Theory of the propagation dynamics of spiral edges of diffusion flames in von Kármán swirling flows

This analysis addresses the propagation of spiral edge flames found in von Kármán swirling flows induced in rotating porous-disk burners. In this configuration, a porous disk is spun at a constant angular velocity in an otherwise quiescent oxidizing atmosphere. Gaseous methane is injected through the disk pores and burns in a flat diffusion flame adjacent to the disk. Among other flame patterns experimentally found, a stable, rotating spiral flame is observed for sufficiently large rotation velocities and small fuel flow rates as a result of partial extinction of the underlying diffusion flame. The tip of the spiral can undergo a steady rotation for sufficiently large rotational velocities or small fuel flow rates, whereas a meandering tip in an epicycloidal trajectory is observed for smaller rotational velocities and larger fuel flow rates. A formulation of this problem is presented in the equidiffusional and thermodiffusive limits within the framework of one-step chemistry with large activation energies. Edge-flame propagation regimes are obtained by scaling analyses of the conservation equations and exemplified by numerical simulations of straight two-dimensional edge flames near a cold porous wall, for which lateral heat losses to the disk and large strains induce extinction of the trailing diffusion flame but are relatively unimportant in the front region, consistent with the existence of the cooling tail found in the experiments. The propagation dynamics of a steadily rotating spiral edge is studied in the large-core limit, for which the characteristic Markstein length is much smaller than the distance from the center at which the spiral tip is anchored. An asymptotic description of the edge tangential structure is obtained, spiral edge shapes are calculated, and an expression is found that relates the spiral rotational velocity to the rest of the parameters. A quasiestatic stability analysis of the edge shows that the edge curvature at extinction in the tip region is responsible for the stable tip anchoring at the core radius. Finally, experimental results are analyzed, and theoretical predictions are tested

Non-linear differential equations and rotating disc electrodes: Padé approximation technique.

Rotating disc electrodes are preferred devices to analyze electrochemical reactions in electrochemical cells and various rotating machinery such as fans, turbines, and centrifugal pumps. This model contains system of fully coupled and highly non-linear equations. This manuscript outlines the steady state solution of rotating disc flow coupled through the fluid viscosity, to the mass-concentration field of chemical species and heat transfer of power-law fluid over rotating disk. Furthermore, a simple analytical expression (Padé approximation) of velocity component/ self-similar velocity profiles is derived from the short and long distance expression. Our analytical results for all distance are compared with previous small and long distance and numerical solutions (Runge-Kutta method), which are in satisfactory agreement

Turbulent Von Kármán flow between two counter-rotating disks

National audienceThe present work considers the turbulent Von Kármán flow generated by two coaxial counter-rotating smooth (viscous stirring) or bladed (inertial stirring) disks enclosed by a cylindrical vessel. Numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM) are compared to velocity measurements performed at CEA. An efficient way to model the rule of straight blades is proposed. The influences of the rotational Reynolds number, the aspect ratio of the cavity, the rotating disk speed ratio and of the presence or not of impellers are investigated to get a precise knowledge of the dynamics and the turbulence properties in the Von Kármán configuration. In particular, we highlighted the transition be-tween the Batchelor and the Stewartson flow structures and the one between the merged and separated boundary layer regimes in the smooth disk case. We determined also the transition between the one cell and the two cell regimes for both viscous and inertial stirrings

CFD Study of Taylor-Like Vortices in Swirling Flows

Swirling flows are complex fluid motions that appear in various natural phenomena and man-made devices. Numerous engineering applications such as turbomachinery, jet engine combustion chambers, mixing tanks and industrial burners involve swirling flows. This wide range of applications is due to unique characteristics offered by swirling flows such as increase in mixing rate, heat transfer rate and wall shear stress. In this study the axisymmetric swirling flow behavior in the context of a hybrid rocket engine have been analyzed. While modeling the flow inside a cylindrical chamber using CFD, a similarity with the Taylor vortices instability has been observed. Similar to the classic Taylor-Couette flow system, a secondary flow field in the form of wavy toroidal vortices spaced regularly along the axial direction appear under certain critical conditions. The dimensionless control parameter governing the formation of the Taylor-like vortices is expressed as the ratio of the tangential to axial velocity components

Direct numerical simulation of axisymmetric turbulence

International audienceThe dynamics of decaying strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow, associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behaviour in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode

Adomian decomposition method simulation of Von Kármán swirling bioconvection nanofluid flow

The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk. It is known that the deformation of the disk is along the radial direction. In addition to that Stefan blowing is considered. The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit. The primitive mass conservation equation, radial, tangential and axial momentum, heat, nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall (disk surface) and free stream boundary conditions. This highly nonlinear, strongly coupled system of unsteady partial differential equations is normalized with the classical Von Kármán and other transformations to render the boundary value problem into an ordinary differential system. The emerging 11th order system features an extensive range of dimensionless flow parameters i.e. disk stretching rate, Brownian motion, thermophoresis, bioconvection Lewis number, unsteadiness parameter, ordinary Lewis number, Prandtl number, mass convective Biot number, Péclet number and Stefan blowing parameter. Solutions of the system are obtained with developed semi-analytical technique i.e. Adomian decomposition method. Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique

Channel flow with large longitudinal ribs

We present data from direct numerical simulations of flow through channels containing large, longitudinal, surface-mounted, rectangular ribs at various spanwise spacings, which lead to secondary flows. It is shown that appropriate modifications to the classical log-law, predicated on a greater wetted surface area than in a plane channel, lead to a log-law-like region in the spanwise-averaged axial mean velocity profiles, even though local profiles may be very different. The secondary flows resulting from the presence of the ribs are examined and their effects discussed. Comparing our results with the literature we conclude that the sense of the secondary flows is largely independent of the particular rib spacing whether normalised by channel depth or rib width. The strength of the secondary flows, however, is shown to depend on the ratio of rib spacing to rib width and on Reynolds number. Topological features of the secondary flow structure are illustrated via a critical point analysis and shown to be characterised in all cases by a free stagnation point above the centre of the rib. Finally, we show that if the domain size is chosen as a ‘minimal channel’ size, rather than a size which allows adequate development of the usual outer layer flow structures, the secondary flows can be affected and this leads inevitably to differences in the near-rib flows so that for ribbed channels, unlike plain channels, it is unwise to use minimal domains to identify details of the near-wall flow

Educing coherent eddy structures in air curtain systems

The work reported here comes within a broader research program dealing with ambiance separation or confining by means of air curtains (plane air jets). The process is studied experimentally by Particle Image Velocimetry (PIV). In this paper, the emphasis is put on the flow structure in the impingement region of such jet systems insofar as it is where transfers occur preferentially. More precisely, a vortex eduction method was implemented under the Matlab environment enabling both the automatic detection of 2D coherent patterns embedded in PIV velocity vector maps, and a statistical analysis of the topological and energy features of these structures. First, the approach is explained in detail. The second part of this paper is devoted to its application in the case of plane turbulent impinging simple- and twin-jets for various jet exit velocities. Results about the size, the shape, the spatial distribution and the energy content of the detected vortices are provided. Although many questions still remain open, new insights into the fashion these structures might form, organize and evolve are given providing an original picture of the plane turbulent impinging jet

Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects

In recent years, significant progress has been made in modern micro- and nanotechnologies related to applications in micro/nano-electronic devices. These technologies are increasingly utilizing sophisticated fluent media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro-organisms. Motivated by bio-nanofluid rotating disk oxygenators in medical engineering, in the current work, a mathematical model is developed for steady convective Von Karman swirling flow from an impermeable power-law radially stretched disk rotating in a Darcy porous medium saturated with nanofluid doped with gyrotactic micro-organisms. Anisotropic slip at the wall and blowing effects due to concentration are incorporated. The nano-bio transport model is formulated using non-linear partial differential equations (NPDEs), which are transformed to a set of similarity ordinary differential equations (SODEs) by appropriate transformations. The transformed boundary value problem is solved by a Chebyshev collocation method. The impact of key parameters on dimensionless velocity components, concentration, temperature and motile microorganism density distributions are computed and visualized graphically. Validation with previous studies is included. It is found that that the effects of suction provide a better enhancement of the heat, mass and microorganisms transfer in comparison to blowing. Moreover, physical quantities decrease with higher slip parameters irrespective of the existence of blowing. Temperature is suppressed with increasing thermal slip whereas nanoparticle concentration is suppressed with increasing wall mass slip. Micro-organism density number increases with the greater microorganism slip. Radial skin friction is boosted with positive values of the power law stretching parameter whereas it is decreased with negative values. The converse response is computed for circumferential skin friction, nanoparticle mass transfer rate and motile micro-organism density number gradient. Results from this study are relevant to novel bioreactors, membrane oxygenators, food processing and bio-chromatography

Lagrangian Visualization and Real-Time Identification of the Vortex Shedding Time in the Wake of a Circular Cylinder

The flow around a circular cylinder, a canonical bluff body, has been extensively studied in the literature to determine the mechanisms that cause the formation of vortices in the cylinder wake. Understanding of these mechanisms has led to myriad attempts to control the vortices either to mitigate the oscillating forces they cause, or to augment them in order to enhance mixing in the near-wake. While these flow control techniques have been effective at low Reynolds numbers, they generally lose effectiveness or require excessive power at Reynolds numbers commonly experienced in practical applications. For this reason, new methods for identifying the locations of vortices and their shedding time could increase the effectiveness of the control techniques. In the current work, two-dimensional, two-component velocity data was collected in the wake of a circular cylinder using a planar digital particle image velocimetry (DPIV) measurement system at Reynolds numbers of 9,000 and 19,000. This experimental data, as well as two-dimensional simulation data at a Reynolds number of 150, and three-dimensional simulation data at a Reynolds number of 400, is used to calculate the finite-time Lyapunov exponent (FTLE) field. The locations of Lagrangian saddles, identified as non-parallel intersections of positive and negative time FTLE ridges, are shown to indicate the timing of von Kármán vortex shedding in the wake of a circular cylinder. The Lagrangian saddle found upstream of a forming and subsequently shedding vortex is shown to clearly accelerate away from the cylinder surface as the vortex begins to shed. This provides a novel, objective method to determine the timing of vortex shedding. The saddles are impossible to track in real-time, however, since future flow field data is needed for the computation of the FTLE fields. In order to detect the Lagrangian saddle acceleration without direct access to the FTLE, the saddle dynamics are connected to measurable surface quantities on a circular cylinder in crossflow. The acceleration of the Lagrangian saddle occurs simultaneously with a maximum in lift in both numerical cases, and with a minimum in the static pressure at a location slightly upstream of the mean separation location in the numerical cases, as well as the experimental data at a Reynolds number of 19,000. This allows the von Kármán vortex shedding time, determined objectively by the acceleration of the Lagrangian saddle away from the circular cylinder, to be detected by a minimum in the static pressure at one location on the cylinder, a quantity that can be measured in real-time using available pressure sensors. These results can be used to place sensors in optimal locations on bluff bodies to inform closed-loop flow control algorithms of the timing of von Kármán vortex shedding