Vortex breakdown mechanics of a laminar confined swirling flow with large expansion ratio using a non-uniform finite difference approximation

Abrupt expansions are a very frequent geometry in mechanical engineering systems, i.e. in combustion chambers, valves, heat exchangers or impinging cooling devices. However, despite the large number of devices that use this geometry, the expanded flow behaviour still needs further research to understand and predict the full system performance. This paper presents the application of the non-uniform finite difference approximation method developed in Sanmiguel et al. for the numerical characterisation of a confined swirling laminar jet discharging with a large expansion ratio. This investigation can be considered an extension of previous work by Revuelta, but now a swirling flow is generated by a rotating pipe upstream the expansion. The structures found when a fully-developed rotating Hagen-Poiseuille flow discharges into a much larger pipe section are summarised in a bifurcation diagram, whose coordinates are the Reynolds number of the jet ( Rej) and the swirl parameter ( L), for which the time-dependent, axisymmetric and incompressible Navier-Stokes equations are integrated numerically. For values of the jet Reynolds number below 200, there is a critical value of the swirl parameter above which stable vortex breakdown appears. For values of the Reynolds number above 200, three different behaviours are observed, and each performance appears for a critical value of the swirl parameter. When increasing the swirl parameter from zero, the flow becomes axisymmetrically unstable, showing an oscillatory behaviour. If further increasing the swirl intensity, the oscillatory flow coexists with a vortex breakdown bubble and, finally, a steady vortex breakdown is reached. The expansion ratio ε considered in all the simulations is 1[Formula: see text]. In previous literature, the exactness of the limiting critical Rej and L values that define these behaviours has been found to be influenced by the variability in the inlet profile conditions, which affects the expanded flow. This enhances the importance in the present investigation to accurately simulate the discharge pipe inlet profiles.

The Search of Optimal Operating Regimes by Studying Velocity Fields in an Air Model of a Microhydroturbine

This article is devoted to the search for conditions for optimal operation of a microhydroturbine model. The experiments were carried out in air medium. Velocity fields were measured in the outlet cone of a hydraulic turbine using an LDA system. It was shown that by modeling the flow in the air, using the integral swirl parameter S, it is possible to quickly determine the optimal regime of operation of the turbine for the given parameters of the water resource.

Effect of Nozzle Confinement in the Axial Swirler

This work is devoted to the study of unsteady flow with the precessing vortex core (PVC) formed at the exit of a compact vane swirler with varying vanes angle and nozzles diameters. Amplitude-frequency characteristics of the PVC were obtained using two microphones. The modified Strouhal number dependence have showed a good generalization of the data for all nozzle diameters. The averaged and phase-averaged distributions of three components of velocity have been measured via the LDA system. The increasing the recirculation zone at increasing nozzle diameter for the swirl parameter Sg=0.53 and Re=1.5·104 was detected. The degeneration of PVC was detected for all studied nozzle diameters D = 30, 40, 50 mm. In case of smallest diameter D = 30 mm the PVC ceases to be periodic due to the absence of a recirculation zone. The three-dimensional structure of the PVC is reconstructed by the phase averaging method and visualized using the Q-criterion. Formation of the shifted recirculation zone, outer secondary vortex (OSV) and inner secondary vortex (ISV) is observed.

Onset conditions for vortex breakdown in supersonic flows

This study proposes an onset condition of shock-free supersonic vortex breakdown from the axial momentum variation, which applies in the presence or absence of a stagnation point. The condition is derived from a comprehensive approach to vortex breakdown. Supersonic breakdown appeared when the swirl parameter and Mach number were small. Moreover, bubble-type breakdowns with a stagnation point, which occur in subsonic conditions, could not occur under the supersonic condition in the present analysis. The predicted breakdowns under this condition were consistent with the results of the three-dimensional numerical simulations for Mach numbers ranging from 1.5 to 5.0. Supersonic vortex breakdowns were clearly captured by the helicity contours in the numerical results. The threshold of the downstream Mach number required for spiral breakdown with no stagnation point was also theoretically derived and verified in numerical results. These findings provide new insights into vortex breakdown in supersonic flows.

Spin-down in rotating Hagen–Poiseuille flow: a simple criterion to detect the onset of absolute instabilities

We conduct experiments in a circular pipe with rotating Hagen–Poiseuille flow (RHPF) to which we apply spin-down or impulsive spin-down to rest, in order to analyse the threshold between convective and absolute instabilities through flow visualisations in the inlet region of the pipe. For a constant value of the Reynolds number,$Re$, the finite-amplitude wave packets generated by the arbitrary perturbation that results by reducing the swirl parameter, propagate upstream or downstream depending on the initial value of the swirl parameter,$L_{0}$. In fact, the main characteristic of the flow is that the velocity front of these wave packets changes from negative to positive when absolutely unstable modes are present in the initial state. The experimental results show that spin-down becomes a precise, reliable procedure to detect the onset of absolute instabilities. In addition, we give evidence of a gradual transition for Reynolds numbers ranging from 300 to 500 where a mode shift from$n=-1$to$n=-2$appears in the absolutely unstable region.

Features of heat transfer at interaction of an impact swirl jet with a dimple

Experimental results on investigation of heat transfer at interaction of an air impact jet with a semi-spherical cavity are presented in this work. This research is continuation of investigations of turbulent jet interaction with complex surfaces and search for the method of heat transfer control. Experiments were carried out with fixed geometry of a semi-spherical cavity (DC = 46 mm) and swirl parameter (R = 0; 0.58; 1.0; 2.74). The distance between the axisymmetric nozzle and obstacle was 2?10 sizes over the nozzle diameter, and the Reynolds number varied within Re0= (1?6)?104. It was found out that with an increase in swirling heat transfer intensity decreases because of fast mixing of the jet with ambient medium. In general, the pattern of swirl jet interaction with a concave surface is complex and multifactor.

Evaluation on Leading Order Vortex Decay behind an Aircraft Using an Analytical Model

A theoretical model in this article which is used to evaluate leading order vortex decay behind an aircraft, is presented. This model is then applied to two important problems. The first evaluates safety separation distances for the super class of aircraft exemplified by the Airbus A380. The second evaluates the swirl parameter which is shown to decay to a sufficiently lowlevel that short-wave instabilities are likely to be instigated. The model uses the Oseen approximation,which assumes that in the far-field the ratio of the perturbed velocity to the aircraft velocity is small, and developed from recent publications by the first author. The atmospheric turbulence is incorporated into the model by using effective viscosity.

Experimental evidence of convective and absolute instabilities in rotating Hagen–Poiseuille flow

Experimental results for instabilities present in a rotating Hagen–Poiseuille flow are reported in this study through fluid flow visualization. First, we found a very good agreement between the experimental and the theoretical predictions for the onset of convective hydrodynamic instabilities. Our analysis in a space–time domain is able to obtain quantitative data, so the wavelengths and the frequencies are also estimated. The comparison of the predicted theoretical frequencies with the experimental ones shows the suitability of the parallel, spatial and linear stability analysis, even though the problem is spatially developing. Special attention is focused on the transition from convective to absolute instabilities, where we observe that the entire pipe presents wavy patterns, and the experimental frequencies collapse with the theoretical results for the absolute frequencies. Thus, we provide experimental evidence of absolute instabilities in a pipe flow, confirming that the rotating pipe flow may be absolutely unstable for moderate values of Reynolds numbers and low values of the swirl parameter.

RESONANCE OF NONMODAL PERTURBATIONS IN THE BATCHELOR VORTEX

The resonance phenomenon for nonmodal perturbation of Batchelor vortex is studied. For azimuthal wavenumber n = - 1, two resonant peaks appear and the left one is always dominant. For n = 1, the resonant character becomes very complicated. There is a resonant mode switch from right peak to left peak as swirl parameter q increases from 2 to infinity. The resonant wavenumber k is the largest when q approaches to infinity for n = - 1 while it is the smallest for n = 1. The maximum value of the optimal energy growth for n = 1 is at q approaches to infinity, whereas it decreases monotonically as q increases for n = - 1. The resonance for n = - 1 is the more important one.

Viscous and inviscid instabilities of non-parallel self-similar axisymmetric vortex cores

A spectral collocation method is used to analyse the linear stability, both viscous and inviscid, of a family of self-similar vortex viscous cores matching external inviscid vortices with velocity u varying as a negative power of the distance r to their axis of symmetry, u ∼ rm−2 (0 < m < 2). Non-parallel effects are shown to contribute at the same order as the viscous terms in the linear governing equations for the perturbations, and are consequently retained. The viscous stability analysis for the particular case m = 1, corresponding to Long's vortex, has recently been performed by Khorrami & Trivedi (1994). In addition to the inviscid non-axisymmetric modes of instability found by these authors, some inviscid axisymmetric unstable modes, and purely viscous unstable modes, both axisymmetric and non-axisymmetric, are also found. It is shown that, while both solution branches (I and II) of Long's vortex are destabilized by perturbations having negative azimuthal wavenumber (n < 0), only the Type II Long's vortex is also unstable for axisymmetric disturbances n = 0, as well as for disturbances with n > 0. Global pictures of instabilities of Long's vortex are given. For m > 1, the vortex cores have the interesting property of losing existence when the swirl number is larger than an m-dependent critical value, in close connection with experimental results on vortex breakdown. The instability pattern for m > 1 is similar to that found for Long's vortex, but with the important difference that the parameter characterizing the different vortices, and therefore their stability, is a swirl parameter, which is precisely the one known to govern the real problem, while this is not the case in the highly degenerate case m = 1.