The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.

Sodium overload stiffens vascular endothelial cells in vitro and promotes arterial hypertension in vivo. The hypothesis was tested that the endothelial glycocalyx (eGC), a mesh of anionic biopolymers covering the surface of the endothelium, participates in the stiffening process. By using a mechanical nanosensor, mounted on an atomic force microscope, height (∼400 nm) and stiffness (∼0.25 pN/nm) of the eGC on the luminal endothelial surface of split-open human umbilical arteries were quantified. In presence of aldosterone, the increase of extracellular sodium concentration from 135 to 150 mM over 5 days (sodium overload) led the eGC shrink by ∼50% and stiffening by ∼130%. Quantitative eGC analyses reveal that sodium overload caused a reduction of heparan sulphate residues by 68% which lead to destabilization and collapse of the eGC. Sodium overload transformed the endothelial cells from a sodium release into a sodium-absorbing state. Spironolactone, a specific aldosterone antagonist, prevented these changes. We conclude that the endothelial glycocalyx serves as an effective buffer barrier for sodium. Damaged eGC facilitates sodium entry into the endothelial cells. This could explain endothelial dysfunction and arterial hypertension observed in sodium abuse.

The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency-ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods are not suitable when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these 'rigid' approaches, we propose a new method termed spectral proper orthogonal decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical systems theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range. The SPOD requires only one additional parameter, which can be estimated from the basic time scales of the flow. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD are only marginally greater than those of the snapshot POD.

a b s t r a c tThe precessing vortex core (PVC) is a coherent flow structure that is often encountered in swirling flows in gas turbine (GT) combustors. In some swirl combustors, it has been observed that a PVC is present under non-reacting conditions but disappears in the corresponding reacting cases. Since numerous studies have shown that a PVC has strong effects on the flame stabilization, it is desirable to understand the formation and suppression of PVCs in GT combustors. The present work experimentally studies the flow field in a GT model combustor at atmospheric pressure. Whereas all non-reacting conditions and detached M-shaped flames exhibit a PVC, the PVC is suppressed for attached V-shaped flames. A local linear stability analysis is then applied to the measured time-averaged velocity and density fields. For the cases where a PVC appeared in the experiment, the analysis shows a global hydrodynamic instability that manifests in a single-helical mode with its wavemaker located at the combustor inlet. The frequency of the global mode is in excellent agreement with the measured oscillation frequency and the growth rate is approximately zero, indicating the marginally stable limit-cycle. For the attached V-flame without PVC, strong radial density/temperature gradients are present at the inlet, which are shown to suppress the global instability. The interplay between the PVC and the flame is further investigated by considering a bi-stable case with intermittent transitions between V-and M-flame. The flame and flow transients are investigated experimentally via simultaneous highspeed PIV and OH-PLIF. The experiments reveal a sequence of events wherein the PVC forms prior to the transition of the flame shape. The results demonstrate the essential role of the PVC in the flame stabilization, and thereby the importance of a hydrodynamic stability analysis in the design of a swirl combustor.

The structure of a screeching axisymmetric jet in the helical C mode at a nozzle pressure ratio of 3.4 issuing from a convergent nozzle is studied using high-resolution particle image velocimetry. Proper orthogonal decomposition (POD) is used to extract the dominant coherent structures within the jet. The first two modes produced by the POD are used to reconstruct a phase-averaged data sequence. A triple decomposition into mean, coherent and random velocity components is performed. The embedded shock structures within the jet are shown to strongly modulate the coherent axial stresses within the shear layer and to weakly modulate the random axial stresses. Analysis of the third and fourth moments of the velocity probability density function is used as an indicator of possible regions of shock–vortex interaction and thus screech tone generation. Peaks of kurtosis (flatness) occur at the second, third and fourth shock–boundary intersection points, with the radial position shifting towards the centreline with increasing downstream distance. Analysis of the coherent component of vorticity shows that the largest fluctuations in coherent vorticity occur at the high-speed side of the shear layer in an area extending from the second to the fourth shock cell. With reference to prior literature, the argument is made that it is this increased magnitude of coherent vorticity fluctuation that is the primary factor in the determination of which shock cells act as dominant screech sources.

This study provides quantitative insight into the formation of vortex breakdown and the onset of global instability in a turbulent swirling jet. A water jet is guided through a rotating honeycomb that imparts the rotational motion, passed through a contraction, and discharged into a large water tank. The flow states evolving at increasing swirl are mapped out via time-resolved particle image velocimetry. The experimental results scale properly with the swirl number based on the axial momentum flux when the commonly used boundary-layer approximations are omitted. The instantaneous velocity field reveals that vortex breakdown occurs intermittently at a wide range of swirl numbers before it appears in the mean flow. At this intermittent state, the evolving breakdown bubble oscillates heavily between two streamwise locations where the vortex core is subcritical. Upon further increasing the swirl, the breakdown oscillations decay and a region of reversed flow appears in the mean flowfield. The formation of this socalled axisymmetric breakdown state is accompanied by a supercritical-to-subcritical transition of the inflowing vortex core. The reversed flow region is found to grow linearly with increasing swirl until the flow undergoes a supercritical Hopf bifurcation to a global single-helical mode, and vortex breakdown adopts a spiral shape. The global mode shape is extracted from the particle image velocimetry snapshots by means of proper orthogonal decomposition and Fourier analysis. The present experiment reveals that, at gradually increasing swirl, the jet first transitions to an axisymmetric breakdown state that remains globally stable until a critical swirl number is exceeded. This sequence of flow states agrees well with the transient formation of vortex breakdown observed in laminar flows.Nomenclature jA sat j = saturation amplitude at limit-cycle oscillation a i = ith temporal proper orthogonal decomposition mode D = nozzle diameter E tot = total coherent energy Fx; r; m; f = complex Fourier coefficient f = frequency f s = measurement acquisition sampling frequency i = index of particle image velocimetry snapshot m = azimuthal wave number N = number of particle image velocimetry snapshots psd = power spectral density pdf = probability density function P RF = probability of reversed flow P VB = probability of vortex breakdown Re = Reynolds number; Eq. (1) r core = radial position where w x is equal to 0 r crit = Benjamin's critical radius; Eq. (9) S = swirl number; Eq. (2) S crit = critical swirl number for Hopf bifurcation; Eq. (11) S VB = minimum swirl number for vortex breakdown St = Strouhal number, fD=U m T = duration of measurement series t = time U cl = axial mean velocity at jet centerline U m = bulk velocity at zero swirl V = mean velocity vector, (U; V; W) v = instantaneous velocity vector, u; v; w v = coherent velocity vector, (ũ;ṽ;w) v 0 = fluctuating velocity vector, (u 0 ; v 0 ; w 0 ) x = position vector in Cartesian coordinates, (x; y; z) x = position vector in cylindrical coordinates, (x; r; ) x...

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