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Turbulent forced convection in a helically coiled square duct with one uniform temperature and three adiabatic walls

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Abstract

In this study, effects of geometrical parameters on the average convection heat transfer characteristics in helical square ducts were investigated both experimentally and numerically. The inner wall of the helical square duct was uniformly temperatured, and the top, bottom, and outer walls were adiabatic. The Renormalization Group (RNG) k–ε turbulence model was used to simulate turbulent flow and heat transfer. The governing equations were solved by a finite volume method. Numerical results were found to be in good agreement with the presented experimental data. The new correlation was proposed for the average heat transfer coefficient on the inner wall of the helical square duct. The results showed that the ratio of pitch to coil radius b/R has no obvious effect on the inner wall convective heat transfer coefficient but the ratio of hydraulic radius to coil radius a/R has considerable effect.

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Abbreviations

A :

Surface area [m2]

A I :

Helical coil inner wall total surface area (outer wet surface area of copper pipe) [m2]

a :

Hydraulic radius [m]

a P :

Coefficient of P cell

b :

Helical coil pitch [m]

C 1ε :

Turbulent model constant

C 2ε :

Turbulent model constant

C p :

Specific heat under constant pressure [J/kg K]

C μ :

Turbulent model constant

c :

Constant part of the source term

D :

Outer diameter of the test section [m]

d h :

Hydraulic diameter [m]

g :

Gravitational acceleration [m/s2]

h :

Convection heat transfer coefficient [W/m2 K]

h fg :

Latent heat of vaporization per one kg of condensed vapor [J/kg]

I :

Turbulent intensity \((= u'/\bar u)\)

k :

Turbulent kinetic energy [m2 /s]

L :

Length [m]

l :

Turbulent mixed length [m]

l ε :

Length scale of turbulent kinetic energy dissipation [m]

l μ :

Length scale of viscosity [m]

m :

Mass flow rate of cooling water [kg/s]

m y :

Mass flow rate of condensation [kg/s]

Nu :

Nusselt number

Nu c :

Nu number calculated from the new correlation

n :

Normal direction

P :

Pressure [Pa]

Pr:

Prandl number

Q :

Rate of heat transfer [W]

q′′:

Wall heat flux [W/m2]

R :

Radius of helical coil [m]

R′:

Represents the effect of strain in ε equation [kg/ms4]

Re:

Re number

Rey :

Re number for a cell which has a distance of y from the nearest wall

S :

Modulus of mean rate of strain tensor [1/s]

T :

Temperature [K]

T ∞ :

Mixed mean temperature [K]

T fl :

Film temperature of condensed vapor [K]

T S1 :

The first contact point temperature of outer surface of copper pipe with cooling water [K]

T S2 :

The mid contact point temperature of outer surface of copper pipe with cooling water [K]

T S3 :

The last contact point temperature of outer surface of copper pipe with cooling water [K]

t :

time [s]

\(\bar u\) :

Time averaged mean velocity [m/s]

u′:

Instantaneous velocity component [m/s]

V :

Velocity [m/s]

y * :

Non-dimensional viscous sublayer thickness

y T * :

Non-dimensional thermal sublayer thickness

α:

Under Relaxation Factor

αε :

Inverse Pr number for dissipation rate of turbulent kinetic energy

α k :

Inverse Pr number for turbulent kinetic energy

α T :

Inverse Pr number for turbulent flow

ΔH :

The pressure drop of the test section [mmHg]

ΔP :

The pressure drop of one turn of helical duct [Pa]

ΔT B :

Large temperature difference [K]

ΔT K :

Small temperature difference [K]

ΔT ln :

Logarithmic mean temperature difference [K]

ε:

Turbulent kinetic energy dissipation rate [m2 /s3]

η:

The rate of strain in turbulent flow (= Sk/ε)

κ:

Von Karman constant (=0.42)

λ:

Thermal conductivity [W/m K]

μ:

Molecular viscosity [kg/ms]

ν:

Kinematic viscosity [m2 /s]

ϕ:

The parameter used in conservation of mass, momentum, and energy equations

ρ:

Density of fluid [kg/m3]

C:

Correlation

eff:

Effective

f:

Film

I:

Inner wall

i:

Inlet

l:

Laminar

nb:

Neighbor cell

o:

Outlet

PE:

Polyethylene

P:

P center cell

r:

Radial direction

S:

Surface

s:

Axial direction

sat:

Saturated vapor

T:

Total

t:

Turbulent

w:

Wall

y:

Expresses vapor condensate

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Authors and Affiliations

  1. Department of Mechanical Engineering, Pamukkale University, 20017, Camlik/Denizli, Turkey

    O. Kaya

  2. Department of Mechanical Engineering, Yildiz Technical University, 34349, Besiktas/Istanbul, Turkey

    I. Teke

Authors
  1. O. Kaya
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  2. I. Teke
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Correspondence to O. Kaya.

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Kaya, O., Teke, I. Turbulent forced convection in a helically coiled square duct with one uniform temperature and three adiabatic walls. Heat Mass Transfer 42, 129–137 (2005). https://doi.org/10.1007/s00231-005-0656-3

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