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Turbulent boundary layer on a mildly curved convex surface

Part 2: Temperature field measurements

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Abstract

Extensive single point turbulence measurements made in the boundary layer on a mildly curved heated convex wall show that the turbulence heat fluxes and Stanton number are more sensitive to a change in wall curvature than the Reynolds stresses and skinfriction coefficient, and that downstream, as the flow adjusts to new curved conditions, the St/c f ratio of Reynolds analogy is appreciably lower than in plane wall flow for the same conditions. Details of the turbulence structure in unheated flow have been documented in an earlier paper; temperature field measurements now described comprise mean temperature distributions, the streamwise variation of wall heat flux, profiles of the temperature variance, transverse and streamwise heat fluxes, and triple correlations. Turbulent diffusion of heat flux is drastically reduced even by mild curvature; changes in the heat fluxes are of the same order as changes in the shear stress, that is, an order of magnitude greater than the ratio of boundary layer thickness to wall radius of curvature. The data include plane flow measurements taken in a developed boundary layer upstream of a change in wall curvature.

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Abbreviations

A, A ϕ :

constants in velocity and temperature laws of the wall

c f :

skin friction coefficient, 2τωU pw 2

c p :

specific heat

H :

boundary layer shape factor

K, K 0 :

constants in velocity and temperature laws of the wall

l 0 :

turbulence scale defined by Eq. (8)

p :

fluctuating pressure

Pr t :

turbulent Prandtl number

q :

heat flux through the wall

q 2 :

u 2+v 2+w 2

R :

radius of curvature of the wall

r :

local radius of curvature

R c :

curvature Richardson number 2S/(1 − S)

S :

strain rate ratio defined by Eq. (4)

St :

Stanton number, qU pw cp (T w - T)

T :

mean temperature

U :

streamwise mean velocity component

u, v, w :

fluctuating velocity components in x, y, z direction

x, y, z :

spatial co-ordinates, x measured along and y measured normal to the wall

Δ:

temperature boundary layer thickness

δ:

velocity boundary layer thickness_

ɛ:

dissipation rate of turbulent energy /12 \(\tfrac{1}{2}\overline {\theta ^2 } \)

εθ :

dissipation rate of \(\tfrac{1}{2}\overline {q^2 } \)

θ:

fluctuating temperature

ϱ:

fluid density

σ:

thermal /mechanical time scale ratio

τw :

wall shear stress

p :

potential flow

ref:

reference condition

w :

wall conditions

2:

integral momentum and temperature thicknesses

∞:

free stream conditions

References

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Gibson, M.M., Verriopoulos, C.A. Turbulent boundary layer on a mildly curved convex surface. Experiments in Fluids 2, 73–80 (1984). https://doi.org/10.1007/BF00261325

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Keywords

  • Boundary Layer
  • Heat Flux
  • Reynolds Stress
  • Turbulent Boundary Layer
  • Boundary Layer Thickness