Nonlinear evolutions of streaky structures in viscoelastic pipe flows

Sun, Gordon H.; Wan, Dongdong; Zhang, Mengqi

doi:10.1016/j.jnnfm.2021.104622

Cited by 6 publications

(2 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nowadays, it is much more common to see the constitutive equations written in terms of the conformation formulation, [27][28][29][30] which ultimately are the basic equations when the principles of mechanics are applied in the context of kinetic theory, followed by phase averaging in a phase space and introducing approximations to arrive at a closed form manageable set of differential equations. We prefer to work with a conformation tensor that reduces to the identity tensor at equilibrium (a situation of no flow or of zero deformation rates), namely, A ¼ hQQi= 1 3 hQ Á Qi eq , and in this case, the previous equation for the FENE-P dumbbell model becomes a pair of equations for the evolution of A and for a definition of stress s from the conformation,…”

Section: A Historical Perspective Of the Fene-p And Ptt Modelsmentioning

confidence: 99%

On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows

et al. 2022

View full text Add to dashboard Cite

For many commonly used viscoelastic constitutive equations, it is well known that the limiting behavior is that of the Oldroyd-B model. Here, we compare the response of the simplified linear form of the Phan-Thien–Tanner model (“sPTT”) [Phan-Thien and Tanner, “A new constitutive equation derived from network theory,” J. Non-Newtonian Fluid Mech. 2, 353–365 (1977)] and the finitely extensible nonlinear elastic (“FENE”) dumbbell model that follows the Peterlin approximation (“FENE-P”) [Bird et al., “Polymer solution rheology based on a finitely extensible bead—Spring chain model,” J. Non-Newtonian Fluid Mech. 7, 213–235 (1980)]. We show that for steady homogeneous flows such as steady simple shear flow or pure extension, the response of both models is identical under precise conditions ([Formula: see text]). The similarity of the “spring” functions between the two models is shown to help understand this equivalence despite a different molecular origin of the two models. We then use a numerical approach to investigate the response of the two models when the flow is “complex” in a number of different definitions: first, when the applied deformation field is homogeneous in space but transient in time (so-called “start-up” shear and planar extensional flow), then, as an intermediate step, the start-up of the planar channel flow; and finally, “complex” flows (through a range of geometries), which, although being Eulerian steady, are unsteady in a Lagrangian sense. Although there can be significant differences in transient conditions, especially if the extensibility parameter is small [Formula: see text], under the limit that the flows remain Eulerian steady, we once again observe very close agreement between the FENE-P dumbbell and sPTT models in complex geometries.

show abstract

Section: A Historical Perspective Of the Fene-p And Ptt Modelsmentioning

confidence: 99%

On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows

et al. 2022

View full text Add to dashboard Cite

show abstract

“…They found that the transition scenarios are affected by the level of the elasticity, where a destabilizing effect is observed at the lowest elasticity and a stabilization effect manifests as the elasticity is further increased. Biancofiore, Brandt & Zaki (2017) and Sun, Wan & Zhang (2021) investigated the nonlinear evolution of disturbed streaky structures in viscoelastic Couette and pipe flows, respectively, where viscoelasticity is found to delay the transition to turbulence in time for high .…”

Section: Introductionmentioning

confidence: 99%

Transition to turbulence in viscoelastic channel flow of dilute polymer solutions

Martinez Ibarra,

Park

2023

J. Fluid Mech.

View full text Add to dashboard Cite

The transition to turbulence in a plane Poiseuille flow of dilute polymer solutions is studied by direct numerical simulations of a finitely extensible nonlinear elastic fluid with the Peterlin closure. The range of Reynolds number ( $Re$ ) $2000 \le Re \le 5000$ is studied but with the same level of elasticity in viscoelastic flows. The evolution of a finite-amplitude perturbation and its effects on the transition dynamics are investigated. A viscoelastic flow begins transition at an earlier time than its Newtonian counterparts, but the transition time appears to be insensitive to polymer concentration in the dilute and semi-dilute regimes studied. Increasing polymer concentration, however, decreases the maximum attainable energy growth during the transition process. The critical or minimum perturbation amplitude required to trigger transition is computed. Interestingly, both Newtonian and viscoelastic flows follow almost the same power-law scaling of $Re^\gamma$ with the critical exponent $\gamma \approx -1.25$ , which is in close agreement with previous studies. However, a shift downward is observed for viscoelastic flow, suggesting that smaller perturbation amplitudes are required for the transition. A mechanism of the early transition is investigated by the evolution of wall-normal and spanwise velocity fluctuations and flow structure. The early growth of these fluctuations and the formation of quasi-streamwise vortices around low-speed streaks are promoted by polymers, hence causing an early transition. These vortical structures are found to support the critical exponent $\gamma \approx -1.25$ . Once the transition process is completed, polymers play a role in dampening the wall-normal and spanwise velocity fluctuations and vortices to attain a drag-reduced state in viscoelastic turbulent flows.

show abstract

Pipeline flow of double fractional Maxwell fluids based on the rheological experiment of xanthan gum

Jiang

Yang

Chen

et al. 2023

Chinese Journal of Physics

View full text Add to dashboard Cite

Nonlinear evolutions of streaky structures in viscoelastic pipe flows

Cited by 6 publications

References 59 publications

On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows

On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows

Transition to turbulence in viscoelastic channel flow of dilute polymer solutions

Pipeline flow of double fractional Maxwell fluids based on the rheological experiment of xanthan gum

Contact Info

Product

Resources

About