Vortex Instability Research Articles

Numerical investigation of the collision of a vortex pair upon a solid wavy wall

The vortex dynamics produced by the collision of a vortex pair with a solid wavy wall are examined numerically using a proposed high-order vortex particle method. The influences of the Reynolds number (ReΓ) of the vortex pair, the wavelength (λw), and the wave amplitude (Aw) of the wall on the induced vortex structures, interactions among vortices, and the instability and reconnection of secondary vortices are discussed. The boundary layers at the top of ripples separate first to form the secondary vortices moving around the primary tubes. Meanwhile, the boundary layers at the bottom of ripples detach late, move vertically upward, and then form incomplete vortex loops due to an unsuccessful reconnection of the secondary vortices. The ReΓ effects cause the appearance of various vortex structures, such as incomplete primary vortex loops from the bottom of ripples at ReΓ=1000, secondary vortex loops due to interactions of the first loops with the wall at ReΓ=2000, and hairpin vortices at ReΓ=4000. The wavelength of the wall induces instability in the secondary vortex tubes. This instability on the secondary tubes appears at the top of ripples at λw=2r0, while it spreads over the whole secondary vortices at λw=4r0, where r0 is the initial spacing between the primary vortex tubes. This instability results in various wavy tubes that robustly interact with the primary tubes. Due to the effects of Aw, the primary vortex tubes significantly decay with time compared to those in the flat wall case.

A comprehensive investigation on flame flickering characteristics of premixed conical flame at different inclination angles

To thoroughly investigate how the inclination angle affects the flickering of premixed conical flames, a series of experiments and simulations were carried out. Propane-air conical flames were established on a Bunsen burner, and various inclination angles were tested, resulting in a wide range of flame flickering frequency data. The findings revealed that the further the inclination angle deviates from 0°, the lower the flickering frequency. Consequently, an empirical correlation that factors in the inclination angle was developed. To gain a more comprehensive understanding of the flame flickering behavior under different gas inclination angles, researchers utilized Particle Image Velocimetry (PIV) and numerical simulation to visualize the velocity fields of a typical flame. The results demonstrated that deviated inclination angles not only alter the shear strength between the burnt gas and surrounding gas but also significantly change the flame flickering mode. These factors lead to various Kelvin-Helmholtz instability patterns and vortex shedding modes, ultimately impacting flickering frequency.

Past rewinding of fluid dynamics from noisy observation via physics-informed neural computing.

Reconstructing the past of observed fluids has been known as an ill-posed problem due to both numerical and physical challenges, especially when observations are distorted by inevitable noise, resolution limits, or unknown factors. When employing traditional differencing schemes to reconstruct the past, the computation often becomes highly unstable or diverges within a few backward time steps from the distorted and noisy observation. Although several techniques have been recently developed for inverse problems, such as adjoint solvers and supervised learning, they are also unrobust against errors in observation when there is time-reversed simulation. Here we present that by using physics-informed neural computing, robust time-reversed fluid simulation is possible. By seeking a solution that closely satisfies the given physics and observations while allowing for errors, it reconstructs the most probable past from noisy observations. Our work showcases time rewinding in extreme fluid scenarios such as shock, instability, blast, and magnetohydrodynamic vortex. Potentially, this can be applied to trace back the interstellar evolution and determining the origin of fusion plasma instabilities.

On the low-frequency flapping motion in flow separation

Transitional separating flow induced by a rectangular plate subjected to uniform incoming flow at Reynolds number (based on the incoming velocity and half plate height) 2000 is investigated using direct numerical simulation. The objective is to unveil the long-lasting mystery of low-frequency flapping motion (FM) in flow separation. At a fixed streamwise-vertical plane or from the perspective of previous experimental studies using pointwise or planar measurements, FM manifests as a low-frequency periodic switching between low and high velocities covering the entire separation bubble. The results indicate that in three-dimensional space, FM reflects an intricate evolution of streamwise elongated streaky structures under the influence of separated shear layer and mean flow reversal. The FM is an absolute instability, and is initiated through a lift-up mechanism boosted by mean flow deceleration near the crest of the separating streamline. At this particular location, the shear bends the vortex filament abruptly, so that one end is vertically struck into the first half of the separation bubble, whereas the other end is extended in the streamwise direction in the second half of the separation bubble. These two ends of vortex filament are mutually sustained and also stretched by the vertical acceleration and streamwise acceleration in the first and second halves of the separation bubble, respectively. This process periodically switches the low-velocity (or high-velocity) streaky structure to a high-velocity (or low-velocity) streaky structure encompassing the entire separation bubble, and thus flaps the separated shear layer up and down in the vertical direction. A ‘large vortex’ shedding manifests when the streaky structure switches signs. This large vortex is fundamentally different from the spanwise vortex shedding residing in the shear layer originated from the Kelvin–Helmholtz instability and successive vortex amalgamation. It is also believed that the three-dimensional evolution of streaky structures in the form of FM is applicable for both geometry- and pressure-induced separating flows.

Multiplex vortex instability in the flow of non-Newtonian fluids through microcavity arrays

Complex fluids always possess obvious non-Newtonian properties that facilitate the occurrence and development of vortex instability in porous media, which is of critical significance in many natural and industrial processes. It is widely known that this flow instability is regulated by both fluid flow and solid structure. However, the quantitative understanding of how structural characteristics of porous space affect the evolution of vortex instability is still nascent, especially in the case of fluids with varying rheological properties. Herein, the flow of polymer solutions with distinct non-Newtonian properties through microcavity arrays is experimentally studied, by which we systematically explore the effect of structural parameters of the cavity array on vortex instability. We find that, for both Newtonian and shear-thinning fluids with negligible elasticity, the vortex evolution behavior in each cavity of the cavity array is identical to those in an isolated cavity. In contrast, for viscoelastic fluids, the vortex instability is visibly affected by cavity number and cavity–cavity interval, and this effect exhibits different forms when the fluid shear-thinning participates or not. Multiplex vortex instabilities are observed under these tested conditions. By multiplex, we mean the vortex formation dynamics and evolution patterns are diversified. These unusual evolution phenomena are then interpreted in terms of the interplay between the elongation and relaxation of polymers as they navigate among neighboring cavities. These results can help us to further understand the flow instability of complex fluids in porous media and evoke new strategies for microfluidic applications of efficient mixing.

Multiscale Modeling of Flow in Rod Bundles: From Direct Numerical Simulation and Subchannel to Coarse-Mesh CFD

Fast and accurate evaluation of flow and heat transfer phenomena in rod bundles is a problem of long-standing interest in nuclear engineering. Computational fluid dynamics (CFD) can provide accurate but relatively time-intensive estimates, such that simulations of very long transients with high spatial detail are infeasible. On the other hand, subchannel codes require relatively low computational time and can provide pin-level estimates, but have substantial empiricism in evaluating aspects such as crossflows and turbulent mixing coefficients. A multiscale method (SC+) for bridging this accuracy/speed gap, based on the Subchannel CFD (SubChCFD) method of Liu et al. [Nucl. Eng. Design, Vol. 355, paper 110318 (2019)], is demonstrated and developed here with a focus on a 5 × 5 square rod bundle geometry. The method has been newly implemented into the commercial code STAR-CCM+ and benchmarked against Liu et al.’s data. The 5 × 5 geometry was chosen in part due to the availability of direct numerical simulation (DNS) data at a relevant Reynolds number of a similar configuration for comparison. The SC+ results are variously compared against results from DNS, large eddy simulation, wall-resolved Reynolds-averaged Navier-Stokes, and coarse-mesh CFD methods. As an expansion to the original SubChCFD approach, a simple Hi2Lo approach is demonstrated using the DNS data as a correction to the original friction factor correlations employed. This is verified to improve the predictions. Additional test cases with geometric perturbations are pursued, illustrating the flexibility of SC+. The potential of this method for modeling the narrow gap vortex instability, which would represent an advancement over standard subchannel approaches, is also assessed. The method is expanded to include transverse flow losses, which was found to improve the results for modeling the gap instability. Initial extensions of SC+ for hexagonal rod bundles are also presented; some inaccuracies for the coarsest meshes prompted a detailed investigation of the mesh convergence behavior of the method. Geometric correction factors were devised that provided substantial improvement on these very coarse meshes, improving the prospects of SC+ for wider usage. Future work plans are to expand the methodology to wire-wrapped rod bundles and to implement the method into Pronghorn, with a unified pipeline via the Cardinal wrapper between the codes NekRS, Pronghorn, and BISON, to solve fuel performance problems of direct interest to industry.

A330-300 Wake Encounter by ARJ21 Aircraft

Today, aviation has grown significantly in importance. However, the challenge of flight delays has become increasingly severe due to the need for safe separation between aircraft to mitigate wake turbulence effects. The primary emphasis of this investigation resides in elucidating the evolutionary attributes of wake vortices in homogeneous isotropy turbulence. The large eddy simulation (LES) method is used to scrutinize the dynamic evolution of wake vortices engendered by an A333 aircraft in the atmospheric milieu and assess its ramifications on the ARJ21 aircraft. The research endeavor commences by formulating an LES methodology for the evolution of aircraft wake vortices, integrating adaptive grid technology to reduce the necessary grid volume significantly. This approach enables the implementation of axial and non-axial grid adaptive refinement, leading to more accurate simulations of both axial and non-axial vortices. Numerical simulations are conducted using the LES approach to scrutinize three distinct rates of turbulence dissipation amidst the ambient atmospheric turbulence, and the results are juxtaposed with Lidar measurements (Wind3D 6000 LiDAR) of wake vortices acquired at Chengdu Shuangliu International Airport (CTU). Subsequently, the rolling moment of the following aircraft is calculated, and three-dimensional hazard zones are determined for the A333. It is found that during the approach phase, the wake turbulence separation minima for an ARJ21 (CAT-F) following an A333 (CAT-B) is 3.35 NM, which represents a reduction of approximately 33% compared to ICAO RECAT (Wake Turbulence Re-categorization). The findings validate the dependability of the fine-grained mesh used in the vortex core region, engendered through the adaptive grid method, which proficiently captures the Crow instability and the interconnected phenomena of vortices in the numerical examination of aircraft wake. The safety of wake encounters primarily depends on the magnitude of environmental turbulence and the development of structural instability in wake vortices.

Influence of thickness and domain structure on the vortex instability of superconducting/ferromagnetic bilayers

We report on the vortex instability in superconducting/ferromagnetic (FM) bilayers. Samples consisting of a 23 nm thick Mo2N superconducting layer with a capping layer of Co, Fe20Ni80, or FePt ferromagnets were grown by sputtering at room temperature on silicon (100). Our study reveals that the critical vortex velocity in these superconducting bilayers is significantly influenced by the thickness of the FM layers rather than the specific magnetic domain structure. When comparing samples with FM layers of 10 nm and 50 nm thickness, we observe a notable increase in vortex velocities at low magnetic fields, with speeds rising from approximately 3.5 km s−1 to around 6 km s−1 as the thickness increases. This trend extends to moderate and high magnetic fields. Furthermore, we establish a direct correlation between vortex velocities and the thermal conductance of the FM layers. These findings provide valuable insights for the interplay of magnetic and thermal properties within these hybrid systems, with potential implications for the design of future devices and applications.

The Reexamination of the Moisture–Vortex and Baroclinic Instabilities in the South Asian Monsoon

Observational analyses reveal that a dominant mode in the South Asian Monsoon region in boreal summer is a westward-propagating synoptic-scale disturbance with a typical wavelength of 4000 km that is coupled with moistening and precipitation processes. The disturbances exhibit an eastward tilt during their development before reaching their maximum activity center. A 2.5-layer model that extends a classic 2-level quasi-geostrophic model by including a prognostic lower-tropospheric moisture tendency equation and an interactive planetary boundary layer was constructed. The eigenvalue analysis of this model shows that the most unstable mode has a preferred zonal wavelength of 4000 km, a westward phase speed of 6 m s−1, an eastward tilt vertical structure, and a westward shift of maximum moisture/precipitation center relative to the lower-tropospheric vorticity center, all of which agree with the observations. Sensitivity experiments show that the moisture–vortex instability determines, to a large extent, the growth rate, while the baroclinic instability helps set up the preferred zonal scale. Ekman-pumping-induced vertical moisture advection prompts an in-phase component of perturbation moisture relative to the low-level cyclonic center, allowing the generation of available potential energy and perturbation growth, regardless of whether or not a low-level mean westerly is presented. In contrast to a previous study, the growth rate is reversely proportional to the convective adjustment time. The current work sheds light on understanding the moisture–vortex and the baroclinic instability in a monsoonal environment with a pronounced easterly vertical shear.

On the propeller wake evolution using large eddy simulations and physics-informed space-time decomposition

A novel modal analysis methodology, denoted as the physics informed sparsity-promoting dynamic mode decomposition (pi-SPDMD) model, was introduced for the reduction and reconstruction analysis of intricate propeller wake flows, aiming to provide insight into the inherent flow structures spanning diverse temporal and spatial scales. Large-Eddy Simulation (LES) was employed to numerically model the wake dynamics of a four-bladed propeller, providing a comprehensive resolution from the proximate to the distant wake regions. The findings indicate that the pi-SPDMD model enhances the efficiency of the sparse-promoting algorithm, producing modes that gravitate towards stability, and the resulting decomposition maintains commendable physical fidelity. Integrating the results from the LES solution and the modal decomposition of pi-SPDMD, the tip vortex exhibits a uniform topological configuration with notable coherence in the proximate domain. In this region, the large-scale vortex is the dominant feature of the propeller wake, and there is a marked intermittency in the turbulence. In the mid-field, the tip vortex system transitions into fine-scale vortices, rapidly diminishing in coherence due to the onset of elliptic instability and subsequent secondary vortex generation. As the tip vortex structures related to physical quantities become fully discretized, the small-scale turbulent patterns quickly intermingle, leading to a more homogeneous distribution in the distant wake.

Effect of Aspect Ratio of Ferroelectric Nanofilms on Polarization Vortex Stability under Uniaxial Tension or Compression.

Mastering the variations in the stability of a polarization vortex is fundamental for the development of ferroelectric devices based on polarization vortex domain structures. Some phase field simulations were conducted on PbTiO3 nanofilms with an initial polarization vortex under uniaxial tension or compression to investigate the conditions of vortex instability and the effects of aspect ratio of nanofilms and temperature on them. The instability of a polarization vortex is strongly dependent on aspect ratio and temperature. The critical compressive stress increases with decreasing aspect ratio under the action of compressive stress. However, the critical tensile stress first decreases and then increases with decreasing aspect ratio, then continues to decrease. There are two inflection points in the curve. In addition, an elevated temperature makes both the critical tensile and compressive stresses decline, and will also cause the aspect ratio corresponding to the inflection point to decrease. These are very important for the design of promising nano-ferroelectric devices based on polarization vortices to improve their performance while maintaining storage density.

Numerical analysis of the influence of hull-modulated inflow on unsteady force fluctuations and vortex dynamics of pump-jet propulsor

The influence of the hull-modulated inflow on the propulsion performance of the propeller is related to the matching design of the propeller–hull system. In the present study, considering the working conditions of the pump-jet propulsor in uniform inflow and two types of hull-modulated inflow, based on improved delay detached eddy simulation, the influence of hull-modulated inflow on unsteady force fluctuations and vortex dynamics of pump-jet propulsor under design conditions is carried out. The results show that the hull-modulated inflow increases the propulsion efficiency of the pump-jet propulsor to varying degrees within the range of the calculated advance coefficient and has a significant influence on the frequency characteristics of the unsteady force spectra characteristics of each component of the pump-jet propulsor. It also shows changes in the magnitude characteristics, that is, the energy transfer process of an individual rotor blade from the stator blade passing frequency to other harmonics of the shaft rotation frequency, and the thrust spectrum of an individual stator blade presents broad-spectrum characteristics in the high-frequency range. Furthermore, the application of hull-modulated inflow directly affects the shape of the stator shedding vortex, causing some of the stator blade shedding vortices to separate early and aggravating its short-wave instability. More secondary vortices are induced to accelerate the instability of the rotor blade tip clearance vortex. The energy transfer mechanism from the rotor blade passing frequency and its harmonics to the broadband spectra appears in the wake field of the pump-jet propulsor.

Far field behaviour of wingtip vortices under synthetic jet-based control

Wingtip vortices have been proven to be detrimental to both aircraft efficiency and safety due to their adverse effects such as wake hazard, blade vortex interaction noise and induced drag. Despite the extensive literature on the subject, the number of experimental works featuring far field velocity measurements under active control is very limited. The present work deals with the experimental investigation of the effectiveness of synthetic jet actuation on the control of wingtip vortices and their wake hazard. In order to preserve the mutual induction of the counter-rotating vortices during their evolution, an unswept, low aspect ratio, squared-tipped, finite-span wing is employed. The synthetic jet actuation is based on triggering the inherent instabilities of Crow and Widnall at different values of the momentum coefficient Cμ with the goal of reducing the vortex strength and obtaining an anticipated vortex break up. Different exit geometries of the synthetic jets have been tested to analyze the effects of the jet velocity and position on the wingtip vortices. Phase-locked measurements of the velocity field in the far wake at a distance from the wing trailing edge from 26 to 80 chord lengths have been performed via stereoscopic particle image velocimetry. The effects of blowing at high momentum coefficient Cμ=1% are demonstrated to be remarkable on the mitigation of the wingtip vortices. On the other hand, both the time and phase-averaged results suggest that, at relatively low values of Cμ (0.2%), using a larger synthetic jet exit section area allows to greatly affect the wingtip vortices' features causing a striking alleviation of the vorticity distribution up to 90% with respect to the baseline reference case. In fact, due to the actuation at low frequency, the vortex instability is prematurely risen up and amplified, leading to early vortices linking and their consequent dissipation.

Maximum Likelihood Identification of Backflow Vortex Instability in Rocket Engine Inducers

Abstract Bayesian estimation is applied to the analysis of backflow vortex instabilities in typical three- and four-bladed liquid propellant rocket engine inducers. The flow in the impeller eye is modeled as a set of equally intense and evenly spaced 2D axial vortices, located at the same radial distance from the axis and rotating at a fraction of the impeller speed. The circle theorem is used to predict the flow pressure in terms of the vortex number, intensity, rotational speed, and radial position. The theoretical spectra so obtained are frequency broadened to mimic the dispersion of the experimental results and parametrically fitted to the measured data by maximum likelihood estimation with equal and independent Gaussian errors. The method is applied to three inducers, tested in water at room temperature and different operating conditions. It successfully characterizes backflow instabilities using the signals of a single pressure transducer flush-mounted in the impeller eye, effectively bypassing the aliasing limitations and the data acquisition/reduction complexities of traditional multiple-sensor cross-correlation methods. The identification returns the estimates of the model parameters and their standard deviations, providing the information necessary for assessing the accuracy and statistical significance of the results. The flowrate is found to be the major factor affecting the backflow vortex instability, which, on the other hand, is rather insensitive to the occurrence of cavitation. The results are consistent with the data reported in the literature, as well as with those generated by the auxiliary models specifically developed for initializing the maximum likelihood searches and supporting the identification procedure.

Effects of viscoelastic fluid on noise reduction of the flow over a circular cylinder

Viscoelastic fluid can suppress instabilities of vortices around a circular cylinder, and has a wide application prospect in flow noise reduction. The effects of elasticity and the maximum polymer extensibility of dilute polymer solution on the noise reduction of flow around a circular cylinder were investigated. FENE−P model was used to simulate flow noise of two-dimensional flow through two different sound source extraction methods with Reynolds number of 100, Weissenberg number of 0 to 40, and the maximum polymer extensibility of 10 to 100. Results show that viscoelastic fluid can inhibit the formation of vortices, reduce the fluid pulsation around cylinder, and reduce intensity of dipole sound source on cylindrical surface. With appropriate maximum polymer extensibility, flow noise is particularly reduced, and elasticity will enhance the noise reduction effect. On condition that the Weissenberg number remains unchanged, a moderate increase in the maximum polymer extensibility can further reduce dipole intensity as well as drag of cylindrical surface, and flow noise will be further reduced. However, if the maximum extensibility of the polymer is too high, solid-like behavior will occur around the cylinder, greatly increasing drag and elastic stress and creating a new dipole around the fluid wall. Finally, noise increases. This study analyses the influence of various parameters in a viscoelastic fluid on noise and provides an idea with promising applications for flow noise reduction.

Instabilities in tidal turbine wakes

We report on the observation of vortex instabilities in the wake of a tidal turbine undergoing harmonic unsteady axial inflow (e.g. due to surface waves). The work was carried out using unsteady RANS (URANS) modelling using the open-source CFD software OpenFOAM, using the `pimpleDyMFoam' solver. The PIMPLE algorithm used in the URANS solver is a combination of the PISO (Pressure Implicit with Splitting of Operator) and SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithms. URANS simulations usually have a limitation on the time step set by the Courant number (C = u (delta t)/(delta x), where delta x is the minimum cell length and u the local velocity. In the PISO algorithm, C<1 is usually required. However, the PIMPLE algorithm allows stable transient simulations at C>>1 by applying under-relaxation to each time-step until a convergence criterion is met, before allowing the time-step to complete with no applied relaxation factors. The turbulence model used was komega-SST, which has been used extensively in tidal turbine modelling.
 As with a wind turbine, the response of a tidal turbine to unsteady flow is heavily influenced by the behaviour of the helical wake that returns in close proximity to the turbine blades times per revolution ( – number of blades). Unsteady inflow causes the blades to shed vorticity into the wake, which in turn leads to a spatial variation in wake vortex strength, such that the vorticity of adjacent returning wake segments can differ, and thus there is a spatially varying velocity deficit in the wake. This spatial variation in velocity deficit triggers instability in the blade tip vortices, the emergence of which we demonstrate is governed by the non-dimensional group relating the blade passing frequency to the gust frequency. If the ratio between these two frequencies is an integer, the wake is stable. If not, the tip vortices exhibit various forms of instability. If the wake is unstable, adjacent wake segments will eventually coalesce as they move downstream, such that the wake consists of larger regions of vorticity with lower spatial frequency, compared to the wake immediately behind the turbine. There is also some indication that these unstable, coalesced wakes persist further downstream, compared with stable wakes. This has implications for wind and tidal farm design, where interaction of a row of turbines with the wakes of upstream turbines is an important consideration.

Rheology mediates transition of vortex evolution patterns in microcavity flow of polymer solutions

Vortex instability in cavity flow is a fundamental component of microfluidic applications such as flow mixing, nanoparticle synthesis, and cell/particle manipulation. In contrast to Newtonian fluids, non-Newtonian fluids exhibit significantly different flow behaviors due to their non-linear flow dynamics. This study experimentally investigates the flow dynamics of polymer solutions with distinct rheological properties through a microcavity and quantifies the influence of the rheological degree on the evolution dynamics of vortices. We find three typical vortex evolution patterns in the cavity flow of polymer solutions and show that the rheological degree mediates the transitions among these patterns. The vortex evolution in the cavity flow of all polymer solutions tested in this study shifts from a basic increasing logistic function to one of three typical patterns as the polymer concentration increases. It is clarified that the pattern transition is related to the elasticity number and shear-thinning index of the fluids, and the phase difference between identical patterns is due to differences in the viscosity and elasticity of the fluids. These results extend our understanding of the vortex dynamics of complex fluids in cavity flow and provide theoretical guidance for enhancing the working efficiency of cavity-structured microfluidic applications using polymer solutions. The results of this study may also inspire developments in the flow regulation of drug delivery in blood through the vascular system.

Anisotropy of turbulence at the core of the tip and hub vortices shed by a marine propeller

Large-eddy simulation on a grid consisting of 5 billion points was utilized to study the properties of turbulence at the core of the tip and hub vortices shed by a marine propeller across working conditions. Turbulence at the core of the tip vortices was found to be initially isotropic, moving towards a ‘cigar-shaped’ axisymmetric state as instability grows, dominated by turbulent fluctuations of the velocity component directed in the radial direction of the cylindrical reference frame centred at the wake axis. The break-up of the coherence of the tip vortices is instead characterized by turbulence recovering an isotropic state. This process is accelerated by growing load conditions of the propeller. In contrast, during instability of the hub vortex, turbulence at its core develops a ‘pancake-shaped’ axisymmetric state, dominated by the fluctuations of the radial and azimuthal velocities. However, at higher propeller loads turbulence at the core of the hub vortex keeps close to isotropy, thanks to a faster instability. Within both tip and hub vortices the deviations from Boussinesq's hypothesis were found very significant, providing evidence of the unsuitability of conventional turbulence modelling. At the core of the tip vortices they become especially large at their break-up and for increasing load conditions of the propeller, equivalent to more intense structures. In contrast, at the core of the hub vortex they were verified to be decreasing functions of the propeller load.

Effect of different vortex models on the linear instability characteristics of wingtip vortex

Different analytical vortex models have been developed to characterize the evolution of wingtip vortex. However, their effect on the instability characteristics has not been well recognized. In this paper, the wingtip vortex generated by an elliptical wing was first experimentally measured in the near-wake and far-wake regions by particle image velocimetry. Then, it was fitted to different one-scale and multiscale vortex models as the base flow for linear stability analysis. The results show that though the eigenvalue spectra by different vortex models exhibit a unified topology with an isolated point around ωi=0 and three continuous branches, the multiscale vortex models tend to overestimate the instability of the wingtip vortex nonphysically. Furthermore, structures of the most unstable eigenmodes (Mode C) also differ between one-scale and multiscale vortex models. On this basis, a meaningful parameter, penetration depth (dp), is defined to predict the instability behavior of one perturbation mode. It is found that the most unstable streamwise wavenumber coincides with the streamwise wavenumber, where 1−dp is the local minimum, regardless of vortex models. The negative correlation between ωi and 1−dp of Mode C indicates that the closer the perturbation vorticity to the vortex boundary, the larger the growth rate. This reminds us that the penetration length might be a candidate measure of the instability behavior of perturbation modes, which deserves to be further studied in a broader parameter space.

Effects of hump deflection angle on streamwise vortex instability over a yawed cone at Mach 6

This paper investigates the influence of three-dimensional smooth humps with varying deflection angles (φ) on the linear stability of streamwise vortices over a yawed cone with a 7° half-angle at a 6° angle-of-attack, free-stream Mach number of 6, and unit Reynolds number of 1.0×107/m. The steady laminar flow is obtained using direct numerical simulations. The eN method based on global stability theory is used to predict the transition location of the streamwise vortices along the centerline on the leeward side of the cone. The results reveal that φ plays a significant role in the outward vortex generation location, with smaller values of φ effectively delaying the outward vortex generation. Moreover, there is a qualitative relationship between the instability of the streamwise vortices and the inward/outward vortex structure characteristics of the base flow over a yawed cone. Namely, the transition delay effect of the streamwise vortices is proportional to the delay in the generation location of the outward vortex, which provides insights into the control of the transition induced by streamwise vortices. In particular, the configuration based on a hump with φ=9° and a height of 0.57 times the local boundary layer thickness delays the transition by approximately 38.2% at the critical N-factor (Ntr=12.5) without significantly increasing the instability of the inner mode.