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Experiments in Fluids

, Volume 16, Issue 2, pp 146–154 | Cite as

Production of temperature fluctuations in grid turbulence: Wiskind's experiment revisited

  • M. M. Gibson
  • T. Dakos
Originals

Abstract

Measurements have been made in nearly-isotropic grid turbulence on which is superimposed a linearly-varying transverse temperature distribution. The mean-square temperature fluctuations,\(\overline {\vartheta ^2 } \), increase indefinitely with streamwise distance, in accordance with theoretical predictions, and consistent with an excess of production over dissipation some 50% greater than values recorded in previous experiments. This high level of\(\overline {\vartheta ^2 } \) production has the effect of reducing the ratio,r, of the time scales of the fluctuating velocity and temperature fields. The results have been used to estimate the coefficient,C, in Monin's return-to-isotropy model for the slow part of the pressure terms in the temperature-flux equations. An empirical expression by Shih and Lumley is consistent with the results of earlier experiments in whichr ≈ 1.5, C ≈ 3.0, but not with the present data where r ≈ 0.5, C ≈1.6. Monin's model is improved when it incorporates both time scales.

Keywords

Temperature Distribution Previous Experiment Temperature Field Theoretical Prediction Early Experiment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

C

coefficient in Monin model, Eq. (5)

M

grid mesh length

m

exponent in power law for temperature variance,\(\overline {\vartheta ^2 } \)x m

n

turbulence-energy decay exponent,q2∝x -n

pϑ

production rate of\(\overline {\vartheta ^2 } /2\)

p

pressure

q2

\(\overline {u^2 } + \overline {\upsilon ^2 } + \overline {w^2 } \)

Rλ

microscale Reynolds number

r

time-scale ratiot/tϑ

T

mean temperature

U

mean velocity

\(\overline {u^2 } + \overline {\upsilon ^2 } + \overline {w^2 } \)

mean-square velocity fluctuations (turbulent energy components)

\(\overline {\upsilon \vartheta } \)

turbulent temperature flux

x, y, z

spatial coordinates

β

temperature gradient dT/dy

γ

thermal diffusivity

ɛ

dissipation rate ofq2/2

βϑ

dissipation rate of\(\overline {\vartheta ^2 } /2\)

λ

Taylor microscale (λ2=5νq2/ε)

λϑ

temperature microscale\((\lambda _{\vartheta ^2 } = 6\gamma \overline {\vartheta ^2 } /\varepsilon _\vartheta )\)

ρ

temperature-flux correlation coefficient,\(\overline {\upsilon \vartheta } \)/v′ϑ′

ξ

dimensionless distance from the grid,x/M

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • M. M. Gibson
    • 1
  • T. Dakos
    • 1
  1. 1.Mechanical Engineering DepartmentImperial College of Science, Technology and MedicineLondonUK

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