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.
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Abbreviations
- 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,q 2 ∝x -n
- p ϑ :
-
production rate of\(\overline {\vartheta ^2 } /2\)
- p :
-
pressure
- q 2 :
-
\(\overline {u^2 } + \overline {\upsilon ^2 } + \overline {w^2 } \)
- R λ :
-
microscale Reynolds number
- r :
-
time-scale ratiot/t ϑ
- 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 ofq 2/2
- β ϑ :
-
dissipation rate of\(\overline {\vartheta ^2 } /2\)
- λ :
-
Taylor microscale (λ2=5νq2/ε)
- λ ϑ :
-
temperature microscale\((\lambda _{\vartheta ^2 } = 6\gamma \overline {\vartheta ^2 } /\varepsilon _\vartheta )\)
- ρvϑ :
-
temperature-flux correlation coefficient,\(\overline {\upsilon \vartheta } \)/v′ϑ′
- ξ :
-
dimensionless distance from the grid,x/M
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Gibson, M.M., Dakos, T. Production of temperature fluctuations in grid turbulence: Wiskind's experiment revisited. Experiments in Fluids 16, 146–154 (1993). https://doi.org/10.1007/BF00944916
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DOI: https://doi.org/10.1007/BF00944916