Study on the Simulation Method for Wall Burning in Liquid-bath Combustor XIAOHAN WANG 1, 2, DAIQING ZHAO 1, LIBO HE 1, YONG CHEN 1 1. Guangzhou Institute of Energy Conversion, the Chinese Academy of Sciences, No.1, Nengyuan Rd., Wushan, Tianhe District, Guangzhou city, Guangdong rovince P. R. CHINA 2. Deartment of Thermal Science and Energy Engineering, the University of Science and Technology of China, the 4 th Mailbox, Hefei city, Anhui rovince P. R. CHINA Abstract: - Considering the limitation of existing simulation method for burning characteristics in the liquid-bath combustor, this aer uts u a new wall-burning model from the true hysical henomenon of coal article deosition. Combined with conventional coal combustion simulation rogram, the total comutational frame also is introduced. From the comarison of simulation results from several kinds of methods, the differences of them are analyzed, which can rovide a new comutational idea for the simulation of liquid-bath combustor. Key-Words: - Coal combustion, liquid-bath, combustor, wall-burning, article deosition, simulation 1 Introduction Almost all rocesses of coal combustion are comrehensive and intensive. With the develoment of comutational fluid dynamics for twenty years, many colleges, institutes and other secial research grous have develoed lots of comutational rograms. But most simulation results from these rograms cannot have the very satisfying agreement with the exerimental data. The ossible reason is the lack of recision of sub-models on one hand, but on the other hand, the most imortant reason is the half-baking of the total combustion model, that is to say, many factors that can affect the burning characteristics have not been considered. For examle, coal ash or articles will deosit on the wall during the rocess of coal combustion. The decreasing or increasing of ash deosition will change the wall boundary condition and affect the heat transfer through the wall and burning characteristics in the combustor. But in existing CFD software, this imortant heat rocess has not been considered, so the authentic combustion condition can not be simulated well, which makes the simulation results can not rovide the good guidance for the design and oeration of coal furnaces or combustors. In a word, it is a critical roblem need to be solved necessarily that how to simulate deosition rocess in order to modify the existing comutational frame of coal combustion. For making the analyzed results more recise and accetable, many researchers have carried on many studies for ash deosition in coal combustors. Wang et al. [1] summarized several existing models and classified total rocess into nine issues: (1) ash formation; (2) fluid dynamics and articles transort; (3) article imaction; (4) article sticking; (5) deosition growth as a function of location in the combustion chamber; (6) deosition roerties and strength develoment; (7) heat transfer through the deosition layer; (8) the effect of deosition on oerating conditions (e.g. temeratures and heat fluxes) in the combustor; (9) deosition structure and its effect on flow atterns in the combustion facility. These issues are shown on Fig.1. Based on this classification and summarization, Wang et al. [1], Lee et al. [2], Fan et al. [3] studied the article deosition resectively. For several exerimental coals used in the solid-bath furnaces, the simulation results have been comared with the exerimental data and accetable agreement was achieved. But in liquid-bath combustor or furnace, the temerature is high, molten slag layer will cover the wall and cature the articles. If these articles contain combustible matters, they will continue to burn on the wall. The left coal ash will flow with the slag layer, which makes the total amount of ash deosition be much more than that in solid-bath combustor and the wall boundary condition change
sharly. So above nine issues are not enough to describe the deosition in liquid-bath combustor. In this aer, the wall-burning model is develoed as the accessory for above nine issues in order to simulate total rocess more reasonably. Tsteam Steam water Heat transfer (7) (8)(9) Tsurface (3)(4)(5) Tube wall Deosit Particulate Highly sintered deosit (6) deosit Low High Deosit strength Convective transfer and incident radiation Reflected radiation and emitted radiation Transort mechanisms (2) Inertially imacting (large articles) Thermohoresis (intermediate-size articles) Fick diffusion (vaors) Flame (1) Bulk concentration of articles Particle flux to wall Distance from wall H 0 where article concentration C=C 0 Particle concentration C Fig.1. Schematic reresentation of issues imortant in modeling ash deosition [1] 2 Mathematical models 2.1 Coal combustion model Under the 2D cylindrical coordinate, the Lagrangian/Eulerian mixed model is used to simulate the coal combustion, the governing equation of mass, momentum and energy for gas and article will be solved under Eulerian and Lagrangian coordinate resectively. Some models, including k-ε/rng model, two cometing stes model, diffusion/dynamics mixed model, EBU/Arrhenius model, stochastic searate flow model and discrete transfer radiation model are used to simulate gaseous turbulent flow, coal devolatilization, char combustion, gaseous combustion, article turbulent flow and radiation heat transfer, as shown in [4]. The governing equation under 2D cylindrical Eulerian coordinate can be described as: 1 ϕ 1 ϕ ( ρϕ u ) ( rρϕ v ) r + = Γ + Γ + S + S (1) x r r x x r r r ϕ ϕ ϕ ϕ Where φ, Γ φ, S φ, S φ stand for some arameters, which are described in detail in [5]. 2.2 Particle deosition model Dominating by drag force, gravity force and other forces (such as Brownian force, thermohoresis force, electrical force, lift force, etc.), some articles will move towards wall, and only art of them can arrive. Deciding by the characteristics of arriving articles and wall, some arriving ones can stick and deosit, others maybe re-bounce and be carried by gas again. So it is a critical roblem while describing article deosition that how to comute the arriving efficiency and sticking efficiency of articles. The different ways to affirm it are given in [1] and they will be selected to simulate coal combustion in this article. 2.2.1 Arriving efficiency of articles The definition of arriving efficiency is: η = (2) im 0 Where is the arriving mass rate of articles, 0 is the total mass rate of articles that ejected into combustor. Borrowing ideas from free-flight model develoed by Friedlander & ohnstone [6]: when articles move to sto distance H 0 (deviated from wall), they will traverse the sub layer at the seed of u d and arrive at wall, as shown on Fig. 2. Usually the results of deosition exeriments or calculations are resented as curves of non-dimensional deosition u + d versus non-dimensional article relaxation time τ +. The deosition, u d, is the articles mass transfer rate,, normalized by the mean or bulk concentration, C 0. All of these can be described as: *2 2 *2 u d u τ τ C ρ c ν 18µ ν + u d 1 ud = * = * u C0 u + = = (3) C c Fig.2. The diagram of mechanism for article arriving 1.1 = 1+ Kn 1.257 + 0.4ex 1 Kn (4) (5) Where u * is friction, C c is Cunningham correction factor. In the comuter simulation, the article
non-dimensional deosition is estimated as: + Nd / t d 1 ud = * N0 / H0 u (6) Where N d is the number of deosited articles in the time duration t d, N 0 is the initial number of articles uniformly distributed in the region within a distance of H 0. In this aer, the distance H 0 is redefined as the osition that is just at the edge of the viscous sub-layer with y + =5, which has been described in the standard wall function. Wood [7] summarized deosition mechanism of different articles. It is observed that the article non-dimensional deosition u + d has a V-shae variation along with the article non-dimensional relaxation time τ +. This can be described by Wood s emirical equations: u + d = 0.1 τ + 10 (7) + -2/3 4 + 2 ud = 0.057Sc + 4.5 10 τ τ + < 10 (8) Sc is Schmidt number, which is given by: Sc ν = 3πνd µ (9) D C κ T bf c b Where D bf is Brownian article diffusivity, κ b is Boltzmann constant. From equations (2)~(9), article arriving rate and article arriving efficiency η im can be comuted. 2.2.2 Sticking efficiency of articles The net rate of deosition deends on both the arriving rate of articles and their ability to stick to wall. The sticking efficiency is used to describe this ability, which is: de f = (10) de Where de is the deosition mass rate of articles, is the arriving mass rate of articles. Walsh [8] thinks that the viscosities of article and deosition surface are the most imortant factors that can affect the article s sticking. For this, he used article s viscosity to describe the sticking robability: µ ref i( T) = ( µ > µ ref) µ ( T ) = 1 ( µ µ ) i ref (11) Where i (T ) is the sticking robability of articles of comosition i, T is the article temerature while imacting, µ ref is critical viscosity with the value 10 5-10 8 Pa.s commonly and with the value 10 3 Pa.s while existing molten slag layer [9]. µ is article s viscosity with the temerature deendence described by Urbain model [10]. Considering the roerties of article and deosition surface, sticking efficiency can be regarded as: f = ( T ) + 1 ( T ) ( T ) k 1 ( T ) [ 1 ( T )] (12) de i i sur s e i sur s Where i (T ) stands for the sticking robability of articles of comosition i at the article s temerature and sur (T s ) stands for the sticking robability of the deosition surface at surface s temerature. k e is the erosion efficiency of dry ash towards its own deosition, which contributes negatively to the article sticking. Basing on equations (10)~(12), the deosition mass rate of articles can be comuted and that will rovide the basis for the following wall burning model. 2.3 Wall burning model In ulverized coal-fired furnace or combustor, esecially in liquid-bath furnace or combustor, the article whose size less than 1mm is at the state of intenerating or melting while deositing, so once they are catured by deosition surface, it is very difficult for them to go back to satial sace and be carried by gas again. Only a few articles with big size more than several millimeters kee its rigidity while deositing, these articles are likely to be carried into gaseous field time after time. In ulverized coal-fired boilers, the size of most articles is less than 1mm, so the hyothesis that the articles cannot go back to satial sace once deositing is reasonable. Following the hyothesis, if there is combustible matter (volatile, char) not being consumed u yet while deositing, the articles will stick to the wall and continue to burn, as shown in Fig.3. The burning characteristics of single article on the molten slag layer deend on contact radius a to a great extent. ohnson et al. [11] develoed KR model that included the effect of adhesion force on the deformation of an elastic shere in contact to an elastic half sace. Accordingly, the contact radius is given as: 3 R a = P+ 3πγ R+ 6πγ RP+ ( 3πγ R) 2 (13) K 4 (1 varticle) (1 v K = + 3 Earticle E 2 2 slag slag 1 (14) Here R is the article radius, K the elastic constant, P external force alied on the article, γ the surface energy, E elastic modulus and ν Poisson ratio. If setting P = 0 in equation (13), the corresonding contact radius is: 2 6πγ R a = K 1/3 (15) For lastic deformation, equation (13) should be modified. But in our resent comuting work, the result from equation (15) is adoted without considering the lastic deformation of articles yet.
Char combustion Volatile devolatilization Slag layer Coal article R a Fig.3. The diagram of article burning on molten slag layer The effective surface area S eff and effective volume V eff, which is exosed to the gas, are: 2 2 S = 2 π R( R+ R a ) (16) eff 4 1 Veff = R ( R R a ) 3 a + ( R R a ) 3 6 3 2 2 2 2 2 2 π π (17) The effective diameter d eff is defined as: d S eff eff = (18) π The effective temerature of the article on the molten slag layer is defined as: T = [ T V + T ( V V )]/ V (19) eff eff slag eff Where, T is article temerature while imacting, T slag is surface temerature and V is article s volume. The effective diameter, effective surface area, effective volume, effective temerature and the content of combustible matter in the article comuted from above equations will hel to gain the char consumtion rate q c and volatile yrolysis rate q v. Accordingly, the heat roduction of char combustion, CO roduction and volatile roduction in the time duration t d will be known. Integrating with all other deositing articles, the total source term roduced from solid-hase will be simulated reasonably. Inut initial conditions (Shae of combustor and grid generation, article roerties, combustion condition Comutation of gaseous field without articles (Velocity, temerature, turbulent roerties of gaseous hase etc.) Comutation of article in satial sace (Turbulent disersion, coal devolatilization, char combustion, radiation heat transfer by articles, article conservation equations for mass fraction, momentum, energy etc.) Comutation of solid hase Comutation of arriving rate and deosition rate of articles Comutation of source terms generated from articles in satial sace and on wall surface (Mass, momentum, energy etc.) Comutation of wall burning for articles deositing on the wall (Coal devolatilization, char combustion etc.) Comutation of gaseous combustion (Volatile combustion, radiation heat transfer,, temerature, concentration, etc.) No Convergence? Yes End and outut results Fig.4. Comutation frame for coal combustion considering the deosition and wall-burning of articles 3 Comutational frame Using above numerical models, the whole burning characteristics near the wall in the combustor will be known. In fact, the rocess of ash deosition is relevant to deosition time stes: at the initial time, articles will deosit on the clean wall. Then with the time increasing, the deositing articles will cumulate on the wall and the thickness of slag layer will increase. Basing on the heat transfer mechanism, the temerature of layer will continue to increase till
it is higher than the fusion temerature of bulk ash. At this time, the thickness of slag layer will not change and the rocess of deosition is regarded as stable. The steady-state comutational frame is given in Fig. 4. From this frame, it should be aid attention to that the transient changing of slag layer thickness has not been considered at resent. So for steady-state comutation, it is suosed that there has been molten slag layer existing on the wall and the comutational wall is the molten slag layer actually. In the comutation case, the temerature of external wall and average heat resistance basing on the exerimental test will be given in order to comute the heat flux through the wall. SIMPLE algorithm is used for -v correction, and TDMA algorithm is used to solve the discretisation equations line by line. 4 Comutational cases The comutational grid of a liquid-bath combustor is shown in Fig. 5. The secondary air is ejected into the combustor chamber through the annular vane with 30mm width at the osition between r = 200mm~230mm. The rimary air with coal articles is ejected into the lace very near the secondary air, which will make the rimary air gain the largest tangential momentum. The external wall surface is cooled by water steam with 373K temerature, the average heat resistance of water steam, steel tube, flame retardant coating and slag layer is 0.03m 2. K/W basing on hot test, the initial article mass rate 0 is 0.0279kg/s, the average size of articles d is 0.075mm and the stoichiometric ratio is 1.03. Other inlet conditions are shown in Table 1. r Combustor grid Φ250 Furnace grid Pressure outlet θ Annular air inlet 5 Axial Radial z (axis) 1000 125 1500 Φ500 Primary air Tangential Fig.5 Comutational grid (Unit: mm) Table 1. Air inlet conditions Inlet temerature (K) Axial Secondary air Radial Tangential Inlet temerature (K) 10.74 0 0 293 10.74 0 102.18 580 For the simulation of interaction between article and wall in liquid-bath combustor, there is about three kinds of methods: (1) elastic imingement between article and wall without considering article deosition mechanism; (2) artially non-elastic or totally non-elastic imingement without considering article deosition mechanism; (3) Partially non-elastic imingement with considering article deosition and wall burning mechanism, which is shown in this aer. Fig. 6 shows all articles information just when the deosition henomenon haens. These information include volatile mass rate, char mass rate, ash mass rate, etc. From the information, it is known that volatile has emitted from coal article during the rocess of satial combustion, so there is almost no volatile content at the time of deosition. But char is burning so slowly that there is much char content in articles during deosition rocess. If the temerature of molten slag layer is high enough to cature these articles, the char will continue to burn on the layer. Fig. 7 gives the comarison of wall temerature calculated from above three methods. It should be noticed that the wall temerature is the temerature of slag layer actually. Calculating with method (1), comutational temerature is too low for steady burning and the results is wrong; calculating with method (2), the results deend on the coefficient of restitution, e. some researchers [12] used the hyothesis of totally non-elastic imingement, which means, e = 0. This hyothesis adats to the condition that the whole wall is covered by molten slag layer includes the lace which is very near the air inlet. By exerimental robe, the temerature at the osition near the air inlet is not high enough to make slag melt and the temerature of articles is low too, which will make the article hardly stick to the wall. In that lace, the coefficient of restitution e cannot be regarded as zero. Reflected from the calculation result, using method (2), the wall temerature near the air inlet is something high; calculating with method (3),
article deosition and wall burning mechanism are combined with artially non-elastic imingement condition with e = 0.5. From the comutational result, it is known that there is an obvious wall-burning region from 0.14m to 0.65m and the 0.0014 temerature is high because of the wall-burning mechanism. From the head of the combustor to 0.14m, the temerature is low because of the cooling by inlet air and external water steam. 1800 Deosition rate (kg/s) 0.0012 0.0010 0.0008 0.0006 0.0004 Total deosition rate Char deosition rate Ash deosition rate Volatile deosition rate Wall temerature (K) 1600 1400 1200 1000 800 Elastic Partially non-elastic (e=0.5) Totally non-elastic (e=0) Wall burning model with artially non-elastic (e=0.5) 0.0002 600 0.0000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Axial osition of the wall (m) Fig.6 Particles roerties 400 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Axial osition of the wall (m) Fig.7 wall temerature of combustor 5 Conclusion For the simulation of liquid-bath combustor, it is the key oint that how to analyze burning characteristics near the wall roerly. In this aer, a new wall-burning model from the true hysical henomenon of coal article deosition is develoed and the total comutational frame is given. Comared with other simulation methods, this comutational idea is more reasonable. But some hyothesis in the aer should be modified further: (1) Once the thickness changing of slag layer will affect the total heat transfer, it should be noticed more thoroughly. Though the transient rogram can comute this rocess more roerly, it will take more comutational CPU time. So the quasi steady-state rogram is the better choice, as discussed in [1]. (2) When articles deosit on molten slag layer, it will move together with the slag flow. The hyothesis that articles should be fixed in the deosition lace will make the local temerature high. Slag flow model should be added in next work. References: [1] Wang H F, Harb N. Modeling of ash deosition in large-scale combustion facilities burning ulverized coal, Progress in Energy and Combustion Sciences, Vol. 23, No. 3, 1997,. 267-282. [2] Lee F C C, Lockwood F C. Modeling ash deosition in ulverized coal-fired alications, Progress in Energy and Combustion Science, Vol. 25, No. 2, 1999,. 117-132. [3] Fan R, Zha X D, Sun P. Simulation of ash deosit in a ulverized coal-fired boiler, Fuel, Vol. 80, No. 5, 2001,. 645-654. [4] Sun X X. Exerimental technology and method of combustion for coal-fired boilers, Chinese electric ower ress, 2001. (In Chinese) [5] Zhou L X. The theory and numerical simulation of turbulent gas-article two-hase flow and combustion, Science ress, 1994. (In Chinese) [6] Friedlander S K, ohnstone H F. Deosition of Susended Particles from Turbulent Gas Streams, Industrial And Engineering Chemistry, Vol. 49, No. 7, 1957,. 1151-1156. [7] Wood N B. Mass transfer of articles and acid vaor to cooled surfaces, ournal of the Institute of Energy, Vol. 54, No. 419, 1981,. 76-93. [8] Walsh P M, Sarofim A F, Beer M. Fouling of convection heat exchangers by lignitic coal ash, Energy & fuels, Vol. 6, No. 6, 1992,. 709-715. [9] Srinivasachar S, Helble, Boni A A. Mineral behavior during coal combustion, Progress in Energy and Combustion Science, Vol. 16, No. 4, 1990,. 281-302. [10] Vargas S, Frandsen F, Dam-ohansen K. Rheological roerties of high-temerature melts of coal ashes and other silicates, Progress in Energy and Combustion science, Vol. 27, No. 3, 2001,. 237-429. [11] ohnson K L, Kendall K, Roberts A D. Surface energy and the contact of elastic solids, Proc. Roy. Soc. London Ser. A., Vol. 324, 1971,. 301-313. [12] Huan B W, Wang Z G. Numerical modeling of the strongly swirling turbulent gas-solid two-hase flow and combustion, Power Engineering, Vol. 18, No. 3, 1998,. 43-48. (In Chinese)