Numerical predictions and measurements of Reynolds normal stresses in turbulent pipe flow of polymers

Resende, Pedro; Escudier, M. P.; Presti, Federico Lo; Pinho, F.T.; Cruz, D. O. A.

doi:10.1016/j.ijheatfluidflow.2005.08.002

Cited by 30 publications

(49 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Turbulence models incorporating fluid rheology were proposed by Malin [30,31] and Cruz et al [32] for power law and viscoplastic fluids devoid of elastic DR. Pinho and co-workers [28,[33][34][35][36] developed some first-and second-order turbulence models, of the low Reynolds number type, in combination with a "toy" constitutive equation that integrated strain-hardening of the Trouton ratio. This enabled the prediction of both the small DR due to shear-thinning of the viscometric viscosity as well as the large DR associated with flows having large extensional viscosities.…”

Section: Introductionmentioning

confidence: 99%

A low Reynolds number turbulence closure for viscoelastic fluids

Pinho

Li²,

Younis

et al. 2008

Journal of Non-Newtonian Fluid Mechanics

Self Cite

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

A low Reynolds number turbulence closure for viscoelastic fluids

Pinho

Li²,

Younis

et al. 2008

Journal of Non-Newtonian Fluid Mechanics

Self Cite

View full text Add to dashboard Cite

“…At large Deborah numbers, there are strong variations in the elastic shear stress very close to the wall (see (15)) creating some convergence problems and oscillations. This is also clear in the oscillation seen in the profile at De t Â 10 3 ¼ 82:2 in Fig.…”

Section: Predictions For A=+1 and At Small Values Of Deborah Number Fmentioning

confidence: 99%

“…This approach was used by Pinho and co-workers [14][15][16], who formulated several low Reynolds number k-ɛ type models and a Reynolds stress model on the basis of a modified Generalized Newtonian constitutive model that accounted for shear-thinning in shear viscosity and shear-thickening of the Trouton ratio. These turbulence models have shown to perform satisfactorily in fullydeveloped pipe and channel flows of polymer solutions and behave qualitatively well in homogeneous isotropic turbulence due to the modification of the molecular viscosity.…”

Section: Introductionmentioning

confidence: 99%

One Equation Model for Turbulent Channel Flow with Second Order Viscoelastic Corrections

Pinho

Sadanandan

Sureshkumar³

2008

Flow Turbulence Combust

View full text Add to dashboard Cite

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 tensors, denoted by P w , for which a closure is developed and tested. This closure is based on arguments of isotropic turbulence and equilibrium in boundary layer flows and a priori P w could be either positive or negative. When P w is positive, it acts to reduce the production of turbulent kinetic energy and the turbulence model predictions qualitatively agree with direct numerical simulation (DNS) results obtained for more realistic viscoelastic fluid models with memory which exhibit drag reduction. In contrast, P w <0 leads to a drag increase and numerical breakdown of the model occurs at very low values of the Deborah number, which signifies the ratio of elastic to viscous stresses. Limitations of the turbulence model primarily stem from the inadequacy of the k-l formulation rather than from the closure for P w . An alternative closure for P w , mimicking the viscoelastic stress work predicted by DNS using the Finitely Extensible Nonlinear Elastic-Peterlin fluid model, which is mostly characterized by P w >0 but has also a small region of negative P w in the buffer layer, was also successfully tested. This second model for P w leads to predictions of drag reduction, in spite of the enhancement of turbulence production very close to the wall, but the equilibrium conditions in the inertial sub-layer were not strictly maintained. Nomenclature A parameter of polymer work model, see (33) b ij tensor defined in (28) C D parameter of turbulence model, see (23) C k parameter of k-l turbulence model C ij time-average component of elastic stress tensor defined in (12) D k Turbulent and molecular diffusion of turbulent kinetic energy, defined in (20b) De Deborah number based on bulk velocity of the flow De l Deborah number of turbulence, De l ¼ u1 =l De t friction Deborah number, De C ¼ u C 1 =H H channel half-height k turbulent kinetic energy l length scale in turbulence in order of magnitude analysis and Prandtl's mixing length in turbulence model p pressure P k Production of turbulent kinetic energy, defined in (20a) P w Polymeric work, defined in (20d) t time T ij designates a time-average tensor u scale of velocity fluctuations in order of magnitude analysis and streamwise velocity component in turbulence model equations u i fluctuating velocity vector u iinstantaneous velocity vector u* streamwise velocity normalized by the friction velocity, u þ ¼ u=u C U i time-average velocity vector u t friction velocity in fully-developed channel flow uv Reynolds shear stress Re Reynolds number based on bulk velocity o...

show abstract

“…As a matter of fact, in a recent work 24) it has been shown that by relying on another k-e turbulence model, i.e., the Launder-Sharma model, better agreement can be obtained between simulations and experimental data for certain polymer solutions. Another scenario which can explain the rather poor performance of Nagano-Hishida k-e method for certain polymer solutions appears to be the numerical values assigned to the empirical parameters inherent in any turbulence modeling.…”

Section: 23)mentioning

confidence: 99%

On the Use of Inverse Methods to Parameter Estimation in Turbulent Pipe Flows of Drag Reducing Polymers

Mehrabadi

Sadeghy

Hakkaki-Fard

et al. 2008

J. Soc. Rheol., Jpn

View full text Add to dashboard Cite

This article investigates the applicability of inverse methods in estimating the best values to be assigned to certain parameters which appear in turbulent flow studies of dilute polymer solutions in circular pipes. These parameters naturally arise when the Nagano-Hishida low-Re, k-e model is combined with a special form of the Generalized Newtonian Fluid model modified in such a way that it could account for the elasticity of dilute polymer solutions. This multi-objective problem is treated by a positively weighted convex sum of the objectives. Then the procedure is followed by a well-known Gauss-Newton nonlinear optimization method for optimizing model parameters in order to better predict the drag reduction phenomenon using polymeric additives. Parameter optimization relies on the availability of experimental data for the velocity profiles, friction factor, and turbulence kinetic energy for at least one concentration of a given polymer. It is shown that using these optimized parameters, it is possible to predict with more accuracy the amount of drag reduction achievable using a given polymeric additive. It is also shown that these parameters may neither work for other concentrations of the same polymer nor necessarily for any concentration of any other polymer, inferring that for non-Newtonian fluids these parameters are not at all universal.

show abstract

Numerical predictions and measurements of Reynolds normal stresses in turbulent pipe flow of polymers

Cited by 30 publications

References 31 publications

A low Reynolds number turbulence closure for viscoelastic fluids

A low Reynolds number turbulence closure for viscoelastic fluids

One Equation Model for Turbulent Channel Flow with Second Order Viscoelastic Corrections

On the Use of Inverse Methods to Parameter Estimation in Turbulent Pipe Flows of Drag Reducing Polymers

Contact Info

Product

Resources

About