Fluidization in Supercritical Water: Heat Transfer between Particle and Supercritical Water

Liping Wei; Youjun Lu

doi:10.1515/ijcre-2017-0249

Article

Fluidization in Supercritical Water: Heat Transfer between Particle and Supercritical Water

Liping Wei and Youjun Lu

Published/Copyright: April 21, 2018

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From the journal International Journal of Chemical Reactor Engineering Volume 16 Issue 7

Abstract

Supercritical water fluidized bed reactor, which is used to gasify biomass and produce hydrogen, is a new member of fluidized bed family. Forced convection heat transfer between supercritical water and particles is a major basic heat transfer mechanism in supercritical water fluidized bed reactor. The object of this paper was to determine the heat transfer characteristics for a forced convection between a spherical particle and supercritical water (SCW) in a range of pressure from 23 to 27 MPa and temperature from 637 to 697 K. A numerical model fully accounting for thermal physical property variation of SCW has been solved using a finite volume method with Reynolds number up to 200. Comparing with constant property flow, high velocity and temperature gradient in the vicinity of the particle surface were observed when the variable thermal physical property of SCW was incorporated in calculation. Based on the numerical results, a correlation that takes into account the large thermal physical property variation was proposed for predicting Nusselt number.

Keywords: supercritical water; Fluidization; sphere particle; heat transfer; variable property

Acknowledgements

This work is currently supported by the National Nature Science Foundation of China (No. 51676158, 91634109), and Key Project of Chinese National Programs for Research and Development (No. 2016YFB0600102)

Nomenclature

C: Constant value
Cd: Drag coefficient
Cp: Special heat [J/(kg⋅K)]
d: Diameter of sphere particle [mm]
H: Height of computed zone [mm]
h: Enthalpy [J/kg]
K: Conductive coefficient [W/(m⋅K)]
n: Coefficient
Nu: Nusselt number
r_i: Particle wall grid number
R: Radius of the computed zone [mm]
R_i: Radius grid number of domain
P: Pressure [MPa]
Pe: Peclet number
Pr: Prandtl number
Re: Reynolds number
SCW: Supercritical water
SCWFB: Supercritical water fluidized bed
T: Temperature [K]
u: Velocity [m/s]
x: Constant coefficient

Greek letters

δ: Boundary layer thickness [mm]
η: Kinetic viscosity [m²/s]
μ: Viscosity [Pa⋅s]
ρ: Density [kg/m³]
θ: Streamwise angle [degree]

Subscripts

∞: Far field
c: Constant property
f: Viscous coefficient
p: Pressure coefficient
T: Thermal
v: Variable property
w: Wall surface

Appendix

A Tests of grid dependence

The resolution of boundary layer is important at low Reynolds number, but the domain zone has to be large enough to meet the requirement of infinite flow (Kotouč, Bouchet, and Dušek 2008). Table 3 shows the results of numerical testing at a certain condition of particle surface temperature of 657 K and free stream temperature of 647 K at far field. It can be seen from Table 3 that as the domain size rate (H/d) change s from 50 to 75, the resulting change in the values of Cd_p, Cd_f, Cd and Nu is found to be 0.03 %, 0.06 %, 0.015 %, and 0.029 %. The domain size rate of 75 and the grid of 100 × 2000 are safer for numerical results at Reynolds number of 5. It is found that numerical results of the domain size of 150 and the grid of 100 × 1000 are accurate enough at Reynolds number of 20. Similar testing was carried out systematically at the two flow regime(Re<20 and Re≥20) and similar accuracies of domain size and grid number are obtained for the two domains in their corresponding regimes.

Table 3:

Test of the grid dependence.

Re	Domian size rate (H/d)	Grid size (r_i×R_i)	Cdp	Cdv	Cd	Nu
5	25	100 × 500	2.862	6.001	8.864	3.896
	50	100 × 1000	2.402	4.780	7.182	3.425
	75	100 × 2000	2.326	4.751	7.077	3.356
20	25	100 × 500	1.026	1.806	2.833	5.149
	40	100 × 800	0.984	1.741	2.726	5.102
	50	100 × 1000	0.979	1.717	2.697	5.020
5	75	100 × 2000	2.326	4.751	7.077	3.356
	75	80 × 1000	2.328	4.794	7.122	3.363
	75	60 × 500	2.360	4.809	7.170	3.401
20	50	100 × 1000	0.979	1.717	2.697	5.020
	50	80 × 500	0.988	1.719	2.707	5.099
	50	60 × 300	0.995	1.732	2.727	5.116

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Received: 2017-12-21

Revised: 2018-01-10

Accepted: 2018-04-08

Published Online: 2018-04-21

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https://doi.org/10.1515/ijcre-2017-0249

Keywords for this article

supercritical water; Fluidization; sphere particle; heat transfer; variable property