Numerical Study on Heat Transfer Performance in Packed Bed
Abstract
:1. Introduction
2. Mathematical Model
2.1. Governing Equations for Solid Particles
2.2. Governing Equations for Gas Phase
2.3. Heat Transfer Models
2.4. Entransy Dissipation
3. Simulation Conditions
4. Results and Discussion
4.1. Model Validation
4.2. The Effect of Particle Diameter Distribution
4.3. The Effect of Distribution Thickness
5. Conclusions
- By changing the radial distribution of the particle size in the bed the velocity distribution and temperature distribution in the bed can be effectively improved, the wall effects are well restrained, and the heat transfer ability between the gas and solid is utilized in the greatest extent.
- The range of wall effects is just one particle diameter (5 mm) away from the wall, and the heat transfer performance can be obviously improved by filling small particles in the near wall region.
- The increase of distribution thickness can obviously improve the heat transfer effects, and the equivalent thermal resistance is reduced compared to the uniform size distribution.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Surface area of particle (m2) | |
Specific heat capacity of gas (J/kg/K) | |
Specific heat capacity of particle i (J/kg/K) | |
D | The diameter of bed (m) |
pore scale hydraulic diameter (m) | |
Particle diameter (m) | |
f | Friction factor |
G | Entransy (W.K) |
Moment of inertia of particle i (kg/m2) | |
L1 | The length of extended domain (m) |
L2 | The length of particle domain (m) |
Mas of particle i (kg) | |
Angular velocity of particle i (rad/s) | |
p | Pressure of gas (Pa) |
Q | Heat flow (J/s) |
equivalent thermal resistance (K/W) | |
Temperature of gas (T) | |
Temperature of particle i (T) | |
Volume of particle (m3) | |
Velocity of particle i (m/s) | |
Energy source | |
Momentum source | |
Density of gas (kg/m3) | |
Porosity of bed | |
entransy dissipation (W.K) | |
Temperature difference (K) | |
Temperature gradient (K/m) | |
k | Thermal conductivity |
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Bed Geometry | Diameter D (mm) | 40 |
---|---|---|
Particle domain L2 (mm) | 180 | |
Extended domain L1(mm) | 90 | |
Particle | diameter d (mm) | 3/4/5 |
Density (kg/m3) | 4540 | |
thermal conductivity (W/(m.K) | 24.6 | |
thermal capacity Cp (J/(kg.K) | 630 | |
initial temperature (K) | 800 | |
Gas | Density (kg/m3) | 0.9944 |
Thermal conductivity (W/(m.K) | 0.03066 | |
thermal capacity Cp (J/(kg.K) | 1009 | |
initial velocity (m/s) | 5 | |
Initial temperature (K) | 293 | |
dynamic viscosity (m2/s) | 2.13e-05 | |
Contact parameter | Poisson ratio | 0.3 |
Young’s modulus (Mpa) | 64.52 | |
rolling friction coefficient | 0.01 | |
static friction coefficient | 0.545 | |
restitution coefficient | 0.2 |
2849.9 | 4132.4 | 5405.3 | 6592.8 | ||
Nu | Sug Lee and Ogawa [50] | 19.108 | 25.962 | 32.270 | 38.200 |
Computation data | 20.290 | 24.950 | 30.124 | 36.148 | |
Deviation | 6.2% | 3.9% | 6.6% | 5.4% | |
f | Demirel [49] | 6.041 | 5.642 | 5.404 | 5.249 |
Computation data | 6.459 | 5.326 | 5.157 | 4.712 | |
Deviation (%) | 6.9% | 5.6% | 4.5% | 10.2% |
Particle Size Distribution | d = 5 mm | Mixing 4–5 mm | d = 4–5 mm | Mixing 3–5 mm | d = 3–5 mm (Case1) | Case2 | Case3 | d = 3 mm |
---|---|---|---|---|---|---|---|---|
Outlet temperature (K) | 584.4 | 605.1 | 606.8 | 624.2 | 636.3 | 652.4 | 662.2 | 672.1 |
Average porosity | 0.4397 | 0.4177 | 0.4177 | 0.4127 | 0.4127 | 0.4114 | 0.589 | 0.41 |
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Wang, S.; Xu, C.; Liu, W.; Liu, Z. Numerical Study on Heat Transfer Performance in Packed Bed. Energies 2019, 12, 414. https://doi.org/10.3390/en12030414
Wang S, Xu C, Liu W, Liu Z. Numerical Study on Heat Transfer Performance in Packed Bed. Energies. 2019; 12(3):414. https://doi.org/10.3390/en12030414
Chicago/Turabian StyleWang, Shicheng, Chenyi Xu, Wei Liu, and Zhichun Liu. 2019. "Numerical Study on Heat Transfer Performance in Packed Bed" Energies 12, no. 3: 414. https://doi.org/10.3390/en12030414