Subharmonic Transition to Turbulence in Channel Flow

1993 ◽  
pp. 43-47
Author(s):  
C. Härtel ◽  
L. Kleiser
Keyword(s):  
Channel Flow ◽  
Transition To Turbulence

Linear and nonlinear evolution of a localized disturbance in polymeric channel flow

2014 ◽  
Vol 760 ◽  
pp. 278-303 ◽  
Author(s):  
Akshat Agarwal ◽  
Luca Brandt ◽  
Tamer A. Zaki
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Polymer Concentration ◽  
Streamwise Velocity ◽  
Transition To Turbulence ◽  
Velocity Perturbation ◽  
Nonlinear Growth ◽  
Energy Growth ◽  
Newtonian Flows

AbstractThe evolution of an initially localized disturbance in polymeric channel flow is investigated, with the FENE-P model used to characterize the viscoelastic behaviour of the flow. In the linear growth regime, the flow response is stabilized by viscoelasticity, and the maximum attainable disturbance-energy amplification is reduced with increasing polymer concentration. The reduction in the energy growth rate is attributed to the polymer work, which plays a dual role. First, a spanwise polymer-work term develops, and is explained by the tilting action of the wall-normal vorticity on the mean streamwise conformation tensor. This resistive term weakens the spanwise velocity perturbation thus reducing the energy of the localized disturbance. The second action of the polymer is analogous, with a wall-normal polymer work term that weakens the vertical velocity perturbation. Its indirect effect on energy growth is substantial since it reduces the production of Reynolds shear stress and in turn of the streamwise velocity perturbation, or streaks. During the early stages of nonlinear growth, the dominant effect of the polymer is to suppress the large-scale streaky structures which are strongly amplified in Newtonian flows. As a result, the process of transition to turbulence is prolonged and, after transition, a drag-reduced turbulent state is attained.

Simulations of natural transition in viscoelastic channel flow

2017 ◽  
Vol 820 ◽  
pp. 232-262 ◽  
Author(s):  
Sang Jin Lee ◽  
Tamer A. Zaki
Keyword(s):  
Growth Rate ◽  
Drag Reduction ◽  
Channel Flow ◽  
Secondary Instability ◽  
Transition To Turbulence ◽  
Newtonian Flow ◽  
Final State ◽  
Periodic State ◽  
Nonlinear Amplification ◽  
Tollmien Schlichting

Orderly, or natural, transition to turbulence in dilute polymeric channel flow is studied using direct numerical simulations of a FENE-P fluid. Three Weissenberg numbers are simulated and contrasted to a reference Newtonian configuration. The computations start from infinitesimally small Tollmien–Schlichting (TS) waves and track the development of the instability from the early linear stages through nonlinear amplification, secondary instability and full breakdown to turbulence. At the lowest elasticity, the primary TS wave is more unstable than the Newtonian counterpart, and its secondary instability involves the generation of $\unicode[STIX]{x1D6EC}$-structures which are narrower in the span. These subsequently lead to the formation of hairpin packets and ultimately breakdown to turbulence. Despite the destabilizing influence of weak elasticity, and the resulting early transition to turbulence, the final state is a drag-reduced turbulent flow. At the intermediate elasticity, the growth rate of the primary TS wave matches the Newtonian value. However, unlike the Newtonian instability mode which reaches a saturated equilibrium condition, the instability in the polymeric flow reaches a periodic state where its energy undergoes cyclical amplification and decay. The spanwise size of the secondary instability in this case is commensurate with the Newtonian $\unicode[STIX]{x1D6EC}$-structures, and the extent of drag reduction in the final turbulent state is enhanced relative to the lower elasticity condition. At the highest elasticity, the exponential growth rate of the TS wave is weaker than the Newtonian flow and, as a result, the early linear stage is prolonged. In addition, the magnitude of the saturated TS wave is appreciably lower than the other conditions. The secondary instability is also much wider in the span, with weaker ejection and without hairpin packets. Instead, streamwise-elongated streaks are formed and break down to turbulence via secondary instability. The final state is a high-drag-reduction flow, which approaches the Virk asymptote.

Mean dynamics and transition to turbulence in oscillatory channel flow

2019 ◽  
Vol 880 ◽  
pp. 864-889
Author(s):  
Alireza Ebadi ◽  
Christopher M. White ◽  
Ian Pond ◽  
Yves Dubief
Keyword(s):  
Reynolds Stress ◽  
Channel Flow ◽  
Layer Structure ◽  
Development Stage ◽  
Transition To Turbulence ◽  
Nonlinear Development ◽  
The Mean ◽  
Balance Of Forces ◽  
Turbulent Wall ◽  
Near Wall

The mean dynamics in oscillatory channel flow is examined to investigate the dynamical mechanisms underlying the transition to turbulence in oscillatory wall-bounded flow. The analyses employ direct numerical simulation data acquired at three Stokes Reynolds numbers: $Re_{s}=648$, 801 and 1009, where the lower $Re_{s}$ flow is transitional over the entire cycle and the two higher $Re_{s}$ flows exhibit flow characteristics similar to steady turbulent wall-bounded flow during part of the cycle. The flow evolution over a half-period of oscillation for all three $Re_{s}$ is as follows: near-wall streamwise velocity streaks develop during the early accelerating portion of the cycle; then at some later point in the cycle that depends on $Re_{s}$, the near-wall streaks breakdown (demarking the onset of the nonlinear development stage), and the near-wall Reynolds stress grows explosively; the Reynolds stress remains elevated for part of the cycle before diminishing (yet remaining finite) during the late decelerating portion of the cycle. This process is then repeated indefinitely. The present findings demonstrate that transition to turbulence occurs when the nonlinear development stage begins during the accelerating portion of the cycle. This crucially leads to the diminishing importance of the centreline momentum source, the emergence of a locally accelerating/decelerating internal layer centred about the edge of the Stokes layer and the wall-normal rearrangement of the mean forces prior to the start of the decelerating portion of the cycle. The rearrangement of mean forces culminates in a four layer structure in the mean balance of forces. This is significant on a number of accounts since empirical and theoretical evidence suggests that the formation of a four layer structure is an important characteristic of a self-similar hierarchal structure that underlies logarithmic dependence of the mean velocity profile in steady turbulent wall-bounded flows (Klewicki et al., J. Fluid Mech., vol. 638, 2009, pp. 73–93). When the nonlinear development stage begins during the decelerating portion of the cycle (i.e. at $Re_{s}=648$), a four layer structure is not observed in the mean balance of forces and the flow remains weakly transitional over the entire cycle.

Delaying transition to turbulence in channel flow: revisiting the stability of shear-thinning fluids

2007 ◽  
Vol 592 ◽  
pp. 177-194 ◽  
Author(s):  
C. NOUAR ◽  
A. BOTTARO ◽  
J. P. BRANCHER
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Channel Flow ◽  
Shear Thinning ◽  
Transition To Turbulence ◽  
Shear Thinning Fluids ◽  
Viable Approach ◽  
The Stability ◽  
Definition Of ◽  
Do So

A viscosity stratification is considered as a possible mean to postpone the onset of transition to turbulence in channel flow. As a prototype problem, we focus on the linear stability of shear-thinning fluids modelled by the Carreau rheological law. To assess whether there is stabilization and by how much, it is important both to account for a viscosity disturbance in the perturbation equations, and to employ an appropriate viscosity scale in the definition of the Reynolds number. Failure to do so can yield qualitatively and quantitatively incorrect conclusions. Results are obtained for both exponentially and algebraically growing disturbances, demonstrating that a viscous stratification is a viable approach to maintain laminarity.

scholarly journals A universal transition to turbulence in channel flow

2016 ◽  
Vol 12 (3) ◽  
pp. 249-253 ◽  
Author(s):  
Masaki Sano ◽  
Keiichi Tamai
Keyword(s):  
Channel Flow ◽  
Transition To Turbulence

scholarly journals Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 53
Author(s):  
Stefania Cherubini ◽  
Francesco Picella ◽  
Jean-Christophe Robinet
Keyword(s):  
Channel Flow ◽  
Degrees Of Freedom ◽  
Slip Length ◽  
Superhydrophobic Surfaces ◽  
Transition To Turbulence ◽  
Growth Mechanisms ◽  
Boundary Slip ◽  
Optimal Perturbation ◽  
Energy Growth ◽  
Optimal Energy

Variational optimization has been recently applied to nonlinear systems with many degrees of freedom such as shear flows undergoing transition to turbulence. This technique has unveiled powerful energy growth mechanisms able to produce typical coherent structures currently observed in transition and turbulence. However, it is still not clear the extent to which these nonlinear optimal energy growth mechanisms are robust with respect to external disturbances or wall imperfections. Within this framework, this work aims at investigating how nano-roughnesses such as those of superhydrophobic surfaces affect optimal energy growth mechanisms relying on nonlinearity. Nonlinear optimizations have been carried out in a channel flow with no-slip and slippery boundaries, mimicking the presence of superhydrophobic surfaces. For increasing slip length, the energy threshold for obtaining hairpin-like nonlinear optimal perturbations slightly rises, scaling approximately with Re−2.36 no matter the slip length. The corresponding energy gain increases with Re with a slope that reduces with the slip length, being almost halved for the largest slip and Reynolds number considered. This suggests a strong effect of boundary slip on the energy growth of these perturbations. While energy is considerably decreased, the shape of the optimal perturbation barely changes, indicating the robustness of optimal perturbations with respect to wall slip.

scholarly journals Transition to Turbulence in Viscoelastic Channel Flow

2015 ◽  
Vol 14 ◽  
pp. 519-526
Author(s):  
Akshat Agarwal ◽  
Luca Brandt ◽  
Tamer A. Zaki
Keyword(s):  
Channel Flow ◽  
Transition To Turbulence
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