arXiv subjects

Martin Skote

Publications and source records attributed to Martin Skote.

7 recordsLinked to original sources

arXiv2023

How wavelength affects the hydrodynamic performance of two accelerating mirror-symmetric slender swimmers

Fish schools are capable of simultaneous linear acceleration. To reveal the underlying hydrodynamic mechanism, we numerically investigate how Reynolds number $ Re = 1000 - 2000 $, Strouhal number $ St = 0.2 - 0.7 $ and wavelength $ λ= 0.5 - 2 $ affect the mean net thrust and net propulsive efficiency of two side-by-side hydrofoils undulating in anti-phase. In total, $ 550 $ cases are simulated using immersed boundary method. The thrust increases significantly with wavelength and Strouhal number, yet only slightly with the Reynolds number. We apply a symbolic regression algorithm to formulate this relationship. Furthermore, we find that mirror-symmetric schooling can achieve a \textit{net} thrust more than ten times that of a single swimmer, especially at low Reynolds numbers. The highest efficiency is obtained at $ St = 0.5 $ and $ λ= 1.2 $, where $ St $ is consistent with that observed in the linear-accelerating natural swimmers, \eg Crevalle jack. Six distinct flow structures are identified. The highest thrust corresponds to an asymmetric flow pattern, whereas the highest efficiency occurs when the flow is symmetric with converging vortex streets.

physics.flu-dyn↗

arXiv2022

Integral relations for the skin-friction coefficient of canonical flows

We show that the Fukagata et al. (2002)'s identity for free-stream boundary layers simplifies to the von Karman momentum integral equation relating the skin-friction coefficient and the momentum thickness when the upper bound in the integrals used to obtain the identity is taken to be asymptotically large. If a finite upper bound is used, the terms of the identity depend spuriously on the bound itself. Differently from channel and pipe flows, the impact of the Reynolds stresses on the wall-shear stress cannot be quantified in the case of free-stream boundary layers because the Reynolds stresses disappear from the identity. The infinite number of alternative identities obtained by performing additional integrations on the streamwise momentum equation also all simplify to the von Karman equation. Analogous identities are found for channel flows, where the relative influence of the physical terms on the wall-shear stress depends on the number of successive integrations, demonstrating that the laminar and turbulent contributions to the skin-friction coefficient is only distinguished in the original identity discovered by Fukagata et al. (2002). In the limit of large number of integrations, these identities degenerate to the definition of skin-friction coefficient and a novel two-fold integration identity is found for channel and pipe flows. In addition, we decompose the skin-friction coefficient as the sum of the change of integral thicknesses with the streamwise direction, following the study of Renard & Deck (2016). We utilize an energy thickness and an inertia thickness, which is composed of a thickness related to the mean-flow wall-normal convection and a thickness linked to the streamwise inhomogeneity of the mean streamwise velocity. The contributions of the different terms of the streamwise momentum equation on the friction drag is thus quantified by these integral thicknesses.

physics.flu-dyn↗

arXiv2021

A review of turbulent skin-friction drag reduction by near-wall transverse forcing

The quest for reductions in fuel consumption and CO2 emissions in transport has been a powerful driving force for scientific research into methods that might underpin drag-reducing technologies for a variety of vehicular transport on roads, by rail, in the air, and on or in the water. In civil aviation, skin-friction drag accounts for around 50% of the total drag in cruise conditions, thus being a preferential target for research. With laminar conditions excluded, skin friction is intimately linked to the turbulence physics in the fluid layer closest to the skin. Thus, research into drag reduction has focused on methods to depress the turbulence activity near the surface. The most effective method of doing so is to subject the drag-producing flow in the near-wall layer to an unsteady and/or spatially varying cross-flow component, either by the action of transverse wall oscillations, by embedding rotating discs into the surface or by plasma-producing electrodes that accelerate the near-wall fluid in the transverse direction. In ideal conditions, drag-reduction margins of order of 50% can be achieved. The present article provides a review of research into the response of turbulent near-wall layers to the imposition of unsteady and wavy transverse motion, encompassing experiments, simulation, analysis and modelling. It covers issues such as the drag-reduction margin in a variety of actuation scenarios, the underlying physical phenomena that contribute to the interpretation of the origin of the drag reduction, the dependence of the drag reduction on the Reynolds number, passive control methods that are inspired by active control, and a forward look towards possible future research and practical realizations. The authors hope that this review, by far the most extensive of its kind for this subject, will be judged as a useful foundation for future research targeting friction-drag reduction

physics.flu-dyn↗

arXiv2021

Perturbation symmetries in shear-thinning viscoelastic pipe flows and the Petrov-Galerkin implementation

The perturbations of the laminar shear-thinning viscoelastic pipe flow under Finitely Extensible Nonlinear Elastic model with Peterlin approximation (FENE-P) are shown to exhibit leading-order power-law behaviours, and the expected odd-even parities with respect to the radial coordinate that depend on the azimuthal wave\-number, $n$. The analysis helps regularizing the governing system of equations at the centreline, and allows for a complete stability analysis of three-dimensional perturbations for a general integer value of $n$, which has hitherto remained a challenge for FENE-P models. It is shown here that the symmetry and analytic behaviours of the velocity and pressure fields of the Newtonian counterpart are both preserved in this flow, and the reason is elucidated. For $|n|=1$, the perturbations to the correlations between the axial component and the radial or azimuthal components of the end-to-end polymer vector exhibit behaviour similar to that of the velocity perturbations close to the centreline, and are traced to the uniformity of axial traction with respect to the azimuthal direction. For all values of $n$, the fluctuation to the end-to-end length of the polymer chain vanishes at the centreline. The ansatzes for the perturbations to the components of conformation tensor arrived here, using heuristics, are later proved in two separate ways: Frobenius method, and a method that utilizes observations from Fourier analysis. We also reveal the existence of natural modes of polymers with trivial velocity perturbations in the limit of vanishing polymer viscosity. The complex frequency spectrum of these modes is continuous with radial stratification. Finally, the ansatzes are implemented using a Petrov--Galerkin spectral scheme.

physics.flu-dyn↗

arXiv2020

Viscoelastic laminar drag bounds in pipe flow

The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the solution. The lower friction factor for the flow of the solution when compared to the latter is tracked to an increased strain rate needed to enhance viscous dissipation. Lastly, we show analytically that the effective viscosity varies similarly to the radial diagonal component of the conformation tensor as observed numerically in turbulent flows, and give a lucid interpretation of shear-thinning through a sequence of underlying constitutive physical phenomena.

physics.flu-dyn↗

arXiv2019

A linear system for pipe flow stability analysis allowing for boundary condition modifications

An accurate system to study the stability of pipe flow that ensures regularity is presented. The system produces a spectrum that is as accurate as Meseguer \& Trefethen (2000), while providing flexibility to amend the boundary conditions without a need to modify the formulation. The accuracy is achieved by formulating the state variables to behave as analytic functions. We show that the resulting system retains the regular singularity at the pipe centre with a multiplicity of poles such that the wall boundary conditions are complemented with precisely the needed number of regularity conditions for obtaining unique solutions. In the case of axisymmetric and axially constant perturbations the computed eigenvalues match, to double precision accuracy, the values predicted by the analytical characteristic relations. The derived system is used to obtain the optimal inviscid disturbance pattern, which is found to hold similar structure as in plane shear flows.

math.NA↗

arXiv2018

Growth mechanisms of perturbations in boundary layers over a compliant wall

The temporal modal and nonmodal growth of three-dimensional perturbations in the boundary-layer flow over an infinite compliant flat wall is considered. Using a wall-normal velocity/wall-normal vorticity formalism, the dynamic boundary condition at the compliant wall admits a linear dependence on the eigenvalue parameter, as compared to a quadratic one in the canonical formulation of the problem. This greatly simplifies the accurate calculation of the continuous spectrum by means of a spectral method, thereby yielding a very effective filtering of the pseudospectra as well as a clear identification of instability regions. The regime of global instability is found to be matching the regime of the favorable phase of the forcing by the flow on the compliant wall so as to enhance the amplitude of the wall. An energy-budget analysis for the least-decaying hydroelastic (static-divergence, traveling-wave-flutter and near-stationary transitional) and Tollmien--Schlichting modes in the parameter space reveals the primary routes of energy flow. Moreover, the flow exhibits a slower transient growth for the maximum growth rate of a superposition of streamwise-independent modes due to a complex dependence of the wall-boundary condition with the Reynolds number. The initial and optimal perturbations are compared with the boundary-layer flow over a solid wall; differences and similarities are discussed. Unlike the solid-wall case, viscosity plays a pivotal role in the transient growth. A slowdown of the maximum growth rate with the Reynolds number is uncovered and found to originate in the transition of the fluid-solid interaction from a two-way to a one-way coupling. Finally, a term-by-term energy budget analysis is performed to identify the key contributors to the transient growth mechanism.

physics.flu-dyn↗