence of ource element in flat terrain. w i the half width of the wind aligned element. Page 4 of 11

5 3. DESCRIPTION OF CACUATION 3.1 Removing redundant part of the ource Often, when conidering a long line or a large area or volume ource there will be part of the ource which give a negligible contribution to the concentration at a given output poition due to their large crowind ditance from the output point. To peed up the calculation uch part of the ource are trimmed and neglected in the calculation for flat terrain, or modelled at low reolution for comple terrain. The model make the conervative aumption that a part of the ource give a negligible contribution at output poition that are more than 4 10 ditant in the crowind direction from the treamline through that part of the ource. Thi i hown in Figure 3. Appling thi condition can have the effect hown in Figure 4 and Decompoing the ource In order to treat a lineareavolume ource a a um of crowind line ource it i necear to decompoe the ource into crowind element which can have different length and width. Thoe nearet the output point have the mallet along-wind width and the element furthet awa will have the greatet along-wind width. Thi i in order to reduce the fractional error in the along-wind ource to receptor ditance. (Ideall the element would have negligible along wind width to approimate to a ero width line ource.) A limit of 10 ource element per output point i ued for the trimmed ource, with an additional per ource end in comple terrain, to balance accurac and computing time. Thee limit were determined b enitivit tudie. The program decompoe the ource for each different met condition and for each different output point. It attempt to ue ource element in which the along wind ditance between adjacent element change b no more than 10%. arger change are ued in ome ituation in order to obe the limit on the number of element. Thee circumtance uuall onl happen for a few output point which are ver cloe to, or inide the ource. The decompoition routine work in wind-aligned co-ordinate with the -ai pointing downwind. Page 5 of 11

6 Figure 4 The effect of trimming an area ource Figure 5 The effect of trimming on a line ource Page 6 of 11

7 From Section 3 we can aume that the part of the ource which need to be included in the decompoition all lie between ome min and ome ma ( min < ma ) and that min i upwind of the output poition r, ( min < r ) For each ource min and ma are elected from: the mot upwind point of the untrimmed ource, the mot downwind point of the untrimmed ource, and the point where the line ± 4 ( m,10 m)10 m cro a ide of the ource (if the do). The net tep i to divide the region up into n element with centre i, i 1, n. The ource i cut at the point i, i0,1, n, where 0 min, n ma, to create the n ource element. The ditance from the receptor to one cut and the ditance from the receptor to the adjacent cut change b no more than a fraction λ i.e. r r i i1 (1 λ) (4) and hence i r ( r - min ) (1 - λ) i. (5) Since n ma we have Increaing n can enure that λ i le than n r - ma λ 1 - (6) r - min 3.3 Replacing the ource element with crowind line ource Once the centre of the ource element i, have been found it i a matter of geometr to find the appropriate value for the area of the ource element, A i, the cro-wind length of each line ource i, and the ource trength per unit length Q l,i of the line ource. For the configuration hown in Figure 6 thee have a imple form: and ( i i ) i A i 1 (7) ( ) 0.5 ( ) i 0.5 i, i 1, i,1 i1,1 (8) AQ i l Q l,i (9) i Page 7 of 11

8 Figure 6 Replacing ource element with crowind line ource. The haded area i the part of the ource which ha been replaced b a crowind line ource of length i. 4. VOUME SOURCES The method of calculation of the concentration field due to a volume ource i the ame a that due to a line or area ource apart from the ource element ued are crowind vertical lice intead of crowind line ource. The concentration ditribution for a vertical lice with vertice (0, -, V ), (0,, V ), (0,, V ) and (0,, V ) i given b equation (3). Volume ource do not have an plume rie. 5. PUME RISE The plume rie model (P110) i ued to calculate plume rie from all ource tpe including line and area ource. Specification P110 decribe how in practice the buoanc and momentum flu from a ground level ource mut eceed certain threhold for the emiion to lift off from ground. In ADMS the following threhold are ued for ground level line and area ource: F M > or F B > 0.01 (10) where F M and F B are the non-dimenional momentum and buoanc flue repectivel: F M ρ w (11) ρ U a Page 8 of 11

9 F B gπdw( ρ ρ ) (1) 4ρ a 3 au w i the emiion velocit, ρ the emiion denit, ρ a the denit of the ambient air and U the wind peed at 10 m. D i a ource dimenion. For an area ource it i the quare root of the ource area and for a line ource it i the minimum dimenion, which will uuall be the line width rather than the line length. For area ource that are large in cro-ection the aumption ued here, that the emiion behave like one plume, if it ha ufficient momentum and buoanc, i not well approimated. The emiion will not in practice behave a a ingle bent over plume. The default value for the emiion velocit or volume flow rate from a line or area ource in the model intace i ero which turn off the plume rie module. Thi default value ha been adopted to reflect the fact that in practice uch ource e.g. road traffic, quarrie, will not uuall have ignificant plume rie. 6. SPECIA TREATMENT IN OW WIND CONDITIONS Section 5 of Technical Specification document P101 decribe the pecial treatment of point ource in low wind condition. A imilar treatment applie to line, area and volume ource. The final concentration due to a line, area or volume ource i a weighted average between the normal gauian concentration C g and a radial concentration C r, where the weighting i a function of the wind peed at 10 m. To calculate C r, the ource i repreented a a erie of radiall-mmetric paive point ubource, each with ource height equal to the maimum plume height from the normal lineareavolume plume rie calculation. The concentration due to each component ub-ource i calculated according to equation (5.1) from P101: C i r π Q ( πr ) ( ) ep U ( ) ep - ( h - ) ep ( h ) ep ( h ) ep where r i the perpendicular ditance from the ub-ource to the current receptor. The total value of C r for a particular receptor i the um of Page 9 of 11 i Cr over all ub-ource. The ource i decompoed (for each receptor) into a erie of point ub-ource uing a imilar approach to that decribed in 3, with the following difference: All of the ource i included in the decompoition of the ource into crowind line ource. Thi mean that the receptor ma lie within the ource. In thi cae the maimum number of cut allowed i ditributed proportionatel between the uptream and downtream portion of the ource and each portion i decompoed eparatel with the finet pacing cloet to the receptor.

10 Once the ource ha been decompoed into crowind line ource, each crowind line ource i further decompoed into up to 10 area ource, uing the ame decompoition algorithm, each of which are then approimated a a point ource. Page 10 of 11

11 7. NOTATION A i area of a ource element (m ) C (,,) D F B F M g V i Q l Q l.i U w i i min ma r 0 ρ a ρ 10 () (,) enemble mean concentration at output point (,,) horiontal dimenion of line or area ource buoanc flu of the emiion momentum flu of the emiion acceleration due to gravit width of a line ource (m) vertical etent (depth) of a volume ource (m) cro-wind width of a ource element (m) ource ma emiion rate per unit length (ma unitm) ource element ma emiion rate per unit length (ma unitm) wind peed in m at 10m half width of ource element (m) downwind ditance (m) downwind location of i th cut (m) downwind location of centre of ource element i (m) downwind location of the mot upwind point of the trimmed ource (m) downwind location of mot downwind point of the trimmed ource (m) downwind location of receptor (m) crowind ditance (m) vertical height (m) ource height (m) urface roughne denit of ambient air denit of the emiion near-field preading rate at the mean plume height, 10m downwind of a point ource (m) horiontal plume pread in metre at downtream ditance horiontal plume pread in metre at height and at downtream ditance Page 11 of 11