Experimental scaling law for the subcritical transition to turbulence in plane Poiseuille flow (original) (raw)
Related papers
Subcritical transition to turbulence in wall-bounded flows: the case of plane Poiseuille flow
arXiv: Fluid Dynamics, 2019
In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane channel flow (plane Poiseuille flow) is more specifically considered via numerical simulations. Previous conflicting observations are reconciled by noting that the two-dimensional directed percolation scenario expected for the decay of turbulence may be interrupted by a symmetry-breaking bifurcation favoring localized turbulent bands. At the other end of the transitional range, a preliminary study suggests that the laminar-turbulent pattern leaves room to a featureless regime beyond a well defined threshold to be determined with precision.
Experiments in Fluids, 2007
The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise-wall-normal plane of a 536 lm capillary over the Reynolds-number range 1,800 £ Re £ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re @ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 £ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are nonlaminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these ''trains'' of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro-and micro-scales. Finally, single-point statistics computed from the nonlaminar subsets at each transitional Re, including rootmean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.
A Microscopic Particle Image Velocimetry Study of Transition to Turbulence in Microscale Capillaries
37th AIAA Fluid Dynamics Conference and Exhibit, 2007
The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise-wall-normal plane of a 536 lm capillary over the Reynolds-number range 1,800 £ Re £ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re @ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 £ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are nonlaminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these ''trains'' of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro-and micro-scales. Finally, single-point statistics computed from the nonlaminar subsets at each transitional Re, including rootmean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.
2017
We present a new experimental set-up that creates a shear flow with zero mean advection velocity achieved by counterbalancing the nonzero streamwise pressure gradient by moving boundaries, which generates plane Couette-Poiseuille flow. We carry out the first experimental results in the transitional regime for this flow. Using flow visualization we characterize the subcritical transition to turbulence in Couette-Poiseuille flow and show the existence of turbulent spots generated by a permanent perturbation. Due to the zero mean advection velocity of the base profile, these turbulent structures are nearly stationary. We distinguish two regions of the turbulent spot: the active, turbulent core, which is characterized by waviness of the streaks similar to traveling waves, and the surrounding region, which includes in addition the weak undisturbed streaks and oblique waves at the laminar-turbulent interface. We also study the dependence of the size of these two regions on Reynolds number...
Quarterly of Applied Mathematics, 2001
This paper presents an instability theory in which a mean flow and multiple wave interactions in the Poiseuille flow transition process are studied. It is shown that not only can this mean flow term come as the result of the Fourier decomposition of a general disturbance, it can also come as an exact solution to the unsteady Navier-Stokes equations. The presence of this term, though small, can produce totally different linear and nonlinear stability behavior for the flow at subcritical Reynolds numbers. In the linear stability case, with the presence of this mean flow perturbation term, the instabilities are obtained well below the critical value of 5772. When this mean flow term is introduced into the interactions with other harmonic perturbation waves, for the plane Poiseuille flow case with Reynolds numbers around 1200, the nonlinear interactions rapidly modify the total mean flow profile toward the mean flow profile observed in turbulence while the other two-and three-dimensional waves remain small. The initial energies needed to trigger the instabilities are much smaller than those reported by previous investigators. The intermittent character of the disturbance observed in transition experiments is also captured.
Journal of Fluid Mechanics, 2021
In this paper we experimentally study the transitional range of Reynolds numbers in plane Couette-Poiseuille flow, focusing our attention on the localized turbulent structures triggered by a strong impulsive jet and the large-scale flow generated around these structures. We present a detailed investigation of the large-scale flow and show how its amplitude depends on Reynolds number and amplitude perturbation. In addition, we characterize the initial dynamics of the localized turbulent spot, which includes the coupling between the small and large scales, as well as the dependence of the advection speed on the large-scale flow generated around the spot. Finally, we provide the first experimental measurements of the large-scale flow around an oblique turbulent band.
Anisotropic decay of turbulence in plane Couette-Poiseuille flow
arXiv (Cornell University), 2020
We report the results of an experimental investigation into the decay of turbulence in plane Couette-Poiseuille flow using 'quench' experiments where the flow laminarises after a sudden reduction in Reynolds number Re. Specifically, we study the velocity field in the streamwise-spanwise plane. We show that the spanwise velocity containing rolls, decays faster than the streamwise velocity, which displays elongated regions of higher or lower velocity called streaks. At final Reynolds numbers above 425, the decay of streaks displays two stages: first a slow decay when rolls are present and secondly a more rapid decay of streaks alone. The difference in behaviour results from the regeneration of streaks by rolls, called the lift-up effect. We define the turbulent fraction as the portion of the flow containing turbulence and this is estimated by thresholding the spanwise velocity component. It decreases linearly with time in the whole range of final Re. The corresponding decay slope increases linearly with final Re. The extrapolated value at which this decay slope vanishes is Re az ≈ 656±10, close to Re g ≈ 670 at which turbulence is self-sustained. The decay of the energy computed from the spanwise velocity component is found to be exponential. The corresponding decay rate increases linearly with Re, with an extrapolated vanishing value at Re Az ≈ 688 ± 10. This value is also close to the value at which the turbulence is self-sustained, showing that valuable information on the transition can be obtained over a wide range of Re.
Turbulent-laminar patterns in plane Poiseuille flow
Physics of Fluids, 2014
Turbulent-laminar banded patterns in plane Poiseuille flow are studied via direct numerical simulations in a tilted and translating computational domain using a parallel version of the pseudospectral code Channelflow. 3D visualizations via the streamwise vorticity of an instantaneous and a time-averaged pattern are presented, as well as 2D visualizations of the average velocity field and the turbulent kinetic energy. Simulations for 2300 ≥ Re m ≥ 700 show the gradual development from uniform turbulence to a pattern with wavelength 20 half-gaps at Re m ≈ 1900, to a pattern with wavelength 40 at Re m ≈ 1300 and finally to laminar flow at Re m ≈ 800. These transitions are tracked quantitatively via diagnostics using the amplitude and phase of the Fourier transform and its probability distribution. The propagation velocity of the pattern is approximately that of the mean flux and is a decreasing function of Reynolds number. Examination of the time-averaged flow shows that a turbulent band is associated with two counter-rotating cells stacked in the cross-channel direction and that the turbulence is highly concentrated near the walls. Near the wall, the Reynolds stress force accelerates the fluid through a turbulent band while viscosity decelerates it; advection by the laminar profile acts in both directions. In the center, the Reynolds stress force decelerates the fluid through a turbulent band while advection by the laminar profile accelerates it. These characteristics are compared with those of turbulent-laminar banded patterns in plane Couette flow.
Streamwise vortices and transition to turbulence
Journal of Fluid Mechanics, 1994
A series of experiments was conducted to determine the conditions under which streamwise vortices can cause transition to turbulence in shear flows. A specially designed obstacle was used to produce a single vortex in a water-table flow, and the design of this obstacle is discussed. Laser-Doppler velocimetry measurements of the streamwise and crossflow velocity fields were made in transitional and non-transitional flows, and flow visualization was also used. It was found that strong vortices (vortices with large circulation) lead to turbulence while weaker vortices do not. Determination of a critical value of vortex strength for transition, however, was complicated by ambiguities in calculating the vortex circulation. The profiles of streamwise velocity were found to be inflexional for both transitional and non-transitional flows. Transition in single-vortex and multi-vortex flows was compared, and no qualitative differences were observed, suggesting no significant vortex interactions affecting transition.