2008
DOI: 10.1007/s10494-008-9134-6
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One Equation Model for Turbulent Channel Flow with Second Order Viscoelastic Corrections

Abstract: A modified second order viscoelastic constitutive equation is used to derive a kl type turbulence closure to qualitatively assess the effects of elastic stresses on fully-developed channel flow. Specifically, the second order correction to the Newtonian constitutive equation gives rise to a new term in the momentum equation involving the time-averaged elastic shear stress and in the turbulent kinetic energy transport equation quantifying the interaction between the fluctuating elastic stress and rate of strain… Show more

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Cited by 14 publications
(6 citation statements)
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“…of Eq. (18), which needs modelling, multiplied by such coefficient of proportionality. The essential feature of the model is to capture this Weissenberg number dependence away from the wall, and because NLT ij is not that important close to the wall any discrepancy in the near wall region will be of little consequence to the turbulence model predictions.…”
Section: (A) (Ldr) and (B) (Idr)mentioning
confidence: 99%
See 1 more Smart Citation
“…of Eq. (18), which needs modelling, multiplied by such coefficient of proportionality. The essential feature of the model is to capture this Weissenberg number dependence away from the wall, and because NLT ij is not that important close to the wall any discrepancy in the near wall region will be of little consequence to the turbulence model predictions.…”
Section: (A) (Ldr) and (B) (Idr)mentioning
confidence: 99%
“…However, this constitutive equation is not truly elastic in nature, therefore it is unable to capture important features of elastic fluids, namely the memory effect and its spatio-temporal variation. To illustrate this feature, using a simplified version of the second order fluid equation, Pinho et al [18] derived a simple one-equation k-l turbulence model that was capable of predicting drag reduction by incorporating the time-average elastic shear stress in the momentum equation. This feature especially required a closure for the elastic stress work (interaction between fluctuating elastic stress and rate of strain tensors) appearing in the transport equation for turbulence kinetic energy, provided the elastic stress work was mostly dissipative.…”
Section: Introductionmentioning
confidence: 99%
“…9 shows a comparison between this model and the DNS results for the quantity appearing in the viscoelastic turbulent transport of k. The main features of CU iiy are well captured by Eq. (29). To comply with the damping effect of the wall, and to match the predictions of the model with the DNS data, it was necessary to introduce a damping function f CU = 1 − exp (−y + /26.5).…”
Section: Closure For Cu Ijkmentioning
confidence: 99%
“…Pinho [28] pointed out that all these models are based on the eddy viscosity concept and require ad-hoc, flow-dependent, modifications since they were developed without reference to fluid rheology or constitutive modeling. More recently Pinho et al [29] developed a one-equation turbulence model which accounts for second-order viscoelastic corrections by employing closure approximations for the correlations between the fluctuations in the rate of strain and the viscoelastic stress. While such models can predict DR by suitable choice of correlation coefficients that mimic DNS data, they are strictly only applicable to small DR values (low Deborah numbers).…”
Section: Introductionmentioning
confidence: 99%
“…While the DNS work cited above is very useful, for instance for lower-resolution model developments (Pinho et al [13], and Thais et al [14]), it appears that it has been limited in the Reynolds number and/or in the channel dimension that could be achieved with the computer power and algorithms available. Earlier DNS computations (Sureshkumar et al [2], and Dimitropoulos et al [3]) started at Re s0 = 125 and Re s0 = 180, where Re s0 = qu s0 h/g 0 is the friction Reynolds number based on the zero-shear friction velocity at the wall u s0 , the channel mid-gap h, the polymer solution density q and zero-shear viscosity g 0 .…”
Section: Introductionmentioning
confidence: 99%