Experiments in Fluids

, Volume 6, Issue 5, pp 344–352 | Cite as

Measurements of fully developed turbulent flow in a trapezoidal duct

  • M. M. A. Khalifa
  • A. C. Trupp
Originals

Abstract

The turbulence characteristics of fully developed isothermal air flows through a symmetric trapezoidal duct were examined experimentally using Pitot tube and hot-wire anemometry over a Reynolds number range of 3.7–11.6×104. The measurements included local wall shear stress and the cross-sectional distributions of mean axial velocity, secondary velocities and Reynolds stresses. Four secondary flow cells were detected in a symmetric half of the duct. Although secondary velocity components were typically less than about 1% of the bulk axial velocity, their effect was especially pronounced on the distributions of turbulent kinetic energy and local wall shear stress.

Keywords

Reynolds Number Turbulent Kinetic Energy Axial Velocity Reynolds Stress Flow Cell 

List of symbols

a, b, c, d

trapezoidal duct dimensions (Fig. 1)

A, B

coefficients in log law (Table 1)

Dh

equivalent hydraulic diameter

f

Darcy friction factor, (2D h /ϱU b 2 ) (dP/dx)

k

turbulent kinetic energy per unit mass, \(\tfrac{1}{2}(\overline {u^2 } + \overline {v^2 } + \overline {w^2 } )\)

k+

dimensionless turbulent kinetic energy, k/(ū*)2

P

static pressure

Re

Reynolds number, ϱU b D h /μ

s

distance along inclined wall, measured from top corner (Fig. 1)

u, v, w

fluctuating components of the velocities in the x, y, z directions

u+, v+, w+

dimensionless turbulence intensities; √u2/ū*, √v2/ū*, √w2/ū*

u*

local friction velocity, (τ w /ϱ)1/2

ū*

average friction velocity, (¯gt/ϱ)1/2

Ū

axial mean velocity (time-average)

Ub

average mean axial velocity

Usec

resultant of ¯V and ¯W, (¯V2+¯2)1/2

U+

dimensionless velocity, Ū/u*

¯V, ¯W

mean velocities in the y, z directions (secondary velocities)

x

axial direction

y, 2

horizontal and vertical directions (Fig. 1)

z+

dimensionless distance from (and normal to) a wall, zu*/v

\(\hat z\)

distance from wall (at y=0) to location of maximum axial velocity

μ

laminar dynamic viscosity

v

kinematic viscosity

ϱ

air density

τw

local wall shear stress

¯τw

average of local wall shear stresses over all walls

¯τ

average wall shear stress, (dP/dx) (D h /4)

φ

corner angle of trapezoidal duct (Fig. 1)

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References

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • M. M. A. Khalifa
    • 1
  • A. C. Trupp
    • 1
  1. 1.Dept. of Mechanical EngineeringUniversity of ManitobaWinnipegCanada

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