Methodological Aspects of the Calculation of the Adiabatic Combustion Temperature of Carbon

Transcription

1 World Aled Scences Journal 24 (): , 203 ISSN IDOSI Publcatons, 203 DOI: /dos.wasj Methodologcal Asects of the Calculaton of the Adabatc Combuston emerature of Carbon Alexander Nkolaevch Loanov, Evgena Aleksandrovna Fanna and Oxana Ncolaevna Guzeeva Belgorod State echologcal Unversty named after V.G.Shukhov, Russa, 30802, Belgorod, Kostyukova st. 46 Submtted: Aug 9, 203; Acceted: Se 6, 203; Publshed: Se 8, 203 Abstract: A method of evaluaton of the adabatc combuston temerature, whch allows to consder the enthaly nternal energy of hase transtons startng materals, reacton roducts and the full use of the heat balance equaton n a stuaton where the heat exhbts roertes fully dfferental. he calculaton of the adabatc combuston temerature of carbon at varous artal combuston reacton of the actve carbon. It s shown that the method of calculatng the adabatc temerature, whch does not take nto account the artal actvty of the comonents can not be used for reasonably accurate estmates of the thermodynamc arameters of thermal systems. Key words: he adabatc combuston temerature of carbon Partal actvty of the comonents of the combuston reacton of carbon. INRODUCION n the change mechansm exlosve rocesses [2, 3]. hus, we defne the crtcal rocess as a henomenon he reacton of the combuston of carbon dscussed assocated wth sontaneous ncreases or decreases n detal n the exermental comarson of thermochemcal the seed of transformaton of matter wth a slght change measurements and thermodynamc calculatons. ake of arameters of nfluence on the system. nto account the heterogeneous nature of the surface One of the mortant arameters of thermodynamc rocesses and the condtons of transton from calculaton of crtcal rocesses s the adabatc combuston n the so-called crtcal regme. hese temerature, whch s related to the actual outut of the studes are mortant not only for the qualtatve and exloson, burnng. Calculatons of the adabatc quanttatve research n the aerosace ndustry, but also temerature of combuston, exloson - the bass of to mrove and create a modern fre detecton system calculatons of thermal rocesses, heat engnes and based on the fundamental studes of the theory of devces. At resent the methodologcal asects of the combuston and exloson. calculaton of the adabatc combuston temerature of Chemcal and hyscal rocesses that are common carbon not worked enough. atterns n the course of tme, such as sontaneous release or absorton of energy. he rate of such Problematc Asects of the Research: he general reactons can sontaneously grow for a certan tme and theoretcal framework and the combuston of carbon then gradually decreases and fades. Many rocesses comounds contanng carbon, consdered n suffcent occur n the case of mnor changes n the system detal. It s shown that an ncrease n combuston rate arameters - ressure, temerature and volume. In ths of carbon occurs at temeratures of C [4]. case, t s ndcated that the rocess s n the crtcal he methods for calculatng the carbon burnng regme []. In crtcal condtons often occur oxdaton, temerature substances ncludng adabatc combuston combuston, hase transtons and almost all the temerature [5-9]. Develo a dynamc mathematcal model exlosons. In artcular, the role of temerature s shown of the combuston of carbon-contanng materals [0]. Corresondng Author: Evgena Aleksandrovna Fanna, Belgorod State echologcal Unversty named after V.G. Shukhov, Russa, 30802, Belgorod, Kostyukova st

2 World Al. Sc. J., 24 (): , 203 Smulaton s carred out numercally, comosed nonlnear dfferental equatons. he equatons are solved by Newton's method based on 2-D dstrbuton by drawng u secfc adatve grds. Smulaton combuston modes deendng on the temerature, seed allowed redct unusual hyscal henomenon - fltraton burnng of carbon. When changng from one seed and temerature to the other arameters changed comoston of the roducts of combuston. herefore, the temerature combuston modes are mortant because they allow you to carry out thermodynamc calculatons of combuston of carbon. he temerature of burnng coal to determne the condtons of yrolyss and calculate the yeld of volatles, whch s mortant for the rocessng technology of coal []. he calculaton of the enthaly or nternal energy need to consder the algebrac sum of thermal caactes of the reacton roducts and startng materals. hs s not mentoned n many textbooks, whch rovdes estmates of the adabatc temerature of combuston, exloson, ncludng, among other thngs, n hs classc monograh of Zel'dovch and colleagues. [2] MAERIALS AND MEHODS ycally, the calculatons of the adabatc combuston temerature s carred out based on the henomenologcal models, whch take nto account the arameters of emrcal rocesses [3-4]. Calculated values??n models adabatc combuston temerature, as a rule, does not correlate wth the condtons. As shown n ths study the adabatc combuston temerature wll deend uon such varables as the artal combuston reacton actve comonents. herefore, the calculatons are gven n the abstract scheme of combuston wthout the artal actvtes of the comonents contan sgnfcant errors. he roblem s comlcated by the fact that, n ractce, to check the adequacy of the roosed methods of calculaton s not ossble, so the adabatc mode of combuston, exloson - t's an mossble deal model. As ndcated, based on the theoretcal concets of crtcal rocesses, you can make a varety of algorthms for calculatng the adabatc temerature, but n terms of methodology, the roblem s not fully develoed. hs s due to the fact that the exermentally verfy the calculatons s not ossble - adabatc rocess s not mlemented n ractce. It should hghlght the man rovsons of calculaton methods. Fundamentals of calculatons based on the frst law of thermodynamcs and ts consequences: du = Q A = 0; Q = dh, Q = du. Alyng Krchhoff equaton rocesses, defne ther enthaly or nternal energy: m m 0 0 V = = H H = C d, U U = C d. Here, H, U - change n enthaly, nternal energy, J/mol; C ð, C v - the sobarc and sochorc heat caacty, J/mol K; v - stochometrc coeffcents of the formal scheme of the rocess, - temerature, K. Snce the roertes of the comlete dfferental dslay enthaly and nternal energy, we construct the followng algorthm to calculate the adabatc temerature of the crtcal rocess, gven that H,H,H,H,H resectvely the enthaly of the rocess, the raw materals, hase transtons, chemcal reactons, the reacton roducts: dh= dh +dh +dh +dh. () du=du +du +du +du. (2) For most crtcal rocesses n the adabatc mode (dh=0; du=0) s satsfed: H, H 2, << H 3, H 4; U, U << 2 U 3, U 4. If you do not take nto account the enthaly (nternal energy) of the startng materals and the hase transtons, the calculaton s smlfed H 3 = - H 4; U 3= - U 4. In the exact calculatons gnore the enthaly (nternal energy) hase transtons and the raw materals can not be aled and the total heat balance equaton - the equatons and 2. ycally, a comlete heat balance equaton s used at suffcently low enthaly of comarable energy to the hase transtons of combuston rocesses. he Man Part: he aer resents a rocedure for evaluatng the crtcal rocess that conssts of the followng stes. Drawng u a formal rocess scheme. Chemcal reacton enthaly H H = H + C d. Drawng u a system of equatons wth the equlbrum constant K. Calculaton of the adabatc temerature: V 484

3 0 3 H = H + C d = +. m = C Smlarly, you can erform calculatons of the crtcal rocess of adabatc temerature at constant volume: World Al. Sc. J., 24 (): , 203 () 0 U3 = U + CVd m. = + = C V Fg. : he algorthm for calculatng the adabatc (2) combuston temerature by comuter he calculatons n the zero aroxmaton usng the deal gas model s unaccetable, as the temerature estmates do not rovde hyscal-chemcal model that adequately reflects the rocess. So, usng the value of the enthaly of carbon monoxde (IV), the value of sobarc heat caacty n accordance wth the theory of deal gases equal to 33.3 J/mol K, we calculated the value of the adabatc combuston temerature () = + = 230?. 33,3 Obvously, t s necessary to take nto account the dssocaton of substances, the temerature deendence of the enthaly and heat caacty of substances. In the embodment of a comuter mlemented calculaton scheme shown n Fg.. Calculatng the number of cycles n accordance wth the calculaton algorthm can be sgnfcantly reduced by usng the ntal condtons close to the adabatc temerature of the combuston rocess (able ). Heat caacty deends on the temerature reresented by a ower seres: C = a + b + c /. 2 Here, a, b, c - the coeffcents of the ower seres, able. In accordance wth an algorthm for calculatng the comoston formal schemes ossble burnng substances and dssocaton of the reacton roducts: C + O = CO, the equlbrum constant ( ) K ; (3) 2 2 ð C+O = CO, the equlbrum constant ( ) K ; (4) 2 ð 2 able : hermodynamc roertes of the test substances he coeffcents of the ower seres Substances C,J/mol K H 0 kj/mol a b 0 c lg K = A + B, lg K = 3; lg K2 = 4,680. K 2 = = = + 2?? ( ) 2 CO ao 4806 ; lg K 4,527.? a CO C 8,53 0 7,5 4,27-8,79 CO 29,5-2 28,4 4,0-0,46 CO2 37,3-393,5 44,4 9,04-8,53 O2 29,36 0 3,46 3,39-3,77 CO =CO+O, the equlbrum constant ( ) K. (5) 2 2 ð Dssocaton of carbon oxde (II) s neglected n connecton wth a mnor reacton was at the secfed route. ake nto account the deendence of the equlbrum constant on temerature s reresented by equaton [4]: Combnng equatons (3-5), we get for the equlbrum constant K: Here, a - actvty of reacton comonent (CO, O, CO ). 2 2 CONCLUSION hus, for calculaton of the adabatc combuston temerature of carbon we need soluton to the system of equatons (6). Analyzng the equatons (6), note that the calculatons of the adabatc combuston temerature 485

4 World Al. Sc. J., 24 (): , 203 Fg. 2: Grahc reresentaton of the arameter Y on the content of carbon monoxde (II) for one and fve teratons (left) should be comared wth the combuston condtons, artcularly the actve comonents wth artal actvtes of combuston formal scheme comonents. hus, after burnng of one mole of carbon n dfferent volumes calormeter system we obtan dfferent values of adabatc temerature deendng on the equlbrum artal ressures of oxygen and carbon oxdes. hs concluson s general n nature and should be aled n the calculaton of the adabatc temerature of all systems that take nto account the deendence of the equlbrum constant wth temerature. he system of equatons for the reacton of carbon combuston has followng form: x ( x)? = ; x H ( CO2) [ ( H ( CO2) H ( CO) ] x = + ; C ( CO2) C ( CO2) C ( CO) C ( O2) x 4806 lg K = + 4,527. ð ð ð Here, H(CO 2), H(CO), C (CO 2), C (CO), C (O 2) - carbon oxdes resectvely enthaly, heat caacty substances. ransformng the system of equatons, we ntroduce the arameter Y, equal to: x ( x) Y = lg{( + x 4806 C ( CO2) x( C ( CO2) C ( CO) C ( O2)) H ( CO ) x[ H ( CO ) H( CO)] 2 2 C ( CO2) x( C ( CO2) C ( CO) C ( O2)) 4,527} (6) able 2: Calculated values of the adabatc combuston temerature of carbon Number of Partal he calculated value of aroxmaton ressure the adabatc combuston (teraton) CO, atm. temerature, K , , , , , , Here x - artal ressure of carbon doxde (II) n a formal scheme (5), atm.; - the ntal artal ressure of carbon doxde (IV) wth the comlete reacton equlbrum shft towards the formaton of CO 2, atm. Usng the condton Y = 0, we defne the arameter x and the adabatc combuston temerature of carbon. hus, n a frst aroxmaton (teraton ) x = 0,860; calculated ower value of the adabatc temerature 3820 K, Fg. 2. Comared wth the zero-order aroxmaton, equal to 230, we note a sgnfcant ncrease n the accuracy of the calculaton, as we get the value of adabatc temerature, whch has a defnte hyscal meanng and a more aroxmate value to the real condtons of combuston of carbon. Calculated cycles of the roosed method converge quckly - t s enough just fve teratons to get the accuracy of the calculaton of adabatc temerature wthn one degree, able 2. By reducng the ressure (er CO 2) from to 0, atm. the equlbrum shfts towards comlete dssocaton of carbon oxde (IV). he artal ressure of carbon monoxde (II) s 0,0988 atm. he adabatc combuston temerature s reduced from 3539 to 242 K. 486

5 World Al. Sc. J., 24 (): , 203 hs examle s to evaluate the mortance of the artal actvtes of the comonents of the combuston reacton. Indeed, when the ressure s reduced to 0 tmes the adabatc combuston temerature of carbon decreased by 000 K. hus, methods of calculatng the adabatc temerature, whch does not take nto account the artal actvty of the comonents can not be used for reasonably accurate estmates of the thermodynamc arameters of thermal systems. We should also hghlght the benefts of the roosed calculaton of the adabatc combuston temerature: the algorthm sgnfcantly reduces the tme requred mathematcal calculatons, software algorthm rovdes a more accurate calculaton, when t does not take nto account the deendence of the enthaly and nternal energy of the temerature, the roosed algorthm allows to estmate the actual temerature wth the heat loss. Gven the heat loss equatons for calculatng the actual combuston temerature s: x ( x)? = ; x { H ( CO2) [ ( H ( CO2) H ( CO) ] x}( ) = + ; C ( CO2) C ( CO2) C ( CO) C ( O2) x 4806 lg K = + 4,527. Here [alha] - ercentage of heat lost n the combuston rocess CONCLUSIONS he algorthm for calculatng the adabatc temerature of a crtcal rocess, whch conssts n drawng u a formal scheme and solvng the system of equatons wth the equlbrum constant of the reacton. he advantages of the roosed algorthm: reducng the tme-consumng calculatons, software algorthm rovdes a more accurate calculaton. he roosed algorthm allows to estmate the actual temerature wth the heat loss of combuston reactons. It s shown that the method of calculatng the adabatc temerature, whch does not take nto account the artal molar actvty of the comonents can not be used for reasonably accurate estmates of the thermodynamc arameters of thermal systems. REFERENCES. Loanov, A.N., 200. Crtcal rocesses: monograh. Belgorod State echnologcal Unversty Publshng House, : Lews, G., Elbe. Burnng, flames and exlosons of gases. Moscow, Mr. Ed Loanov, A.N., 202. he Molecular Modelng of Detonatng and Exlosve Processes Based on the Actvated Comlex heory // Internatonal Research Journal of Pure & Aled Chemstry. V. 2(4): Nagle, J. and F. Strckland-Constabler, 962. "Oxdaton of Carbon between C // n Proceedngs of the Ffth Carbon Conference, : Burghardt, M.D. and J.A. Harbach, 993. Engneerng hermodynamcs, 4th ed. Harer Collns College Publshers, New York, 372: Hmmelblau. D.M., 996. Basc Prncles and Calculatons n Chemcal Engneerng, 6th ed. Prentce-Hall, Inc. Englewood Clffs, New Jersey. : Horvath, L., 996. Calculatons n Industral Chemstry, John Wley and Sons, Inc. New York, : Hseh, J.S., 993. Engneerng hermodynamcs, Prentce-Hall, Inc. Englewood Clffs, New Jersey, : Jones, J.B. and R.E. Dugan, 996. Engneerng hermodynamcs, Prentce-Hall, Inc. Englewood Clffs, New Jersey, : Bekker, A.V., I. Lvk and E.V. Polanczyk, Modellng of non-unque snatonary regmes n carbon fltraton combuston // Ffth Internatonal Conference on CFD n the Process Industres CSIRO, Melbourne, Australa, : Kobayash, H., B. Howard and A.F. Sarfm, 977. "Coal Devolatlzaton at Hgh emeratures" // n Sxteenth Symosum (Internatonal) on Combuston, he Combuston Insttute, Pttsburgh, PA, : Zel'dovch, Y.B., G.I. Barenblatt, V.B. Lbrovch and G.M. Makhvladze he mathematcal theory of combuston and exloson. Moscow: Nauka. : Androsov, A.S. and V.P. Saleev, Examles and roblems on the course "heory of combuston and exloson" Moscow: Academy of Russan Mnstry for Emergency Stuatons, :

6 World Al. Sc. J., 24 (): , Abduragmov, I.M., A.S. Androsov, L.K. Isaev and 5. Karaet'yants, M.H., 975. Chemcal E.V. Krylov, 984. Combuston rocesses. M. hermodynamcs. Moscow: Chemstry. : 584. VIPSH, :