Vortex Kinetic Energy Research Articles

Aeroacoustic simulation of transient vortex dynamics inside double-degree-of-freedom orifice-cavity structure subjected to high-intensity acoustic waves

As a noise reduction device commonly used for aero-engines at present, the double-degree-of-freedom acoustic liner has the advantage of broadband noise elimination, which is related to the energy transformation during the process of vortex generation and shedding from its dual orifice-cavity unit when subjected to high-intensity acoustic waves. Based on the compressible linear Navier-Stokes equations with the influence of nonlinear thermo-viscous acoustics, this study simulated the three-dimensional acoustic-vortex coupling field of dual orifice-cavity structures with different orifices' distances under high-intensity acoustic waves with different frequencies. The first and second resonance frequencies of the structures were found by the transmission loss coefficient. Then, through the vortex dynamics analysis, the interference behavior of the vortex shedding with fusion and shifting was observed under the first resonance frequency when the orifices' distance was close. By establishing an energy transfer model, it was found that the energy transfer was concentrated at the upper orifice under the second resonance frequency, and the interference effect increased the vortex kinetic energy and viscous dissipation energy here under the first resonance frequency. The relevant research results provide a theoretical basis for the structural optimization of aerodynamic noise control devices of modern aircraft.

Simulation Calculation of New Steel Tube Structure based on Vortex-Induced Vibration Control Technology of Steel Tube Tower

This paper proposes a new three-tube structure to replace the original steel tube. The vortex-induced vibration of the three-tube structure is simulated by two-way fluid-structure coupling. With the control variable method, the simulation calculation of multiple groups of three-pipe structures under uniform incoming flow at different wind speeds is carried out. By analyzing the vortex kinetic energy diagram and displacement diagram, the best outer diameter and tube center distance of the three-tube structure to suppress vortex-induced vibration in the leeward direction are obtained. By summarizing the situation of a symmetrical vortex, the conditions of the symmetrical vortex are understood. Then, by comparing the amplitude of the vortex-induced vibration of the original structure with that of the three-tube structure, the three-tube structure is further optimized to obtain a new structural design that can effectively control vortex-induced vibration.

Aeroacoustic simulation of transient vortex dynamics subjected to high-intensity acoustic waves

The transient vortex dynamics within a microsecond-level acoustic cycle were numerically investigated when an orifice–cavity structure, which is a unit component of an acoustic liner, was subjected to high-intensity acoustic waves. Three-dimensional vortex-acoustic coupling fields were determined by solving the compressible linearized Navier–Stokes equations (LNSEs) and considering the nonlinear thermoviscous effect around the micro-orifice. First, the LNSE results were well validated by literature results in terms of the sound absorption coefficient, reflection coefficient, acoustic resistance, acoustic reactance, acoustic impedance, and the spatial features of acoustically induced vortex structures. Subsequent cross correlation analysis demonstrated that attenuated standing-waves were generated inside the back cavity when the incident acoustic wave propagated across the orifice. Aeroacoustic energy analysis revealed that the periodic production of vortex kinetic energy contributed more to the sound attenuation in the orifice structure than the viscous dissipation effect. Then, the acoustically induced vortex dynamics were characterized in terms of a phase-dependent evolution process, and the formation, convection, and dissipation regions were classified. Finally, dynamic mode decomposition analyses were conducted to extract the dominant vortex structures by determining their frequency spectra. The dominant modes contained large-scale vortices around the orifice, while the high-order modes contained a series of small-scale vortices toward the upstream incident tube and downstream cavity.

Synthesis of Large-Area MXenes with High Yields through Power-Focused Delamination Utilizing Vortex Kinetic Energy.

Evaluating the delamination process in the synthesis of MXenes (2D transition metal carbides and nitrides) is critical for their development and applications. However, the preparation of large defect‐free MXene flakes with high yields is challenging. Here, a power‐focused delamination (PFD) strategy is demonstrated that can enhance both the delamination efficiency and yield of large Ti3C2T x MXene nanosheets through repetitive precipitation and vortex shaking processes. Following this protocol, a colloidal concentration of 20.4 mg mL–1 of the Ti3C2T x MXene can be achieved after five PFD cycles, and the yield of the basal‐plane‐defect‐free Ti3C2T x nanosheets reaches 61.2%, which is 6.4‐fold higher than that obtained using the sonication–exfoliation method. Both nanometer‐thin devices and self‐supporting films exhibit excellent electrical conductivities (≈25 000 and 8260 S cm‐1 for a 1.8 nm thick monolayer and 11 µm thick film, respectively). Hydrodynamic simulations reveal that the PFD method can efficiently concentrate the shear stress on the surface of the unexfoliated material, leading to the exfoliation of the nanosheets. The PFD‐synthesized large MXene nanosheets exhibit superior electrical conductivities and electromagnetic shielding (shielding effectiveness per unit volume: 35 419 dB cm2 g–1). Therefore, the PFD strategy provides an efficient route for the preparation of high‐performance single‐layer MXene nanosheets with large areas and high yields.

Evolution Characteristics of Suction-Side-Perpendicular Cavitating Vortex in Axial Flow Pump under Low Flow Condition

In order to study the evolution characteristics of suction-side-perpendicular cavitating vortex in an axial-flow pump under low flow conditions, model tests, high-speed imaging, and an SST-CC turbulence model were used to simulate the external characteristics and cavitation morphology of the pump. The evolution law of suction-side-perpendicular cavitating vortex (SSPCV) was revealed by turbulent kinetic energy, liutex vortex identification, and vorticity transport equation. The results show that the evolution of suction-side-perpendicular cavitating vortex at low cavitation number can be divided into three stages: generation, development, and breaking stage. In the generation stage, the turbulent kinetic energy, velocity gradient and vortex kinetic energy continue to increase, reaching the maximum at the early stage of development. Afterwards, due to the viscosity of the water, the vortex slowly dissipates and enters the stage of development. Finally, it is affected by the next blade and enters the breaking stage, which accelerates the dissipation of the vortex. The vortex stretching term and vortex expansion term are the main contributors to the vorticity. During the development of the vortex, the vorticity is mainly caused by the deformation of the fluid micelle. The breaking stage mainly affects the stretching term, and the Coriolis force term cannot be ignored in the rotating coordinates.

Study of the Mechanisms of Vortex Variability in the Lofoten Basin Based on Energy Analysis

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy was studied. Mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23·1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one, and the mean available potential energy into the vortex available potential one (baroclinic and barotropic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. Increase in the available potential energy is confirmed by a significant positive trend and by decrease of the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.

Issledovaniye vikhrevoy izmenchivosti v Lofotenskoy kotlovine na osnove analiza dostupnoy potentsial'noy i kineticheskoy energii

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy were studied. The mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23⋅1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one and the mean available potential energy into the vortex available potential one (barotropic and baroclinic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that the kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. An increase in the available potential energy is confirmed by a significant positive trend and by a decrease in the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.

Impact of myocardial infarction on intraventricular vortex and flow energetics assessed using computational simulations.

Flow energetics have been proposed as early indicators of progressive left ventricular (LV) functional impairment in patients with myocardial infarction (MI), but its correlation with individual MI parameters has not been fully explored. Using electro-fluid-structure interaction LV models, this study investigated the correlation between four MI parameters: infarct size, infarct multiplicity, regional enhancement of contractility at the viable myocardium area (RECVM), and LV mechanical dyssynchrony (LVMD) with intraventricular vortex and flow energetics. In LV with small infarcts, our results showed that infarct appearance amplified the energy dissipation index (DI), where substantial viscous energy loss was observed in areas with high flow velocity and near the infarct-vortex interface. The LV with small multiple infarcts and RECVM showed remarkable DI increment during systole and diastole. In correlation analysis, the systolic kinetic energy fluctuation index (E') was positively related to ejection fraction (EF) (R2 =0.982) but negatively correlated with diastolic E' (R2 =0.970). Diastolic E' was inversely correlated with vortex kinetic energy (R2 =0.960) and vortex depth (R2 =0.876). We showed an excessive systolic DI could differentiate infarcted LV with normal EF from healthy LV. Strong flow acceleration, LVMD, and vortex-infarct interactions were predominant factors that induced excessive DI in infarcted LVs. Instead of causing undesired flow turbulence, high systolic E' suggested the existence of energetic flow acceleration, while high diastolic E' implied an inefficient diastolic filling. Thus, systolic E' is not a suitable early indicator for progressive LV dysfunction in MI patients, while diastolic E' may be a useful index to indicate diastolic impairment in these patients.

Quantitative analysis of intraventricular flow-energetics and vortex in ischaemic hearts.

This study investigated the intraventricular flow dynamics in ischaemic heart disease patients. Fourteen patients with normal ejection fraction and 16 patients with reduced ejection fraction were compared with 20 healthy individuals. Phase-contrast MRI was used to assess intraventricular flow variables and speckle-tracking echocardiography to assess myocardial strain and left ventricular (LV) dyssynchrony. Infarct size was acquired using delayed-enhancement MRI. The results obtained showed no significant differences in intraventricular flow variables between the healthy group and the patients with normal ejection fraction group, whereas considerable reductions in kinetic energy (KE) fluctuation index, E' (P<0.001) and vortex KE (P=0.003) were found in the patients with reduced ejection fraction group. In multivariate analysis, only vortex KE and infarct size were significantly related to LV ejection fraction (P<0.001); furthermore, vortex KE was correlated negatively with energy dissipation, energy dissipation index (r=-0.44, P=0.021). This study highlights that flow energetic indices have limited applicability as early predictors of LV progressive dysfunction, whereas vortex KE could be an alternative to LV performance.

Determinants of kinetic energy of blood flow in the four-chambered heart in athletes and sedentary controls.

The kinetic energy (KE) of intracardiac blood may play an important role in cardiac function. The aims of the present study were to 1) quantify and investigate the determinants of KE, 2) compare the KE expenditure of intracardiac blood between athletes and control subjects, and 3) quantify the amount of KE inside and outside the diastolic vortex. Fourteen athletes and fourteen volunteers underwent cardiac MRI, including four-dimensional phase-contrast sequences. KE was quantified in four chambers, and energy expenditure was calculated by determining the mean KE/cardiac index. Left ventricular (LV) mass was an independent predictor of diastolic LVKE (R(2) = 0.66, P < 0.001), whereas right ventricular (RV) end-diastolic volume was important for diastolic RVKE (R(2) = 0.76, P < 0.001). The mean KE/cardiac index did not differ between groups (control subjects: 0.53 ± 0.14 mJ·l(-1)·min·m(2) and athletes: 0.56 ± 0.21 mJ·l(-1)·min·m(2), P = 0.98). Mean LV diastolic vortex KE made up 70 ± 1% and 73 ± 2% of total LV diastolic KE in athletes and control subjects (P = 0.18). In conclusion, the characteristics of the LV as a pressure pump and the RV as a volume pump are demonstrated as an association between LVKE and LV mass and between RVKE and end-diastolic volume. This also suggests different filling mechanisms where the LV is dependent on diastolic suction, whereas the RV fills with a basal movement of the atrioventricular plane over "stationary" blood. Both groups had similar energy expenditure for intracardiac blood flow, indicating similar pumping efficiency, likely explained by the lower heart rate that cancels the higher KE per heart beat in athletes. The majority of LVKE is found within the LV diastolic vortex, in contrast to earlier findings.

Intraventricular vortex properties in nonischemic dilated cardiomyopathy

Vortices may have a role in optimizing the mechanical efficiency and blood mixing of the left ventricle (LV). We aimed to characterize the size, position, circulation, and kinetic energy (KE) of LV main vortex cores in patients with nonischemic dilated cardiomyopathy (NIDCM) and analyze their physiological correlates. We used digital processing of color-Doppler images to study flow evolution in 61 patients with NIDCM and 61 age-matched control subjects. Vortex features showed a characteristic biphasic temporal course during diastole. Because late filling contributed significantly to flow entrainment, vortex KE reached its maximum at the time of the peak A wave, storing 26 ± 20% of total KE delivered by inflow (range: 1-74%). Patients with NIDCM showed larger and stronger vortices than control subjects (circulation: 0.008 ± 0.007 vs. 0.006 ± 0.005 m(2)/s, respectively, P = 0.02; KE: 7 ± 8 vs. 5 ± 5 mJ/m, P = 0.04), even when corrected for LV size. This helped confining the filling jet in the dilated ventricle. The vortex Reynolds number was also higher in the NIDCM group. By multivariate analysis, vortex KE was related to the KE generated by inflow and to chamber short-axis diameter. In 21 patients studied head to head, Doppler measurements of circulation and KE closely correlated with phase-contract magnetic resonance values (intraclass correlation coefficient = 0.82 and 0.76, respectively). Thus, the biphasic nature of filling determines normal vortex physiology. Vortex formation is exaggerated in patients with NIDCM due to chamber remodeling, and enlarged vortices are helpful for ameliorating convective pressure losses and facilitating transport. These findings can be accurately studied using ultrasound.

Evolution of a hairpin vortex in a shear-thinning fluid governed by a power-law model

The effect of a shear-thinning fluid governed by a power-law model on the evolution of a hairpin vortex in a wall-bounded flow was studied by means of direct numerical simulation. With a fixed Reynolds number and hairpin vortex strength, the effect of shear-thinning on vortex evolution could be isolated. The primary observation is that very early in time shear-thinning has the effect of reducing the production of vortex kinetic energy and dramatically increasing viscous dissipation. This leads to a delay in the transition of the flow to a turbulent state. Three-dimensional flow visualizations reveal that the increased dissipation is associated with an instability in which the hairpin vortex is broken down into small-scale structures. It is suggested that the finite amplitude of the hairpin creates a lowering of viscosity near the hairpin vortex core which leads to this instability.

Vortical dynamics in the wake of water strider locomotion

Previous studies reported that the hydrodynamic propulsion of the water strider also results from transferring momentum to the underlying fluid through hemispherical dipolar vortices shed by its driving legs. However, there are no accuracy experimental measurements of these vortical structures to prove the mechanics of vortical propulsion. Here, we reveal the vortical structures by reporting the simultaneous measurements of the water strider’s motion and the fluid velocity field with the high-speed PIV, and proposing a new method of calculating the vortex kinetic energy and vortex momentum. We found that the asymmetrical vortical structure in each dipolar vortex, generated by one driving stroke, propels the water strider forward, and the outer elliptic vortex is weaker than the inner circular vortex. The movement of the dipolar vortex is divided into two stages: (1) translating backward and (2) return curving. In this way, the water strider obtains the maximum velocity with minimal consumption of energy. The fluid vortical momentum, generated by the driving stroke, accounts for about 64–90% of the water strider’s momentum.

Finite vortex numbers and symmetric vortex structures in a rotating trapped Fermi gas in the BCS-BEC crossover

The ground state of a three-dimensional (3D) rotating trapped superfluid Fermi gas in the BCS-BEC crossover is mapped to finite Nv-body vortex states by a simple ansatz. The total vortex energy is measured from the ground-state energy of the system in the absence of the vortices. The vortex state is stable since the vortex potential and rotation energies are attractive while the vortex kinetic energy and interaction between vortices are repulsive. By combining the analytical and numerical works for the minimal vortex energy, the 2D configurations of Nv vortices are studied by taking into account of the finite size effects both on xy-plane and on z-direction. The calculated vortex numbers as a function of the interaction strength are appropriate to the renew experimental results by Zwierlein in [High-temperature superfluidity in a ultracold Fermi gas, Ph.D. thesis, Massachusetts Institute of Technology, 2006]. The numerical results show that there exist two types of vortex structures: the trap center is occupied and unoccupied by a vortex, even in the case of Nv < 10 with regular polygon and in the case of Nv≥ 10 with finite triangle lattice. The rotation frequency dependent vortex numbers with different interaction strengths are also discussed.

Dynamics of ring vortices impinging on planar shock waves

In the present paper the encounter of vortex rings with planar shock waves is studied in a three-dimensional environment, with the objective to assess the influence of shock and vortex strength and vortex orientation on the dynamics of the process. The study relies on numerical simulations performed by means of a state-of-the-art hybrid compact/WENO (weighted essentially nonoscillatory) shock-capturing algorithm to solve the Euler equations of gas dynamics. The study focuses on the characterization of the interaction in terms of the evolution of the geometrical parameters of the vortex and the mean flow properties such as kinetic energy and enstrophy. The vortex is compressed as it passes through the shock, and its characteristic dimensions decrease; at the same time its axis is deflected and the ring follows a complex dynamic evolution, even though a nearly steady state is reached for the global quantities. In particular, it has been found that the total vortex kinetic energy is generally nonincreasing after the interaction, while the enstrophy always increases. A simple theory is developed here to shed some light onto the physical phenomena involved, which is found to compare reasonably well with the results of the computations. Some final comments are made regarding the extension of the results reported in the present study to the analysis of shock-compressed turbulence.

Time-accurate computation of unsteady free surface flows using an ALE-segregated equal-order FEM

Arbitrary Lagrangian–Eulerian (ALE) finite element formulations based on segregated equal-order interpolation are presented with the aim of computing unsteady free surface flows time-accurately. A standing vortex problem is solved using both fixed and moving grids to design a solution method which is time-accurate in the sense that it conserves vortex kinetic energy. It turns out that the ‘Chorin type SIMPLE algorithm’ serves this purpose satisfactorily when it is used in conjunction with the Galerkin spatial discretization and the Crank–Nicolson temporal discretization. Then, a small amplitude sloshing problem is solved to assure that the Crank–Nicolson/central difference scheme among others used for discretizing the kinematic condition preserves the oscillating amplitude of the free surface. Lastly, the most time-accurate numerical technique thus designed is applied to solve a solitary wave propagation problem, which shows that the predicted maximum run-up heights for various initial heights are in good agreement with existing experiment.

Trapping of vortices by impurities in thin 4He films

Quantum vortices are excitations which are spontaneously created in thin superfluid 4He films at low temperatures. They are trapped by impurity atoms. We have calculated microscopically the chemical potentials of 3He and hydrogen isotope impurities as well as vortex creation using a variational many-body wave function. Our results for the vortex core parameters agree with recent Monte Carlo calculations. Those chemical potentials are compared with the energy required to create the vortex excitation around the impurity. We find that the energy gained is ≈4 K at the saturation density of the 2 D 4 He fluid and increases with the density. The unknown parameter in our model is the vortex mass. We discuss two choices; the mass is set equal to the mass of the expelled superfluid volume and secondly the vortex kinetic energy is set equal to zero, which reduces the energy gain by 2 K.

Dry vortices in thin helium films

A very thin superfluid film on a weakly attractive surface (such as rubidium metal) should display an unusual vortex structure, with a dry core larger than the standard core radius λ. In this structure, the capillary energies are slightly increased, but the vortex kinetic energy is reduced.

Investigation of Throughflow Hypothesis in a Turbine Cascade Using a Three-Dimensional Navier–Stokes Computation

The results of a computation, performed with a three-dimensional Navier–Stokes computation at ONERA, have been averaged in the blade-to-blade direction; the spatial fluctuations around the averaged flow variables have also been determined. It has then been possible to estimate all terms in the average components of the momentum equations. The comparison of the two-dimensional balances of these three equations shows that the shear stress plays a minor role in the momentum balance, except on the dissipation of the passage vortex kinetic energy downstream of the blade trailing edges. The kinetic energy of the spanwise component of the velocity spatial fluctuations has a very strong influence on the radial pressure gradient; it introduces a convection effect. This is a key effect for all these balances.

Detailed investigation of energy transfers in homogeneous stratified turbulence*

This paper investigates some irreversible mechanisms occurring in homogeneous stably stratified turbulent flows. In terms of the eigenmodes of the linear regime, the velocity-temperature field is decomposed into a vortex and two wavy components. Using an eddy-damped quasinormal Markovian (EDQNM) closure with the axisymmetry hypothesis, an analysis of the anisotropic energy transfers between the vortex kinetic energy, the wave kinetic and potential energy is made. Within the light of triadic exchanges, and by analogy of the resonance condition for three linearly interacting gravity waves, the closure model allows one to compute the detailed transfers for eight types of interactions. Results of the calculations include time evolution plots, for the isotropic closure model as well as two different types of the anisotropic closure. The pure vortical interactions are shown to be responsible for the irreversible anisotropic structure created by stable stratification, and this structure prevents the inverse cascade of two-dimensional turbulence.