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The primary energy demand increases, but a large amount of waste heat resources w ere not effectively used. To explore the influence of particle stacking structure on waste heat recovery process, CFD method was used to simulate. An unsteady heat transfer model of two particles was established, effect of particle stacking angle on heat transfer characteristics of the particles close to the wall under different initial temperature conditions was studied. Results show that: higher initial temperature, resulting in increased heat transfer time, the larger particle stacking angle causes the shortening of heat transfer time. When initial temperature is 1073 K, the average wall heat flux shows a trend of rapid decline first and then a slow one. At the same moment, the larger stacking angle causes smaller particle average temperature. The change of particle stacking angle shows a greater impact on the temperature of the particles close to adiabatic wall. The increase in the stacking angle resulting in better heat transfer characteristics between particles.

The rapid growth of the global economy has promoted the rapid development of the industrial field, which increases the consumption of primary energy. China has low energy efficiency and high energy consumption per unit of GDP, which is 2.5 times the world average. In 2019, China’s total primary energy production was 3.97 million tons, while the total energy consumption was 4.87 million tons [

A large number of high-temperature solid particles are produced in the industrial field [

Porosity [

Therefore, an unsteady heat transfer model of two particles near the wall is established by CFD method in this paper, considering the influence of initial temperature, and the effect of particle stacking angle change on average wall heat flux and particle temperature at the initial temperature of 1073 K is studied. The results may provide basic theoretical support for the high-temperature solid particle waste heat recovery technology.

The fluidity of gas in the packed bed is poor, Zheng’s method [

radiation was considered. DO model is used to simulate the radiation heat transfer. The radiation heat transfer is calculated into the source term (S_{t}). The heat conduction and radiation equations can be expressed as:

1) Heat condition equation

ρ c ∂ T ∂ t = λ ( ∂ 2 T ∂ x 2 + ∂ 2 T ∂ y 2 + ∂ 2 T ∂ z 2 ) + S t (1)

2) Radiation equation

s ⋅ ∇ I = 0 (2)

I ( r w ⋅ s ) = ε w σ T 4 π + ( 1 − ε w ) q i n π (3)

q i n = ∫ s ⋅ n > 0 I i n s ⋅ n d Ω (4)

In the formula, ρ is Density, kg∙m^{−3}; T is Temperature, K; t is time, s; λ is Thermal conductivity, W∙m^{−1}∙K^{−1}; S_{t} is Radiation item; s is Radiation direction; I is Partial surface radiation intensity, W∙m^{−2}∙sr^{−1}; ε w is Surface emissivity of the particle; q i n is Particle surface radiation heat flow, W∙m^{−2}; n is Unit normal vector; Ω is Spatial angle, sr.

The solid phase is meshed before gas phase, to ensure accurate and fast calculation results. The overall grid and local encryption are shown in

In this paper, effect of the initial temperature condition on the heat transfer time (t_{ht}) is considered. The initial temperature is 1073 K is selected, the average wall heat flux ( q ¯ ) and particle temperature ( T ¯ , T ¯ P 1 , T ¯ P 2 ) are studied, the values under different heat transfer times are selected as the evaluation criteria. The average wall heat flux is defined by Equation (5).

q ¯ = Q t / A t (5)

In the formula, q ¯ is Average wall heat flux, W∙m^{−2}; Q_{t} is Total heat transfer rate, W; A_{t} is Heat transfer area, m^{−2}.

Parameter name | Value | |
---|---|---|

1 | Particle material | Ceramic ball |

2 | Particle size | 16 mm |

3 | Initial temperature | 873 K - 1273 K |

4 | Cooling wall temperature | 300 K |

5 | Internal emissivity | 0.32 |

6 | Surface emissivity | 0.85 |

different initial temperature conditions. When particles with the same α, the higher initial temperature causes an increase of t_{ht}. As α increases, the difference caused by different initial temperatures decreases. When initial temperature is the same, t_{ht} decreases as α increases. The higher initial temperature causes the angle change to have a more obvious effect on t_{ht}. When the initial temperature is 873 K, the increase in α reduces the t_{ht} by 5.5 min, and when the initial temperature is 1273 K, the t_{ht} decreases by 10 min. The curves in the figure are all obtained by cosine function fitting, the maximum errors are all less than 2%, and the correlation coefficients are all above 0.955.

difference between the particles and the cooling wall is small, and the heat transfer process is slow.

_{2}. The thermal conductivity of the particles is much greater than that of the gas phase, resulting in uneven heat transfer between the gas and solid phases. At 10 min, the temperature of the entire characteristic surface is further reduced. Among them, α has a more obvious influence on P_{1}. At 20 min, 90% of the energy contained in the particles with α = 60˚ and α = 75˚ has been transferred to cooling wall, so the overall temperature is smaller. The temperature of P_{2} with α = 0˚ and α = 15˚ still maintains a higher value.

_{1} and P_{2} evolution, α has a more obvious impact on the temperature of P_{2}. At 1min, the temperature of P_{1} was below 900 K, while P_{2} was kept at a higher temperature. A larger α causes an increase of the temperature drop rate. The larger the α, the smaller the overall heat transfer distance, resulting in it easier for the heat of P_{2} to be transferred to cooling wall.

In this paper, an unsteady heat transfer model between two particles is established, and the effect of particle stacking angle under different initial temperature conditions on the heat transfer process of the particles close to the wall is analyzed. The major results are as follows:

1) When the initial temperature is the same, the heat transfer time decreases with the increase of α. The higher the initial temperature causes the longer the required heat transfer time, and the more obvious the effect of particle stacking angle.

2) The average wall heat flux decreases rapidly first and then slowly decreases. First the larger stacking angle forms the greater the average wall heat flux. After 9 min, the opposite result appeared

3) The larger the particle stacking angle causes the lower the average temperature. The change of particle stacking angle has a more obvious effect on the temperature of P_{2}.

This work was supported by National Key R & D Program of China (2017YFB0603504-2), and Shandong Provincial Natural Science Foundation, China (ZR2020ME176 and ZR2020ME182).

The authors declare no conflicts of interest regarding the publication of this paper.

Zhang, K., Sun, P., Zheng, B., Xu, J.G., Wang, Y.T., Wang, Z.L., Wang, Q.Z. and Liu, Y.Q. (2021) Effects of Particle Stacking Angle on Heat Transfer Characteristics of Particles Close to the Wall. World Journal of Engineering and Technology, 9, 83-91. https://doi.org/10.4236/wjet.2021.91006