Dataset for the Heat-Up and Heat Transfer towards Single Particles and Synthetic Particle Clusters from Particle-Resolved CFD Simulations

Heat transfer to particles is a key aspect of thermo-chemical conversion of pulverized fuels. These fuels tend to agglomerate in some areas of turbulent flow and to form particle clusters. Heat transfer and drag of such clusters are significantly different from single-particle approximations commonly used in Euler–Lagrange models. This fact prompted a direct numerical investigation of the heat transfer and drag behavior of synthetic particle clusters consisting of 44 spheres of uniform diameter (60 μm). Particle-resolved computational fluid dynamic simulations were carried out to investigate the heat fluxes, the forces acting upon the particle cluster, and the heat-up times of particle clusters with multiple void fractions (0.477–0.999) and varying relative velocities (0.5–25 m/s). The integral heat fluxes and exact particle positions for each particle in the cluster, integral heat fluxes, and the total acting force, derived from steady-state simulations, are reported for 85 different cases. The heat-up times of individual particles and the particle clusters are provided for six cases (three cluster void fractions and two relative velocities each). Furthermore, the heat-up times of single particles with different commonly used representative particle diameters are presented. Depending on the case, the particle Reynolds number, the cluster void fraction, the Nusselt number, and the cluster drag coefficient are included in the secondary data. Dataset: 10.17632/97y842jr5m.1. Dataset License: Creative Commons Attribution 4.0 International (CC BY 4.0).


Summary
Virtual prototyping and digital twins of industrial processes for investigation and optimization have become increasingly popular with increasing computational power. Pulverized coal boilers [1,2] and blast furnaces [3,4] show great potential for optimization using computational investigations. In both cases, pulverized fuel particles are injected into the furnace, where the thermo-chemical conversion starts immediately. Even though computational power has increased drastically in recent years, the fully resolved simulation of most industrial-scale processes is still not viable. In order to enable simulations of these processes, assumptions and simplifications need to be made.
For pulverized coal and blast furnaces, a common approach for modeling the pulverized fuel particles is the Eulerian-Lagrange (EL) approach. In EL models, the carrier phase is described as an Eulerian phase, while the fuel particles are tracked as Lagrangian particles. Usually, particles are lumped into parcels to reduce the computational effort. The parcels are assumed to consist of an arbitrary number of particles with a single representative size [5,6]. Heat transfer, mass transfer, and particle drag are calculated based on the representative particle diameter for each parcel, neglecting any agglomeration or grouping effects. It is essential to consider flow shielding, radiation shading, and other inter-particle effects to predict the particle heat up and the thermo-chemical conversion within particle clouds or dense particle jets correctly [7][8][9][10][11][12][13][14].
Lu et al. [15] used two immersed boundary methods to simulate the gas-solid heat transfer of dense particle packing in tubes. They provide plots of the heat transfer coefficients for each of the up-to-570 particles in the packing and for Reynolds numbers of up to 1800. They observed that the heat transfer coefficients of particles located at the fluid entrance section of the packing are higher than those located further downstream.
The particle resolved Viscous Penalty Method (VPM) was used by Chadil et al. [16] to determine the local and global Nusselt numbers of single spheres, a regular face-centered cubic array of spheres, and randomly arranged spheres. A good agreement of the global Nusselt number compared with different established correlations was found for low Reynolds numbers (Re = 50 and 100) and void fractions of φ = 0.4-0.95.
The influence of the Reynolds number and void fraction on the overall convective heat transfer in randomly distributed arrays of spherical and sphero-cylindrical particles was shown by Tavassoli et al. [17] and Tavassoli et al. [18], respectively. For Re < 180, the authors provide plots of the Nusselt numbers for three and six void fractions for spheres and sphero-cylinders, respectively.
All of the mentioned studies show how convective heat transfer is influenced by the relative velocity and the void fraction of clustered particles. Radiative heat transfer is neglected in all of them. None of the mentioned studies provide detailed and comprehensive information about the heat transfer or heat-up times of the individual particles in the arrangement. In most studies, the data are only presented graphically and are thus hard to retrieve and re-use.
Yin [19] shows the importance of particle radiation in pulverized coal-fired utility boilers. They state that an accurate description of the particles' emissivity and scattering properties influences the temperature and reaction extend of the coal particles, the temperature profiles in the furnace, and thus the entire combustion process. Possible particle clustering effects are not taken into account.
To evaluate the effect of particle clustering on the heat transfer, heat-up, and drag behavior of pulverized fuels in high-temperature environments, clusters with various cluster void fractions were constructed. Using particle-resolved direct numerical simulation synthetic particle clusters with various cluster void fractions at different relative velocities, we derived models that do consider particle clustering effects in EL simulations in the main research paper: Bösenhofer et al. [20]. A detailed description of the data gathered in [20] is presented here.
The data set presented in the current work includes additional information about convective and radiative heat fluxes, averaged particle temperatures, and the particle position of each particle in the cluster. The data presented in this article can help understand the convective and radiative heat transfer, and drag behavior of single particles in a clustered arrangement and particle clusters at void fractions close to packed beds up to single spheres. Heat transfer and drag models can be derived from the data. The influence of flow shading and radiation shielding on the heat transfer and particle heat-up depending on the particle's position in the cluster can be investigated. Thus, the presented data have the potential to improve the simulation of heat transfer in any turbulent gas-solid flow where clustering effects occur. These phenomena include, among others, pulverized particle combustion, pulverized carbon carrier injection in iron making, or pharmaceutical and chemical processes. Correct heat transfer prediction and the associated improvements of the modeling results provide a huge potential to reduce the overall emission and to improve efficiencies of the target processes. The full dataset is available in Mendeley Data [21].

Data Description
The data presented in this work consist of the primary dataset (averaged simulated raw data) and secondary dataset, which is derived from the primary dataset.

Primary Dataset
The primary dataset represents three different computational fluid dynamics (CFD) simulations:
Transient simulation of the flow around single spheres, including particle heat up (dataset 3).
As the raw data of a single case are too big to be presented here, the averaged particle temperatures, and integral heat fluxes and forces are provided here.

ad 1
The primary dataset consists of the data presented in Table 1 and the data provided in dataset 1.
Dataset 1 contains the case id, the exact position of particles in the cluster, the integral convective heat fluxQ conv (in mW), and the integral radiative heat fluxQ rad (in mW) for each individual particle in the cluster. The case id, relative velocity U rel (in m/s), the distance between particles (in µm), the integral convective heat fluxQ conv , the integral radiative heat fluxQ rad for the whole particle cluster, and the net force in flow direction F acting upon the particle cluster (in µN) are presented in Table 1.
As the velocity of the particle clusters is zero, the relative velocity in Table 1 is the superficial velocity. The distance between particles is defined as the distance between particle centers. The convective and radiative heat fluxes are given as absolute values. Here, as the temperature of particles is lower than the temperature of the surroundings, Q conv andQ rad are the total heat fluxes from the surroundings to the particles or the cluster. The fluxes and forces presented in Table 1 are the integrated heat fluxes over all particles. The integrated heat fluxes for each individual particle and the exact particle position in the cluster are provided in dataset 1 for all cases ST1-ST85. Particle positions are given relative to the reference sphere marked in Figure 1. Cases ST61-ST65 represent single sphere simulations. Cases ST66-ST85 are simulations of random clusters with a particle size distribution (PSD) according to the Weibull distribution [22]. ad 2 Dataset 2 contains the mass averaged temperature profile (in K) and the exact position of each individual particle in the cluster for conditions given in Table 2. The data are provided for simulation with and without radiation-coupled regions. ad 3 Dataset 3 contains the mass averaged sphere temperature profile (in K) of size equivalent (SE), mass equivalent (ME), area equivalent (AE), and area and mass equivalent (AME) single-sphere simulations. Simulation conditions are shown in Table 3.

Secondary Dataset
The secondary dataset contains additional information, derived from the primary dataset. This includes the particle Reynolds number Re P (all cases), the cluster void fraction φ (cases ST1-ST85 and T1-T6), the Nusselt number Nu, and the cluster drag coefficient ξ (cases ST1-ST85). Secondary data are included in Tables 1-3.

Simulation Setup and Conditions
The synthetic particle clusters were constructed as regular rhomboid-shaped to enable a systematic approach. The distance between particles was varied to evaluate the influence of the cluster void fraction on the drag and heat transfer behavior. Void fractions were chosen to close the gap from loosely packed beds (void fraction φ = 0.477) to single particles in cross flow (φ → 1). This range of void fractions represents solid-to-gas mass ratios of 1737 to 1 for φ = 0.477 to 0.999, respectively. For pulverized fuel particles injected by dense-phase pneumatic conveying, the initial solid-to-gas mass ratio can exceed 100 [23][24][25][26]. It is known that particles tend to cluster randomly in turbulent flows [8,27,28]. To account for this, simulations for four randomly shaped particle clusters with a fixed void fraction consisting of spheres with a particle size distribution according to the Weibull distribution were carried out.
The data were gathered from particle resolved direct numerical simulations using the open-source CFD toolbox OpenFOAM ® v7 [29]. The particles were fixed in space to avoid numerical expensive moving and deforming meshes in the simulations and to allow for the investigation of different relative velocities. The numerical meshes consist of a base cell size of 60 µm, with significant refinement in the wake of the cluster and towards the particles, resulting in up to 14 million cells. Simulations were carried out using the chtMultiRegionFoam solver, which couples fluid and solid regions explicitly in space and time. Radiation was modeled by the finite volume discrete ordinates model (fvDOM) [30] with 16 discrete rays. Gas phase radiation was modeled by gray mean absorption [31]. The boundary conditions are summarized in Table 4. A uniform fixed value was set for the velocity at the inlet patch, while a zero gradient, no slip and slip boundary condition was set at the outlet, the particles, and the remaining patches, respectively. The pressure was set to a fixed value at the outlet. A zero gradient boundary condition was used for all other patches. The temperature was fixed at the fluid inlet, while a zero gradient condition was imposed at all other patches. The particle surface temperature was set to a uniform fixed value in all steady-state simulations (ST1-ST85). For particle and cluster heat-up simulations (SE, ME, AE, AME single-sphere simulations, and T1-T6), a coupled boundary condition was used. This boundary condition couples the diffusive, convective, and radiative heat fluxes between the solid and fluid regions. All surfaces were treated as gray bodies with an emissivity of = 1. The inlet velocity was varied based on values given in Tables 1-3. The temperature of the gas at the inlet was set to 2500 K, and the pressure at the outlet was fixed to 5 bar (a) . In ST1-ST85, the particle temperature was fixed to a value 2450 K. The initial temperature of particles in the transient simulations was set to 400 K.
The thermo-physical properties of the GRI3.0 mechanism [32] were applied for the gas phase species, while particle properties were kept constant (Table 5).
Single-sphere simulations for dataset 3 used the same case setup as the cluster simulations, with the exception of the cluster being replaced by a single sphere with diameter according to Table 3. The different sphere diameters present different commonly used representative particle diameters. Here, the particle clusters were substituted by a single particle with one of the following:

1.
A size equivalent sphere (SE): The single-sphere diameter is equal to the size of the particles in the cluster (d = 60 µm); 2.
A mass equivalent sphere (ME): The single-sphere mass is equal to the mass of the cluster (d = 211.8 µm); 3.
A surface area equivalent sphere (AE): The single-sphere surface area is equal to the surface area of the cluster (d = 397.8 µm);

4.
A surface and mass equivalent sphere (AME): The single-sphere surface area and mass are equal to the cluster. The sphere diameter is equal to the AE case, but the particle density is reduced to 165.8 kg/m 3 .
A cross section of the cluster's simulation domain is shown in Figure 1. The size of the simulation domain in the cluster simulation was scaled with the cluster diameter d cluster using the constant scaling factors a, b, and c. The inlet velocity and cluster void fraction were varied according to Tables 1 and 2. A constant particle diameter of 60 µm was used in the cluster simulations, except for cases ST66-ST85, where a PSD was used.  Table 5. Gas phase composition and thermo-physical properties as well as solid thermo-physical properties used in the simulations. Adapted from [20]. The resulting velocity and temperature field and the velocity and temperature contours in the horizontal cross section for cases ST4, ST29, ST59, and ST69 are shown in  Note that the whole cluster and not only the horizontal cross section is shown. Due to the file size for each case, the computational meshes and the respective fields cannot be provided.

Bulk Gas Phase Thermo-Physical Properties
The convective (Q conv ) and radiative (Q rad ) heat fluxes of each sphere in the particle cluster for cases ST1-ST5, ST26-ST30, ST56-ST60, and ST66-ST70 are shown in Figure 6a-d, respectively.

Data Collection
Simulations ST1-ST85 were evaluated after a steady state was reached (steady value of the drag force and heat transfer rates). Transient simulations were carried out until the mean particle temperatures were close to the gas temperature (2500 K).
The cluster void fraction was calculated from Equation (1), where d is the particle diameter, x is half the distance between sphere centers (Figure 1), and 17.8251 is the graphically determined number of full spheres in the considered volume (the biggest possible rhomboid through the particle centers).
The particle temperature was calculated from the simulated cell values as the massweighted average using Equation (2), where ρ is the particle density, V is the cell volume, T is the cell temperature, and N is the number of cells in the particle.
The particle Reynolds number Re P , Nusselt number Nu, and the drag coefficient ξ are calculated from Equations (3)-(5), respectively [33,34]. Here,Q conv is the integrated cluster heat flux, T ∞ is the gas temperature at the inlet, T is the mass averaged cluster (dataset 1 and dataset 2) or particle (dataset 3) temperature, κ is the thermal conductivity of the gas, A CL,S is the cluster (dataset 1 and dataset 2) or particle (dataset 3) surface area, and A CL is the cluster cross-sectional area. All thermo-physical gas properties are calculated at 2500 K and 5 bar (a) . Cases ST61-ST65 are the simulations of a single sphere in cross-flow. Cases ST66-ST85 represent random clusters with a particle size distribution according to the Weibull distribution (Equation (6)) [22] with a shape parameter of k = 1.14 and a scale parameter of λ = 120 µm. The diameter used to calculate Re P in Table 1 is the first moment of the PSD:d = d max d min d q(d) dd = 114.5 µm.

Abbreviations
The following abbreviations are used in this manuscript: