Azimuthal Forcing Research Articles

Impact of azimuthal forcing on the Brillouin limit in a collisional two-species Ohkawa filter

This paper investigates the physics of plasma separation in a two species rotating collisional Ohkawa filter, when the source of rotation is an orbital angular momentum carrying wave. The electric field is treated self-consistently with ion and electron radial motion. The injection of angular momentum causes radial currents leading to charge penetration and electric field build up. The electric field varies until an equilibrium with the friction forces is reached. Both collisions with neutrals and Coulomb collisions are considered. In the case where the electric field is driven by the resonant wave, there is no collisional breakdown of the Brillouin limit [Rax et al., Phys. Plasmas 22, 092101 (2015)]; on the contrary, the maximum achievable electric field decreases when the collision frequency is increased. When two species are present, one that undergoes the wave forcing while the second does not interact with the wave, we find the following: the first species is confined, while the second species can be expelled or confined depending on the charge to mass ratio and the collisionalities. Assuming equal charge numbers, if the second species is the heavy one, it is always expelled, which is a standard result. When the second species is the light one, it can also be expelled in the common case where neutral collisions dominate over Coulomb collisions, which constitutes a new result.

Azimuthal flame response and symmetry breaking in a forced annular combustor

In the current study azimuthal forcing of an annular combustor with swirling flames has been performed to present for the first time the Heat Release Rate (HRR) response to all possible pressure fields of the first azimuthal mode up to a finite amplitude limit. The response is first quantified through the conventional Flame Describing Function (FDF) framework, showing a difference in response which depends on whether the acoustic field rotates anti-clockwise or clockwise, albeit with some scatter. Additionally and somewhat surprisingly, a finite HRR response is observed for flames exactly in the pressure node. An Azimuthal FDF is introduced, based on the decomposition of the spatial HRR response through Bloch theory, to better highlight the difference in HRR response to the anti-clockwise and clockwise components of the acoustic field and reduce scatter. A clear difference in response is observed, with a significantly higher response to the anti-clockwise forcing component compared to the clockwise component, independent of the prescribed pressure mode. The difference is attributed to the systematic symmetry breaking introduced by using an annular enclosure of finite curvature and width with swirling flames. It is argued that the finite curvature and width of the geometry and the swirl need to be both present to observe this effect. The difference in response results in a difference between the nature angle of the HRR mode and that of the acoustic field, explaining the relatively large HRR response observed for flames in the pressure node. The Azimuthal FDF describe all of these phenomena well, and is therefore considered more suitable than the conventional FDF to characterise the response in an annular combustor.

Flame dynamics of azimuthal forced spinning and standing modes in an annular combustor

Azimuthal forcing has been applied to flames in a laboratory scale annular combustor in order to accurately control the azimuthal mode of excitation. A new forcing configuration permitted not only the pressure amplitude, but also the spin ratio and mode orientation to be accurately controlled, in order to generate standing modes and for the first time strong spinning modes in both a clockwise (CW) and anti-clockwise (ACW) direction. The phase averaged heat release dynamics of these modes was compared and a number of differences observed depending on the direction of pressure wave propagation, demonstrating characteristic ACW and CW heat release patterns. A new spin compensating averaging method was then introduced to analyse the flame dynamics, and it was shown that through the application of this method the dynamics of standing wave oscillations could be decomposed to recover the characteristic ACW and CW heat release responses. The global heat release response was also assessed during strongly spinning modes, and the magnitude of the response was shown to depend strongly on the direction of propagation, demonstrating the importance of the local swirl direction on the global heat release response, with important implications for the modelling of such flows.

Azimuthally forced flames in an annular combustor

The application of azimuthal acoustic forcing to flames in a laboratory scale annular combustor is demonstrated in the present paper, which not only allows large amplitude azimuthal modes to be excited, but permits control to be exerted over their frequency, amplitude, and their modal dynamics, including parameters such as the spin ratio and orientation. The effect of forcing frequency is investigated, and it is found that the excitation can be well controlled into a standing wave oscillation over a range of amplitudes for selected frequencies. However, close to the natural frequency of the system, the modal dynamics cannot be well controlled, and instead these tend towards their self-excited state, resulting in a mixed mode. Comparing the phase-averaged structure of the forced and self-excited responses for similar operating conditions, illustrate similar flame dynamics, making this novel forcing approach extremely useful for the study of these instabilities in annular systems.

Axisymmetric Jet Subjected to Radial and Azimuthal Forcing

Results of an experimental investigation of axisymmetric jet that was subjected to radial and azimuthal forcing at a Reynolds number of 5200 are reported. Subharmonic forcing at Strouhal numbers of 0.1 and 0.125 attenuated large coherent structures in the initial region of the jet, resulting in an overall reduction in turbulence levels and the turbulent kinetic energy. Forcing also resulted in the velocity decay and spreading of the jet. Proper orthogonal decomposition analysis of the particle image velocimetry data revealed exchange of modal energy to higher modes and highlighted streamwise vortex filaments located between successive large-scale structures of the jet. These filaments play a pivotal role in the entrainment of ambient fluid. The meandering and distortion of the vortex filaments increased due to additional strain imposed by the forcing.

Mean zonal flow generated by azimuthal harmonic forcing in a rotating cylinder

In this paper, we study analytically the flow in a rotating container subjected to an azimuthal forcing. We show that this mechanical forcing generates a correction to the solid body rotation called mean zonal flow, similar to the time oscillation of the rotation rate of an axisymmetric container. This axisymmetric correction induced by nonlinear effects in the Ekman layers modifies the solid-body rotation of the fluid in the container. At the leading order, the contribution in the bulk is shown to be an azimuthal flow which scales as the square of the amplitude of the multipolar deformation and is independent of the Ekman number. We also show that the mean zonal flow depends on the symmetry of the angular forcing n and the ratio of the angular rate of the deformation to the angular rate of the cylinder . We found that for an elliptical forcing, n = 2, the rotation rate of the zonal flow does not depend on the radial position. In addition, the angular rate is found to be asymmetric with respect to . These scalings are similar to the time harmonic forcing in a cylinder. The particular case of a tidal forcing is also considered.

AN ANALYTIC MODEL FOR BUOYANCY RESONANCES IN PROTOPLANETARY DISKS

Zhu, Stone, and Rafikov (2012) found in 3D shearing box simulations a new form of planet-disk interaction that they attributed to a vertical buoyancy resonance in the disk. We describe an analytic linear model for this interaction. We adopt a simplified model involving azimuthal forcing that produces the resonance and permits an analytic description of its structure. We derive an analytic expression for the buoyancy torque and show that the vertical torque distribution agrees well with results of Athena simulations and a Fourier method for linear numerical calculations carried out with the same forcing. The buoyancy resonance differs from the classic Lindblad and corotation resonances in that the resonance lies along tilted planes. Its width depends on damping effects and is independent of the gas sound speed. The resonance does not excite propagating waves. At a given large azimuthal wavenumber k_y > 1/h (for disk thickness h), the buoyancy resonance exerts a torque over a region that lies radially closer to the corotation radius than the Lindblad resonance. Because the torque is localized to the region of excitation, it is potentially subject to the effects of nonlinear saturation. In addition, the torque can be reduced by the effects of radiative heat transfer between the resonant region and its surroundings. For each azimuthal wavenumber, the resonance establishes a large scale density wave pattern in a plane within the disk.

STAR FORMATION IN TWO LUMINOUS SPIRAL GALAXIES

We have examined star formation in two very luminous (M_V=-22 to -23) Sc-type spiral galaxies, NGC 801 and UGC 2885, using ultra-deep Halpha images. We combine these with UBV and 2MASS JHK images and HI maps to explore the star formation characteristics of disk galaxies at high luminosity. Halpha traces star formation in these galaxies to 4-6 disk scale lengths, but the lack of detection of Halpha further out is likely due to loss of Lyman continuum photons. Considering gravitational instabilities alone, we find that the gas and stars in the outer regions are marginally stable in an average sense, but considering dissipative gas and radial and azimuthal forcing, the outer regions are marginally unstable to form spiral arms. Star formation is taking place in spiral arms, which are regions of locally higher gas densities. Furthermore, we have traced smooth exponential stellar disks over 3-orders of magnitude and 4-6 disk scale lengths, in spite of a highly variable gravitational instability parameter. Thus, gravitational instability thresholds do not seem relevant to the stellar disk. One possibility for creating an exponential disk is that the molecular cloud densities and star formation rates have exponential profiles and this forces the stellar disk to build up such a profile. Another possibility is that the stellar disk is continuously adjusted to an exponential shape regardless of the star formation profile, for example through global dynamical process that scatter stars. However, such scattering processes are only known to operate in spiral systems, in which case they cannot explain the same dilemma of smooth exponential disks observed in dwarf irregular galaxies.

Development and characterization of plasma actuators for high-speed jet control

Active control of high Reynolds number and high-speed jets has been hampered due to the lack of suitable actuators. Some of the attributes that would make an actuator suitable for such flows are: high amplitude and bandwidth; small size for distribution around the jet; phase-locking ability for jet azimuthal mode forcing; and sufficient ruggedness for hot jets. We have been developing a class of actuators termed ‘localized arc filament plasma actuators,’ which possess such characteristics. In this paper, we present the development and characterization of these actuators as well as preliminary results on their applications in high Reynolds number Mach 0.9 and ideally expanded Mach 1.3 jets.

The role of Ekman pumping and the dominance of swirl in confined flows driven by Lorentz forces

We are concerned here with confined, axisymmetric flows of small viscosity driven by a prescribed Lorentz force. In a previous paper we examined the case where the body force is purely azimuthal, generating a swirling motion. We showed that, in such cases, Ekman pumping provides the means by which the flow establishes a steady state. In this paper we examine a problem which, superficially, looks rather different. That is, we consider the case where the dominant Lorentz force is poloidal (F r,0,F z) in (r,θ,z) coordinates, while the azimuthal component of force is taken to be small but finite. This characterizes many important industrial processes and it is well known that such flows exhibit a curious phenomenon. That is, provided the azimuthal forcing exceeds a relatively low threshold (about one percent of the poloidal force), the flow is dominated, not by poloidal motion, but by swirl. Previous explanations of this phenomenon are inconsistent-with the experimental evidence. Here we offer an alternative view. We show that, once again, the pool dynamics are controlled by Ekman pumping, and that the dominance of swirl is a direct consequence of the suppression of the poloidal motion by the radial stratification of angular momentum.

Three‐dimensional Waves Generated at Lindblad Resonances in Thermally Stratified Disks

We analyze the linear, three-dimensional response to tidal forcing of a disk that is thin and thermally stratified in the direction normal to the disk plane. We model the vertical disk structure locally as a polytrope that represents a disk of high optical depth. We solve the three-dimensional gasdynamics equations semianalytically in the neighborhood of a Lindblad resonance. These solutions match asymptotically onto those valid away from resonances (previously obtained by Korycansky & Pringle) and provide solutions valid at all radii r. We obtain the following results: (1) A variety of waves are launched at the resonance, including r-modes and g-modes. However, the f-mode carries more than 95% of the torque exerted at the resonance. (2) These three-dimensional waves collectively transport exactly the amount of angular momentum predicted by the standard two-dimensional resonant torque formula. (3) Near resonance, the f-mode behaves compressibly and occupies the full vertical extent of the disk. Away from resonance, the f-mode behaves incompressibly, becomes confined near the surface of the disk, and, in the absence of other dissipation mechanisms, damps via shocks. In general, the radial length scale for this process is roughly rL/m (for resonant radius rL and azimuthal tidal forcing wavenumber m), independent of the disk thickness H. This wave-channeling process is due to the variations of physical quantities in r and is not due to wave refraction. (4) However, the inwardly propagating f-mode launched from an m = 2 inner Lindblad resonance experiences relatively minor channeling (accompanied by about a factor of 5 increase in nonlinearity), all the way to the radial center of the disk. We conclude that for binary stars, tidally generated waves at Lindblad resonances in highly optically thick circumbinary disks are subject to strong nonlinear damping by the channeling mechanism, while those in circumstellar accretion disks are subject to weaker nonlinear effects. We also apply our results to waves excited by young planets for which m ≈ r/H and conclude that the waves are likely damped on the scale of a few H.

Large-Eddy Simulations of Forced Three-Dimensional Impinging Jets

Large-eddy simulations of the flow field around twin three-dimensional impinging jets were carried out to simulate the near-ground hover configuration of a vertical takeoff and landing (VTOL) aircraft. Both the impinging jet and the upwash caused by the collision of the wall jets are modeled in this study. The evolution of the vortical structures in the impinging jet flow field, due to the introduction of axisymmetric and azimuthal perturbations at the jet exit, has been investigated. The vortical structures formed in the jet shear layer due to azimuthal forcing, show significant three-dimensional vortex stretching effects when compared to the structures formed during axisymmetric forcing. Breakdown of the large-scale structures into smaller vortices also occurs much earlier during azimuthal forcing. When compared to the upwash formed during axisymmetric forcing, the azimuthally perturbed jet forms an upwash that is less coherent and results in a weaker upload or lift-off force on the aircraft undersurface. Comparison with available experimental data indicates good agreement for the centerline velocity decay, the wall pressure variation and the phase speed of the vortical structures.

Three-dimensional vorticity dynamics in a coflowing turbulent jet subjected to axial and azimuthal perturbations

The effect of axial and azimuthal forcing on the spreading and mixing characteristics in the near field (x/D 2000) water jet is studied by means of planar, laser induced fluorescence (PLIF) visualizations. Measurements of both the initial spreading rate of the jet and the decay of the concentration along the centerline of the jet show a marked increase in the mixing of the jet as a result of the axial forcing. The mixing enhancement, which is shown to depend on the wavenumber of the azimuthal forcing, the frequency of the axial forcing, and the Reynolds number of the jet, results from the formation of vortex loops caused by the global induction of the jet's vorticity. This vortex induction mechanism appears to be similar to the vorticity modes earlier found in laminar coflowing jets (Lasheras et al., Lect. Appl. Math., 28, 1991).

Elliptic jets. Part 3. Dynamics of preferred mode coherent structure

The dynamics of the preferred mode structure in the near field of an elliptic jet have been investigated using hot-wire measurements. A 2:1 aspect ratio jet with an initially turbulent boundary layer and a constant momentum thickness all around the nozzle exit perimeter was used for this study. Measurements were made in air at a Reynolds number ReDe (≡ UeDe/v) = 3.5 × 104. Controlled longitudinal excitation at the preferred mode frequency (StDe ≡ fDe/Ue = 0.4) induced periodic formation of structures, allowing phase-locked measurements with a local trigger hot wire. The dynamics of the organized structure are examined from educed fields of coherent vorticity and incoherent turbulence in the major and minor symmetry planes at five successive phases of evolution, and are also compared with corresponding data for a circular jet. Unlike in a circular jet, azimuthally fixed streamwise vortices (ribs) form without the aid of azimuthal forcing. The three-dimensional deformation of elliptic vortical structures and the rib formation mechanism have also been studied through direct numerical simulation. Differential self-induced motions due to non-uniform azimuthal curvature and the azimuthally fixed ribs produce greater mass entrainment in the elliptic jet than in a circular jet. The turbulence production mechanism, entrainment and mixing enhancement, and time-average measures and their modification by excitation are also discussed in terms of coherent structure dynamics and the rib-roll interaction. Various phase-dependent and time-average turbulence measures documented in this paper should serve as target data for validation of numerical simulations and turbulence modelling, and for design and control purposes in technological applications. Further details are given by Husain (1984).

Vorticity dynamics in three-dimensional pulsating co-flowing jet diffusion flames

The vorticity dynamics in the near field of laminar (Re=10 3 ) co-flowing jets subjected to the single or combined effects of axial and azimuthal forcing is analyzed. It is shown that the interaction of the three-dimensional vortex structure resulting from the growth of the two and three-dimensional instabilities may result in large changes in the entrainment and mixing characteristics of the jet. For each azimuthal forcing, and for a fixed velocity ratio between the inner and outer jet, we show the existence of several instability modes leading to a pattern of lateral ejections of closed vortex loops. These modes and their topological changes are analyzed in view of the three-dimensional inviscid induction of the two concentric array of vortex rings emanating from the jet's exit nozzle. For the case of methane-air diffusion flames, flow visualizations revealed the existence of qualitatively similar patterns of closed flame cells and fingers.

Large-eddy simulations of excitation effects on a VTOL upwash fountain

The responses of an upwash fountain to various azimuthal and axisymmetric excitations, applied at the exits of its neighboring jets, are investigated. Kinematic arguments are used to determine the interactions of large-scale structures in the fountain and the effects of these interactions on the fountain’s characteristics. Numerical simulations of a row of impinging jets, which contain the essential features of twin jets impinging on the ground, are used to simulate the hovering configuration of a vertical takeoff and landing (VTOL) aircraft. The flow is assumed to be governed by the time-dependent, incompressible Navier–Stokes equations. The large-eddy simulation approach is followed. Distinct fountain characteristics are shared among the cases in which azimuthal perturbations are applied at both jet exits in the same direction. These include a high fountain spreading rate, a strong lateral interaction with the neighboring jets, and a weak upload at the aircraft’s undersurface. A strong similarity in fountain characteristics also exists for the cases of axisymmetric forcing and azimuthal forcing in opposite directions at the two jet exits. The similar characteristics here include a low fountain spreading rate and a strong upload at the aircraft’s undersurface.