APPLICATION OF WATER EQUIVALENTS METHOD TO CALCULATION OF RADIATION RECUPERATORS WITH MICROFINNED SURFACE

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1 METALLURGY AND FOUNDRY ENGINEERING Vol. 34, 008, No. 1 Krzysztof Krczewski APPLICATION OF WATER EQUIVALENTS METHOD TO CALCULATION OF RADIATION RECUPERATORS WITH MICROFINNED SURFACE NOTATION: α c convection het-trnsfer coefficient of furnce s, W/(m K) α convection het-trnsfer coefficient (microfinned element), W/(m K) α c c het-trnsfer coefficient of furnce s, W/(m K) het cpcity of ir, kj/(m 3 K) het cpcity of furnce s, kj/(m 3 K) D, d equivlent dimeter, m F hetin surfce re, m H heiht of recupertor, m h heiht of micro-fin, m l distnce between xes of micro-fines, m r equivlent rdius, m s thickness, m k over-ll het-trnsfer coefficient, W/(m K) Δp pressure, P T, t temperture of furnce s, K, o C * Ph.D., Fculty of Metls Enineerin nd Industril Computer Science, AGH University of Science nd Technoloy, Crcow, Polnd; ztcos@h.edu.pl 39

2 T w, t w wll temperture, K, o C T, t temperture of ir, K, o C Re Reynolds Number N Number of Het Trnsfer Units Q het trnsfer rte, W q het flux, W/m V volumetric rte of fluid flow, m 3 /s W W wter equivlent of ir, W/K wter equivlent of furnce s, W/K w velocity, m/s η dynmic viscosity fctor, (k m)/s λ number of hydrulic resistnce (microfinned element) ρ density, k/m 3 Y intensifiction function. 1. INTRODUCTION Rdition recupertors re used for the recovery of het from wste ses with industril het furnces, lss furnces nd foundry ones [1 3, 5 7, 9, 1, 13]. The rdition recupertors work in rne tempertures 700 o C 1500 o C. For clcultion of this recupertors zonl model [8], sinle-zone model [11] nd universl method of clcultion [10] were elborted. In these models were pplied the results of reserch on convective het-trnsfer coefficients nd numbers hydrulic resistnce of microfinned recupertor elements. In clcultion of het exchners the wter equivlents method is very importnt [6, 9, 1, 14]. This method is more universl thn blnce method. The im of this pper is mthemtic lorithm by wter equivlents method to clcultion of rdition recupertors with microfinned surfce nd ppliction in this lorithm the model reserches.. SIMILARITY FUNCTION USED TO CALCULATE THE HEATING SURFACE OF PARALLEL-FLOW RECUPERATORS Rdition recupertors with microfinned surfce belon to prllel-flow het exchners roup. The wter equivlent method enble to clculte the construction prmeters of het exchners. In recupertors recovered furnce s from industril furnces wter equivlent of furnce s is W V c (1) 40

3 V c volumetric rte of furnce s flow, het cpcity of furnce s. Wter equivlent of ir is W V c () V c volumetric rte of ir, het cpcity of ir. Wter equivlent of furnce s is reter thn ir wter equivlent W > W (3) The similrity function is expressed by eqution W θ f,n W (4) t t θ t t (5) t ir preheted temperture outlet, t ir temperture inlet to recupertor, t furnce s temperture inlet to recupertor, N Number of Het Trnsfer Units. The Number of Het Trnsfer Units is the mesure of het surfce re nd is expressed by eqution kf N W (6) k over-ll het trnsfer coefficient, F het trnsfer surfce re, wter equivlent of ir. W 41

4 Similrity function by eqution (4) illustrtes Fiure 1 nd Fiure. W Fi. 1. Similrity function θ f,n W used in prllel-flow het exchners [9, 15] W Fi.. Similrity function θ f,n W used in counter-flow het exchners [9, 15] 4

5 3. THE CALCULATIONS OF RADIATION RECUPERATORS WITH MICROFINNED SURFACE BY WATER EQUIVALENT METHOD The proposed lorithm of clcultion of rdition recupertors with microfinned surfce lorithm consist of: equtions by wter equivlents method, similrity equtions by model reserches (9), (11), (0), (1), equtions verifyin vlue of over-ll het-trnsfer coefficient (1 19). The microfinned surfce re of recupertor is NW F k (7) N Number of Het Trnsfer Units, W wter equivlent of ir, k over-ll het trnsfer coefficient. The wter equivlent of ir is W V c, V volumetric rte of ir flow, c het cpcity of ir. The heiht of recupertor is F H Πd o (8) where d o outer dimeter of center tube. The convective het-trnsfer coefficient to ir (microfinned element) is 0.8 ( 1 )( 3.5t t ) ( D d ) α +Υ + w o 0. (9) Y intensifiction function, w velocity of ir, D dimeter of inner cover, d o outer dimeter of center tube. 43

6 The symbol t denotes ir rithmetic men temperture t + t t (10) The intensifiction function is 0.35 l h l Y 36.5 e Re h 0.36 (11) 4000 Re 1000, 5 l h 40, h > h r > 0. l micro-fin pitch, h heiht of micro-fin, h r heiht of rouhhes. The het-trnsfer coefficient of furnce s is iven by eqution: α k α (1) The weihted men temperture of microfinned center tube is t w α t+αt α +α (13) The symbol t denotes rithmetic men temperture of furnce s t t + t (14) ( ) c Vc t t t t c ξv c (15) 44

7 V volumetric rte of ir flow, c het cpcity of ir, V volumetric rte of furnce s flow, c, c het cpcity of furnce s, ξ number of losses, t furnce s temperture inlet to recupertor, t ir preheted temperture outlet, t ir temperture inlet. The het trnsfer rte is ( ) Q Vc t t (16) V c volumetric rte of ir flow, het cpcity of ir, t ir prehet temperture outlet, t ir temperture inlet. The het flux throuh recupertor wll is Q q F (17) The het-trnsfer coefficient of furnce s is α t q t w (18) The over-ll het-trnsfer coefficient is 1 k α α p (19) The pressure drop of ir is [1, 6] wρ Δ p λ H D di (0) 45

8 r λ h h l l h e (1).67 r h 16, 5 l h 40, h > h r > THE CALCULATIONS OF RADIATION RECUPERATOR WITH MICROFINNED SURFACE TO HEAT FURNACE The prllel flow rdition recupertor with microfinned surfce is instlled in het furnce. The recupertor is determined by the followin conditions: volumetric rte of furnce s flow V 1130 m 3 /h (0.314 m 3 /s), furnce s temperture inlet to recupertor t 150o C, volumetric rte of ir flow V 1030 m 3 /h (0.86 m 3 /s), ir prehet temperture t C, inner dimeter of center tube d i 1.00 m, thickness of center tube wll s m, outer dimeter of center tube d o 1.01 m, dimeter of inner cover D 1.05 m. The ir wter equivlent is W V c W/K, c 1330 J/(m 3 K). The furnce s wter equivlent is W V c W/K, c 1640 J/(m 3 K). The simplex of wter equivlent is W W 510 The temperture simplex is expressed by eqution t t ε t t

9 The Number of Het Trnsfer Units by Fiure 1 is The over-ll het-trnsfer coefficient is 33 W/(m K). The microfinned surfce re of recupertor is NW F 6.91/ m. k 33 The heiht of recupertor is F 6.91 H.0m. Πd o Π 1.00 The ir men temperture is t + t o t 60 C. The velocity of ir is w V m/s. Π ( ) Π D do ( ) 4 4 The equivlent dimeter of ir p is d h D d o m. The convection het-trnsfer coefficient (smooth center tube) to ir equls w 4.4 α o ( t) ( ) 4.8 W/(m K). d The Reynolds number in ir p is w dhρo Re 866, η h 0.04 w 4.4 m/s velocity of ir, ρ o 1.7 k/m 3 density of ir, p o 1000 hp, T o 73 K, d h 0.04 m hydrulic dimeter, η (k m)/s dynmic viscosity fctor. 47

10 The intensifiction function is 0.35 l h l Y 36.5 e Re e h The het-trnsfer coefficient of microfinned center tube is α (1 + Y) α o (1 +.19) W/(m K). The het-trnsfer coefficient of furnce s is 1 1 α 56.5 W/(m K) k α The furnce s temperture outlet from recupertor is ( ) o c Vc t t t t C. c ξv c t 150 C furnce s temperture inlet to recupertor, c 1.64 kj/(m 3 K), c 1.55 kj/(m 3 K) het cpcity of furnce s, The furnce s men temperture is t 0 o C ir temperture inlet, t 500 o C ir prehet temperture outlet, c 1.33 kj/(m 3 K) het cpcity of ir, ξ 0.9 number of losses. t o 1078 C. The weihted men temperture of microfinned center tube is t w α t+αt α +α, t w o 60 C

11 The het trnsfer rte is ( ) ( ) Q V c t t W. The het flux throuh recupertor wll is Q 1858 q 643 W/m. F 6.91 The het-trnsfer coefficient of furnce s is α 643 q 55.5 W/(m K). t t w The over-ll het-trnsfer coefficient is 1 1 k 3.5 W/(m K) α α The error clcultion of over-ll het-trnsfer coefficient is Δ 1.5%. The rdition recupertor with microfinned surfce illustrtes Fiure 3. Fi. 3. Rdition recupertor: 1 microfinned center tube, inner cover, 3 outer cover, 4 inlet chmber, 5 outlet chmber, 6 het insultion 49

12 The number of hydrulic resistnce in ir chnnel is l l h 0.0 r λ e e 0.18, h h r 0.0 m equivlent hydrulic rdius, h m heiht of micro-fin, l 0.04 micro-fin pitch. The pressure drop of ir is wρ H Δ p λ P. D do INFERENCES Wter equivlents method hs ret importnce in clcultion of het exchners. The lorithm elborted to clcultions of rdition recupertors with microfinned surfce consists of: eqution by wter equivlents method, similrity equtions nd control ones. The results of reserch on convective het-trnsfer coefficients nd numbers hydrulic resistnce of microfinned elements for rnes were pplied in the lorithm: 400 < Re < 1000, 5 < l h < 40,.67 < r h < 16, h > h r > 0. This new lorithm mde possible the projects of rdition recupertor with microfinned surfce to lss furnces nd het furnces. The work ws mde in contrct no REFERENCES [1] Krczewski K.: Zeszyty nukowe AGH, Metluri i odlewnictwo, 16 (1990), 133 [] Krczewski K.: Hutnik, 58 (1991), [3] Krczewski K.: Rdition Recupertors with Microfinned Surfce. Int. Symp. Technicl University of Kosice, 1994 [4] Krczewski K.: Metllury nd Foundry Enineerin, 4 (1998), [5] Krczewski K.: Metllic Recupertors to Glss Tnks. Technicl University of Kosice, Kosice, 1998 [6] Krczewski K.: Wp³yw mikrou ebrowni powierzchni równole³opr¹dowych rekupertorów metlowych n ich cechy konstrukcyjne i eksplotcyjne. UWND AGH, Krków,

13 [7] Krczewski K.: Metllury nd Foundry Enineerin, 9 (003), [8] Krczewski K.: Metllury nd Foundry Enineerin, 30 (004), [9] Krczewski K.: Obliczeni cieplne rekupertorów metlowych dl pieców przemys³owych. UWND AGH, Krków, 004, SU 1667 [10] Krczewski K.: Metllury nd Foundry Enineerin, 31 (005), [11] Krczewski K.: Metllury nd Foundry Enineerin, 33 (007), [1] Mikheyev M.: Fundmentls of Het Trnsfer, Moscow 1968, Mir Publishers [13] Seo K., Kim V.: Int. J. Het nd Mss Trnsfer, 43 (000), [14] Szrut J., Ziêbik A., Kozio³ J., Mjz E.: Przemys³ow eneri odpdow. Zsdy wykorzystni. Urz¹dzeni. WNT, Wrszw, 1993 [15] Tjc N.: Rszczety nrewtielnych pieczej. Moskw, 1969 Received October

APPLICATION OF WATER EQUIVALENTS METHOD TO CALCULATION OF CERAMIC HEAT EXCHANGERS

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