USING FLUENT CODE TO PREDICT DEPOSITION DURING COMBUSTION OF SOLID FUELS

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1 Proceedings of International Conference on Heat Exchanger Fouling and Cleaning (Peer-reviewed) June 05-10, 2011, Crete Island, Greece Editors: M.R. Malayeri, A.P. H. Müller-Steinhagen Watkinson and H. and Müller-Steinhagen A.P. Watkinson Published online USING FLUENT CODE TO PREDICT DEPOSITION DURING COMBUSTION OF SOLID FUELS K. Wacławiak 1 and S. Kalisz 2 1 Deartment of Metallurgy, Silesian University of Technology, ul.krasinskiego 8, Katowice, Poland, krzysztof.waclawiak@olsl.l (Corresonding author) 2 Institute of Power Engineering and Turbomachinery, Silesian University of Technology, ul.konarskiego 20, Gliwice, Poland ABSTRACT Different mechanisms describe formation of deosits, deending on thermal and flow conditions in boilers. Deosit shae and height deend on arrangement of the tubes in suerheaters too. There are several kinds of deosits found in boilers firing solid fuels. In case of owdery deosition the balance of forces acting on a article of ash imacting onto boiler suerheater tubes determines if the article bounces off the surface or stays there building the owdery deosit. On contrary, one of ossible mechanisms describing formation of bonded deosit is that gaseous salts of sodium and otassium condense from flue gas onto heat exchange surfaces and roduce a sticky layer caturing imacting articles of ash, so called wet imaction. The build-u of bonded deosits is further enhanced by lastic ash articles which stick to the surface on imact. The aer resents examles of numerical, twodimensional modeling of the above mentioned deosit kinds on heater tubes. The deosition rocess can be modeled with use of Fluent dynamic mesh otion. This feature allows a user to move the grid vertices indeendently, simulating deosit formation. This way continuous calculations are ossible. Formation mechanisms of these kinds of deosits and all modifications to temerature of the tube surface and its shae were erformed using User Defined Files. DEFINE_DPM_EROSION rocedure defines deosition flux by using mass flow rate of ash articles, area of the face being hit by the articles, and an angle of imaction. Taking into account time and deosit density one can calculate the growth of the deosit. This leads to shift of the vertices of each face of the tube hit by ash articles in DEFINE_GRID_MOTION rocedure. Since formation of deosits insulates the tube, the new surface temerature is worked out and continuously modified in the DEFINE_PROFILE rocedure. INTRODUCTION Deosits found in ower boilers are formed during combustion of ractically all solid fuels. The source of deosit formation in boilers is the resence of mineral matter in the fuel. Mineral substance undergoes hysical and chemical rocesses roducing articles of ash and volatile gases which mix with the flue gas. The volatiles may condense either heterogeneously or homogeneously along boiler ducts. Ash articles floating in the flue gas strike heat exchange surfaces. Steam heaters in ower boilers are covered either with owdery deosits, loosely staying on the surface, or bonded ones, stuck firmly on the surface. Sacing of boiler tube banks influences the velocity field of the flue gas and trajectories of ash articles. Tyically the tube arrangements of in-line tube banks are ket in the range of s 1 /d t =1.5-2 and s 2 /d t =1.5-3 for convective, or s 1 /d t =5-10 and s 2 /d t = for radiant suerheaters (Orłowski et.al., 1979). Ash article size distribution ranges from a few microns u to 200 m. Because of this size range, inertia is the major henomenon influencing trajectories of ash articles. In case of the smallest grains turbulent disersion must be considered to mirror their trajectories. Tyical velocity range within suerheater bundles is 5-15 m/s. Tyical temerature of flue gas in this area varies from 500 to 1000 C. All these highly variable features must be modeled accordingly since they constitute quite different conditions resulting in various history of deosits formation. Practical observations indicate that owdery deosit are formed by articles smaller than 30 microns, while bonded deosits may also include large articles in the form of matrix filled with small articles (Laursen and Frandsen, 1999). MODELING OF DEPOSITION ON SUPERHEATERS IN COAL-FIRED BOILERS Constant rogress in numerical methods results in wide range of utility alications including comutational fluid dynamics (CFD) codes, such as Fluent, solving thermal and flow issues. This comutational tool may be also alied for redicting fouling henomena occurring at heating surfaces of ower boilers. Some examles of using Fluent code for this urose can be found in ublications (Huang et.al., 1996), (Yilmaz and Cliffe, 2000), (Kaer et.al., 2005), (Tomeczek and Wacławiak, 2009). This work resents a summary of two-dimensional CFD modeling of deosition 294

2 Waclawiak and Kalisz / Using of Fluent Code to Predict Deosition of various kinds. Slagging and fouling are comlex henomena. The shae of deosit, its comosition and deosition rate are influenced by a number of factors and the major influence is associated with comosition and article size distribution of original mineral matter in the fuel as well as the gasdynamic and thermal conditions in the flue gas duct. Alhough it is unlikely to describe recisely all kinds of deosition mechanisms, some attemts can be made. In this aer 3 formation mechanisms were analyzed contributing to build u of owdery (loose) and bonded deosits. In the latter case either by condensing salts or by lastic (sticky) ash articles. The basic equation (Eq. 1) for each deosition flux includes mass flow rate m of articulate matter striking the deosition surface A and the angle of imaction.. d m m f, A Pf sin( ) (1). da The real suerheater is a tube bank comosed of several tube rows. Nevertheless, in order to shorten the comutational time, the mesh shown in Fig. 1 has been reared. The mesh is a simlified 3-tube reresentation of an in-line (arallel) real tube bank array. Such a size limitation is sufficient for quantitative and qualitative modeling of fouling at all sides of tubes in the bank, nevertheless the flow direction. It must be stressed that the mesh allows for the study of the influence of neighboring tube rows. For instance, it is ossible to study the trajectories of articles rebounding from the neighboring tube rows. In case of ower boilers where the deosit is in macro scale, with its height of u to tens centimeters and is built with majority of grains of more than m in diameter, the inertia lays the major role in article transort, so the mesh can have larger cells. Esecially, because of the dynamic mesh otion, the cells should be larger in order to avoid the negative volume error. Fig. 1. Mesh for modeled in-line suer heater tube bank. Powdery deosits Regarding owdery, loose deosits it is assumed that deosition is governed by inertial imaction and subsequent cature of certain fraction of articles at the deosition surface (Fig. 2). In contrast to wet imaction it could be called dry imaction. The cature condition is a fulfillment of a vectorial equation of forces affecting the article on imact (Eq. 2). These forces are the normal elastic rebound force F s,n, Van der Waals adhesion force F vw and normal comonent of gravity F G F s, n ( F vw F G ) The gravity force may enhance or hinder the article cature deending on the flue gas flow direction. For the secific case of owdery deosits the robability of deosition P f has been calculated uon the following assumtions: P f 0, if ( FS, n ( FVW FG, n ) (3) 1, if ( F ( F F ) S, n VW G, n Combustion gas (N 2, CO 2, O 2, H 2 O) imacting ash articles surface of tube&deosit F S,n F G suerheater tube m F VW T A F G,n Fig. 2. A schematic view of the owdery deosition. Equations of forces needed for calculating robability P f have been taken after an author of a book in Russian (Tekenov, 1985). The author exlains that in a zone of contact between grain and surface some microscoic deformation takes lace which results in reaction called a rebounding force. The equations were cited later in a ublication (Pronobis, 1986) together with further considerations on fouling. The normal elastic rebound force is given as F Kd w S, n where: K is a roortionality constant deending on elasticity of article and deosition surface. In order to obey the relationshi F s <F g for smaller articles and F s >F g for larger articles, an effort has been (2) (4) 295

3 Heat Exchanger Fouling and Cleaning 2011 made to develo an own aroach linking constant K with article diameter d in the following form d n K ( d ) G( ) dref (5) where: G is a constant, d ref is a reference diameter and n is an exonent, which should be assumed and tested in the course of comutational runs to verify their correctness in redicting the deosit height. The Van der Waals force is calculated uon F VW Bd 2 6 where: B is a molecular interaction constant and is a distance between article and deosition surface. The gravity force affecting article is given by (6) a) y, m b) c) 1 h 2 h 15 h 28 h 32 h Tube 0,03 0,02 0,01 0,00-0,05-0,04-0,03-0,02-0,01 0,00 0,01 0,02 0,03-0,01 deosit height, mm x, m -0,02-0,03 simulation measured time, h F G 1 = πd 6 3 ρ g where: g is gravitational acceleration. In another aer (Bouris and Bergeles, 1996) a similar aroach describing deosit formation by the imactadhesion model is resented, this time using the energy balance at the oint of imaction and consider the material roerties of the article and surface. Formation of loose deosits requires only major flue gas constituents to be considered (vol.%): CO 2 =13.6, O 2 =4.7, H 2 O=10.0, rest N 2. The velocity of flue gas has been 7 m/s and its temerature in the range of C. The concentration of fly ash in the flue gas ranged from 6 to 8 g/m 3. The initial velocity of articles was equal to flue gas velocity. From results reorted by Kalisz and Pronobis (2005), the steam reheater was chosen for modeling. It is an in-line arranged heating surface comosed of d t =51 mm horizontally aligned tubes, with transverse and longitudinal itches s 1 /d t =1.68 and s 2 /d t =1.49. The article-laden flue gas flows downwards following the gravity force direction. The deosit height measurement was carried out at the uwind side of the first, uer tube in the bank. The maximum height was reorted to be 12 mm after about 32 hours of deosition. For numerical rediction of fouling the assumtions were made: flue gas temerature 550 C and the surface temerature 440 C. In order to roduce the exected deosit growth, in Eq. (5) describing constant K in the elastic rebound force, the reference article diameter was set as d ref = 20 m, the exonent n=2 and G=1. The modeling results are shown in Fig. 3, i.e. the shae and the rogress of fouling. (7) Fig. 3. Shae of redicted deosit on the steam reheater tubes of the modeled boiler after 32 hours of oeration (a), change of the shae (b) and deosit height (c) on the first tube vs. time of oeration. Bonded deosits - lastic ash articles mechanism In case of deosits made from lastic, soft ash articles, efficiency of deosition P f of articles on a surface of tubes deends only on their temerature and is given by Eq. (8) 1, for T Tsoftening Pf (8) 0, for T Tsoftening where: T softening can be comuted by correlations resented by Seggiani and Pannocchia (2003) or measured by standard or new (Wall et.al, 1998) methods. A schematic view of roosed mechanism used in the modeling is resented in Fig. 4. Basic mechanism describing formation of lastic ash deosits is inertia. Ash articles move close to the tube surface, strike it and stick forming deosit there. Crucial factor in this mechanism is temerature of ash articles. In modeling of deosition of soft, lastic ash articles the flue gas consists of 4 comounds (% vol.): CO 2 =14, O 2 =5, H 2 O=10, N 2 (rest). Flue gas and ash articles velocity is 10 m/s. Gas and ash temerature is 1300 C, and it was assumed that the ash articles are lastic and erfectly (i.e. all) stick to the surface if only the threshold temerature is exceeded. Ash concentration in the flue gas is 6 g/m 3, article size distribution obeying Rosin-Rammler equation is characterized by d min =5 m, d mean =40 m, d max =200 m, and olydisersion arameter n=0.8. Temerature of the tube surface is 527 C. Calculations were done for a recurrent 3-tube section of laten suerheater with tube arrangement described by relative itches s 1 /d t =5, and s 2 /d t =1.2. Tube diameter was 38 mm. 296

4 Waclawiak and Kalisz / Using of Fluent Code to Predict Deosition Flue gas (N 2, CO 2, O 2, H 2 O) More on this simulations can be found in (Wacławiak and Kalisz, 2010). imacting ash articles 1 h 2 h 3h Tube 4 h 5 h 0,02 bouncing off ash articles surface of tube or deosit m suerheater tube y, m -0,10-0,09-0,08-0,07-0,06-0,05-0,04-0,03-0,02-0,01 0,00 0,01 0,02 0,03-0,01 Fig. 6. Shae of redicted deosit on the first suerheater tube vs. time of oeration. 0,01 0,00-0,02 x, m 1 h 2 h 3 h 4 h 5 h T Fig. 4. A schematic view of deosition mechanism from lastic ash articles. During the modeling it was assumed that the forming deosit had a high aarent density of 2200 kg/m 3. An examle of the simulations is shown in Figs. 5 and 6, where the deosit on the first tube grew to nearly 74 mm after 5 h of simulated oeration. A temerature, K faces of the erihery Fig. 7. Predicted surface temerature of deosit on the first suerheater tube vs. time of oeration. Bonded deosits - condensation mechanism Fig. 5. Shae of redicted bonded deosit formed by lastic ash articles on the suerheater tubes after 5 hours of oeration. As it can be seen in Fig. 5 in few hours, it is retty close to a moment when the sace between the tubes is filled u with the ash articles The change of the shae leads to a change in temerature of the surface, which is shown in Fig. 7, where faces of the erihery are counted from the right, rear sot, from 1 to 30 clockwise. This kind of deosit grows the fastest, because all the articles build it u. In a aer by Tomeczek et.al (2004) one of ossible mechanisms exlaining how bonded deosits are created was resented. Authors assumed that as the flue gas cools down flowing through suerheaters, the condensing salts (KCl, NaCl, K 2 SO 4, Na 2 SO 4 ) diffuse towards the tube surface and condense there. This creates conditions for the solid ash articles to deosit. The articles aroaching the surface may rebounce or stick to it, forming deosit. The resence of a sticky layer, formed by condensed vaors, is required for the solid articles to stay on the surface (Fig. 8). As the deosit grows, its temerature increases, slowing the condensation rocess. This eventually terminates the deosition rocess. In case of bonded deosits the robability of the solid articles to remain on the surface P f is roortional to the flux of condensing vaors: c,a P f S m, (9) where constant S must be estimated on basis of final deosit size formed on a single suerheater tube as shown by Tomeczek et.al. (2004). It could be comuted by aroach similar to wet imaction. However, it is not straightforward. In reality the condensing salts roduce a layer which cannot grow thick, because of the gravity, tube 297

5 Heat Exchanger Fouling and Cleaning 2011 shae, influence of the flue gas, so the thickness of the layer is unknown. Moreover, when the deosit begins growing the surface conditions are not defined in the way as they are defined during laboratory exeriments. Also the ash articles having jumed off the surface are artially wetted, so the conditions for next imactions will change as well. Flue gas (N 2, CO 2, O 2, SO 2, H 2 O, KCl, NaCl, HCl, K 2 SO 4, Na 2 SO 4 ) ash articles condensing salts tube-deosit surface m d,kcl, NaCl, K2SO4, Na2SO4 m ash suerheater tube T Fig. 8. A schematic view of deosition with the condensation henomenon. The flux of condensable gaseous i-th comonent of artial ressure i, diffusing through the tube boundary layer towards the surface area and condensing later on it can be calculated by equation i s,i mc, A,i i g, (10) where: s,i - saturation ressure of i-th comonent, - flue gas ressure, and i - mass transfer coefficient of i-th comonent, calculated using the Sherwood number, diffusion coefficient D i and tube diameter d t, where: i ShD i / d t. (11) Surface temerature is calculated from known heat flux to the surface and assumed deosit heat transfer coefficient. Pressure i in Eq. (9) must be taken for the gas stream outside the boundary layer of the tube. The saturation ressure for the otassium and sodium salts was calculated by formula s, i n ex( Ai Bi /( T Ci )), (12) where the A i, B i, C i constants are given in Tomeczek and Wacławiak (2009) and n =10 5 Pa. In order to test this model in a two-dimensional geometry 10 gaseous comounds of flue gas were considered (vol.): CO 2 =13.6%, O 2 =4.7%, H 2 O=10%, SO 2 =500m, K 2 SO 4 =3.5m, Na 2 SO 4 =1m, A KCl=18m, NaCl=15m, HCl=9m, rest N 2 ; inlet velocity for flue gas and ash articles- 8 m/s; inlet temerature of the flue gas and ash articles 1000 C, temerature of tube surface- 527 C; ash articles size distribution by Rosin-Rammler: minimum diameter- 1 m, maximum diameter 200 m, mean diameter 40 m, and olydisersion arameter 0.80; deosit density 850 kg/m 3 ; deosit heat transfer coefficient 1.0 W/m K; ash concentration in the flue gas 2 g/m 3. Basically, the shae of the deosits is similar to that shown in Fig. 5. To imrove this model it is required to find out more recise data on true contents of the alkali salts in the flue gas and deosit growth in shorter eriods of boiler oeration. SOME ASPECTS OF USING FLUENT CODE The Fluent itself does not include deosition model. Only the Discrete Phase anel let a user comute in ostrocessing the Accretion/Erosion rate which is in case of accretion, simly the flux of the solid matter striking the surface of any obstacles. However the deositon (accretion) rate can be modified by DEFINE_DPM_EROSION, which is a user defined file available for the code. The trajectories of ash articles are solved by Fluent code in a Lagrangian aroach including inertia, hydrodynamic drag, the force of gravity and otionally other forces like thermohoretic, Brownian, Saffman s lift. In order to redict trajectories of small articles it is ossible to inlcude the disertion of the articles because of the turbulence. It can be done by means of Discrete Random Walk model or article cloud tracking. The deosit growth can be modeled with Fluent dynamic mesh otion. This feature allows the user to change, move the grid vertices indeendently, simulating formation of the deosits. This change makes continuous calculations ossible, however the movement in one ste must be restricted and the changing face cannot overla the neighboring face (Fig. 9), otherwise an error- negative volume, terminating the calculations occurs. Basically the movements are indeendent although a vertex drags two faces while moving. Because of the movement the most suitable grid for this kind of modeling seems to be a grid with triangles (Fig. 1). Nevertheless, ossible drawbacks are lower accuracy for solving thermal and flow issues. Each described mechanism of deosition is modeled with DEFINE_DPM_EROSION rocedure, where the Eq. (1) is imlemented. This most imortant rocedure defines deosition flux by using mass flowrate of ash articles, area of the face being hit by the articles, and an angle of imaction. Uon assumtion of time and deosit density one can calculate the growth of the deosit for each face hit by the articles. This leads to a shift of the vertices of each face in DEFINE_GRID_MOTION rocedure. In some models the surface temerature may be crucial, for instance for bonded deosits described by condensation mechanism. For all models the temerature is required to comute heat transferred from the flue gas to the steam or water in the tubes. The forming deosit insulates the tube, so the new surface temerature is worked out and modified in the rocedure DEFINE_PROFILE. 298

6 Waclawiak and Kalisz / Using of Fluent Code to Predict Deosition a) rime mesh c) the vertex moved too far b) allowed shift of the vertex overlaing faces- negative volume NOMENCLATURE A area, m 2 d diameter, m D diffusion coefficient of i-th gaseous comonent through flue gas, m 2 /s F s,n normal elastic rebound force, N F vw Van der Waals adhesion force, N F G gravity force, N m mass flux, kg/s m 2 ressure, Pa P f deosition robability, dimensionless s 1, s 2 transverse, longitudinal itch of tube bundle, m Sh Sherwood number, dimensionless T temerature, K w erendicular comonent of imaction velocity, m/s mass transfer coeffcient, m/s angle of imaction, density, kg/m 3 Fig. 9. Allowed and incorrect movement of face vertices. CONCLUSIONS This work is a survey on modeling deosit formation with use of 3 deosition mechanisms. The modeling is aiming at imroving the thermal and flow calculations of steam heaters in boilers. Currently there are rare examles of redicting the shae of deosits on steam heater tube bundles in ower boilers. The develoment of numerical methods and the availability of CFDs rograms are a chance to obtain answers on otimal sacing of tubes in suerheaters, flow velocities, article size distribution of ash, gas comosition so as the formation of deosits during boiler oeration is roerly controlled. The basic feature of the Fluent software which makes rediction of deosit formation ossible is dynamic mesh, that is, ossibility to change the osition of the vertices at the grid during comuting. Nevertheless, this feature sometimes lead to negative volume error, as a vertex is moved too far and overlas any side face. The following modeling aroaches are roosed in resent work: 1. In the case of owdery deosit equations of elastic rebound, adhesion and gravity forces were considered. Balance of these forces determines whether ash article remains on the surface and builds the deosit or bounces off at the time of imact. 2. For deosits from lastic ash articles the characteristic ash fusion temeratures can be used to determine if the articles stick to or jum off the surface. 3. In the case of deosits bonded by condensing alkali salts, condensation of otassium and sodium salts is roosed as one of ossible mechanisms describing their formation. Such deosit forms a sticky layer roducing the binder to the imacting ash articles. Subscrit A- area c condensing f fouling g gas i i-th comonent n normal ash article ref reference s saturation t tube ACKNOWLEDGMENTS Investigations resented in this work were erformed within the frame of the Polish Strategic Research Programme on Advanced Technologies for Power Generation (contract No.SP/E/1/67484/10). REFERENCES Bouris D., Bergeles G., 1996, Particle-surface interactions in heat exchanger fouling, Journal of Fluid Engineering, Vol. 118, Huang L.Y., Norman J.S., Pourkashanian M., Williams A., 1996, Prediction of ash deosition on suerheater tubes from ulverized coal combustion, Fuel, Vol. 75, No. 3, Kaer S.K., Rosendhal L.A., Baxter L.L., 2005, Towards a CFD based mechanistic deosit formation model for straw-fired boilers, Fuel, Vol. 85, Kalisz S., Pronobis M., 2005, Investigations on fouling rate in convective bundles of coal-fired boilers in relation to otimization of sootblower oeration, Fuel, Vol. 84, Laursen K., Frandsen F.J., 1999, Classification System for Ash Deosits based on SEM Analysis, in Imact of Mineral Imurities in Solid Fuel Combustion, eds R.P. Guta et al., Kluwer Academic/Plenum Publishers, New York,

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