clinker cooler balance

Journal of Computational Information Systems 9: 20 (2013) 8281–8288Available 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

1Institute of Information Technology and Engineering, Yanshan University, Qinhuangdao 066004,China

2Institute of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, 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 mechanismmodel. The calculation results obtained in the paper are consistent with the fluctuation tendency of themeasured temperature and the error is small. The control mechanism model can reflected heat transfercharacteristics 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 dischargedby 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 heatrecovery efficiency. The main reason for this problem is the insufficient research for heat transfercontrol mechanism of grate cooler. Therefore, research on heat transfer control mechanism ofgrate cooler has become a hot topic.

Taking the clinker in grate cooler as a continuum, Touil [1] divided finite element of grate coolerand calculated clinker cooling process numerically. Mujumdar [2] applied the heat conductiontheory on heat transfer analysis of the grate cooler, he took the grate cooler as a whole and carriedon overall heat balance calculation of double-input and multiple-output. Locher [3] established acontrol model based on the heat transfer equation of gas through the particle bed and the unsteadyheat transfer equation, he studied the influence of grate speed and particle size distribution onclinker cooling process, but he didn’t give the specific law of the influence of parameters onheat 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. 51076135) and the Science andTechnology Support Program of Hebei Province (No. 12215616D).

∗Corresponding author.Email address: [email protected] (Meiqi WANG).

1553–9105 / Copyright © 2013 Binary Information PressDOI: 10.12733/jcis8323October 15, 2013

8282 B. Liu et al. /Journal of Computational Information Systems 9: 20 (2013) 8281–8288

heat transfer process in cement clinker. Some scholars used seepage heat transfer theory of porousmedia to study the control model of heat transfer equipment between gas and the accumulation ofparticles. Hu [4] calculated the seepage heat transfer process of high temperature gas in movingparticulate 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 calciningprocess of limestone and the research results showed that inlet flow velocity, inlet gas temperatureand solid particle size were important parameters to the system characteristics. Zhang [6] usedFluent 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 coolingresearch, basic control mechanism model was established, but he didn’t solve the model. Usingseepage heat transfer theory and Darcy law, Wen [8] established seepage heat transfer controlmechanism model for cement clinker cooling process, and solved the model approximately withignoring multiple factors. Although introducing seepage heat transfer theory of porous mediainto cement clinker cooling research has made a certain progress, effective seepage heat transfercontrol mechanism model of grate cooler and corresponding heat transfer law of cement clinkerhaven’t obtained because of the difficulties for solving nonlinear partial differential equations ofthe complex model.

A control mechanism model of grate cooler is established by seepage heat transfer theory ofporous media in this paper. In the model, we take into account variable physical properties of gasand clinker, thermal dispersion effect and thermal non-equilibrium in the gas-solid heat transferprocess. Seepage heat transfer control mechanism model is calculated by the combined analyticaland implicit difference method. We obtain the cooling control law of cement clinker in grate coolerand verify the correctness of the control model by comparing the field measurement temperatureand 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 layermoves slowly on grate bed. Cooling air blows into the clinker layer vertically from the bottom ofthe clinker, permeates and diffuses in the clinker to cool the red-hot clinker. Cooling air becomeshot 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: 20 (2013) 8281–8288 8283

According to cement clinker cooling condition in grate cooler, we establish the heat transferphysical model as shown in Fig. 2. On grate bed clinker particles that temperature is T0 get intothe three-dimensional area from the left side and get out the area from the right side, cooling airthat temperature is Tgin flows into this area and exchanges heat energy with clinker, and thenoutflows from the top. In Fig. 2, x is the length direction of the bed, y is the thickness directionof 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 gasvertically cross flow, clinker layer moving speed is relatively slow, the gas flow and the gas-solidheat transfer in the thickness direction are the main factors.

According to the law of conservation of mass, gas continuity equation can be described as:

∂ (ρgVy)

∂y= 0 (1)

where ρg 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 todescrib gas motion equation:

∂P

∂y= −µg

KVy + βρgVy

2 (2)

where P is gas pressure, K is permeability of clinker layer, µg is gas dynamic viscosity, β isnon-Darcy coefficient.

Because of the forced cooling to the clinker layer of grate cooler and fast gas flow rate, theporous clinker layer and cooling gas can not reach thermal equilibrium state, so we use the localthermal non-equilibrium theory [9] to establish seepage heat transfer energy equation of gratecooler.

Gas energy control equation can be described as:

ϕρgCg∂Tg

∂t+

∂ (ϕρgCgvgTg)

∂y=

∂

[(ϕλg + λd) ·

∂Tg

∂y

]∂y

+ Sα (Ts − Tg) (3)

Clinker energy control equation can be described as:

(1− ϕ) ρsCs∂Ts

∂t=

∂[(1− ϕ)λs · ∂Ts

∂y

]∂y

− Sα (Ts − Tg) (4)

where Tg is gas temperature, Ts is cement clinker temperature, Cg is gas specific heat capacity, Cs

is cement clinker specific heat capacity, vg is actual gas velocity, λg is gas thermal conductivity,λs is cement clinker thermal conductivity, λd is thermal dispersion conductivity, S is effectiveheating 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 statevariables in order to make control equations closed:

ρg =PM

zRTg

(5)


In the above formulas: Cg = 955 + 0.143× Tg + 3.85× 10−5 × T 2g + 2.10× 10−10 × T 3

g + 1.20×10−13 × T 4

g , Cs = 699 + 0.318× Ts − 6.23× 10−5 × T 2s − 1.37× 10−10 × T 3

s − 5.13× 10−14 × T 4s ,

K = 0.23ϕ3d2/1.5712 [10], vg = V /ϕ, µg = 1.72 × 10−5 [(273 + 114)/(Tg + 114)] (Tg/273)

1.5,

λg = 0.0244(Tg/273)0.759, λs = 0.244 [1 + 0.00063 (Ts − 273)] [11, 12], S = 6 (1− ϕ)/d, d is the

clinker particle diameter.

α = 1/(1/h+ θd/2λs) [13], where h is the convective heat transfer coefficient, h can be describedas: h = λgNu/d. Because particles in the clinker layer are bulky relatively, Nusselt number can

be described as follow: Nu = 2 + 1.8Pr13Re

12 [13], where Prandtl number is Pr = µgCg/λg,

Reynolds number is Re = vgd/νg, kinetic viscosity is νg = µg/ρg.

When Reynolds number in the clinker layer of air is high, calculation formula of the thermaldispersion conductivity is: λd = 0.04ρgCgdνg(1− ϕ)/ϕ [14].

The discharge temperature of rotary kiln is T0, therefore the initial condition of the model is:

Ts = T0, Tg = T0

When y = 0, the boundary condition is:

P = Pin, Tg = Tgin, −λs∂Ts

∂y= h (Ts − Tgin)

When y = H (where H is the thickness of clinker layer), the boundary condition is:

P = Pout, −λg∂Tg

∂y= h (Tg − Ts) , −λs

∂Ts

∂y= h (Ts − Tg)

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 theseepage heat transfer control mechanism model. Formulas (1, 2) and (5) are seepage field controlequations of flow gas in clinker layer and formulas (3, 4) are temperature field control equationsof heat transfer relationship between cooling air and clinker particle in clinker layer. In eachdiscrete micro time segment we use analytical method to calculate seepage field control equationsand adopt implicit difference method to calculate temperature field equations. The two fieldsiterate 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 tem-perature field during each micro time segment. Due to partial derivative of variable physicalparameters in temperature field control formulas, we decompose and reorganize the formulasbefore dispersion. From formula (3) and formula (4), we have:

ϕρgCg∂Tg

∂t+

∂ (ϕρgCgvgy)

∂yTg + ϕρgCgvgy

∂Tg

∂y

=∂ (ϕλg + λd)

∂y

∂Tg

∂y+ (ϕλg + λd)

∂2Tg

∂y2+ Sα (Ts − Tg)

(6)


(1− ϕ) ρsCs∂Ts

∂t= (1− ϕ)

∂λs

∂y

∂Ts

∂y+ (1− ϕ)λs

∂2Ts

∂y2− Sα (Ts − Tg) (7)

We use the implicit backward difference method to disperse energy equations and the adopteddifference scheme is unconditional stability. We divide the solved region into grids and assumethe time step as ∆t while the spatial step as ∆y. Thus node equations in moment n×∆t can beexpressed as follow:

ϕρgCg

Tgn+1i − Tg

ni

∆t+

∂ (ϕρgCgvgy)

∂yTg

n+1i + ϕρgCgvgy

Tgn+1i+1 − Tg

n+1i−1

2∆y

=∂ (ϕλg + λd)

∂y

Tgn+1i+1 − Tg

n+1i−1

2∆y+ (ϕλg + λd)

Tgn+1i+1 − 2Tg

n+1i + Tg

n+1i−1

∆y2+ Sα

(Ts

n+1i − Tg

n+1i

) (8)

(1− ϕ) ρsCsTs

n+1i − Ts

ni

∆t

= (1− ϕ)∂λs

∂y

Tsn+1i+1 − Ts

n+1i−1

2∆y+ (1− ϕ)λs

Tsn+1i+1 − 2Ts

n+1i + Ts

n+1i−1

∆y2− Sα

(Ts

n+1i − Tg

n+1i

) (9)

Reorganize formulas (8, 9) and get the recurrence formulas as follow:

A1ni Tg

n+1i−1 +B1

ni Tg

n+1i + C1

ni Tg

n+1i+1 +D1

ni Tg

n+1i = E1

ni Tg

ni (10)

A2ni Ts

n+1i−1 +B2

ni Ts

n+1i + C2

ni Ts

n+1i+1 +D2

ni Ts

n+1i = E2

ni Ts

ni (11)

where A1-E1 and A2-E2 are coefficients of formulas (10, 11) after reorganizing formulas (8, 9).

We calculate formulas (10, 11) using bivariate tridiagonal-matrix algorithm (COTDMA) andthen get temperature of the whole clinker layer thickness in moment n×∆t. Then we computeseepage field during this micro time segment.

For seepage control equations, we reorganize formula (2) and get formula (12) as follow:

∂P

∂y= −µg

KVy + βρgVy

2 = −µg

KVy

(1− βρgKVy

µg

)(12)

Let δ = 1− βρgKVy/µg, then formula (12) turns to:

Vy = −δK

µg

∂P

∂y(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:

d

[(MP

zRTg

)·(−δk

µg

· dPdy

)]/dy = 0 (14)


From formula (14), we have:

P =

√−2

µgzR

KMδ· C1

∫Tgdy + 2C2 (15)

Let formula (15) be substituted in formula (5) and get formula (16) as follow:

ρg =M

zRTg

√−2

µgzR

KMδ· C1

∫Tgdy + 2C2 (16)

Let formula (15) be substituted in formula (11) and get formula (17) as follow:

Vy = −δK

µg

(d

√−2

µgzR

KMδ· C1

∫Tgdy + 2C2

/dy

)(17)

where C1 and C2 are corresponding integral constant. On the basis of temperature field resultin this micro time segment and seepage field result in last micro time segment, coefficients inequations are obtained. We can get P , Vy and ρg 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 theequations in next micro time segment. We can complete the solving process of control mechanismmodel and gain the law of clinker heat transfer in great cooler through the calculations of allmicro times segment.

4 Model Verification

We take the cement clinker as the object to validate seepage heat transfer control mechanismmodel and make the corresponding model calculation conditions as follow: the length of gratecooler is 20m, the cement clinker temperature of grate bed feed end is 1600K, the cooling airfrom the bottom of clinker layer is 303K, the pressure on the top of the clinker layer is standardatmospheric pressure, air supply pressure is Pin=6000Pa, the grate speed is vs=0.008m/s. Forsolving the control model of great cooler, we use the calculation conditions mentioned aboveand obtain the gas temperature distribution as shown in Fig. 3 and the clinker temperaturedistribution as shown in Fig. 4.

It can be seen from the Fig. 3 and Fig. 4 that the temperature of gas and clinker increasegradually from the bottom to the top and decrease gradually with the motion of clinker layerfrom the inlet to the outlet. This is due to when the cooling gas gets into the clinker layer fromthe bottom, it makes heat exchange continuously with clinker and then absorbs heat as the gasmoves up, which makes the gas temperature increase gradually and air cooling effect of clinker getworse and worse. With the clinker layer moving to the discharge port, cooling gas continuouslyflows 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 islower and lower as well.


0 5 10 15 20 0

0.5500

1000

1500

y/mx/m

Tg/K

Fig. 3: Air temperature distribution

0 5 10 15 20 0

0.5500

1000

1500

y/mx/m

Ts/K

Fig. 4: Clinker temperature distribution

Fig. 5 is the field temperature data which is collected by temperature measurement and imagingsystem installed inside the great cooler. Fig. 6 indicates the temperature contrast diagrambetween the field measurement of 1 to 6 and the simulated calculation value.

Fig. 5: Field data of clinker temperature ingrate cooler

0 5 10 15 20

400

600

800

1000

1200

1400

1600

x/m

Ts/K

simulation

measurement

Fig. 6: Comparison of clinker temperature be-tween simulation and field in the top of clinkerlayer

As shown in Fig. 6, the distribution trend of temperature in the top of clinker layer throughsimulation is consistent with measured data, and the absolute value of max error is 4.35%, lessthan 10%. At the same time, practical production of cement clinker requires that the clinkertemperature in the outlet of great cooler must below 368K (65K+ambient temperature). We cansee from Fig. 4 that the highest clinker temperature away from grate bed is 380.40K and theaverage temperature is 338.83K, which is fit well with the actual situation. Therefore, the gratecooler control model which is constructed by seepage and heat transfer theory can reflect the heattransfer rules of cement clinker particles in great cooler.

5 Conclusion

This paper establishes a control mechanism model of grate cooler which adopt the porous mediaseepage and heat transfer theory, and then calculate the model by combining analytical methodand implicit difference method. The simulation results tallies with the field measurement data andit is preferably to simulate the cooling process of cement clinker in grate cooler. Using the seepageand heat transfer theory to establish the grate cooler control mechanism model provide a new


way for the establishment of other moving particulate bed equipment control mechanism models.It promotes the application of advanced control strategy of heat field in moving particulate bedand has the important theory significance and the practical significance.

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