An experimental device previously developed for studying rotating baroclinic flows has been used to investigate undular bores formation, propagation and collision. Up to our knowledge this is the first experimental study of undular bores in a circular channel. For a setup without barriers, this geometry accomplishes in a natural way the periodic lateral boundary conditions, very often used in numerical simulations. An excellent agreement between the experiment and simulation has been achieved. The spatio-temporal structure of bores is well reproduced for the first few reflections or collisions.
This study presents an analysis of thermal performance in a both sided wavy enclosure with various moving walls. The plane walls of the enclosure are allowed to move in its own plane at a constant speed. Furthermore, one of the plane walls is heated nonuniformly while all other walls are maintained at constant cold temperature. The governing Navier–Stokes (N-S) equations in streamfunction–vorticity ( ) form coupled with the energy equation representing incompressible viscous flows are solved using our recently proposed fourth order compact scheme on nonuniform curvilinear grids (Pandit and Chattopadhyay, 2017). In order to observe the effects of the pertinent dimensionless parameters such as Richardson number ( ), Grashof number ( ), the wavy surface amplitude ( ), and number of undulations ( ) along the wavy surfaces on the fluid flow and the thermal performance of the cavity, the streamlines, isotherms contours and Nusselt numbers are studied. We have carried out nine cases (Case-1 to Case-9) for moving both the plane walls depending on the direction of moving walls and inclination angles. The issues of entropy generation are also analyzed based on the obtained dimensionless velocity and temperature values.
This paper briefly reviews the influence that the rapid evolution of computer power in the last decades has had on turbulence research. It is argued that it can be divided into three stages. In the earliest (‘heroic’) one, simulations were expensive and could at most be considered as substitutes for experiments. Later, as computers grew faster and some meaningful simulations could be performed overnight, it became practical to use them as (‘routine’) tools to provide answers to specific theoretical questions. More recently, some turbulence simulations have become trivial, able to run in minutes, and it is possible to think of computers as ‘Monte Carlo’ theory machines, which can be used to systematically pose a wide range of ‘random’ theoretical questions, only to later evaluate which of them are interesting or useful. Although apparently wasteful, it is argued that this procedure has the advantage of being reasonably independent of received wisdom, and thus more able than human researchers to scape established paradigms. The rate of growth of computer power ensures that the interval between consecutive stages is about fifteen years. Rather than offering conclusions, the purpose of the paper is to stimulate discussion on whether machine- and human-generated theories can be considered comparable concepts, and on how the challenges and opportunities created by our new computer ‘colleagues’ can be made to fit into the traditional research process.
It is known from linear theory that bottom oscillations in uniform open-channel flow can produce resonant surface waves with zero group velocity and diverging amplitude (Tyvand and Torheim 2012). This resonance exists for Froude numbers smaller than one, at a critical frequency dependent on the Froude number. This resonance phenomenon is studied numerically in the time domain, with fully nonlinear free-surface conditions. An oscillatory 2D bottom source is started, and the local elevation at resonance grows until it may reach a saturation amplitude. Four waves exist at subcritical Froude numbers, where resonance represents the third and the fourth wave merging. In the zero-frequency limit, the dispersive second and fourth wave merge into a steady wave with finite group velocity and amplitude, and no other periodic waves exist. In the time-dependent nonlinear analysis at zero frequency, a transient undular bore may emerge as the dominating phenomenon.
In this paper, absolutely new analytical ansatz for solving Kelvin–Kirchhoff equations has been presented. The aforesaid approach was formulated first in Ershkov (2017) for solving Poisson equations; furthermore, a new type of the solving procedure for Euler–Poissonequations (rigid body rotation over the fixed point) is implemented here for solving momentum equation of Kelvin–Kirchhoff. The system of equations of Kelvin–Kirchhoff problem has been explored with regard to the existence of an analytic way of presentation of the analytical solution. A new and elegant ansatz is suggested in this publication whereby, in solving, the momentum equation is reduced to a system of three linear ODEs of 1st order in regard to the three components of the velocity of the spherical particle (dependent on time ). In this premise, a proper elegant partial solution has been obtained due to the invariant dependence between temporary components of the solution. We conclude that the system of Kelvin–Kirchhoff equations has not the analytical presentation of solution (in quadratures) even in case of zero components of fluid force, influencing on the motion of the particle.
Direct numerical simulations are carried out to investigate the flow features responsible for secondary tones arising in trailing-edge noise at moderate Reynolds numbers. Simulations are performed for a NACA 0012 airfoil at freestream Mach numbers 0.1, 0.2 and 0.3 for angle of incidence 0 deg. and for Mach number 0.3 at 3 deg. angle of incidence. The Reynolds number based on the airfoil chord is fixed at . Flow configurations are investigated where noise generation arises from the scattering of boundary layer instabilities at the trailing edge. Results show that noise emission has a main tone with equidistant secondary tones, as discussed in literature. An interesting feature of the present flows at zero incidence is shown; despite the geometric symmetry, the flows become non-symmetric with a separation bubble only on one side of the airfoil. A separation bubble is also observed for the non-zero incidence flow. For both angles of incidence analyzed, it is shown that low-frequency motion of the separation bubbles induce a frequency modulation of the flow instabilities developed along the airfoil boundary layer. When the airfoil is at 0 deg. angle of attack an intense amplitude modulation is also observed in the flow quantities, resulting in a complex vortex interaction mechanism at the trailing edge. Both amplitude and frequency modulations directly affect the velocity and pressure fluctuations that are scattered at the trailing edge, what leads to secondary tones in the acoustic radiation.
This study investigates interaction between an impact liquid drop and a sessile drop on both flat and cylindrical substrates, focusing mainly on the combined liquid spreading and oscillation under low impact velocity with aid of high-speed photography. Different from the coaxial interaction with spreading and recoiling one after another, the off-center interaction presents an asymmetric liquid motion featured by the concomitant spreading and recoiling. Rim thickness in recoiling decreases appreciably with increasing the offset distance. Results also show that the height of combined liquid is more representative of liquid oscillation than the diameter, based on which the interaction is grouped into four major phases: impingement phase, unsteady damped oscillation phase, steady damped oscillation phase, and static phase. Also presented in this study are maximum spreading diameter and minimum height of the combined liquid. This is followed by investigations of unsteady duration, oscillation period, and height profile with regards to Weber number and offset distance.
This article investigates the effect of permeability of a Brinkman medium on the thermophoresis for the quasi-steady translational motion of a spherical particle located at the center of a spherical cavity filled with a porous medium under a prescribed temperature gradient. The Knudsen number is assumed to be small so that the fluid flow through a porous medium is described by a continuum model with a temperature jump, a thermal creep, and a viscous slip and thermal stress at the solid surfaces of the particle and cavity. An analytic expression for the thermophoretic velocity of the confined particle is obtained for various values of the Brinkman number characterizing the permeability of the medium, the thermal properties of the porous medium and particle and the particle-to-cavity radius ratio. Limiting cases of Stokes and Darcy’s flows are discussed.
The vortex dynamics in a two-dimensional oscillatory lid-driven cavity with depth-to-width ratio 1:2 has been investigated, covering a wide range of Reynolds numbers and Stokes numbers where this flow is known to be in the two-dimensional regime. Numerical simulations show that the present flow can be divided into four flow patterns based on the vortex dynamics. The regions of these flow patterns are given in the Stokes number and Reynolds number space. For the flow pattern with lowest Reynolds number, there is no transfer of vortices between two successive oscillation half-cycles while for the three other patterns, vortices are carried over from one oscillation half-cycle to the next. For a given Stokes number, the flow pattern appears sequentially as the Reynolds number increases, showing that the transition between the different flow patterns depends strongly on the Reynolds number. However, if the frequency of oscillation is increased (i.e., the Stokes number is increased) for a given Reynolds number, the extrema of the stream function have less time to grow and the center of the primary vortex has less time to move away from the lid. To compensate these effects, the amplitude has to be increased with increasing frequency to maintain the same flow pattern.
We have investigated the non-axisymmetric Homann stagnation-point flow of a viscoelastic fluid over a rigid plate. In a recent paper Weidman (2012) has modified Homann’s stagnation point flow and made it non-axisymmetric over a rigid plate. Now if the fluid is non-Newtonian a new family of asymmetric stagnation-point flows arises depending on the shear to strain-rate ratio and the viscoelastic parameter . Here , are the strain rate and shear rate of the stagnation-point flow. The governing momentum equations are solved numerically using fourth order Runge–Kutta method with shooting technique. The effect of the various parameters on the wall shear stress parameters, the dimensionless velocities, the displacement thicknesses and the velocity distributions are analysed. Numerical results of wall shear stress and displacement thicknesses are compared with their large value behaviours and those behaviours give a good agreement with the corresponding numerical solutions.
We study the flow of a thin layer of fluid over a flat surface. Commonly, the 1-D Shallow-water or Saint-Venant set of equations are used to compute the solution of such flows. These simplified equations may be obtained through the integration of the Navier–Stokes equations over the depth of the fluid, but their solution requires the introduction of constitutive relations based on strict hypothesis on the flow régime. Here, we present an approach based on a kind of boundary layer system with hydrostatic pressure. This relaxes the need for closure relations which are instead obtained as solutions of the computation. It is then demonstrated that the corresponding closures are very dependent on the type of flow considered, for example laminar viscous slumps or hydraulic jumps. This has important practical consequences as far as the applicability of standard closures is concerned.
Complex flows or vortical structures are observed around flapping wings. In particular, as observed in various experiments and numerical simulations, these flows are affected when kinematic parameters and translational velocity functions are changed. In the present study, numerical simulations of three-dimensional flows around a flapping wing are conducted to investigate parameters and translational velocity functions on the stroke reversal stage using immersed boundary lattice Boltzmann method. We consider a flapping Drosophila wing without pitching motion, and the effects of the stroke amplitude and stroke reversal duration are investigated. First, at high stroke amplitude, we found that a hairpin-like vortex loop is obviously observed. Second, the stroke reversal duration affects remnant vortex structures in the wake. In addition, this parameter affects a time instant which the wake capture occurs. Third, it is shown that the translational velocity function has a significant effect on drag force. If the translational velocity function is modeled with trigonometric function, the drag force has a discrepancy with well-known experimental data. In order to solve the problem, we suggest a higher order polynomial. As a result, our function shows a better agreement with the experimental data.
In this study we present a computational model for unprecedented simulations of the left heart in realistic physiological conditions. To this aim, models for the electrical network of contractile muscular fibers (electrophysiology bidomain model), the myocardium mechanics (shells with hyperelastic and orthotropic constitutive relations) and the complex hemodynamics (direct numerical simulation of the Navier–Stokes equations) have been developed and multi-way coupled. The resulting multi-physics model, relying on the immersed-boundary method to cope with the complex fluid–structure interaction, is then validated by replicating the dynamics of the left heart considering simultaneously its atrium and ventricle, with the embedded aortic and mitral valves, and the thoracic aorta where blood is pumped. It is shown that the developed model, when given as input the parameters for the human heart, can reproduce the physiologic velocity and pressure signals obtained by cardiographic diagnostics of real patients.
The impact of an axisymmetric liquid jet on a flat rigid wall wet with a thin film of the same liquid is numerically studied, using the two-dimensional Euler equations with axial symmetry solved by CIP-CUP method. The main attention is paid to the film effect on the liquid pressure field and the wall pressure load for the impact velocities 150 350 m/s. Such a velocity range is important for applications related to liquid and cavitation damage and erosion. Small film thicknesses up to 1/5 of the jet radius are considered because they may result in high pressure load on the wall, comparable to that in the dry wall case. The initial most intense period of the impact is investigated. The results show that for the film thickness up to about 1/10 of the jet radius throughout the impact-velocity range considered, a pressure peak appears at the periphery of the loaded zone on the wall, which is similar to the dry wall case. For sufficiently thin films and large impact velocities, the peripheral pressure peak may exceed the water hammer pressure. With increasing the film thickness, the wall-pressure distribution becomes more uniform, the maxima of the wall pressure in the center and at the periphery of the loaded area decrease. Unlike the dry wall case, the level of the wall pressure in terms of its ratio to the water hammer pressure lowers with decreasing the impact velocity because of an increase in the curvature of the shock wave incident on the wall. Rather large negative pressures arise in a small liquid zone near the wall as the expansion wave, generated by interaction between the shock wave and the film surface, reflects from the wall. With increasing the film thickness or lowering the impact velocity, their magnitude decreases. The dependences of the maximum average and maximum local wall pressure on the film thickness and the impact velocity have been determined. The impact of the jet without allowing for its axial symmetry has also been considered. It is found that the neglect of the axial symmetry may significantly reduce the damping effect of the film. With decreasing the film thickness and increasing the impact velocity, the reduction gradually vanishes.
Experimental investigations were carried out to elucidate the roles of surface wettability and inclination on the post-impact dynamics of droplets. The maximum spreading diameter and spreading time were found to decrease with increasing inclination angle and normal Weber number (We ) for superhydrophobic (SH) surfaces. The experiments on SH surfaces were found to be in excellent agreement with an existing analytical model, albeit with the incorporation of modifications for the oblique impact conditions. The energy ratios and elongation factors were also determined for different inclination angles. On inclined SH surfaces, different features like arrest of secondary droplet formation, reduced pinch-off at the contact line and inclination dependent elongation behavior were observed. On the contrary, the hydrophilic surfaces show opposite trends of maximum spreading factor and spreading time with inclination angle and We , respectively. This is caused by the dominance of tangential kinetic energy over adhesion energy and gravitational potential at higher inclination angles. Further, the influence of the surface tension (using surfactant solutions, without significantly changing the viscosity) and viscosity (using colloids, without significantly changing the surface tension) for impact on SH and hydrophilic surfaces are probed. The exercise allows better insight on the exact hydrodynamic mechanisms at play during the impact events. Overall, the article provides a comprehensive picture of post-impact dynamics of droplets on inclined surfaces, encompassing a broad spectrum of governing parameters like Reynolds number (Re), Weber number (We), degree of inclination and surface wettability.
The three-dimensional flow separation over the Rood wing-body junction is an exemplar application of separation affecting many important flows in turbomachinery and aerodynamics. Conventional Reynolds Averaged Navier Stokes (RANS) methods struggle to reproduce the complexity of this flow. In this paper, an unconventional use is made of a hybrid Reynolds Averaged Navier Stokes (RANS) model to tackle this challenge. The hybridization technique combines the Menter model with the one equation sub-grid-scale (SGS) model by Yoshizawa through a blending function, based on the wall-normal distance. The hybrid RANS turbulence closure captured most of the flow features reported in past experiments with reasonable accuracy. The model captured also the small secondary vortex at the corner ahead of the wing nose and at the trailing edge. This feature is scarcely documented in the literature. The study highlights the importance of the spatial resolution near the wing leading edge, where this localized secondary recirculation was observed by the hybrid RANS model. It also provides evidence on the applicability of the hybrid Menter and Yoshizawa turbulence closure to the wing-body junction flows in aircraft and turbomachines, where the flows are characterized by a substantially time-invariant three-dimensional separation.