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.

Implantable left ventricular assist devices (LVADs) became the therapy of choice in treating end-stage heart failure. Although survival improved substantially and is similar in currently clinically implanted LVADs HeartMate II (HM II) and HeartWare HVAD, complications related to blood trauma are frequently observed. The aim of this study was to compare these two pumps regarding their potential blood trauma employing computational fluid dynamics. High-resolution structured grids were generated for the pumps. Newtonian flow was calculated, solving Reynolds-averaged Navier-Stokes equations with a sliding mesh approach and a k-ω shear stress transport turbulence model for the operating point of 4.5 L/min and 80 mm Hg. The pumps were compared in terms of volumes subjected to certain viscous shear stress thresholds, below which no trauma was assumed (von Willebrand factor cleavage: 9 Pa, platelet activation: 50 Pa, and hemolysis: 150 Pa), and associated residence times. Additionally, a hemolysis index was calculated based on a Eulerian transport approach. Twenty-two percent of larger volumes above 9 Pa were observed in the HVAD; above 50 Pa and 150 Pa the differences between the two pumps were marginal. Residence times were higher in the HVAD for all thresholds. The hemolysis index was almost equal for the HM II and HVAD. Besides the gap regions in both pumps, the inlet regions of the rotor and diffuser blades have a high hemolysis production in the HM II, whereas in the HVAD, the volute tongue is an additional site for hemolysis production. Thus, in this study, the comparison of the HM II and the HVAD using numerical methods indicated an overall similar tendency to blood trauma in both pumps. However, influences of turbulent shear stresses were not considered and effects of the pivot bearing in the HM II were not taken into account. Further in vitro investigations are required.

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.

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The internal flow characteristics of a fluidic oscillator were investigated experimentally. Particle image velocimetry and time-resolved pressure measurements were employed in water to visualize and quantify the internal flow patterns. The method of proper orthogonal decomposition was applied to random flow field snap shots for phase reconstruction of one oscillation cycle. The resulting phase-averaged information provides detailed insight into the oscillation mechanism as well as into the interaction between the main chamber of the oscillator and its feedback channels. A growing recirculation bubble between the main jet and the attachment wall is identified as an underlying mechanism that causes the main jet to oscillate. The flow field measurements are complemented by time-resolved pressure measurements at various internal locations which yield additional comprehension of the switching behavior and accompanying timescales. Geometrical features, in particular at the inlet and outlet of the mixing chamber, are found to have a crucial impact on important flow characteristics such as oscillation frequency and jet deflection.Peer ReviewedPostprint (published version

An experimental method to determine the thermoacoustic properties of a gas turbine combustor using a lean-premixed low emission swirl stabilized burner is presented. To model thermoacoustic oscillations, a combustion system can be described as a network of acoustic elements, representing for example fuel and-air supply, burner and flame, combustor, cooling channels, suitable terminations, etc. For most of these elements, simple analytical models provide an adequate description of their thermoacoustic properties. However, the complex response of burner and flame (involving a three-dimensional flow field, recirculation zones, flow instabilities and heat release) to acoustic perturbations has -at least in a first step -to be determined by experiment. In our approach, we describe the burner as an active acoustical two-port, where the state variables pressure and velocity at the inlet and the outlet of the two port are coupled via a four element transfer matrix. This approach is similar to the "black box" theory in communication engineering. To determine all four transfer matrix coefficients, two test states, which are independent in the state vectors, have to be created. This is achieved by using acoustic excitation by loudspeakers upstream and downstream of the burner, respectively. In addition, the burner might act as an acoustic source, emitting acoustic waves due to an unsteady combustion process. The source characteristics were determined by using a third test state, which again must be independent from the two other state vectors. In application to a full size gas turbine burner, the method's accuracy was tested in a first step without combustion and the results were compared to an analytical model for the burner's acoustic properties. Then the method was used to determine the burner transfer matrix with combustion. An experimental swirl stabilized premixed gas-turbine burner was used for this purpose. The treatment of burners as acoustic two-ports with feedback including a source term and the experimental determination of the burner transfer matrix is novel. NOMENCLATURE

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...