The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 16
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While chemiluminescence may normally be neglected, particulates aswell as gas radiation generally must be accounted for.Radiative Properties of Molecular GasesWhen a photon (or an electromagnetic wave) interacts with a gas molecule, it may be absorbed, raisingthe energy level of the molecule. Conversely, a gas molecule may spontaneously lower its energy levelby the emission of an appropriate photon. This leads to large numbers of narrow spectral lines, whichpartially overlap and together form so-called vibration-rotation bands. As such, gases tend to be transparent over most of the spectrum, but may be almost opaque over the spectral range of a band.
Theabsorption coefficient kl is defined as a measure of how strongly radiation is absorbed or emitted alonga path of length, L, leading to the spectral absorptivity and emissivity for this path, oral = el = 1 - e-kl L(4.3.28)Although gases are distinctly nongray, for simple heat transfer calculations we often need to determinethe total emissivity for an isothermal path (compare Equation (4.3.9))e=© 1999 by CRC Press LLC1Eb¥ò (1 - e ) E (T ) dl0-kl Lblg(4.3.29)4-73Heat and Mass TransferFor a mixture of gases the total emissivity is a function of path length L, gas temperature Tg, partialpressure(s) of the absorbing gas(es) pa, and total pressure p.
For the — in combustion applications mostimportant — mixture of nitrogen with water vapor and/or carbon dioxide, the total emissivity may becalculated from Leckner.8 First, the individual emissivities for water vapor and carbon dioxide, respectively, are calculated separately fromæ eöe pa L, p, Tg = e 0 pa L, Tg ç ÷ pa L, p, Tgè e0 ø()()()(4.3.30a)2épa L) m ù ö ùúæ eö(a - 1) (1 - PE ) æ é(êç e ÷ pa L, p, Tg = ê1 - a + b - 1 + P expçç -c êlog10 p L ú ÷÷ úè 0øúû øEaè êëêëúû()é Ne 0 pa L, Tg = exp êêë i=0()Nååj =0jæ Tg ö æp L öc ji ç ÷ ç log10 a ÷è T0 ø è( pa L ) 0 øiùúúû(4.3.30b)(4.3.30c)Here e0 is the total emissivity of a reference state, i.e., for the case of p = 1 bar and pa ® 0 (but paL >0), and the correlation constants a,b,c,cji, PE (pa L)0, (pa L)m, and T0 are given in Table 4.3.2 for watervapor and carbon dioxide.
(For convenience, plots of e0 are given in Figures 4.3.15 for CO2 and 4.3.16for H2O.) The total emissivity of a mixture of nitrogen with both water vapor and carbon dioxide iscalculated from(4.3.31)e CO2 + H2O = e CO2 + e H2O - DeTABLE 4.3.2 Correlation Constants for the Determination of the Total Emissivity for Water Vapor andCarbon DioxideGasWater VaporM, Nc00Mc0 MLOLc N1Mc NMPE(paL)m/(paL)0abc–2.21180.85667–0.108382,2–1.19870.93048–0.17156Carbon Dioxide2,30.035596–0.143910.045915( p + 2.56 pa / t )/ p013.2t22.144,t < 0.751.88 – 2.053 log10 t, t > 0.751.10/t1.40.5Note: T0 = 1000 K, p0 = 1 bar, t = T/T0, (pa L)0 = 1 bar cm.© 1999 by CRC Press LLC–3.98931.2710–0.236782.7669–1.10900.19731–2.10811.0195–0.19544(p + 0.28pa)/p00.054/t2, t < 0.70.225t2, t > 0.71 + 0.1/t1.450.231.470.39163–0.218970.0446444-74Section 4()æpH2O + pCO2 L öæöz÷De = ç- 0.0089z10.4 ÷ ç log10è 10.7 + 101zøç( pa L)0 ÷øè2.76(4.3.32)pH 2 Oz=pH2O + pCO2FIGURE 4.3.15 Total emissivity of water vapor at reference state (total gas pressure p = 1 bar, partial pressure ofH2O pa ® 0).where the De compensates for overlap effects between H2O and CO2 bands, and the e CO2 and e H2O arecalculated from Equation (4.3.30).If radiation emitted externally to the gas (for example, by emission from an adjacent wall at temperatureTs) travels through the gas, the total amount absorbed by the gas is of interest.
This leads to the absorptivityof a gas path at Tg with a source at Ts:()a pa L, p, Tg , Ts =1Eb (Ts )¥æò è1 - e0( ) ö E T dlbl ( s )- k l Tg Lø(4.3.33)which for water vapor or carbon dioxide may be estimated fromæ Tg öa pa L, p, Tg , Ts = ç ÷è Ts ø(© 1999 by CRC Press LLC)12æöTeç pa L s , p, Ts ÷Tgèø(4.3.34)4-75Heat and Mass TransferFIGURE 4.3.16 Total emissivity of carbon dioxide at reference state (total gas pressure p = 1 bar, partial pressureof CO2 pa ® 0).where e is the emissivity calculated from Equation (4.3.30) evaluated at the temperature of the surfaceTs, and using an adjusted pressure path length, paLTs /Tg.
For mixtures of water vapor and carbon dioxideband overlap is again accounted for by takinga CO2 + H2O = a CO2 + a H2O - De(4.3.35)with De evaluated for a pressure path length of paLTs/Tg.Example 4.3.6Consider a layer of a gas mixture at 1000 K and 5 bar that consists of 10% carbon dioxide and 70%nitrogen.
What is its emissivity for a path length of 1.76 m, and its absorptivity (for the same path) ifthe layer is irradiated by a source at 1500 K?Solution. First we calculate the total emissivity of the CO2 at the reference state (p = 1 bar, pa ® 0).for a length of 1.76 m from Equation (4.3.30c) or Figure 4.3.15. WithTg = 1000 K = 727°C andpa L = 0.1 ´ 5 bar ´ 1.76 m = 88 bar cmone gets, interpolating Figure 4.3.15, e0 @ 0.15. The correction factor in Equation (4.3.30b) is calculatedfrom Table 4.3.2 with PE = 5 + 0.28 ´ 0.5 = 5.14, a = 1.1, b = 0.23, c = 1.47, and (paL)m = 0.225 barcm.
Thus,2æ0.1 ´ (-4.14)0.225 ö öe@1expç -1.47æ log10= 1è88 ø ÷ø0.33 + 5.14e0è© 1999 by CRC Press LLC4-76Section 4ande @ 0.15To calculate the absorptivity e0 must be found for a temperature ofTs = 1500 K = 1227°C andpa LTs= 88 ´ 1500 1000 = 132 bar cmTgFrom Figure 4.3.15 it follows that e0 @ 0.15 again and, with e/e0 pretty much unchanged, from Equation(4.3.34),1000 öa@æè 1500 ø12´ 0.15 ´ 1.00 = 0.122Radiative Properties of Particle CloudsNearly all flames are visible to the human eye and are, therefore, called luminous (sending out light).Apparently, there is some radiative emission from within the flame at wavelengths where there are novibration–rotation bands for any combustion gases. This luminous emission is known today to comefrom tiny char (almost pure carbon) particles, call soot, which are generated during the combustionprocess.
The “dirtier” the flame is (i.e., the higher the soot content), the more luminous it is.Radiative Properties of Soot. Soot particles are produced in fuel-rich flames, or fuel-rich parts of flames,as a result of incomplete combustion of hydrocarbon fuels.
As shown by electron microscopy, sootparticles are generally small and spherical, ranging in size between approximately 50 and 800 Å (0.005to 0.08 mm), and up to about 3000 Å in extreme cases. While mostly spherical in shape, soot particlesmay also appear in agglomerated chunks and even as long agglomerated filaments. It has been determinedexperimentally in typical diffusion flames of hydrocarbon fuels that the volume percentage of sootgenerally lies in the range between 10–4 to 10–6%.Since soot particles are very small, they are generally at the same temperature as the flame and,therefore, strongly emit thermal radiation in a continuous spectrum over the infrared region.
Experimentshave shown that soot emission often is considerably stronger than the emission from the combustiongases.For a simplified heat transfer analysis it is desirable to use suitably defined mean absorption coefficientsand emissivities. If the soot volume fraction fv is known as well as an appropriate spectral average ofthe complex index of refraction of the soot, m = n – ik, one may approximate the spectral absorptioncoefficient by (Felske and Tien, 1977).k l = C0fnlC0 =36pnk(n22-k +2)2+ 4n 2 k 2(4.3.36)and a total, or spectral-average value may be taken ask m = 3.72 f n C0 T C2(4.3.37)where C2 = 1.4388 mK is the second Planck function constant. Substituting Equation (4.3.37) intoEquation (4.3.29) gives a total soot cloud emissivity ofe( f n TL) = 1 - e - k m L = 1 - e -3.72C0 fnTL C2© 1999 by CRC Press LLC(4.3.38)4-77Heat and Mass TransferPulverized Coal and Fly Ash Dispersions.
To calculate the radiative properties of arbitrary size distributions of coal and ash particles, one must have knowledge of their complex index of refraction as afunction of wavelength and temperature. Data for carbon and different types of coal indicate that its realpart, n, varies little over the infrared and is relatively insensitive to the type of coal (e.g., anthracite,lignite, bituminous), while the absorptive index, k, may vary strongly over the spectrum and from coalto coal.
If the number and sizes of particles are known and if a suitable average value for the complexindex of refraction can be found, then the spectral absorption coefficient of the dispersion may beestimated by a correlation given by Buckius and Hwang, 1980. Substitution into Equation (4.3.29) canthen provide an estimate of the total emissivity. If both soot as well as larger particles are present in thedispersion, the absorption coefficients of all constituents must be added before applying Equation(4.3.29).Mixtures of Molecular Gases and Particulates.
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