Numerical analysis of turbulent flow and heat transfer enhancement using V-shaped grooves mounted on

Abstract

Keywords: Heat Transfer Enhancement; K -Ω Sst Model; Rotary Ciment Kiln; V-Shaped Groove

Introduction

Algeria’s cement industry has gradually improved in recent years as the number of cement production lines has increased. The rotary kiln is the primary piece of equipment used in cement production, from limestone calcination to cement manufacturing. It is a type of heat exchanger that consists of a steel tube lined with refractory brick. The rotary kiln rotates at 0.5 to 5 revolutions per minute and is inclined from 1 to 4 degrees. The rotary kiln is divided into four sections [1]: Preheating/drying, calcining /decomposition, burning, cooling (Figure 1).

The heat transfer phenomenon in a rotary kiln is complicated because it includes conduction, convection, and radiation all at the same time. Many researchers investigated the heat transfer mechanism in refractory kilns, as shown in [2,3]. Sass [4] created a heat transfer model for rotary kiln dryer radiation transfer calculations using empirical relations. Ghoshdastidar et al. [5] created a heat transfer model for a wet iron ore heating rotary kiln. This model was accurate in terms of kiln length, axial solid and gas temperatures. Ghoshdastidar and Agarwal [6] also conducted a numerical study of heat exchange in a rotary kiln for drying and preheating wood chips. Schmidt and

*Corresponding author. *E-mail address: attou_youcef@yahoo.com This paper was recommended for publication in revised form by Editorin-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/).

Nikrityuk [7] conducted a two-dimensional (2D) numerical simulation of transient heat transfer in a horizontal rotary kiln using DNS. They demonstrated that the gas vortex enhanced convective heat transfer in the top of the particulate bed. Sonavane and Specht [8] performed a numerical simulation using the Finite Element Method (FEM) to predict temperature fluctuations in the rotary kiln wall. In addition, Cook and Cundy [9] created a mathematical model to predict heat transfer between a rotating cylinder’s heated wall and an adjacent wet granular medium. Elattar et al. [10,11] used a two-dimensional (2D) CFD simulation to investigate the impact of rotary kiln operating conditions and burner geometrical parameters on flame characteristics such as heat and fluid flow when using gaseous fuels. They also investigated the effects of primary air ratio, burner geometry on the flow field, and kiln wall peak temperature. Mirhosseini et al. [12] recently investigated numerically the influence of an absorber placed around a rotary kiln on heat transfer characteristics. As a future study, the absorber is specifically designed for heat recovery. They discovered

Figure 1. Figure 1. Schematic view of the rotary cement kiln [29]. Adapted from: Csernyei C, Christopher M. Numerical Modelling of a Rotary Cement Kiln with External Shell Cooling Fans. Electronic Thesis and Dissertation Repository. 2016. Available at: https://ir.lib.uwo.ca/etd/3682.

that the contribution of radiative heat transfer to the total heat transferred from the kiln to the absorber is significant. A few studies have been conducted to investigate jet impingement cooling of circular cylinders [13,14]. Csernyei et al. [15] conducted a numerical investigation to study the convective heat exchange caused by multiple circular jets impinging on a horizontal cylinder, as evidenced by the cooling of rotary cement kilns using large axial fans. The effect of changing the geometric parameters of the shell cooling fans on the kiln’s shell temperature was also investigated. Grooved channels, which are the major components in annular spaces, are widely used in industrial applications to improve heat transfer [16-18]. Nouri-Borujerdi et al. [19,20] provide comprehensive reviews of rotating cylinder cooling. These reviews are primarily concerned with the cooling of grooved cylinders. More recently, Moumin et al. [21] conducted an experimental study of heat transfer to the bed inside a rotary kiln. They used sand as a granular material and cement raw meal as a powdery material, as well as a rotating cylinder with rotational speeds of 1, 2, and 3 rpm heated through the outer shell. Many experimental and numerical studies on thermal performance enhancement using V-shaped fins, such as heat exchangers, turbines, impingement cooling, and solar air receiver/heater have been widely conducted [30-32]. Promvonge et al. [33] carried out an experimental study to investigate thermal behaviors in a heat exchanger channel with V-shaped ribs and grooves. They discovered that the thermal enhancement factor (TEF) is around 2.12, 2.14, and 2.11, indicating that the baffle-groove performs better than the rib-groove by about 13%. Kaur et al. [34] investigated numerically the effect of six V-rib configurations on thermal-hydraulic performance in a square channel. They found that the mean heat transfer and pressure drop values of compound ‘V-rib and V-protrusion’ configurations provided the best thermal-hydraulic performance value and the highest Nusselt number ratio at a fixed Reynolds number of 50,000. The temperature increases outside the furnace in the case of the failure of furnace refractory bricks by crusting, bricks wear (where it exceeds 650°C) and therefore influences the behavior

Figure 2. Deformation of the outer wall of the rotary cement kiln.

Figure 3. Two-dimensional model of rotary kiln: (a) Smooth walls, (b) grooved wall with h/D=0.1, (c) grooved wall with h/D=0.2, (d) grooved wall with h/D=0.3, (e) grooved wall with h/D= 0.4. of the shell material (Figure 2). The use of V-shaped grooves mounted on rotary kiln’s outer wall has been no reported in any research article. The purpose is to analyze the variation of the depth of grooves with different depth ratio from 0.1 to 0.4 on the heat transfer intensification in rotary kilns.

lower than 10-6 is chosen to achieve the convergence criterion for all variables [24]. The governing conservation equations for air flow and heat transfer inside the rotary kiln are as follows: Continuity Equation

Problem Statement

Figure 3 depicts a schematic representation of a two-dimensional grooved wall with depths (h/D) ranging from 0.1 to 0.4. The type of rotary cement kin used in this research, from Lafarge Cement Plant [22] which is located in Oggaz (Wilaya of Mascara, Algeria). The kiln diameter D and length L were 5 and 40 meters, respectively, and d is the diameter of the burner. Rotary kiln is titled of 3 degrees. Furthermore, the V-shaped grooves are installed on the kiln’s burning wall to improve heat exchange and protect the outer cylinder. Simulation Procedure and Governing Equation ANSYS FLUENT is used in this work to numerically solve the governing equations (Patankar and Spalding [23]), and the convective terms are solved using a second order upwind scheme. The SIMPLE algorithm, on the other hand, is used for velocity-pressure coupling. The residuals

(1) Movement Quantity Equation (2) Energy Equation (3) All of these equations have 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 local Nusselt number is displayed along the grooved kiln wall as follows:

(9) Where vt is turbulent kinematic viscosity computed by combining k and ε: (10)

(5) Turbulence and Mathematical Models In this study, four turbulence models (RANS approach) were tested: k-ε standard, k-ε Realizable, k-ω SST and k-ε RNG. According to the findings, the k-ω SST model is more accurate than the others in validating CFD results. The Menter [25] k- SST (Shear Stress Transport) model is used to treat turbulence. This model combines two models: Wilcox’s [26] k-ω model for the area close to the wall and Jones and Launder’s [27] standard k-ε model for the area far from the wall. Under adverse pressure gradients, the k-ω SST model provides highly accurate predictions of the beginning and amount of flow separation (Bardina et al. [28]). It is recommended for high accuracy boundary layer simulations, making it the ideal model for the current simulation. The k and ω transport equations of SST turbulence model are: (6)

(7) With: Pk represents production of turbulent kinetic energy due to the gradient of the average velocity: (8)

Boundary Conditions and Grid Distribution The computational domain’s boundary conditions were primary and secondary air velocities, the temperature of the rotary kiln’s outer wall and air is considered as the working fluid (Figure 4). The following boundary conditions are appropriate for this study: primary air velocity of 23.3m/s at 1573 K, secondary air velocity of 2.35m/s at 373 K. Thereafter, the constant wall temperature is then applied and the kiln rotational speed is set to 4 rpm (≈0.42 rad/s). In our study, we used the 2D channel without and with V-shaped grooves, and simulations were performed using the mesh generated in ANSYS ICEM as a preprocessing program with structured mesh (hexahedral mesh). Several grids were used, including 20.000, 40.000, and 100.000 nodes, and the mesh is very refined near the heated wall to capture the maximum amount of data for the various depth values (Figure 5). Mesh Sensivity Three structured grids are tested to examine mesh quality and its impact on simulation calculations. As illustrated in Figure 6, the mesh number ranged from 20,000 to 100,000 nodes. The three curves are found to have the same profile as the experimental data. The temperature varies significantly along the kiln; the first grid (20,000 nodes) represents a good compromise between result accuracy and computational cost and time.

Figure 5. Grid of the computational domain: (a) smooth walls; (b) grooved walls.

Turbulence Model Validation The code verification was performed based on the boundary conditions and geometry with real values used in the rotary kilns of Lafarge cement plant (Mascara, Algeria). To ensure proper validation, we used the same grid generated by the ICEM CFD software, with 20,000 nodes retained. Figure 7 depicts the current numerical results

as well as the temperature profile of the Lafarge cement plant. The graph shows that the general trend of increasing temperature T along the wall is correct. Several turbulence models are tested, including k-ε Standard, k-ε RNG, k-ε realizable, and the shear-stress transport k-ω (SST). It should be noted that all turbulence models follow the same profiles as the experimental data. As a result, there is a

good agreement between the k-ω SST model and the kiln temperature. Therefore, this turbulence model was used to carry out the simulation work.

Analysis And Interpretation Of Results

Temperature Evolution Along the Kiln Length Figure 8 depicts the effect of groove depth mounted on the rotary kiln’s outer wall on temperature profiles along the axial wall. The highest temperatures were recorded in case 1 (configuration without grooves), while the other cases had the lowest temperature profiles. It should be noted that the temperature of the four configurations with depths h/D (0.1, 0.2, 0.3, and 0.4) follows the same pattern and provides good kiln wall cooling when compared to the smooth case. Furthermore, the peaks of temperature profiles can be seen

in configurations with grooves. On the other hand, the temperature rises along the groove base as a result of air recirculation (the formation of vortices) within the grooves. At (X = 35m), a temperature difference of 120 °C is observed between the grooved wall with depth (h/D = 0.4) and the smooth wall. As a result, the V-shaped configurations provide significant wall cooling to protect the external walls from deformations. Local Nusselt Number Evolution Figure 9 depicts four grooved channel configurations as well as a smooth channel. This figure illustrates the same evolution of Nusselt number profiles. In contrast to the smooth walls, the four graphs that include grooves with different depths (h/D=0.1, 0.2, 0.3, and 0.4) show a significant increase in Nusselt number. Furthermore, the presence of grooves on the burning part can be used to achieve the peaks (15-32m). Increases in groove depth h result in greater heat exchange enhancement due to an increase in the size of the recirculation zone. The grooved wall with h/D=0.4 has the highest Nu on the kiln burning part (Nu=1700), while the smooth wall case has the lowest Nu (Nu=600).

Figure 8. Temperatures evolution graph as a function of kiln length.

Variation of the Local Friction Coefficient Cf The variation of the friction coefficient Cf along the axial wall of the rotary kiln for different groove depths (h/ D=0.1, 0.2, 0.3, and 0.4) is shown in Figure 10. It can be seen that the amplitudes (h/D=0.2, 0.3, and 0.4) have the same evolution along the wall as the flat wall. The Cf coefficient decreases from (Cf =0.17) at the kiln’s inlet to (Cf=0.005) at position (X=10m) then we see the appearance of the peaks for each groove. We also notice that as the depth of the groove increases, so does the Cf. As can be seen, the highest values of Cf are found at the kiln burning part (Cf =0.06), particularly at the top of the V-shaped grooves where the flow is recirculated.

Figure 9. Local Nusselt number versus kiln length for different grooves depth.

Figure 10. local friction coefficients versus kiln length for different grooves depth.

Temperature Contours Figure 11 shows the effect of mounting different V-shaped groove depths on the temperature distribution in a rotary kiln. According to the temperature contours, the high temperature zone area is located near the burner, and the maximum air temperature produced by the burner is (T=1573K), as shown in figure 11. It is

also discovered that the lowest temperature values are found inside the grooves. As a result of the creation of a recirculation zone inside the fins, the V-shaped grooves improve air mixing near the wall, particularly for the fourth and fifth configurations (h/D=0.3 and 0.4). Therefore, increasing the groove depth lowers the temperature of the kiln walls.

Figure 11. Isotherm contours of rotary kiln at different groove depths.

Streamline Contours Figure 12 depicts velocity pathlines within the rotary kiln for each of the five configurations with and without V-shaped grooves. Because of the high velocity and temperature of the primary air, the air flow is deflected away from the burner, producing a large turbulence that is filled with hot air and distributed along the kiln wall, according to the streamlines. It is also shown that the air inside the grooved channel is distinguished by the presence of a recirculation zone formed within each groove along the longitudinal axis. Furthermore, as seen in the streamlines plot, the growth of the recirculation region inside the groove

Conclusion

The work discussed in this paper enabled the use of a commercial CFD code to study the numerical simulation of the forced convection of a turbulent flow over grooved walls of a rotary cement kiln. The results are obtained by the computational simulation of cooling the rotary kiln’s outer wall through four grooved configurations.

Figure 12. Streamlines of air velocity for different groove depths.

The numerical results presented in this study demonstrate that the use of V-shaped grooves mounted on the burning part of the rotary kiln contributes to a consequent heat exchange, with the effects of this improvement visible in the Nusselt number and temperature profiles, which increase in value when compared to the smooth kiln wall. According to the findings of this study, the grooved channel with depths h/D=0.3 and 0.4 provides significant wall cooling and significantly higher turbulence than the other cases to protect the rotary kiln’s outer walls from deformations.

Nomenclature

Length of the kiln, [m] Kiln diameter, [m] Burner diameter, [m] Temperature, [K] hydraulic diameter , [m] axial speed of fluid, [m.s-1] Nusselt number Coefficient of friction Turbulence kinetic energy, [m2.s-2] Convective heat transfer coefficient, [W.m-2.K-1],

Greek symbols ρ Fluid density, [kg/m3] λ Thermal conductivity, [W.m-1. K-1] ν Kinematic viscosity, [m2.s-1] ε Turbulence dissipation rate, [m2.s-3] νt Turbulent kinematic viscosity, [m2.s-1] τij Viscous stress tensor δij Kronecker delta 𝜙 Generalized variable ω Specific dissipation rate, [s-1]

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