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Fluid flow and heat transfer in transitional boundary layers: effects of surface curvature and free stream velocity

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Abstract

Velocity and wall temperature measurements, over flat plate, concave and convex walls, were experimentally investigated in a low-speed wind tunnel with inlet velocities of 4 and 12 m/s encompassing the transitional region with streamwise distance Reynolds numbers from 3.15×105 to 1.04×106. As the velocity profiles, recorded by a semi-circular pitot tube and a digital constant-temperature hot-wire anemometer, were compared to exact Blasius profile and (1/7)th power law, experimental local Stanton numbers to analytical flat plate solution and turbulent correlation formula. Intermittency factors, derived from velocities and local Stanton numbers, were presented both in streamwise and pitchwise directions. It was found that the convex curvature delayed transition up to Re x =1.04×106, with a mean intermittency value of 0.61 and a shape factor of 1.81, where the similar intermittency and shape factors were determined at Re x of 8.33×105 and 4.25×105 for the flat plate and concave wall, indicating the enhancing role of concave curvature on the transition mechanism. The thinner boundary layers of the concave surface resulted in higher intermittency values, corresponding to higher skin friction and Stanton numbers; moreover the lowest gap between the measured and derived Stanton numbers were also obtained over the concave surface. Destabilising role of the concave wall caused Stanton numbers to increase up to 22%, whereas the convex wall, due to its stabilising character, produced lower Stanton numbers by 12% with respect to those of the flat plate.

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Abbreviations

A, a, b, c :

correlation constants (dimensionless)

C f :

skin friction (dimensionless)

C p :

constant pressure specific heat (J/kg K)

h :

heat transfer coefficient (W/m2 K)

H :

shape factor (dimensionless)

q :

heat flux (W/m2)

Pr:

Prandtl number (dimensionless)

R :

radius of curvature (cm)

Re x :

streamwise distance Reynolds number (dimensionless)

Reθ :

momentum thickness Reynolds number (dimensionless)

St:

Stanton number (dimensionless)

T w :

wall temperature (°C)

T o :

free stream temperature (°C)

Tu:

turbulence level (%)

u :

streamwise velocity (m/s)

U :

mean free stream velocity (m/s)

x, y, z :

streamwise, pitchwise and spanwise directions (mm)

x l :

unheated starting length (mm)

δ:

boundary layer thickness (mm)

\(\varphi\) :

transition parameter (dimensionless)

γ:

local intermittency factor (dimensionless)

\(\bar{\gamma}\) :

mean intermittency factor (dimensionless)

θ:

momentum thickness (mm)

ν:

kinematic viscosity (m2/s)

ρ:

density (kg/m3)

τw :

wall shear stress (Pa)

o:

flow-off

f:

flow-on

L:

laminar

T:

turbulent

te:

transition end

ts:

transition onset

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Acknowledgements

This work is partly supported by the Uludag University Research Fund.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Uludag, 16059, Gorukle, Bursa, Turkey

    H. Umur & A. A. Ozalp

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  1. H. Umur
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  2. A. A. Ozalp
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Correspondence to H. Umur.

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Umur, H., Ozalp, A.A. Fluid flow and heat transfer in transitional boundary layers: effects of surface curvature and free stream velocity. Heat Mass Transfer 43, 7–15 (2006). https://doi.org/10.1007/s00231-005-0080-8

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