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arXiv2018

On relative input of viscous shear into the elasticity equation at near-front, near-inlet and the major part of a hydraulic fracture

The input of the hydraulically induced shear traction into the elasticity equation is estimated for the entire fracture surface. It is established that, except for negligibly small vicinities of a pointed source and of the fluid front, the relative input of the viscous shear does not exceed 10 - 4 of the input of the conventionally accounted term. The estimation is true for Newtonian, as well as non-Newtonian thinning fluids. This implies that there is no need to account for viscous shear not only in the form of conventional near-front asymptotics and fracture conditions, but also in factors entering them.

physics.flu-dyn↗

arXiv2018

Numerical simulation of flow instability and heat transfer of natural convection in a differentially heated cavity

This paper numerically investigates the physical mechanism of flow instability and heat transfer of natural convection in a cavity with thin fin(s). The left and the right walls of the cavity are differentially heated. The cavity is given an initial temperature, and the thin fin(s) is fixed on the hot wall in order to control the heat transfer. The finite volume method and the SIMPLE algorithm are used to simulate the flow. Distributions of the temperature, the pressure, the velocity and the total pressure are obtained. Then, the energy gradient theory is employed to study the physical mechanism of flow instability and the effect of the thin fin(s) on heat transfer. Based on the energy gradient theory, the energy gradient function K represents the characteristic of flow instability. It is observed from the simulation results that the positions where instabilities take place in the temperature contours accord well with those of higher K value, which demonstrates that the energy gradient theory reveals the physical mechanism of flow instability. Furthermore, the effects of the fin length, the fin position, the fin number, and Ra on heat transfer are investigated. It is found that the effect of the fin length on heat transfer is negligible when Ra is relatively high. When there is only one fin, the most efficient heat transfer rate is achieved as the fin is fixed at the middle height of the cavity. The fin blocks heat transfer with a relatively small Ra, but the fin enhances heat transfer with a relatively large Ra. The fin(s) enhances heat transfer gradually with the increase of Ra under the influence of the thin fin(s). Finally, a linear correlation of Kmax with Ra is obtained which reveals the physical mechanism of natural convection from different approaches.

physics.flu-dyn↗

arXiv2018

Surface permeability, capillary transport and the Laplace-Beltrami problem

We have established previously, in a lead-in study, that the spreading of liquids in particulate porous media at low saturation levels, characteristically less than 10% of the void space, has very distinctive features in comparison to that at higher saturation levels. In particular, we have found that the dispersion process can be accurately described by a special class of partial differential equations, the super-fast non-linear diffusion equation. The results of mathematical modelling have demonstrated very good agreement with experimental observations. However, any enhancement of the accuracy and predictive power of the model, keeping in mind practical applications, requires the knowledge of the effective surface permeability of the constituent particles, which defines the global, macroscopic permeability of the particulate media. In the paper, we demonstrate how this quantity can be determined through the solution of the Laplace-Beltrami Dirichlet problem, we study this using the well-developed surface finite element method.

physics.flu-dyn↗

arXiv2018

Boundary layer instability control in the unsteady cloud cavitating flow

In this article, we propose a passive boundary layer control method to control the vortex structure of the cavity on the suction side and wake region of the CAV2003 benchmark hydrofoil. This method may be used in different applications such as marine, turbomachinery and hydraulic machinery. First, we used a hybrid URANS model for turbulence to simulate the 3D unsteady cloud cavitating flow and validated it based on experimental data. We performed the numerical simulations using open source code OpenFOAM and an Euler-Euler cavitation model. Second, we studied the effect of passive boundary layer control method on vortex structure on the suction side of the hydrofoil and in wake region. We showed that this control method may influence the boundary layer structure on the hydrofoil surface and also near the trailing edge. Using this technique the pressure distribution and the fluctuating part of the velocity field on the hydrofoil surface were modified over the chord length. This method induced a stabilization of the boundary layer and delay its separation. Therefore a significant reduction in cavitation-induced vibration may be expected.

physics.flu-dyn↗

arXiv2018

Hairpin vortex generation around a straight vortex tube in a laminar boundary-layer flow

Direct numerical simulation (DNS) was conducted to investigate the evolution of a straight vortex tube based on Hon & Walker's model, which was originally proposed for a symmetric hairpin vortex tube (Hon,T.L. & Walker, J.D.A, Computers & Fluids, 20(3), pp. 343-358, 1991), under the shear of a laminar boundary-layer flow and its response of the near-wall flows. Here, the streamwise vortex tube is a lifted streamwise vortex. The circulation and angle-to-wall of the vortex tube are varied. Circulation above a threshold produces multiple hairpin vortices that align in the streamwise direction over the vortex tube. Stability of the disturbances according to the situation of the vortex tube inside the boundary layer such as the fraction of the vortex tube inside the boundary layer in addition to the circulation and angle-to-wall is shown by a linear stability analysis. The contribution of linear and nonlinear terms in the dynamics of the disturbance evolution is clarified by a fully-nonlinear disturbance analysis that is conducted concurrently with the DNS. When the circulation is sufficiently large, two unstable modes, namely the `off-wall mode' and `near-wall mode', appear. The presence of these two modes generates a corkscrew-like disturbance around the vortex tube, and becomes a precursor for the generation of hairpin vortices. The dominant structure of disturbances appearing around the vortex tube along the elapse of time is also analyzed by the proper orthogonal decomposition. The present DNS of the model allowing continuous variation of the characteristics of the vortex tube clarifies this new aspect of the nonlinear boundary-layer stability regarding the generation of hairpin vortices.

physics.flu-dyn↗

arXiv2018

Time dependent singularities in incompressible potential flow

The flowfield resulting from a starting source type singularity is presented. This is a generalization of the classical source in potential flow to time dependent situations, including sources in oncoming flow. This model is applicable to initial spreading of oil on the surface of the sea resulting from an underwater leak

physics.flu-dyn↗

arXiv2018

Directional free-surface flows on a microfluidic chip with interplay of electrical and thermal fields

Free-surface electrokinetic flows have been attracting increasing attention from the research community over recent times, as attributable to their diverse fields of applications ranging from fluid mixing, particle manipulation to bio-chemical processing on a chip. Traditional electrokinetic processes governing free surface flows are mostly effective in manipulating fluids having characteristically low values of the electrical conductivity (lower than 0.085 S/m). Biological and biochemical processes, on the other hand, typically aim to manipulate fluids having higher electrical conductivities. To circumvent the problem of traditional electrokinetic processes in manipulating highly conductive fluids mediated by free surface flows, here we demonstrate a novel on-chip methodology for the same by exploiting the interaction between an alternating electric current and a thermal field. The consequent local gradients in electrical properties can be tuned to direct the flow towards a specific direction on the interface, opening up a new realm of on-chip process control without necessitating the creation of a geometric confinement. Similar concept of free-surface flow can be used to trigger the fluid along a open-channel flow

physics.flu-dyn↗

arXiv2018

Numerical Evaluation of Entropy Generation in Isolated Airfoils and Wells Turbines

In recent years, a number of authors have studied entropy generation in Wells turbines. This is potentially a very interesting topic, as it can provide important insights into the irreversibilities of the system, as well as a methodology for identifying, and possibly minimizing, the main sources of loss. Unfortunately, the approach used in these studies contains some crude simplifications that lead to a severe underestimation of entropy generation and, more importantly, to misleading conclusions. This paper contains a re-examination of the mechanisms for entropy generation in fluid flow, with a particular emphasis on RANS equations. An appropriate methodology for estimating entropy generation in isolated airfoils and Wells turbines is presented. Results are verified for different flow conditions, and a comparison with theoretical values is presented.

physics.flu-dyn↗

arXiv2018

Revisiting Wells Turbine Hysteresis in Light of Existing Literature on Moving Airfoils

A Wells turbine is an axial-flow turbine consisting of a rotor usually with symmetric (uncambered) blades staggered at a 90 degree angle relative to the incoming flow. This turbine is used within oscillating water column (OWC) systems, which convert the sea-wave motion into a bi-directional flow of air. During its normal operation, the turbine blades experience a continuous change in incidence angle. that according to many authors is at the origin of an hysteresis in its force coefficients. Aerodynamic hysteresis in rapidly moving airfoils is a well-known phenomenon, but happens only at non-dimensional frequencies significantly larger than the ones encountered in Wells turbine. This work presents a re-examination of the two phenomena, that shows the unlikeliness of the presence of any aerodynamic hysteresis in Wells turbines. A simple and efficient lumped parameter analysis is used to prove how the real cause of the hysteresis is likely to be found in a completely different phenomenon, overlooked by many previous experimental and numerical analyses.

physics.flu-dyn↗

arXiv2018

Viscous flow regimes in unit square: Part 4. Vorticity dynamics from monopoles to multipoles

The initial-boundary value problem of the vorticity equation has been solved numerically by an iterative method. A variety of initial vorticity distributions is specified. All of them can be described by simple mathematical functions: there are a vorticity source-sink pair, circular shears out of a localised monopole, a cat's-eye topology and a few flows originating from single or multiple vortices. Our computational results show diverse flow phenomena, such as roll-ups of shear layers, vortex merging or impingement, as well as birth of spiral structures.

physics.flu-dyn↗

arXiv2018

Emerging Trends in Numerical Simulations of Combustion Systems

Numerical simulations have played a vital role in the design of modern combustion systems. Over the last two decades, the focus of research has been on the development of the large eddy simulation (LES) approach, which leveraged the vast increase in computing power to dramatically improve predictive accuracy. Even with the anticipated increase in supercomputing capabilities, the use of LES in design is limited by its high computational cost. Moreover, to aid decision making, such LES computations have to be augmented to estimate underlying uncertainties in simulation components. At the same time, other changes are happening across industries that build or use combustion devices. While efficiency and emissions reduction are still the primary design objectives, reducing cost of operation by optimizing maintenance and repair is becoming an important segment of the enterprise. This latter quest is aided by the digitization of combustors, which allows collection and storage of operational data from a host of sensors over a fleet of devices. Moreover, several levels of computing including low-power hardware present on board the combustion systems are becoming available. Such large data sets create unique opportunities for design and maintenance if appropriate numerical tools are made available. As LES revolutionized computing-guided design by leveraging supercomputing, a new generation of numerical approaches is needed to utilize this vast amount of data and the varied nature of computing hardware. In this article, a review of emerging computational approaches for this heterogeneous data-driven environment is provided. A case is made that new but unconventional opportunities for physics-based combustion modeling exist in this realm.

physics.comp-ph↗

arXiv2018

Concentration banding instability of a sheared bacterial suspension

We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneously sheared suspension is shown to support exponentially growing layering perturbations in the shear-rate and bacterial concentration. Non-linear simulations show that the instability eventually leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the bands. Our results show that long-ranged hydrodynamic interactions are sufficient to explain recent observations of shear-bands in bacterial suspensions.

physics.flu-dyn↗

arXiv2018

Statistical State Dynamics Based Study of the Role of Nonlinearity in the Maintenance of Turbulence in Couette Flow

While linear non-normality underlies the mechanism of energy transfer from the externally driven flow to the perturbation field that sustains turbulence, nonlinearity is also known to play an essential role. The goal of this study is to better understand the role of nonlinearity in sustaining turbulence. The method used in this study is implementation in Couette flow of a statistical state dynamics (SSD) closure at second order in a cumulant expansion of the Navier-Stokes equations in which the averaging operator is the streamwise mean. The perturbations are the deviations from the streamwise mean and two mechanisms potentially contributing to maintaining these perturbations are identified. These are parametric perturbation growth arising from interaction of the perturbations with the fluctuating mean flow and transient growth of perturbations arising from nonlinear interaction between components of the perturbation field. By the method of comparing the turbulence maintained in the SSD and in the associated direct numerical simulation (DNS) in which these mechanisms have been selectively included and excluded, parametric growth is found to maintain the perturbation field of the turbulence while the more commonly invoked mechanism of transient growth of perturbations arising from scattering by nonlinear interaction is found to suppress perturbation growth. In addition to verifying that the parametric mechanism maintains the perturbations in DNS it is also verified that the Lyapunov vectors are the structures that dominate the perturbation energy and energetics in DNS. It is further verified that these vectors are responsible for maintaining the roll circulation that underlies the self-sustaining process (SSP) and in particular the maintenance of the fluctuating streak that supports the parametric perturbation growth.

physics.flu-dyn↗

arXiv2018

A Comparison of Constitutive Models of Blood

Mathematical models that accurately predict the mechanical behavior of blood can contribute to the development of biomedical devices and medications which are relevant in clinical applications. The models existing in the literature are complex enough in order to agree with various in vitro experimental observations. Latest technological advancements opened the possibility of studying blood flow in vivo which could play an important role in the creation of biocompatible implants for health monitoring and treatment purposes. However, most of existing models may fail to predict blood behavior in vivo because they require many parameters which are difficult to find in vivo and they do not incorporate pertinent coupled chemo-mechanical dynamics specific to blood flow in a living body. Recently, we used the fractional model of continuum mechanics proposed by Drapaca and Sivaloganathan [J. Elast.,107: 105-123, 2012] to study blood circulation. In this mathematical formulation the spatial derivatives of the rate of deformation tensor are expressed using Caputo fractional derivatives. The aim of this paper is to compare the Poiseuille flows of blood through an axi-symmetric circular rigid and impermeable pipe where the blood is described by the above mentioned fractional model, the Casson's model, and the power law model. Although the velocity profiles of these three models look similar, the fractional model provides a better fitting to published experimental data.

physics.flu-dyn↗

arXiv2019

D'Alembert-type solution of the Cauchy problem for a Boussinesq-Klein-Gordon equation

In this paper we construct a weakly-nonlinear d'Alembert-type solution of the Cauchy problem for a Boussinesq-Klein-Gordon equation. Similarly to our earlier work based on the use of spatial Fourier series, we consider the problem in the class of periodic functions on an interval of finite length (including the limiting case of an "infinite" interval with zero boundary conditions), and work with the equation describing a deviation from the mean value. Unlike our earlier paper, here we develop a novel multiple-scales procedure involving fast characteristic variables and two slow time scales, which allows us to construct an explicit and compact d'Alembert-type solution of the nonlinear problem in terms of solutions of two Ostrovsky equations emerging at the leading order and describing the right- and left-propagating waves. Validity of the constructed solution follows from our earlier results, and is illustrated numerically for a number of instructive examples, both for periodic solutions on a finite interval, and the well-studied scenario for localised solutions on a large ("infinite") interval. Importantly, in all cases the initial conditions for the leading-order Ostrovsky equations by construction have zero mass. Thus, the so-called "zero-mass contradiction" has been completely by-passed.

nlin.PS↗

arXiv2018

Dynamics of a spatially developing liquid jet with slower coaxial gas flow

A three-dimensional round liquid jet within a low-speed coaxial gas flow is numerically simulated and explained via vortex dynamics ($λ_2$ method). The instabilities on the liquid-gas interface reflect well the vortex interactions around the interface. Certain key features are identified for the first time. Two types of surface deformations are distinguished, which are separated by a large indentation on the jet stem: First, those near the jet start-up cap are encapsulated inside the recirculation zone behind the cap. These deformations are directly related to the dynamics of the growing cap and well explained by the vortices generated there. Second, deformations occurring farther upstream of the cap are mainly driven by the Kelvin-Helmholtz (KH) instability at the interface. Three-dimensional deformations occur in the vortex structures first, and the initially axisymmetric KH vortices deform and lead to several liquid lobes, which stretch first as thinning sheets and then either continue stretching directly into elongated ligaments - at lower relative velocity - or perforate to create liquid bridges and holes - at higher relative velocity. The different scenarios depend on Weber and Reynolds numbers based on the relative gas-liquid velocity as was found in the temporal studies. The deformations in the upstream region are well portrayed in a frame moving with the convective velocity of the liquid jet. The usefulness of the temporal analyses are now established.

physics.flu-dyn↗

arXiv2018

Folding a focalized acoustical vortex on a flat holographic transducer: miniaturized selective acoustical tweezers

Acoustical tweezers based on focalized acoustical vortices hold the promise of precise contactless 3D manipulation of millimeter down to sub-micrometer particles, microorganisms and cells with unprecedented combined selectivity and trapping force. Yet, the widespread dissemination of this technology has been hindered by severe limitations of current systems in terms of performance and/or miniaturization and integrability. In this paper, we unleash the potential of focalized acoustical vortices by developing the first flat, compact, single-electrodes focalized acoustical tweezers. These tweezers rely on holographic Archimedes-Fermat spiraling transducers obtained by folding a spherical acoustical vortex on a flat piezoelectric substrate. We demonstrate the ability of these tweezers to grab and displace micrometric objects in a standard microfluidic environment with unique selectivity. The simplicity of this system and its scalability to higher frequencies opens tremendous perspectives in microbiology, microrobotics and microscopy.

physics.class-ph↗

arXiv2018

Asymptotic structure incorporating double and triple decks, original version

The stagnation point flow toward a rotating disk of finite radius is known to develop -- near the edge of the disk -- into a triple deck structure when the flow is strictly a stagnation point flow, and into a double deck structure when the flow is strictly a rotating disk flow. It is shown here that the transfer from one structure to another is singular; requiring matching of two main decks. The double deck structure is, in essence, a triple deck structure with collapsing upper deck.

physics.flu-dyn↗