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This paper presents bifurcation analyses characterising the nonlinear dynamics of fully developed laminar annular jets with respect to the centrebody diameter${ {d}}$, Reynolds number${ {Re}}$, and swirl ratio${ {S}}$. Similar flows appear in numerous applications and feature a vibrant range of topological and dynamical characteristics associated with phenomena including shear layer separation and vortex breakdown. Our results begin by describing the non-monotonic evolution of the axisymmetric jet's steady topology under varying${ {S}}$. In accord with earlier reports, the jet progresses through a sequence of wake, breakdown and wall jet regimes in a qualitatively similar manner across a wide span of${ {d}}$and${ {Re}}$values. In the wake regime, the non-swirling jet bifurcates to a plane-symmetric, but not axisymmetric, steady flow pattern beyond a${ {d}}$-dependent critical${ {Re}}$value. With further increase in${ {Re}}$, the steady non-swirling jet destabilises subsequently via multiple distinct Hopf bifurcations. Introducing${ {S}}>0$to the jet also induces unsteadiness by twisting the singly azimuthally periodic ($|m|=1$) asymmetric wake structure and causing it to precess periodically in time about the central axis. Intermediate swirl stabilises this unsteady dynamics and restores the jet's axisymmetry. This stabilising effect is then reversed in the breakdown regime at higher${ {S}}$, where a variety of different$|m|=1$and$|m|=2$instabilities bifurcate from the steady flow as${ {S}}$is increased. Several instances of hysteresis and subcritical behaviour are reported and discussed, including one that manifests precessing vortex core oscillations.

Hydrogen (H2) fuel for gas turbines is a promising approach for long duration storage and dispatchable utilization of intermittent renewable power. A major global discussion point, however, is the potential air quality impact of hydrogen combustion associated with nitrogen oxide (NOx) emissions. Indeed, several studies in the combustion literature have reported elevated NOx concentrations in terms of dry ppmv NOx at 15% oxygen (O2) as a fuel’s H2 fraction is increased. Yet, as emphasized in this work, this practice of directly comparing emissions on the basis of dry ppmv at a reference O2 concentration (ppmvdr) is inappropriate across hydrogen and hydrocarbon fuel blends due to differing concentration changes induced by drying and referencing the corresponding exhaust gasses. This paper addresses three distinct approaches for comparing emissions consistently across fuel blends. Furthermore, it presents examples that quantify the differences in the apparent pollutant emissions between each approach and the usual ppmvdr reporting practice across the full range of hydrogen-methane mixture ratios. In the first approach, ppmvdr emissions values are related to their actual volume concentration. Here, our calculations demonstrate that hydrogen and methane flames producing the same true pollutant concentration exhibit a 40% relative difference in ppmvdr values, resulting in a significant potential exaggeration of NOx emissions for high %H2 fuels. However, this concentration-based approach does not account for changes in the volumetric flow rate of exhaust gasses or the slightly different amounts of heat release required to achieve the same flame temperature across fuels. These effects are captured naturally in the second approach, where the emissions are quantified in terms of the emitted mass per unit of heat release. With this cycle-independent approach, our comparative calculations at equal mass-per-heat emission rates reveal 36% higher ppmvdr values for hydrogen flames than methane flames. Finally, the third approach accounts not only for the thermodynamic properties of the mixture, but also for the system’s overall cycle efficiency, which is shown to depend weakly upon the fuel composition. This method quantifies emissions in terms of the emitted mass per unit of useful shaft work output, a metric also used by environmental regulators. Illustrative results within a simulated F-class gas turbine cycle are presented, indicating 39% higher ppmvdr values for hydrogen flames at equal mass-per-work emission rates. Hence, in all of the considered approaches, ppmvdr emissions values are inflated for H2 fuel blends relative to hydrocarbon fuels, making them unsuitable for direct comparisons of emissions among conventional and alternative fuels.

Flow data are often decomposed using proper orthogonal decomposition (POD) of the space–time separated form, $\boldsymbol {q}'\left (\boldsymbol {x},t\right )=\sum _j a_j\left (t\right )\boldsymbol {\phi }_j\left (\boldsymbol {x}\right )$ , which targets spatially correlated flow structures in an optimal manner. This paper analyses permuted POD (PPOD), which decomposes data as $\boldsymbol {q}'\left (\boldsymbol {x},t\right )=\sum _j a_j\left (\boldsymbol {n}\right )\boldsymbol {\phi }_j\left (s,t\right )$ , where $\boldsymbol {x}=(s,\boldsymbol {n})$ is a general spatial coordinate system, $s$ is the coordinate along the bulk advection direction and $\boldsymbol {n}=(n_1,n_2)$ are along mutually orthogonal directions normal to the advection characteristic. This separation of variables is associated with a fundamentally different inner product space for which PPOD is optimal and targets correlations in $s,t$ space. This paper presents mathematical features of PPOD, followed by analysis of three experimental datasets from high-Reynolds-number, turbulent shear flows: a wake, a swirling annular jet and a jet in cross-flow. In the wake and swirling jet cases, the leading PPOD and space-only POD modes focus on similar features but differ in convergence rates and fidelity in capturing spatial and temporal information. In contrast, the leading PPOD and space-only POD modes for the jet in cross-flow capture completely different features – advecting shear layer structures and flapping of the jet column, respectively. This example demonstrates how the different inner product spaces, which order the PPOD and space-only POD modes according to different measures of variance, provide unique ‘lenses’ into features of advection-dominated flows, allowing complementary insights.

This paper characterises the steady and time-periodic behaviour of swirling jets using numerical bifurcation analysis. Its objective is to elucidate the dynamics of fully developed, unconfined, laminar swirling jets under variations in the Reynolds number $\textit {Re}$ and swirl ratio $S$ . Within the $(0,0)\leq (\textit {Re},S)\leq (300,3)$ range, the steady, axisymmetric flow exhibits several distinct patterns ranging from a quasi-columnar jet along the central axis at low $S$ to a radial jet attached to the containing wall at high $S$ with various forms of vortex breakdown in between. A cusp bifurcation appears in the steady solution manifold which triggers bistable behaviour due to a competition between inner and outer low pressure regions associated with vortex breakdown and entrainment of the ambient fluid, respectively. Instability of the steady flow is linked to eigenmodes which are singly ( $|m|=1$ ) or doubly ( $|m|=2$ ) azimuthally periodic, although additional instabilities with other azimuthal wavenumbers occur at $(\textit {Re},S)$ -values beyond the leading neutral curves. The various branches of limit cycle solutions stemming from these neutral curves are associated with both super- and sub-critical Hopf bifurcations. The resulting unsteady flow fields exhibit a wide array of rotating, three-dimensional flow structures, and comparisons between the time-averaged and steady flow patterns highlight the role of these unsteady nonlinear interactions on the overall behaviour of swirling jets. Similarities and differences between this laterally unconfined jet and broader classes of swirling flows, including confined swirling jets and unconfined vortex models, are also discussed.

This paper presents 5 kHz stereo particle image velocimetry and OH planar laser induced fluorescence measurements of transversely forced swirl flames. The presence of transverse forcing on this naturally unstable flow both influences the natural instabilities, as well as amplifies disturbances that may not necessarily manifest themselves during natural oscillations. By manipulating the structure of the acoustic forcing field, both axisymmetric and helical modes are preferentially excited away from the frequency of natural instability. The paper presents a method for spatially interpolating the phase locked $r{-}z$ and $r{-}\unicode[STIX]{x1D703}$ planar velocity and flame position data, extracting the full three-dimensional structure of the helical disturbances. These helical disturbances are also decomposed into symmetric and anti-symmetric disturbances about the jet core, showing the subsequent axial evolution (in magnitude and phase) of each of these underlying disturbances. It is shown that out-of-phase acoustic forcing excites $m=\pm 1$ modes, but the flow field preferentially amplifies the counter-winding, co-rotating helical disturbance over the co-winding, counter-rotating helical disturbance. This causes the flow and flame to transition from a transverse flapping near the jet exit to a precessing motion further downstream. In contrast, in-phase forcing promotes axisymmetric $m=0$ disturbances which dominate the flow field over the entire axial domain. In both cases, the amplitudes of the anti-symmetric disturbances about the jet core grow with downstream distance before saturating and decaying, while the symmetric disturbances appear nearly negligible. It is suggested that this saturation and decay is due to linear effects (e.g. a negative spatial growth rate), rather than nonlinear interactions.

This study of an externally forced, amplifier-type turbulent reacting swirling annular jet presents a low-order model for the flow response to transverse acoustic excitation and compares the model's predictions with experimental measurements. The model is formulated based on linear stability calculations about the turbulent mean flow and eddy viscosity fields obtained from separate measurements of the unforced flow. The stability calculations yield weakly global spatial modes associated with the forcing frequency, which serve as a basis upon which to project the forcing input. Thus, the model constitutes a hydrodynamic transfer function connecting the input forcing to the output coherent flow response through the linearized low Mach number compressible Navier–Stokes equations. Following a detailed presentation of the stability analysis underlying the model, the response predictions are evaluated against previously reported experiments where the jet was transversely excited at both an acoustic pressure node and an antinode. The results reveal excellent agreement between the predicted response and the measured fluctuating fields, suggesting that the low-order linear model based on the turbulent mean flow field captures the essential physics of the mode selection process in this forced configuration. This work provides further evidence that linear hydrodynamics govern the growth and decay of spatiotemporally coherent vortical structures in the swirling, turbulent jet flame, and, in particular, explains the dominance of co-rotating spiral structures.

This work is motivated by the thermoacoustic instability challenges associated with ultra-low emissions gas turbine (GT) combustors. It demonstrates the first use of high-speed dual-plane orthogonally-polarized stereoscopic-particle image velocimetry (PIV) and synchronized OH planar laser-induced fluorescence in a premixed swirling flame. We use this technique to explore the effects of combustion and longitudinal acoustic forcing on the time- and phase-averaged flow field—particularly focusing on the behavior of the Reynolds stress in the presence of harmonic forcing. We observe significant differences between ensemble-averaged and time-averaged Reynolds stress. This implies that the large-scale motions are nonergodic, due to coherent oscillations in Reynolds stress associated with the convection of periodic vortical structures. This result has important implications on hydrodynamic stability models and reduced-order computational fluid dynamics simulations, which do show the importance of turbulent transport on the problem, but do not capture these coherent oscillations in their models.

In the current work, polycrystalline silicon microdevices are treated with a 1H,1H,2H,2H-Perfluorodecyltrichlorosilane (FDTS) self-assembled monolayer (SAM) film. Using a microelectromechanical systems-based tribometer, the adhesion characteristics of the FDTS-treated surfaces are compared to those of untreated surfaces over a range of approximately 10 × 106 impact cycles. FDTS-treated surfaces showed a lower zero-hour adhesion force compared to untreated surfaces under identical environmental conditions. The presence of the monolayer did not have a discernible effect on the number of cycles to initiate the surface degradation that was manifested as an increase in the adhesion force. Based on trends in degradation, it is concluded that similar chemical and physical wear mechanisms dominate the evolution of adhesion in both treated and untreated devices. The qualitative results of the experiment are reinforced by molecular dynamics (MD) simulations of a single nanoasperity contact coated with an octadecyltrichlorosilane (ODTS) SAM. MD simulations show cleavage of bonds along the aliphatic chains of ODTS resulting in adhesion fluctuations. In agreement with experimental observations, the MD simulation shows a logarithmic increase in adhesion force with increasing number of cycles. MD simulations also predict a logarithmic decrease in adhesion energy with increasing cycles. These results provide insight into the physicohemical changes occurring during repetitive impact of surfaces coated with low surface energy films.