Numerical Analysis of Turbulent Momentum and Heat Transfer in a

Rectangular Helical Duct using Water and Freon-12

Nathaniel H WernerME513-Sp 2015

Penn State University

Helical Duct GeometryGeometric ParametersParameters 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=𝑎𝑏 ,𝛿=

𝑎𝑅 ,𝜆=

𝑝2𝜋 𝑅 ,𝐷𝐻=

2 𝛿𝑅1+𝑐 ,𝐿𝐸≥

20𝛿 𝑅1+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

Boundary Conditions and Fluid PropertiesBoundary 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 TemperatureProperty 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=𝑉 𝐷𝐻

𝜈 ,Recrit=2100 (1+12𝛿1/2 ) ,𝑇 film=𝑇 inlet−𝑇 wall

2

* Inlet velocity calculated using the inlet temperature given by Xing et. al.

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

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

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

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

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