Particle Heat Transfer Research Articles

The Effect of Ellipsoidal Particle Surface Roughness on Drag and Heat Transfer Coefficients Using Particle-Resolved Direct Numerical Simulation

The purpose of this study is to estimate the effect of roughness layer thickness on the heat transfer and drag coefficients of ellipsoidal particles. Using an OpenFOAM-based particle-resolved direct numerical simulation (PR-DNS) method, we calculated the drag coefficient and Nusselt number for an isolated axisymmetric nonspherical particle with a rough surface in a uniform flow. The PR-DNS results indicate that the drag coefficient varies linearly with the effective roughness Sef at different angles, which can be expressed as CD=kSef−1+CD0. The changes in k are consistent with the Happel and Brenner equation. Furthermore, the influence of roughness on the heat transfer efficiency factor can be represented by Ef=Sef−65. The models for the drag coefficient and Nusselt number are valid within the ranges 1.25≤Ar≤2.5,1≤Sef≤2, and 10≤Rep≤200, thereby extending the applicability of the equations developed for smooth particles. These newly developed correlations for the drag coefficient and Nusselt number can be utilized for non-isothermal flows of particle mixtures containing materials with various rough-surfaced ellipsoids.

Insight into particle size distribution and particle-scale reactions in a supercritical water fluidized bed reactor by CPFD method

Supercritical water gasification (SCWG) provides a promising solution for converting coal into hydrogen-rich gaseous. However, the modelling of the coal SCWG process still poses challenges due to the heterogeneous particle distribution, large quantity of particles, and complex chemical reactions. This study presents a novel three-dimensional numerical model based on computational particle fluid dynamics (CPFD) to study coal particle gasification in the reactor. The model integrates realistic coal particle size distribution, heat and mass transfer phenomena alongside heterogeneous/homogeneous chemical reactions across phases, elucidating multi-scale reacting flow behaviors and illustrating particle volume fraction, size, and velocity distributions. The obtained results reveal the evolution of coal composition, particle scale gasification process, and distribution of gaseous product components in the supercritical fluidized bed reactor. This work aims to serve as a reference for understanding the flow and heat transfer phenomena between supercritical water and coal particles in SCWG reactors.

Configuration optimization of a biomass chemical looping gasification (CLG) system combined with CO2 absorption

Biomass chemical looping gasification (CLG) combined with CO2 absorption in a dual circulating fluidized bed (DCFB) has emerged as an advanced technology for clean and efficient biomass utilization, yet the reactor design for achieving higher gasification performance and the in-depth understanding of physical-thermal-chemical characteristics is still lacking. This study presents an optimized design aimed at enhancing hydrogen production and carbon reduction in the biomass CLG process with a DCFB reactor by employing the multiphase particle-in-cell (MP-PIC) method integrated with thermochemical sub-models. The proposed reactor is comprehensively compared with the original reactor from the experimental setup in terms of particle mixing, heat transfer, and gasification behaviors. The results indicate that compared to the original setups, the proposed CLG system demonstrates: (i) an improved gas-solid mixing, as evidenced by the particle mixing index rising from 0.23 to 0.34; (ii) an enhanced particle heat transfer coefficient, which boosts heat and mass transfer process; (iii) a 10.11 % increase in H2 concentration alongside a 23.71 % decrease in CO2 concentration; (iv) a particle distribution characterized by higher concentration at the bottom and lower concentration at the top, along with intensified particle back-mixing. The pressure drop inside the combustor is higher than that in the gasifier. A smaller absorbent mean particle diameter and lower-positioned biomass feeding port contribute to the improvement of the CLG performance.

Stokes-type conjugate heat transfer and thermoelasticity analysis of a hollow spherical particle in a slip flow

Conjugate heat transfer around a spherical particle submerged in a viscous heat-conducting fluid at very low Reynolds numbers is analytically investigated. The cases of spherically symmetric and axisymmetric temperature fields are solved. The temperature jump condition of dilute gas dynamics is assumed. The induced thermal stresses in the sphere in the case of spherical symmetry are analytically solved as well. The effect of temperature jump, heat conductivity ratio between the solid and fluid media, the heat generation and the inner radius of the sphere on the temperature, displacement, radial stress and circumferential stresses are studied. Furthermore, an exact correlation is proposed between the Reynolds, Knudsen and Nusselt numbers as well as the drag coefficient of the sphere, which is valid for slip flow at the Stokes limit. Whether it is accurate at higher Reynolds numbers would need further research.

Influence of Central Coke Ratio on the Internal State of Blast Furnace

Central coke charging (CCC) is a widely used burden distribution method for blast furnaces (BFs). Adjusting the central coke ratio can change the burden temperature field and affect the smooth operation of BF. This study presents a coupled physical and mathematical model, incorporating particle motion, gas flow, and heat transfer between the burden and gas in two 5500 m3 BFs. The central coke ratios of the blast furnace A (BFA) and blast furnace B (BFB) is 15% and 20%, respectively. The root positions of the cohesive zone in the BFA and BFB are in the lower part of the stack and bosh zones, respectively. In the central area of the BF, the gas flow rate, gas temperature, and burden temperature of the BFB are higher. In the edge area of the BF, the gas flow rate, gas temperature, and burden temperature of the BFA are higher. The actual top gas temperature and gas pressure verify the accuracy of the proposed model. This model investigates the influence of the central coke ratio on the position of the cohesive zone, gas flow rate, gas temperature, and burden temperature, providing a cost‐effective method for studying the effect of the burden distribution matrix on the internal state of the BF.

Analysis of heat transfer of ellipsoidal particles mixed composite with bounded domains

Analysis of heat transfer of ellipsoidal particles mixed composite with bounded domains

Heat transfer of cohesive particles in a rotary drum: Effect of material properties and processing conditions

This study examines the effect of cohesive particle properties and rotary drum operating conditions on heat transfer. Simulations were performed using the Discrete Element Method and Johnson–Kendall–Roberts contact model. Key variables analyzed include material properties (surface energy, particle size, thermal conductivity), fill level, and rotational speed. Angle of repose (AOR) tests were simulated for varying surface energies to establish a correlation between cohesion and bulk properties. Results showed that the AOR was proportional to the particle Bond number and maintaining a constant Bond number across different particle sizes produced similar heating patterns. This enables practical mapping of properties for future modeling and experimentation. Cohesion between particles was found to linearly decrease the rate of heat transfer, whereas adhesion between particles and the drum walls linearly increased it, leading to temperature non-uniformity among particles. Additionally, baffles enhanced heat transfer under cohesive conditions, although their effectiveness decreased with increased adhesion.

Numerical investigation of the physical-thermal-chemical behaviours of particles during coal combustion and desulfurization processes in a CFB combustor

The desulfurization process has been practised for the clean utilization of coal in chemical engineering fields, yet the physical, thermal, and chemical characteristics of particles are still lacking understanding. In this work, a comprehensive numerical model based on the Eulerian-Lagrangian framework was established to study the particle behaviours during coal combustion and desulfurization processes in a pilot-scale circulating fluidized bed (CFB) combustor. After model validation, the effects of several crucial operation parameters (e.g., excess air ratio, calcium to sulphur ratio, and calcium oxide size) on particle behaviours are illuminated. The results show that density-induced segregation causes coal particles to accumulate in the upper part of the riser. The sand, coal, and CaO particles have time-averaged Reynolds numbers of 15, 6.5, and 0.5, respectively. The particle temperature is higher in areas with lower solid concentrations. Increasing excess air ratio (ϕg) decreases the temperature of sand particles but elevates that of coal and CaO particles. The average particle heat transfer coefficients (HTCs) for sand, coal, and CaO particles are 205 W/m2·K, 172 W/m2·K, and 275 W/m2·K, respectively. With the increase in ϕg, the HTC of sand particles increases but that of CaO particles remains unchanged, additionally, the mass of coal particles decreases and the mass of carbon in coal particles decreases along with the riser. The influence of the Ca/S ratio and CaO size on the axial distribution of coal particle mass and carbon mass fraction is negligible. For each particle species, the axial dispersion coefficient (Dz) is two orders of magnitude greater than the radial ones (Dx, Dy), indicating that the vertical introduction of the fluidizing gas dominates the dense gas-solid flow in the riser.

Numerical modeling of heat transfer behavior for two-phase flow in a nozzle considering phase change

The heat transfer and phase change of alumina particles in the gas-particle flow of the nozzle plays an important role in solid rocket motors (SRM) due to the coupling between the heat transfer and two-phase flow. However, it lacks precise modeling of the heat transfer behaviors of condensed particles in the nozzle, especially the phase change effect. In this article, we determine that the Drake model has the highest accuracy in calculating the convective heat flux between two phases, and propose a correlation to obtain radiative heat flux between the particle and walls. Then, a one-dimensional two-phase non-equilibrium model is established to consider the effects of heat transfer and solidification of particles on the two-phase flow in the nozzle. The results show that considering the phase change of particle improves the outlet thrust of the nozzle, but such increment decreases with the gas inlet temperature. When the supercooling phenomenon is considered, the nozzle thrust is reduced by 1.14% compared with that considering no supercooling. As the particle size increases, the outlet temperature of the particle phase rises and can even surpass the solidification temperature of particles and the velocity of the particle phase decreases significantly.

Convective heat transfer coefficients models for biomass cylindrical particles from low to high aspect ratio

This study investigates the heat transfer of co-firing biomass in coal-fired power station boilers, with a focus on practical application for realistic particle shapes. At present, there are no heat transfer or Nusselt number (Nu) correlations available for biomass particles of cylindrical shape such as straw particles. In this study, a direct numerical simulation (DNS) of the heat transfer between cylindrical particles in a heated flow are performed with OpenFOAM-using a body-fitted mesh. The impact of the Reynolds number Re, aspect ratio AR, and angle of incidence θ in the range of (10 ≤ Re ≤ 2000, 1 ≤ AR ≤ 18, 0° ≤ θ ≤ 90°) on the Nusselt number are determined using a systematical analysis of the thermal flow characteristics for different particle temperature fields. The results show that the aerodynamics and geometrical factors of the cylindrical shape play a dominant role in the heat transfer. A model for the Nusselt number is proposed based on a curve fit of the simulation results, which has a root mean square error (RMSE) of 2.2 × 10-2 and an average relative error of 1.15 %. The independence test of the model has an average error of 5.1 %, indicating a high prediction accuracy. Compared to experimental and simulated data from the literature, the model demonstrates reasonable accuracy within its range of applicability, with a relative error of only 5.05 %. This study provides insights into the heat transfer of biomass particles with cylindrical shape and presents a new mathematical model for the Nusselt number, which can be used to improve the accuracy of the heat transfer prediction using point particle models.

Quaternionic generalization of telegraph equations

Using non-commutative spacetime quaternion algebra, we represent the generalization of one-dimensional and three-dimensional telegraph equations, which are widely applied to consider the propagation of an electromagnetic signal in communication lines, as well as to describe particle diffusion and heat transfer. It is shown that the system of telegraph equations can be represented in compact form as a single quaternion equation taking into account the spacetime properties of physical quantities. The distinctive features of the one-dimensional and three-dimensional telegraph equations are discussed.

Two-Fluid and Discrete Element Modeling of a Parallel Plate Fluidized Bed Heat Exchanger for Concentrating Solar Power

Abstract A novel high-temperature particle solar receiver is developed using a light trapping planar cavity configuration. As particles fall through the cavity, the concentrated solar radiation warms the boundaries of the receiver and in turn heats the particles. Particles flow through the system, forming a fluidized bed at the lower section, leaving the system from the bottom at a constant flowrate. Air is introduced to the system as the fluidizing medium to improve particle heat transfer and mixing. A laboratory scale cavity receiver is built by collaborators at the Colorado School of Mines and their data are used for model validation. In this experimental setup, near IR quartz lamp is used to provide flux to the vertical wall of the heat exchanger. The system is modeled using the discrete element method and a continuum two-fluid method. The computational model matches the experimental system size and the particle size distribution is assumed monodisperse. A new continuum conduction model that accounts for the effects of solid concentration is implemented, and the heat flux boundary condition matches the experimental setup. Radiative heat transfer is estimated using a widely used correlation during the post-processing step to determine an overall heat transfer coefficient. The model is validated against testing data and achieves less than 30% discrepancy and a heat transfer coefficient greater than 1000 W/m2 K.

Temperature statistics of settling particles in homogeneous isotropic turbulence

Heat transfer of settling particles in homogeneous isotropic turbulence is investigated in one-way coupled Eulerian–Lagrangian direct numerical simulations. In the absence of gravity, our observations highlight that there was a correlation between particles concentration and temperature fronts, which are characterized by high-temperature gradients. The particle clustering is mainly influenced by the preferential concentration and the non-local effect, the latter being the memory of their interaction with the flow along their trajectories. Nevertheless, gravity significantly affects the clustering of particles, which further influence the heat transfer of particles with the fluid. We find that the heat transfer of particles is intricately related to particle dynamic inertia and thermal inertia, which can be quantified by the particle Stokes number St and particle thermal Stokes number Stθ, respectively. In this study, we observe that the variance of particle temperature rate of change is independent of Stθ at small thermal inertia but inversely proportional to Stθ2 for large thermal inertia. In the presence of gravity, the variance converges to Stθ−1 for particles with negligible thermal inertia. Our findings reveal that the second-order structure function of the particle temperature, indicating the enhancement of Lagrangian scalar intermittency, adheres to a power-law behavior with limited thermal inertial particles in the dissipation region, denoted as r2. However, as Stθ increases, the power law of the structure function of the particle temperature is disrupted leading to ‘thermal caustics’. The present findings of the heat transfer behavior of settling particles advance the understanding of gravity effect, and are valuable for the modeling of heat transfer in particle-laden turbulent flows.

Numerical study of particle behaviours and heat transfer in a complex rotary kiln

Rotary kiln is widely used for thermal disposal of solid waste due to its effectiveness and high efficiency in recent years. To further improve the processing efficiency, a newly designed rotary kiln with three-section structure is proposed, and the behaviours of particle motion and heat transfer are investigated. Firstly, a lab-scale rotary kiln is manufactured, and experiments are carried out. Verified by experimental data, a CFD-DEM numerical model is developed to analyze the particle motion and heat transfer characteristics with the effects of inlet flue gas temperature, feeding rate and rotating speed. The results show that the outlet temperature increases linearly with the flue gas temperature, while it is negatively correlated with the feeding rate and rotating speed. In addition, the volumetric heat transfer coefficient in this complex rotary kiln is analyzed, the overall heat transfer coefficient is between 200 and 700 W/(m3 K).

A powder-scale multiphysics framework for powder bed fusion of fiber-reinforced polymer composites

Additive manufacturing of fiber-reinforced polymer composites has garnered great interest due to its potential in fabricating functional products with lightweight characteristics and unique material properties. However, the major concern in polymer composites remains the presence of pore defects, as a thorough understanding of pore formation is insufficient. In this study, a powder-scale multiphysics framework has been developed to simulate the printing process of fiber-reinforced polymer composites in powder bed fusion additive manufacturing. This numerical framework involves various multiphysics phenomena such as particle flow dynamics of fiber-reinforced polymer composite powder, infrared laser–particle interaction, heat transfer, and multiphase fluid flow dynamics. The melt depths of one-layer glass fiber–reinforced polyamide 12 composite parts fabricated by selective laser sintering are measured to validate modelling predictions. The numerical framework is employed to conduct an in-depth investigation of pore formation mechanisms within printed composites. Our simulation results suggest that an increasing fiber weight fraction would lead to a lower densification rate, larger porosity, and lower pore sphericity in the composites.

Numerical study of near-field radiative heat transfer between bio-inspired spiny particles

The spine-like structure appears on some smooth organisms and has a high light absorption cross-section. Inspired by the spiny structure in the nature, this study establishes models of solid and hollow spiny particles. The effects of spine cross-section size, uniform and nonuniform spine distribution, hollow size, gap, and spine dislocation on near-field radiative heat transfer of spiny particles are investigated based on the thermal discrete dipole approximations method. The spectral radiative conductance and volumetric net power distribution are obtained. The results indicate that the coupling of localized surface phonons between two particles is affected by spine cross-section size and spine distribution. Near-field radiative heat transfer of spiny particles is enhanced maximumly when the frequencies are slightly lower than the resonance frequency of smooth particles. The peak of the spectral conductance is red-shifted and decreases with the increase of hollow size. The uniformity of volumetric power absorbed distribution increases and the variation of the relative spectral conductance decreases with increasing gap. The influence of two particles’ spine dislocation on near-field radiative heat transfer and volumetric power absorbed distribution is not obvious.

Effect on Rotation Speed on Thermal Dehydration Characteristics of Waste Gypsum Particles in a Constant Volume Rotary Vessel by Heating.

This study examined the thermal dehydration characteristics of CaSO4∙2H2O in a constant-volume rotary vessel. The experiment used CaSO4∙2H2O particles obtained from the crushed waste gypsum board. The particle size ranged from 850 to 2000 μm, and the experiment was carried out at varying rotation speeds of 1, 10, and 35 rpm, with the vessel temperature heated to 180 °C. Temperature and pressure inside the vessel were measured simultaneously using the thermocouple and the pressure sensor. The XRPD measurement analyzed the transition of CaSO4∙2H2O after the heating of particles. The result showed that the temperature growth rate was similar for high rotation speeds of 10 and 35 rpm, while periodic temperature changes occurred at the low rotation speed of 1 rpm. A distinguishing flow pattern was observed at the low rotation speed, and the particles inside the vessel collapsed periodically downward. This particle behavior was related to the temperature distribution of the rotation speed of 1 rpm. Additionally, the pressure in the vessel increased rapidly at higher rotation speeds. This trend indicates the desorption of the crystal water of CaSO4∙2H2O due to the increasing temperature in the case of high rotation speed. Also, the XRPD measurement results showed the appearance of CaSO4∙0.5H2O under the higher rotation speed conditions, and the mass fraction of CaSO4∙0.5H2O increased with the rotation speed. Overall, the present study suggests that rotation speed plays a crucial role in determining the heat conduction and heat transfer of particles in a constant-volume rotary vessel.

Numerical simulations on film cooling performance of turbine blade before and after particles deposition

In the present study, a C3X turbine blade with film holes is selected to investigate the effect of blowing ratio on particle deposition and heat transfer characteristics on the blade surface. The deposition characteristics of the blade surface are obtained based on the EI⁃Batsh particle deposition model, and the surface morphology of the deposited layer is reproduced using the dynamic mesh model. The results show that the particle deposition mainly occurs at the leading edge and pressure surface of the blade, but the large-size particles will be deposited on the suction surface due to rebound. The effect of blowing ratio on large-size particles is more obvious, and the deposition rate tends to decrease and then increase with the increase of blowing ratio. Within the range of blowing ratios in this paper, particle deposition leads to an improvement in the cooling efficiency of the air film in the pressure surface along the flow direction near the air film hole region, but a significant decrease in the cooling efficiency near the trailing edge region. Overall, particle deposition caused an increase in overall blade temperature.

Insights into the gas-solid hydrodynamics and thermochemical characteristics in a pilot-scale chemical looping combustion unit using MP-PIC

Chemical looping combustion (CLC) emerges as an efficient pathway for CO2 capture and storage, yet complex in-furnace phenomena are still far from being understood. Accordingly, the multiphase reactive flow during the CLC process in a pilot-scale dual circulation fluidized bed (DCFB) is numerically investigated by the multi-phase particle-in-cell method considering thermochemical sub-models. After model validations, the thermochemical behaviors and the impact of operating parameters on CLC performance are explored, followed by unveiling the underlying mechanisms of heat and mass transfer characteristics. The pressure gradient is explicitly correlated with the solid holdup in two reactors. Gas-solid flow in the fuel reactor (FR) is more heterogeneous than that in the air reactor (AR) due to complex reactions and large amounts of gas/particle exchanges with other parts of the DCFB, and the whole CLC unit shows good circulating and heat transfer performance. Higher temperatures improve fuel conversion and increase CO2 yield. Elevating the air/fuel ratio (ψ) significantly enhances CLC performance at ψ ≤ 1.0 but it insignificantly affects the CLC performance at ψ > 1.0. A higher total inlet flow rate leads to suppressed fuel conversion and a subsequent decline in CO2 yield. The particle heat transfer coefficient (HTC) in the AR is approximately 450 W/(m2·K), significantly higher than that in the FR of about 300 W/(m2·K).

Effect of immersed tubes configurations on mixing and heat transfer of mixed biomass and silica sand in a bubbling fluidized bed using CFD-DEM and statistical experimental design analysis

The presence of immersed tubes within fluidized beds enhances mixing efficiency and heat transfer. However, the influence of design parameters remains unexplored systematically. This study investigates the impact of design parameters on mixed biomass fluidized beds with immersed tubes employing a combined approach of CFD-DEM simulations and 2k factorial design analysis. Findings reveal that the angle between tubes and tube diameter are primary influential parameters, significantly influences particle mixing and heat transfer efficiency. Optimal conditions, identified through analyses of averaged mixing index and heat transfer coefficient, point to a staggered configuration with specific dimensionless of tube diameter per column width of 0.0515 and a tube spacing per tube zone height of 0.14. These insights offer valuable guidance for optimizing and emphasize the significance of design parameters incorporating immersed tubes, providing practical guidelines for enhancing mixing efficiency and heat transfer in various applications, especially those employing mixed biomass and silica sand.