Spatial Stability Analysis Research Articles

Nested Cross-Validation for HBV Conceptual Rainfall–Runoff Model Spatial Stability Analysis in a Semi-Arid Context

Nested Cross-Validation for HBV Conceptual Rainfall–Runoff Model Spatial Stability Analysis in a Semi-Arid Context

Connections between propulsive efficiency and wake structure via modal decomposition

We present experiments on oscillating hydrofoils undergoing combined heaving and pitching motions, paying particular attention to connections between propulsive efficiency and coherent wake features extracted using modal analysis. Time-averaged forces and particle image velocimetry measurements of the flow field downstream of the foil are presented for a Reynolds number of $Re=11\times 10^3$ and Strouhal numbers in the range $St=0.16\unicode{x2013}0.35$ . These conditions produce 2S and 2P wake patterns, as well as a near-momentumless wake structure. A triple decomposition using the optimized dynamic mode decomposition method is employed to identify dominant modal components (or coherent structures) in the wake. These structures can be connected to wake instabilities predicted using spatial stability analyses. Examining the modal components of the wake provides insightful explanations into the transition from drag to thrust production, and conditions that lead to peak propulsive efficiency. In particular, we find modes that correspond to the primary vortex development in the wakes. Other modal components capture elements of bluff body shedding at Strouhal numbers below the optimum for peak propulsive efficiency and characteristics of separation for Strouhal numbers higher than the optimum.

Fluid-Dynamic Mechanisms Underlying Wind Turbine Wake Control with Strouhal-Timed Actuation

A reduction in wake effects in large wind farms through wake-aware control has considerable potential to improve farm efficiency. This work examines the success of several emerging, empirically derived control methods that modify wind turbine wakes (i.e., the pulse method, helix method, and related methods) based on Strouhal numbers on the O(0.3). Drawing on previous work in the literature for jet and bluff-body flows, the analyses leverage the normal-mode representation of wake instabilities to characterize the large-scale wake meandering observed in actuated wakes. Idealized large-eddy simulations (LES) using an actuator-line representation of the turbine blades indicate that the n=0 and ±1 modes, which correspond to the pulse and helix forcing strategies, respectively, have faster initial growth rates than higher-order modes, suggesting these lower-order modes are more appropriate for wake control. Exciting these lower-order modes with periodic pitching of the blades produces increased modal growth, higher entrainment into the wake, and faster wake recovery. Modal energy gain and the entrainment rate both increase with streamwise distance from the rotor until the intermediate wake. This suggests that the wake meandering dynamics, which share close ties with the relatively well-characterized meandering dynamics in jet and bluff-body flows, are an essential component of the success of wind turbine wake control methods. A spatial linear stability analysis is also performed on the wake flows and yields insights on the modal evolution. In the context of the normal-mode representation of wake instabilities, these findings represent the first literature examining the characteristics of the wake meandering stemming from intentional Strouhal-timed wake actuation, and they help guide the ongoing work to understand the fluid-dynamic origins of the success of the pulse, helix, and related methods.

Simulation of instability and sound production in a turbulent channel flow with an acoustic liner

Acoustic liners are used to absorb sound waves in ducts with flow. These liners can become unstable and some experiments have shown that in this case they do not damp sound as they should. This situation is addressed numerically. A turbulent plane channel flow at a friction Reynolds number of about 400 is computed using direct numerical simulation of the compressible Navier–Stokes equations. The channel is in spatial development, and the inflow is fully turbulent, non-reflecting, and can inject an incident acoustic wave. The liner is modeled by an acoustic impedance placed on a portion of the channel bottom wall. Several liners are simulated, stable or unstable. Spatial instabilities are observed and well modeled by a linear spatial stability analysis. The scattering of the instability at the liner trailing edge triggers backpropagating acoustic waves, as well as sound emission downstream of the liner. Backpropagating waves make a feedback loop possible on the liner, so that instabilities are observed even in convectively unstable situations without excitation. The effect of an incident acoustic wave is discussed.

Numerical study of the steady core-annular flow in a focusing geometry in the presence of soluble surfactants

The steady state core annular flow of two immiscible fluids in the presence of soluble surfactants is investigated numerically in an axisymmetric tubular or flow focusing geometry. The two immiscible fluids form an interface onto which surfactants can be adsorbed/desorbed from the annular fluid where they are dissolved. The finite element method is employed to discretize the governing equations using the spine method to create the computational mesh, follow the shape of the interface and the axisymmetric wall and capture the flow domain. An unknown pressure distribution is imposed along the interface that quantifies the pressure discontinuity, while allowing the bulk pressure to remain continuous in each phase. GMRES is employed to accommodate the nearly singular nature of the jacobian matrix. The bulk surfactant concentration varies only inside a thin boundary layer of thickness δ∼Pe−1, which justifies omission of the advection-diffusion equation in the annulus bulk. Simulations reveal that the onset of Marangoni stresses tends to decelerate the velocity at the interface which is seen to translate towards the wall/axis of symmetry when the more viscous fluid is the inner/outer fluid, respectively. Finally, simulations in flow-focusing nozzles capture the development of spatially growing instabilities in the downstream region of the interface, with wavelength on the order of the nozzle radius, especially when the outer fluid is more viscous or when the surfactant concentration increases. Raising the volumetric flow rate in the annular region suppresses growth of waves due to interfacial friction. Spatial stability analysis verifies downstream growth of waves and recovers the relevant wavelength. Possible repercussions on the onset of jetting instabilities in devices with liquid focusing are discussed.

Impact of density stratification and azimuthal velocity on the growth of coherent structures in a convectively unstable swirl flame

Large-scale coherent structures resulting from hydrodynamic instabilities can interact with turbulent swirl flames and lead to combustion instabilities. The present work investigates the impact of density stratification and azimuthal velocity on the growth of coherent structures in a convectively unstable swirl flame. Flame structure and flow field are measured by simultaneous hydroxyl planar laser-induced fluorescence and stereoscopic particle image velocimetry (S-PIV) at a repetition rate of 10 kHz and are analyzed by using the spectral proper orthogonal decomposition (SPOD) and spatial linear stability analysis (LSA). The SPOD reveals that the dominant symmetric and anti-symmetric modes are within the frequency range from 156 to 585 Hz, accounting for more than 25% of the turbulent kinetic energy. The spatial growths of these coherent structures are quantified by the LSA that predicts large growth rates near the nozzle exit with the corresponding frequency band matching well with the SPOD analysis. The LSA results show that both density stratification and azimuthal velocity have little effect on the instability frequencies of the most spatially unstable modes. However, the flame-induced density stratification suppresses the growth of the coherent structures by altering the pressure gradient and viscous diffusion, whereas the azimuthal velocity promotes flow instabilities through the changes in convection and production of the coherent perturbations. The results also suggest that the conventional PIV technique with two-component velocity measurement is inadequate for linear modeling of coherent structures, and the density stratification should also be taken into account in convectively unstable swirl flames.

The axisymmetric screech tones of round twin jets examined via linear stability theory

Spatial linear stability analysis is used to study the axisymmetric screech tones generated by twin converging round nozzles at low supersonic Mach numbers. Vortex-sheet and finite-thickness models allow for identification of the different waves supported by the flow at different conditions. Regions of the frequency–wavenumber domain for which the upstream-propagating guided jet modes are observed to be neutrally stable are observed to vary as a function of solution symmetry, jet separation,$S$, and the velocity profile used. Screech-frequency predictions performed using wavenumbers obtained from both models agree well with experimental data. Predictions obtained from the finite-thickness model better align with the screech tones measured experimentally and so are seen to be an improvement on predictions made with the vortex sheet. Additionally, results from the finite-thickness model predict both symmetric and antisymmetric screech tones for low$S$that are found in the vortex-sheet model only at greater$S$. The present results indicate that the feedback loop generating these screech tones is similar to that observed for single-jet resonance, with equivalent upstream and downstream modes.

The stabilizing effect of grooves on Görtler instability-induced boundary layer transition in hypersonic flow

Görtler vortex-induced hypersonic boundary layer transition controlled by grooves is investigated using direct numerical simulations and spatial bi-global stability analysis. In the simulations, Görtler vortices are excited by wall steady blowing and suction with spanwise wavelengths of 3 mm. It is found that when the wall is covered with grooves, the Görtler streaks keep more regular even at the end of the model. In addition, the skin friction coefficient is reduced efficiently. Furthermore, the wall-normal and spanwise velocity shear are both reduced, suppressing growths of secondary instabilities. In conclusion, grooves can delay Görtler vortex-induced transition by modifying the Görtler streaks structure and instability, which would shed light on hypersonic boundary layer transition control.

Acoustic emission due to the interaction between shock and instability waves in two-dimensional supersonic jet flows

An analytical model is developed to study the sound produced by the interaction between shock and instability waves in two-dimensional supersonic jet flows. The jet is considered to be of vortex-sheet type and two-dimensional Euler equations are linearized to determine the governing equations for shock and instability waves and their interaction. Pack's model is used to describe shock waves, while instability waves are calculated using spatial stability analysis. The interaction between shock and instability waves can be solved analytically by performing Fourier transform and subsequently using the method of steepest descent. Sound produced by the interaction between the instability wave and a single shock cell is studied first, after which that due to a number of cells follows. We find that the model developed in this study can correctly predict the frequencies of the fundamental screech tone and its first and second harmonics. We show that the predicted sound directivity, even from a single shock cell, is in good agreement with experimental data. In particular, this model shows the strongest noise emission close to the upstream direction but the emitted noise starts to rapidly decay as the observer angle approaches $180^\circ$ , which is in accordance with experimental results; this suggests that the effective noise from a single shock cell is far from of the monopole type as assumed in the classical Powell's model. We find that the noise directivity is very sensitive to the local growth rate of the instability waves and the noise is generated primarily through the Mach wave mechanism.

Linear stability of real-fluid mixing layers at supercritical pressures

Linear stability analysis is a useful tool for the exploration of the initial evolution of flow motions in mixing layers. A real fluid mixing layer exhibits strong property variations and, thus, may present stability behaviors distinct from its ideal gas counterpart. The present study carries out spatial and temporal stability analyses of nitrogen mixing layers at supercritical conditions, with special attention to the density stratification induced by the temperature and velocity gradients across the mixing layer. The differences between the ideal gas and real fluid approaches are discussed. The maximum spatial growth rate and the most unstable frequency evaluated based on the real fluid density profile are found to be substantially lower than their ideal gas counterparts near the critical point, where an inflection of the density distribution occurs in the mixing layer. Across the inflection point, the strong density stratification arising from the real fluid effect tends to stabilize the mixing layer. The maximum growth rate and the most unstable frequency do not show a monotonic trend with the ratios of temperature and density. In the absence of the inflection point, however, the mixing layer is destabilized and features a substantially higher maximum spatial growth rate at lower ratios of density and temperature. The most unstable frequency and the maximum spatial growth rate increase with increasing pressure. The real fluid effect diminishes when the pressure is away from the critical value or when there is no inflection point in the density profile. The temporal stability analysis also indicates that a detailed density distribution plays a key role in dictating the stability characteristics of mixing layers at supercritical pressures.

Instability mechanisms in meandering streamwise vortex pairs of upswept afterbody wakes

Wakes of upswept afterbodies are often characterized by counter-rotating streamwise vortex pairs which meander in space. One application concerns aft regions of cargo aircraft, which are characterized by a relatively flat upswept base. Here we consider a canonical configuration comprised of a cylinder with upswept basal surface. The resulting longitudinal vortices, which are much closer to each other than wing-tip vortices, can adversely influence paratrooper and cargo drop operations as well as trailing aircraft. The unsteady dynamics of these vortices are examined using spatio-temporally resolved Large-Eddy Simulations (LES) and stability considerations. Emphasis is placed on understanding the potential instability dynamics responsible for meandering, which was observed, characterized and quantified at a representative location downstream of the body. The dynamics is then successfully mapped to a matched Batchelor vortex pair, and spatial and temporal stability analyses are performed with both counter-rotating vortices in the computational domain. Both spatial and temporal analyses reveal dipole structures associated with |m|=1 elliptic modes as dominant modes in afterbody vortices. A short-wave elliptic instability mode is found to dominate the meandering motion in the vortex pair; this mode was stable in the case of an isolated vortex. Further, the strain due to axial velocity plays a key role in the instability and therefore breakdown. The low frequency of the unstable mode (Strouhal number StD≃0.3 based on cylinder diameter) is consistent with the spectral analysis of meandering in the LES. Stability analyses at very low-wavenumber do not exhibit any unstable mode suggesting an absence of the Crow instability.

Global and local modal characteristics of supersonic open cavity flows

Flows past cavities at high-speeds have become increasingly important in applications such as flame-holding and propulsion unstart control. Recently maturated linear techniques have helped discern the underlying mechanisms in the subsonic and low supersonic speed regime (M∞<1.4). Here, we combine these linear methods with fully non-linear two- and three-dimensional simulations to assimilate the significant changes observed when the Mach number is increased further to the 1.4≤M∞≤3 range. The resolvent method is first employed to analyze cavity-shear layer coupled oscillations and modal characteristics, which are found to differ in key respects from those reported at lower Mach numbers. At higher speeds, more 2D coupled modes are obtained with the dominant modes containing secondary waves displaying elaborate patterns. The role of the shear layer on the cavity dynamics is then examined with local spatial stability analyses. In addition to the well-known Kelvin–Helmholtz instability encountered in the subsonic and transonic regimes, forward-propagating (k+) supersonic shear layer instabilities are detected at higher speeds. These are associated with Mach wave reflections between the shear layer and the cavity floor and may introduce higher order coupled modes. Furthermore, 3D modal analysis indicates a shift toward the dominance of 3D modes compared to 2D modes; although consistent with compressible free shear layer observations, 2D cavity modes remain significant to higher convective Mach number. When the Reynolds number is increased, resolvent-based mode shapes and frequencies continue to compare favorably with Dynamic Mode Decomposition of large-eddy simulations because of inviscid instability dominance.

The effect of wavy surface on boundary layer instabilities of an airfoil

PurposeThe purpose of this paper is to investigate airfoil’s tonal noise reduction mechanism when deploying surface irregularities, such as surface waviness by means of spatial stability analyses.Design/methodology/approachFlow field calculations over smooth and wavy-surface NACA 0012 airfoils at 2° angle of attack and at Reynolds number of 200,000 are performed using the large eddy simulation (LES) approach. Three geometrical configurations are considered: a smooth NACA 0012 airfoil, wavy surface on the suction side (SS) and wavy surface on the pressure side (PS). The spatial stability analyses using the LES-generated flow fields are conducted and validated against the Orr-Sommerfeld stability analysis for the smooth airfoil configuration.FindingsThe spatial stability analyses show that inclusion of the wavy-type modification on the SS of the airfoil does not lead to altering of the acoustic feedback loop mechanism, with respect to the mechanism observed for the smooth airfoil configuration. In contrast, applying the surface modifications to the airfoil PS leads to a significant reduction of the amplification range of disturbances in the vicinity of the trailing edge for the frequency of the acoustic feedback loop mechanism.Practical implicationsThe spatial analyses using, for example, LES-generated flow fields can be widely used to determine acoustic sources and associated distributions of amplifications for a wide range of applications in the aeroacoustics.Originality/valueThe spatial stability analysis approach based on flow fields computed a priori using the LES method has been introduced, validated and used to determine behaviour of the acoustic feedback loop when accurate reconstruction of geometry effects is required.

Stability analysis and transition prediction of streamwise vortices over a yawed cone at Mach 6

An investigation into the linear instability of streamwise vortices over a yawed blunt cone with a half-angle of 7° at 6° angle of attack, a free-stream Mach number of 6, and a Reynolds number of 1.0 × 107/m was performed. The steady laminar base flow obtained using direct numerical simulation (DNS) has a mushroom structure. Three classes of unstable modes (inner mode, outer mode, and Mack mode modified by the streamwise vortices) were identified using a two-dimensional spatial global stability analysis (bi-global). Among them, the inner mode and the modified Mack mode were discovered for the first time for such a configuration. Notably, the inner mode appears only over a short distance upstream of the cone, and its energy is mainly in the vicinity of the symmetry plane of the mushroom structure. By comparing with DNS results, it was shown that multiple instability modes can coexist physically during the transition in the leeward plane. In addition, the eN method based on global stability theory was used to predict the location of the transition along the centerline on the leeward side of the cone. It was found that the inner modes grow rapidly in the upstream region, while the outer mode near the stem of the mushroom structure dominates the transition in the downstream region. Further analysis suggests that the inner modes dominate the transition only in a noisy environment, whereas the traditional centerline modes dominate the transition in quiet free-stream conditions.

Investigation on long-term daily load follow operation capability of soluble boron-free SMR

Soluble boron-free reactors inherently have larger reactivity feedback than conventional pressurized water reactors during power transients. The purpose of this study is to verify the capability of the long-term load follow operation with only control rods for the soluble boron-free small modular reactors. The effects of the long-term load follow operation on burnup distribution, power distribution, reactivity balance and spatial xenon stability are investigated throughout the whole cycle.The reactivity balance results show that the control rod design of the soluble boron-free SMR successfully manages the reactivity changes introduced by power and xenon changes during the daily load follow operation. The spatial xenon stability analysis demonstrates that the SMR model has enough capability to suppress the axial and quadrant xenon oscillation without a second peak during the load follow operation. The load follow simulation results showed that safety parameters including peaking factor, axial offset and shutdown margin satisfy design limits.

P1389Periodicity and Spatial Stability of Complex Propagation Patterns in Atrial Fibrillation

Abstract Introduction Non-contact charge density mapping identifies complex wavefront propagation including localised rotational activation (LRA), localised irregular activation (LIA) and focal firing (FF). However, the duration of mapping required to reveal underlying patterns and their temporal stability is unknown. Purpose We sought to evaluate the variability in propagation patterns over increasing durations of recordings up to 30 seconds and examine the stability of these patterns between 2 separate maps with the aim of identifying the minimum duration required to reveal underlying patterns and how they represent the stable arrhythmia substrate. Methods Patients undergoing first time AcQMap guided catheter ablation were studied. 30s recordings of left atrial propagation were analysed. LIA, LRA, and FF were quantified for frequency, percentage time present and percentage surface area affected (for FF only frequency was assessed) at increasing durations up to 30s in 1s increments. At each incremental recording duration the percentage change in each variable was calculated. For occurrence frequency the results for every possible combination of maps of increasing duration within the 30s recording were compared whilst for occurrence time and surface area a 5s moving average at 1s increments was calculated. The point at which variability was seen to plateau represents the minimum optimal mapping duration. Spatial stability was assessed by correlating the frequency of patterns at each vertex of the anatomy over 2 separate 30s recordings. Stability of regions with the most repetitive patterns were compared using Cohen’s kappa statistic. Results 15 patients were analysed (age 63 ± 9, 10 male, BMI 30 ± 5, CHA2DS2Vasc 1 ± 1.3, ejection fraction 54 ± 12%, left atrial diameter 46 ± 7mm, paroxysmal 1, persistent 14) with 11 included in the spatial stability analysis due to availability of recordings of sufficient duration. LRA demonstrated most variability followed by LIA and FF. Variability in LIA, LRA and FF decrease at increasing durations. LIA and FF variability plateau by 13 and 17s respectively. LRA plateaus at 23s. Variability of <10% is reached in all parameters at 18s. LIA demonstrated the greatest stability with average R2 of 0.76 ± 0.14 (figure). Average R2 for LRA and FF were 0.45 ± 0.16 and 0.47 ± 0.12. Low frequency focal firings were widely distributed across the atrial surface. For FF occurring at a frequency ≥10 over the 30s, average R2 value was 0.65 ± 0.14. Cohen kappa statistic was 0.70 for LIA and 0.45 for LRA. Conclusion Mapping durations of ≥23s are required to identify all temporally variable propagation patterns although shorter durations will identify less variable LIA and FF. LIA demonstrates high spatiotemporal stability and may best reflect disrupted conduction caused by the underlying atrial substrate and tissue architecture. Regions of high frequency FF are temporally stable and may represent important targets for ablation. Abstract Figure 1

Instability and dripping of electrified liquid films flowing down inverted substrates

The multiphysics problem of a liquid film wetting an inclined substrate under the influence of a stabilizing electric field is considered. The use of a spatial stability analysis to predict the threshold of dripping suppression is assessed via reduced-order modeling and direct numerical simulation.

Анализ устойчивости прямоточных струй с градиентом плотности

Using Chebyshev spectral collocation method, the temporal and spatial stability analysis of a round jet with tangential velocity profile and transverse density gradient is carried out. The characteristic frequencies, wave numbers and eigen modes of the most unstable normal perturbations are analyzed. It is concluded that considering transverse density gradient in most cases leads to decrease in the growth rates and phase velocities of all unstable modes. It is shown that the relations between the phase and group velocities obtained from the temporal and spatial stability analysis of round jet turn out to be valid only for large shear layer thicknesses.

The evolution of wingtip vortex wandering: a stability analysis based on stereo-PIV experiment

Instability, as a potential mechanism for vortex flow control, is manifested typically in the phenomenon of wingtip vortex wandering. In this paper, the evolution of wingtip vortex generated by a NACA0015 rectangular wing within six chord lengths of its wake at Rec= 2.1 × 105–3.5 × 105 and AoA = 4°–10° is investigated by stereo particle image velocimetry experiment. The streamwise evolution of vortex wandering is clearly captured, which demonstrates strong anisotropy. The amplitude of vortex wandering increases under all conditions, which exhibits greater growth rates in the condition of larger AoA. To account for such phenomenon, spatial linear stability analysis is performed on the base flow obtained by SPIV experiment to investigate quantitatively the amplification of small disturbance and disturbance modes at the experiment conditions. It is discovered that the wingtip vortex in the experiment is marginally stable under all conditions. Furthermore, the spatial growth rates of instability by AoA correspond well with that of wandering amplitude, indicating that the quick enlargement of the amplitude of wandering at larger AoA condition is caused by larger spatial growth rate of disturbance. In addition, the least-stable disturbance mode by LSA reveals a non-zero directed velocity perturbation in the vortex core, which rotates periodically. Such perturbation developing in both time and space, which is stirred by vortex instability, leads to the behavior of wingtip vortex wandering.

Instability of forced planar liquid jets: mean field analysis and nonlinear simulation

The stability of forced planar liquid jets in a still gaseous environment is explored using nonlinear simulation and spatial linear stability analysis. Harmonic modulation of the transverse component of the inlet velocity leads to an excitation of sinuous modes in the jet. Two forcing amplitudes, 1 % and 5 %, are investigated. While for 1 % forcing, the interfacial disturbance retains a sinuous shape throughout the domain, for 5 % forcing, an increasing downstream deviation from the sinuous wave shape is found. Both forcings lead to sufficient mean flow correction to render linear stability analysis on a base flow unfeasible. Hence, an analysis on the time-averaged mean flow is performed. A correction scheme is introduced, to account for the spreading of the interface position in the mean flow. Comparison of eigenfunctions and growth rates with their counterparts from the nonlinear simulation shows an excellent agreement for 1 % forcing. For 5 % forcing, agreement of the eigenfunctions deteriorates significantly and growth rates are falsely predicted, resulting in a breakdown of the stability model. Subsequent analysis reveals a strong interaction of the fundamental wave with the second higher harmonic wave for 5 % forcing and a reversed energy flow from the coherent motion to the mean flow. These findings provide an explanation for the failure of the linear stability model for large forcing amplitudes. The study extends the applicability of mean flow stability analysis to convectively unstable planar liquid/gas jets and supports previous findings on the limits of mean flow stability, involving pronounced influence of higher harmonic modes.