Layer Vortices Research Articles

Interpretation of wake instability at slip line in rotating detonation

ABSTRACTIn studies on instabilities of flowfield in rotating detonation, one of the most common concerns is the instability at the slip line originating from the conjunction of the detonation wave and oblique shock. Using Euler equations associated with the 7-species-and-8-reaction finite-rate chemical reaction model of hydrogen/air mixtures, further studies are performed to simulate the 2-D rotating detonation, and the flow mechanism of instability at the slip line is investigated in depth. The results show that the distinct wake profile exists at the slip line, which is different from the typical mixing layer. Analysis indicates that the generation of wake is caused by the transition shock between the detonation wave and oblique shock. Because of the wake profile, the vorticity distribution therein appears in a double-layer layout, and different evolutions exist in different vorticity layers. Based on the velocity profile across the slip line, the analysis by the linear stability theory is made, and two main unstable modes which have different shape profiles and phase velocities are found. Discrete Fourier transformation is utilised to analyse the numerical results, and similar shape profiles are obtained. A general coincidence in velocity of vortex movement is also attained between the theoretical predictions and simulations. Investigations show that the wake instability is responsible for the unstable mechanism, and corresponding unstable structures differ from the canonical ones in typical mixing layers.

Mixing layer instability and vorticity amplification in a creeping viscoelastic flow

We report quantitative evidence of mixing-layer elastic instability in a viscoelastic fluid flow between two widely spaced obstacles hindering a channel flow at $Re\ll1$ and $Wi\gg1$. Two mixing layers with nonuniform shear velocity profiles are formed in the region between the obstacles. The mixing-layer instability arises in the vicinity of an inflection point on the shear velocity profile with a steep variation in the elastic stress. The instability results in an intermittent appearance of small vortices in the mixing layers and an amplification of spatio-temporal averaged vorticity in the elastic turbulence regime. The latter is characterized through scaling of friction factor with $Wi$, and both pressure and velocity spectra. Furthermore, the observations reported provide improved understanding of the stability of the mixing layer in a viscoelastic fluid at large elasticity, i.e. $Wi\gg1$ and $Re\ll1$, and oppose the current view of suppression of vorticity solely by polymer additives.

Representation of the Vortex Sheets in the Perfect Fluid

We discuss representation of the vortex sheets in the perfect fluid. In the preface of his book, I. Imai claimed “hyperfunction = vortex layer”, the proof of which had not been given. In 2009, K. Uchikoshi-Y. Noro gave a hyperfunctional representation of the vortex layers in the 2-dimensional fluid. Their idea being highly dependent on identifying the two dimensional Euclidean plane with the complex plane, it is difficult to interpret their representation in the real fluid phenomena. Its 3-dimensional extension was also difficult. To solve these problems, we give a new representation of the vortex sheets (or layers) by the real flow velocity vectors, whose other merits are also discussed.

Numerical investigation of nanosecond pulsed plasma actuators for control of shock-wave/boundary-layer separation

This study numerically explores the flow physics associated with nanosecond pulsed plasma actuators that are designed to control shock-wave induced boundary-layer separation in a Mach 2.8 supersonic flow. By using two dielectric barrier surface discharge actuator configurations, parallel and canted with respect to the flow velocity vector, a previous experiment suggested that the actuator worked in two ways to influence the interaction: boundary layer heating and vorticity production. The heating effect was enhanced with the parallel electrode and made the boundary-layer separation stronger, while the canted electrode produced vorticity and suppressed the boundary-layer separation due to the momentum transfer from the core flow. Because the detailed physical processes are still unclear, in this paper a numerical investigation is undertaken with a large eddy simulation and an energy deposition model for the plasma actuation, in which the dielectric barrier discharge produced plasma is approximated as a high temperature region. The flow characteristics without the plasma actuation correspond to the experimental observation, indicating that the numerical method successfully resolves the shock-wave/boundary-layer interaction. With the plasma actuation, complete agreement between the experiment and calculation has not been obtained in the size of the shock-wave/boundary-layer interaction region. Nevertheless, as with the experiment, the calculation successfully demonstrates definite difference between the parallel and canted electrodes: the parallel electrode causes excess heating and increases the strength of the interaction, while the canted electrode leads to a reduction of the interaction strength, with a corresponding thinning of the boundary layer due to the momentum transfer. The counter flow created by the canted actuator plays an important role in the vortex generation, transferring momentum to the boundary layer and, consequently, mitigating the shock induced boundary layer separation.

Effects of Density and Blowing Ratios on the Turbulent Structure and Effectiveness of Film Cooling

Large eddy simulations (LES) were performed to investigate film cooling of a flat plate, where the cooling jets issued from a plenum through one row of circular holes of diameter D and length 4.7D that are inclined at 35 deg relative to the plate. The focus is on understanding the turbulent structure of the film-cooling jet and the film-cooling effectiveness. Parameters studied include blowing ratio (BR = 0.5 and 1.0) and density ratio (DR = 1.1 and 1.6). Also, two different boundary layers (BL) upstream of the film-cooling hole were investigated—one in which a laminar BL was tripped to become turbulent from near the leading edge of the flat plate, and another in which a mean turbulent BL is prescribed directly. The wall-resolved LES solutions generated were validated by comparing its time-averaged values with data from PIV and thermal measurements. Results obtained show that having an upstream BL that does not have turbulent fluctuations enhances the cooling effectiveness significantly at low velocity ratios (VR) when compared to an upstream BL that resolved the turbulent fluctuations. However, these differences diminish at higher VRs. Instantaneous flow reveals a bifurcation in the jet vorticity as it exits the hole at low VRs, one branch forming the shear-layer vortex, while the other forms the counter-rotating vortex pair (CRVP). At higher VRs, the shear layer vorticity is found to reverse direction, changing the nature of the turbulence and the heat transfer. Results obtained also show the strength and structure of the turbulence in the film-cooling jet to be strongly correlated to VR.

Mixing of swirling inclined dense jets – A numerical study

Recent experimental investigations demonstrated the possibility that the addition of swirls at the discharge outlet can lower the terminal rise height of inclined dense jets and increase the dilution at the return point, which can potentially influence the outfall design in coastal waters. In the present study, we further examined the effect of swirls on the mixing characteristics of 45 degree inclined dense jets using numerical simulations with two different approaches. The first approach was the Large Eddy Simulation (LES) with the dynamic Smargorinsky Sub-grid Model, and the second one was the Reynolds-Averaged Navier-Stokes (RANS) with the standard k − ε turbulence closure. The comparison showed that the trajectories of the non-swirling inclined dense jet predicted by LES were closer to the experimental results, while RANS underpredicted the centreline peak height. This was consistent with the previous findings and can be attributed to the fact that the turbulence characteristics of non-swirling dense jets were highly anisotropic. Both approaches however underestimated the additional spreading in the lower half of the inclined dense jet due to the convective mixing by the buoyancy induced instability, and also the dilution in general. With swirls, the RANS predictions matched the jet trajectory better compared to LES, which was probably because the turbulence anisotropy was reduced and the distributions were more axisymmetric. The dilutions of swirling jets remained underestimated by both approaches, until the Swirl Number became sufficiently large at 0.33. Finally, strong swirls up to twice the highest value in the experiments were attempted in the numerical simulations to explore the possibility of jet breakup and disintegration at the outlet. It was found that the high swirl intensity did not lead to significant changes beyond what were observed at G = 0.33. The turbulence kinetic energy spectrum of the swirling inclined dense jet was also analysed along the trajectory based on the LES results. The spectral analysis confirmed that the effects of swirls were different depending on the magnitude, with strong swirls producing turbulence energy at the range of frequencies just before the inertial range probably due to eddy break up around the vortical layer, while extremely strong swirls increased the turbulence energy production range overall with the additional formation of large eddies.

Atlantic Water Transformation Along Its Poleward Pathway Across the Nordic Seas

AbstractThe warm and salty Atlantic Water is substantially modified along its poleward transit across the Nordic Seas, where it reaches deeper isopycnals. In particular, the Lofoten Basin, exposed to intense air‐sea interactions, plays a crucial role in the transformation of Atlantic Water. Averaged over a seasonal cycle, Atlantic Water releases approximately 80 W/m2 of heat to the atmosphere over a large area, leading to winter mixed layer depths of up to 500 m (locally exceeding 1,000 m in the Lofoten Basin Eddy, a permanent vortex located in the basin center) and substantial water mass transformation. We investigate spiciness injection (temperature and salinity increase) by winter mixing, by performing an isopycnal analysis using a comprehensive observational data set covering the 2000–2017 period. Compared to the Atlantic Water properties at the Svinøy section, representative of the inflowing Atlantic Water, some isopycnals reveal an important warming (up to 1.5°C) and salinification (up to 0.2 g/kg). Key areas for spiciness injection are the western Lofoten Basin and west of Bear Island. The modified spicy Atlantic Waters coincide with low potential vorticity with strongly density‐compensated layers at their base, allowing double‐diffusion processes to occur farther downstream toward the Arctic. Despite its limited spatial extent, the Lofoten Basin Eddy exhibits the greatest spiciness injection, as well as the deepest mixed layer and thickest low potential vorticity layer of the Norwegian Seas. The Atlantic Water spiciness at Svinøy shows a downstream correlation in the Lofoten Basin and farther north toward the Arctic with a lag of 1 to 1.5 years.

The Problems in Terms of Stresses of Diffusion-Vortex Class in Infinite Rigid Viscoplastic Space

The statements and exact self-similar solutions of diffusion-vortex problems in terms of stresses simulating a nonstationary one-dimensional shear in some curvilinear orthogonal coordinate systems of a two-constant stiff-viscous plastic medium (Bingham body) are analyzed. Such problems include the diffusion of plane and axisymmetric vortex layers, as well as the diffusion of avortex filament. The shear occurs in regions of unlimited space expanding with time with a pre-unknown boundary, and a possible way of specifying an additional condition at infinity is described. A generalized vortex diffusion is introduced into consideration, containing a formulation with several parameters, including the order of the singularity peculiarities at zero. Self-similar solutions are constructed in which the order of the singularity corresponds to or does not correspond to the type of shift in the selected coordinate system.

Flame propagation across a flexible obstacle in a square cross-section channel

Flame propagation across a single flexible fence-type obstacle was studied experimentally in a square cross-section channel, and compared to results obtained using similar blockage ratio (BR) rigid obstacles. The experiments were carried out with different BRs in premixed stoichiometric hydrogen-air mixtures, at initial conditions of 101 kPa and 298 K. High-speed Schlieren photography was employed to gain insight into the flame front structure and the flame tip velocity. Pressure transducers were used to measure the pressure at different axial positions near the obstacle. Flame propagation was found to be strongly influenced by the flow contraction of the unburned gas upstream of the obstacle, and the separated flow downstream of the obstacle. The most significant effect of the flexible obstacle, compared to the rigid obstacle, was observed for BRs above 0.71. The flame front evolution was dominated by the shear layer coming off the obstacle leading-edge and the vortex downstream from the obstacle. For the rigid obstacle BRs tested, the shear layer coming off the obstacle leading-edge reattached to the top of the obstacle, resulting in a vortex (i.e., recirculation-zone) downstream of the obstacle. For the high BR flexible obstacles (BR > 0.43), significant obstacle deformation (downstream tilt and vertical compression), and an associated decrease in BR, resulted in slightly lower flame tip velocities past the obstacle. The downstream obstacle tilt resulted in a different type of separated flow, compared to that observed in the rigid obstacle, where the shear layer didn't reattach to the top of the obstacle. The resulting vortex and strong shear layer confined the flame tip to the top part of the channel, delaying the consumption of the unburned gas immediately downstream of the obstacle. The deformation of the flexible obstacle reduced the peak pressure and the rate of pressure rise compared to that obtained with the rigid obstacles.

Sensitivity of Tropical Cyclone Intensity and Structure to Planetary Boundary Layer Parameterization

The advanced weather research and forecasting model is used to investigate the influence of planetary boundary layer (PBL) processes on intensity and structure of the storm Phailin (2013). Five simulations are conducted with five PBL schemes; Yonsei University (YSU), Mellor−Yamada−Nakanishi−Niino order2.5 (MYNN2), Assymetric Convective Model2 (ACM2), Medium Range Forecast (MRF), and Bougeault and Lacarrere (BouLac). The simulation duration includes the pre − intensification and rapid intensification phase of Phailin before landfall. Results indicate that during the pre − intensification phase, storm’s track and intensity are not much sensitivity to PBL but structural changes are noted. A significant sensitivity of track and intensity to PBL parameterizations are found during rapid intensification phase. BouLac and MRF produced two extremes with 39 hPa intense and 16 km compact storm for BouLac than MRF. Further analysis reveals an outward movement of air parcel just above the boundary layer which causes spin-down for YSU and MYNN2. BouLac is associated with stronger eddy diffusivity and moisture fluxes within the boundary layer and stronger cyclonic vorticity just above the boundary layer than other experiments. Stronger cyclonic vorticity above the boundary layer in BouLac favors intense updraft, facilitating more moisture transport from the boundary layer to upper layers aiding stronger secondary circulation and robustly intensifying the storm. A relatively deeper and drier inflow layer associated with weaker cyclonic vorticity just above the boundary layer reduces the moisture transport and weaken the secondary circulation for MRF than others.

Ground-state phases of spin–orbit coupled spin-1 Bose–Einstein condensate in a plane quadrupole field

We study the ground-state phases of two-dimensional spin–orbit coupled spin-1 Bose–Einstein condensate loaded in a plane quadrupole field. In the absence of rotation, for the fixed spin-orbit coupling strength, the ordinary stripe phase is found when the strength of the magnetic field gradient is small. As the strength of magnetic field gradient enhances, the system realizes the phases with three layer vortices along the radial direction. The number of vortices in the second layer is successively increased and the vortices in the outermost layer disappear when the strength of magnetic field gradient surpass the critical value. For the large strength of magnetic field gradient, the system only has the inner layer vortices. The magnetic field inhibits the region of vortices. For the fixed magnetic field gradient strength, the vortices of the system elongate along the radial direction and form a series of vortex lines, the number of the vortex line increases as the strength of spin-orbit coupling enhances. By adding the rotation, for the fixed strengths of spin-orbit coupling and magnetic field gradient, the number of second layer vortices also successively increases as the rotational frequency increases. The number of vortices in the certain layer of the ground-state density can be regularly changed under the effects of the magnetic field and spin–orbit coupling.

Aerodynamic Flow Control of Axisymmetric Bluff Body by Coupled Wake Interactions

The stability and steering of nonspinning airborne bodies of revolution have traditionally relied on stationary or moving fins that affect controlled interactions with the oncoming flow to modify the inherent aerodynamic loads. An alternative approach for manipulation of these loads in the absence of external control surfaces can be realized by exploiting the reciprocal coupling between a moving bluff body and its near wake by either breaking or restoring the natural azimuthal near-wake symmetry using segmented fluidic actuation. The present paper reviews fluidic actuation of the near-wake dynamics by using an azimuthally segmented four-quadrant array of aft-facing synthetic jet modules around the tail end of an axisymmetric bluff-body model. Each actuator controls a segment of the aft separated vorticity layer using a hybrid configuration with a passive Coanda surface. The actuation allows for controlled suppression or enhancement of near-wake asymmetries and consequently of the associated aerodynamic forces and moments on a stationary model and in rigid-body motion. It is shown that the effects of actuation on the near-wake and aerodynamic loads of the static body are comparable to the effects of its combined pitch and yaw motions in the absence of actuation. The actuation provides significant suppression and augmentation of the motion-induced aerodynamic loads with concomitant controlled deflection or decoupling between the motions of the body and its near wake. It is anticipated that controlled manipulation of these fundamental coupling mechanisms can lead to active control of the motion and stability of flight platforms.

Aerodynamic stability analysis of geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction. Considering flow separation, the wind field around membrane structure is simulated as the superposition of a uniform flow and a continuous vortex layer. By the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics, aerodynamic pressure acting on membrane surface can be determined. And based on the large amplitude theory of membrane and D\'Alembert\'s principle, interaction governing equations of wind-structure are established. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction governing equations into a system of second-order nonlinear differential equation with constant coefficients. Through judging the frequency characteristic of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy, geometrical nonlinearity and scantling of structure is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the model without considering flow separation, it\'s basically consistent about the divergence instability regularities in the flow separation model.

Correlation Between Pressure Recovery of Highly Loaded Annular Diffusers and Integral Stage Design Parameters1

Exhaust diffusers significantly enhance the available power output and efficiency of gas and steam turbines by allowing lower turbine exit pressures. The residual dynamic pressure of the turbine outflow is converted into static pressure, which is referred to as pressure recovery. Since total pressure losses and construction costs increase drastically with diffuser length, it is strongly preferred to design shorter diffusers with steeper opening angles. However, these designs are more susceptible to boundary layer separation. In this paper, the stabilizing properties of tip leakage vortices generated in the last rotor row and their effect on the boundary layer characteristics are examined. Based on analytical considerations, for the first time, a correlation between the pressure recovery of the diffuser and the integral rotor parameters of the last stage, namely, the loading coefficient, flow coefficient, and reduced frequency, is established. Experimental data and scale-resolving simulations, carried out with the shear stress transport scale-adaptive simulation (SST-SAS) method, both show excellent agreement with the correlation. Blade tip vortex strength predominantly depends on the amount of work exchanged between fluid and rotor, which in turn is described by the nondimensional loading coefficient. The flow coefficient influences mainly the orientation of the vortex, which affects the interaction between vortex and boundary layer. The induced velocity field accelerates the boundary layer, essentially reducing the thickness of the separated layer or even preventing separation locally.

Experimental Validation of Fluid–Structure Interaction Computations of Flexible Composite Propellers in Open Water Conditions Using BEM-FEM and RANS-FEM Methods

In the past several decades, many papers have been published on fluid–structure coupled calculations to analyse the hydro-elastic response of flexible (composite) propellers. The flow is usually modelled either by the Navier–Stokes equations or as a potential flow, by assuming an irrotational flow. Phenomena as separation of the flow, flow transition, boundary layer build-up and vorticity dynamics are not captured in a non-viscous potential flow. Nevertheless, potential flow based methods have been shown to be powerful methods to resolve the hydrodynamics of propellers. With the upcoming interest in flexible (composite) propellers, a valid question is what the consequences of the potential flow simplifications are with regard to the coupled fluid–structure analyses of these types of propellers. This question has been addressed in the following way: calculations and experiments were conducted for uniform flows only, with a propeller geometry that challenges the potential flow model due to its sensitivity to leading edge vortex separation. Calculations were performed on the undeformed propeller geometry with a Reynolds-averaged-Navier–Stokes (RANS) solver and a boundary element method (BEM). These calculations show some typical differences between the RANS and BEM results. The flexible propeller responses were predicted by coupled calculations between BEM and finite element method (FEM) and RANS and FEM. The applied methodologies are briefly described. Results obtained from both calculation methods have been compared to experimental results obtained from blade deformation measurements in a cavitation tunnel. The results show that, even for the extreme cases, promising results have been obtained with the BEM-FEM coupling. The BEM-FEM calculated responses are consistent with the RANS-FEM results.

The turbulent airflow over wind generated surface waves

The airflow dynamics above the air–sea interface are believed to have a significant impact on the fluxes of momentum and scalars across the ocean surface. We present an experimental study of the turbulent structure of the airflow above wind generated surface waves. Measurements, taken at a fetch of 22.7 m in University of Delaware’s large wind-wave–current facility, are reported for wind wave experiments with 10-m extrapolated wind speeds spanning from 2.19 m s−1 to 16.63 m s−1. In order to complete this study, we developed a complex imaging system, combining particle image velocimetry with laser induced fluorescence techniques. High resolution two-dimensional (18.7 cm x 9.7 cm) velocity fields were measured as close as 100 μm above the air–water interface (on average). In addition, we acquired high spatial and temporal resolution wave field data simultaneously with the airflow measurements. Using this imaging system, we were able to perform phase averaging and separate the turbulent, mean and wave-induced velocity fields. We observe direct evidence of airflow separation events past the crests of wind waves, starting at low to moderate wind speeds (U10>2.19 m s−1). In general, the turbulent boundary layer in the air is characterized by numerous velocity sweeps and ejections, accompanied by intense downwind-tilted spanwise vorticity (shear) layers stemming from the surface. We were able to directly observe these turbulent events, and estimate their statistical significance using quadrant analysis. These events become phase-locked in the presence of waves, and, when U10≥5 m s−1, they are accompanied by intermittent airflow separation events past wave crests. The production of TKE also shows wave phase locked features indicating that further analysis of the wave-coherent contributions to the TKE balance is needed.

Experimental study on the vortex structure and path instability of freely falling annular disks

Bodies freely falling in steady water or air are common scenes encountered in various scientific and engineering fields, including the flapping flight of birds and the reentry of a space shuttle. In this work, the freely falling annular thin disks with small dimensionless moments of inertia I* and Reynolds number Re are investigated experimentally in a water tank. We use stereoscopic vision to record the position and orientation of the disks. The flow structure behind the disks is studied by applying fluorescent dye visualization and PIV method. Varying the geometry dimensionless parameter (the inner to outer diameter ratio η and I*) of the disks reveals two new falling patterns. When ηcrit1=0.6 0.8, the circular vortex loops shed frequently from the disk, which causes a lengthways vibration superimposed onto straight vertical motion. We also observe another two falling patterns reported previously: hula-hoop and helical motion. By comparing the wake structure of the two motions, we find that the vortex layer twists more violently in the hula-hoop motion, which is the reason for the different trajectory between them. Further research on flow field reveals that the torque on the disk that causes the vibration is due to the formation, elongation and shedding of the vortex.

The role of surface vorticity during unsteady separation

Unsteady flow separation in rotationally augmented flow fields plays a significant role in a variety of fundamental flows. Through the use of time-resolved particle image velocimetry, vorticity accumulation and vortex shedding during unsteady separation over a three-dimensional airfoil are examined. The results of the study describe the critical role of surface vorticity accumulation during unsteady separation and reattachment. Through evaluation of the unsteady characteristics of the shear layer, it is demonstrated that the buildup and shedding of surface vorticity directly influence the dynamic changes of the separation point location. The quantitative characterization of surface vorticity and shear layer stability enables improved aerodynamic designs and has a broad impact within the field of unsteady fluid dynamics.

Applications of a Cole–Hopf transform to the 3D Navier–Stokes equations

ABSTRACTThe Navier–Stokes equations written in the vector potential can be recast as non-linear Schrödinger equations at imaginary times, i.e. heat equations with a potential term, using the Cole–Hopf transform. On this basis, we study two kinds of Navier–Stokes flows by means of direct numerical simulations. In an experiment on vortex reconnection, it is found that the potential term takes large negative values in regions where intensive reconnection takes place, whereas the signature of the non-linear term is more broadly spread. For decaying turbulence starting from a random initial condition, such a correspondence is also observed in the early stage when the flow is dominated by vorticity layers. At later times, when the flow features several tubular vortices, this correspondence becomes weaker. Finally, a similar set of transformations is presented for the magneto–hydrodynamic equations, which reduces them to a set of heat equations with suitable potential terms, thereby obtaining new criteria for the regularity of their solutions.

Performance of high-order implicit large eddy simulations

The performance of parallel implicit Large Eddy Simulations (iLES) is investigated in conjunction with high-order weighted essentially non-oscillatory schemes up to 11th-order of accuracy. Simulations were performed for the Taylor Green Vortex and supersonic turbulent boundary layer flows on High Performance Computing (HPC) facilities. The present iLES are highly scalable achieving performance of approximately 93% and 68% on 1536 and 6144 cores, respectively, for simulations on a mesh of approximately 1.07 billion cells. The study also shows that high-order iLES attain accuracy similar to strict Direct Numerical Simulation (DNS) but at a reduced computational cost.