Thermal performance of a single-layer packed metal pebble-bed exposed to high energy fluxes

doi:10.1007/s11708-019-0638-7

Frontiers in Energy

2021, Vol. 15

Issue (2): 513-528 https://doi.org/10.1007/s11708-019-0638-7

本期目录

Thermal performance of a single-layer packed metal pebble-bed exposed to high energy fluxes

Shengchun ZHANG¹, Zhifeng WANG¹(

), Hui BIAN², Pingrui HUANG¹

¹. Key Laboratory of Solar Thermal Energy and Photovoltaic System, Chinese Academy of Sciences, Beijing 100190, China; Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100190, China; Beijing Engineering Research Center of Solar Thermal Power, Beijing 100190, China
². Lanzhou University of Technology, Lanzhou 730050, China

全文: PDF(3023 KB) HTML

Abstract：

It is difficult to accurately measure the temperature of the falling particle receiver since thermocouples may directly be exposed to the solar flux. This study analyzes the thermal performance of a packed bed receiver using large metal spheres to minimize the measurement error of particle temperature with the sphere temperature reaching more than 700°C in experiments in a solar furnace and a solar simulator. The numerical models of a single sphere and multiple spheres are verified by the experiments. The multiple spheres model includes calculations of the external incidence, view factors, and heat transfer. The effects of parameters on the temperature variations of the spheres, the transient thermal efficiency, and the temperature uniformity are investigated, such as the ambient temperature, particle thermal conductivity, energy flux, sphere diameter, and sphere emissivity. When the convection is not considered, the results show that the sphere emissivity has a significant influence on the transient thermal efficiency and that the temperature uniformity is strongly affected by the energy flux, sphere diameter, and sphere emissivity. As the emissivity increases from 0.5 to 0.9, the transient thermal efficiency and the average temperature variance increase from 53.5% to 75.7% and from 14.3% to 27.1% at 3.9 min, respectively. The average temperature variance decreases from 29.7% to 9.3% at 2.2 min with the sphere diameter increasing from 28.57 mm to 50 mm. As the dimensionless energy flux increases from 0.8 to 1.2, the average temperature variance increases from 13.4% to 26.6% at 3.4 min.

Key words： packed bed solar thermal power plants high heat fluxes radiative heat transfer

收稿日期: 2018-09-26 出版日期: 2021-06-18

Corresponding Author(s): Zhifeng WANG

引用本文:

. [J]. Frontiers in Energy, 2021, 15(2): 513-528.
Shengchun ZHANG, Zhifeng WANG, Hui BIAN, Pingrui HUANG. Thermal performance of a single-layer packed metal pebble-bed exposed to high energy fluxes. Front. Energy, 2021, 15(2): 513-528.

链接本文:

https://academic.hep.com.cn/fie/CN/10.1007/s11708-019-0638-7
https://academic.hep.com.cn/fie/CN/Y2021/V15/I2/513

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Equation name		Equation	Equation number
Energy equation in each sphere		$ρ s, i ps, i c ∂ T s, i ∂ τ = 1 r 2 ∂ ∂ r (λ s, i r 2 ∂ T s, i ∂ r) + 1 r 2 sin ? 2 θ ∂ ∂ φ (λ s, i ∂ T s, i ∂ φ) + 1 r 2 sin ? θ ∂ ∂ θ (λ s, i sin ? θ ∂ T s, i ∂ θ)$	(11)
	Initial condition	$T s, i \| τ = 0 = T s 0$	(12)
	Boundary condition	$λ s, i ∂ T s, i ∂ r \| r = 0 = 0$	(13)
	Boundary condition	$λ s, i ∂ T s, i ∂ r \| r = R = q i − h s (T s, i \| r = R − T a) + E i A i$	(14)
	Convective heat transfer coefficient	$h s = λ f Nu L L$	(15)
		$Nu L = 0.228 Re ? L 0.731 ? Pr ? 1 / 3$ [29]	(16)
		$Nu L = 0.228 Re ? L 0.731 ? Pr ? 1 / 3$ [29]	(16)
Wall energy equation		$ρ w, i c pw, i ∂ T w, i ∂ τ = λ w, i ∂ 2 T w, i ∂ x 2$	(17)
	Initial condition	$T s, i \| τ = 0 = T w 0$	(18)
	Boundary condition	$− λ w, i ∂ T w, i ∂ x \| x = 0 = q i − h w (T w, i \| x = 0 − T a) + E i A i$	(19)
	Boundary condition	$λ w, i ∂ T w, i ∂ x \| x = l = h a (T a − T w, i \| x = l)$	(20)
	Convective heat transfer coefficient	$h w = 0$	(21)
Thermal radiation calculation		$A i q in, i = ∑ j = 1 N A j F j, i q o, j$	(22)
		$q o, i = (1 − ε i) q in, i + ε i σ T i 4$	(23)
		$q i = q in, i − q o, i$	(24)

Tab.1

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

1	Z R Liao, X Li, C Xu, C Chang, Z F Wang. Allowable flux density on a solar central receiver. Renewable Energy, 2014, 62: 747–753 https://doi.org/10.1016/j.renene.2013.08.044
2	X Li, W Q Kong, Z F Wang, C Chang, F W Bai. Thermal model and thermodynamic performance of molten salt cavity receiver. Renewable Energy, 2010, 35(5): 981–988 https://doi.org/10.1016/j.renene.2009.11.017
3	R Pitz-Paal, B Hoffschmidt, M Böhmer, M Becker. Experimental and numerical evaluation of the performance and flow stability of different types of open volumetric absorbers under non-homogeneous irradiation. Solar Energy, 1997, 60(3–4): 135–150 https://doi.org/10.1016/S0038-092X(97)00007-8
4	C K Ho. A review of high-temperature particle receivers for concentrating solar power. Applied Thermal Engineering, 2016, 109: 958–969 https://doi.org/10.1016/j.applthermaleng.2016.04.103
5	C K Ho, J M Christian, D Romano, J Yellowhair, N Siegel, L Savoldi, R Zanino. Characterization of particle flow in a free-falling solar particle receiver. Journal of Solar Energy Engineering, 2017, 139(2): 021011 https://doi.org/10.1115/1.4035258
6	S Y Jiang, X T Yang, Z W Tang, W J Wang, J Y Tu, Z Y Liu, J Li. Experimental and numerical validation of a two-region-designed pebble bed reactor with dynamic core. Nuclear Engineering and Design, 2012, 246: 277–285 https://doi.org/10.1016/j.nucengdes.2012.02.005
7	S H Kim, H C Kim, J K Kim, J M Noh. A study on evaluation of pebble flow velocity with modification of the kinematic model for pebble bed reactor. Annals of Nuclear Energy, 2013, 55: 322–330 https://doi.org/10.1016/j.anucene.2012.11.035
8	Y J Li, Y Xu, S Y Jiang. DEM simulations and experiments of pebble flow with monosized spheres. Powder Technology, 2009, 193(3): 312–318 https://doi.org/10.1016/j.powtec.2009.03.009
9	Z F Wang, F W Bai, X Li, Solid pebble flow receiver for solar thermal power generation. China Patent, CN 101634490B, 2009
10	W van Antwerpen, C G du Toit, P G Rousseau. A review of correlations to model the packing structure and effective thermal conductivity in packed beds of mono-sized spherical particles. Nuclear Engineering and Design, 2010, 240(7): 1803–1818 https://doi.org/10.1016/j.nucengdes.2010.03.009
11	P Zehner, E U Schlünder. Effective thermal conductivity at moderate temperatures. Chemical Engineering Technology, 1970, 42(14): 933–941 (in German) https://doi.org/10.1002/cite.330421408
12	J A M Kuipers, W Prins, W P M Van Swaaij. Numerical-calculation of wall-to-bed heat-transfer coefficients in gas-fluidized beds. AIChE Journal, 1992, 38(7): 1079–1091 https://doi.org/10.1002/aic.690380711
13	J Martinek, Z W Ma. Granular flow and heat-transfer study in a near-blackbody enclosed particle receiver. Journal of Solar Energy Engineering, 2015, 137(5): 051008 https://doi.org/10.1115/1.4030970
14	J Marti, A Haselbacher, A Steinfeld. A numerical investigation of gas-particle suspensions as heat transfer media for high-temperature concentrated solar power. International Journal of Heat and Mass Transfer, 2015, 90: 1056–1070 https://doi.org/10.1016/j.ijheatmasstransfer.2015.07.033
15	Y T Feng, K Han, D R J Owen. Discrete thermal element modelling of heat conduction in particle systems: pipe-network model and transient analysis. Powder Technology, 2009, 193(3): 248–256 https://doi.org/10.1016/j.powtec.2009.03.001
16	T Oschmann, M Schiemann, H Kruggel-Emden. Development and verification of a resolved 3D inner particle heat transfer model for the Discrete Element Method (DEM). Powder Technology, 2016, 291: 392–407 https://doi.org/10.1016/j.powtec.2015.12.008
17	T Tsory, N Ben-Jacob, T Brosh, A Levy. Thermal DEM–CFD modeling and simulation of heat transfer through packed bed. Powder Technology, 2013, 244: 52–60 https://doi.org/10.1016/j.powtec.2013.04.013
18	A J Slavin, F A Londry, J Harrison. A new model for the effective thermal conductivity of packed beds of solid spheroids: alumina in helium between 100°C and 500°C. International Journal of Heat and Mass Transfer, 2000, 43(12): 2059–2073 https://doi.org/10.1016/S0017-9310(99)00290-2
19	M A Gómez, D Patiño, R Comesaña, J Porteiro, M A Álvarez Feijoo, J L Míguez. CFD simulation of a solar radiation absorber. International Journal of Heat and Mass Transfer, 2013, 57(1): 231–240 https://doi.org/10.1016/j.ijheatmasstransfer.2012.09.061
20	G J Cheng, A B Yu. Particle scale evaluation of the effective thermal conductivity from the structure of a packed bed: radiation heat transfer. Industrial & Engineering Chemistry Research, 2013, 52(34): 12202–12211 https://doi.org/10.1021/ie3033137
21	H Wu, N Gui, X T Yang, J Y Tu, S Y Jiang. Numerical simulation of heat transfer in packed pebble beds: CFD-DEM coupled with particle thermal radiation. International Journal of Heat and Mass Transfer, 2017, 110: 393–405 https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.035
22	R Grena. Thermal simulation of a single particle in a falling-particle solar receiver. Solar Energy, 2009, 83(8): 1186–1199 https://doi.org/10.1016/j.solener.2009.02.001
23	Q B Zhu, Y M Xuan. Pore scale numerical simulation of heat transfer and flow in porous volumetric solar receivers. Applied Thermal Engineering, 2017, 120: 150–159 https://doi.org/10.1016/j.applthermaleng.2017.03.141
24	A Koekemoer, A Luckos. Effect of material type and particle size distribution on pressure drop in packed beds of large particles: extending the Ergun equation. Fuel, 2015, 158: 232–238 https://doi.org/10.1016/j.fuel.2015.05.036
25	Z Tan, G W Guo. Thermophysical Properties of Engineering Alloys. Beijing: Metallurgical Industry Press, 1994
26	N Gregory, K Sanford. Heat Transfer. New York: Cambridge University Press, 2009
27	G J Cheng, A B Yu, P Zulli. Evaluation of effective thermal conductivity from the structure of a packed bed. Chemical Engineering Science, 1999, 54(19): 4199–4209 https://doi.org/10.1016/S0009-2509(99)00125-6
28	Z Y Zhou, A B Yu, P Zulli. Particle scale study of heat transfer in packed and bubbling fluidized beds. AIChE Journal, 2009, 55(4): 868–884 https://doi.org/10.1002/aic.11823
29	A C Yunus. Heat Transfer: A practical approach. New York: McGraw-Hill, 2003
30	ANSYS Inc. ANSYS Fluent 12.0 UDF Manual. 2009
31	T L Bergman, F P Incropera. Fundamentals of Heat and Mass Transfer. Jefferson City: John Wiley & Sons, 2011

Viewed

Full text

Abstract

Cited

Shared

Discussed