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arXiv2014

Fluid Vesicles in Flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.

cond-mat.soft↗

arXiv2012

Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel-Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of the blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.

physics.flu-dyn↗

arXiv2013

Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a "heuristic argument" that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper "side-by-side" comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages") are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

nlin.CD↗

arXiv2013

Do peaked solitary water waves indeed exist?

Many models of shallow water waves admit peaked solitary waves. However, it is an open question whether or not the widely accepted peaked solitary waves can be derived from the fully nonlinear wave equations. In this paper, a unified wave model (UWM) based on the symmetry and the fully nonlinear wave equations is put forward for progressive waves with permanent form in finite water depth. Different from traditional wave models, the flows described by the UWM are not necessarily irrotational at crest, so that it is more general. The unified wave model admits not only the traditional progressive waves with smooth crest, but also a new kind of solitary waves with peaked crest that include the famous peaked solitary waves given by the Camassa-Holm equation. Besides, it is proved that Kelvin's theorem still holds everywhere for the newly found peaked solitary waves. Thus, the UWM unifies, for the first time, both of the traditional smooth waves and the peaked solitary waves. In other words, the peaked solitary waves are consistent with the traditional smooth ones. So, in the frame of inviscid fluid, the peaked solitary waves are as acceptable and reasonable as the traditional smooth ones. It is found that the peaked solitary waves have some unusual and unique characteristics. First of all, they have a peaked crest with a discontinuous vertical velocity at crest. Especially, the phase speed of the peaked solitary waves has nothing to do with wave height. In addition, the kinetic energy of the peaked solitary waves either increases or almost keeps the same from free surface to bottom. All of these unusual properties show the novelty of the peaked solitary waves, although it is still an open question whether or not they are reasonable in physics if the viscosity of fluid and surface tension are considered.

physics.flu-dyn↗

arXiv2013

Vortical and Self-similar Flows of 2D Compressible Euler Equations

This paper presents the vortical and self-similar solutions for 2D compressible Euler equations using the separation method. These solutions complement Makino's solutions in radial symmetry without rotation. The rotational solutions provide new information that furthers our understanding of ocean vortices and reference examples for numerical methods. In addition, the corresponding blowup, time-periodic or global existence conditions are classified through an analysis of the new Emden equation. A conjecture regarding rotational solutions in 3D is also made.

math-ph↗

arXiv2026

Nonlinear flame describing function and mean shift kinematics of slit flames under combined axial-transverse forcing

This study investigates the nonlinear kinematics of a premixed slit flame using a two-dimensional $G$-equation level-set framework. Results show that combined forcing induces nonlinear saturation in the FDF, characterized by early gain flattening and premature phase drops, which intensify with the transverse forcing amplitude. Kinematic analysis reveals that this geometric nonlinearity manifests as a reduction in the time-averaged flame height, defined as the mean shift. In the quasi-steady limit, this mean shift is analytically quantified via a multivariate asymptotic expansion, where fourth-order terms successfully capture the saturation mechanism at elevated amplitudes. By introducing a scaling parameter to account for transverse dominance, the frequency-dependent decay of the mean shift in the compact limit collapses onto a single master curve, enabling the derivation of a unified theoretical model that integrates this asymptotic response with a second-order low-pass filter. Furthermore, because the mean shift reduces the physical extent of the flame, it alters the wrinkle propagation time. Correcting the Strouhal number using the measured mean shift collapses the dispersed nonlinear FDF curves onto the linear theory prediction. The analysis is further extended to disturbances convected at a finite speed, for which the linear transfer function is derived analytically and the correction with the measured mean shift continues to collapse the nonlinear FDF. These findings establish that the nonlinear FDF behavior under multidimensional forcing is fundamentally governed by the kinematic mean shift, providing a theoretical baseline for decoupling geometric nonlinearities from other thermo-diffusive or hydrodynamic instabilities in turbulent flames.

physics.comp-ph↗

arXiv2013

High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex

We compute the solutions of Prandtl's and Navier-Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl's equation develops, in a finite time, a separation singularity. We investigate the different stages of unsteady separation for Navier-Stokes solution at different Reynolds numbers $Re=10^3-10^5$, and we show the presence of a large-scale interaction between the viscous boundary layer and the inviscid outer flow. We also see a subsequent stage, characterized by the presence of a small-scale interaction, which is visible only for moderate-high Re numbers $Re=10^4-10^5$. We also investigate the asymptotic validity of boundary layer theory by comparing Prandtl's solution to Navier-Stokes solutions during the various stages of unsteady separation.

math-ph↗

arXiv2014

Simplified numerical model for clarifying scaling behavior in the intermediate dispersion regime in homogeneous porous media

The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained with a variety of models. {We present and use a simplified numerical model which does not contain any turbulence, Taylor dispersion, or fractality. With it, we show that the non-linearity in the intermediate regime nevertheless occurs. Furthermore,} we show that that the intermediate regime can be regarded as a phase transition between random, diffusive transport at low flow velocity and ordered transport controlled by the geometry of the pore space at high flow velocities. This phase transition explains the first-order behavior in the intermediate regime. A new quantifier, the ratio of the amount of solute in dominantly advective versus dominantly diffusive pore channels, plays the role of `order parameter' of this phase transition. Taylor dispersion, often invoked to explain the supra-linear behavior of longitudinal dispersion in this regime, was found not to be of primary importance. The novel treatment of the intermediate regime paves the way for a more accurate description of dispersion as a function of flow velocity, spanning the whole range of Péclet numbers relevant to practical applications, such as ground water remediation.

physics.flu-dyn↗

arXiv2017

AFiD-GPU: a versatile Navier-Stokes Solver for Wall-Bounded Turbulent Flows on GPU Clusters

The AFiD code, an open source solver for the incompressible Navier-Stokes equations ({\color{blue}\burl{http://www.afid.eu}}), has been ported to GPU clusters to tackle large-scale wall-bounded turbulent flow simulations. The GPU porting has been carried out in CUDA Fortran with the extensive use of kernel loop directives (CUF kernels) in order to have a source code as close as possible to the original CPU version; just a few routines have been manually rewritten. A new transpose scheme, which is not limited to the GPU version only and can be generally applied to any CFD code that uses pencil distributed parallelization, has been devised to improve the scaling of the Poisson solver, the main bottleneck of incompressible solvers. The GPU version can reduce the wall clock time by an order of magnitude compared to the CPU version for large meshes. Due to the increased performance and efficient use of memory, the GPU version of AFiD can perform simulations in parameter ranges that are unprecedented in thermally-driven wall-bounded turbulence. To verify the accuracy of the code, turbulent Rayleigh-Bénard convection and plane Couette flow are simulated and the results are in good agreement with the experimental and computational data that published in previous literatures.

physics.flu-dyn↗

arXiv2013

Heat transport and flow structure in rotating Rayleigh-Bénard convection

Here we summarize the results from our direct numerical simulations (DNS) and experimental measurements on rotating Rayleigh-Bénard (RB) convection. Our experiments and simulations are performed in cylindrical samples with an aspect ratio Γvarying from 1/2 to 2. Here Γ=D/L, where D and L are the diameter and height of the sample, respectively. When the rotation rate is increased, while a fixed temperature difference between the hot bottom and cold top plate is maintained, a sharp increase in the heat transfer is observed before the heat transfer drops drastically at stronger rotation rates. Here we focus on the question of how the heat transfer enhancement with respect to the non-rotating case depends on the Rayleigh number Ra, the Prandtl number Pr, and the rotation rate, indicated by the Rossby number Ro. Special attention will be given to the influence of the aspect ratio on the rotation rate that is required to get heat transport enhancement. In addition, we will discuss the relation between the heat transfer and the large scale flow structures that are formed in the different regimes of rotating RB convection and how the different regimes can be identified in experiments and simulations.

physics.flu-dyn↗

arXiv2013

Investigating the use of nanofluids to improve high heat flux cooling systems

The thermal performance of high heat flux components in a fusion reactor could be enhanced significantly by the use of nanofluid coolants, suspensions of a liquid with low concentrations of solid nanoparticles. However, before they are considered viable for fusion, the long-term behaviour of nanofluids must be investigated. This paper reports an experiment which is being prepared to provide data on nanofluid stability, settling and erosion in a HyperVapotron device. Procedures are demonstrated for nanofluid synthesis and quality assessment, and the fluid sample analysis methods are described. The end results from this long-running experiment are expected to allow an initial assessment of the suitability of nanofluids as coolants in a fusion reactor.

physics.ins-det↗

arXiv2013

Fluid-particle flow and validation using two-way-coupled mesoscale SPH-DEM

First, a meshless simulation method is presented for multiphase fluid-particle flows with a two-way coupled Smoothed Particle Hydrodynamics (SPH) for the fluid and the Discrete Element Method (DEM) for the solid phase. The unresolved fluid model, based on the locally averaged Navier Stokes equations, is expected to be considerably faster than fully resolved models. Furthermore, in contrast to similar mesh-based Discrete Particle Methods (DPMs), our purely particle-based method enjoys the flexibility that comes from the lack of a prescribed mesh. It is suitable for problems such as free surface flow or flow around complex, moving and/or intermeshed geometries and is applicable to both dilute and dense particle flows. Second, a comprehensive validation procedure for fluid-particle simulations is presented and applied here to the SPH-DEM method, using simulations of single and multiple particle sedimentation in a 3D fluid column and comparison with analytical models. Millimetre-sized particles are used along with three different test fluids: air, water and a water-glycerol solution. The velocity evolution for a single particle compares well (less than 1% error) with the analytical solution as long as the fluid resolution is coarser than two times the particle diameter. Two more complex multiple particle sedimentation problems (sedimentation of a homogeneous porous block and an inhomogeneous Rayleigh Taylor instability) are also reproduced well for porosities 0.6 <= ε<= 1.0, although care should be taken in the presence of high porosity gradients. Overall the SPH-DEM method successfully reproduces quantitatively the expected behaviour in the test cases, and promises to be a flexible and accurate tool for other, realistic fluid-particle system simulations.

physics.flu-dyn↗

arXiv2014

Drag correlation for dilute and moderately dense fluid-particle systems using the lattice Boltzmann method

This paper presents a numerical study of flow through static random assemblies of monodisperse, spherical particles. A lattice Boltzmann approach based on a two relaxation time collision operator is used to obtain reliable predictions of the particle drag by direct numerical simulation. From these predictions a closure law $F(Re, φ)$ of the drag force relationship to the bed density $φ$ and the particle Reynolds number $Re$ is derived. The present study includes densities $φ$ ranging from $0.01$ to $0.35$ with Re ranging up to $300$, that is compiled into a single drag correlation valid for the whole range. The corelation has a more compact expression compared to others previously reported in literature. At low particle densities, the new correlation is close to the widely used Wen & Yu - correlation. Recently, there has been reported a discrepancy between results obtained using different numerical methods, namely the comprehensive lattice Boltzmann study of Beetstra et al. (2007) and the predictions based on an immersed boundary - pseudo-spectral Navier-Stokes approach (Tenneti et al., 2011). The present study excludes significant finite resolution effects, which have been suspected to cause the reported deviations, but does not coincide exactly with either of the previous studies. This indicates the need for yet more accurate simulation methods in the future.

physics.flu-dyn↗

arXiv2014

On dynamics of imploding shock waves in a mixture of gas and dust particles

In this paper, the generalized analytical solutions for one-dimensional adiabatic flow behind the imploding shock waves propagating in a dusty gas are obtained using the geometrical shock dynamics theory. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. Shock jump relations given by Anand for a dusty gas are taken into consideration to explore the effects due to an increase in (i) the propagation distance from the centre of convergence, (ii) the mass fraction of solid particles in the mixture and (iii) the ratio of the density of solid particles to the initial density of the gas, on the shock velocity, pressure, temperature, density, velocity of mixture, speed of sound, adiabatic compressibility of mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of solid particles influences the flow field behind the imploding shock front.

astro-ph.HE↗

arXiv2014

The Flow of Newtonian and power law fluids in elastic tubes

We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier-Stokes equations.

physics.flu-dyn↗

arXiv2013

Numerical and experimental study of the interaction between two marine current turbines

The understanding of interaction effects between marine energy converters represents the next step in the research process that should eventually lead to the deployment of such devices. Although some a priori considerations have been suggested recently, very few real condition studies have been carried out concerning this issue. Trials were run on 1/30th scale models of three-bladed marine current turbine prototypes in a flume tank. The present work focuses on the case where a turbine is placed at different locations in the wake of a first one. The interaction effects in terms of performance and wake of the second turbine are examined and compared to the results obtained on the case of one single turbine. Besides, a three-dimensional software, based on a vortex method is currently being developed, and will be used in the near future to model more complex layouts. The experimental study shows that the second turbine is deeply affected by the presence of an upstream device and that a compromise between individual device performance and inter-device spacing is necessary. Numerical results show good agreement with the experiment and are promising for the future modelling of turbine farms.

physics.flu-dyn↗

arXiv2010

Energy Loss Distribution in the Plane Couette Flow and the Taylor-Couette Flow between Concentric Rotating Cylinders

The distribution of energy loss due to viscosity friction in plane Couette flow and Taylor-Couette Flow between concentric rotating cylinders are studied in detail for various flow conditions. The energy loss is related to the industrial processes in some fluid delivery devices and has significant influence on the flow efficiency, flow stability, turbulent transition, mixing, and heat transfer behaviours, etc. Therefore, it is important to know about the energy loss distribution in the flow domain and to know its influence on the flow for better understanding of the flow physics. The calculation or methodology of calculating the energy loss distribution in the Taylor-Couette flow between concentric rotating cylinders is not readily found in the open literature. In this paper, the principle and the calculation are given for single cylinder rotation of either the inner or outer cylinder, and counter and same direction rotation of two cylinders. For comparison, the distribution of energy loss in a plane Couette flow is also derived for various flow conditions. Discussions of the effect of energy loss on the flow behaviour are carried out from which some findings are suggested.

physics.flu-dyn↗

arXiv2017

A robust upscaling of the effective particle deposition rate in porous media

In the upscaling from pore- to continuum (Darcy) scale, reaction and deposition phenomena at the solid-liquid interface of a porous medium have to be represented by macroscopic reaction source terms. The effective rates can be computed, in the case of periodic media, from three-dimensional microscopic simulations of the periodic cell. Several computational and semi-analytical models have been studied in the field of colloid filtration to describe this problem. They often rely on effective deposition rates defined by simple linear reaction ODEs, neglecting the advection-diffusion interplay, and assuming slow reactions. Therefore, when these rates are inserted into general macroscopic transport equations, they can lead to conceptual inconsistencies and, therefore, often qualitatively wrong results. In this work, we study the upscaling of Brownian deposition on face-centred spherical arrangements using a linear effective reaction rate, defined by volume averaging, and a macroscopic advection-diffusion-reaction equation. The case of partial deposition, defined by an attachment probability, is studied and the limit of ideal deposition is retrieved as a particular case. We make use of a particularly convenient computational setup that allows the direct computation of the asymptotic stationary value of effective rates. This allows to drastically reduce the computational domain down to the scale of the single repeating periodic unit: the savings are ever more noticeable in the case of higher Peclet numbers, when larger physical times are needed to reach the asymptotic regime, and thus, equivalently, a much larger computational domain and simulation time would be needed in a traditional setup. We show how this new definition of deposition rate is more robust and extendable to the whole range of Péclet numbers; it also is consistent with the classical heat and mass transfer literature.

physics.flu-dyn↗