Cam fırını yan duvar refrakterinde oluşan korozyon ve sıcaklıkların sayısal olarak hesaplanması ve deneysel değerlerle karşılaştırılması /
Yazar: MAHMUT AYDIN
Danışman: PROF. DR. E. TANER ÖZKAYNAK
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Enerji Bilim Dalı
Derece: Doktora, 1998
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Cam fırını = Glass furnace ; Refrakter = Refractory ; Sınır elemanlar yöntemi = Boundary element method

Özet:
ÖZET Günümüzde cam fırınlarının ilk yatırım maliyetinin yüksek olması nedeniyle fırınların kampanya ömrünün mümkün olduğunca uzun olması istenir. Bundan dolayı fırın ömrünü belirleyici faktör olan refrakter aşınmasının kontrol edilmesi, işletmeci firma açısından önemlidir. Ayrıca fırının projelendirme aşamasında, öngörülen performansın gerçekleşmesi ve üretim akışını en az oranda etkileyecek programlı bakım ve onarımın yapılması gibi önemli hedefler fırın ömrünün doğru tahmin edilmesine bağlıdır. Piyasadaki ticari cam fırınlarında oluşan refrakter korozyonunun kontrol edilmesi için en etkili yöntem, refrakter dış yüzeyinde uygulanan etkin hava ve su soğutmasıdır. Bu çalışmada, dış yüzeyinden hava soğutulması yapılan bir cam fırının refrakter duvar bloğundaki korozyon sıcaklık ve ısı kayıpları nümerik olarak hesaplanmıştır. Bu nedenle P. Hrma'nın [19] çalışmasında ortaya koyduğu aşınmanın zamana göre değişimini veren diferansiyel denklem kullanılmıştır. Duvar boyunca oluşan toplam ısı geçiş katsayısının aşınmanın bir fonksiyonu olmasından dolayı diferansiyel denklemin çözümünde sonlu farklar yaklaşımı iteratif yöntemle beraber kullanılmıştır. Farklı hız ve sıcaklıklardaki hava ile yapılan soğutmada, sıvı cam sıcaklığının ve blok kalınlığının refrakter aşınma ömrüne olan etkisi incelenmiş ve sonuçlar grafik olarak sunulmuştur. Ayrıca hesaplanan refrakter duvarı korozyon profillerinden faydalanarak bloktaki eşsıcaklık (isothermal) eğrileri elde edilmiştir. Bu amaçla probleme ait sıcaklık sınır şartlarının lineer olmaması nedeniyle, Laplace diferansiyel denkleminin çözümünde Sonlu Farklar (Finite Difference) ve Sınır Eleman (Boundary Element) metodları ayrı ayrı İteratif Yöntemle beraber kullanılmışlardır. Elde edilen sıcaklık değerleri kullanılarak hava soğutulmasıyla refrakter bloğundan çekilen ısı yükleri ve bunların zamanla olan değişimleri hesaplanmış ve sonuçlar grafik olarak verilmiştir. Son olarak, refrakter bloğunda sayısal olarak elde edilen korozyon ve sıcaklık değerleri fırın üzerinden deneysel olarak elde edilen verilerle karşılaştırılarak sonuçlar irdelenmiştir. XVI

Abstract:
NUMERICAL AND EXPERIMENTAL STUDY OF THE CORROSION AND TEMPERATURE DISTRIBUTION IN THE SIDEWALLS REFRACTORY BLOCK OF A GLASS FURNACE SUMMARY Glass is a material from which many articles are manufactured it plays an important part in daily life, industry, technology, and science. Its transparence, chemical resistance, and relatively high hardness are the reasons for its unique position. However its peculiarities, such as its brittleness and relatively high weight, must be borne in mind when considering its applications. All glasses are manufactured from carefully selected raw materials, referred to as batch, being melted in furnaces and then manufactured into the desired articles. The manufacturing processes vary widely according to the quantities of glass required. In consequence, melting capacities of individual furnaces also vary widely, covering a range from 100 kg/day for special glasses up to 800 t/day for flat glass. There has been a steady improvement of furnace performance over the years and much of this can be attributed to improved refractories. The processes by which refractories are corroded in contact with glass are now largely understood. It has been clearly demonstrated that the solution of refractories below glass level is a diffusion controlled process, and that the disturbance of the diffusion barrier leads to the increased rates of attack, such as flux-line corrosion and upward drilling. Of course, these processes are also temperature dependent and the higher the temperature at a given point, the faster the reaction proceeds. The flow past the side walls of a tank furnace is affected by density currents, due to refractory solution and temperature, which are modified by the pull on the tank. At the flux-line the glass is pulled up into the meniscus above the general glass level by surface tension forces and the increased rate of attack at this point is caused by the stirring action brought about by a surface tension gradient. This stirring action has been clearly demonstrated in* a mathematical model of the system. In the model, driving force is taken as a function of surface tension gradient developed as a result of the solution of the refractory. The flux-line corrosion of current refractories is considerably faster at glass-melting temperature than that of below the glass level. Accordingly, the corrosion below the glass level is not considered with a special care. However, this is not the case when the cooling is taken into account. If the wall thickness has been considerably reduced owing to the developed corrosion, the cooling may essentially diminish the temperature of the inner wall surface. But from a certain temperature downward, the corrosion at the glass level (flux-line corrosion) becomes slower than that below it, as it is the corrosion for a lower temperature, apparent from a number of experimental observations. XVIIThe most important factors governing the rate of corrosion of glass furnace sidewalls are: (1) bouyancy convection produced by changes in density resulting from the concentration gradients connected with the dissolution process; (2) throughput and circulation flows inside the furnace; (3) surface convection induced by the concentration gradient at the glass-melt interface. The surface convection brings about either flux-line corrosion or upward drilling by bubbles trapped in horizontal joints or cracks. The impact of these factor is modified by the lack of uniformity of the temperature field in the furnace, wall inhomogeniety, and outer cooling or insulation of the walls. The problem investigated in this thesis can be studied only by means of mathematical modelling because of its complexity. Although the model presented in this thesis covers most of the above factors for the flows mentioned in (2), upward drilling and wall inhomogeneity are not included. However, the flows mentioned in (1) and (3), that is the flows induced by concentration gradients either within the melt or on its surface, are taken into account. The model thus represents the situation in which homogeneous furnace sidewalls without horizontal joints or cracks (so that no bubble can be trapped) are dissolved by a melt in which buoyancy convection connected with the corrosion process prevails over the throughput and thermally induced circulation flows. The analysis of the Hrma [9] leads to X -Yt = f,(l + jf2dÇ)-1/4 (1) where Y is the wall thickness, subscribt t indicates, the time derivate of Y, hence Y( is the dissolution rate, and fi and f2 are functions defined by f, = K, exp(-e,/Ti + e1F/TF) (2) and f2 = K2 exp(-e2/Ti + 92F/TF) (3) where Ti is the temperature at the melt/wall interface, TF is the value of Ti at x = 0, and Ki, K2, 9], 92 are coefficients determined by the material properties of both melt and wall. Eq.(l) also involves the flux-line corrosion as a source and the dissolution rate at x = 0 is not, therefore, infinite but has a finite value of fi. The temperature at the melt/wall interface is determined by the bulk temperature of the melt and the rate of heat transfer through the wall. For simplicity, the temperature field inside the wall is assumed to be one dimensional. Thus the temperature of the melt/wall interface is Ti = TM-(TM-TA)(U/h,) (4) XVIIlwhere U = (hf1 + Y/k + hE1)- (5) Eq.(5) is the overall heat transfer coefficient, hi and hE are the melt/wall and wall/ambient heat transfer coefficients, TA is the abient temperature, and k is the heat conductivity of the wall. TM is the melt temperature and function of the depth of the glass. If TM, TA, hi and k are given, Ti may be controlled by hE (Fig. 1), that is by cooling or insulating the wall; in addition, T; also depends on the wall thickness, Y. Eqs.(l) and (3) are coupled and can not be solved independently. Eq.(l) was transformed in the finite difference form and was solved numerically using a time increments of 0.25 month. The integral in Eq.(l) evaluated by using the trapezoidal rule. y.* Figure 1 Refractory has a initial wall thickness of Y0, temperature distribution Tm on the surface and heat transfer coefficient, k In the computer program 10"6 % accuracy for all variables was taken. After solving Eq.(l), corrosion profiles of the refractory was found. In order to find the steady-state temperature distribution in the refractory by using corrosion profile at time t, Finite Difference Method is employed with iterative method due to non-linear temperature boundary conditions. When the boundary of the region is not such that the network can be drawn to have the boundary coincide with the nodes of the mesh, the procedure must be different at points near the boundary. Consider the general case of a group of five points whose spacing is non-uniform, arranged in a unequal-armed star. Each distance is represented by OR h, where OR is the fraction of the standard spacing h that the particular distance represents (Fig. 2). XIXAlong the line from 9 (1-1, J) to G (I, J) to 9 (1+1, J), the first derivatives may be approximate as: dQ) _ 9(1, J) -9(1-1, J) dx 1-0 ORl-h 1.- Similarly, Figure 2 Non-lineer mesh points 09^ _ 9(1 + 1,1) -6(1, J) 3xy 0-3 OR3h d2Q d (dÖ\ Consdenng - T = T-[-T' dx2 dxydxJ d2Q dx2 6(I-1,J)-9(I,J) 6(1 + 1, J) -9(1, J) ORl(ORl + OR3) + OR3(ORl + OR3) (6) Similarly, d2Q dy2 9(I,J + 1)-9(I,J) 9(I,J-1)-9(I,J) OR2(OR2 + OR4) OR4(OR2 + OR4) (7) The expressions in Eqs.(6) and (7) have errors 0(h). Combining Eqs.(6) and (7) in the Laplace Eq. (8), we get: V29 d2Q d2Q dx2 dy2 (8) XXv2e = 6(1-1, J) + ¦ e(u + i) + ¦ 9(1 + 1, J) 0R1(0R1 + 0R3) OR2(OR2 + OR4) OR3(ORl + OR3) 8(I,J-1) f 1 1 + OR4(OR2 + 0R4) V0R1 OR3 OR2 OR4 e(i,J) (9) In order to solve the Eq.(9) in the region described in Fig. 3, associated temperature boundary conditions of the problem is given in the following equations. y.+ 62 Figure 3 Cross-section area of cooled refractory wall in contact with glass a) Due to insulation between A and B points, 829 ox 0 (10) b) The boundary condition in the combustion region between B and C points, 9 = 9V (ID c) Region, between C and D points (refractory block contact with melted glass) e = eM(x) (12) d) The boundary condition between D and E points, 59 gs2Th /A4 dy+ k(9) (e^ - l)= 0 (y-direction) (13) XXI50 crs2Th3 / A \ & + ~m~(Bd ~ V = ° (x-directIon) (14) e) The boundary condition at the region between E and F points 00 OE,Th3 i. \ f) Last boundary condition, can be written between F and A points, where 9d, dimensionless temperature at the outside of the isolation material, a, Steffan-Boltzman constant (5.67x1 0"8 W/m2K4), Si, emissivity coefficient of the refractory material, e2, emissivity coefficient of the isolation material, Th, ambiant air temperature (K), h, convection coefficient of the air-jet (W/m2K) Eq.(9) is to be solved numerically by using Finite Difference Method with boundary conditions given above. Due to non-linear terms in the boundary conditions, iterative method is employed in combination with Finite Difference Method. For this purpose, a suitable computer code is written. The code starts the iteration with an arbitrary temperature profiles and run until obtaining the accuracy value (10"6 %) for all variables. After that, temperature distribution obtained in the mesh points of the refractory block is utilized to see the cooling effect which is applied outside of the refractory. For this purpose, outside of the refractory is completly insulated against the heat transfer, in this case heat transfer (qO stored per weight is defined by Eqs.(17) and (18): MM LL MM LL X 2>i(U)=Z I Th (9,(1, J) -1.0) (17) 1=1 J=l 1=1 J=l and j MM LL q; = rr Z Z Aei(i,j)cp(ei) (is) 1N 1=1 J=l where XXIIA6i, temperature difference in the refractory block (K), 8j, dimensionless temperature in the refractory block, Cp, specific heat value (J/kg°C), N, total number of the mesh points, MM, total number of mesh points at the y-direction, LL, total number of mesh points at the x-direction, Th, ambiant temperature (K) On the other hand, at the different air blowing velocity, one can obtain the stored heat transfer (q0) per weight of the refractory [19,20]. MM LL MM LL 2 2>(I,J) =2 X Th(9(I,J)-1.0) (19) 1=1 J = l 1=1 J=l and, MM LL qo=TrE £ A9(I,J)Cp(9) (20) 1N 1=1 J=l where A9, temperature difference appeared in the refractory block at the certain blowing air velocity (K), 9, dimensionless temperature appeared in the refractory block at the certain blowing air velocity Finally, in order to obtain the heat transfer between air-jet and refractory block, it is possible to following equation: Aq = qi-q0 (21) In order to remove the assumption and perform a better approach, at the boundary of the refractery block contacted with melted glass and compare finite difference results with different numerical method, Boundary Element Formulation is applied to find the steady-state temperature distribution in the refractory block. Some general principles of boundary element solution in 2-D should first be considered. 5 = $ on T, (23) and natural boundary conditions q = q = - on T2 (24) on The weighted residual statement is formed as: J(v2 $) (x-x^)nx+(y-y^)ny - In r - TA - ^ 271 ' " 27t V r-r* df = 0 (32) where and.(j) on r, 9 = 1 - [§ on r2 or in Q fq on T2 Iq on Tj (33) (34) If the point r( is on the boundary, there is a fractional constant multiplied by $(r£)inEq.(32). Usually Eq.(32) is written as c*fe)+^l 2%' I " | ~(r-r^)n qln|r-r^|-(j) ^ _ r-r, dr = o (35) where Ct 1 for f| gQ, gT 1 - a / 271 for rp e T (36) Now, it is the time to discretize Eq. (35) into a system of elements on the boundary. It proceeds by breaking F down into distinct segments (Fig. 5), and defining an assumed functional behavior of § and q over each segment. XXVApproximation to fy on any particular element will be detoned by (j) e. Each elements functional formulation will be: M m=l (37) where c[)e is the value of $ at node m, and Nm is the shape function associate with node m. M denotes the number of nodes in the element. Figure 5 The discretization of the boundary into "E" elements (each denoted as re) For the regular linear element, 0>)-- 2İÎ 2ti e=l (r-r,)-n K *( Vre |r-rJ s'l 1- - 'e V Ley dr+isp-; (f-r^)n S I2 L ar (40) From Eq.(40), each linear element passes contributions to each of its nodes in a manner prescribed by the shape functions. Note that node 1 of element "e" is node 2 of element "e-1", as described in Fig. 7. e+1 Node 1 of "e" Node 2 of "e-1" e-1 Figure 7 Illustration of nodal connectivity between elements In order to solve Eq.(40) in the refractory block depicted in Fig. 3, corrosponding temperature boundary conditions of the problem is given by Eqs.(10) through (16). Due to non-linear terms in the boundary conditions, boundary element Eq. (40) is solved iteratively by using Boundary Element Method. Finally, in order to test the mathematical models, the numerical results of the corrosion profiles of the refractory block and temperature values obtained by using Finite Difference and Boundary Element Methods are compared with the experimental data taken on the glass furnace. Both methods gave similar results confirming the correctness of the approach. XXVII