METALLURGY AND FOUNDRY ENGINEERING Vol. 35, 2009, No. 2 Krzysztof Krczewski* APPLICATION OF WATER EQUIVALENTS METHOD TO CALCULATION OF CERAMIC HEAT EXCHANGERS Nottion: c het cpcity of ir, kj/(m 3 K), c g het cpcity of furnce gs, kj/(m 3 K), D, d dimeter, m, ε het effectiveness, F heting surfce re, m 2, k over-ll het-trnsfer coefficient, W/(m 2 K), N Number of Het Trnsfer Units, T, t temperture, K, o C, V volumetric rte of fluid flow, m 3 /h, m 3 /s, W wter equivlent of ir, W/K, W g wter equivlent of furnce gs, W/K. 1. INTRODUCTION Cermic recupertors re used for the recovery of het from wste gses with industril het furnces nd glss tnks [1, 2, 3, 5]. In ZM Ropczyce [10] production of new genertion mgnesi shpes to cermic recupertors ws developed nd included to glss furnces. On ccount of mteril costs the cermic recupertor re clculted by mthemticl * Ph.D.: Fculty of Metls Engineering nd Industril Computer Sciences, AGH University of Science nd Technology, Krków, Polnd; e-mil: ztc@gh.edu.pl 137
method to chieve required construction nd service chrcteristic for miniml number of shpes. For clcultion of cermic recupertor mde of new genertion shpes the blnce method were elborted [5]. In clcultion of het exchngers the wter equivlents method is very importnt [7, 8, 9]. This method is more universl thn blnce method. The im of this pper is presenttion of mthemtic model nd clcultion lgorithm by wter equivlents method the cermic recupertor mde of mgnesi shpes. 2. SIMILARITY FUNCTION USED TO CALCULATE THE HEATING SURFACE OF CROSS-FLOW CERAMIC HEAT EXCHANGERS Cermic recupertors belong to cross-flow het exchngers group. The wter equivlent method enbles to clculte the construction prmeters of het exchngers. In recupertors recovered furnce gs from industril furnces wter equivlent of furnce gs is: W g = V g c g V g volumetric rte of furnce gs flow, het cpcity of furnce gs. c g (1) Wter equivlent of ir is: W = V c V volumetric rte of ir, het cpcity of ir. c (2) Wter equivlent of furnce gs is bigger thn ir wter equivlent: W g > W (3) The similrity function (Fig. 1) used in cross-flow het exchngers is [4, 9] expressed by eqution: Wg ε= f,n (4) W t t ε= tg t t ir preheted temperture outlet, t ir temperture inlet to recupertor, t g furnce gs temperture inlet to recupertor, N Number of Het Trnsfer Units. (5) 138
) b) Wg Fig. 1. Similrity function ε= f,n used in cross-flow exchngers [9]: W ) prllel flow; b) counter flow The Number of Het Trnsfer Units is the mesure of het surfce re nd is expressed by eqution: kf N = W k over-ll het trnsfer coefficient, F het trnsfer surfce re, W wter equivlent of ir. (6) 139
3. THE CALCULATION OF CERAMIC HEAT EXCHANGERS BY WATER EQUIVALENT METHOD The proposed lgorithm of clcultion of cermic recupertor consists eqution. The volumetric rte of ir outlet from recupertor is = 1 n where n untight of ir chnnel. (7) The rithmetic men of volumetric rte of ir + = 2 The bsolute untight of ir equls Δ = The volumetric rte of furnce gs outlet from recupertor is V = V +ΔV g g (8) (9) (10) The ir wter equivlent is W = c where c het cpcity of ir. (11) The rithmetic men of volumetric rte of furnce gs is V g Vg + Vg = 2 The furnce gs wter equivlent equls (12) Wg = Vgcg (13) where c g het cpcity of furnce gs. The microfinned surfce re of cermic recupertor is NW F = k N Number of Het Trnsfer Units, W wter equivlent of ir, k over-ll het trnsfer coefficient. (14) 140
4. THE CALCULATIONS OF CERAMIC RECUPERATOR TO GLASS TANK The cermic recupertor uses het of wste gs from glss tnk. Preheting in recupertor ir is used directly in combustion of fuel. The recupertor works in cross-flow nd hs the following prmeters: volumetric rte of ir V = 1000 m 3 /h (0.278 m 3 /s), inlet ir temperture t C, outlet ir temperture t C, volumetric rte of furnce gs inlet to recupertor V g = 1200 m 3 /h (0.33 m 3 /s), inlet furnce gs to recupertor t g = 1300 o C. The recupertor mde of mgnesi shpes illustrtes Figure 2 with the following dimensions: outer dimeter of tube D = 0.187 m, inner dimeter of tube d = 0.145 m, thickness of tube wll s = 0.021 m, totl height h = 0.312 m, height of het element h 1 = 0.232 m, pitch of shpes p = 0.11 m. Fig. 2. Mgnesi M98G recupertor shpe 141
The volumetric rte of ir inlet to recupertor is: 1000 3 3 = = = 1176 m /h (0.327 m /s), 1 n 1 0.15 where n untight of ir chnnel. The rithmetic men of volumetric rte of ir is: + 0.278 + 0.327 3 = = = 0.303 m /s. 2 2 The bsolute untight of ir equls: 3 Δ = = 1176 1000 = 176 m /h. The volumetric rte of furnce gs outlet from recupertor is: 3 3 V = V +Δ V = 1200 + 176 = 1376 m /h = 0.382 m /s. g g The ir wter equivlent is: W = V c = 0.303 1350 = 409.1 W/K, where het cpcity of ir c = 1350 J/(m 3 K). The rithmetic men of volumetric rte of furnce gs equls: V g Vg + Vg 0.333 + 0.382 3 = = = 0.358 m /s. 2 2 The furnce gs wter equivlent is: Wg = Vg cg = 0.358 1640 = 587.1 W/K, where het cpcity of furnce gs c g = 1640 J/(m 3 K). The simplex of wter equivlent is: Wg 587.1 1.44. W = 409.1 = 142
The het effectiveness of recupertor is expressed by eqution: t t 600 20 ε= = = 0.45. t t 1300 20 g The Number of Het Trnsfer Units by Figure 1b is N = 0.8. The over-ll het-trnsfer coefficient is k = 7.5 W/(m 2 K). The surfce re of recupertor is NW 0.8 409.1 2 F = = = 43.6 /m. k 7.5 The number of shpes in recupertor equls: F 43.6 L = = = 321, dmitted 336. f1 0.136 The het surfce re [10] of cermic shpe is f 1 = 0.136 m 2. The recupertor row of shpes in lger is: x y = 8 7 = 56. The number of rows on height of recupertor equls: L 336 z = = = 6. 56 56 The cermic het exchnger chmbers over-ll dimensions re the following: length 8 0.187 + 8 0.11 = 2.4 m, width 7 0.187 + 7 0.11 = 2.1 m, height 6 0.312 + 0.52 = 2.4 m. The het surfce res clculted by blnce method [6] is 45.3 m 2. The het surfce re clculted by wter equivlents method is 43.6 m 2. The differences of surfce is: 45.3 43.6 Δ= 100% = 3.8%. 45.3 The cermic recupertor to glss tnk using Glsmg M98G mterils illustrtes Figure 3. 143
Fig. 3. Cermic recupertor to tnk furnce 5. INFERENCES Cermic exchngers using energy of flue gses from glss melting furnces on ccount of high-temperture, dust, nd therml shocks work in very difficult conditions. The service life of glss melting tnks is determined by effectiveness of het exchngers. Therefore new models of cermic recupertors mde of mgnesi or luminmullite-zircon shpes re introduce into service. By wter equivlents method mthemtic model nd lgorithm of clcultions the recupertors mde of mgnesi shpes were elborted. This model mkes possible to define recupertor s design: over ll dimensions, het surfce re nd lttice work of shpes. By the model cermic recupertor to glss melting tnk were clculted. The difference of het surfce res clculted by blnce method nd wter equivlents method is 3.8%. REFERENCES [1] Krczewski K.: Metllic Recupertors to Glss Tnks, Technicl University of Kosice, Kosice, 1998 [2] Krczewski K.: Wp³yw mikrou ebrowni powierzchni równoleg³opr¹dowych rekupertorów metlowych n ich cechy konstrukcyjne i eksplotcyjne, UWND AGH, Krków, 2000 144
[3] Krczewski K.: Foundry nd Metllurgy Engineering, 29 (2003) 47 65 [4] Krczewski K.: Obliczeni cieplne rekupertorów metlowych dl pieców przemys³owych, UWND AGH, Krków, 2004, SU 1667 [5] Krczewski K.: Metllurgy nd Foundry Engineering, 32 (2006) 47 65 [6] Krczewski K.: Metllurgy nd Foundry Engineering, 34 (2008) 39 50 [7] Mikheyev M.: Fundmentls of Het Trnsfer. Mir Publishers, Moscow, 1968 [8] Senkr T.: Obliczeni pieców grzewczych w hutnictwie elz, Wyd. Œl¹sk, Ktowice, 1983 [9] Tjc N.: Rszczety ngrewtielnych pieczej. Miet³³urgij, Moscow, 1969 [10] Ctlog: Glss-Mking Industry, ZM Ropczyce, 2004 Received November 2009 145