Investigation of Pressure Drop Calculation for Twisted Tape Swirl Tubes by Conventional Channel Flow Correlations with Fusion Applications

Abstract

Twisted tape inserts are commonly used for heat transfer enhancement in fusion applications. Although these devices have been extensively studied, existing correlations relating friction factor to Reynolds number and system geometry are applicable only for tight-fitting inserts and cannot account for system roughness and fouling. In this work, we examine pressure losses in twisted tapes of various twist ratios using both a typical twisted tape correlation and a newer formulation that incorporates conventional channel flow correlations. We study flows down to a Reynolds number of 4000 and find that the channel flow treatment predicts experimental outcomes well for turbulent conditions, like those expected in the ITER divertor. For calculations at low Reynolds numbers (expected during start-up and show-down of the divertor), we propose that channel flow correlations be merged with twisted tape correlations. This new, merged correlation is seen to be applicable across all Reynolds numbers observed, although it predicts small divergences among tape pitches at low Reynolds numbers that are not clearly reflected in our experimental data. Experimental and legacy data show that conventional channel flow friction factor correlations can be used under this formulation for pressure drop predictions at Reynolds number above 15 000. We suggest the use of this twisting channel treatment for loose-fitting inserts and systems in which fouling and roughness may be of concern, allowing existing straight channel models to be used for twisted tape pressure drop calculations.

Keywords:

• Twisted tape
• swirl flow
• friction factor
• divertor design
• plasma-facing components

Nomenclature

Axs =	=	cross-sectional area of pipe with twisted tape insert
D =	=	pipe inner diameter
Dh =	=	hydraulic diameter of pipe with insert, $\frac{4A_{xs}}{P_w}$
f =	=	friction factor based on empty pipe dimensions; Darcy friction factor is used unless specified otherwise
f* =	=	friction factor based on swirl parameters
H =	=	twisted tape length per 180-deg twist
k =	=	swirl coefficient, $\frac{\pi }{2y}$
L =	=	length of pipe across which pressure drop is considered
L* =	=	apparent length of twisting channel
Pw =	=	wetted perimeter of pipe with insert
Q =	=	mass flow rate
ReD =	=	Reynolds number based on empty pipe dimensions, $\frac{uD}{\nu }$
Resw =	=	swirl Reynolds number, $\frac{u_{sw}D}{\nu }$
Re* =	=	Reynolds number based on swirl flow conditions, $\frac{u^{\ast }{D}_h}{\nu }$
u =	=	mean velocity in empty pipe, $\frac{Q}{\frac{1}{4}\pi D^2}$
ua =	=	mean axial velocity in pipe with twisted tape, $\frac{Q}{A_{xs}}$
usw =	=	swirl flow velocity (alternative), $u_a\sqrt{1+{(\pi /2y)}^2}$
u* =	=	swirl flow velocity, $u_a\sqrt{1+k^2}$
Sw =	=	swirl number, $\frac{\mathrm{R}{\mathrm{e}}_{sw}}{\sqrt{y}}$
w =	=	twisted tape width
y =	=	twisted tape pitch, $\frac{H}{D}$
Greek	=
ΔP =	=	pressure drop
δ =	=	twisted tape thickness
ν =	=	kinematic viscosity

Acknowledgments

The authors are grateful to Boris Solomonov and members of the Virginia Commonwealth University Maker Garage for welding the test sections used in this work. Meryem Murphy, Candler Langston, and Ryan McGuire assisted with pressure drop data collection. Financial support for this research was provided by the Virginia Commonwealth University.