Homogeneous Turbulence

Gence, J. N.

doi:10.1146/annurev.fl.15.010183.001221

Cited by 15 publications

(9 citation statements)

References 18 publications

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“…Figure 6 (d) indicates that the RTI process is slower in the expansion case than in the contraction case (ρ(t) takes a greater value if the RTI is faster and is negative during the slight increase of anisotropy in the expansion case). This result is consistent with the discussions in Gence (1983) and Choi & Lumley (2001).…”

Section: Turbulence Subjected To Axisymmetric Expansion or Contractionsupporting

confidence: 93%

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

2015

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International audienceA nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\hat{R}_{ij}(\mathbf k,t)$, the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\mathbf k$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy

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Section: Turbulence Subjected To Axisymmetric Expansion or Contractionsupporting

confidence: 93%

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

2015

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“…In order to derive these quasi-analytical solutions, we focus on the form h(t) = (f (t) À g(t))=t (equation 7), which is included in the governing equations (equation (5)). Initially, the temporal profile of the form h(t) is numerically examined using the total strain s(t) (equation (8)).…”

Section: Resultsmentioning

confidence: 99%

“…Here, the condition t = 250 is used for the comparison. Values of the coefficients are calculated by least-square fitting h(t)=S(t) to the numerical results, where h(t) is the primary part of the inhomogeneous term of equation of f (t) as shown in equations (5) and 7. The present derived forms of the coefficients are shown in equation 16for S(t) = S o and equation 17for S(t) = d t St, respectively.…”

Section: Three Constants and Dependency Of Reynolds Number And Initiamentioning

confidence: 99%

“…4 For decades, numerous studies have investigated and summarized the results of decaying homogeneous turbulence. [5][6][7] DNS has significantly contributed to investigating the characteristics of decaying homogeneous turbulence. [8][9][10] The turbulent Reynolds number, which can be set, had been critically limited to be low in previous DNS studies.…”

Section: Introductionmentioning

confidence: 99%

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Quasi-analytical solutions of a turbulence-modeling equation on the robustness of decaying homogeneous turbulence

Suzuki

Mochizuki

2020

Advances in Mechanical Engineering

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The present study introduces third-order quasi-analytical solutions of a turbulence-modeling equation, where the standard [Formula: see text] model equation is used because this model is commonly and widely used in engineering applications. These quasi-analytical solutions describe the robustness of decaying homogeneous turbulence. In the present study, decaying homogeneous turbulence influenced by a weak fluid acceleration of mean flow, which is equivalent to the small strain of the mean flow, is considered. Here, the small strain of the mean flow only slightly affects the anisotropy of the decaying homogeneous turbulence, as shown in previous experiments. Simplified governing equations are derived from the governing equations of the turbulence modeling by introducing the conditions of the small strain. Here, two nondimensional functions are introduced in order to describe the influence on the turbulent kinetic energy and its dissipation using decay laws of the turbulent kinetic energy and its dissipation. Three constants included in the quasi-analytical solutions could be obtained using observable parameters.

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“…Theoretical, experimental, and numerical studies of this kind of turbulent flow are considered to reveal the influences of mean velocity gradients on the turbulent stresses ͑Reynolds stresses͒ in homogeneous turbulence. 1 In an axisymmetric turbulent field, the correlations are invariant under arbitrary translations in planes normal to the symmetry axis and, furthermore, invariant under rotations and reflections along the symmetry axis in planes normal to the symmetry axis. Owing to these purely mathematical constraints, the Reynolds stress tensor has no off-diagonal components, the transverse and lateral components are equal to each other, and the transverse and lateral mean velocities are zero, where the bar over the symbols denotes the time-mean of any flow quantity.…”

Section: Introductionmentioning

confidence: 99%

On the high contraction ratio anomaly of axisymmetric contraction of grid-generated turbulence

Ertunç

Durst

2008

Physics of Fluids

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The present paper deals with the anomalous increase in second-order moments of longitudinal velocity fluctuations reported in experiments carried out to measure properties of axisymmetric strained turbulence when the strain is provided by axisymmetric contractions ͑nozzles͒. Experimental evidence is provided that the increase is due to inaccuracies in the measurements. It is shown that the imperfect spatial resolution of X-wire probes, the mass flow rate fluctuations in the flow facility, and the electronic noise contaminate the hot-wire measurements of not only the longitudinal but also the transverse velocity fluctuation components. These kinds of contaminations start to dominate the measurements, especially when the contraction ratio of the nozzle is high and/or the turbulence level is low and turbulence length scales are small. A series of measurement and correction methods is proposed employing two single normal wires and one inclined wire to detect and eliminate all three types of contaminations of longitudinal and transverse velocity fluctuation measurements. These methods are subsequently employed to carry out turbulence measurements of grid turbulence strained in a converging nozzle with a high contraction ratio. The resulting Reynolds stress developments along the nozzle do not involve an erroneous increase in longitudinal turbulent velocity fluctuations and are consistent with theoretical expectations such as the direct numerical simulations and the rapid distortion theory. The corrected results revealed that turbulence along the nozzle reaches the two-component axisymmetric state when looked at through the anisotropy of Reynolds stresses. Furthermore, the anisotropy of Reynolds stresses exhibits zero gradient at that state. For the first time in the literature, experimental confirmation of rapid distortion theory is supplied for the axisymmetric contraction of turbulence within nozzles having a contraction ratio higher than 9. Finally, a set of experimental data is provided for the validation of turbulence models.

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Homogeneous Turbulence

Cited by 15 publications

References 18 publications

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

Quasi-analytical solutions of a turbulence-modeling equation on the robustness of decaying homogeneous turbulence

On the high contraction ratio anomaly of axisymmetric contraction of grid-generated turbulence

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