PIV measurements and CFD simulations of the particle-scale flow distribution in a packed bed

Chemical Engineering Journal 374 (2019) 189–200

Contents lists available at ScienceDirect

Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej

PIV measurements and CFD simulations of the particle-scale flow distribution in a packed bed Abhijeet H. Thaker1, G.M. Karthik1,2, Vivek V. Buwa

T

⁎

Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India

H I GH L IG H T S

G R A P H I C A L A B S T R A C T

for packed bed geometry • Methodology reconstruction from PIV scans. velocity and turbulence • Particle-scale measurements using PIV. CFD simulations of • Particle-resolved turbulent flow in packed beds. of particle-resolved CFD • Validation simulations with SST k − ω turbulence model.

A R T I C LE I N FO

A B S T R A C T

Keywords: Packed bed Particle image velocimetry Computational fluid dynamics Particle-resolved simulations

A comparison of the particle-scale PIV measurements with the corresponding particle-resolved CFD simulations in the turbulent flow regime using SST k − ω model is performed. A cylindrical packed bed containing spherical particles with the tube-to-particle diameter ratio of ∼ 4.3 operating at Rebed in the range of 1100–6600 was considered. The measured and predicted distribution of the first-order (Vx and Vy ) and second-order (vorticity and strain rate) mean velocity quantities showed a reasonable agreement, which improved with the increase in the Rebed . The observed deviations were caused by the differences in the geometry (particle position and upstream packing condition) used in the CFD model compared to the measurements. On the other hand, the turbulent quantities (k and ε ) were under-predicted in the simulations. However, for the ε , the agreement with the measurements was found to be better at higher Rebed compared to that of the k illustrating the influence of the turbulence model on the predictions. From the results, it can be inferred that the SST k − ω turbulence model appears to be more suitable for the high-Re flows. The present work helps to establish a methodology to validate the particle-resolved CFD simulations in the turbulent flow regime.

1. Introduction Packed beds are commonly used in chemical process industries to perform solid catalyzed gas-phase reactions (e.g., methane steam reforming, water gas shift reaction, methanol synthesis). This is due to the

high surface area-to-volume (STV) ratio offered by the catalyst particles that helps in the effective heat transport to and from the particles for the endothermic and exothermic reactions, respectively. The particles with different shapes and sizes are randomly placed inside the packed beds and the reactions occur both on the external (particle-scale) and

⁎

Corresponding author. E-mail address: [email protected] (V.V. Buwa). 1 Equal contribution. 2 Presently working at Haldor Topsoe India Private Limited, Faridabad, India. https://doi.org/10.1016/j.cej.2019.05.053 Received 12 January 2019; Received in revised form 3 April 2019; Accepted 9 May 2019 Available online 11 May 2019 1385-8947/ © 2019 Elsevier B.V. All rights reserved.

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

Nomenclature

Rebed V Vs

Symbols

dh dp dp, avg dp, piv dt hb ht k P Rep

Bed Reynolds number [–] Fluid velocity [m/s] Superficial fluid velocity [m/s]

Greek symbols

Hydraulic diameter of the inlet cross-section [m] Particle diameter [m] Mean particle diameter [m] PIV seeding particle diameter [m] Exposure time delay [μ.s] Bed height packed with glass particles [m] Bed height packed with hydrogel particles [m] Turbulent kinetic energy [m2/s2 ] Fluid pressure [Pa] Particle Reynolds number [–]

μ μt ω ρ τ τt εbed

Fluid viscosity [Pa.s] Turbulent viscosity [Pa.s] Turbulent eddy frequency [Hz] Fluid density [kg/m3 ] Viscous stress tensor [N/m2 ] Turbulent stress tensor [N/m2 ] Bed porosity [–]

to compare the point measurements with the CFD simulations. Prof. Dixon and co-workers [14–16] performed validation of the temperature profiles predicted by the particle-resolved CFD simulations using the measurements in a fixed-bed and reported a satisfactory agreement. Calis et al. [17] compared the velocity profile on a cross-section of the packed bed (square channel, TPDR of 1–2, structured packing) measured using the Laser Doppler Anemometry (LDA) technique and the corresponding CFD simulations, and showed deviations were within acceptable limits. Dumas et al. [18] used the tri-segmented microelectrodes to measure the local velocity gradients and flow direction in a packed bed (rectangular channel, TPDR of 10, structured packing) and compared it with the numerical predictions, and reported a good agreement. However, these bed-scale and point-scale validations still do not fully test the ability of CFD to predict the particle-scale information with a good accuracy. Robbins et al. [19] and Lovreglio et al. [20] compared the CFD simulations with the velocity distributions measured using the Magnetic Resonance Imaging (MRI) in a packed bed (TPDR of up to 7) under the laminar conditions (particle Reynolds number, Rep up to 216), and reported a reasonable agreement. Yang et al. [21] also presented an experimental validation of the CFD simulations for the particle-scale flow in a packed bed (TPDR of 17.6) measured using the MRI technique for the Rebed of 0.6. The simulated and measured velocity fields were similar. However, the comparison of the local velocity and velocity histogram showed deviations which were mainly attributed to the limitations of the MRI measurements. Similarly, Wood et al. [22] performed experimental validation of the CFD simulations for the particle-scale flow (Rebed = 3.5) in a packed bed (TPDR of 4.7) with the Particle Image Velocimetry (PIV) technique due to its ability to provide the high-resolution particle-scale velocity fields and reduced measurement errors. In their case, the deviations in the measured and simulated velocity histograms were smaller and these deviations arose mainly due to the differences in the particle positions considered in the experiments and simulations. Apart from that, several researchers (e.g., [23–27]) performed the PIV measurements of the particle-scale flow in packed beds comprised of square columns of 30–100 mm in the cross-section, particle diameter of 5–15 mm and Rebed up to 4000. These measurements were used to understand the flow characteristics inside packed beds. As evidenced from the aforementioned literature review, to the best of authors knowledge, only a few validation studies [19–22] were performed under the laminar flow conditions which allowed the corresponding researchers to use the direct numerical simulations (DNS). The laminar flow has two main advantages: (a) it reduces the computational cost and (b) eliminates the uncertainties introduced by the use of a turbulence model. However, most of the industrial-scale packed beds reactors operate in the turbulent flow regime, for which the DNS is prohibitively expensive. Due to this reason, almost all the researchers have extensively used the eddy-viscosity based two-equation turbulence

internal (pore-scale) surfaces of the particles. The particle shape has a significant influence on the local heat and mass transport phenomena and hence the reactor performance. Therefore, an understanding of the particle-scale flow and its impact on the reactor performance is crucial for the optimal particle design to improve the performance. Also, this is of particular importance for the low tube-to-particle diameter ratio (TPDR < 10 ) beds that are used in a methane-steam reformer where the wall effects also have a strong influence on the local transport phenomena. Typically, reduced-order models with semi-empirical correlations based on simplified assumptions are used for predicting the bed-scale performance characteristics of the packed bed reactors like the pressure drop, dispersion coefficients, reactant conversion, etc. These semi-empirical correlations for the bed-scale parameters were developed using the data from the bed-scale experiments. However, these bed-scale experiments do not provide the detailed information on the particlescale flow that governs the local transport and in turn the bed-scale performance. Therefore, these semi-empirical correlations have certain limitations in predicting the reactor performance due to the lack of information on the local transport phenomena. On the contrary, a large number of particle-resolved computational fluid dynamics (CFD) simulations were performed to predict and to understand the influence of the particle-scale flow on the performance of these packed bed reactors (e.g., [1–9]). These simulations resolve the flow in the interstitial voids between the particles thereby providing a detailed insight into the particle-scale transport phenomena and its impact on the reactor performance. In our previous works [9,10], particle-resolved CFD simulations were performed to understand the effect of particle shape on the pressure drop, dispersion characteristics, temperature and concentration distributions for the methane-steam reforming reactors. These simulations were also used to understand the mass and heat transfer limitations. However, the accuracy of the particle-resolved simulations highly depends on the model parameters like the generated mesh and turbulence model. To overcome the mesh dependency, researchers usually performed a sensitivity analysis with the meshes of different resolutions to identify the mesh resolution beyond which the predicted results did not change significantly. However, the dependency of the predicted results on the turbulence model could not be assessed without the help of the experimental validation. Therefore, it is imperative to validate the predictions of the particle-resolved CFD simulations with the corresponding experimental data to improve the fidelity of the CFD simulations. Since the focus of the present work is an experimental validation of the particle-resolved simulations, only the literature that reports such experimental validations is discussed here. Some researchers compared the CFD predictions for the bed-scale parameters like the pressure drop, heat, and mass transfer coefficient, etc., against the corresponding empirical correlations from the literature or experimental data which showed a reasonable agreement (for example [11–13]). Apart from that, only a few studies were performed 190

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

cylinder as the packed bed (see Fig. 1) due to the following reasons. The design provided two flat surfaces for avoiding the incident laser light reflection and also contained one curved surface to capture the influence of wall on the particle-scale flow. Due to the smaller domain size and therefore due to the reduced computational cost, it was possible to consider the entire cross-section of the geometry in the CFD model. A 90° section of the cylindrical column (dt = 91.2 mm ) made of transparent plexiglass (PMMA) was used in the present work. To minimize the light reflection from the curved surface, it was enclosed by three flat PMMA plates (two sides and one bottom) on the outer side and the annular region was filled with the refractive index (RI) matched fluid. The packings were made of transparent hydrogel material which closely matched the refractive index of the working fluid. The particles were spherical in shape with the mean particle diameter, dp, avg = 21 ± 1 mm . This led to a TPR of ∼ 4.3. These dimensions are typical for some of the industrial-scale tubular methane steam reformer. Initially, the entire column was filled with the hydrogel particles. Due to their soft nature, these particles deformed thereby affecting the bed structure and flow pattern into the measurement section. To overcome this issue, the bottom section of the column was packed with the spherical glass particles (hb = 500 mm ) followed by the hydrogel particles (ht = 90 mm) in the top section. These glass particles served as the entry length and also acted as a support for the hydrogel particles. Demineralized water with the seeding particles (silver-coated hollow glass spheres, dp, piv = 10 μm ) was used as the working fluid. The system was operating under the room temperature (25 °C) and pressure (1 atm). PIV experiments were performed for packed bed Reynolds number (Rebed ) of 1100, 2200 and 6600. Rebed is calculated as [(ρUs dh)/(μεbed )], where dh is the hydraulic diameter of the inlet crosssection, εbed is the bed porosity (0.36 in the present work), Us is the superficial velocity, ρ and μ are the density and viscosity of the fluid, respectively.

models e.g., either the k − ε models (for example [28–30]) or the k − ω models (for example [5,31,32]) for the particle-resolved simulations of the turbulent flow inside the packed beds. However, there is a lack of experimental validation of the particle-resolved CFD simulations in packed beds operating under the turbulent flow regime. In the present work, the PIV is used to measure the velocity distributions. This is due to their ability to provide high spatial resolution, good accuracy, and controllable measurement errors. The CFD simulations were performed using the SST k − ω turbulence model as it is one of the most widely used turbulence models in the literature to simulate the particle-scale flow in packed beds. This is also because of its reduced computational cost and ability to predict the boundary layer accurately. The objectives of the present work are: (a) to demonstrate a simple yet effective methodology for the geometry reconstruction from the PIV scans with a good accuracy and (b) to compare the CFD predictions with the PIV measurements in the turbulent flow regime by comparing the first-order & second-order velocity quantities and turbulence parameters.

2. Methodology 2.1. Experiments 2.1.1. Experimental set-up Though the cylindrical beds are used in the industry, the curved surface of the cylindrical bed leads to a strong reflection of the incident laser light during the PIV measurements. To overcome this limitation, many researchers used the square columns with flat walls and thereby avoided the laser light reflection. This may be acceptable for the largesized (diameter) packed beds where the wall does not have a major influence on the flow in the core region. However, for the beds with a low tube-to-particle diameter ratio (TPD ⩽10), it is important to capture the wall (shape) effects which dominate the local transport phenomena around the particle. Therefore, in the present work, we considered a 90° section of the

2.1.2. PIV set-up The PIV experiments were performed to measure the velocity field

Fig. 1. Experimental set-up used for the PIV measurements. 191

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

However, the model demands a fine mesh resolution ( y+ ⩽ 1) in the near-wall region for resolving the boundary layer flow accurately. The detailed model equations for the SST k − ω turbulence model as defined in the ANSYS manual are provided in the supplementary information.

around the hydrogel particles using a time-resolved 2D-PIV system (TSI, India) as shown in Fig. 1. The measurement section covered a height of 72 mm in the top section of the column containing the hydrogel particles. The total measurement area (field of view) spanned close to 4 rows of the hydrogel particles. A Litron Nd:YLF dual cavity high-speed laser (Litron, UK) with a maximum energy of 30 mJ per pulse was used to illuminate the desired measurement plane. In the present work, three different X-Y planes along the Z-direction (Z = 4, 21 and 36 mm) were considered for the measurements. A high-speed CMOS PIV camera (Phantom M310, with 3200 fps at 1280 × 800 pixels 2 resolution) mounted on the computer controlled 3D traverse system (Make: Isel) was used for the image acquisition. The camera and laser were synchronized by the laser-pulse synchronizer unit (TSI Incorporated, USA) with the help of a workstation (Dell Precision). In the experiments, images were captured at the rate of 200 frames per second for a time duration corresponding to three residence times. The time between the two consecutive images (exposure time delay, Δt ) was set at 800, 400 and 200 μs for the Rebed of 1100, 2200 and 6600, respectively. The captured images were processed using the commercial software Insight4G (TSI Incorporated, USA) with a Fast Fourier Transform (FFT) cross-correlation algorithm. The sensitivity of the PIV measurement parameters and the image processing parameters is discussed in detail in Section 3.1. The final parameters used for the PIV measurements for different experimental conditions are summarised in Table 1.

2.2.2. Geometry The accuracy of the CFD predictions strongly depends on the recreation of particles packed in the bed in the experiments and the application of appropriate boundary conditions. In order to recreate the packed bed geometry, an accurate and detailed information on the key parameters like the size, shape, and position for each particle inside the measurement section was needed. In this work, a simple yet very effective methodology for the geometry reconstruction, as explained below, was used. The main advantages of this methodology are (a) it is inexpensive as it does not require any additional resources (e.g., 3D scanning) apart from the PIV system and (b) relatively less time consuming as the meshing is easier with the geometry created using the CAD tools compared to the other techniques (e.g., 3D scanning) which usually requires a laborious geometry cleanup process to make it suitable for the meshing. As a first step, the images (scans) of the packed bed in the X-Y plane were taken in the presence of the PIV particles/fluorescent dye under the flowing conditions for every 1 mm distance in the Z-direction (Z = 0–45.6 mm) (see Fig. 2). Each of this snapshot showed the particle boundaries and the void regions between the particles (and the tube wall) were highlighted by the PIV particles in the PIV scans. The second step was to arrange these scans in the sequential order (Z = 0–45.6 mm) in a software tool for easier visualization of the scans. The position, size, and shape of a particular particle on the X-Y plane was quantified by analyzing multiple planes in the Z-direction. It was observed that the diameter of the circular cross-sectional area started increasing till it reached a maximum value equal to the sphere diameter and then started decreasing. This information was used to identify the X-Y plane that showed the maximum value of the diameter for each sphere. The third step was to extract the size, shape, and position from the identified plane for each sphere. The particle shape was extracted using the profile mapping technique available in the open-source image processing tool (ImageJ). For the particle position, the identified plane provided the Z-coordinate and the X and Y coordinates were extracted from the image. The success of this methodology depends on the accurate extraction of the size, shape, and position from the scans. The sensitivity of the results towards the minor variations in these key parameters is discussed in detail in Section 3.2. In the present work, best efforts were made to extract the accurate information from the scans which was later used for the geometry reconstruction. A 90° section of a cylindrical tube (dt = 91.2 mm ) containing spherical particles (dp, avg = 21 ± 1 mm ) similar to the experimental setup was used in the CFD model. The particles were placed inside the packed bed using the size, shape, and position extracted from the PIV scans of the measurement section. Using this approach, the geometry of a measurement block with a height of 90 mm and containing 18 particles in five different layers was generated. Due to the computational limitations, it was not possible to simulate the entire height of the packed bed used in the experiments. However, our earlier work [10] has shown

2.2. Simulations 2.2.1. Governing equations Corresponding to the experiments, the flow simulations were performed for the three different Rebed of 1100, 2200 and 6600. In the literature [7,33], it has been reported that the flow inside the packed beds exhibits the turbulent characteristics for particle Reynolds number (Rep = ρVs dp/ μ ) >300. Based on this information, it was found that the three Rebed corresponds to the Rep of 200, 800 and 2400 chosen in the present work can be considered to be in the turbulent flow regime except for the Rep of 200 which is inthe transition flow regime. For the flow simulations, the Reynolds-averaged equations of mass (Eq. (1)) and momentum conservation (Eq. (2)) for the turbulent flow as defined below were solved.

∂ρ + ∇ ·⎜⎛ρV ⎟⎞ = 0 ∂t ⎝ ⎠

(1)

∂ (ρV ) + ∇·⎛⎜ρV V ⎞⎟ = −∇P − ∇ ·⎛⎜τ + τt ⎞⎟ + ρg ∂t ⎝ ⎠ ⎝ ⎠

(2)

where V and P are the mean (Reynolds-averaged) fluid velocity and pressure, respectively. τ and τt are the viscous stress tensor and turbulent stress tensor, respectively. τ for a Newtonian fluid is given by

2 τ = −μ (∇V + (∇V )T ) − ⎛ μ − κ ⎞ ⎜⎛∇ ·V ⎟⎞ δ ⎝3 ⎠⎝ ⎠

(3)

where μ is the molecular viscosity and the second term on the righthand side of the Eq. (3) corresponds to the rate of change in the fluid volume. τt (also known as Reynolds stress tensor) is modelled using the Boussinesq hypothesis as follows

τt = μt (∇V + (∇V )T ) −

2 (μ (∇ ·V ) + ρk ) δ 3 t

Table 1 Parameters used for the PIV measurements.

(4)

Parameter

where μt is the turbulent viscosity. Based on the literature and our earlier studies [9,10] on particle-resolved simulations of packed beds, the shear stress transport (SST) k − ω turbulence model was used for the closure of turbulence terms. The SST k − ω model was chosen for its capability to resolve the flow variables also inside the boundary layer which negates the need for any approximations with wall function.

Rebed Exposure time delay (dt), μs Interrogation spot size, pixels 2 Averaging time, s Image acquisition rate, fps

192

Values 1100 800 16 × 16

2200 400 16 × 16

6600 200 16 × 16

3.84 200

1.68 200

0.84 600

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

pressure drop, there were significant deviations in the pressure distribution on the midline between the fine and very fine mesh. However, the corresponding differences were much smaller between the very fine and ultrafine mesh (see Supplementary Fig. 1(b)). Therefore, the very fine mesh settings were considered for the further analysis (see Fig. 3(b)). The number of mesh elements per particle used in the present work is ∼0.1 million/particle (slightly higher compared to the other works reported in the literature to the best of authors knowledge). 2.2.4. Boundary conditions & solver For the flow simulations, the fluid was defined with the properties of water, and the system reference pressure was set to 101325 Pa. A mass flow inlet with uniform velocity distribution and a pressure outlet with a specified value of 0 Pa (gauge pressure) was applied as the boundary conditions (see Fig. 3(a)). Following the flow rates used in the PIV experiments, the simulations were performed for three different Rebed of 1100, 2200 and 6600 under the steady state and isothermal (298.15 K) conditions. For solving the mass and momentum conservation equations, a finite-volume method based commercial solver Ansys CFX 18.0 was used. The pressure-based solver employs an iterative numerical technique using the coupled method to solve the system of conservations equations. The Rhie and Chow algorithm, which is applicable for the unstructured grids, was used for the pressure-velocity coupling. The convective and diffusion terms in the equations were discretized using a second-order differencing scheme. The simulations were performed on a high-performance computing (HPC) cluster using 128 cores. The calculations were run till the mass imbalances, and the residuals of the conserved quantities in the solution domain reached below the target criteria of 0.1% and 1 × 10−6 , respectively.

Fig. 2. Methodology used for the generation of the CFD model using the PIV scans.

that three layers of particles upstream the measurement section were sufficient for the flow to fully develop. Based on this information, the bed length considered in the simulation was increased by adding three layers and two layers of particles to the upstream and downstream section, respectively to account for the entrance and exit effects. This led to the final packing arrangement with a total packed bed height of 180 mm having 36 particles in 10 layers (see Fig. 3(a)) which was used for the further analysis.

3. Results & discussion 3.1. Effects of the PIV measurement parameters

2.2.3. Meshing Meshing the interstitial voids between the particles with the high quality of mesh elements is difficult due to the presence of the curved surfaces and a large number of contact points (particle-particle and particle-wall). At these contact points, where the two curved surfaces of the particles (or particle-wall) touch each other, the space between the contacting surfaces is very small and leads to the low-quality mesh elements. To overcome the difficulty, the particle volumes were enlarged by 1% of their original volume and thereby allowed to overlap in the present work. This was based on the observation from the PIV scans which showed a overlap-like behaviour at the contacts points, caused by the non-rigid hydrogel particles. In addition, it should be noted that the bed porosity in the measurement section was maintained similar to the experiments through a minor displacement of the particles to compensate for the increase in the particle volume. The model required a large number of mesh elements for resolving the curved surfaces of the spheres and the boundary layers. The boundary layers were essential for the accurate prediction of the wall shear. Five layers of cells were used on all the surfaces for the boundary layer prediction. Also, the first layer thickness was adjusted to meet the y+ ∼ 1 requirement of the SST k − ω turbulence model. The mesh sensitivity analysis was performed with four different mesh resolutions namely the medium (0.7 million elements), fine (1.3 million elements), very fine (2.6 million elements) and ultrafine (4.3 million elements). The predicted pressure drop and the pressure distribution on the midline of the X–Y plane at Z = 4 mm were plotted for the different meshes (see Supplementary Fig. 1). The results showed that the medium mesh over-predicted the pressure drop by around 15% whereas the differences in the predicted pressure drop between the fine, very fine and ultrafine mesh were less than 3% (see Supplementary Fig. 1(a)). Although the fine, very fine and ultrafine mesh predicted a similar

Preliminary PIV experiments were performed to quantify the effects of the different measurement parameters. During the processing of the images, unrealistic velocity vectors were observed inside the hydrogel particles due to the numerical artifacts. These artifacts were eliminated by removing the areas covered by the particles through a polygon mask

Fig. 3. (a) CFD solution domain with the boundary conditions and (b) typical mesh used in the present work. 193

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

distribution for the constant (average) dp and variable (actual) dp (see Supplementary Fig. 3) showed that the constant dp slightly over-predicted the velocity magnitude in the vicinity of certain particles due to variations in the local porosity compared to that for the variable dp . This can also be seen in the histogram of PDF of velocity magnitude. Since the NRMSDV between the two cases was 8.0%, the variable dp was used for the further analysis. During the experiments, the hydrogel particles deformed to ellipsoidal shape due to the weight of the particles above it. A comparison of the velocity distribution for the spherical and ellipsoidal particle shapes (see Supplementary Fig. 4) showed a slightly higher velocity magnitude near the particle wall region for the spherical particle compared to that for the ellipsoidal particle as the change in shape influenced the local flow behavior. The histogram of PDF of velocity magnitude also showed regions of higher values for the spherical particle shape. As the NRMSDV between these two cases was found to be around 6.5%, the ellipsoidal particle shape was considered in the subsequent simulations. Since the particle positions were extracted from the PIV scans acquired at every 2 mm, the particle centroid may exist between any 2 scanned planes. A comparison of the velocity distribution for the packing configuration-1 (PC-1, based on the PIV scans) and packing configuration-2 (PC-2, some particles displaced by 1 mm) showed that the PC-2 exhibited a considerable differences compared to the PC-1 as the shift in the particle positions altered the interstitial void regions in different planes (see Supplementary Fig. 5). The histogram of PDF of velocity magnitude for the PC-2 also showed certain regions of lower and higher velocities compared to the PC-1. The NRMSDV between the two cases was found to be 14.6% which is appreciable. Although the PC-1 were retained for the subsequent analysis, it is important to account for this effect while comparing the measured and simulated velocity distributions. Due to the presence of the glass particles upstream of the measurement section, the PIV scans of exact upstream particle geometry could not be performed. A comparison of the velocity distributions for the upstream packing condition-1 (UPC-1, three layers of hydrogel particles included before the measurement section begins indicated by the red color in Supplementary Fig. 6(a)) and upstream packing condition-2 (UPC-2, three layers of glass particles arranged in a structured way before the measurement section begins) showed some difference in the velocity magnitude in certain regions (see Supplementary Fig. 6) as the changes in the upstream porosity distribution influenced the inlet velocity profile into the measurements section. Since the corresponding NRMSDV was relatively small (7.9%) between the cases, the UPC-2 was

technique. This led to realistic (zero) velocity magnitudes inside the particle regions. The laser pulse delay (Δt ) has an impact on the velocity measurements as the Δt value must be sufficient enough for capturing the particle movement within the interrogation area. Therefore, the effect of Δt on the velocity measurements was studied for 5 different values in the range of 200–1000 μs for the Rebed of 2200 (see Supplementary Fig. 2). The velocity magnitude on the reference line was found to increase with an increase in the Δt from 200–400 μs , remained constant from 600–800 μs and then decreased. Therefore, the Δt of 800 μs was used for the Rebed of 2200. Also, since the range of optimum value for Δt is expected to change with the Rebed , a similar analysis was also performed for higher Rebed of 6600. Due to the increased velocity at higher Rebed of 6600, the optimum value of Δt was found to be 200 μs which was 3 times smaller in comparison to the Rebed of 2200. This also met the recommended Courant number criterion (<0.25) calculated based on the highest value of the measured velocity for both the Rebed , thereby providing the confidence for scaling the Δt for the other Rebed based on the Rebed ratio. Since the interrogation spot size controls the spatial resolution of the velocity measurements, the effect of interrogation spot-size on the velocity magnitude was analyzed for the spot sizes of 8 × 8, 16 × 16, 24 × × 24 and 32 × 32 pixels 2 . The velocity magnitude was comparable for the spot sizes of 16 × 16 and 24 × 24 pixels 2 . Since the spatial resolution was better for the 16 × 16 pixels 2 (0.7 × 0.7 mm2), it was chosen for the further processing of the measurements. Therefore, fluctuating behavior of large eddies (> 0.7 mm) is captured in the present work. The velocity fluctuations and turbulent kinetic energy measurements reported in the subsequent sections correspond to eddies of size > 0.7 mm. In order to obtain the time-averaged velocity distribution, the time-averaging analysis was carried out by considering measurement times corresponding to 1, 2 and 3 residence times for the Rebed of 2200. The velocity magnitude on the reference line was found to be marginally different. The time-averaging of ∼3 residence time was used to obtain the time-averaged velocity measurements. The reproducibility of the measurements was verified by repeating the experiments three times for the Rebed of 2200. While similar velocity magnitude distributions were observed in all the three measurements, the velocity magnitude on the reference line (see Fig. 4) showed a marginal difference (± 6%).

3.2. Sensitivity of the CFD model Though the computational model was generated from the PIV scans (as explained in Section 2.2.2), some minor variations can be expected. Therefore, the preliminary CFD simulations were performed at the Rebed of 2200 to understand and to quantify the sensitivity of the key geometric parameters (size, shape, and positions of particles) on the velocity distribution inside the packed bed. The results from the simulations are presented in three different forms. First, the velocity contours on three different X–Y planes at Z = 4 mm (Plane 4), 21 mm (Plane 21) and 36 mm (Plane 36) are shown for qualitative comparison of the results. Second, the probability density function (PDF) of the velocity magnitude over the combined X-Y planes as a histogram for quantitative comparison of the predictions. Third, the normalized root mean

(

)

∑i = 1 (ϕi,1 − ϕi,2)2 / N / ⎛⎜ϕmax − ϕmin⎞⎟, ⎠ ⎝ where ϕ is the parameter, (ϕmax − ϕmin ) is the value range of the parameter, N is the total number of data points and the subscripts 1 and 2 denotes the results 1 and 2, respectively, used for the comparison) of the velocity magnitude was computed to quantify the overall deviation of different parameters. The measured particle diameters (dp ) were in the range of 20–22 mm (dp, avg = 21 ± 1 mm ) caused by the differences in the swelling behavior of the hydrogel particles. A comparison of the velocity square deviation (NRMSDϕ =

i=N

Fig. 4. Reproducibility of the measured velocity magnitude on the reference line shown in the insert for the Rebed of 2200 (R∗ = 44 mm ). 194

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

velocity distribution, both in terms of the velocity values and the pattern, particularly in the regions close to the wall were seen on Plane 21. In comparison to the measurements, the simulated velocity distribution on plane 36 showed a similar pattern but over-predicted the velocity values. These deviations can only be explained by the combined differences in the particle positions and upstream packing conditions used in the experiments and simulations. Particularly, the upstream packing conditions have the potential to reduce the flow to certain cross-section thereby reducing the velocity magnitude (refer to Section 3.2). Further, the observed deviations could also arise due to small differences in the particle positions that affect the flow around these particles (refer to Section 3.2). Apart from these differences, the simulated low-velocity regions around the particles agreed reasonably well with the measurements for all the planes. A comparison of the PDFs of measured and predicted Vx and Vy are shown in Fig. 5(b). The PDF of predicted Vx agreed well with the measurements. Since the flow is in the Y-direction, it is more important to compare the PDF of measured and predicted Vy . The negative values of Vy indicated the presence of reverse (or back) flow regions. The backflow was caused by the flow impacting on the particles leading to the flow separation and thereby formation of the recirculation regions behind the particles. The predicted PDF of Vy was comparable with the measurements. Unlike the PDF of Vx , there was a small over-prediction of high-velocity regions. Also, there was a small under-prediction of Vy below 0 m/s that represented the backflow region. As discussed earlier, this may be due to the effect of particle positions and upstream packing conditions influencing the flow behavior in the measurement plane. The NRMSD for Vx and Vy were 15.4 % and 7.1 %, respectively indicating a reasonable agreement between the measurements and simulations. Even though the PDF of Vx showed a better agreement, the

used in the further analysis. 3.3. PIV measurements & simulations Following the analysis of the effects of the PIV measurement parameters and the CFD model effects, the predictions were compared with the PIV measurements. Initially, the comparisons were made for the Rebed of 2200. The 2D-PIV measurements provided only the two components (X and Y) of the velocity whereas the CFD predicted the three components (X, Y, and Z) of the velocity. In order to make a rational comparison, the velocity components corresponding to the measurement were taken from the CFD simulations. The results were compared in the following ways: (i) the velocity contours on three different X–Y planes at Z = 4 mm (Plane 4), 21 mm (Plane 21) and 36 mm (Plane 36) for understanding the qualitative differences, (ii) the PDF of the X-velocity component (Vx ) and Y-velocity component (Vy ) over the combined X-Y planes as a histogram for a quantitative comparison and (iii) NRMSD of the Vx & Vy magnitude of the PIV measurements and CFD simulations were computed for the overall quantification of the deviations. A comparison of the measured and predicted quantities for the Rebed of 2200 are shown in Fig. 5. 3.3.1. Velocity distribution The comparison of the measured and predicted velocity distribution on plane 4 showed a similar pattern (see Fig. 5(a)). However, the predicted peak velocity values were slightly lower in comparison with the measurements. Also, higher values of velocity in the regions close to the outer wall were observed in the experiments as a consequence of higher flow in those regions. However, it was not captured in the simulations. Noticeable deviations in the measured and predicted

Fig. 5. Comparison of the measured and simulated (a) distribution of velocity magnitude, (b) PDF of Vx (figure on the left-side) and Vy (figure on the right-side) over the combined X-Y planes at Z = 4, 21 and 36 mm for the Rebed of 2200. 195

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

simulated data for the comparison.

NRMSD was higher due to the denominator term where the range of Vx values was smaller compared to the range of Vy values. In spite of the differences caused by the upstream packing conditions, a reasonable agreement between the measured and predicted velocity components was due to the geometric similarly with respect to the global void distribution inside the measurement section. A decrease of flow in one region was compensated by the corresponding increase of flow in the other region, and therefore the volumetric velocity distribution was not affected significantly. However, only the three planes considered for the comparison were not enough to capture the complete information, and therefore the effect of upstream packing condition is still prevalent. Later, the measured and predicted Vx and Vy distributions were compared for the Rebed of 1100 and 6600 (see Figs. 6 and 7, respectively). As seen for the Rebed of 2200, the results at other two Rebed showed a similar pattern with respect to the velocity distribution. However, the velocity values were different due to the change in the flow rate. The Vx histograms showed a closer agreement compared to the Vy histograms. The NRMSD of Vy were found to decrease with the increase in the Rebed . This may be due to the influence of the turbulence model and needs to be investigated further.

∂Vy ∂Vx ⎞ ω=⎛ − ∂y ⎠ ⎝ ∂x ⎜

S=

⎟

(5)

∂Vy ⎞ 1 ⎛ ∂Vx + ∂x ⎠ 2 ⎝ ∂y ⎜

⎟

(6)

A quantitative comparison of the PDF of the vorticity and strain rate over the combined X-Y planes as histograms for the Rebed of 1100, 2200 and 6600 is presented in Fig. 8. Overall, it can be observed that the magnitude of both the vorticity and strain rate increased with an increase in the Rebed . This is due to the higher velocities in the interstitial voids caused by the increase in the flow rate thereby leading to the large velocity gradients. The histograms of measured and simulated vorticity distribution showed a satisfactory agreement for all the Rebed . There was a small over-prediction in the vorticity in the regions with the vorticity value close to 0 compared to the measurements. This may be due to the coarse resolution of the region close to the particle surface in the measurements because of the limitations on the spatial resolution achieved in the measurements. Also, there was a small systematic under-prediction in the regions of positive vorticity in comparison to the measurements. This may be due to the under-prediction of velocity values causing lower vorticity values in the corresponding regions. The agreement between the measurements and the simulations was satisfactory for the strain rate histograms for all the Rebed . The small deviations in the measured and predicted quantities are expected due to the differences in the spatial resolutions achieved in the measurements and simulations.

3.3.2. Vorticity and strain rate Apart from the first order flow quantities (e.g., Vx and Vy ), it is important to compare the second order flow quantities for a rigorous validation. Since the vorticity depicts the degree of rotation and the strain rate depicts the rate at which the fluid element deforms, the vorticity and strain rate variables were considered for the second order flow quantities. As only the two components of the velocity were measured, the vorticity (ω ) and strain rate (S) calculated based on those two velocity components, as described below and were taken from the

Fig. 6. Comparison of the measured and simulated (a) distribution of velocity magnitude, (b) PDF of Vx (figure on the left-side) and Vy (figure on the right-side) over the combined X-Y planes at Z = 4, 21 and 36 mm for the Rebed of 1100. 196

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

Fig. 7. Comparison of the measured and simulated (a) distribution of velocity magnitude, (b) PDF of Vx (figure on the left-side) and Vy (figure on the right-side) over the combined X-Y planes at Z = 4, 21 and 36 mm for Rebed of 6600.

turbulence model in predicting the k for lower Rebed . On the other hand, the ε histograms showed a comparable magnitudes for higher Rebed of 6600, but a considerable differences in the values and distribution between the measurements and the predictions were seen for lower Rebed of 1100 and 2200. Even for the Rebed of 6600, the simulations showed a much higher peak for lower values of ε leading to a relatively lower mean ε compared to the measurements. As discussed earlier for the other parameters based on the mean velocity, the geometric dissimilarities alone cannot explain the observed significant deviations in the turbulence quantities. Therefore, there is a strong influence of the turbulence model on the predictions and needs to be investigated further. From the results, it can be inferred that the SST k − ω turbulence model appears to be more suitable for the high Reynolds number flows. Even though a comparison of the flow variables on the line profiles provides a rigorous validation of the predictions with the measurements, it was more difficult for the packed bed with relatively large TPDR (>4 ). Several other researchers [21,22] have used the PDF histograms to illustrate the differences between the measurements and simulations. This is because of the relatively large TPDR (4.7 and 17.6), comparable to that used in the industrial applications, was considered in their work which posed challenges in replicating the geometry in the simulations with good accuracy and therefore the line profile comparisons were difficult. As the TPDR considered in the present work is around 4.3, the PDF histograms were used for the comparison of the measurements and simulations for the same reasons. In addition, the reported literature on the comparison of the particle-scale measurements and simulations were for Re in the laminar flow regime (Rebed < 3.5 and Rep < 216) [19–22]. The low Re allowed the use of the DNS to resolve the particle-scale flow field. On the other hand, as discussed earlier, the flows in several industrial processes are

3.3.3. Turbulent quantities Finally, the turbulent quantities like the turbulent kinetic energy (k) and turbulent eddy dissipation (ε ) predicted by the turbulence model were compared against the measurements. Such validation is crucial in understanding the ability of the turbulence model to predict the turbulence parameters. The PIV measurements provide only the two fluctuating velocity components (vx′ and vy′ ) for the computation of k. However, the k modeled by the SST k − ω turbulence model represents all the three components of the velocity fluctuations (vx′, vy′ and vz′). Therefore, for the sake of comparison, it was assumed that the vz′ would be the same as the vx′ in the measurements. This assumption can be justified by the fact that both are lateral components and the magnitudes of fluctuations in the lateral direction will be much smaller compared to the axial (flow) direction. The k and ε are computed using the expressions given below.

k=

1 ((vx′ )2 + (vy′ )2 + (vz′)2) 2

2 2 ∂vy′ ⎞2 ⎛ ∂v′ ⎛ ∂vx′ + ∂vy′ ⎟⎞ ⎞ ε = ν ⎜ ⎛ x ⎞ + ⎜⎛ ⎟ + 2⎜ ∂x ⎠ ∂x ⎠ ⎟ ⎝ ∂y ⎠ ⎝ ∂y ⎠ ⎝⎝ ⎜

(7)

⎟

(8)

where ν is the kinematic viscosity of the fluid and vx′, vy′ and vz′ are the fluctuating velocity components in the X, Y and Z directions, respectively. The histograms of the PDF of k and ε over the combined X-Y planes for the Rebed of 1100, 2200 and 6600 are presented in Fig. 9. The k-histograms showed a significant difference between the measurements and the CFD predictions. The predicted k values were orders of magnitude lower for the Rebed of 1100. However, the deviations between the measured and predicted k-values were seen to improve with an increase in the Rebed . This indicated the limitations of the 197

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

Fig. 8. Comparison of the measured and simulated PDF of vorticity (figures on the left-side) and strain rate (figures on the right-side) combined over the X-Y planes at Z = 4, 21 and 36 mm for the Rebed of (a) 1100, (b) 2200 and (c) 6600.

turbulent in nature for which the DNS is prohibitively expensive and as a result, the eddy-viscosity models are used to perform the particleresolved simulations. However, these simulations lack the rigorous experimental validation, particularly using the particle-resolved measurements. The present work addresses this gap by comparing the particle-resolved simulations using one of the most commonly used turbulence model in the literature, the SST k − ω turbulence model with the particle-resolved PIV measurements. The results showed that the SST k − ω model was able to predict the mean velocity quantities in reasonable agreement with the measurements. However, the turbulence quantities were severely under-predicted by the model. Further work is required to compare the predictions of the different eddy-viscosity models and Large-eddy simulations (LES) to make a quantitative comparison and recommendations. Such work is being carried out and will be reported separately.

section of a cylindrical packed bed containing spherical particles with a tube-to-particle diameter ratio of ∼ 4.3. The comparisons were performed for the three different Rebed of 1100, 2200 and 6600 in the turbulent flow regime. The most widely used SST k − ω turbulence model was used to model the turbulence in the particle-resolved CFD simulations. Preliminary investigations were carried out to identify the optimal experimental parameters for the PIV measurements and to quantify the sensitivity of the CFD predictions with the key geometric parameters (particle size, shape, and position) and mesh resolution. The measured and predicted PDF of velocity distribution (Vx and Vy ) showed a reasonable agreement. The normalised root mean square deviation (NRMSD) values for Vx and Vy for the Rebed of 2200 were 15.4% and 7.1%, respectively and these values were found to decrease with the increase in the Rebed . Also, the predictions of the second order flow quantities like the vorticity and strain rate showed a good agreement with the measurements. The observed deviations in the predictions were mainly due to the differences in the particle positions and upstream packing conditions used in the CFD model. Even though the agreement was reasonable for the quantities based on the mean velocities, the turbulent quantities like the turbulent kinetic energy (k) and

4. Conclusions A comparison of the particle-scale PIV measurements with the corresponding particle-resolved CFD simulation is reported for a 90° 198

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

Fig. 9. Comparison of the measured and simulated PDF of turbulent kinetic energy (figures on the left-side) and turbulent eddy dissipation (figures on the right-side) over the combined X-Y planes at Z = 4, 21 and 36 mm for the Rebed of (a) 1100, (b) 2200 and (c) 6600.

turbulent dissipation rate (ε ) were under-predicted in the simulations compared to the measurements. The agreement for the ε was found to be better with an increase in the Rebed compared to the k. This indicated that the turbulence model also has a significant influence on the predictions, in addition to the geometric differences. From the results, it can be inferred that the SST k − ω turbulence model appears to be more suitable for the high-Re flows. The primary motivation of the present work was to make the local (line profile) comparison for the validation of the CFD simulations with the PIV measurements. However, despite a reasonable agreement seen in the measured and predicted overall velocity (PDF histogram), the differences caused by the particle position and upstream packing conditions were found to have considerable influence on the local velocity. Therefore, it would be inappropriate to perform the line profile comparison in the present work as it may lead to biases in the conclusion depending on the plane and position of the line profile. However, the present work still highlights the limitation of the SST k − ω turbulence model in the predictions of the turbulence quantities for the flow through packed beds. Further measurements in an improved

experimental set-up employing the glass particles with the refractiveindex matched liquid for the better geometry creation and the possibility of measuring the upstream velocity distribution is being performed. A comparison of the predictions of the different turbulence models and LES with the aforementioned measurements is also being carried out and results will be reported separately. Acknowledgments The financial grant received from the Department of Science & Technology, New Delhi, Government of India through its FIST program to set up the PIV and LIF measurement facilities is gratefully acknowledged. One of the author (Karthik G.M.) gratefully acknowledges the Haldor Topsoe company for providing the CFD hardware and software support for this research. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the 199

Chemical Engineering Journal 374 (2019) 189–200

A.H. Thaker, et al.

online version, athttps://doi.org/10.1016/j.cej.2019.05.053.

[17] H.P.A. Calis, J. Nijenhuis, B.C. Paikert, F.M. Dautzenberg, C.M.V.D. Bleek, CFD modelling and experimental validation of pressure drop and low profile in a novel structured catalytic reactor packing, Chem. Eng. Sci. 56 (2001) 1713–1720. [18] T. Dumas, F. Lesage, M.A. Latifi, Modelling and measurements of the velocity gradient and local flow direction at the pore scale of a packed bed, Chem. Eng. Res. Des. 88 (3) (2010) 379–384. [19] D.J. Robbins, M.S. El-Bachir, L.F. Gladden, R.S. Cant, E. von Harbou, CFD modeling of single-phase flow in a packed bed with MRI validation, AIChE J. 58 (12) (2012) 3904–3915. [20] P. Lovreglio, S. Das, K.A. Buist, E.A.J.F. Peters, L. Pel, J.A.M. Kuipers, Experimental and numerical investigation of structure and hydrodynamics in packed beds of spherical particles, AIChE J. 64 (5) (2018) 1896–1907. [21] X. Yang, T.D. Scheibe, M.C. Richmond, W.A. Perkins, S.J. Vogt, S.L. Codd, J.D. Seymour, M.I. McKinley, Direct numerical simulation of pore-scale flow in a bead pack: comparison with magnetic resonance imaging observations, Adv. Water Resour. 54 (2013) 228–241. [22] B.D. Wood, S.V. Apte, J.A. Liburdy, R.M. Ziazi, X. He, J.R. Finn, V.A. Patil, A comparison of measured and modeled velocity fields for a laminar flow in a porous medium, Adv. Water Resour. 85 (2015) 45–63. [23] Tchikango S. Adeline, C. Knieke, G. Brenner, Measurement of flows in randomly packed beds using the Particle Image Velocimetry, 13th Int Symp on Applications of Laser Techniques to Fluid Mechanics, 2006, pp. 26–29. [24] Y.A. Hassan, E.E. Dominguez-Ontiveros, Flow visualization in a pebble bed reactor experiment using PIV and refractive index matching techniques, Nucl. Eng. Des. 238 (11) (2008) 3080–3085. [25] V.A. Patil, J.A. Liburdy, Turbulent flow characteristics in a randomly packed porous bed based on particle image velocimetry measurements, Phys. Fluids 25 (4) (2013) 043304. [26] V.A.V. Patil, J.J.A. Liburdy, Flow characterization using PIV measurements in a low aspect ratio randomly packed porous bed, Exp. Fluids 54 (4) (2013) 1497. [27] S. Khayamyan, T. Lundström, P. Gren, H. Lycksam, J. Hellström, Transitional and turbulent flow in a bed of spheres as measured with stereoscopic particle image velocimetry, Transp. Porous Media 117 (1) (2017) 45–67. [28] G.D.G. Wehinger, C. Füterer, M. Kraume, Contact modifications for CFD simulations of fixed-bed reactors: cylindrical particles, Ind. Eng. Chem. Res. 56 (1) (2017) 87–99. [29] T. Eppinger, G.D. Wehinger, N. Jurtz, R. Aglave, M. Kraume, A numerical optimization study on the catalytic dry reforming of methane in a spatially resolved fixedbed reactor, Chem. Eng. Res. Des. 115 (2016) 374–381. [30] R.K. Reddy, J.B. Joshi, CFD modeling of pressure drop and drag coefficient in fixed beds: Wall effects, Particuology 8 (1) (2010) 37–43. [31] A.G. Dixon, M.E. Taskin, M. Nijemeisland, E.H. Stitt, CFD method to couple threedimensional transport and reaction inside catalyst particles to the fixed bed flow field, Ind. Eng. Chem. Res. 49 (19) (2010) 9012–9025. [32] J. Yang, Q. Wang, M. Zeng, A. Nakayama, Computational study of forced convective heat transfer in structured packed beds with spherical or ellipsoidal particles, Chem. Eng. Sci. 65 (2) (2010) 726–738. [33] I. Ziółkowska, D. Ziółkowski, Fluid flow inside Packed Beds, Chem. Eng. Process. 23 (3) (1988) 137–164.

References [1] P.R. Gunjal, V.V. Ranade, R.V. Chaudhari, Computational study of a single-phase flow in packed beds of spheres, AIChE J. 51 (2) (2005) 365–378. [2] A.G. Dixon, M. Nijemeisland, E.H. Stitt, Packed tubular reactor modeling and catalyst design using computational fluid dynamics, Adv. Chem. Eng. 31 (06) (2006) 307–389. [3] A. Jafari, P. Zamankhan, S.M. Mousavi, K. Pietarinen, Modeling and CFD simulation of flow behavior and dispersivity through randomly packed bed reactors, Chem. Eng. J. 144 (3) (2008) 476–482. [4] M.E. Taskin, A. Troupel, A.G. Dixon, M. Nijemeisland, E.H. Stitt, Flow, transport, and reaction interactions for cylindrical particles with strongly endothermic reactions, Ind. Eng. Chem. Res. 49 (2010) 9026–9037. [5] A.G. Dixon, J. Boudreau, A. Rocheleau, A. Troupel, M.E. Taskin, M. Nijemeisland, E.H. Stitt, Flow, transport, and reaction interactions in shaped cylindrical particles for steam methane reforming, Ind. Eng. Chem. Res. 51 (49) (2012) 15839–15854. [6] M.V. Tabib, S.T. Johansen, S. Amini, A 3D CFD-DEM methodology for simulating industrial scale packed bed chemical looping combustion reactors, Ind. Eng. Chem. Res. 52 (34) (2013) 12041–12058. [7] G. Wehinger, T. Eppinger, M. Kraume, Detailed numerical simulations of catalytic fixed-bed reactors: heterogeneous dry reforming of methane, Chem. Eng. Sci. 122 (2015) 197–209. [8] A. Singhal, S. Cloete, S. Radl, R. Quinta-Ferreira, S. Amini, Heat transfer to a gas from densely packed beds of monodisperse spherical particles, Chem. Eng. J. 122 (2017) 27–37. [9] G.M. Karthik, V.V. Buwa, Effect of particle shape on fluid flow and heat transfer for methane steam reforming reactions in a packed bed, AIChE J. 63 (1) (2017) 366–377. [10] G.M. Karthik, V.V. Buwa, Particle-resolved simulations of methane steam reforming in multilayered packed beds, AIChE J. 64 (11) (2018) 4162–4176. [11] H. Freund, T. Zeiser, F. Huber, E. Klemm, G. Brenner, F. Durst, G. Emig, Numerical simulations of single phase reacting flows in randomly packed fixed-bed reactors and experimental validation, Chem. Eng. Sci. 122 (2003) 197–209. [12] 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 (1–3) (2003) 3–13. [13] A.R. Miroliaei, F. Shahraki, H. Atashi, R. Karimzadeh, Comparison of CFD results and experimental data in a fixed bed Fischer-Tropsch synthesis reactor, J. Ind. Eng. Chem. 18 (6) (2012) 1912–1920. [14] 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. [15] 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. 207–208 (2012) 690–700. [16] 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 pilot-scale fixed bed tube, Chem. Eng. J. 200–202 (2012) 344–356.

200