Gas Radiation. MEL 725 Power-Plant Steam Generators (3-0-0) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi

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1 Gas Radiation ME 725 Powr-Plant Stam Gnrators (3-0-0) Dr. Prabal Talukdar Assistant Profssor Dpartmnt of Mchanical Enginring T Dlhi

2 Radiation in absorbing-mitting mdia Whn a mdium is transparnt to radiation, radiation propagating through such a mdia rmains unchangd Howvr gass such as CO, NO, CO 2, SO 2, H 2 O and various hydrocarbons absorb and mit radiation ovr crtain wavlngth rgions calld absorption bands W will discuss a vry simpl analysis of radiation xchang in an absorbing and mitting mdium, xchang btwn a body of hot gas and its black nclosur

3 Br s aw f o is th intnsity of radiation at th sourc and is th obsrvd intnsity aftr a givn path, thn optical dpth τ is dfind by th following quation: o / S = xp β (s)ds 0 o τ = Extinction cofficint β is a function of tmpratur T, prssur P, composition of th matrial (concntration C i of th i th componnts) and wavlngth of incidnt radiation β s

4 Charactrization of Participating Mdia Absorption: attnuation of intnsity Emission: augmntation of intnsity Scattring n-scattring: augmntation of intnsity Out-scattring: attnuation of intnsity

5 Equation of Radiativ Tranfr ncras in ntnsity of radiation pr unit lngth along th dirction of propagation is d (s) ds d ds (s) = κ b d (s) ds mission pr absorption pr = unit volum unit volum (T) κ Th boundary condition for this quation is (s) (0) at s = 0 (s) =

6 Transmissivity, Absorptivity and Emissivity Solution of Radaitiv Transfr Equation with th assumption that κ and b (T) ar constant vrywhr in th mdium, givs At th boundary surfac S =, intnsity will b (s) = () = (0) (0) s + (1 + (1 s ) b ) (T) b (T) This is du to xtrnal irradiation Slf mission

7 Ngligibl mission f th mission of radiation by th mdium is ngligibl in comparison to th contribution to th xtrnally incidnt radiation, w gt b (T) = 0 and thn th solution bcoms, () = (0) Thn th spctral transmissivity τ () = = (0)

8 Spctral absorptivity f th mdium is non-rflcting, τ + α =1 And th spctral absorptivity α ovr th path is α = 1 Whn Kirchhoff s law is applicabl, th spctral absorptivity α is qual to spctral missivity ε ε = 1 For no xtrnally incidnt radiation, () = (1 ) b (T)

9 Absorption and Emission Proprtis of Matrials Absorption and mission charactristics of gass ar quit diffrnt from thos of solids Th absorption (or mission) of radiation by gass dos not tak plac continuously ovr th ntir wavlngth spctrum; rathr it occurs ovr a larg numbr of rlativly narrow strips of intns absorption (or mission) n smitransparnt solids, th absorption spctrum is mor or lss continuous

10 Spctral Absorptivity

11 Radiation Exchang btwn a Gas Body and its Black Enclosur Assumption: Entir gas body is isothrmal Enclosur wall is black Considr a hmisphrical body of gas at uniform tmpratur T g and walls ar at tmpratur T w Th intnsity of spctral radiation () striking th surfac lmnt da as a rsult of th mission of radiation by th gas along th path is dtrmind from () = b (T g )(1 k )

12 Spctral Emissivity of Gas Th spctral radiativ hat flux q bcaus of incidnt radiation from th ntir hmisphr q 2π = π E b b π/ 2 = = φ= 0 θ= 0 (T (T g () cosθsin θdθdφ g )(1 )(1 ) ) Spctral missivity of gas for th path lngth q = ε E b (T g )

13 Man Bam ngth Th simpl xprssion for th hmisphr of gas is not applicabl for othr gomtris A concpt of man bam lngth is introducd for nginring calculations This is an quivalnt path lngth which rprsnts th avrag contributions of diffrnt bam lngths from th gas body to th striking surfac n th absnc of information availabl, man bam lngth is approximatly calculatd as V 3.5 A Whr A=total surfac ara of th nclosur and V = total volum of th gas

14 Chart for Equivalnt path lngth

15 Emissivity Charts Hottl masurd gas missivity ε g and prsntd missivity charts for gass such as CO 2, H20, CO, ammonia, SO2, tc. as a function of tmpratur and product trm P i, whr P i is th partial prssur (in atmosphrs) of gas i in th gas mass and is th bam lngth.

16 Charts

17

18 Calculation of Radiation xchang btwn a Gas Body and ts nclosur Th nt radiativ hat xchang Q btwn th gas mass at tmpratur T g and its black surroundings at tmpratur T w is Q = Q Q a = σa( ε g T 4 g α g T 4 w ) W

19 Problm A flu gas at T g =1000K and total prssur P T = 2 atm containing 10 prcnt watr vapor by volum flows ovr a tub bank arrangd in an quilatral triangl array, having a tub with Diamtr D = 7.6 cm and a spacing S = 2D. Th tubs ar maintaind at a uniform tmpratur T w = 500K and considrd black. Calculat th nt radiation hat xchang btwn th gas and th tubs pr squar mtr of tub wall surfac

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