Inner-layer intensities for the flat-plate turbulent boundary layer combining a predictive wall-model with large-eddy simulations

Inoue, Michio; Mathis, Romain; Marušić, Ivan; Pullin, D. I.

doi:10.1063/1.4731299

Cited by 38 publications

(23 citation statements)

References 40 publications

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“…For example, figure 12(b) illustrates how the more energetic large scales at Re τ = 10 5 and 10 6 further increase the inner peak relative to Re τ = 10 4 by amplifying the universal function W 2 . Figure 13 is adapted from figure 8 in Marusic et al (2010a) where the DNS and ex- (Inoue et al 2012). The diamonds are the predicted inner peak intensities obtained from the present model for turbulent channels.…”

Section: Predictions At High Reynolds Numbersmentioning

confidence: 99%

“…The second possibility, motivated by the fact that the large scales increase the energy of the small scales, is to extrapolate following line 3 which is parallel to line 2 that captures the variation of the outer peak with Re τ . The data (open triangles) from large-eddy simulations of boundary layers (Inoue et al 2012) combined with the wall-model of Marusic et al (2010b) are shown for comparison. The current understanding, at least for relatively small intervals of Reynolds numbers, suggests logarithmic growth of the inner peak.…”

Section: Predictions At High Reynolds Numbersmentioning

confidence: 99%

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Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

et al. 2013

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We study the Reynolds number scaling and the geometric self-similarity of a gainbased, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (2010), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier-Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behavior with Reynolds number on the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it was shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wallnormal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (Re τ ≈ 10 3 − 10 10 ). Results from this low-rank model of the Navier-Stokes equations compare favorably with experimental results in the literature.

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Section: Predictions At High Reynolds Numbersmentioning

confidence: 99%

Section: Predictions At High Reynolds Numbersmentioning

confidence: 99%

Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

et al. 2013

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show abstract

“…Based on this understanding of the large-and small-scale behaviour, a simple and elegant empirical model was constructed to mathematically describe the relationship between them [11]. The utility of such a model lies in its ability to predict small-scale fluctuations when only the large-scale signal is available, as is typically the case in high Reynolds numbers experimental scenarios or large-eddy simulations [12].…”

Section: Introductionmentioning

confidence: 99%

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence

Subrahmanyam

McKeon

2017

Phil. Trans. R. Soc. A.

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“…To provide the velocity boundary condition, Chung & Pullin (2009) developed a log-like relationship obtained from the stretched-vortex subgrid model under an assumption of linear scaling of the wall-parallel vortex scale with distance from the wall. The virtual-wall model has been applied and validated for LES of both smooth-and rough-wall channel flow (Saito, Pullin & Inoue 2012;Saito & Pullin 2014) and to fully-developed turbulent boundary-layer flow for both zero pressure gradient (Inoue & Pullin 2011;Inoue et al 2012) and attached-flow APG cases (Inoue et al 2013). As an alternative to the sub-virtual wall modelling leading to a log-variation for the slip velocity, Cheng & Samtaney (2014) used a power-law relation for the virtual-wall slip velocity.…”

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confidence: 99%

Large-eddy simulation of separation and reattachment of a flat plate turbulent boundary layer

2015

Self Cite

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We present large-eddy simulations (LES) of separation and reattachment of a flat-plate turbulent boundary-layer flow. Instead of resolving the near wall region, we develop a two-dimensional virtual wall model which can calculate the timeand space-dependent skin-friction vector field at the wall, at the resolved scale. By combining the virtual-wall model with the stretched-vortex subgrid-scale (SGS) model, we construct a self-consistent framework for the LES of separating and reattaching turbulent wall-bounded flows at large Reynolds numbers. The present LES methodology is applied to two different experimental flows designed to produce separation/reattachment of a flat-plate turbulent boundary layer at medium Reynolds number Re θ based on the momentum boundary-layer thickness θ. Comparison with data from the first case at Re θ = 2000 demonstrates the present capability for accurate calculation of the variation, with the streamwise co-ordinate up to separation, of the skin friction coefficient, Re θ , the boundary-layer shape factor and a non-dimensional pressure-gradient parameter. Additionally the main large-scale features of the separation bubble, including the mean streamwise velocity profiles, show good agreement with experiment. At the larger Re θ = 11 000 of the second case, the LES provides good postdiction of the measured skin-friction variation along the whole streamwise extent of the experiment, consisting of a very strong adverse pressure gradient leading to separation within the separation bubble itself, and in the recovering or reattachment region of strongly-favourable pressure gradient. Overall, the present two-dimensional wall model used in LES appears to be capable of capturing the quantitative features of a separation-reattachment turbulent boundary-layer flow at low to moderately large Reynolds numbers.

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Inner-layer intensities for the flat-plate turbulent boundary layer combining a predictive wall-model with large-eddy simulations

Cited by 38 publications

References 40 publications

Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence

Large-eddy simulation of separation and reattachment of a flat plate turbulent boundary layer

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