Particle-fluid heat transfer close to the bed wall: CFD simulation and experimental study of particle shape influence on the formation of hot zones

International Journal of Thermal Sciences 150 (2020) 106223

Contents lists available at ScienceDirect

International Journal of Thermal Sciences journal homepage: http://www.elsevier.com/locate/ijts

Particle-fluid heat transfer close to the bed wall: CFD simulation and experimental study of particle shape influence on the formation of hot zones Mahdi Zare, Seyed Hassan Hashemabadi * Computational Fluid Dynamics Research Laboratory, School of Chemical, Petroleum and Gas Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran

A R T I C L E I N F O

A B S T R A C T

Keywords: Non-spherical catalyst particle Heat transfer Packed bed reactor Computational fluid dynamics (CFD) Wall effects Hot zones

This paper investigated the heat transfer from a wall-affected non-spherical particle to the turbulence gas flow both numerically and experimentally. In the numerical section, a three-dimensional finite element method was used to solve the partial equations using FEMLAB version 2.3. In the experimental section, the axial flow over a single naphthalene particle with the tube to particle diameter ratio (N) ranging within 4.5–6.7 was examined and the Nusselt number was calculated by heat and mass transfer analogy. The effects of the tube wall, particle shape, and particle rotation angle were tested on the formation of hot zones in detail. The results indicated that the wall effect can be ignored when particle-tube wall distance per particle diameter was greater than 0.143 (yc/Dp � 0.143). Internal holes did not play an important role in reducing the hot zones though they increased the heat transfer rate per unit volume of the particle and reduced the pressure drop due to the higher porosity of packed bed. The minimum hot zones were observed for the tri-lobe particle at the axial rotation angle of zero when the particle leaned against the wall tangentially. The predicted results were well congruent with the experimental results. The results obtained by this study can be applied to discovering more about the hot spots and obtain a better catalyst particle for packed bed reactors.

1. Introduction Packed bed columns for gas-solid interaction are widely used as re­ actors, separators, dryers, filters, and heat exchangers in the chemical and food industry [1,2] as well as in environmental protection including water purification and SO2 removal [3,4]. Because of the strong diffu­ sional limitations, reactions can occur only in a thin layer adjacent to the particle surface [5], suggesting that the reaction rate depends on the surface area of particles [6,7]. One of the major advantages of packed beds is the efficient heat transfer rate in highly endothermic or exothermic reactions due to the high surface area to volume ratio offered by the catalyst particles [8]. Over time, normal catalyst particles have transitioned from spheres, cylinders, and Raschig rings to multi-hole pellets and/or external gapped pellets [9,10]. Modified pellets provide larger particle surface areas to volume ratios, leading to a higher catalyst activity [11,12]. In this regard, there are many studies on the flow around single particles such as spheres, cylinders, etc. [13–17], while multi-lobe particles have been used only in a few of them [18,19].

Multi-lobe particles are important as they have a higher heat and mass transfer rate thanks to providing a higher surface area to volume ratio. The problems of understanding and predicting the hydrodynamics and the rate of heat transfer in a fixed-bed reactor have been examined extensively [20–23]. There are many difficulties in predicting the hy­ drodynamics of fixed beds with low tube to particle diameter ratios (3 < N < 8), due to the presence of wall effects across the entire bed section [24,25]. One of the most important issues in industries for reducing the life­ time of particles and bed wall, especially reactors with a high heat of reactions, is the development of hot zones [26–28]. Hot zones can be created in the center of bed (highly exothermic reactions) or on the tube wall (highly endothermic reactions) [29,30]. In reactors with highly endothermic reactions (e.g. steam methane reforming), the required energy to start and continue the reaction is usually supplied from the tube wall. A hot spot is formed within the tube wall when the amount of released heat is much larger than that of consumed heat [31]. This en­ ergy must be transferred to the fluid flow to support the reaction. When

* Corresponding author. E-mail address: [email protected] (S.H. Hashemabadi). https://doi.org/10.1016/j.ijthermalsci.2019.106223 Received 16 July 2019; Received in revised form 6 November 2019; Accepted 5 December 2019 Available online 15 December 2019 1290-0729/© 2019 Elsevier Masson SAS. All rights reserved.

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

a particle leaned to the tube wall, a small area with low fluid velocity is created which reduces the heat transfer rate from the tube wall to the fluid flow. This reduction in the heat transfer makes a small area with high temperature, called hot zones (or hot spots), which damages the bed wall and reduce its lifespan by over 50% for a 20 � C hotter tube wall. A common rule of thumb in Steam Methane Reforming reactors (SMR) suggests that, taking on-site expenditure into account, the complete re-tubing of a typical reformer reactor with 300–400 tubes costs be­ tween 5 and 8 million USD [25]. In this regard, packed beds have remained the subject of ongoing investigations, where a large number of studies have been conducted to reduce the hot zones [26,32,33]. Early computations in fixed beds were performed by Sørensen and Stewart [34]. Two/three dimensional CFD simulation of fluid flow over a single particle [35–38], two spheres near a wall [39,40], and several particles along a straight line were studied [41–43]. Three-dimensional CFD simulation of heat transfer over a small number of spherical par­ ticles was undertaken by Dixon et al. [13,44–46]. Partopour and Dixon [47] studied the non-steady state effect of reactions inside the porous media using a simplified reaction model. Dixon and Nijemeisland noted that CFD simulation is a good technique for predicting the fixed beds with low tube to particle diameter ratios (N < 8) [48,49]. A rapidly growing segment of the computer hardware industry has made it possible to simulate entire beds loaded with a simple geometry of particles [50–52]. An isothermal packed bed of spherical particles with N ¼ 5 was studied by Esterl et al. [53], and a complete bed of 44 spheres with N ¼ 2 was presented by Nijemeisland and Dixon [54]. They tested the temperature and velocity profiles inside the pores [25,48,55]. In another work, they modeled small groups of structured spherical particles (N ¼ 2) by Finite Volume Method (FVM) and suggested that the dominant heat transfer mechanism is conduction [48]. They further observed that consideration of the effects of wall-particle conduction improves the heat transfer through the bulk of particles [25]. The heat transfer coefficient distribution on the spheres in a three-dimensional (3D) array in pebble bed reactors (PBRs) was investigated by Kao et al. [56]. They used different turbulence models and found that the

effect of tortuosity on the heat transfer in packed beds was investigated by Zare and Hashemabadi [19]. They calculated the tortuosity by a numerical method and modified a correlation in which the tortuosity was considered as a new parameter. The role of various features of complex particles affected by the tube wall, and the consequences of heat transfer and hot zones formation, have not been well integrated into the current literature. More experi­ mental and simulation studies are required to capture the effects of particle shape on the hydrodynamics as well as heat and mass transfers. Accordingly, this study investigated the effects of non-spherical particle shapes on the formation of hot zones when they are affected by the bed wall, which has not been studied so far. To this end, the effect of particle shape, particle rotation angle, and the internal holes was studied on the formation of hot zones. Non-spherical particles used in this study include two widely used particles (Cylindrical and Surface Gapped Cylindrical) and a tri-lobe particle. 2. Experimental study Fig. 1 presents the experimental setup used in this study to measure the particle-fluid heat transfer according to the Chilton–Colburn heat and mass transfer analogy [18,41,58,64]. Among many analogies (e.g. Reynolds analogy, Prandtl–Taylor analogy) developed to directly relate heat and mass transfer coefficients, Chilton and Colburn J-factor anal­ ogy proved to be the most accurate one [65]. As demonstrated in Fig. 1A, the bed was composed of a glass cylinder of 66 mm diameter and 300 mm high. The tube to particle diameter ratios (or bed aspect ratio, N) were 4.5, 5.1, and 6.7 for cylindrical, Sg-cylindrical (surface gapped cylindrical), and tri-lobe particles, respectively. Compressed air entered through a distributor located at the bottom of the bed and was withdrawn after passage over the particle. The airflow rate was measured by a rotameter with an accuracy of 0.1 m3/h. To study the particle shape effects, three different particles, cylin­ drical, Sg-cylindrical, and tri-lobe particles (Fig. 2A–C) were examined. The particles were fabricated by molding a mixture of NaCl salt and a suitable glue. Note that immersion is a practical method for making naphthalene particles [41,64]. Accordingly, the particles fabricated with NaCl were submerged in molten naphthalene. After a few seconds,

f turbulence model best predicts the heat transfer characteristics. In addition to the κ ε equations, this model solves two more turbulence quantities, the normal stress function (v2) and the elliptic function (f). Thom� eo and Grace [57] examined spherical glass beads and found that a two-region heat transfer model can be applied with two thermal energy balances, one for the central core, and the other for the wall region. Ahmadi Motlagh and Hashemabadi worked on CFD simulation and experimental validation of particle-to-fluid heat transfer in a randomly packed bed loaded with cylindrical particles which were coated by naphthalene [41]. The heat and mass transfer analogy was employed to validate the numerical results. They proposed a correlation for the Nusselt number by considering the tube to particle diameter ratio (N) as a new effective parameter. Mirhashemi et al. [58] tested the wall effect by extending the tube to particle diameter ratio (N) from 1.66 to 18. They found that the bed wall had no significant effect on the Nusselt number if the bed aspect ratio (N) was greater than 12. The heat transfer in a fixed bed of spheres was examined by Dixon et al. both numerically and experimentally [59,60]. They treated contact points in four ways: Increasing (overlaps)/reducing (gaps) the size of a particle, locally inserting bridges (bridges), and surface flattening (caps) at contact points. Zare and Hashemabadi [18] proposed a correlation to predict the heat transfer coefficient of a multi-lobe particle in a bed affected by the wall. Furthermore, the methane steam reforming process over a cylindri­ cal particle with one internal hole was studied by Dixon [61]. He studied rotation angles of 0� to 90� and analyzed the reaction rate around the particle. The non-uniform local flow of gas inside a randomly porous media for 1.5 < N < 5 was investigated experimentally and numerically [62]. The experimental and numerical average bed porosity were compared and the same results as Zou’s model were observed [63]. The

ν2

Fig. 1. The studied experimental setup loaded by the tri-lobe particle as an instance; A) Experimental setup, B) Schematic view; Note that all the particles in Fig. 2 were studied experimentally. 2

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

Fig. 2. Catalyst particle shapes and the created meshes; A) cylindrical, B) Sg-cylindrical, C) tri-lobe, D) multi-hole cylindrical, E) multi-hole Sg-cylindrical, F) multihole tri-lobe.

a thin naphthalene layer was coated on the surface of the particles. In this condition the concentration of naphthalene in the surface of particle was constant and equaled to its saturation concentration, as described in Refs. [18,64]. The same methodology was used to calculate the mass transfer rate as explained in detail in our previous works [18,58,66]. In this method, the particle was placed in the center of the glass tube with a low tube to particle diameter ratio. A turbulent flow of air at 22 � C (Pr ¼ 0.74, Sc ¼ 2.284) passed through the bed to obtain a high mass transfer rate for achieving precise results [66,67]. The experiments were conducted in 6, 8, and 10 m3/h airflow rates separately for three different shapes of particles with and without holes (Fig. 2A–F). The mass transfer rate was calculated based on the weight loss of the particle (due to the subli­ mation) during each experiment, divided by its time. Finally, the Chilton-Colburn heat and mass transfer analogy was applied to calculate the Nusselt number [41,66]. The bed aspect ratio, N, is defined as the tube diameter, DB, divided by the equivalent particle diameter, Dp, as follows: N¼

DB Dp

Nu ¼ Sh �

� �n Pr Sc

(2)

where the exponent “n”, is an empirical constant within the range of 1/3 to 0.4. According to the Chilton–Colburn analogy, which was used in this work, the “n” exponent equals 1/3 [65]. The detailed calculation procedure of Sherwood and Nusselt number from this analogy was described by Ahmadi Motlagh and Hashemabadi [66]. 3. CFD simulations 3.1. Geometry development This work presents the heat transfer behavior of a single catalyst particle, incorporated in a cylindrical domain with small N. Three par­ ticle shapes, with and without internal holes, were studied including cylindrical, Sg-cylindrical, and tri-lob particles (Fig. 2A–F). The particle surface area-to-volume ratios, as indicated in Fig. 2A–F, were 201.6, 226.9, 248.2, 409.9, 464.4, and 607.7, respectively. The diameter of internal holes (multi-hole particles) was 4 mm giv­ ing an outer-to-internal radius ratio of 3.5. To study the wall effects on the formation of hot zones in the fixed bed, the behavior of one particle close to the tube wall was studied. Accordingly, the particle was placed next to the tube wall with a 66 mm diameter where the tube height was long enough to make a fully developed flow before and after the particle.

(1)

The average Sherwood number was calculated by the mass transfer rate gained from the experimental work [66]. The average Nusselt number was calculated as follows:

3

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

3.2. Governing equations

section (Uin, Tin), and hydrodynamically & thermally fully-developed flow, at the outlet section, were considered. In the experiments, the concentration of naphthalene at the surface of particles was assumed to remain constant and equaled its saturation concentration [18,64]. In the CFD simulations, the particle surface temperature was considered con­ stant since, in the heat and mass transfer analogy, a particle with a constant surface temperature in the heat transfer equation is equal to the particle with a constant surface concentration in mass transfer equation [64]. In the endothermic reactions (e.g. steam reforming reactions) the catalyst bed temperature decreased when the reaction started; but after certain time when steady state condition was reached, the temperature remained constant [72]. Therefore, the particle surface temperature in all situations was considered constant, Ts, where the free stream tem­ perature was T∞ (Table 1). Due to the constant temperature of the particle surface, the heat transfer inside the solid particles was not considered. To reduce the variations in the thermo-physical properties of fluid with temperature, the particle temperature was considered to be 22 � C warmer than the fluid temperature. To solve the equations of continuity, momentum, and energy individually, the fluid flow proper­ ties were assumed to be constant. Because of the long experimental time (each test 30 min), the experiments were assumed to be steady-state, with the governing equations (Eqs. (3)–(7)) being solved in steady conditions.

The fluid flows are usually modeled as incompressible flow when the Mach number (the ratio of flow velocity to the speed of sound) is less than 0.3 [68]. Therefore, the conservation equations of mass, mo­ mentum, and energy were resolved simultaneously for the incompress­ ible fluid phase (Ma ¼ 0.0014–0.0023) over a particle. The general form of these equations for gas turbulence flow under steady-state conditions is as follows [18]: (3)

r ⋅ ðρUÞ ¼ 0 r ⋅ ðρUUÞ ¼

(4)

rp þ r⋅½ðμ þ μt0 ÞðrU þ rU y Þ�

�

(5)

r ⋅ ρCp UT ¼ r ⋅ ððk þ kt0 ÞrTÞ þ Sh

where Sh is the sink or source term, μt0 represents the turbulence vis­ cosity, and kt0 is the turbulence thermal conductivity of the fluid. The standard κ ε turbulence model, which is one of the most commonly used models in industrial applications, has been implemented in CFD simulations [18,41,64,69]. The κ ε turbulence model consists of a turbulent kinetic energy part: � � �� ∂κ C κ2 κ2 νþ μ (6) rκ þ Cμ ðrU þ rU y Þ2 ε þ U ⋅ rκ ¼ r ⋅ ∂t σk ε ε along with a turbulence dissipation rate part: � � �� ∂ε C κ2 rε þ Ce1 Cμ κðrU þ rU y Þ2 νþ μ þ U ⋅ rε ¼ r ⋅ ∂t σe ε

Ce2

ε2 κ

4. Results and discussion 4.1. Mesh independency

(7)

The wall yþ is often used to create a suitable mesh near the wall whose value depends on the selected turbulence model. To achieve good accuracy, when the wall function boundary condition is used, the yþ range should be between 30 and 300, or at least between 10 and 1000 [73]. The mesh independence study was performed at the flow rates of 6, 8, and 10 m3/h for each particle type where the distance of the first mesh from the particle surface was chosen to obtain yþ>10. Then, volume meshes were created from “extra coarse” to “extra fine” sizes. The average Nusselt number over the tri-lobe particle (Fig. 2C) versus the meshes generated by different precision at the flow rate of 6 m3/h was presented in Fig. 3 as an instance. It showed that increasing the mesh refinement from 78,846 (finer type) to 125,154 (extra fine type) didn’t make a significant change on the average Nusselt number. Therefore, the finer mesh type was chosen for simulating the tri-lobe particle at the flow rate of 6 m3/h. The same approach was also applied for other particles (Fig. 2A–F) to find the optimal mesh density. The CFD simu­ lations were performed with a core i7, 3.2 GHz HP workstation XW8000 with a 6 MB cache memory and 20 GB RAM memory. The same procedure was used for flow rates of 8 and 10 m3/h. The optimum mesh chosen for each particle in terms of accuracy and the computational cost was reported in Table 2.

where κ is the turbulent kinetic energy, ε represents the turbulence dissipation rate, v is the kinematic viscosity, rUy denotes the transpose of velocity gradient tensor, and Cμ ; σk ; σ e ; Ce1 , Ce2 refer to empirical constants for Eqs. (6) and (7) [58]. In the numerical work, the average heat transfer coefficient and the average Nusselt number for each par­ ticle were calculated by integrating Eq. (8) and Eq. (9) on the particle surface, respectively [41]. � � k ∂T h¼ (8) Ts Tb ∂η s Nu ¼

� � hDp Dp ∂T ¼ k Ts Tb ∂η s

(9)

where η shows the normal direction to the pellet surface. The most important parameter influencing the average Nusselt number is the mesh quality close to the pellet surface because of its effect on the temperature gradient. Judging the applicability of wall functions, one of the most prominent dimensionless parameter is the distance from the wall (yþ). yþ ¼

u* y

ν

where u* is the friction velocity (u* ¼

(10)

4.2. Validation

qffiffiffi τw ρ ), y is the distance to the

The calculated Nusselt numbers were compared with the experi­ mental data, with the result displayed in Fig. 4. According to the figure,

nearest wall, and ν is the local kinematic viscosity of the fluid [70]. The range of yþ guarantees the mesh quality near the particle and tube wall boundaries which was discussed in Section 4.1. According to the Kawaguti [71], the critical Reynolds number for the flow past a sphere is 51, indicating that in this study (2100 < Re < 3700) the flow has been fully turbulent.

Table 1 Hydrodynamics and heat transfer boundary conditions. Equation

Boundaries

Type

Unit

Value

Hydrodynamics

Tube wall Particle surface Inlet

No-slip condition No-slip condition Velocity Inlet

– – m/s

Outlet Tube wall Particle surface Inlet Outlet

Pressure Outlet Thermal insulation Constant temperature Constant temperature Convective flux

atm – K K –

– – Qf =Ac

3.3. Boundary conditions Energy

In all simulations, wall boundaries were set to “no-slip condition” with the “standard wall function” applied to solve the turbulent flow near the wall. Uniform velocity and temperature profiles at the inlet 4

0 – 320 298 –

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

the CFD simulations were in good agreement with the experimental data. The mean absolute percentage errors were 5.15, 5.47, 9.21% for solid cylindrical, Sg-cylindrical, tri-lobe particles, 4.57, 3.78 and 6.20 for multi-hole cylindrical, Sg-cylindrical, and tri-lobe particles, respec­ tively. To check the accuracy of the results, each experiment was carried out three times. The mean value of the measured variable was plotted as the data point and the corresponding standard deviation of the repeated measurements was indicated as an error bar on the data point. As mentioned in our paper [18], under-prediction of CFD results for naphthalene coated particles occurred due to the naphthalene subli­ mation during the process of loading onto the tube or unloading off the tube. 4.3. Flow behavior around a single particle The effects of various particle shapes (Fig. 2A–C) were investigated at a flow rate of 6 m3/h. The temperature and velocity profiles in hor­ izontal and vertical sections are shown in Fig. 5. As can be seen in Fig. 5A, when the flow passed over the particle the passing flow crosssection was reduced and the fluid velocity rose due to the particle presence. Further, the fluid velocity on the particle surface was zero because of the no-slip boundary condition. Therefore, a turbulence area with high-velocity gradients was observed around the particle (Fig. 5A–C). There were three important areas around the particle. The first one was the low-velocity zone next to the particle surface, called the viscous/laminar sub-layer. High-temperature gradients were observed across the laminar sub-layer due to the low fluid velocity and high particle surface temperature (Fig. 5D–F). The second area was the space between the tube wall and the particle. In this area, the fluid velocity was substantial and the heat transfer rate was also considerable. This section played an important role in particle-to-fluid heat transfer since hot zones can be created if the heat was transferred at a low rate (Fig. 5A–C). The third zone was located behind the particle. In this area, the particle-to-fluid heat transfer was reduced because of fluid circula­ tion and long fluid residence time (Fig. 5G–I) [61]. Fig. 6 shows the radial temperature and velocity profile of fluid flow through the bed by a cylindrical particle. It’s obvious that near the tube wall the fluid temperature is minimum and it increased as it got closer to the particle. Fig. 6 also shows that the velocity is maximum in the dis­ tance between the particle and tube wall and it decreases as it get closer

Fig. 3. The effect of mesh density on the average Nusselt number for the trilobe particle (Fig. 2C) at the flow rate of 6 m3/h; a similar procedure was applied to all other particles and flow rates. Table 2 Suitable mesh for different particle shapes. Particle cylindrical Sg-cylindrical tri-lobe multi-hole cylindrical multi-hole Sg-cylindrical multi-hole tri-lobe

Flow rate (m3/h) 6

8

10

35,048 35,924 53,567 59,767 60,661 64,765

36,164 38,119 57,253 65,396 68,231 72,122

36,503 41,845 64,153 73,656 78,275 81,364

Fig. 4. Comparing CFD simulation and empirical investigation of Nu number for an axial flow over a solid tri-lobe [18], Sg-cylindrical, cylindrical particles (Fig. 4A), multi-hole tri-lobe, Sg-cylindrical, and cylindrical particles (Fig. 4B) located in the center of the tube, with volume flow rates of 6, 8, and 10 m3/h. 5

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

Fig. 5. The axial flow velocity (A–C), temperature profiles (D–F), and velocity contours (G–I) over solid cylindrical, Sg-cylindrical, and tri-lobe particles, respectively.

to the particle surface and tube wall due to the no-slip boundary con­ dition. It is worth mentioning that due to applying wall function, the velocity on the tube and particle walls, and the fluid temperature on the particle surface doesn’t reach zero, and 322 K, respectively [19,74–76].

4.4. Parameters affecting hot zones Three different geometries of particles, with and without internal holes (Fig. 2A–F), were simulated by CFD techniques to investigate the effects of particle geometry on heat transfer rates and formation of hot zones. The heat transfer behavior of cylindrical, Sg-cylindrical, and tri6

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

Fig. 6. The radial flow temperature (A) and flow velocity (B) over a solid cylindrical particle.

lobe catalyst particles has been illustrated in Fig. 7. The wall effects were investigated by moving the particle horizon­ tally from the tube center towards the tube wall (Fig. 7). Note that the contact points between the particles and the tube wall are a key factor in CFD simulations to create an appropriate mesh grid, especially in tur­ bulent flows [46,54,77]. To study the wall effect on heat transfer, the particle was placed near the tube wall with the clearance of yc consid­ ered between the particle and the tube wall to allow for creating good quality meshes. The results indicated that the wall effects could be ignored when the particle-tube wall distance was greater than 4 mm (yc/Dp � 0.143). For yc/Dp < 0.143, the Nusselt number decreased while the maximum temperature on the tube wall increased. When a particle was located near the tube wall, the heat was transferred at a low rate because of the small local flow rate in the distance between the particle and tube wall (yc). Therefore, some small areas with high surface temperature (hot zones) were created which damaged the tube wall. Fig. 7 indicates that the maximum surface temperature of the tube wall for the tri-lobe particle did not change even once the particle-tube wall distance

diminished to less than 4 mm (yc/Dp � 0.143). This can occur probably because of the concave areas on the surface of tri-lobe particles. These concave areas made a space between the particle and the wall, contributing to the elevation of flow and heat transfer rate. Fig. 8 reveals the axial rotation of Sg-cylindrical and tri-lobe particles which were located near the tube wall tangentially (axial flow). To create a suitable mesh in particle-tube wall contact point, a small dis­ tance (yc ¼ 0.3 mm or yc/Dp � 1%) was considered between them. It was observed that by rotating the particle around its axis, the convex surface was located near the wall (at 60� ), which reduced the flow rate area; therefore, the heat transfer rate decreased and consequently, the surface temperature increased. The results suggested that the maximum temperature of the tube wall occurred when the concave area of the particle leaned to the tube wall (θ ¼ 60) where the maximum temper­ ature for the Sg-cylindrical (Td,max ¼ 0.953) was the same as that of the cylindrical particle (Td,max ¼ 0.957). However, for the tri-lobe particles (Td,max ¼ 0.827), it was still less than that of the cylindrical one sug­ gesting that utilization of tri-lobe particles in packed beds reduced the hot zones.

Fig. 7. Heat transfer behavior of different catalyst particles; A) Average Nusselt number, B) Dimensionless maximum temperature coefficient. 7

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

Afterwards, the heat transfer behavior of the particles normal to the tube wall (cross flow) was studied. According to Fig. 9, the dimension­ less maximum temperatures on the tube wall for particle rotation angles of 0-60� were less than 0.16 (Td,max<0.16), indicating that the heat transfer was good and no hot zone was created in the normal position. In the normal position, there was a distance between the particle surface and the tube wall (for all rotation angles), leading to a good heat transfer rate in this section. Fig. 9 also showed that the internal holes, particle shapes, and the rotation angle did not play any significant role in the formation of hot zones where the most important issue in the formation of hot zones was the particle surface area leaning against the tube wall. To find more about the shape of the hot zone, and its relation to the shape of particles, the temperature contours of fluid on the surface of cylindrical, Sg-cylindrical, and tri-lobe particles are displayed in Fig. 10 when they were located near the tube wall (yc ¼ 0.3 mm). Fig. 10 indicated that when a particle leaned against the tube wall tangentially (axial flow), a high-temperature of fluid near the particle surface was created. The largest area with the highest dimensionless maximum temperature of 0.957 (Td,max ¼ 0.957) was seen on the cy­ lindrical particle (Fig. 10A). In comparison with the cylindrical particle, the maximum fluid temperature was lower for Sg-cylindrical particle (Td,max ¼ 0.662 at 0 and Td,max ¼ 0.953 at 60� ), due to the presence of gaps on its surface. The lowest maximum fluid temperature was observed in the tri-lobe particle due to its concave and convex surfaces (Td,max ¼ 0.589 at 0 and Td,max ¼ 0.827 at 60� ). Therefore, in reducing hot zones, the tri-lobe particle has been better than its cylindrical and Sg-cylindrical counterparts. Fig. 11 illustrates the velocity vectors in the area between the par­ ticle and tube wall to interpret the temperature profile of fluid around the cylindrical particle (Fig. 10A). Fig. 11A reveals that after colliding with the particle, the fluid flow deviates around the sides of the particle. Once moved around the particle, the flow area grows and creates a va­ cuity space with low pressure, creating a downward flow behind the particle. Downward and upward flows collided at the distance of 8 mm (Zp ¼ 0.235) from the beginning of the particle (Fig. 11B) and were pushed sideways. Therefore, a small area with small flow velocity and conse­ quently, low particle-fluid heat transfer rate was created on the surface of the particle (Fig. 11A and C). Accordingly, a symmetric hightemperature surface can be seen near the cylindrical particle (Fig. 10A). The heat transfer rate per unit volume of the particle against the dimensionless radius (Rd) and particle rotation degrees (θ) has been demonstrated in Fig. 12A and B, respectively. The number of loaded

Fig. 8. The dimensionless maximum temperature of the tube wall against the axial rotation of Sg-cylindrical and tri-lobe particles with and without holes close to the tube wall (yc ¼ 0.3 mm); note that the particles are placed tangential to the tube wall (axial flow).

Fig. 8 also indicates that the maximum dimensionless temperature of the tube wall for the tri-lobe particle was less than for its Sg-cylindrical counterpart (12–17%). This confirmed that tri-lobe particles were better in terms of heat transfer than Sg-cylindrical and cylindrical particles employed widely in industries, while the use of tri-lobe particles reduced the hot zones. It also showed that hot zones occurred due to the weak heat transfer in particle-tube wall distance; the internal holes did not have any important effect on that. Therefore, the tri-lobe particle can be a good alternative to the common cylindrical and Sg-cylindrical particles.

Fig. 9. The dimensionless maximum temperature of the tube wall against the axial rotation of Sg-cylindrical and tri-lobe particles with and without holes close to the tube wall (yc ¼ 0.3 mm); Note that the particles are placed normal to the tube wall (cross flow). 8

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

Fig. 10. Fluid temperature contours around the particles; A) cylindrical, B) Sg-cylindrical at θ ¼ 0, C) Sg-cylindrical at θ ¼ 60, D) tri-lobe at θ ¼ 0, E) tri-lobe at θ ¼ 60.

particles and consequently, the active area of packed bed increases as the particle size decreases. Therefore, the heat transfer rate per particle unit volume is used as an important parameter for investigating the heat transfer of particles in a fixed bed reactor. Fig. 12A shows that Q/V is nearly the same for both the solid tri-lobe and solid cylindrical particles. Creating internal holes lead to a better heat transfer, especially for the tri-lobe particle (84%–125%). Fig. 12B indicates that the multi-hole trilobe particle enjoys the best heat transfer rate per unit volume, which doesn’t change significantly by axial rotation. Also, internal holes develop the heat transfer rate by enhancing the particle surface area, and they reduce the pressure drop by increasing the bed porosity as well. The local axial pressure was calculated by integrating the pressure on the horizontal flat surfaces in different heights (Fig. 13). An additional pressure drop can be seen at the particle-fluid contact area (Zp ¼ 0) due to the sudden contraction of flow passing area and particle-fluid inter­ action. Another pressure drop can be observed at the particle end (Zp ¼

1) because of the sudden expansion of the flow passing area. Behind the particle, the fluid velocity is reduced and the kinetic energy is converted to static energy, which amplifies the local pressure and reduces the total pressure drop. Fig. 13 also displays that in comparison to solid particles, multi-hole particles have a lower pressure drop at Zp ¼ 0 (about 30–40%) where the minimum and maximum pressure drops have been developed by multi-hole tri-lobe and solid cylindrical particles, respec­ tively. Among the solid particles, the tri-lobe particle had the smallest cross-sectional area (front area) thereby generating the minimum pres­ sure drop. 5. Conclusions In this study, the heat transfer of a non-spherical particle was investigated (cylindrical, Sg-cylindrical, and tri-lobe) close to the tube wall in tangential and normal positions both numerically and 9

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

Fig. 11. Normalized velocity vectors; A) around the particle, B) between the particle and the tube wall, C) near the particle surface; Particle is placed near the tube wall tangentially.

Fig. 12. The axial flow heat transfer rate per unit volume of the particle versus A) dimensionless radius, B) tri-lobe particle rotation angle around its axis (axial flow).

experimentally. The Finite Element Method (FEM) was used to solve the partial equations of continuity, momentum, and energy. Further, for modeling the turbulent flow through the computational domain, the κ ε turbulence model was employed. In brief, the following points can be mentioned as the main findings of this study:

Sg-cylindrical, tri-lobe particles, 4.57, 3.78 and 6.20% for multi-hole cylindrical, Sg-cylindrical, and tri-lobe particles, respectively. � In the tangential position, the wall effects could be ignored when particle-tube wall distance per particle diameter ratio was greater than 0.143 (yc/Dp � 0.143). � The minimum temperature in hot zones was observed for the tri-lobe particle at the axial rotation angle of zero (Td,max ¼ 0.551). � The internal holes did not play an important role in the formation of hot zones, as the hot zones were formed mainly due to the weak heat transfer in the particle-tube wall contact point.

� The simulation results were validated with the experimental data obtained from the heat and mass transfer analogy. The Mean abso­ lute percentage errors were 5.15, 5.47, 9.21% for solid cylindrical,

10

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223

� � �

�

�

between the particle and the tube wall and the heat could be trans­ ferred to the fluid flow. The shape of hot zones was studied by the velocity vectors in the particle-tube wall contact area. The maximum temperature for tri-lobe and Sg-cylindrical particles was less than the cylindrical counterpart. By considering the heat transfer rate per unit volume, it was found that the particle rotation angle doesn’t have any significant effect on it and multi-holes tri-lobe particle offered better performance. The local axial pressure revealed that there were two sudden declines in pressure distribution at the beginning and end of the particle, with a lower pressure drop obtained by the multi-hole tri-lobe particle. The results obtained by this study can be practical to find more about the hot spots and achieve a better catalyst particle for packed bed reactors.

Fig. 13. The local axial pressure distributions as a function of bed height; the particles are placed tangentially.

� No hot zones were observed when the particle leaned against the tube wall normally, as in this position there was enough space

Nomenclature Ac Ap Cp DB Dp h k L Ma N Nu P Pr Q Qf

r RB RC Rd Re Sc Sh Sh T t Td,max Tw,max U V yc yþ Zp Z0

ρ κ

Tube surface area, [m2] Particle surface area, [m2] Specific heat of fluid at constant pressure, [kJ/(kg.K)] Tube diameter, [m] Equivalent spherical particle diameter, [m], 6V/(Ap ϕp) Convection heat transfer coefficient, [W/(m2.K)] Thermal conductivity of fluid, [W/(m.K)] The Axial length of the particle, [m] Mach number, [] Tube to particle diameter ratio or bed aspect ratio, [] The Nusselt number, [] Pressure, [Pa] Prandtl Number, [] Heat transfer rate, [J/s] Flow rate, [m3/s] The radial distance from the tube center, [m] Bed radius, [m] Inscribed cylinder radius of the particle, [m] Dimensionless radius, r/(RB-RC), [] Reynolds number, [] Schmidt Number, [] Sink or source term, [W/m3] Sherwood Number, [] Temperature, [K] Time, [s] The dimensionless maximum temperature on the tube wall, i.e. (Tw,max-Tin)/(Ts-Tin), [] The Maximum temperature on the tube wall, [K] Fluid velocity, [m/s] Particle volume, [m3] The distance between the particle and the tube wall, [m] Dimensionless distance from the wall, [] The distance from the bottom of the particle to the axial length of the particle, Z0 /L, [] The distance from the bottom of the particle, [m] The density of the fluid, [kg/m3] Turbulent kinetic energy, [] 11

M. Zare and S.H. Hashemabadi

ϕ

Dissipation rate of turbulent kinetic energy, [] Kinematic viscosity, [m2/s] Dynamic viscosity, [Pa.s] The rotation angle of the particle, [� ] Normal direction to the particle surface, [m] Sphericity, []

t ∞ s b in B C

Turbulence condition Free stream Particle surface Fluid bulk Tube inlet Bed/tube Cylindrical particle

þ y

Dimensionless Transpose

ϵ

ν μ θ

η

0

International Journal of Thermal Sciences 150 (2020) 106223

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijthermalsci.2019.106223.

References

[17] F. Dierich, P.A. Nikrityuk, A numerical study of the impact of surface roughness on heat and fluid flow past a cylindrical particle, Int. J. Therm. Sci. 65 (2013) 92–103, https://doi.org/10.1016/j.ijthermalsci.2012.08.009. [18] M. Zare, S. Hashemabadi, Experimental study and CFD simulation of wall effects on heat transfer of an extrudate multi-lobe particle, Int. Commun. Heat Mass Transf. 43 (2013) 122–130, https://doi.org/10.1016/j.icheatmasstransfer.2013.02.010. [19] M. Zare, S.H. Hashemabadi, CFD simulation and experimental validation of tortuosity effects on pellet-fluid heat transfer of regularly stacked multi-lobe particles, Chem. Eng. J. (2018), https://doi.org/10.1016/j.cej.2018.10.188. [20] S. Das, N.G. Deen, J.A.M. Kuipers, Multiscale modeling of fixed-bed reactors with porous (open-cell foam) non-spherical particles: hydrodynamics, Chem. Eng. J. 334 (2018) 741–759, https://doi.org/10.1016/j.cej.2017.10.047. [21] R.E. Critoph, R. Thorpe, Momentum and heat transfer by forced convection in fixed beds of granular active carbon, Appl. Therm. Eng. 16 (1996) 419–427, https://doi. org/10.1016/1359-4311(95)00023-2. [22] S.S. Halkarni, A. Sridharan, S.V. Prabhu, Experimental investigation on effect of random packing with uniform sized spheres inside concentric tube heat exchangers on heat transfer coefficient and using water as working medium, Int. J. Therm. Sci. 133 (2018) 341–356, https://doi.org/10.1016/j.ijthermalsci.2018.05.023. [23] C.-A. Wang, Q.-Z. Lai, T.-R. Shen, J.-Y. Tan, Numerical investigation of radiation transfer in packed bed of semitransparent coated spherical particles, Int. J. Therm. Sci. 127 (2018) 1–6, https://doi.org/10.1016/j.ijthermalsci.2017.12.021. [24] C.I. M�endez, J. Ancheyta, F. Trejo, Modeling of catalytic fixed-bed reactors for fuels production by Fischer-Tropsch synthesis, Energy Fuels 31 (2017) 13011–13042, https://doi.org/10.1021/acs.energyfuels.7b01431. [25] A.G. Dixon, M. Nijemeisland, E.H. Stitt, CFD study of heat transfer near and at the wall of a fixed bed reactor Tube: effect of wall conduction, Ind. Eng. Chem. Res. 44 (2005) 6342–6353, https://doi.org/10.1021/ie049183e. [26] B.D. Young, D.F. Williams, A.W. Bryson, Two-dimensional natural convection and conduction in a packed bed containing a hot spot and its relevance to the transport of air in a coal dump, Int. J. Heat Mass Transf. 29 (1986) 331–336, https://doi.org/ 10.1016/0017-9310(86)90240-1. [27] N. Haneishi, S. Tsubaki, M.M. Maitani, E. Suzuki, S. Fujii, Y. Wada, Electromagnetic and heat-transfer simulation of the catalytic dehydrogenation of ethylbenzene under microwave irradiation, Ind. Eng. Chem. Res. 56 (2017) 7685–7692, https://doi.org/10.1021/acs.iecr.7b01413. [28] S.S. Halkarni, A. Sridharan, S.V. Prabhu, Measurement of local wall heat transfer coefficient in randomly packed beds of uniform sized spheres using infrared thermography (IR) and water as working medium, Appl. Therm. Eng. 126 (2017) 358–378, https://doi.org/10.1016/j.applthermaleng.2017.07.174. [29] O. Levenspiel, Chemical Reaction Engineering, third ed., John Wiley and sons, New York, 1999. [30] M. Nijemeisland, A.G. Dixon, E.H. Stitt, Catalyst design by CFD for heat transfer and reaction in steam reforming, Chem. Eng. Sci. 59 (2004) 5185–5191. [31] J. Chen, B. Liu, X. Gao, D. Xu, Production of hydrogen by methane steam reforming coupled with catalytic combustion in integrated microchannel reactors, Energies 11 (2018) 2045. [32] R. Agrawal, D.H. West, V. Balakotaiah, Modeling and analysis of local hot spot formation in down-flow adiabatic packed-bed reactors, Chem. Eng. Sci. 62 (2007) 4926–4943, https://doi.org/10.1016/j.ces.2006.11.057. [33] L. Chen, J. Lee, Experimental analysis of the thermal field and heat transfer characteristics of a pebble-bed core in a high-temperature gas-cooled reactor, Ann. Nucl. Energy 110 (2017) 338–348, https://doi.org/10.1016/j. anucene.2017.06.046.

[1] R.H. Perry, D.W. Green, J.O. Maloney, Perry’s Chemical Engineers’ Handbook, seventh ed., McGraw-Hill, 1997. [2] R.H. Mohammed, O. Mesalhy, M.L. Elsayed, L.C. Chow, Scaling analysis of heat and mass transfer processes in an adsorption packed bed, Int. J. Therm. Sci. 133 (2018) 82–89, https://doi.org/10.1016/j.ijthermalsci.2018.07.017. [3] J.M. Rosas, R. Ruiz-Rosas, J. Rodríguez-Mirasol, T. Cordero, Kinetic study of SO2 removal over lignin-based activated carbon, Chem. Eng. J. 307 (2017) 707–721, https://doi.org/10.1016/j.cej.2016.08.111. [4] M.F.J. Dijkstra, H. Buwalda, A.W.F. de Jong, A. Michorius, J.G.M. Winkelman, A.A. C.M. Beenackers, Experimental comparison of three reactor designs for photocatalytic water purification, Chem. Eng. Sci. 56 (2001) 547–555, https://doi. org/10.1016/S0009-2509(00)00259-1. [5] M.N. Pedernera, J. Pi~ na, D.O. Borio, V. Bucal� a, Use of a heterogeneous twodimensional model to improve the primary steam reformer performance, Chem. Eng. J. 94 (2003) 29–40, https://doi.org/10.1016/S1385-8947(03)00004-4. [6] W. Li, J. Yan, Z. Yan, Y. Song, W. Jiao, G. Qi, Y. Liu, Adsorption of phenol by activated carbon in rotating packed bed: experiment and modeling, Appl. Therm. Eng. 142 (2018) 760–766, https://doi.org/10.1016/j. applthermaleng.2018.07.051. [7] E. Magyari, Linear stability analysis of the steady thermal regimes of a packed bed reactor with an organized structure, Int. J. Therm. Sci. 48 (2009) 1523–1529, https://doi.org/10.1016/j.ijthermalsci.2008.12.005. [8] G.M. Karthik, A.H. Thaker, V.V. Buwa, Particle-resolved Simulations of Catalytic Fixed Bed Reactors: Comparison of Turbulence Models, LES and PIV Measurements, Powder Technology, 2019, https://doi.org/10.1016/j. powtec.2019.05.012. [9] S. Sie, R. Krishna, Process development and scale up: II. Catalyst design strategy, Rev. Chem. Eng. 14 (1998) 159–202, https://doi.org/10.1515/ REVCE.1998.14.3.159. [10] O.B. Kovalev, A.V. Gusarov, Modeling of granular packed beds, their statistical analyses and evaluation of effective thermal conductivity, Int. J. Therm. Sci. 114 (2017) 327–341, https://doi.org/10.1016/j.ijthermalsci.2017.01.003. [11] S.P. Bruno, G.F. Barreto, M.G. Gonzalez, Effect of the geometric characteristics of commercial catalysts for steam reforming, Chem. Eng. J. 39 (1988) 147–156, https://doi.org/10.1016/0300-9467(88)80022-4. [12] T. Gronarz, M. Schnell, C. Siewert, L. Schneiders, W. Schr€ oder, R. Kneer, Comparison of scattering behaviour for spherical and non-spherical particles in pulverized coal combustion, Int. J. Therm. Sci. 111 (2017) 116–128, https://doi. org/10.1016/j.ijthermalsci.2016.08.014. [13] S.A. Logtenberg, A.G. Dixon, Computational fluid dynamics studies of the effects of temperature-dependent physical properties on fixed-bed heat transfer, Ind. Eng. Chem. Res. 37 (1998) 739–747, https://doi.org/10.1021/ie970382q. [14] M. Behnam, A.G. Dixon, P.M. Wright, M. Nijemeisland, E.H. Stitt, Comparison of CFD simulations to experiment under methane steam reforming reacting conditions, Chem. Eng. J. 207 (2012) 690–700, https://doi.org/10.1016/j. cej.2012.07.038. [15] S. Kumar, S. Dasappa, Modeling and analysis of single particle conversion of biomass in a packed bed gasification system, Appl. Therm. Eng. 112 (2017) 1382–1395, https://doi.org/10.1016/j.applthermaleng.2016.10.170. [16] M. Bidabadi, M. Mafi, Time variation of combustion temperature and burning time of a single iron particle, Int. J. Therm. Sci. 65 (2013) 136–147, https://doi.org/ 10.1016/j.ijthermalsci.2012.10.019.

12

M. Zare and S.H. Hashemabadi

International Journal of Thermal Sciences 150 (2020) 106223 [56] M.T. Kao, Y.H. Tung, Y.M. Ferng, C.C. Chieng, M.K. Chyu, 3D measurements and numerical computations of heat transfer coefficients on spheres in an array, Int. J. Therm. Sci. 68 (2013) 110–118, https://doi.org/10.1016/j. ijthermalsci.2013.01.014. [57] J. Thom�eo, J. Grace, Heat transfer in packed beds: experimental evaluation of onephase water flow, Braz. J. Chem. Eng. 21 (2004) 13–22, https://doi.org/10.1590/ S0104-66322004000100003. [58] F. Mirhashemi, S. Hashemabadi, S. Noroozi, CFD simulation and experimental validation for wall effects on heat transfer of finite cylindrical catalyst, Int. Commun. Heat Mass Transf. 38 (2011) 1148–1155, https://doi.org/10.1016/j. icheatmasstransfer.2011.05.001. [59] A.G. Dixon, G. Walls, H. Stanness, M. Nijemeisland, E.H. Stitt, Experimental validation of high Reynolds number CFD simulations of heat transfer in a pilotscale fixed bed tube, Chem. Eng. J. 200 (2012) 344–356, https://doi.org/10.1016/ j.cej.2012.06.065. [60] A.G. Dixon, M. Nijemeisland, E.H. Stitt, Systematic mesh development for 3D CFD simulation of fixed beds: contact points study, Comput. Chem. Eng. 48 (2013) 135–153, https://doi.org/10.1016/j.compchemeng.2012.08.011. [61] A.G. Dixon, CFD study of effect of inclination angle on transport and reaction in hollow cylinder catalysts, Chem. Eng. Res. Des. 92 (2014) 1279–1295, https://doi. org/10.1016/j.cherd.2013.11.018. [62] F. Alzahrani, M. Aldehani, H. Rusi, M. McMaster, D.L. Abreu Fernandes, S. Assabumrungrat, M. Nic an tSaoir, F. Aiouache, Gas Flow visualization in low aspect ratio packed beds by three-dimensional modeling and near-infrared tomography, Ind. Eng. Chem. Res. 54 (2015) 12714–12729, https://doi.org/ 10.1021/acs.iecr.5b02635. [63] R. Zou, A. Yu, The packing of spheres in a cylindrical container: the thickness effect, Chem. Eng. Sci. 50 (1995) 1504–1507, https://doi.org/10.1016/0009-2509 (94)00483-8. [64] F.S. Mirhashemi, S.H. Hashemabadi, Experimental and CFD study of wall effects on orderly stacked cylindrical particles heat transfer in a tube channel, Int. Commun. Heat Mass Transf. 39 (2012) 449–455, https://doi.org/10.1016/j. icheatmasstransfer.2012.01.007. [65] C.J. Geankoplis, Transport Processes and Separation Process Principles: (Includes Unit Operations), Prentice Hall Professional Technical Reference, 2003. [66] A. Ahmadi Motlagh, S. Hashemabadi, 3D CFD simulation and experimental validation of particle-to-fluid heat transfer in a randomly packed bed of cylindrical particles, Int. Commun. Heat Mass Transf. 35 (2008) 1183–1189, https://doi.org/ 10.1016/j.icheatmasstransfer.2008.07.014. [67] R.J. Goldstein, H. Cho, A review of mass transfer measurements using naphthalene sublimation, Exp. Therm. Fluid Sci. 10 (1995) 416–434. [68] J.D. Anderson Jr., Fundamentals of Aerodynamics, Tata McGraw-Hill Education, 2010. [69] A.G. Dixon, A.K. Gurnon, M. Nijemeisland, E.H. Stitt, CFD testing of the pointwise use of the Zehner–Schlünder formulas for fixed-bed stagnant thermal conductivity, Int. Commun. Heat Mass Transf. 42 (2013) 1–4, https://doi.org/10.1016/j. icheatmasstransfer.2012.12.013. [70] H. Versteeg, W. Malalasekera, Computational Fluid Dynamics, the Finite Volume Method, 1995. [71] M. Kawaguti, The critical Reynolds number for the flow past a sphere, J. Phys. Soc. Jpn. 10 (1955) 694–699, https://doi.org/10.1143/JPSJ.10.694. [72] E.L.G. Oliveira, Sorption Enhanced Steam Methane Reforming Process for Continuous Production of Hydrogen in Pressure Swing Adsorptive Reactors, 2009. [73] S. Romkes, F. Dautzenberg, C. Van den Bleek, H. Calis, CFD modelling and experimental validation of particle-to-fluid mass and heat transfer in a packed bed at very low channel to particle diameter ratio, Chem. Eng. J. 96 (2003) 3–13, https://doi.org/10.1016/j.cej.2003.08.026. [74] M. Nijemeisland, A.G. Dixon, CFD study of fluid flow and wall heat transfer in a fixed bed of spheres, AIChE J. 50 (2004) 906–921. [75] W. Frei, Which Turbulence Model Should I Choose for My CFD Application?, 2013. https://www.comsol.com/blogs/which-turbulence-model-should-choose-cfd-app lication/. [76] A. Jones, in: Development of a Near-Wall Domain Decomposition Method for Turbulent Flows, The University of Manchester, United Kingdom, 2016. [77] G.D. Wehinger, C. Fütterer, M. Kraume, Contact modifications for CFD simulations of fixed-bed reactors: cylindrical particles, Ind. Eng. Chem. Res. 56 (2017) 87–99, https://doi.org/10.1021/acs.iecr.6b03596.

[34] J.P. Sørensen, W.E. Stewart, Computation of forced convection in slow flow through ducts and packed beds—II velocity profile in a simple cubic array of spheres, Chem. Eng. Sci. 29 (1974) 819–825, https://doi.org/10.1016/0009-2509 (74)80200-9. [35] T.F. McKenna, R. Spitz, D. Cokljat, Heat transfer from catalysts with computational fluid dynamics, AIChE J. 45 (1999) 2392–2410, https://doi.org/10.1002/ aic.690451113. [36] A.G. Dixon, M.E. Taskin, M. Nijemeisland, E.H. Stitt, Systematic mesh development for 3D CFD simulation of fixed beds: single sphere study, Comput. Chem. Eng. 35 (2011) 1171–1185, https://doi.org/10.1016/j.compchemeng.2010.12.006. [37] G.D. Wehinger, F. Klippel, M. Kraume, Modeling pore processes for particleresolved CFD simulations of catalytic fixed-bed reactors, Comput. Chem. Eng. 101 (2017) 11–22, https://doi.org/10.1016/j.compchemeng.2017.02.029. [38] B. Sreenivasulu, B. Srinivas, Mixed convection heat transfer from a spheroid to a Newtonian fluid, Int. J. Therm. Sci. 87 (2015) 1–18, https://doi.org/10.1016/j. ijthermalsci.2014.08.002. [39] M. Dalman, J. Merkin, C. McGreavy, Fluid flow and heat transfer past two spheres in a cylindrical tube, Comput. Fluids 14 (1986) 267–281, https://doi.org/10.1016/ 0045-7930(86)90025-3. [40] G. Juncu, Unsteady forced convection heat/mass transfer around two spheres in tandem at low Reynolds numbers, Int. J. Therm. Sci. 46 (2007) 1011–1022, https://doi.org/10.1016/j.ijthermalsci.2006.12.008. [41] A.H. Ahmadi Motlagh, S.H. Hashemabadi, CFD based evaluation of heat transfer coefficient from cylindrical particles, Int. Commun. Heat Mass Transf. 35 (2008) 674–680, https://doi.org/10.1016/j.icheatmasstransfer.2008.01.005. [42] L. Jiang, H. Liu, S. Suo, M. Xie, M. Bai, Simulation of propane-air premixed combustion process in randomly packed beds, Appl. Therm. Eng. 141 (2018) 153–163, https://doi.org/10.1016/j.applthermaleng.2018.05.104. [43] W. Peng, M. Xu, X. Huai, Z. Liu, 3D CFD simulations of acetone hydrogenation in randomly packed beds for an isopropanol–acetone–hydrogen chemical heat pump, Appl. Therm. Eng. 94 (2016) 238–248, https://doi.org/10.1016/j. applthermaleng.2015.10.130. [44] O.R. Derkx, A.G. Dixon, Determination of the fixed bed wall heat transfer coefficient using computational fluid dynamics, Numer. Heat Transf. A 29 (1996) 777–794, https://doi.org/10.1080/10407789608913819. [45] S.A. Logtenberg, A.G. Dixon, Computational fluid dynamics studies of fixed bed heat transfer 1, Chem. Eng. Process: Process Intensif. 37 (1998) 7–21, https://doi. org/10.1016/S0255-2701(97)00032-9. [46] S. Logtenberg, M. Nijemeisland, A.G. Dixon, Computational fluid dynamics simulations of fluid flow and heat transfer at the wall–particle contact points in a fixed-bed reactor, Chem. Eng. Sci. 54 (1999) 2433–2439, https://doi.org/10.1016/ S0009-2509(98)00445-X. [47] B. Partopour, A.G. Dixon, Computationally efficient incorporation of microkinetics into resolved-particle CFD simulations of fixed-bed reactors, Comput. Chem. Eng. 88 (2016) 126–134, https://doi.org/10.1016/j.compchemeng.2016.02.015. [48] A.G. Dixon, M. Nijemeisland, CFD as a design tool for fixed-bed reactors, Ind. Eng. Chem. Res. 40 (2001) 5246–5254, https://doi.org/10.1021/ie001035a. [49] B. Partopour, A.G. Dixon, Reduced microkinetics model for computational fluid dynamics (CFD) simulation of the fixed-bed partial oxidation of ethylene, Ind. Eng. Chem. Res. 55 (2016) 7296–7306, https://doi.org/10.1021/acs.iecr.6b00526. [50] Y. Dong, M. Geske, O. Korup, N. Ellenfeld, F. Rosowski, C. Dobner, R. Horn, What happens in a catalytic fixed-bed reactor for n-butane oxidation to maleic anhydride? Insights from spatial profile measurements and particle resolved CFD simulations, Chem. Eng. J. (2018), https://doi.org/10.1016/j.cej.2018.05.192. [51] B. Baghapour, M. Rouhani, A. Sharafian, S.B. Kalhori, M. Bahrami, A pressure drop study for packed bed adsorption thermal energy storage, Appl. Therm. Eng. 138 (2018) 731–739, https://doi.org/10.1016/j.applthermaleng.2018.03.098. [52] S.K. Yeboah, J. Darkwa, Experimental investigations into the adsorption enhancement in packed beds using Z-Annular flow configuration, Int. J. Therm. Sci. 136 (2019) 121–134, https://doi.org/10.1016/j.ijthermalsci.2018.10.027. [53] S. Esterl, K. Debus, H. Nirschl, A. Delgado, Three dimensional calculations of the flow through packed beds, in: Fluid Dynamics and Process Automation. Eur. Comput. Fluid Dyn. Conf, 1998, pp. 692–696. [54] M. Nijemeisland, A.G. Dixon, Comparison of CFD simulations to experiment for convective heat transfer in a gas–solid fixed bed, Chem. Eng. J. 82 (2001) 231–246, https://doi.org/10.1016/S1385-8947(00)00360-0. [55] A.G. Dixon, M.E. Taskin, M. Nijemeisland, E.H. Stitt, Wall-to-particle heat transfer in steam reformer tubes: CFD comparison of catalyst particles, Chem. Eng. Sci. 63 (2008) 2219–2224, https://doi.org/10.1016/j.ces.2008.01.017.

13