Vortex dynamics of accelerated flow past a mounted wedge

This study is concerned with the simulation of a complex fluid flow problem involving flow past a wedge mounted on a wall for channel Reynolds numbers $Re_c=1560$, $6621$ and $6873$ in uniform and accelerated flow medium. The transient Navier-Stokes (N-S) equations governing the flow has been discretized using a recently developed second order spatially and temporally accurate compact finite difference method on a nonuniform Cartesian grid by the authors. All the flow characteristics of a well-known laboratory experiment of Pullin and Perry (1980) have been remarkably well captured by our numerical simulation, and we provide a qualitative and quantitative assessment of the same. Furthermore, the influence of the parameter $m$, controlling the intensity of acceleration, has been discussed in detail along with the intriguing consequence of non-dimensionalization of the N-S equations pertaining to such flows. The simulation of the flow across a time span significantly greater than the aforesaid lab experiment is the current study's most noteworthy accomplishment. For the accelerated flow, the onset of shear layer instability leading to a more complicated flow towards transition to turbulence have also been aptly resolved. The existence of coherent structures in the flow validates the quality of our simulation, as does the remarkable similarity of our simulation to the high Reynolds number experimental results of Lian and Huang (1989) for the accelerated flow across a typical flat plate. All three steps of vortex shedding, including the exceedingly intricate three-fold structure, have been captured quite efficiently.Comment: 28 pages, 27 figures, 2 table

Comprehensive study of forced convection over a heated elliptical cylinder with varying angle of incidences to uniform free stream

In this paper we carry out a numerical investigation of forced convection heat transfer from a heated elliptical cylinder in a uniform free stream with angle of inclination $\theta^{\circ}$. Numerical simulations were carried out for $10 \leq Re \leq 120$, $0^{\circ} \leq \theta \leq 180^{\circ}$, and $Pr = 0.71$. Results are reported for both steady and unsteady state regime in terms of streamlines, vorticity contours, isotherms, drag and lift coefficients, Strouhal number, and Nusselt number. In the process, we also propose a novel method of computing the Nusselt number by merely gathering flow information along the normal to the ellipse boundary. The critical $Re$ at which which flow becomes unsteady, $Re_c$ is reported for all the values of $\theta$ considered and found to be the same for $\theta$ and $180^\circ -\theta$ for $0^\circ \leq \theta \leq 90^\circ$. In the steady regime, the $Re$ at which flow separation occurs progressively decreases as $\theta$ increases. The surface averaged Nusselt number ($Nu_{\text{av}}$) increases with $Re$, whereas the drag force experienced by the cylinder decreases with $Re$. The transient regime is characterized by periodic vortex shedding, which is quantified by the Strouhal number ($St$). Vortex shedding frequency increases with $Re$ and decreases with $\theta$ for a given $Re$. $Nu_{\text{av}}$ also exhibits a time-varying oscillatory behaviour with a time period which is half the time period of vortex shedding. The amplitude of oscillation of $Nu_{\text{av}}$ increases with $\theta$

Supraconservative finite-volume methods for the Euler equations of subsonic compressible flow

It has been found advantageous for finite-volume discretizations of flow equations to possess additional (secondary) invariants, next to the (primary) invariants from the constituting conservation laws. The paper presents general (necessary and sufficient) requirements for a method to convectively preserve discrete kinetic energy. The key ingredient is a close discrete consistency between the convective term in the momentum equation and the terms in the other conservation equations (mass, internal energy). As examples, the Euler equations for subsonic (in)compressible flow are discretized with such supra-conservative finite-volume methods on structured as well as unstructured grids

Time reversibility and non deterministic behaviour in oscillatorily sheared suspensions of non-interacting particles at high Reynolds numbers

Collections of inertial particles suspended in a viscous fluid and subjected to oscillatory shear have recently attracted much attention due to their relevance to a number of industrial applications and natural phenomena. It is known that, even at very low values of the flow Reynolds number, particle-to-particle interactions can lead to complex chaotic displacements despite the reversibility of the overarching fluid-dynamics (Stokes) equations. For high-Re flows, the loss of predictability after a finite time horizon is generically ascribed to the non-linear nature of the Navier-Stokes equations. Where the sources of nonlinearity are located exactly and how they influence the motion of particles, however, has not been clarified yet. We show that assuming particle interactions to be negligible, surprisingly, at high values of the Reynolds number the major source of non-deterministic behaviour comes from effects of stationary nature in the carrier flow. We report numerical simulations showing precisely how for geometries of finite extent such stationary effects emerge as the time-averaged non-linear response of the Navier-Stokes equations to the applied oscillatory forcing. They cause small deviations of the inertial particle’s trajectory from the streamlines of the instantaneous oscillatory flow, which accumulate in time until the system behaviour becomes essentially non reversible