Research on Control Mechanism Model of Grate Cooler Based on Seepage Heat Transfer Theory

Journal of Computational Information Systems 9: 2 (213) 8281 8288 Available at http://www.jofcis.com Research on Control Mechanism Model of Grate Cooler Based on Seepage Heat Transfer Theory Bin LIU 1, Meiqi WANG 1,, Yan WEN 2, Xiaochen HAO 1, Xinfeng FAN 1 1 Institute of Information Technology and Engineering, Yanshan University, Qinhuangdao 664, China 2 Institute of Mechanical Engineering, Yanshan University, Qinhuangdao 664, China Abstract A control mechanism model of grate cooler is established by seepage heat transfer theory of porous media. This paper combines analytical method and implicit difference method to solve the control mechanism model. The calculation results obtained in the paper are consistent with the fluctuation tendency of the measured temperature and the error is small. The control mechanism model can reflected heat transfer characteristics between the cooling air and clinker in great cooler. Keywords: Cement Clinker; Porous Media; Seepage Heat Transfer; Control Mechanism Model 1 Introduction Cement grate cooler can make fast cooling of high temperature cement clinker which is discharged by cement rotary kiln, while it recovers the heat energy from high temperature clinker. At present, a backward control model and control strategy of grate cooler make energy waste and lower heat recovery efficiency. The main reason for this problem is the insufficient research for heat transfer control mechanism of grate cooler. Therefore, research on heat transfer control mechanism of grate cooler has become a hot topic. Taking the clinker in grate cooler as a continuum, Touil [1] divided finite element of grate cooler and calculated clinker cooling process numerically. Mujumdar [2] applied the heat conduction theory on heat transfer analysis of the grate cooler, he took the grate cooler as a whole and carried on overall heat balance calculation of double-input and multiple-output. Locher [3] established a control model based on the heat transfer equation of gas through the particle bed and the unsteady heat transfer equation, he studied the influence of grate speed and particle size distribution on clinker cooling process, but he didn t give the specific law of the influence of parameters on heat transfer. But it has certain limitations to use theory of convective heat transfer to analyze Project supported by the National Nature Science Foundation of China (No. 5176135) and the Science and Technology Support Program of Hebei Province (No. 12215616D). Corresponding author. Email address: mickeyysu@163.com (Meiqi WANG). 1553 915 / Copyright 213 Binary Information Press DOI: 1.12733/jcis8323 October 15, 213

8282 B. Liu et al. /Journal of Computational Information Systems 9: 2 (213) 8281 8288 heat transfer process in cement clinker. Some scholars used seepage heat transfer theory of porous media to study the control model of heat transfer equipment between gas and the accumulation of particles. Hu [4] calculated the seepage heat transfer process of high temperature gas in moving particulate bed and provided gas velocity, gas temperature and solid temperature in the bed. Li [5] established a chemical reaction and heat-mass transfer coupling control model for calcining process of limestone and the research results showed that inlet flow velocity, inlet gas temperature and solid particle size were important parameters to the system characteristics. Zhang [6] used Fluent software to simulate and optimize gas flow and heat transfer in sinter circular cooler, and got the optimal control parameters combination for goal of improving waste heat utilization. In recent years, aiming at high temperature cement clinker with porous media characteristics, Zheng [7] introduced seepage heat transfer theory of porous media into the cement clinker cooling research, basic control mechanism model was established, but he didn t solve the model. Using seepage heat transfer theory and Darcy law, Wen [8] established seepage heat transfer control mechanism model for cement clinker cooling process, and solved the model approximately with ignoring multiple factors. Although introducing seepage heat transfer theory of porous media into cement clinker cooling research has made a certain progress, effective seepage heat transfer control mechanism model of grate cooler and corresponding heat transfer law of cement clinker haven t obtained because of the difficulties for solving nonlinear partial differential equations of the complex model. A control mechanism model of grate cooler is established by seepage heat transfer theory of porous media in this paper. In the model, we take into account variable physical properties of gas and clinker, thermal dispersion effect and thermal non-equilibrium in the gas-solid heat transfer process. Seepage heat transfer control mechanism model is calculated by the combined analytical and implicit difference method. We obtain the cooling control law of cement clinker in grate cooler and verify the correctness of the control model by comparing the field measurement temperature and the simulation calculation results. 2 Model Building 2.1 Physical model As shown in Fig. 1, high temperature clinker get into grate cooler from rotary kiln. Clinker layer moves slowly on grate bed. Cooling air blows into the clinker layer vertically from the bottom of the clinker, permeates and diffuses in the clinker to cool the red-hot clinker. Cooling air becomes hot air after exchanging heat energy with clinker. Fig. 1: The schematic diagram of grate cooler Fig. 2: Physical model of grate cooler

B. Liu et al. /Journal of Computational Information Systems 9: 2 (213) 8281 8288 8283 According to cement clinker cooling condition in grate cooler, we establish the heat transfer physical model as shown in Fig. 2. On grate bed clinker particles that temperature is T get into the three-dimensional area from the left side and get out the area from the right side, cooling air that temperature is T gin flows into this area and exchanges heat energy with clinker, and then outflows from the top. In Fig. 2, x is the length direction of the bed, y is the thickness direction of the bed and z is the width direction of the bed. 2.2 Seepage heat transfer control mechanism model of grate cooler During normal operation of the grate cooler, its internal state is stable. Clinker particles and gas vertically cross flow, clinker layer moving speed is relatively slow, the gas flow and the gas-solid heat transfer in the thickness direction are the main factors. According to the law of conservation of mass, gas continuity equation can be described as: (ρ g V y ) = (1) where ρ g is gas density, ϕ is porosity of clinker layer, V is gas seepage speed. Because gas flow rate is quite high, motion equation uses Darcy-Forchheimer equation to describ gas motion equation: P = µ g K V 2 y + βρ g V y (2) where P is gas pressure, K is permeability of clinker layer, µ g is gas dynamic viscosity, β is non-darcy coefficient. Because of the forced cooling to the clinker layer of grate cooler and fast gas flow rate, the porous clinker layer and cooling gas can not reach thermal equilibrium state, so we use the local thermal non-equilibrium theory [9] to establish seepage heat transfer energy equation of grate cooler. Gas energy control equation can be described as: ϕρ g C g t + (ϕρ gc g v g T g ) = [ (ϕλ g + λ d ) T ] g + Sα (T s T g ) (3) Clinker energy control equation can be described as: [ T (1 ϕ) λ s T ] s s (1 ϕ) ρ s C s t = Sα (T s T g ) (4) where T g is gas temperature, T s is cement clinker temperature, C g is gas specific heat capacity, C s is cement clinker specific heat capacity, v g is actual gas velocity, λ g is gas thermal conductivity, λ s is cement clinker thermal conductivity, λ d is thermal dispersion conductivity, S is effective heating area per unit volume of the bed particles, α is integrated heat transfer coefficient. For compressible flow, we add gas state equation to reflect the relationship between state variables in order to make control equations closed: ρ g = P M zrt g (5)

8284 B. Liu et al. /Journal of Computational Information Systems 9: 2 (213) 8281 8288 In the above formulas: C g = 955 +.143 T g + 3.85 1 5 T 2 g + 2.1 1 1 T 3 g + 1.2 1 13 T 4 g, C s = 699 +.318 T s 6.23 1 5 T 2 s 1.37 1 1 T 3 s 5.13 1 14 T 4 s, K =.23ϕ 3 d 2/ 1.571 2 [1], v g = V /ϕ, µ g = 1.72 1 5 [(273 + 114)/(T g + 114)] (T g /273) 1.5, λ g =.244(T g /273).759, λ s =.244 [1 +.63 (T s 273)] [11, 12], S = 6 (1 ϕ)/d, d is the clinker particle diameter. α = 1/(1/h + θd/2λ s ) [13], where h is the convective heat transfer coefficient, h can be described as: h = λ g Nu/d. Because particles in the clinker layer are bulky relatively, Nusselt number can be described as follow: Nu = 2 + 1.8P r 1 3 Re 1 2 [13], where Prandtl number is P r = µ g C g /λ g, Reynolds number is Re = v g d/ν g, kinetic viscosity is ν g = µ g /ρ g. When Reynolds number in the clinker layer of air is high, calculation formula of the thermal dispersion conductivity is: λ d =.4ρ g C g dν g (1 ϕ)/ϕ [14]. The discharge temperature of rotary kiln is T, therefore the initial condition of the model is: When y =, the boundary condition is: T s = T, T g = T P = P in, T g = T gin, λ s T s = h (T s T gin ) When y = H (where H is the thickness of clinker layer), the boundary condition is: P = P out, λ g = h (T g T s ), λ s T s = h (T s T g ) Seepage heat transfer control mechanism model of grate cooler is constituted by the formulas (1) (5), the initial condition and the boundary condition, which are given above. 3 Solving Method for Control Mechanism Model Using the method combined analytical method and implicit difference method, we solve the seepage heat transfer control mechanism model. Formulas (1, 2) and (5) are seepage field control equations of flow gas in clinker layer and formulas (3, 4) are temperature field control equations of heat transfer relationship between cooling air and clinker particle in clinker layer. In each discrete micro time segment we use analytical method to calculate seepage field control equations and adopt implicit difference method to calculate temperature field equations. The two fields iterate mutually to solve the control model. The specific solving method is as follow. We divide the cooling time of cement clinker into micro time segments and calculate the temperature field during each micro time segment. Due to partial derivative of variable physical parameters in temperature field control formulas, we decompose and reorganize the formulas before dispersion. From formula (3) and formula (4), we have: ϕρ g C g t + (ϕρ gc g v gy ) T g + ϕρ g C g v gy = (ϕλ g + λ d ) + (ϕλ g + λ d ) 2 T g 2 + Sα (T s T g ) (6)

B. Liu et al. /Journal of Computational Information Systems 9: 2 (213) 8281 8288 8285 T s (1 ϕ) ρ s C s t = (1 ϕ) λ s T s + (1 ϕ) λ 2 T s s Sα (T 2 s T g ) (7) We use the implicit backward difference method to disperse energy equations and the adopted difference scheme is unconditional stability. We divide the solved region into grids and assume the time step as t while the spatial step as y. Thus node equations in moment n t can be expressed as follow: T g i ϕρ g C g t T g n i = (ϕλ g + λ d ) + (ϕρ gc g v gy ) T g i+1 T g i + ϕρ g C g v T g i 1 gy 2 y T g i+1 T g i 1 + (ϕλ g + λ d ) T g i+1 2T g i + T g i 1 + Sα ( T 2 y y 2 s i T g i ) (8) T s i (1 ϕ) ρ s C s = (1 ϕ) λ s T s n i t T s i+1 T s i 1 T s i+1 + (1 ϕ) λ 2T s i + T s i 1 s Sα ( T 2 y y 2 s i T g i ) (9) Reorganize formulas (8, 9) and get the recurrence formulas as follow: n A 1 i T g i 1 + B 1 n n i T g i + C 1 i T g i+1 + D 1 n n n i T g i = E 1 i T g i (1) n A 2 i T s i 1 + B 2 n n i T s i + C 2 i T s i+1 + D 2 n n n i T s i = E 2 i T s i (11) where A 1 -E 1 and A 2 -E 2 are coefficients of formulas (1, 11) after reorganizing formulas (8, 9). We calculate formulas (1, 11) using bivariate tridiagonal-matrix algorithm (COTDMA) and then get temperature of the whole clinker layer thickness in moment n t. Then we compute seepage field during this micro time segment. For seepage control equations, we reorganize formula (2) and get formula (12) as follow: P = µ g K V y + βρ g V 2 y = µ ( g K V y 1 βρ ) gkv y µ g Let δ = 1 βρ g KV y /µ g, then formula (12) turns to: (12) V y = δ K µ g P (13) In every micro time segment, each variable is the only function of y, so we will turn formula (1) and formula (13) into corresponding ordinary differential equations. Then we make formula (5) and formula (13) substituted in formula (1) and get formula (14) as follow: [( ) ( MP d δk dp )]/ dy = (14) zrt g µ g dy

8286 B. Liu et al. /Journal of Computational Information Systems 9: 2 (213) 8281 8288 From formula (14), we have: P = 2 µ gzr KMδ C 1 T g dy + 2C 2 (15) Let formula (15) be substituted in formula (5) and get formula (16) as follow: ρ g = M zrt g 2 µ gzr KMδ C 1 T g dy + 2C 2 (16) Let formula (15) be substituted in formula (11) and get formula (17) as follow: V y = δ K µ g (d 2 µ gzr KMδ C 1 T g dy + 2C 2 /dy ) (17) where C 1 and C 2 are corresponding integral constant. On the basis of temperature field result in this micro time segment and seepage field result in last micro time segment, coefficients in equations are obtained. We can get P, V y and ρ g in this micro time segment via solving formulas (15)-(17). According to the data of temperature field and seepage field obtained in this micro time segment, the equation coefficients in next micro time segment are updated and and we proceed to solve the equations in next micro time segment. We can complete the solving process of control mechanism model and gain the law of clinker heat transfer in great cooler through the calculations of all micro times segment. 4 Model Verification We take the cement clinker as the object to validate seepage heat transfer control mechanism model and make the corresponding model calculation conditions as follow: the length of grate cooler is 2m, the cement clinker temperature of grate bed feed end is 16K, the cooling air from the bottom of clinker layer is 33K, the pressure on the top of the clinker layer is standard atmospheric pressure, air supply pressure is P in =6Pa, the grate speed is v s =.8m/s. For solving the control model of great cooler, we use the calculation conditions mentioned above and obtain the gas temperature distribution as shown in Fig. 3 and the clinker temperature distribution as shown in Fig. 4. It can be seen from the Fig. 3 and Fig. 4 that the temperature of gas and clinker increase gradually from the bottom to the top and decrease gradually with the motion of clinker layer from the inlet to the outlet. This is due to when the cooling gas gets into the clinker layer from the bottom, it makes heat exchange continuously with clinker and then absorbs heat as the gas moves up, which makes the gas temperature increase gradually and air cooling effect of clinker get worse and worse. With the clinker layer moving to the discharge port, cooling gas continuously flows through the clinker layer and takes the heat away, so the clinker temperature decreases. Correspondingly, cooling gas takes less and less heat from clinker and the gas temperature is lower and lower as well.

8287 B. Liu et al. /Journal of Computational Information Systems 9: 2 (213) 8281 8288 15 Ts/K Tg/K 15 1 5 5.5 5 1 1.5 15 x/m 2 5 y/m Fig. 3: Air temperature distribution 1 15 x/m 2 y/m Fig. 4: Clinker temperature distribution Fig. 5 is the field temperature data which is collected by temperature measurement and imaging system installed inside the great cooler. Fig. 6 indicates the temperature contrast diagram between the field measurement of 1 to 6 and the simulated calculation value. 16 simulation 14 measurement Ts/K 12 1 8 6 4 5 1 x/m 15 2 Fig. 5: Field data of clinker temperature in Fig. 6: Comparison of clinker temperature be- grate cooler tween simulation and field in the top of clinker layer As shown in Fig. 6, the distribution trend of temperature in the top of clinker layer through simulation is consistent with measured data, and the absolute value of max error is 4.35%, less than 1%. At the same time, practical production of cement clinker requires that the clinker temperature in the outlet of great cooler must below 368K (65K+ambient temperature). We can see from Fig. 4 that the highest clinker temperature away from grate bed is 38.4K and the average temperature is 338.83K, which is fit well with the actual situation. Therefore, the grate cooler control model which is constructed by seepage and heat transfer theory can reflect the heat transfer rules of cement clinker particles in great cooler. 5 Conclusion This paper establishes a control mechanism model of grate cooler which adopt the porous media seepage and heat transfer theory, and then calculate the model by combining analytical method and implicit difference method. The simulation results tallies with the field measurement data and it is preferably to simulate the cooling process of cement clinker in grate cooler. Using the seepage and heat transfer theory to establish the grate cooler control mechanism model provide a new

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