# Measurements of fully developed turbulent flow in a trapezoidal duct

- 147 Downloads
- 4 Citations

## 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 3.7–11.6×10^{4}. 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)

*D*_{h}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; √

*u*^{2}/*ū*^{*},*√v*^{2}/*ū*^{*},*√w*^{2}/*ū*^{*}*u*^{*}local friction velocity, (

*τ*_{ w }/*ϱ*)^{1/2}*ū*^{*}average friction velocity, (

*¯gt/ϱ*)^{1/2}*Ū*axial mean velocity (time-average)

*U*_{b}average mean axial velocity

*U*_{sec}resultant of

*¯V*and*¯W*, (*¯V*^{2}+*¯*^{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

*τ*_{w}local wall shear stress

*¯τ*_{w}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)

## Preview

Unable to display preview. Download preview PDF.

### References

- Alshamani, K. M. M. 1978: Correlations among turbulent shear stress, turbulent kinetic energy and axial turbulent intensity. AIAA J. 16, 859–861Google Scholar
- Alshamani, K. M. M. 1979: Relationships between turbulent intensities in turbulent pipe and channel flow. Aeronaut. J. 83, 159–161Google Scholar
- Aly, A. M. M. 1977: Turbulent flows in equilateral triangular ducts and rod bundle sub-channels. Ph.D. Thesis, University of Manitoba, CanadaGoogle Scholar
- Aly, A. M. M.; Trupp, A. C.; Gerrard, A. D. 1978: Measurements and predictions of fully developed turbulent flow in an equilateral triangular duct. J. Fluid Mech. 85, 57–83Google Scholar
- Brundrett, E.; Baines, W. D. 1964: The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19, 375–394Google Scholar
- Chiranjivi, C.; Sankara Rao, P. S. 1971: Laminar and turbulent forced convection heat transfer in a symmetric trapezoidal channel. Ind. J. Technol. 9, 416–420Google Scholar
- Gerrard, A. D. 1976: Turbulent flow in an equilateral triangular duct. M.Sc. Thesis, University of Manitoba, CanadaGoogle Scholar
- Khalifa, M. M. A.; Trupp, A. C. 1985: Turbulent flow characteristics in a trapezoidal duct-experimental results. Dept. of Mech. Eng., University of Manitoba Rep. No. ER 25.39Google Scholar
- Khalifa, M. M. A. 1986: Measurements and predictions of turbulent flow and heat transfer in trapezoidal ducts. Ph.D. Thesis, University of Manitoba, CanadaGoogle Scholar
- Laufer, J. 1954: The structure of turbulence in fully developed pipe flows. NACA Rep. TN 1174Google Scholar
- Lawn, C. J. 1969: Turbulent measurements with hot wires at B.N.L. Central Elec. Gen. Board, Berkeley Nuclear Labs. Rep. RD/B/M 1277Google Scholar
- Lyall, H. G. 1971: Measurements of flow distribution and secondary flow in ducts composed of two square interconnected subchannels. Symposium on internal flows, University of Salford, England, April 20–22, pp. E16-E23Google Scholar
- Nakayama, A.; Chow, W. L.; Sharma, D. 1983: Calculation of fully developed turbulent flows in ducts of arbitrary cross-section. J. Fluid Mech. 128, 199–217Google Scholar
- Nikuradse, J. 1930: Untersuchungen über turbulente Strömungen in nicht kreisförmigen Rohren. Ing. Arch. 1, 306–332Google Scholar
- Ower, E.; Pankhurst, R. C. 1966: The measurement of air flow, 4th Ed. Pergamon, Oxford.Google Scholar
- Patel, V. C. 1965: Calibration of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 25, 185–208Google Scholar
- Rapley, C. W.; Gosman, A. D. 1984: The prediction of turbulent flow and heat transfer in a narrow isosceles triangular duct. Int. J. Heat Mass Transfer 27, 253–262Google Scholar
- Rodet, E. 1960: Etude de l'écoulement d'un fluïde dans un tunnel prismatique de séction trapézoidale. Publ. Sci. Tech. Minist. Air. (Fr.) 369, pp. 1–96Google Scholar
- Seale, W. J. 1982: Measurements and predictions of fully developed turbulent flow in a simulated rod bundle. J. Fluid Mech. 123, 399–423Google Scholar
- Shah. R. K.: London. A. L. 1978: Laminar flow forced convection in ducts. Adv. Heat Transfer suppl. 1. New York: Academic PressGoogle Scholar