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The relationship between absolute vorticity flux along the main flow and convection heat transfer in a tube inserting a twisted tape

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Abstract

As passive enhancement devices, twisted tape insert has been used for almost a century, the most dominant heat transfer enhancement mechanism of circular tube fitted with twisted tape is the secondary flow generated by the tape. There is a parameter to specify the intensity of secondary flow, but this parameter cannot be applied to more general cases. Here cross-averaged absolute vorticity flux in the main flow direction is used to specify the intensity of secondary flow produced by twisted tape inserted in a tube. The relationship between the intensity of secondary flow and the intensity of laminar convective heat transfer is studied using a numerical method. The results reveal that the cross-averaged absolute vorticity flux in the main flow direction can reflect the intensity of secondary flow and a significant relationship between this cross-averaged absolute vorticity flux and Nusselt number exists for studied cases. The presented results validate that the cross-averaged absolute vorticity flux in the main flow direction is a general specifying of the intensity of secondary flow and can be used in other cases.

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Abbreviations

A :

Area of cross section (m2)

c p :

Specific heat capacity [kJ/(kg K)]

D :

Tube internal diameter, hydraulic diameter (m)

f :

Friction factor: f = ΔpD/(2ρu 2 m L)

g :

Acceleration due to gravity (m/s2)

Gr :

Grashof number: Gr = gρ 2 D 3 β(T w − T bulk)/μ 2

h :

Heat transfer coefficient [W/(m2 K)]

H :

Twist pitch length (m)

J n :

Vorticity flux along the normal direction of cross section (s−1)

J nABS :

Absolute vorticity flux along the normal direction of cross section (s−1)

L :

Axial length (m)

n :

Normal direction of the cross section or wall surface

Nu :

Nusselt number: Nu = hD/λ

p :

Static pressure (Pa)

Pr :

Prandtl number: Pr = µc p/λ

q :

Heat flux (W/m2)

Re :

Reynolds number: Re = ρu m D/μ

s :

Local coordinates (m)

Sw :

Dimensionless swirl parameter defined in Eq. 1

T :

Temperature (K)

T r :

Twist ratio of the twisted tape: T r = H/D

u i , u, v, w :

Components of velocity vector (m/s)

u :

Velocity (m/s)

x i , x, y, z :

Coordinates axes (m)

α 1, α 2, β 1, β 2 :

Interpolation coefficients used in Eqs. 15 and 16

β :

Coefficient of isobaric thermal expansion (K−1)

δ :

Tape thickness (m)

ε :

Relative error defined in Eq. 41

η :

Coordinate (m)

λ :

Thermal conductivity [W/(m K)]

µ :

Viscosity (Pa s)

ρ :

Density (kg/m3)

Θ:

Dimensionless temperature

Δp :

Pressure drop (Pa)

ω :

Vorticity (s−1)

ξ, ζ :

Coordinates axes (m)

bulk:

Cross averaged value

f:

Fluid

in:

Inlet

local:

Local value

m :

Averaged value

out:

Outlet

s:

Solid

w:

Wall surface

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Authors and Affiliations

  1. Department of Mechanical Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, Gansu, People’s Republic of China

    Zhi-Min Lin, Dong-Liang Sun & Liang-Bi Wang

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  1. Zhi-Min Lin
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  2. Dong-Liang Sun
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  3. Liang-Bi Wang
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Correspondence to Liang-Bi Wang.

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Lin, ZM., Sun, DL. & Wang, LB. The relationship between absolute vorticity flux along the main flow and convection heat transfer in a tube inserting a twisted tape. Heat Mass Transfer 45, 1351–1363 (2009). https://doi.org/10.1007/s00231-009-0511-z

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  • DOI: https://doi.org/10.1007/s00231-009-0511-z

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