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Liu, Han Xiao, Zhong Liu, Huai Liang Li, Xin Xin Feng i Zhen Zhong Xing. "Multiple Vortex Body Vortex Numerical Simulation". Advanced Materials Research 328-330 (wrzesień 2011): 1755–58. http://dx.doi.org/10.4028/www.scientific.net/amr.328-330.1755.
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In this paper, the continuity equation, momentum equation and the k-ε turbulence equation were introduced to simulate the flow field of the multiple vortex bodies in different spacing cases. Found that each vortex body had good effect in producing vortex, and the greater flow field spacing, the smaller the highest velocity; the turbulence intensity is increasing gradually from the former vortex body to the next one, and there may be a best spacing between the vortex bodies which makes the best turbulent intensity. All of these theories provide a train of thought for the turbulent coalescence mechanism.
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Ashworth Briggs, Alexander, Alan Fleming, Jonathan Duffy i Jonathan R. Binns. "Tracking the vortex core from a surface-piercing flat plate by particle image velocimetry and numerical simulation". Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 233, nr 3 (23.07.2018): 793–808. http://dx.doi.org/10.1177/1475090218776202.
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The wake flow around the tip of a surface piercing flat plate at an angle of incidence was studied using two-dimensional particle image velocimetry as part of benchmarking the particle image velocimetry technique on the moving carriage in the Australian Maritime College towing tank. Particle image velocimetry results were found to be in close agreement with those of the benchmarking work presented by the Hydro Testing Alliance, and a method of tracking the tip-vortex core near a free surface throughout numerical simulation has been demonstrated. Issues affecting signal to noise ratio, such as specula reflections from the free surface and model geometry were overcome through the use of fluorescing particles and a high-pass optical filter. Numerical simulations using the ANSYS CFX Solver with the volume of fluid method were validated against the experimental results, and a methodology was developed for tracking the location of the wandering vortex core experimentally and through simulation. The ability of the scale-adaptive simulation shear stress transport turbulence model and the shear stress transport model to simulate three-dimensional flow with high streamline curvature was compared. The scale-adaptive simulation shear stress transport turbulence model was found to provide a computationally less resource-intensive method of simulating a complex flow topology with large eddies, providing an insight into a possible cause of tip-vortex aperiodic wandering motion. At high angles of attack, vortex shedding from the leading edge separation of the test geometry is identified as a possible cause of the wandering phenomena. In this study, the vortex centre and point of extreme core velocity were found not to be co-located. The point of extreme stream wise velocity within the vortex core was found to be located within half the vortex radius of the vortex centre.
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Kerr, Robert M., i Fazle Hussain. "Simulation of vortex reconnection". Physica D: Nonlinear Phenomena 37, nr 1-3 (lipiec 1989): 474–84. http://dx.doi.org/10.1016/0167-2789(89)90151-6.
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Sun, Qiji, Chenxi Xu, Xuan Zou, Wei Guan, Xiao Liu, Xu Yang i Ao Ren. "Shape Optimization of the Triangular Vortex Flowmeter Based on the LBM Method". Symmetry 17, nr 4 (31.03.2025): 534. https://doi.org/10.3390/sym17040534.
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In this paper, the D3Q19 multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) for large eddy simulation (LES) was employed to optimize the shape of the vortex generator in a triangular vortex flowmeter. The optimization process focused on the vortex shedding frequency, lift force per unit area, and symmetry of the vortex street. The optimal shape of the vortex generator was determined to feature a 180° incoming flow surface, a concave arc side with a curvature radius of 25 mm, and a fillet radius of 4 mm at the end. Numerical simulations revealed that the optimized vortex generator achieves a 2.72~13.8% increase in vortex shedding frequency and a 17.2~53.9% reduction in pressure drop and can adapt to the flow conditions of productivity fluctuations (6.498 × 105 ≤ Re ≤ 22.597 × 105) in the gas well production. The results demonstrated significant advantages, including low pressure loss, minimal secondary vortex generation, high vortex shedding frequency, and substantial lift force. These findings underscore the robustness and efficiency of the LBM-LES method in simulating complex flow dynamics and optimizing vortex generator designs.
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Azarpira, Maryam, Amir Zarrati i Pouya Farrokhzad. "Comparison between the Lagrangian and Eulerian Approach in Simulation of Free Surface Air-Core Vortices". Water 13, nr 5 (7.03.2021): 726. http://dx.doi.org/10.3390/w13050726.
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The problematic consequences regarding formation of air-core vortices at the intakes and the drastic necessity of a thorough investigation into the phenomenon has resulted in particular attention being placed on Computational Fluid Dynamics (CFD) as an economically viable method. Two main approaches could be taken using CFD, namely the Eulerian and Lagrangian methods each of which is characterized by specific advantages and disadvantages. Whereas many researchers have used the Eulerian approach for vortex simulation, the Lagrangian approach has not been found in the literature. The present study dealt with the comparison of the Lagrangian and Eulerian approaches in the simulation of vortex flow. Simulations based on both approaches were carried out by solving the Navier–Stokes equations accompanied by the LES turbulence model. The results of the numerical model were evaluated in accordance with a physical model for steady vortex flow using particle image velocimetry (PIV), revealing that both approaches are sufficiently capable of simulating the vortex flow but with the difference that the Lagrangian method has greater computational cost with less accuracy.
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Reyes, Jefferson Alberto Porras, Luis Miguel Navarrete Lopez, Jorge Ivan Armijo Martinez i Daniel Andrés Navarrete Proaño. "Hydrodynamic phenomena in a vertical-axis vortex turbine". Region - Water Conservancy 7, nr 1 (25.07.2024): 105. http://dx.doi.org/10.32629/rwc.v7i1.2431.
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The present work aims to develop a safely designed simulation by generating a sustainable hydraulic system coupled with energy study needs, which collaborates with less costs and more benefits. Based on simulations with the scale model using the ANSYS tool, it aims to find the efficiency at the time of executing this simulation at full scale. Mainly the motivations of the work are based on new methods of obtaining energy for the conservation of the environment. This is how the idea of designing and simulating a new gravitational vortex turbine system, with geometries according to what has been found in the literature and in previous studies, is materialized. In this way we proceed to design and simulate a turbine device composed of a vortex impeller that can resist erosion and sediments and allows the development of a gravitational vortex with a considerable hydraulic power. Once the turbine geometry is defined, a modeling is made in ANSYS software, in order to know the behavior of the vortex, define the geometric configuration of it, which will also work under the concept of "drag".
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Liu, Yongwei, Yalin Li i Dejiang Shang. "The Generation Mechanism of the Flow-Induced Noise from a Sail Hull on the Scaled Submarine Model". Applied Sciences 9, nr 1 (29.12.2018): 106. http://dx.doi.org/10.3390/app9010106.
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Flow-induced noise from the sail hull, which is induced by the horseshoe vortex, the boundary layer separation and the tail vortex shedding, is a significant problem for the underwater vehicles, while has not been adequately studied. We have performed simulations and experiments to reveal the noise generation mechanism from these flows using the scaled sail hull with part of a submarine body. The large eddy simulation and the wavenumber–frequency spectrum are adopted for simulations. The frequency ranges from 10 Hz to 2000 Hz. The simulation results show that the flow-induced noise with the frequency less than 500 Hz is mainly generated by the horseshoe vortex; the flow-induced noise because of the tail vortex shedding is mainly within the frequency of shedding vortex, which is 595 Hz in the study; the flow-induced noise caused by the boundary layer separation lies in the whole frequency range. Moreover, we have conducted the experiments in a gravity water tunnel, and the experimental results are in good accordance with the simulation results. The results can lay the foundation for the design of flow control devices to suppress and reduce the flow-induced noise from the sail hull.
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Liu, Xiao Lei, Song Li, Jing Shan Jiao, Yong Xue Liu, Lei Ming i Xiu Juan Liu. "Numerical Simulation of Tip Vortex in Air Refueling". Advanced Materials Research 712-715 (czerwiec 2013): 1217–20. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.1217.
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Based on analysis on the tip vortex in air refueling, a model for simulating the tip vortex of air refueling is established in this paper, and the simulation results is studied. The results show that the established model is suitable for different aerial environments and mission requirements.
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Lu, Yixiong, Tongwen Wu, Xin Xu, Li Zhang i Min Chu. "Improved Simulation of the Antarctic Stratospheric Final Warming by Modifying the Orographic Gravity Wave Parameterization in the Beijing Climate Center Atmospheric General Circulation Model". Atmosphere 11, nr 6 (1.06.2020): 576. http://dx.doi.org/10.3390/atmos11060576.
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The Antarctic stratospheric final warming (SFW) is usually simulated with a substantial delay in climate models, and the corresponding temperatures in austral spring are lower than observations, implying insufficient stratospheric wave drag. To investigate the role of orographic gravity wave drag (GWD) in modeling the Antarctic SFW, in this study the orographic GWD parameterization scheme is modified in the middle-atmosphere version of the Beijing Climate Center Atmospheric General Circulation Model. A pair of simulations are conducted to compare two orographic GWD schemes in simulating the breakdown of the stratospheric polar vortex over Antarctica. The control simulation with the default orographic GWD scheme exhibits delayed vortex breakdown and the cold-pole bias seen in most climate models. In the simulation with modified orographic GWD scheme, the simulated vortex breaks down earlier by 8 days, and the associated cold-pole bias is reduced by more than 2 K. The modified scheme provides stronger orographic GWD in the lower stratosphere, which drives an accelerated polar downwelling branch of the Brewer–Dobson circulation and, in turn, produces adiabatic warming. Our study suggests that modifying orographic GWD parameterizations in climate models would be a valid way of improving the SFW simulation over Antarctica.
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Chiu, Ching-Kai, T. Machida, Yingyi Huang, T. Hanaguri i Fu-Chun Zhang. "Scalable Majorana vortex modes in iron-based superconductors". Science Advances 6, nr 9 (luty 2020): eaay0443. http://dx.doi.org/10.1126/sciadv.aay0443.
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The iron-based superconductor FeTexSe1−x is one of the material candidates hosting Majorana vortex modes residing in the vortex cores. It has been observed by recent scanning tunneling spectroscopy measurement that the fraction of vortex cores having zero-bias peaks decreases with increasing magnetic field on the surface of FeTexSe1−x. The hybridization of two Majorana vortex modes cannot simply explain this phenomenon. We construct a three-dimensional tight-binding model simulating the physics of over a hundred Majorana vortex modes in FeTexSe1−x. Our simulation shows that the Majorana hybridization and disordered vortex distribution can explain the decreasing fraction of the zero-bias peaks observed in the experiment; the statistics of the energy peaks off zero energy in our Majorana simulation are in agreement with the experiment. These agreements lead to an important indication of scalable Majorana vortex modes in FeTexSe1−x. Thus, FeTexSe1−x can be one promising platform having scalable Majorana qubits for quantum computing.
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Fan, Dingfan, Min Yu, Zhixiang Yao, Yang Du i Hang Liu. "A Method for Real-Time Measurement of the Vertical Vortex at Flood Discharge Outlets Using Ultrasonic Sensors". Sensors 24, nr 17 (28.08.2024): 5583. http://dx.doi.org/10.3390/s24175583.
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In this study, ultrasonic sensors were used to measure the vertical vortex at flood discharge outlets in real time, and numerical simulations and model experiments were conducted. When a sound signal passes through a vortex, its propagation characteristics will change, which helps to determine the existence of the vortex. Moreover, its characteristic parameters can be obtained through inversion. In this paper, first, the theories of acoustic measurement methods were introduced and their feasibility was verified through a comparison between Particle Image Velocimetry (PIV) measurement and numerical simulation results. Then, the Computational Fluid Dynamics (CFD) method was used to simulate the vertical vortex at the flood discharge outlets of hydraulic structures and the simulation data were restored to the actual size at scale. Finally, acoustic numerical simulations of actual vortex data were conducted, and ultrasonic sensors were used to measure the velocity of a simplified vertical vortex model under laboratory conditions. The research results indicate that the acoustic measurement method proposed in this article is effective in the measurement of the characteristic parameters of vertical vortex with a core radius of 0.03~0.05 m and a maximum tangential velocity of 0.5 m/s, the measurement error of the maximum tangential velocity is within 10%.
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Kiya, Masaru, i Hajime Ishii. "Vortex dynamics simulation of interacting vortex rings and filaments". Fluid Dynamics Research 3, nr 1-4 (wrzesień 1988): 197–202. http://dx.doi.org/10.1016/0169-5983(88)90065-2.
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Tryggvason, Grétar. "Simulation of vortex sheet roll-up by vortex methods". Journal of Computational Physics 80, nr 1 (styczeń 1989): 1–16. http://dx.doi.org/10.1016/0021-9991(89)90087-9.
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Hu, Zilong, Jiale Pan, Ran Tao, Yanzhao Wu, Di Zhu i Ruofu Xiao. "Large Eddy Simulation of Hydrofoil Tip Leakage Vortex". Journal of Physics: Conference Series 2463, nr 1 (1.03.2023): 012021. http://dx.doi.org/10.1088/1742-6596/2463/1/012021.
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Abstract The axial-flow turbomachinery is important in water supply and drainage. However, there is a gap between the blade tip and the casing, which is easy to cause tip leakage vortex. Tip leakage of axial-flow turbomachinery has bad impact on the operation stability. In this case, the numerical simulation is used to study the simplified hydrofoil model with clearance. Then the change of tip leakage vortex core position and the pressure distribution are analyzed. Results show that with the fluid flows downstream, the longitudinal position of the tip leakage vortex core first drops and then rises. On different streamwise planes, the vortex core has the lowest pressure. From the downstream to the vortex generating position, the vortex core pressure decreases gradually, and the cavitation is most likely to occur at the location where the vortex occurs.
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Gao, Qinggang, Christian Zeman, Jesus Vergara-Temprado, Daniela C. A. Lima, Peter Molnar i Christoph Schär. "Vortex streets to the lee of Madeira in a kilometre-resolution regional climate model". Weather and Climate Dynamics 4, nr 1 (2.02.2023): 189–211. http://dx.doi.org/10.5194/wcd-4-189-2023.
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Abstract. Atmospheric vortex streets are a widely studied dynamical effect of isolated mountainous islands. Observational evidence comes from case studies and satellite imagery, but the climatology and annual cycle of vortex shedding are often poorly understood. Using the non-hydrostatic limited-area COSMO model driven by the ERA-Interim reanalysis, we conducted a 10-year-long simulation over a mesoscale domain covering the Madeira and Canary archipelagos at high spatial (grid spacing of 1 km) and temporal resolutions. Basic properties of vortex streets were analysed and validated through a 6 d long case study in the lee of Madeira Island. The simulation compares well with satellite and aerial observations and with existing literature on idealised simulations. Our results show a strong dependency of vortex shedding on local and synoptic-flow conditions, which are to a large extent governed by the location, shape and strength of the Azores high. As part of the case study, we developed a vortex identification algorithm. The algorithm is based on a set of criteria and enabled us to develop a climatology of vortex shedding from Madeira Island for the 10-year simulation period. The analysis shows a pronounced annual cycle with an increasing vortex-shedding rate from April to August and a sudden decrease in September. This cycle is consistent with mesoscale wind conditions and local inversion height patterns.
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Liu, Zhenxiong. "The numerical simulation research of civil aviation engineer internal flow stability". Journal of Physics: Conference Series 2955, nr 1 (1.02.2025): 012022. https://doi.org/10.1088/1742-6596/2955/1/012022.
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Abstract Steady three-dimensional numerical simulations have been used for the civil aviation engineer model to research internal flow stability. A comparison of the numerical method with empirical data validates the accuracy of CFD predictions, revealing a high level of agreement between the two. The simulation of the internal flow field indicates that the tip leakage vortex retains its form in the downstream area beyond the shock wave, achieving peak efficiency, while maintaining a stable vortex vector direction. When the vortex nears a stall condition, vigorous interaction between the vortex and the shock wave leads to the disintegration of the vortex, resulting in a spiral formation. The presence of a low-energy fluid region at the rotor blade’s tip is attributed to the intrusion of the leakage vortex, which may trigger flow instability. The characteristics of this phenomenon resemble those of rotational instability, highlighting the intricate nature of the flow dynamics.
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Barannikova, D. D., V. E. Borzykh i A. G. Obukhov. "Numerical simulation of fire vortex". IOP Conference Series: Materials Science and Engineering 357 (maj 2018): 012040. http://dx.doi.org/10.1088/1757-899x/357/1/012040.
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Mansfield, John R., Omar M. Knio i Charles Meneveau. "Towards lagrangian large vortex simulation". ESAIM: Proceedings 1 (1996): 49–64. http://dx.doi.org/10.1051/proc:1996019.
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Tao, Rui, Hongxiang Ren, Delong Wang i Xiangen Bai. "Research on smoke simulation with vortex shedding". PLOS ONE 17, nr 6 (16.06.2022): e0269114. http://dx.doi.org/10.1371/journal.pone.0269114.
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The Lagrangian vortex method has the advantage of producing highly detailed simulations of fluids such as turbulent smoke. However, this method has two problems: the construction of the velocity field from the vorticity field is inefficient, and handling the boundary condition is difficult. We present a pure Lagrangian vortex method, including a nested grid to accelerate the construction of the velocity field, and a novel boundary treatment method for the vorticity field. Based on a tree structure, the nested grid algorithm considerably improves the efficiency of the velocity computation while producing visual results that are comparable with the original flow. Based on the vortex-generating method, the least square method is used to compute the vorticity strength of the new vortex elements. Further, we consider the mutual influence between the generated vortex particles. We demonstrate our method’s benefits by using a vortex ring and various examples of interaction between the smoke and obstacles.
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Saban, D., J. F. Whidborne i A. K. Cooke. "Simulation of wake vortex effects for UAVs in close formation flight". Aeronautical Journal 113, nr 1149 (listopad 2009): 727–38. http://dx.doi.org/10.1017/s0001924000003389.
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AbstractThis paper addresses the development of multiple UAV deployment simulation models that include representative aerodynamic cross-coupling effects. Applications may include simulations of autonomous aerial refuelling and formation flying scenarios. A novel wake vortex model has been developed and successfully integrated within a Matlab/Simulink simulation environment. The wake vortex model is both sufficiently representative to support studies of aerodynamic interaction between multiple air vehicles, and straightforward enough to be used within real time or near real time air-to-air simulations. The model integration process is described, and computational results of a two-vehicle-formation flight are presented.
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Forster, Kyle J., Sammy Diasinos, Graham Doig i Tracie J. Barber. "Large eddy simulation of transient upstream/downstream vortex interactions". Journal of Fluid Mechanics 862 (9.01.2019): 227–60. http://dx.doi.org/10.1017/jfm.2018.949.
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Experimentally validated large eddy simulations were performed on two NACA0012 vanes at various lateral offsets to observe the transient effects of the near field interactions between two streamwise vortices. The vanes were separated in the streamwise direction, allowing the upstream vortex to impact on the downstream geometry. These vanes were evaluated at an angle of incidence of $8^{\circ }$ and a Reynolds number of 70 000, with rear vane angle reversed to create a co-rotating or counter-rotating vortex pair. The downstream vortex merged with the upstream in the co-rotating condition, driven by the suppression of one of the tip vortices of the downstream vane. At close proximity to the pressure side, the vane elongated the upstream vortex, resulting in it being the weakened and merging into the downstream vortex. This produced a transient production of bifurcated vortices in the wake region. The downstream vortex of the co-rotating pair experienced faster meandering growth, with position oscillations equalising between the vortices. The position oscillation was determined to be responsible for statistical variance in the merging location, with variation in vortex separation causing the vortices at a single plane to merge and separate in a time-dependent manner. In the counter-rotating condition position oscillations were found to be larger, with higher growth, but less uniform periodicity. It was found that the circulation transfer between the vortices was linked to the magnitude of their separation, with high separation fluctuations weakening the upstream vortex and strengthening the downstream vortex. In the case of upstream vortex impingement on the downstream vane, the upstream vortex was found to bifurcate, with a four vortex system being formed by interactions with the shear layer. This eventually resulted in a single dominant vortex, which did not magnify its oscillation amplitudes as it travelled downstream due to the destruction of the interacting vortices.
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Belotsercovsky, Sergei, i Nikolay Khlapov. "Simulation of vortex diffusion influence on jet turbulent characteristics". Izvestiya VUZ. Applied Nonlinear Dynamics 3, nr 2 (15.12.1995): 94–103. https://doi.org/10.18500/0869-6632-1995-3-2-94-103.
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The method is suggested for calculation of molecular diffusion on the base of Discret Vortex Method. A lot of examples: diffusion of infinit vortex filament, motion of vortex pair and issue of plane jet are exemplified. An approximate calculation of vortex diffusion is also presented.
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KEVLAHAN, N. K. R., i M. FARGE. "Vorticity filaments in two-dimensional turbulence: creation, stability and effect". Journal of Fluid Mechanics 346 (10.09.1997): 49–76. http://dx.doi.org/10.1017/s0022112097006113.
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Vorticity filaments are characteristic structures of two-dimensional turbulence. The formation, persistence and effect of vorticity filaments are examined using a high-resolution direct numerical simulation (DNS) of the merging of two positive Gaussian vortices pushed together by a weaker negative vortex. Many intense spiral vorticity filaments are created during this interaction and it is shown using a wavelet packet decomposition that, as has been suggested, the coherent vortex stabilizes the filaments. This result is confirmed by a linear stability analysis at the edge of the vortex and by a calculation of the straining induced by the spiral structure of the filament in the vortex core. The time-averaged energy spectra for simulations using hyper-viscosity and Newtonian viscosity have slopes of −3 and −4 respectively. Apart from a much higher effective Reynolds number (which accounts for the difference in energy spectra), the hyper-viscous simulation has the same dynamics as the Newtonian viscosity simulation. A wavelet packet decomposition of the hyper-viscous simulation reveals that after the merger the energy spectra of the filamentary and coherent parts of the vorticity field have slopes of −2 and −6 respectively. An asymptotic analysis and DNS for weak external strain shows that a circular filament at a distance R from the vortex centre always reduces the deformation of a Lamb's (Gaussian) vortex in the region r[ges ]R. In the region r<R the deformation is also reduced provided the filament is intense and is in the vortex core, otherwise the filament may slightly increase the deformation. The results presented here should be useful for modelling the coherent and incoherent parts of two-dimensional turbulent flows.
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Huan, Nguyen Van. "A HAIR AND HAIR VORTEX SIMULATION TECHNIQUE BASED ON VECTOR FIELDS ON A MANIFOLD". Vietnam Journal of Science and Technology 54, nr 1 (20.02.2016): 109. http://dx.doi.org/10.15625/0866-708x/54/1/6016.
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Hair is an important component in the virtual human simulation system. During hair simulation, not only the time required to ensure that there are required to express the physical characteristics, chemical such as hair styles, colors, curves, twists, parting one’s hair and hair vortex (swirl), ... to represent the authenticity of the hair and improve hair simulation quality. While the studies has announced today that they mainly focus on simulating the styles, the motion of the hair that has not been expressed characteristics of hair as hair vortex,... The paper introduces the concept of scalp model as a manifold in 3-dimensional space. Based on the nature of the singularity of the vector field on the manifold, the paper proposes a hair simulation technique on the scalp surface model based on vector field on the manifold. Thus, we can simulate appropriately the hair vortex on the scalp model.
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Arnold, M., S. Filopoulos, W. White i M. Kamruzzaman. "A semi-empirical model for time-domain tower Vortex induced Vibration load simulations of wind turbines". Journal of Physics: Conference Series 2767, nr 2 (1.06.2024): 022032. http://dx.doi.org/10.1088/1742-6596/2767/2/022032.
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Abstract A new method for simulating aeroelastic resonances between vortex shedding and structural eigenfrequencies of a wind turbine tower is presented in this publication. This aero-elastic effect of Vortex induced Vibrations (ViV) has the potential to disrupt installation processes and cause fatigue and extreme loads on the tower. Despite this issue, there are no established simulation methods available in literature, able and sufficiently efficient to predict the ViV in turbulent and site specific design load conditions. This state-of-the-art is extended by introducing an efficient semi-empirical, time-domain simulation method, which is capable of analyzing the tower ViV excitations and aeroelastic responses in wind turbine load simulations of the isolated tower or the full turbine for fatigue and extreme loads. The method is based on an adaptive harmonic equation, which is automatically tuned to the instantaneous tower motions.
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ZHANG, YANZHI, WEIZHU BAO i QIANG DU. "Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation". European Journal of Applied Mathematics 18, nr 5 (październik 2007): 607–30. http://dx.doi.org/10.1017/s0956792507007140.
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The rich dynamics of quantized vortices governed by the Ginzburg-Landau-Schrödinger equation (GLSE) is an interesting problem studied in many application fields. Although recent mathematical analysis and numerical simulations have led to a much better understanding of such dynamics, many important questions remain open. In this article, we consider numerical simulations of the GLSE in two dimensions with non-zero far-field conditions. Using two-dimensional polar coordinates, transversely highly oscillating far-field conditions can be efficiently resolved in the phase space, thus giving rise to an unconditionally stable, efficient and accurate time-splitting method for the problem under consideration. This method is also time reversible for the case of the non-linear Schrödinger equation. By applying this numerical method to the GLSE, we obtain some conclusive experimental findings on issues such as the stability of quantized vortex, interaction of two vortices, dynamics of the quantized vortex lattice and the motion of vortex with an inhomogeneous external potential. Discussions on these simulation results and the recent theoretical studies are made to provide further understanding of the vortex stability and vortex dynamics described by the GLSE.
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Domfeh, Martin Kyereh, Samuel Gyamfi, Mark Amo-Boateng, Robert Andoh, Eric Antwi Ofosu i Gavin Tabor. "Numerical Simulation of an Air-Core Vortex and Its Suppression at an Intake Using OpenFOAM". Fluids 5, nr 4 (26.11.2020): 221. http://dx.doi.org/10.3390/fluids5040221.
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A common challenge faced by engineers in the hydraulic industry is the formation of free surface vortices at pump and power intakes. This undesirable phenomenon which sometimes entrains air could result in several operational problems: noise, vibration, cavitation, surging, structural damage to turbines and pumps, energy losses, efficiency losses, etc. This paper investigates the numerical simulation of an experimentally observed air-core vortex at an intake using the LTSInterFoam solver in OpenFOAM. The solver uses local time-stepping integration. In simulating the air-core vortex, the standard k − ε, realizable k − ε, renormalization group (RNG) k − ε and the shear stress transport (SST) k − ω models were used. The free surface was modelled using the volume of fluid (VOF) model. The simulation was validated using a set of analytical models and experimental data. The SST k − ω model provided the best results compared to the other turbulence models. The study was extended to simulate the effect of installing an anti-vortex device on the formation of a free surface vortex. The LTSInterFoam solver proved to be a reliable solver for the steady state simulation of a free surface vortex in OpenFOAM.
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Nguyen, Leon T., i John Molinari. "Simulation of the Downshear Reformation of a Tropical Cyclone". Journal of the Atmospheric Sciences 72, nr 12 (19.11.2015): 4529–51. http://dx.doi.org/10.1175/jas-d-15-0036.1.
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Abstract The downshear reformation of Tropical Storm Gabrielle (2001) was simulated at 1-km horizontal resolution using the Weather Research and Forecasting (WRF) Model. The environmental shear tilted the initial parent vortex downshear left and forced azimuthal wavenumber-1 kinematic, thermodynamic, and convective asymmetries. The combination of surface enthalpy fluxes and a lack of penetrative downdrafts right of shear allowed boundary layer moist entropy to increase to a maximum downshear right. This contributed to convective instability that fueled the downshear convection. Within this convection, an intense mesovortex rapidly developed, with maximum boundary layer relative vorticity reaching 2.2 × 10−2 s−1. Extreme vortex stretching played a key role in the boundary layer spinup of the mesovortex. Cyclonic vorticity remained maximized in the boundary layer and intensified upward with the growth of the convective plume. The circulation associated with the mesovortex and adjacent localized cyclonic vorticity anomalies comprised a developing “inner vortex” on the downshear-left (downtilt) periphery of the parent cyclonic circulation. The inner vortex was nearly upright within a parent vortex that was tilted significantly with height. This inner vortex became the dominant vortex of the system, advecting and absorbing the broad, tilted parent vortex. The reduction of tropical cyclone (TC) vortex tilt from 65 to 20 km in 3 h reflected the emerging dominance of this upright inner vortex. The authors hypothesize that downshear reformation, resulting from diabatic heating associated with asymmetric convection, can aid the TC’s resistance to shear by reducing vortex tilt and by enabling more diabatic heating to occur near the center, a region known to favor TC intensification.
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Li, Zhi Chuan, Qi Hu Sheng, Liang Zhang, Zhi Ming Cong i Jin Jiang. "Numerical Simulation of Blade-Wake Interaction of Vertical Axis Tidal Turbine". Advanced Materials Research 346 (wrzesień 2011): 318–23. http://dx.doi.org/10.4028/www.scientific.net/amr.346.318.
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To study the blade-wake interaction of vertical axis tidal turbine (VATT)，particles were placed in the flow field to trace blade wake during numerical simulation. Numerical simulations were conducted utilizing Euler-Lagrange model. In the simulations, the continuous phase was solved by Reynolds-averaged Navier-Stocks(RANS) equation combined with SST turbulence model and the particle trajectories of the dispersed phase were determined by momentum equation. Numerical results of predicting instantaneous blade forces and blade wakes showed good agreement with the test data. The model was also compared with previous classic free vortex model (V-DART), vortex method combined with finite element analysis (FEVDTM) and 2-D vortex panel model (VPM2D). It showed that the present model was much better than the former.
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Cai, Qiurui, Zhengnong Li, Ricky W. K. Chan, Han Luo, Guodi Duan, Bin Huang i Honghua Wu. "Study on the Vibration Characteristics of Marine Riser Based on Flume Experiment and Numerical Simulation". Journal of Marine Science and Engineering 11, nr 7 (28.06.2023): 1316. http://dx.doi.org/10.3390/jmse11071316.
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This study investigated vortex-induced vibrations of marine risers in Ocean Thermal Energy Conversion systems. Flume experiments were conducted under two conditions: Condition 1 was with a fixed riser bottom, and Condition 2 was with a fixed bottom on a mooring platform. The cross-flow acceleration of the riser was measured at different current velocities, and corresponding vibration responses were analyzed. Numerical simulations based on the flume experiments were employed to validate the reliability of the simulation method. Results from the flume experiments revealed vortex-induced resonance in Condition 1 when the flow velocity approached the riser’s natural frequency. In Condition 2, similar vibration responses were observed, with maximum acceleration occurring during flow velocity-induced vortex-induced vibrations. However, at higher flow velocities, the acceleration response showed a decrease followed by an increase, indicating the excitation of higher-order modes. The numerical simulations matched the flume experiments in Condition 1. In Condition 2, while the acceleration response and frequency agreed during vortex-induced resonance, discrepancies arose in the flow velocity that caused vortex-induced vibrations compared to the flume experiments. This study demonstrated the accuracy of numerical simulations in reflecting vortex-induced vibrations of risers, providing a foundation for further research on complex riser systems.
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Heyes, A. L., S. J. Hubbard, A. J. Marquis i D. A. Smith. "On the roll-up of a trailing vortex sheet in the very near field". Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 217, nr 5 (1.05.2003): 263–69. http://dx.doi.org/10.1177/095441000321700501.
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This paper addresses a discrepancy found between the rate of roll-up of a trailing vortex sheet calculated from point vortex simulations and that from measured data. Measurements of the wake behind a rectangular planform NACA 0012 section wing at 7.5° angle of attack show that some 50 per cent of the circulation in the wake is already present in the vortex core or “rolled-up region” at the trailing edge of the wing, and that there is no increase in the circulation contained within this region within one chord length downstream of the trailing edge. This conflicts with two-dimensional point vortex simulations of sheet roll-up which predict no initial core at the trailing edge and a constantly increasing value of circulation in the vortex in the downstream direction. A modification to include the effect of the tip vortex in the simulation is proposed and is shown to represent the behaviour of the vortex sheet in the very near field accurately.
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Yan, Jie, Nan Gui, Gongnan Xie i Jinsen Gao. "Direct Numerical Simulation and Visualization of Biswirling Jets". Advances in Mechanical Engineering 6 (1.01.2014): 193731. http://dx.doi.org/10.1155/2014/193731.
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Two parallel swirling/rotating jets with a distance between them are termed biswirling jets here, which have important and complicated vortex structures different from the single swirling jet due to the negligible vortex-vortex interactions. The visualization of vortex-vortex interaction between the biswirling jets is accomplished by using direct numerical simulation. The evolution of vortex structures of the biswirling jets is found rather complicated. The turbulent kinetic energy and turbulence dissipation in the central convergence region are augmented locally and rather strongly. The modulation of turbulent kinetic energy by jet-jet interaction upon different scales of vortices is dominated by the swirling levels and the distance between the jets. The turbulent kinetic energy upon intermediate and small scale vortices in bijets with not very high swirling level and at a very close distance is smaller than that in single swirling jets, whereas the opposite is true under a far distance, and so forth.
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Pacioni, Carlo, i Florian Mayer. "vortex R: an R package for post Vortex simulation analysis". Methods in Ecology and Evolution 8, nr 11 (2.05.2017): 1477–81. http://dx.doi.org/10.1111/2041-210x.12786.
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Fedirko, V. A., S. V. Polyakov, A. L. Kasatkin i M. V. Fedirko. "Numerical Simulation of Abrikosov Vortex at Columnar Defect in Superconductor". EPJ Web of Conferences 224 (2019): 02007. http://dx.doi.org/10.1051/epjconf/201922402007.
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We report a numerical modeling of single vortex depinning and its subsequent dynamics in HTS film with extended linear defects under the influence of the transport current. Numerical simulation of stable pinned vortex state and its escape from a linear defect has been performed. The non-stationary dynamics of vortex escape has been investigated and time-dependent solution for vortex displacement from the defect has been obtained. The delay effect in vortex escape process has been studied and the time delay has been estimated. The impact of processes being studied on electrodynamic properties of a superconductor has also been discussed. The dynamics of vortex escape from columnar pinning site described in the present work is important both for understanding of vortex dynamics and applying high-Tc superconductors with columnar defects.
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Vechtel, D. "In-flight simulation of wake encounters using deformed vortices". Aeronautical Journal 117, nr 1196 (październik 2013): 997–1018. http://dx.doi.org/10.1017/s0001924000008654.
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Abstract During the decay process the shape of wake vortices changes significantly which has an influence on the encounter characteristics, hence on the encounter hazard. In order to evaluate the influence of vortex deformation on the wake encounter hazard, in-flight simulations with the DLR research aircraft ATTAS were carried out. For a realistic analysis of wake encounters flow fields of matured vortices were generated with large eddy simulations. These flow fields were used for the determination of histories of induced forces and moments acting on the wake encountering aircraft. The force and moment histories were then fed into the equations of motions of the non-linear six degree-of-freedom in-flight simulation of the DLR research aircraft ATTAS. In order to compare different stages of vortex deformation, encounters were simulated in flight with wavy vortices and vortex rings. The most important benefit of the in-flight-simulation is the realistic environment, which enables a realistic assessment of pilots’ encounter acceptance. The analysed scenario was of a wake encounter during final approach. The encounter conditions correspond to separation distances of about 4nm and 5nm behind an aircraft of the ‘heavy’ category. During the encounters the ATTAS was flown under manual control. Altogether 31 encounters were simulated in flight, 9 with wavy vortices and 22 with vortex rings.
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Grooß, Jens-Uwe, Paul Konopka i Rolf Müller. "Ozone Chemistry during the 2002 Antarctic Vortex Split". Journal of the Atmospheric Sciences 62, nr 3 (1.03.2005): 860–70. http://dx.doi.org/10.1175/jas-3330.1.
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Abstract In September 2002, the Antarctic polar vortex was disturbed, and it split into two parts caused by an unusually early stratospheric major warming. This study discusses the chemical consequences of this event using the Chemical Lagrangian Model of the Stratosphere (CLaMS). The chemical initialization of the simulation is based on Halogen Occultation Experiment (HALOE) measurements. Because of its Lagrangian nature, CLaMS is well suited for simulating the small-scale filaments that evolve during this period. Filaments of vortex origin in the midlatitudes were observed by HALOE several times in October 2002. The results of the simulation agree well with these HALOE observations. The simulation further indicates a very rapid chlorine deactivation that is triggered by the warming associated with the split of the vortex. Correspondingly, the ozone depletion rates in the polar vortex parts rapidly decrease to zero. Outside the polar vortex, where air masses of midlatitude origin were transported to the polar region, the simulation shows high ozone depletion rates at the 700-K level caused mainly by NOx chemistry. Owing to the major warming in September 2002, ozone-poor air masses were transported into the midlatitudes and caused a decrease of midlatitude ozone by 5%–15%, depending on altitude. Besides this dilution effect, there was no significant additional chemical effect. The net chemical ozone depletion in air masses of vortex origin was low and did not differ significantly from that of midlatitude air, in spite of the different chemical composition of the two types of air masses.
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Park, Ilryong, Jein Kim, Bugeun Paik i Hanshin Seol. "Numerical Study on Tip Vortex Cavitation Inception on a Foil". Applied Sciences 11, nr 16 (9.08.2021): 7332. http://dx.doi.org/10.3390/app11167332.
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In this paper, the inception of tip vortex cavitation in weak water has been predicted using a numerical simulation, and a new scaling concept with variable exponent has also been suggested for cavitation inception index. The numerical simulations of the cavitating flows over an elliptic planform hydrofoil were performed by using the RANS approach with a Eulerian cavitation model. To ensure the accuracy of the present simulations, the effects of the turbulence model and grid resolution on the tip vortex flows were investigated. The turbulence models behaved differently in the boundary layer of the tip region where the tip vortex is developed, which resulted in different pressure and velocity fields in the vortex region. Furthermore, the Reynolds stress model for the finest grid showed a better agreement with the experimental data. The tip vortex cavitation inception numbers for the foil, predicted by using both wetted and cavitating flow simulation approaches, were compared with the measured cavitation index values, showing a good correlation. The current cavitation scaling study also suggested new empirical relations as a function of the Reynolds number substitutable for the two classic constant scaling exponents. This scaling concept showed how the scaling law changes with the Reynolds number and provided a proper scaling value for any given Reynolds numbers under turbulent flow conditions.
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Kumar, Vikash, i Kailash Jha. "Effects of convergent–divergent vortex finders on the performance of cyclone separators using computational fluid dynamics simulations". SIMULATION 96, nr 1 (13.05.2019): 31–42. http://dx.doi.org/10.1177/0037549719846570.
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This study investigates the effect of convergent–divergent vortex finders on the performance of cyclone separators, which is measured in terms of pressure drop and collection efficiency. Six cyclone models (two with uniform diameter and four with convergent–divergent vortex finders) were numerically simulated. The numerical simulations have been carried out using the commercial computational fluid dynamics code (CFD) Fluent v15. The simulation procedure has been validated using experimental data from the published literature where a good agreement between the numerical results and the experimental data is seen. A grid independence test has been carried out by using two levels of grids for correctness of our simulation. The Reynolds averaged Navier–Stokes (RANS) and continuity equations have been solved for the flow simulation. The Reynolds stress model is used for modeling the stress tensor and closing the RANS equations. The results show that a convergent–divergent vortex finder is capable of producing better performance (pressure drop and collection efficiency) than the uniform diameter cyclones. Only one performance parameter can be improved in uniform diameter cyclones. In comparison to the standard uniform vortex finder cyclones, the convergent–divergent vortex finder improves the pressure drop by 6% and also reduces the cut-size to 1.4 from 1.6 µm. It is further seen that decreasing the throat area or increasing only the lower diameter of the vortex finder causes the performance to degrade. This study proves that convergent–divergent instead of uniform diameter vortex finders can be used in gas cyclones for obtaining a better performance with the same geometry.
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Huang, Haiming, Guo Huang, Xiaoliang Xu i Weijie Li. "Simulation of co-rotating vortices based on compressible vortex method". International Journal of Numerical Methods for Heat & Fluid Flow 24, nr 6 (29.07.2014): 1290–300. http://dx.doi.org/10.1108/hff-03-2013-0095.
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Purpose – Relevant analyses are presented on the base of the compressible vortex method for simulating the development of two or three co-rotating vortices with different characteristic Mach numbers. The paper aims to discuss this issue. Design/methodology/approach – In addition to having vorticity and dilatation properties, the vortex particles also carry density, enthalpy, and entropy. Taking co-rotating vortices in two-dimensional unsteady compressible flow for an example, truncation of unbounded domains via a nonreflecting boundary condition was considered in order to make the method computationally efficient. Findings – For two identical vortices, the effect of the vortex Mach number on merging process is not evident; if two vortices have the same circulation rather than different radiuses, the vorticity and dilatation fields of the vortex under a vortex Mach number will be absorbed by the vortex under a higher vortex Mach number. For three vortices, if the original arrangement of the vortices is changed, the evolvement of the vorticity and dilatation fields is different. Originality/value – The paper reveals new mechanism of the three co-rotating vortices by a feasible compressible vortex method.
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Vechtel, D. "Simulation study of wake encounters with straight and deformed vortices". Aeronautical Journal 120, nr 1226 (kwiecień 2016): 651–74. http://dx.doi.org/10.1017/aer.2016.14.
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ABSTRACTA simulation study was conducted in order to investigate the influence of vortex deformation on wake encounter characteristics. Wake vortices tend to be strongly deformed during the decay process, depending on the atmospheric conditions in terms of turbulence and thermal stratification. For quantification of the influence of vortex deformation, encounters of an aircraft of the ‘Medium’ category behind a generator aircraft of the ‘Heavy’ category were simulated with straight vortices and with realistically deformed vortices derived from large-eddy simulations. All relevant parameters that influence the encounter characteristics, such as encounter angles and positions, were varied within a wide range. In order to cover all kinds of vortex deformation, encounters with different vortex ages from 16-136 seconds were simulated. Hence, all relevant phases during the vortex decay from nearly straight and wavy vortices to vortex rings were considered.The parameter variation study revealed that on average the impact on the encountering aircraft is less with deformed vortices than with straight vortices of comparable strength. Especially with vortex rings, the encountering aircraft is exposed to a much smaller impact. However, the results also show a larger aircraft response during encounters with wavy vortices just prior to vortex linking. The maximum aircraft response with wavy vortices is stronger than with straight vortices of comparable strength. Also, the strongest encounters occur under greater encounter angles with deformed vortices than with straight ones.
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Zhang, Wenqiang, Tao Yang, Jun Shen i Qiangqiang Sun. "Lessons Learnt from the Simulations of Aero-Engine Ground Vortex". Aerospace 11, nr 9 (26.08.2024): 699. http://dx.doi.org/10.3390/aerospace11090699.
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With the startup of the aero-engine, the ground vortex is formed between the ground and the engine intake. The ground vortex leads to total pressure and swirl distortion, which reduces the performance of the engine. The inhalation of the dust and debris through a ground vortex can erode the fan blade, block the seals and degrade turbine cooling performance. As the diameter of the modern fan blade becomes larger, the clearance between the intake lip and the ground surface is smaller, which enhances the strength of the ground vortex. Though considerable numerical studies have been conducted with the predictions of the ground vortex, it is noted that the accurate simulation of the ground vortex is still a tough task. This paper presents authors’ simulation work of the ground vortex into an intake model with different crosswind speeds. This paper tackles the challenge with a parametric study to provide useful guidelines on how to obtain a good match with the experimental data. The influence of the mesh density, performance of different turbulence models and how the boundary layer thickness affects the prediction results are conducted and analysed. The detailed structure of the flow field with ground vortex is presented, which can shed light on the experimental observations. A number of suggestions are presented that can pave the road to the accurate flow field simulations with strong vorticities.
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Lin, Dong Long, Zhao Pang, Ke Xin Zhang i Shuang You. "Fluid-Structure Interaction Simulation of Wind Turbine". Applied Mechanics and Materials 678 (październik 2014): 556–60. http://dx.doi.org/10.4028/www.scientific.net/amm.678.556.
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The model of wind turbine was created by CATIA software, and then the simulation for blades and wind field was conducted by ANSYS software. The phenomena, such as tip vortex of blade, center vortex, and spiral trailing edge vortex caused by the rotating wind turbine, were presented explicitly and the pressure distribution of wind field was obtained. This paper provides some guiding significance to the arrangement of wind turbine and the studies about loading, deformation, and stress of blades.
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Tian, Shuling, Yisheng Gao, Xiangrui Dong i Chaoqun Liu. "Definitions of vortex vector and vortex". Journal of Fluid Mechanics 849 (18.06.2018): 312–39. http://dx.doi.org/10.1017/jfm.2018.406.
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Although the vortex is ubiquitous in nature, its definition is somewhat ambiguous in the field of fluid dynamics. In this absence of a rigorous mathematical definition, considerable confusion appears to exist in visualizing and understanding the coherent vortical structures in turbulence. Cited in the previous studies, a vortex cannot be fully described by vorticity, and vorticity should be further decomposed into a rotational and a non-rotational part to represent the rotation and the shear, respectively. In this paper, we introduce several new concepts, including local fluid rotation at a point and the direction of the local fluid rotation axis. The direction and the strength of local fluid rotation are examined by investigating the kinematics of the fluid element in two- and three-dimensional flows. A new vector quantity, which is called the vortex vector in this paper, is defined to describe the local fluid rotation and it is the rotational part of the vorticity. This can be understood as that the direction of the vortex vector is equivalent to the direction of the local fluid rotation axis, and the magnitude of vortex vector is the strength of the location fluid rotation. With these new revelations, a vortex is defined as a connected region where the vortex vector is not zero. In addition, through direct numerical simulation (DNS) and large eddy simulation (LES) examples, it is demonstrated that the newly defined vortex vector can fully describe the complex vertical structures of turbulence.
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Lipecki, T., i A. Flaga. "Application of Simulation Methods of Stochastic Processes to Vortex Excitation". Archives of Civil Engineering 63, nr 1 (28.03.2017): 77–98. http://dx.doi.org/10.1515/ace-2017-0006.
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AbstractA description of direct simulation of crosswind loads caused by critical vortex excitation and the response of the structure to these loads are presented in this paper. Tower-like structures of circular cross-sections are considered. A proposed mathematical model of vortex excitation has been numerically implemented and a selfserving computer program was created for the purpose. This software, cooperating with the FEM system, allows for a simulation of a crosswind load and lateral response in real time, meaning that at each time step of the calculations the load is generated using information regarding displacements seen beforehand. A detailed description of the mathematical model is neglected in this paper, which is focused on numerical simulations. WAWS and AR methods are used in simulations.
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Tukkee, Ali M., Hussain H. Al-Kayiem i Syed I. U. Gilani. "Humidity Effect on the Simulation Accuracy of Solar Vortex Engine Performance". Journal of Solar Energy Research Updates 8 (31.10.2021): 118–29. http://dx.doi.org/10.31875/2410-2199.2021.08.10.
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In this study, a validated computational simulation is presented to investigate the effect of humidity on the performance prediction of the solar vortex engine system. Data from an experimental model are used to validate the CFD simulation. Three humidity cases are considered: dry air, 40% and 80% humid air. An expansion process with heat addition is taking place inside the vortex generator. When the vortex field continues outside the system, a compression process with heat rejection occurs, eventually bringing the air vortex to be thermal and mechanical equilibrium with the surrounding atmosphere. The change in total energy and the heat transfer rate for both processes, inside the vortex generator and outside the vortex generator, increase with increased humidity in the working fluid. The humidity increases the energy required by the system to generate and maintain the air vortex. Compared to the dry air, the pressure drop at the center of the vortex field decreases by (2-5%) and (4-9%) for the 40% and 80% humid air, respectively. Reduced pressure drop decreases the stability of the air vortex when it is in contact with the atmosphere. The intensity of the air vortex is not affected by the increase in humidity.
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Konstantinovskaya, T. V., V. E. Borisov i A. E. Lutsky. "Visualization Methods of Vortex Structures Acting on the Wing in High-Speed Flows". Scientific Visualization 16, nr 4 (listopad 2024): 109–19. http://dx.doi.org/10.26583/sv.16.4.10.
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This paper considers the use of vortex structures scientific identification and visualization methods in analyzing the effects of these structures on the wing at an angle of attack in supersonic flows. The results of applying the methods of scientific identification and visualization of vortex flows for the analysis and processing of numerical data of supersonic flow are presented. In the considered problem, the generator wing and the main wing are located at an angle of attack of 20° degrees to the incoming flow. Two configurations with different length of the vortex generator are considered. The simulation was carried out using URANS equations. Numerical simulations were performed on the hybrid supercomputer system K-60 at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences. The scientific visualization of the simulation results was carried out primarily using the Liutex vortex structures identification criterion, which belongs to the third generation of such methods. And this method was effectively complemented and enhanced by the use of other methods.
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Donghyuk, Kang, Shimamura Taisuke, Fujiwara Marie, Yokota Kazuhiko i Sato Kotaro. "1035 NUMERICAL SIMULATION OF SYNTHETIC JET BY DISCRETE VORTEX METHOD". Proceedings of the International Conference on Jets, Wakes and Separated Flows (ICJWSF) 2013.4 (2013): _1035–1_—_1035–6_. http://dx.doi.org/10.1299/jsmeicjwsf.2013.4._1035-1_.
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LEE, Mi Young, Tetuya KAWAMURA i Kunio KUWAHARA. "Numerical Simulation of Shock Wave in a Vortex Dominant Flow". Proceedings of the JSME annual meeting 2004.2 (2004): 19–20. http://dx.doi.org/10.1299/jsmemecjo.2004.2.0_19.
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Liu, Zhe, Peng Lin, Qi Zhou i Dong Xia Li. "Single Vortex Simulation around a Square Cylinder". Applied Mechanics and Materials 405-408 (wrzesień 2013): 3204–7. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.3204.
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This paper presents a numerical method to simulate singel vortex based on unsteady RNAS model, and the influece of such a single vortex on the flow characteristics around a square cylinder is discussed.
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Satrio, Martin A., David J. Bodine, Anthony E. Reinhart, Takashi Maruyama i Franklin T. Lombardo. "Understanding How Complex Terrain Impacts Tornado Dynamics Using a Suite of High-Resolution Numerical Simulations". Journal of the Atmospheric Sciences 77, nr 10 (1.10.2020): 3277–300. http://dx.doi.org/10.1175/jas-d-19-0321.1.
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AbstractA simulated vortex within a large-eddy simulation is subjected to various surface terrain, implemented through the immersed boundary method, to analyze the effects of complex topography on vortex behavior. Thirty simulations, including a control with zero-height terrain, are grouped into four categories—2D sinusoidal hills, 3D hills, valleys, and ridges—with slight modifications within each category. A medium-swirl-ratio vortex is translated over shallow terrain, which is modest in size relative to the vortex core diameter and with no explicitly defined surface roughness. While domain size restricts results to the very near-field effects of terrain, vortex–terrain interaction yields notable results. Terrain influences act to increase the variability of the near-surface vortex, including a notable leftward (rightward) deflection, acceleration (deceleration), and an expansion (a contraction) of the vortex as it ascends (descends) the terrain owing to changes in the corner flow swirl ratio. Additionally, 10-m track analyses show stronger horizontal wind speeds are found 1) on upslope terrain, resulting from transient subvortices that are more intense compared to the control simulation, and 2) in between adjacent hills simultaneous with strong pressure perturbations that descend from aloft. Composite statistics confirm that the region in between adjacent hills has the strongest horizontal wind speeds, while upward motions are more intense during ascent. Overall, valley (ridge) simulations have the largest horizontal (vertically upward) wind speeds. Last, horizontal and vertical wind speeds are shown to be affected by other terrain properties such as slope steepness and two-dimensionality of the terrain.