An official website of the United States government
The effect of slip surfaces on the laminar–turbulent separatrix of plane Poiseuille flow is studied by direct numerical simulation. In laminar flows, the inclusion of the slip surfaces results in a drag reduction of over 10 %, which is in good agreement with previous studies and the theory of laminar slip flows. Turbulence lifetimes, the likelihood that turbulence is sustained, is investigated for transitional flows with various slip lengths. We show that slip surfaces decrease the likelihood of sustained turbulence compared to the no-slip case, and the likelihood is further decreased as slip length is increased. A more deterministic analysis of the effects of slip surfaces on a transition to turbulence is performed by using nonlinear travelling-wave solutions to the Navier–Stokes equations, also known as exact coherent solutions. Two solution families, dubbed P3 and P4, are used since their lower-branch solutions are embedded on the boundary of the basin of attraction of laminar and turbulent flows (Park & Graham, J. Fluid Mech. , vol. 782, 2015, pp. 430–454). Additionally, they exhibit distinct flow structures – the P3 and P4 are denoted as core mode and critical-layer mode, respectively. Distinct effects of slip surfaces on the solutions are observed by the skin-friction evolution, linear growth rate and phase-space projection of transitional trajectories. The slip surface appears to modify the transition dynamics very little for the core mode, but quite considerably for the critical-layer mode. Most importantly, the slip surface promotes different transition dynamics – an early and bypass-like transition for the core mode and a delayed and H- or K-type-like transition for the critical-layer mode. We explain these distinct transition dynamics based on spatio-temporal and quadrant analyses. It is found that slip surfaces promote the prevalence of strong wall-toward motions (sweep-like events) near vortex cores close to the channel centre, inducing an early transition, while long sustained ejection events are present in the region of the $$\unicode[STIX]{x1D6EC}$$ -shaped vortex cores close to the critical layer, resulting in a delayed transition. This should motivate flow control strategies to fully exploit these distinct transition dynamics for transition to turbulence.
more »
« less
On Stokes' second problem solutions in cylindrical and Cartesian domains
It is well known that drag created by turbulent flow over a surface can be reduced by oscillating the surface in the direction transverse to the mean flow. Efforts to understand the mechanism by which this occurs often apply the solution for laminar flow in the infinite half-space over a planar, oscillating wall (Stokes’ second problem) through the viscous and buffer layer of the streamwise turbulent flow. This approach is used for flows having planar surfaces, such as channel flow, and flows over curved surfaces, such as the interior of round pipes. However, surface curvature introduces an additional effect that can be significant, especially when the viscous region is not small compared to the pipe radius. The exact solutions for flow over transversely oscillating walls in a laminar pipe and planar channel flow are compared to the solution of Stokes’ second problem to determine the effects of wall curvature and/or finite domain size. It is shown that a single non-dimensional parameter, the Womersley number, can be used to scale these effects and that both effects become small at a Womersley number of greater than about 6.51, which is the Womersley number based on the thickness of the Stokes’ layer of the classical solution.
more »
« less
- Award ID(s):
- 1944568
- PAR ID:
- 10388145
- Date Published:
- Journal Name:
- Physics of fluids
- Volume:
- 34
- Issue:
- 10
- ISSN:
- 1527-2435
- Page Range / eLocation ID:
- 103615
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Accurately identifying the onset of transitional and turbulent flow within any pipe flow environment is of great interest. Most often, the critical Reynolds number (Re) is used to pinpoint the onset of turbulence. However, the critical Re is known to be highly variable, depending on the specifics of the flow system. Thus, for flows (e.g., blood flows), where only one realization (i.e., one mean Re) exists, the presence of transitional and turbulent flow behaviors cannot be accurately determined. In this work, we aim to address this by evaluating the extent to which instantaneous time-frequency (TF)-based analysis of the fluctuating velocity field can be used to evaluate the onset of transitional and turbulent flow regimes. Because current TF analysis methods are not suitable for this, we propose a novel “wavelet-Hilbert time-frequency” (WHTF) method, which we validate herein. Using the WHTF method, we analyzed the instantaneous dominant frequency of three planar particle image velocimetry-captured pipe flows, which included one steady and two pulsatile with Womersley numbers of 4 and 12. For each case, data were captured at Re's spanning 800–4500. The instantaneous dominant frequency analysis of these flows revealed that the magnitude, size, and coherence of two-dimensional spatial frequency structures were uniquely different across flow regimes. Specifically, the transitional regime maintained the most coherent, but lowest magnitude frequency structures, while the laminar regime had the highest magnitude, lowest coherence, and smallest frequency structures. Overall, this study demonstrates the efficacy of TF-based metrics for characterizing the progression of transition and turbulent flow development.more » « less
-
Reducing wall drag in turbulent pipe and channel flows is an issue of great practical importance. In engineering applications, end-functionalized polymer chains are often employed as agents to reduce drag. These are polymers which are floating in the solvent and attach (either by adsorption or through irreversible chemical binding) at one of their chain ends to the substrate (wall). We propose a PDE model to study this setup in the simple setting where the solvent is a viscous incompressible Navier–Stokes fluid occupying the bulk of a smooth domain Ω⊂ℝ𝑑, and the wall-grafted polymer is in the so-called mushroom regime (inter-polymer spacing on the order of the typical polymer length). The microscopic description of the polymer enters into the macroscopic description of the fluid motion through a dynamical boundary condition on the wall-tangential stress of the fluid, something akin to (but distinct from) a history-dependent slip-length. We establish the global well-posedness of strong solutions in two-spatial dimensions and prove that the inviscid limit to the strong Euler solution holds with a rate. Moreover, the wall-friction factor ⟨𝑓⟩ and the global energy dissipation ⟨𝜀⟩ vanish inversely proportional to the Reynolds number 𝐑𝐞. This scaling corresponds to Poiseuille’s law for the friction factor ⟨𝑓⟩∼1/𝐑𝐞 for laminar flow and thereby quantifies drag reduction in our setting. These results are in stark contrast to those available for physical boundaries without polymer additives modeled by, for example, no-slip conditions, where no such results are generally known even in two-dimensions.more » « less
-
This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.more » « less
-
Motivated by the saturation of drag reduction effectiveness at high non-dimensional riblet spacing in turbulent boundary layer flows, this study seeks to investigate the influence of a secondary blade riblet structure on flow statistics and friction drag reduction effectiveness in comparison to the widely explored single-scale blade riblet surface. The turbulent flow dynamics and drag reduction performance over single- and multi-scale blade riblet surfaces were experimentally examined in a flow visualization channel across various non-dimensional riblet spacings. The shear velocity was quantified by the streamwise velocity distributions from the logarithmic layer via planar Particle Image Velocimetry (PIV) measurements, whereas the near-wall flow dynamics were characterized by a Micro Particle Image Velocimetry (micro-PIV) system. The results highlighted that although both riblet surfaces exhibited similar drag reduction performances at low non-dimensional riblet spacings, the presence of a secondary riblet blade structure can effectively extend the drag reduction region with the non-dimensional riblet spacing up to 32 and achieve approximately 10% lower friction drag in comparison to the single-scale riblet surface when the non-dimensional riblet spacing increases to 44.2. The average number of uniform momentum zones (UMZs) on the multi-scaled blade riblet has also reduced by 9% compared to the single-scaled riblet which indicates the reduction of strong shear layers within a turbulent boundary layer. The inspection of near-wall flow statistics demonstrated that at high non-dimensional riblet spacings, the multi-scale riblet surface produces reduced wall-normal velocity fluctuations and Reynolds shear stresses. Quadrant analysis revealed that this design allows for the suppression of both the sweep and ejection events. This experimental result demonstrated that surfaces with spanwise variations of riblet heights have the potential to maintain drag reduction effectiveness across a wider range of flow speeds.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0118838
