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Experimental study of heat flux in mixed convective flow over solid waves

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Abstract

In this experimental study, we address transport processes in a mixed convective flow over a heated wavy surface. Therefore, we combine digital particle image velocimetry (DPIV) and two-color planar laser induced fluorescence (PLIF) to simultaneously measure the velocity and temperature field. For this, we propose to use the dye combination Rhodamine B and Rhodamine 110, both excited with the Nd:YAG laser also used for the PIV measurements. We investigate the influence of mixed convection over a wavy surface on the velocity field, turbulence statistics, the temperature field and the heat flux. By computing these quantities we find a correlation between the maximum in the Reynolds stress profiles and the components of the heat flux vector, thus regions of maximum momentum and scalar transport coincide. In addition, we apply a proper orthogonal decomposition (POD) to extract the most dominant flow structures in a measurement plane above the wavy surface. This first POD mode is identified as streamwise-oriented, counter-rotating vortices whose spanwise scaling is also correlated with the maximum of heat flux.

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Abbreviations

a :

half-amplitude of the wave profile

B :

channel width

g :

acceleration due to gravity

Gr H :

Grashof number

H :

full channel height

\({\dot{q}}\) :

heat flux

Re H :

Reynolds number

t :

time

T :

temperature

u,v,w :

components of the instantaneous fluid velocity

U B :

bulk velocity (channel flow)

x,y,z :

Cartesian coordinates

X :

spatiotemporal set of data

y w :

profile of the wavy bottom wall

α:

amplitude-to-wavelength ratio, 2a/Λ

β:

volumetric thermal expansion coefficient

λ i :

eigenvalue of POD mode i

Λ:

wavelength of the sinusoidal profile at the bottom wall

ν:

kinematic viscosity

Π i :

eigenfunction of POD mode i

CCD:

charge coupled device

DPIV:

digital particle image velocimetry

FOV:

field of view

Nd:YAG:

neodymium:yttrium aluminium garnet (Y3Al5O12) crystal

PLIF:

planar laser-induced fluorescence

PVC:

poly vinyl chloride

B :

bulk quantity

H :

channel height (used as length scale)

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Acknowledgments

We gratefully acknowledge financial support from the Swiss National Science Foundation (SNF). Measurement technology is partially provided by ILA GmbH.

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Authors and Affiliations

  1. Institute of Process Engineering, ETH Zurich Sonneggstrasse 3, 8092, Zurich, Switzerland

    Simon Kuhn & Philipp Rudolf von Rohr

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  1. Simon Kuhn
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  2. Philipp Rudolf von Rohr
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Correspondence to Philipp Rudolf von Rohr.

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Kuhn, S., Rudolf von Rohr, P. Experimental study of heat flux in mixed convective flow over solid waves. Exp Fluids 44, 973–984 (2008). https://doi.org/10.1007/s00348-007-0456-2

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  • DOI: https://doi.org/10.1007/s00348-007-0456-2

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