1. Numerical Analysis of Turbulent
Momentum and Heat Transfer in
a Rectangular Helical Duct using
Water and Freon-12
Nathaniel H Werner
ME513-Sp 2015
Penn State University

2. Helical Duct Geometry
Geometric Parameters
Parameters Units Value
Width (a) mm 1.0
Height (b) mm 1.2
Hydraulic Diameter (DH) mm 1.09
Entry Length (LE) mm 11
Radius (R) mm 5.208
Pitch (p) mm 3.6
Non-Dim Curvature (δ) 0.192
Non-Dim Torsion (λ) 0.11
Helical Duct
𝑐 =
𝑎
𝑏
, 𝛿 =
𝑎
𝑅
, 𝜆 =
𝑝
2𝜋𝑅
, 𝐷 𝐻 =
2𝛿𝑅
1 + 𝑐
, 𝐿 𝐸 ≥
20𝛿𝑅
1 + 𝑐
As developed from Xing Y., Fengquan Z., and Zinyu Z., “Numerical Study of
Turbulent Flow and Convective Heat Transfer Characteristics in Helical
Rectangular Ducts” Journal of Heat Transfer

3. Boundary Conditions and Fluid Properties
Boundary Conditions
• Inlet Reynolds Number – 55,000
• Critical Reynolds Number – 13,150
• Inlet Temperature – 283 K
• Wall Temperature – 370 K
• Inlet Film Temperature – 327 K
• Outlet Pressure – 1 atm
• Inlet Turbulence Intensity – 5%
• Inlet Turbulence Length Scale – 1.09
mm
• A k-ω model was implemented to
solve the Navier Stokes and energy
equations
Fluid and Flow Properties at Inlet Film
Temperature
Property Units Water Freon-12
Density (kg/m3) 988.1 1200
Kinematic
Viscosity
(m2/s) 5.146e-7 1.852e-7
Thermal
Conductivity
(W/m*K) 0.653 0.693
Inlet Velocity (m/s) 25.97 9.35
Inlet Velocity* (m/s) 78.11 10.2
Re =
𝑉𝐷 𝐻
𝜈
, Recrit = 2100 1 + 12𝛿1 2
, 𝑇film =
𝑇inlet − 𝑇wall
2
* Inlet velocity calculated using the inlet temperature given by Xing et. al.

4. Velocity Contours in Water
• Fluent
• The maximum velocity at the inlet is concentrated
in the top inner corner
• The maximum velocity shifts entirely to the outer
wall
• The maximum velocity eventually develops into two
concentrations near the top and bottom outer
corners
• Becomes fully developed after 1½ revolutions
• CFX
• Same shape of velocity at the inlet
• The maximum velocity shifts to the outer, top and
bottom side of the duct wall
• Lower maximum velocity
• Becomes fully developed after 1 revolutions

5. Temperature Contours in Water
• Fluent
• The temperature field becomes fully developed after
2 revolutions, note that this is after the velocity field
becomes fully developed
• Temperature field resembles the shape of the velocity
field
• CFX
• The temperature field becomes fully developed after
the same location, again after the velocity field
becomes fully developed
• The overall temperature spectrum is consistent with
the results from Fluent

6. Velocity and Temperature
Contours in Freon-12
• Velocity field becomes fully developed after 1½
revolutions
• Velocity field shifts to outer half of the duct, with a
small motion inward moving towards the bottom
wall
• Temperature field resembles the shape of the
velocity field
• However the temperature field never appears to
become fully developed as it is still changing
between 2½ and 3 revolutions, this is likely due to
the lower kinematic viscosity and higher thermal
conductivity of Freon-12 compared to water

7. Turbulent Intensity Contours in Water
• Lowest amount of turbulence remains in the
center region of the duct but gradually moves
toward the top and bottom walls
• During the transition process, between the
inlet and ½ of a revolution, it is asymmetric
about both axes, it becomes symmetric about
the horizontal axis after 1 revolution
• This becomes fully developed after 1½
revolutions which is the same as the velocity
profile
• In the fully developed region the lowest
turbulence appears to be where the highest
velocity is
• The location where the turbulence breaks up
into the two concentrations is the first
instance of the maximum velocity developing
into two regions near the top and bottom wall

8. Turbulent Intensity Contours in Freon-12
• The low turbulence region develops
similar to how it does in water until it
becomes fully developed
• The process is delayed as the
turbulence does not become fully
developed until 2 revolutions
• The turbulence intensity becomes
completely asymmetric when it
becomes fully developed
• The turbulence field resembles the
shape of the velocity field
• The lowest turbulence region develops
asymmetrically in the regions of the
maximum velocity