Numerical simulation of the shell cooling of a rotary kiln

Abstract

Keywords: Efficiency; Fins; Heat Transfer; Rotary Kiln; Shell; Temperature Distribution

Introduction

The rotary kiln is considered to be the heart of a cement plant, for the production of clinker. It is subjected to very high thermal and mechanical loads. The temperature of the material inside the oven can reach 1500°C and that of the flame exceeds 2000°C, which can cause a certain number of problems on all the parts of this equipment. Among these organs, we have the shell of the furnace which is made of cylindrical steel sheet. This is

the part that can suffer from damage such as red spots (hot spot), elastic and even plastic deformations. Our work is based on the study of heat transfer in the kiln, in order to find how to reduce the temperature of the shell. Research works has focused on the problem, among which we will cite those of Shvachko et al. [2] who present a method for increasing the efficiency of rotary kilns by varying the thickness of the crust, considered to insulate and allow the conservation heat. A. Gallo, et al. [3] developed a laboratory-scale rotary kiln and tested it using a

*Corresponding author. *E-mail address: mohamedbouhafs@yahoo.fr, bouhafs.mohamed@univ-oran2.dz This paper was recommended for publication in revised form by Editor-in-Chief Ahmet Selim Dalkılıç Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

solar simulator. The numerical results showed a good agreement with the experimental data, so the thermal losses could be quantified in detail. Wirtz et al. [4], make a study which consists in estimating the crusting layer in the rotary kiln in order to control the temperature of the shell. This temperature is introduced into a heat transfer model, in order to deduce the thickness of this layer. Rindang et al. [5] conducted an experimental study to deduce a heat and mass transfer model within a rotary dryer, by varying the air injection velocity and the drying temperature. C. Gu et al. [6] proposed a mathematical model of heat and mass transfer, in order to study the drying characteristics of biomass particles. The simulation results indicated that the drum temperature can have a significant influence on the drying behaviors of the particles. Bongo Njeng et al. [7] develop a model based on dimensional analysis for the calculation of the wall-material heat transfer coefficient for heating temperatures varying from 100 to 500°C, while considering the service conditions. Mirhosseini et al. [8] studied the effect of an absorber in the form of an arc placed around the rotary kiln, in order to permit the recovery of a part of this quantity of heat dissipated by the rotary kiln for use in d other applications. K. Wang et al. [9] experimentally and numerically studied a new heat exchanger using batteries of tubes arranged in a certain orientation. The numerical results indicate that these batteries of tubes are more efficient when they are arranged in a certain orientation. Yin et al. [10] propose a system for recovering waste heat from a rotary kiln by establishing mathematical relationships linking the heat transfer zones in the kiln to the mass flow rates of the recovery exchangers. Ramanenka et al. [11], models a hot rotary kiln lined with three types of bricks, using the finite element method. They studied the reliability of this modeling, by highlighting the level of tensile stress that can potentially occur. Qian Yin et al. [12] carried out an experimental work which consists of the design of a system for recovering the heat lost by a rotary kiln. It is designed with nine heat exchangers for heating the water. This design is mathematically modeled taking into account the exchange surface, the total energy, the regenerated entropy and the temperatures of the fluids. Agrawal et al. [13] present a modeling of the heat transfer of convection, radiation and conduction between the hot gas and the surface of the refractory wall. Steady-state finite differences are assumed. Parametric analysis of humidity rate, material flow, gas flow, angle of inclination and rotational velocity of the kiln are made. M. Csernyei et al. [14] described the process used for the numerical analysis of convective heat transfer from multiple large jets. The inclusion of forced convection in the kiln resistance model resulted in a decrease in shell temperature compared to free convection. Yin et al. [15] present a mathematical model to analyze shell temperatures and heat loss rates in different regions of the rotary kiln. They established a heat exchange surface optimization model to

describe the relationship between the design parameters and the mass flow rate of each heat exchanger. Shahin et al. [16] developed a mathematical model of energy balance equations including coupled mechanisms of heat transfer and chemical reaction. This should allow thermal energy analysis for lime production. Ustaoglu et al. [17] perform an energy and exergy performance analysis of a wet rotary kiln was performed based on actual data. The results showed that a large amount of thermal energy is discharged from the kiln chimney. Csernyei [18] highlights through a numerical simulation, the heat transfer by forced convection resulting from the jets oriented on the shell of a rotary kiln, which allows to deduce a correlation representing the cooling of the kiln. Liu et al. [19] numerically simulated the two-dimensional dynamic and thermal behavior between matter and hot gases, on a cross-section inside a rotary kiln. This work has been validated by experimental data. Goshayeshi and Poor [20] have established a complete model of the kiln in order to reduce its energy consumption during the production of cement, taking into account the parameters having a great influence, such as the change in the temperature of the coating, the phase change of the material and the temperature of the combustion gases. Gaurav and Khanam [21] simulated different closure models on a rotary kiln, in order to be able to determine and optimize the temperature profiles of the gas and the material. The input parameters of this simulation are the angle of inclination, the number of rotations of the kiln and the mass flow. Csernyei and Straatman [22], the importance of their study lies in the heat transfer by convection allowing the cooling of rotary cement kilns using large axial fans. From this work, a numerical model was highlighted using turbulence models. Goshayeshi and Poor [23] carried out a simulation in order to know the behavior of the operating parameters of the rotary kiln, namely, the phase change of the material, the temperature of the gas and the internal coating of the kiln. Moussi et al. [24] model a rotary kiln in a dry process cement plant. This simulation resides in the coupling between the mass balance equations and the heat transfer equation. This model is validated by experimental measurements permitting to obtain the temperature, the compositions of the gas and the material along the different zones of the kiln. Luo et al. [25] proposed waste heat recovery thermoelectric generating units to reduce heat losses from rotary kilns. The simulation results show more than 32.85% of waste heat is saved from the kiln surface. Atmaca and Yumrutas [26] show the effects of refractory bricks and the formation of a crust layer on the specific energy consumption of a rotary kiln through a numerical simulation. This allows the energy balance of the system to be calculated. Ariyaratne et al. [27] present a three-dimensional modeling carried out on a cement rotary kiln with a multi-channel air vortex burner, and at high impulse for the combustion of coal as well as for the combustion of animal meal. Yi et al. [28] numerically process

the mathematical model of the heat transfer of an alumina rotary kiln to predict the gas and material temperature profiles in the axial direction. A.C. Caputo et al. [29] proposed the possibility of recovering the radiant heat lost through the furnace surface by a set of pressurized water transport tubes arranged in a longitudinal plane on the surface of a coaxial cylindrical outer shell with the rotary kiln. S. B. Paramane and Sharma [30] have numerically studied the free flow and the heat transfer by forced convection through a rotating cylinder for Re numbers from 20 to 160. They found that the rotation of the cylinder allows the reduction of the number of Nu. I. A. S. Larsson et al. [31] have studied the rotary kiln process numerically and the results obtained show that in steady state they can be used to gain insight into the main characteristics of the flow field. The purpose of the numerical study of G. Krishnayatra et al. [32], is to know the effect of the dimensions, the number and the material of the fins installed on a cylinder on the heat transfer during a natural convection with a constant Rayleigh number. S. K. Rout et al. [33] presents in this work, the effects of the height, the width and the number of fins on the improvement of the heat transfer with the variation of the Nusselt number, the friction factor and the Reynolds number. T. Bano and Ali [34] presents a modeling of heat transfer by condensation on smooth horizontal tubular surfaces with fins, which focuses on three-dimensional (3D) geometric effects, fin density, fin spacing and thickness. S. Mohamad et al. [35], the main objective of their study is to evaluate the entropy production and estimate the cooling time of the furnace. A simulation was carried out to calculate the free convection of the blast furnace with respect to the variation of its cross-sectional area. S. Mohamad et al. [36] present a numerical solution of the continuity, momentum and energy equations for a fluid domain surrounding the outer cylindrical surface of a vertical cylinder with the specific longitudinal section using ANSYS FLUENT 18. The main parameters of this study are the cylinder length, diameter, Rayleigh number, and surface temperature of the cylinder. S. Kumar Rout et al. [37] in their work, the wall temperature of a tube provided with internal fins has been calculated numerically for different numbers, heights and shapes of fins through the resolution of the equations of conservation of mass, momentum and energy in using Fluent. F. Mebarek-Oudina et al. [38], in their study the effects of the Richardson number and the Reynolds number ratio are demonstrated through the numerical study of mixed convection inside a horizontal rectangular pipe combined with an open trapezoidal cavity and heated using two heat sources. The main objective of our work is to represent the temperature profile of the rotary kiln shell. Our novelty lies in adding fins to the external surface of the kiln shell in its burning zone, and examining the impact of the fins on the temperature profile compared to the kiln shell without fins.

Description Of The Problem

The rotary kiln is subjected to high temperatures, which poses a problem of damage to the shell. In this work, we carried out a numerical simulation of the thermal behavior of the shell of the rotary kiln in the firing zone of the cement plant. The purpose of this study is to deduce the distribution of the outside temperature of the shell of the cooking zone for two distinct cases. The first case is, the study of the evolution of the external temperature of the kiln in the cooking zone, with a smooth shell as it exists in industry. In the second case, the outer surface of the shell is equipped with fins. Figure 1 gives us a vision of the rotary kiln in our site, where our study was carried out. The dimensions of this kiln are shown in Table 1. The study was carried out on the cooking zone of the 17 m long rotary kiln. This part is considered to be the most thermally stressed. The outside temperatures in this area often exceed 400°C, and as the shell of the furnace is made of A42 steel, this can lead to elastic and even plastic deformations.

Mathematical Model Our study consists of an approach of a flow around a horizontal cylinder with a wall at high temperature. For this, it is necessary to quote the adequate formulation for this case. The resolution of the equations governing this flow is done by the K-ω-SST model of the ANSYS-CFX code, the comparison of the results of which constitutes the essential objective of this work. By adopting the SST model simulates the heat transfer of this flow. The Navier Stocks equations [39,40] considered for this incompressible fluid are: (1) Momentum Transport Equations

(7) (8) The empirical constants of the SST model are presented in Table 2: This study deals with heat transfer through the laminar regime convection between the steel shell and its external environment. It describes the movement of a fluid due to changes in density as a function of temperature. Thus, there is a coupling between the dynamic and the thermal. For all convection problems, the wall heat exchanges are measured by highlighting the value of the Nu number. Since our study has an orientation towards heat transfer with the existence of a rectangular fin with a finite end, we give the equation that governs this phenomenon [41]:

For heat transfer by natural convection, The Nusselt number correlation for the horizontal cylinder with plate fins (Nu) is given by [41,42]:

All these equations can be written in the following general form: (4) Term 1 : transport of 𝜙 by convection. Term 2 : transport of 𝜙 by diffusion. Term 3 : local production of 𝜙. The 𝑆𝑆T model has a form similar to the standard 𝑘−𝜔 model [40] (5)

duction de k, ω respectively. The effective diffusivities for the SST model are given by:

(10) The fin efficiency η, which is written as follows [41,42]: (11)

Mesh Optimization The quality of the simulation results is closely linked to the model used, the mesh used and optimized. The choice of the model is subordinated to the type of information that we want to obtain from the simulation.

Validation We validated our simulation results with a curve taken on-site in the control room of the cement plant. In this real case, all thermal, mechanical, and physico-chemical phenomena present in this type of equipment, as well as the state of the refractory brick, the state of the crust, and the actual thickness of the shell, are taken into account. In our simulation, we neglected certain parameters that we could not control. Despite this, the shapes of the curves (simulated and real) are similar, and the maximum error does not exceed 30% at a single point, while the average error is around 12%.

Figure 3. Evolution of the outer shell temperature as a function of the hot air velocity.

Figure 2. Distribution of the temperature outside the shell of the furnace (case of validation).

Results And Discussion

Variation of the Hot Air Injection Velocity of the Burner The purpose of this case study is to determine the effect of air injection velocity at the kiln burners on the thermal behavior of the shell. Five tests were carried out, this velocity was varied from 13.74 m/s to 53.74 m/s to deduce the maximum temperature value of the shell. Figure 3 shows the evolution of temperature as a function of hot air velocity. We notice that as the air velocity increases, the outside temperature of the shell increases, which is logical, because a higher velocity leads to a hotter flame, which leads to an increase in the temperature. The temperature increases relatively with the increase in the velocity of injection of hot air from the burner. The temperature profiles have the same trend and the same shape, with a gradual increase up to the distance of 11 m, where the maximum temperature is found, then there is a slight decrease in this parameter. We also note that the velocity of the air injection has a moderate impact, since it is necessary to choose this velocity well in order to protect our shell from heating. It can also be seen that the maximum increase in temperature is 5% from one velocity value to another.

The Variation of the Internal Temperature of the Kiln In this part, we wanted to know the effect of another parameter which is the variation of the hot air temperature of the burner inside the kiln. Figure 4 shows the variation in the outside temperature of the shell as a function of the hot air temperature inside the oven. The same rate is observed for each variation as well as a gradual increase in temperature up to the hottest point located at the 11 m length of the kiln. There is a decrease in the curve and a decrease in the temperature values. The maximum values reach significant values, thus for the value of 1050°C of the air inside the kiln, we have an outside temperature of the shell of 416°C, while for the value of 1450°C, which is the operating temperature of a cement kiln, the external temperature reaches 496°C. This high temperature can damage the shell by plastic deformation.

Figure 4. Outside temperature of the shell as a function of inside temperature of the furnace.

We note that we have a maximum variation of the temperature of 12%, this value has an important significance in the category of high temperatures and thus it is necessary to choose this parameter well during the operation of such industrial equipment, in order to to preserve. Variation in Shell Temperature as a Function of Ambient Air Temperature In this part, we wanted to know the effect of the variation of the ambient air injection temperature. Figure 5 represents the variation in the outside temperature of the shell as a function of the ambient air temperature. We observe the same shape as the previous curves, with a progression of the temperature up to the length of 11 m and then begins a decrease. We took 5 values of the ambient temperature from 5°C to 48°C and this according to the geographical location of our site and in relation to the different winter and summer seasons. It can be seen that this parameter does not have a significant impact, because the maximum variation does not exceed the value of 3%, i.e. a deference of 5°C (from 18°C to 28°C) in the temperature of the shell, which insignificant for such equipment whose temperature exceeds 1400°C. Note that the change in temperature from 5°C (winter) to 48°C (summer) may have an influence on the variation in the temperature outside the shell.

Comparison of Shell Temperatures with E Without Fins The Figure 7 shows that the shell fitted with fins has a temperature gain of 32% compared to that without fins and 42% for that on site. The maximum temperature reached by the finned shell is 380°C, while that on site is 430°C and that without fins is 480°C. It can be concluded that the insertion of the fins on the outer surface of the shell section which is the cooking zone, gives a considerable reduction in the temperature of the shell. This difference makes the oven work well and prolongs its life.

Figure 5. Outside temperature of the shell as a function of the ambient air temperature. Shell Fitted with Fins This second part of our study will be the same as the previous one, but modifying the geometry of the kiln in the cooking zone by adding rectangular fins. Figure 6 shows the new geometry of the shell of the rotary kiln studied. This zone is equipped with 72 fins, of 1 m length, 15 cm wide, and 15 cm high. These fins are spaced 1 m apart. Thus we will have 9 fins along the length and 8 on the circumference.

For the simulation, we took the same boundary conditions as that of the smooth shell and in order to deduce the effect of these fins on the behavior of the temperature parameter of the shell. The first part showed us that the temperature of the shell reaches values exceeding 500°C. At these temperatures, the shell steel reaches the plastic phase and the deformation will be permanent, which will cause problems for the installation of the refractory brick.

reel kiln results simulation, shell without fins simulation, shell with fins

Figure 7. Comparison between the outside temperature of the shell with and without fins.

Table 4. The variation of the outside temperature of the shell as a function of the inside temperature of the kiln. Temperature inside the kiln (°C)

The Variation of the Hot Air Temperature of the Burner In this part, we wanted to know the effect of the variation of the hot air temperature of the burner. For this, we deduced the distribution of the external temperature of the shell with respect to the length of the kiln near the cooking zone. From Table 4 we can see that the reduction in the maximum temperature exceeds 20%, in the case of shell with fin than that without fin. In Figure 8, the shapes of the curves are the same with a progressive increase, until reaching a maximum at the distance of 11 m, then decreases. The external temperature values of the shell fitted with fins are lower, with an overall reduction that can reach 40%. Similarly, the variation in the internal temperature of the kiln has a clear impact on the shell without fin, with an increase of approximately 11%, whereas it is approximately 12% in the case of the shell with fin.

300 Shell without fin, Tair kiln = 1050 °C Shell with fin, Tair kiln = 1050 °C Shell without fin, Tair four = 1150 °C Shell with fin, Tair kiln = 1150 °C Shell without fin, Tair kiln = 1250 °C Shell with fin, Tair kiln = 1250 °C Shell without fin, Tair kiln = 1350 °C Shell with fin, Tair kiln = 1350 °C Shell without fin, Tair kiln = 1450 °C Shell with fin, Tair kiln = 1450 °C

Figure 8. The variation in the outside temperature of the shell as a function of the inside temperature of the shell.

Variation of the Hot Air Injection Velocity of the Burner Table 5 shows the simulation results of the maximum external temperature of the shell in the cooking zone for the two cases with and without fins. The increase in the air injection velocity of the burner causes an increase in temperature, this is the same for both cases. But we notice for the temperatures of the case without fins are more important than that with fins. Thus for the velocity of 13.75 m/s, we have a temperature of 470°C for the case without fins and 385°C for the case with fins, so a difference of 85°C (18%). This difference reaches its maximum at 20.6% for the velocity of 53.74 m/s. which will allow a greater flow of heat to be evacuated and protect our shell from hot spots. In figure 9, we wanted to show the variation of the external temperature of the shell for the two cases with and without fins on the section of shell according to different hot air injection velocities. The temperature profiles have the same trend and the same appearance. This representation gives us a very clear idea of the efficiency of the fins installed on the external surface of the shell section of the cooking zone. The temperature reduction varies between 30% and exceeds 33%, which is very important for this type of industry. With a shell without fins, the maximum temperature reached is 510°C, while when the fins are installed it only reaches 405°C, therefore we have a reduction of 105°C. Ambient Air Temperature Variation Figure 10 shows the variation in the outside temperature of the shell as a function of the ambient air temperature. The representation is made for both cases, namely without and with fins. The curves have the same trend, an increasing progression up to a maximum at the distance of 11 m, then a decrease. With regard to the effect of ambient temperature, it can be seen that its effect is minimal, since the curves are very close. We notice a very clear difference between the curves with fins and those without fins. The maximum temperature is 390°C for the finned case, while

Tableau 5. Maximum shell temperature as a function of hot air injection velocity Vitesse d’air chaud (m/s)

300 Shell without fin, V = 13,75 m/s Shell with fin, V = 13,75 m/s Shell without fin, V = 23,75 m/s Shell with fin, V = 23,75 m/s Shell without fin, V = 33,75 m/s Shell with fin, V = 33,75 m/s Shell without fin, V = 43,75 m/s Shell with fin, V = 43,75 m/s Shell without fin, V = 53,75 m/s Shell with fin, V = 53,75 m/s

Figure 9. The external temperature of the shell with fins as a function of the hot air velocity.

Shell without fin, Tair = 5 °C Shell with fin, Tair = 5 °C Shell without fin, Tair = 18 °C Shell with fin, Tair = 18 °C Shell without fin, Tair = 28 °C Shell with fin, Tair = 28 °C Shell without fin, Tair = 38 °C Shell with fin, Tair = 38 °C Shell without fin, Tair = 48 °C Shell with fin, Tair = 48 °C

than 40%. This has a considerable impact on the protection of the ferrule. We also wanted to see the impact of some factors such as the hot air injection velocity, the internal air temperature of the kiln and the ambient temperature on the development of the temperature of the shell. Thus, it could be deduced that the velocity of hot air injection has a considerable effect on the behavior of the external temperature of the shell. We noticed an increase in temperature during the transition from one value to another of the air inside the kiln, until reaching its maximum at T= 1450°C. This observation is the same for the two cases where the shells was with or without fins, while the comparison of the two leads to a reduction in the external temperature of the shell of approximately 40% at most. For the third parameter, which is the ambient temperature, we see that its effect is very small and does not exceed 3%. But when changing from the simple shell to a shell with fin, the reduction in temperature is significant and reaches the value of 33%. This study allowed us to determine a way to reduce the outside temperature of the shell in the hottest part of the kiln, namely the cooking zone. Thus, the cooling of a shell of a cement rotary kiln was numerically simulated by the insertion of 72 fins on the external surface of the shell. As a perspective to this work, we opt for an optimization in the shape and dimensions of the fins. As well as the transition from a numerical to an experimental study that can identify the more global problem.

Nomenclature

Figure 10. Shell temperature variation as a function of ambient air temperature. it is 495°C for the finless case, so there is a reduction of 105°C, which is very interesting for the protection of this equipment.

Conclusion

The main purpose of our work is to highlight the impact of the cooling of the shell of a rotary kiln in the cooking zone over a length of 17 m, which is thermally stressed. We chose cooling by the use of fins, which is an innovative solution installed on the rotary kiln. The integration of fins on the external surface of the shell has given us very interesting results, since the reduction of the external temperature reaches values of more

Nu Nusselt number h Heat transfer coefficient, W/m2°C p Fin perimeter, m D Cylinder diameter, m A Area, m2 Ac Fin cross-sectional area, m2 Af Fin surface area, m2 η Fin efficiency N Fins number g Gravitational acceleration, m/s2 H Fin height, m L Fin length, m t Fin thickness, m Pr Prandt number Ra Rayleigh number U, U’ Mean velocity in tensor notation P Pressure μ Dynamic viscosity, kg/m.s λ Thermal conductivity, W/m.°C T Temperature ρ Density of the fluid, kg/m3 Cp Specific heat, J/kg.K SΦ Local production of 𝜙. Φ Generalized variable Γ Coefficient of diffusion

Γ Effective diffusivity ɳ Efficiency SΦ Local production of 𝜙. ω Specific dissipation rate Gk Term of production of k Gω Term of production of ω Sk Mean strain rate tensor σ Normal viscous stress, N/m2 α Thermal diffusivity (λ/ρCp) indice i, j Indices according to the axes ‘ Fluctuation index

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

Reference

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