Numerical investigation of flow and heat transfer of supercritical carbon dioxide in the vertical helically-coiled tube under half-side heating condition

ABSTRACT

The supercritical boiler is one of the ways to enable sustainable energy development. Its revolution cannot be separated from the study of the characteristics of supercritical carbon dioxide in a spiral pipe. This research article provided an industrially compliant model of a water-cooled wall spiral pipe with one-side heating for heat transfer. The simulation was set for various parameters including P = 30.42 MPa, T_in = 578–643 K, q = 105–180 kW/m², G = 1784–2348 kg/m²s. The article discussed in detail factors such as buoyancy and secondary flow for these cases. The results showed that in the range of high parameters, mass fluxes, heat fluxes, and inlet temperature all had a substantial influence on the temperature and velocity fields, with the mass flux showing a non-monotonic trend on the HTC and the heat flux having a more subtle influence on the HTC. The inhomogeneous heating pattern affected the buoyancy and secondary flow motion, changing the temperature field in the tube, and enhancing the velocity field at the bend and on the heating side. A new empirical correlation for supercritical CO₂ with non-uniform heating was proposed.

KEYWORDS:

• Buoyancy effect
• heat flux
• half-side heating
• numerical simulation
• supercritical carbon dioxide

Nomenclature

$C_p$	=	specific heat (kJ kg−1 K−1)
$\overline{C_p}$	=	average specific heat on the cross-section (kJ kg−1 K−1)
D	=	outside diameter (mm)
d	=	inside diameter (mm)
G	=	mass flux (kg m−2 s−1)
h	=	local heat transfer coefficient (kWm−2 K−1)
L	=	tube length (m)
Nu	=	Nusselt number
P	=	pressure (MPa)
Pr	=	Prantl number
q	=	heat flux(kWm−2)
Re	=	Reynolds number
T	=	temperature (K)
$\mathit{\upsilon }$	=	velocity (m/s)
$y^{+}$	=	nondimensional distance from wall
HTC	=	Heat transfer coefficient
UDF	=	User-Defined Function
BMCR	=	Boiler Maximum Continuous Rating
Greek symbols	=
$\mathit{\phi }$	=	axial angle,°
$\mathit{\mu }$	=	dynamic viscosity (Pa s)
$\mathit{\tau }$	=	shear stress (N/m2)
λ	=	thermal conductivity (Wm−1 K−1)
$\mathit{\epsilon }$	=	turbulent dissipation rate (m2 s−3)
ρ	=	density (kg m−3)
Subscripts	=
b	=	bulk
cr	=	critical
$\mathit{f}$	=	flow fluid
t	=	turbulent
i, j, k	=	general spatial indices
w	=	wall
in	=	inlet
Abbreviations	=
PRE	=	results given by correlations
CAL	=	numerical results
RD	=	relative deviation
+(RD)max	=	maximum positive relative deviation
−(RD)max	=	maximum negative relative deviation
MRD	=	mean absolute relative deviation
MARD	=	mean absolute relative deviation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Sen Zhang

Sen Zhang and Qi Zhang are postgraduate students at University of Shanghai for Science and Technology.

Xiaohong Hao

Xiaohong Hao is an associate professor and supervisor of master candidate at University of Shanghai for Science and Technology. Research interests in the preparation of biodiesel and the supercritical fluid heat and mass transfer.

Su Du

Su Du was awarded a Master's degree in Power Engineering at University of Shanghai for Science and Technology in 2022.

Qi Zhang

Qiguo Yang is currently the Dean of the Institute of Energy and Power Engineering at University of Shanghai for Science and Technology .

Qiguo Yang

Sen Zhang and Qi Zhang are postgraduate students at University of Shanghai for Science and Technology.