Session: Research Posters

Paper Number: 173123

Onset of Laminar-Turbulent Transition in Viscoelastic Channel Flow 

The addition of small amounts of flexible long-chain polymers into a turbulent flow has been known to significantly reduce skin friction in wall-bounded flows since the 1940s. Such phenomenon, known as turbulent drag reduction, has been the subject of extensive numerical and experimental studies mainly due to the many applications that benefit directly from its drag-reducing effects, including liquid transport in pipelines and agriculture. The nature of the transition to turbulence in wall-bounded shear flows for polymer solutions has been relatively less studied than its drag-reducing effects. Therefore, the role that polymers play in the onset of transition remains unclear for polymer solutions. We perform direct numerical simulations of a laminar base flow disturbed by a small finite-amplitude perturbation for both Newtonian and viscoelastic flows. The perturbation amplitude A ranges as 0.014 ≤ A ≤ 0.14 relative to the total energy of the laminar base flow. The temporal behavior of the transition dynamics is characterized by the evolution of the disturbance energy, wall shear stress, and bulk polymer stretching using a repeatable perturbation structure. Here, the transition time T_t is introduced to define the time at which the wall shear stress reaches a chosen threshold of the base laminar state, signaling the onset of transition. For Reynolds numbers ranging as 2000 ≤ Re ≤ 5000, the overall trend shows a decrease in T_t with increasing perturbation amplitude. Interestingly, T_t for viscoelastic flows is observed to be smaller than that of its Newtonian counterpart. Next, we identify the minimum perturbation amplitude required to trigger transition for both Newtonian and viscoelastic flows, also known as critical perturbation amplitude. The critical perturbation amplitude decreases with increasing Reynolds number. Interestingly, the viscoelastic flow also follows the same behavior. However, the viscoelastic flow is observed to require a smaller amplitude for transition, shifting the curve downward for the entire range of Re. Early amplification of spanwise and wall-normal velocity fluctuations in viscoelastic flows, with respect to its Newtonian counterpart, eludes the early transition in viscoelastic flows mentioned above. Such destabilization by polymers is further observed by the early formation of quasi-streamwise vortices around low-speed streaks in the viscoelastic flow, while its Newtonian counterpart remains undisturbed. Secondly, we expand these results by looking at the effect that different perturbation structures have on the statistics of the laminar-turbulent transition behavior. Very evidently, it is possible to see the effect that different perturbation structures have on both Newtonian and viscoelastic flows. With a constant Re and A, there are perturbation types that trigger transition for viscoelastic flows, but not for their Newtonian counterpart. Similarly, it is possible to observe perturbation structures that manage to trigger the transition, but at different transition times, for both Newtonian and viscoelastic flows. By using a statistical approach and calculating the probability of survival of the laminar state, the effect of the perturbation magnitude and Reynolds number can be observed. With a constant Re, the survival of the laminar state decreases rapidly for both Newtonian and viscoelastic flows. However, the survival of the laminar state is always lower for the viscoelastic flows at all perturbation magnitudes. Now, with a fixed perturbation magnitude, the survival of the laminar state decreases with Reynolds number. Very evidently, however, the survival of the viscoelastic flow is lower than its Newtonian counterpart. However, the decrease in the survival of the laminar state is slower than that of the perturbation magnitude. Next, we look at the effect that different perturbation structures have on polymer dynamics, which result in earlier or delayed transition within the viscoelastic flow.

Presenting Author: Alexia Martinez Ibarra University of Nebraska - Lincoln

Presenting Author Biography: Alexia Martinez Ibarra is a PhD candidate in Mechanical and Materials Engineering at the University of Nebraska–Lincoln, working under the supervision of Dr. Jae Sung Park. Her research focuses on computational fluid dynamics and the study of drag-reducing viscoelastic flows. She holds both a Bachelor and Master of Science in Mechanical Engineering from the University of Texas–Rio Grande Valley.

Authors:

Alexia Martinez Ibarra University of Nebraska - Lincoln
Jae Sung Park University of Nebraska - Lincoln