Transitional and Turbulent Dynamics in Viscoelastic Wall-bounded Flows

Authors

• Alexia Martinez Ibarra, University of Nebraska-LincolnFollow

First Advisor

Jae Park

Degree Name

Doctor of Philosophy (Ph.D.)

Committee Members

Adam Larios, Nitesh Nama, Piyush Grover

Department

Mechanical Engineering

Date of this Version

4-22-2026

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College at the University of Nebraska in partial fulfillment of requirements for the degree Doctor of Philosophy

Major: Mechanical Engineering

Under the supervision of Professor Jae Park

Lincoln, Nebraska, May 2026

Comments

Copyright 2026, Alexia Martínez Ibarra. Used by permission

Abstract

The addition of small amounts of long-chain polymers to a turbulent flow has been reported to modify the flow phenomena when compared to Newtonian flows, resulting in a significant skin-friction reduction. Although polymer-induced drag reduction has been extensively studied through both experimental and numerical studies, a unified and predictive understanding of the phenomenon is still lacking. This dissertation focuses on better understanding of this phenomenon, particularly on the transitional regime, which remains largely unexplored but is of utmost importance for both practical and fundamental purposes.

Firstly, direct numerical simulations are performed to study the effect of polymers on the laminar-turbulent transition by introducing controlled disturbances to the laminar velocity field. The viscoelastic flow requires a lower critical perturbation amplitude to trigger transition and exhibits an early temporal transition, when compared to the Newtonian flow, suggesting the destabilizing effect polymers on the flow. The early temporal transition of the viscoelastic flow is attributed to an early growth of the wall-normal and spanwise velocity fluctuations due to the polymers. The simulation was extended to study the effect of different disturbance characteristics on the transitional behavior of viscoelastic flows utilizing a probabilistic approach. A higher probability of transition was observed for the viscoelastic flows, regardless of perturbation and flow characteristics. However, significant differences on the transition dynamics were observed for two distinct disturbance structures. A perturbation structure with small-scale and localized vortical structures requires the smallest critical amplitude to trigger transition for both flows, while a perturbation with much larger-scale and more elongated vortices along the streamwise direction requires the largest critical amplitude to trigger transition. We then attempt to illustrate how the addition of polymers modifies transition dynamics with these two distinct perturbations in state space.

Secondly, we investigated the effects of fluid elasticity on the onset of drag reduction using an approach that has not yet been used in computational studies. Different drag reduction regimes are characterized by using flow and polymer dynamics. The onset Reynolds number was shown to decrease rapidly with increasing fluid elasticity, followed by an asymptotic behavior towards the transitional Reynolds number of channel flows. We also attempted to elucidate the underlying mechanisms of the onset of drag reduction based on two of the most influential interpretations: viscous and elastic theories. By characterizing the stretching behavior of the polymers, we observed that polymers tend to be stretched locally up to the onset of drag reduction. Once drag reduction occurs, more local regions of stronger turbulence are suppressed. As the elasticity number increases, polymers are highly stretched, not only locally but also globally, resulting in drag reduction at a lower Reynolds number.

Thirdly, we investigated the effect of mechanical polymer degradation as it is one of the primary causes of efficiency loss in polymer-induced drag reduction. We studied the effect of various polymer and flow characteristics on the loss of drag reduction efficiency. We showed that fluid elasticity is the main modulator of efficiency loss as polymers undergo several rounds of scission. Given the necessity of polymer injection to regain drag reduction effects, we also studied the effect of sudden polymer injection in the flow. We showed that polymer concentration and injection site characteristics play an important role in the instability characteristics observed after injection.

Lastly, given the recent use of dynamical systems theory on transitional and turbulent flows, we implement a method for the calculation of the so-called exact coherent solutions to viscoelastic channel flows in the form of traveling wave. While convergence to a solutions was not achieved, we identified key challenges for the computation of ECSs. Future efforts should be focused on improved initialization strategies and parameter-space exploration of relevant to viscoelastic transition and turbulent flows.

Recommended Citation

Martinez Ibarra, Alexia, "Transitional and Turbulent Dynamics in Viscoelastic Wall-bounded Flows" (2026). Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–. 453.
https://digitalcommons.unl.edu/dissunl/453