Turbulent vortex rings in weakly turbulent and in turbulent ambient flow

Turbulent vortex rings were investigated in weakly turbulent flow and in three different grid generated turbulent flows to clarify the reciprocal action of the vortex ring with defined external turbulence. Assuming self-similarity and turbulent viscosity as proportional to V₀D₀ the equations for the ring diameter D(t) and the velocity of propagation V(t) were derived. The time difference Δt between the virtual origins of 1/V(t) respectively D²(t) led to an invariant term. The equation of momentum is fulfilled. – Position and diameter of the vortex rings were determined till their decay by means of an optical system, which did not disturb the vortex rings. The experimental results in weakly turbulent ambient flow obtained by the author and by others confirm the theory very well. The ambient turbulence was nearly constant in the measuring region; its effect could be described by simply adding its viscosity to the vortex ring’s internal turbulent viscosity. The results could be represented in unified non-dimensional diagrams. Moreover, an explanation was found as to why the mean internal turbulent viscosity is constant.     

Acoustic waves emitted by a vortex ring passing near a circular cylinder

Acoustic waves emitted by a vortex ring moving near a circular cylinder have been studied experimentally and theoretically. The vortex rings used in the experiments had a translational speed ν₀ in the range 26 ⪅ ν₀ ⪅ 58 m/s and a radius of about 4·7 mm comparable in size with the cylinder radius. The acoustic pressure signals were detected by four microphones in the far field, and analyzed by digital methods. The observed pressure p obeys the scaling law p ∞ ν₀³L⁻⁴, where L is the impact distance of the vortex path to the cylinder. The observed sound wave is of dipole radiation type, and the direction of the dipole axis rotates as the vortex position changes relative to the cylinder. The direction of the dipole axis is related to that of the normal to the plane of the vortex ring. The instantaneous resultant force exerted on the cylinder by the vortex motion has also been examined, and the magnitude and the direction determined experimentally as a function of time. The theory of vortex sound predicts that the wave profile is proportional to the second time derivative of the volume flux (of a hypothetical potential flow around the cylinder) through the vortex ring. The observed scaling law and dipole directivity of the pressure are in good agreement with the theoretical predictions. The pressure profiles are calculated by using the observed vortex motion. These profiles also agree well with the observed ones, confirming the validity of the theory.     

Interaction between a composite compression wave and a vortex in a thermodynamically nonideal medium

A numerical analysis is presented of two-dimensional interaction between a transverse vortex and a composite compression wave that can exist in a thermodynamically nonideal medium. It is shown that the interaction of a composite wave involving a “neutrally stable” shock with a vortex generates weakly damped outgoing acoustic waves; i.e., the shock is a source of sound. This phenomenon increases the post-shock acoustic noise level in an initially turbulent flow.     

Prediction of aerodynamic sound from circular rods via spanwise statistical modelling

The Ffowcs Williams and Hawkings’ acoustic analogy is combined in the time domain with a statistical model in order to take into account the three-dimensional character of the vortex shedding process from a rod in a uniform stream. By applying the model to a two-dimensional unsteady Reynolds averaged Navier-Stokes flow computation, it is shown that the three-dimensional effects, like spectral broadening around the shedding frequency, are partially recovered. The ad hoc statistical model relates a spanwise random distribution of the vortex shedding phase and wall pressure modulations to an arbitrary spanwise correlations. The phase distribution is applied to the tonal pressure signals of the computation and the resulting ad hoc signals are fed into the acoustic analogy. The study is carried out for a rod based Reynolds number of 2.2×10⁴ for which the rod wake is turbulent. Numerical results compare favourably to those of an accompanying experiment.     

A numerical study of transient flow around a cylinder and aerodynamic sound radiation

The fully 3D turbulent incompressible flow around a cylinder and in its wake at a Reynolds number Re = = 9×10⁴ based on the cylinder diameter and Mach number M = 0.1 is calculated using Large Eddy Simulations (LES). Encouraging results are found in comparison to experimental data for the fluctuating lift and drag forces. The acoustic pressure in far-field is commutated through the surface integral formulation of the Ffowcs Williams and Hawkings (FWH) equation in acoustic analogy. Five different sound sources, the cylinder wall and four permeable surfaces in the flow fields, are employed. The spectra of the sound pressure are generally in quantitative agreement with the measured one though the acoustic sources are pseudo-sound regarding the incompressible flow simulation. The acoustic component at the Strouhal number related to vortex shedding has been predicted accurately. For the broad band sound, the permeable surfaces in the near wake region give qualitative enough accuracy level of predictions, while the cylinder wall surface shows a noticeable under-prediction. The sound radiation of the volumetric sources based on Lighthill tensors at vortex shedding is also studied. Its far-field directivity is of lateral quadrupoles with the weak radiations in the flow and cross-flow directions.     

Large Eddy Simulation of a Vortex Ring Impacting a Bump

A vortex ring impacting a three-dimensional bump is studied using large eddy simulation for a Reynolds number Re=$4$x$10^4$ based on the initial diameter and translational speed of the vortex ring. The effects of bump height and vortex core thickness for thin and thick vortex rings on the vortical flow phenomena and the underlying physical mechanisms are investigated. Based on the analysis of the evolution of vortical structures, two typical kinds of vortical structures, i.e., the wrapping vortices and the hair-pin vortices, are identified and play an important role in the flow state evolution. The boundary vorticity flux is analyzed to reveal the mechanism of the vorticity generation on the bump surface. The circulation of the primary vortex ring reasonably elucidates some typical phases of flow evolution. Further, the analysis of turbulent kinetic energy reveals the transition from laminar to turbulent state. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the flow evolution and the flow transition to turbulent state.     

Formation of vortices in a laminar jet under the action of acoustic field

Results on visual investigation of a structure of a round minijet under the action of an acoustic field are presented. Characteristic features of the laminar jet structure in the acoustic field were revealed from the data of video and photo records of a flow picture. In the flow we observed characteristic large-scale vortex structures and violent turbulent mixing zones.We revealed formation of vortex structures in a laminar jet under acoustic field and an oscillating jet flow regime at the outlet from the pipe 1.35 mm in diameter.     

Effect of Acoustic Field on the Structure of a Round Minijet

Presented are results of visual studying the structure of a round minijet flowing into the atmosphere exposed to an acoustic field. The studies were performed with the laminar jet flow. According to the photo and video recording of the flow pattern we revealed characteristic features of the jet structure in the acoustic field. Characteristic vortex structures and zones with intensive turbulent mixing were detected in the flow.We revealed the process of formation of vortex structures in a laminar jet under the action of the acoustic field, vibrational and rotational jet flows at the outlet of the pipe 1.35 mm in diameter. The present study is a continuation of the research on a minijet structure in an acoustic field [13].     

Weak-focused acoustic vortex generated by a focused ring array of planar transducers and its application in large-scale rotational object manipulation

Contactless manipulation of multi-scale objects using the acoustic vortex(AV) tweezers offers tremendous perspectives in biomedical applications.However,it is still hindered by the weak acoustic radiation force(ARF) and torque(ART)around the vortex center.By introducing the elevation angle to the planar transducers of an N-element ring array,the weakfocused acoustic vortex(WFAV) composed of a main-AV and N paraxial-AVs is constructed to conduct a large-scale object manipulation.Different from the traditional focused AV(FAV) generated by a ring array of concave spherical transducers,a much larger focal region of the WFAV is generated by the main lobes of the planar transducers with the size inversely associated with the elevation angle.With the pressure simulation of the acoustic field,the capability of the rotational object driving in the focal plane for the WFAV is analyzed using the ARF and the ART exerted on an elastic ball based on acoustic scattering.With the experimental system built in water,the generation of the WFAV is verified by the scanning measurements of the acoustic field and the capability of object manipulation is also analyzed by the rotational trapping of floating particles in the focal plane.The favorable results demonstrate the feasibility of large-scale rotational manipulation of objects with a strengthened ART and a reduced acousto-thermal damage to biological tissues,showing a promising prospect for potential applications in clinical practice.     

Collison nebulizer as a new soft ionization source for mass spectrometry

We have proposed that a Collison-type nebulizer be used as an ionization source for mass spectrometry with ionization under atmospheric pressure. This source does not require the use of electric voltage, radioactive sources, heaters, or liquid pumps. It has been shown that the number of ions produced by the ⁶³Ni radioactive source is three to four times larger than the number of ions produced by acoustic ionization sources. We have considered the possibility of using a Collison-type nebulizer in combination with a vortex focusing system as an ion source for extractive ionization of compounds under atmospheric pressure. The ionization of volatile substances in crossflows of a charged aerosol and an analyte (for model compounds of the amine class, viz., diethylaniline, triamylamine, and cocaine) has been investigated. It has been shown that the limit of detecting cocaine vapor by this method is on the level of 4.6 × 10^–14 g/cm³.     

Acoustic Vortex Beam Generation by a Piezoelectric Transducer Using Spiral Electrodes

We propose an innovative method to generate acoustic vortex waves based on a disc piezoelectric transducer that is coated with multi-arm coiled electrodes. Finite element simulation results for single-arm to four-arm coiled electrodes indicate that the method could modulate amplitude and phase spatial distribution of the acoustic waves near the acoustic axis by acoustic field synthesis principle, making the waves rotate spirally in space and form stable focused vortex beams. Compared with the traditional method that requires electronic control of an array consisting of a large number of transducers, this method provides a more effective and compact solution.     

Sound generated by a vortex convected past an elastic sheet

We study the motion and sound generated when a line vortex is convected in a uniform low-Mach flow parallel to a thin elastic sheet. The linearized sheet motion is analyzed under conditions where the unforced sheet (in the absence of the line vortex) is stationary. The vortex passage above the sheet excites a resonance mode of motion, where the sheet oscillates at its least stable eigenmode. The sources of sound in the acoustic problem include the sheet velocity and fluid vorticity. It is shown that the release of trailing-edge vortices, resulting from the satisfaction of the Kutta condition, has two opposite effects on sound radiation: while trailing-edge vortices act to reduce the pressure fluctuations occurring owing to the direct interaction of the line vortex with the unperturbed sheet, they extend and amplify the acoustic signal produced by the motion of the sheet. The sheet motion radiates higher sound levels as the system approaches its critical conditions for instability, where the effect of resonance becomes more pronounced. It is argued that the present theory describes the essential mechanism by which sound is generated as a turbulent eddy is convected in a mean flow past a thin elastic airfoil.     

Statistical equilibrium solutions of the shallow water equations

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2D fluid flow with a free surface, is described. The model contains a competing acoustic turbulent direct energy cascade, and a 2D turbulent inverse energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrains the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.     

Mechanism of stratification of turbulent heat transfer in a sound field in the presence of rotational anisotropy of the flow

It is established that the stratification of the heat transfer intensity coefficients into n discrete levels, as discovered previously in the turbulent flow accompanying rotation of a supersonic flow, is described by the formula α _n ² /α ₁ ² =2 ⁿ⁻¹, n=1,2,3,.... It is found that the ratio of the measured amplitudes of the discrete components of the pressure-pulsation spectrum is of a similar form and corresponds to the pressure field from multipole sources. As expected, similarly to the case of acoustic paramagnetic resonance, the selection of discrete frequencies of intense acoustic radiation from the external flow occurs under the influence of resonances with the radiation of multipoles of turbulent vortices oriented in the rotational anisotropy field. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 145–149 (25 January 1997)     

Parametric Study of the Noise from Vortex Rings with Various Diameters

A technique for studying the aeroacoustic parameters of vortex rings with various diameters in an anechoic chamber is developed. The motion trajectories of vortex rings produced by a piston generator with nozzles with various exit diameters are studied. Spectral analysis of the noise of vortex rings for various distances from nozzles with various diameters is carried out. For the first time, the dependences of the fundamental radiation frequency on the time of a ring’s motion are obtained in dimensionless form. The data on noise from turbulent vortex rings confirm the conclusion that sound from rings with different diameters and velocities is emitted by the same mechanism.     

Lattice Boltzmann Study of a Vortex Ring Impacting Spheroidal Particles

Interaction of vortex rings with solid is an important research topic of hydrodynamic. In this study, a multiple-relaxation time (MRT) lattice Boltzmann method (LBM) is used to investigate the flow of a vortex ring impacting spheroidal particles. The MRT-LBM is validated through the cases of vortex ring impacting a flat wall. The vortex evolution due to particle size, the aspect ratio of a prolate particle, as well as Reynolds $(Re)$ number are discussed in detail. When the vortex ring impacting a stationary sphere, the primary and secondary vortex rings wrap around each other, which is different from the situation of the vortex ring impacting a plate. For the vortex ring impacting with a prolate spheroid, the secondary vortex ring stretches mainly along the long axis of the ellipsoid particle. However, it is found that after the vortex wrapping stage, the primary vortex recovers along the short axis of the particle faster than that in the long axis, i.e., the primary vortex ring stretches mainly along the short axis of the particle. That has never been addressed in the literature.     

圆柱绕流气动声的偶极子及四极子源法定量研究

以亚临界三维圆柱绕流的气动噪声为对象,研究声类比理论中偶极子及四极子源模型在预测低Mach数流动气动声的可靠性及准确性。使用大涡模拟(LES)得到非定常流场,并依据声类比中的Curle等效偶极子面源和Lighthill四极子体源模型,提取相应的声源数据,经Fourier变换得到涡脱落频率处的声源信息,进而定量预测圆柱绕流的气动声。结果表明:Curle模型的结果与实验结果吻合良好,Lighthill体源模型预测的准确性依赖于声源区域截断,不恰当的声源截断将导致错误的声场预测。      

Different methods of calculating the pinning energy of plane vortices in a 3D Josephson medium: A comparative study

The pinning energy of plane (laminar) vortices in a 3D Josephson medium is calculated within a continuous vortex model considering functions of two types: V=1−cosϕ and V= 2/π⁴ϕ²(2π−ϕ)². The shape and energy of the stable and unstable vortices are found with an algorithm for the exact numerical solution of a set of difference equations. The vortex magnetic and Josephson energies diverge. The magnetic and Josephson components of the pinning energy are close in magnitude but differ in sign; as a result, the total pinning energy is smaller than its components by one order of magnitude. This result is confirmed analytically. An analytical computing method within the continuous vortex model is suggested. This method preserves the difference terms in the energy expression. The magnetic energy found by this method differs from the Josephson energy in magnitude, and the magnetic component of the pinning energy is opposite in sign to the Josephson component. Comparative analysis of the approximate approaches to energy calculation within the continuous vortex model when the difference terms are retained and when they are replaced by derivatives is performed. It is shown that the continuous vortex model gives incorrect values of the Josephson and magnetic components of the pinning energy. The actual values are several tens or several hundreds of times higher than those obtained with the continuous vortex model. Yet, since the Josephson and magnetic components of the pinning energy have different signs, the exact value of the total pinning energy and the approximate value obtained within the continuous vortex model differ insignificantly.