Journal articles on the topic 'Trapped vortex'

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1

Vengadesan, S., and C. Sony. "Enhanced vortex stability in trapped vortex combustor." Aeronautical Journal 114, no. 1155 (May 2010): 333–37. http://dx.doi.org/10.1017/s000192400000378x.

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Abstract The Trapped Vortex Combustor (TVC) is a new design concept in which cavities are designed to trap a vortex flow structure established through the use of driver air jets located along the cavity walls. TVC offers many advantages when compared to conventional swirl-stabilised combustors. In the present work, numerical investigation of cold flow (non-reacting) through the two-cavity trapped vortex combustor is performed. The numerical simulation involves passive flow through the two-cavity TVC to obtain an optimum cavity size to trap stable vortices inside the second cavity and to observe the characteristics of the two cavity TVC. From the flow attributes, it is inferred that vortex stability is achieved by circulation and the vortex is trapped inside when a second afterbody is added.
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2

Li, Qiong, Meng Meng Zhao, and Fei Xing. "Experimental Investigation of Airflow Distribution for a Novel Combustor Mode." Applied Mechanics and Materials 284-287 (January 2013): 743–47. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.743.

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This paper investigated the airflow distribution performance of the combustor which utilized trapped vortex in the cavity to improve the flame stability. Hole-filling method was used to study trapped vortex combustor airflow distribution at normal temperature and pressure condition. The influence of inlet velocity and mainstream flow-passage height were investigated. The results show that, inlet velocity hardly impacts the airflow distribution of trapped vortex combustor, but chamber height is a key parameter for airflow distribution. The size, number and opening area of the holes in trapped vortex combustor are important to airflow distribution, and increasing cavity back body air flow could bring well lean blowout limit. The research results may serve as a useful reference in further development and engineering application of trapped vortex combustor.
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3

Garcia, Darwin L., and Joseph Katz. "Trapped Vortex in Ground Effect." AIAA Journal 41, no. 4 (April 2003): 674–78. http://dx.doi.org/10.2514/2.1997.

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4

Molina-Terriza, Gabriel, Lluis Torner, Ewan M. Wright, Juan J. García-Ripoll, and Víctor M. Pérez-García. "Vortex revivals with trapped light." Optics Letters 26, no. 20 (October 15, 2001): 1601. http://dx.doi.org/10.1364/ol.26.001601.

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5

Deng, Yangbo, and Fengmin Su. "Low emissions trapped vortex combustor." Aircraft Engineering and Aerospace Technology 88, no. 1 (January 4, 2016): 33–41. http://dx.doi.org/10.1108/aeat-09-2013-0172.

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6

DAVYDOVA, T. A., and V. M. LASHKIN. "Drift-wave trapping by drift vortices." Journal of Plasma Physics 58, no. 1 (July 1997): 11–18. http://dx.doi.org/10.1017/s002237789700562x.

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The possibility for a drift dipole vortex to trap free drift waves is demonstrated. Drift perturbations can be trapped near the centre of the vortex or at its sides. The localization domain and eigenfrequencies of trapped modes are obtained.
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7

Hsu, K. Y., L. P. Goss, and W. M. Roquemore. "Characteristics of a Trapped-Vortex Combustor." Journal of Propulsion and Power 14, no. 1 (January 1998): 57–65. http://dx.doi.org/10.2514/2.5266.

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8

Zhu, Qing-Li, and Jin An. "Surface Excitations, Shape Deformation, and the Long-Time Behavior in a Stirred Bose–Einstein Condensate." Condensed Matter 3, no. 4 (November 25, 2018): 41. http://dx.doi.org/10.3390/condmat3040041.

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The surface excitations, shape deformation, and the formation of persistent current for a Gaussian obstacle potential rotating in a highly oblate Bose–Einstein condensate (BEC) are investigated. A vortex dipole can be produced and trapped in the center of the stirrer even for the slow motion of the stirring beam. When the angular velocity of the obstacle is above some critical value, the condensate shape can be deformed remarkably at the corresponding rotation frequency followed by surface wave excitations. After a long enough time, a small number of vortices are found to be either trapped in the condensate or pinned by the obstacle, and a vortex dipole or several vortices can be trapped at the beam center, which provides another way to manipulate the vortex.
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9

Chen, Song, Randy S. M. Chue, Simon C. M. Yu, and Jörg U. Schlüter. "Spinning Effects on a Trapped Vortex Combustor." Journal of Propulsion and Power 32, no. 5 (September 2016): 1133–45. http://dx.doi.org/10.2514/1.b36005.

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10

Kunze, Eric, and Emmanuel Boss. "A Model for Vortex-Trapped Internal Waves." Journal of Physical Oceanography 28, no. 10 (October 1998): 2104–15. http://dx.doi.org/10.1175/1520-0485(1998)028<2104:amfvti>2.0.co;2.

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11

Madarassy, Enikő J. M., and Carlo F. Barenghi. "Vortex Dynamics in Trapped Bose-Einstein Condensate." Journal of Low Temperature Physics 152, no. 3-4 (May 14, 2008): 122–35. http://dx.doi.org/10.1007/s10909-008-9811-9.

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12

Andersen, Timothy, and Chjan Lim. "Trapped slender vortex filaments in statistical equilibrium." PAMM 6, no. 1 (December 2006): 865–68. http://dx.doi.org/10.1002/pamm.200610412.

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13

Mishra, Prasad, Renganathan Sudharshan, and Kumar Ezhil. "Numerical study of flame/vortex interactions in 2-D Trapped Vortex Combustor." Thermal Science 18, no. 4 (2014): 1373–87. http://dx.doi.org/10.2298/tsci111006162m.

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The interactions between flame and vortex in a 2-D Trapped Vortex Combustor are investigated by simulating the Reynolds Averaged Navier Stokes (RANS) equations, for the following five cases namely (i) non-reacting (base) case, (ii) post-vortex ignition without premixing, (iii) post-vortex ignition with premixing, (iv) pre-vortex ignition without premixing and (v) pre-vortex ignition with premixing. For the post-vortex ignition without premixing case, the reactants are mixed well in the cavity resulting in a stable ?C? shaped flame along the vortex edge. Further, there is insignificant change in the vorticity due to chemical reactions. In contrast, for the pre-vortex ignition case (no premixing); the flame gets stabilized at the interface of two counter rotating vortices resulting in reduced reaction rates. There is a noticeable change in the location and size of the primary vortex as compared to case (ii). When the mainstream air is premixed with fuel, there is a further reduction in the reaction rates and thus structure of cavity flame gets altered significantly for case (v). Pilot flame established for cases (ii) and (iii) are well shielded from main flow and hence the flame structure and reaction rates do not change appreciably. Hence, it is expected that cases (ii) and (iii) can perform well over a wide range of operating conditions.
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14

Sivakumar, Adhithiya, and Jeffrey B. Weiss. "Volume Transport by a 3D Quasigeostrophic Heton." Fluids 7, no. 3 (March 2, 2022): 92. http://dx.doi.org/10.3390/fluids7030092.

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Oceanic flows self-organize into coherent vortices, which strongly influence their transport and mixing properties. Counter-rotating vortex pairs can travel long distances and carry trapped fluid as they move. These structures are often modeled as hetons, viz. counter-rotating quasigeostrophic point vortex pairs with equal circulations. Here, we investigate the structure of the transport induced by a single three-dimensional heton. The transport is determined by the Hamiltonian structure of the velocity field induced by the heton’s component vortices. The dynamics display a sequence of bifurcations as one moves through the heton-induced velocity field in height. These bifurcations create and destroy unstable fixed points whose associated invariant manifolds bound the trapped volume. Heton configurations fall into three categories. Vertically aligned hetons, which are parallel to the vertical axis and have zero horizontal separation, do not move and do not transport fluid. Horizontally aligned hetons, which lie on the horizontal plane and have zero vertical separation, have a single parameter, the horizontal vortex half-separation Y, and simple scaling shows the dimensional trapped volume scales as Y3. Tilted hetons are described by two parameters, Y and the vertical vortex half-separation Z, rendering the scaling analysis more complex. A scaling theory is developed for the trapped volume of tilted hetons, showing that it scales as Z4/Y for large Z. Numerical calculations illustrate the structure of the trapped volume and verify the scaling theory.
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15

Kang, Yiqin, Chenlu Wang, Gangyi Fang, Fei Xing, and Shining Chan. "Flow and Combustion Characteristics of Wave Rotor–Trapped Vortex Combustor System." Energies 16, no. 1 (December 28, 2022): 326. http://dx.doi.org/10.3390/en16010326.

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Breaking through the limit of conventional compression and combustion, wave rotor and trapped vortex combustors are able to improve the thermal efficiency of gas turbines. Detailed two-dimensional numerical simulations based on Ansys Fluent were performed to study the flow and combustion characteristics of the wave rotor–trapped vortex combustor system. The calculated pressure characteristics agree with the experimental results giving a relative error for average pressure of 0.189% at Port 2 and of 0.672% at Port 4. The flow stratification characteristics and the periodic fluctuations were found to benefit the zonal organized combustion in the trapped vortex combustor. For the six cases of different rotor speeds, as the rotor speed increased, the oxygen mass fraction at the combustor inlet rose and then fell. The proportion of exhaust gas recirculation fell at first and then rose, and the combustion mode became unstable with the dominant frequencies of the fluctuations increasing.
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16

Fischer, Uwe R., Petr O. Fedichev, and Alessio Recati. "Vortex liquids and vortex quantum Hall states in trapped rotating Bose gases." Journal of Physics B: Atomic, Molecular and Optical Physics 37, no. 7 (March 24, 2004): S301—S310. http://dx.doi.org/10.1088/0953-4075/37/7/074.

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17

Yang, Yi, and Siyuan Huang. "Trapping and rotation of microparticles using a metasurface exciting by linearly polarized beam." Nanomaterials and Nanotechnology 11 (January 1, 2021): 184798042110151. http://dx.doi.org/10.1177/18479804211015107.

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We numerically demonstrate trapping and rotation of particles using a metasurface formed by arranging nanocavities as a right-handed Archimedes’ spiral. Excited by a 90° linearly polarized beam, a focused surface plasmon polariton (SPP) field is formed at the center of the spiral, and the particle can be trapped by the field. While excited by −45° linearly polarized beams, a vortex SPP field carrying orbital angular momentum is formed, and the particles can be trapped and rotated in the clockwise direction at the vortex field.
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18

Barboza, R., U. Bortolozzo, M. G. Clerc, S. Residori, and E. Vidal-Henriquez. "Light–matter interaction induces a single positive vortex with swirling arms." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2027 (October 28, 2014): 20140019. http://dx.doi.org/10.1098/rsta.2014.0019.

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Homeotropic nematic liquid crystal cells with a photosensitive wall and negative dielectric anisotropy exhibit, under the influence of local illumination, stable vortexes with swirling arms that are trapped at the illuminated area. Close to the Fréedericksz transition an amplitude equation is derived, which allows us to understand the origin of the induced vortex and the competition between the illuminating profile and the elastic anisotropy generating the swirling of the arms.
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19

Torres, Pedro, R. Carretero-González, S. Middelkamp, P. Schmelcher, Dimitri Frantzeskakis, and P. G. Kevrekidis. "Vortex interaction dynamics in trapped Bose-Einstein condensates." Communications on Pure and Applied Analysis 10, no. 6 (May 2011): 1589–615. http://dx.doi.org/10.3934/cpaa.2011.10.1589.

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20

Zhu, Qingli. "VORTEX DIPOLE EXCITATIONS IN TRAPPED BOSE-EINSTEIN CONDENSATE." International Journal of Advanced Research 6, no. 1 (January 31, 2018): 654–61. http://dx.doi.org/10.21474/ijar01/6270.

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21

Lamperska, Weronika, Jan Masajada, Sławomir Drobczyński, and Piotr Wasylczyk. "Optical vortex torque measured with optically trapped microbarbells." Applied Optics 59, no. 15 (May 15, 2020): 4703. http://dx.doi.org/10.1364/ao.385167.

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22

Agarwal, Krishna Kant, S. Krishna, and R. V. Ravikrishna. "Mixing Enhancement in a Compact Trapped Vortex Combustor." Combustion Science and Technology 185, no. 3 (February 27, 2013): 363–78. http://dx.doi.org/10.1080/00102202.2012.721034.

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23

Ghenai, Chaouki, Khaled Zbeeb, and Isam Janajreh. "Combustion of alternative fuels in vortex trapped combustor." Energy Conversion and Management 65 (January 2013): 819–28. http://dx.doi.org/10.1016/j.enconman.2012.03.012.

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24

HUTCHINSON, D. A. W., and P. B. BLAKIE. "PHASE TRANSITIONS IN ULTRA-COLD TWO-DIMENSIONAL BOSE GASES." International Journal of Modern Physics B 20, no. 30n31 (December 20, 2006): 5224–28. http://dx.doi.org/10.1142/s0217979206036302.

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We briefly review the theory of Bose-Einstein condensation in the two-dimensional trapped Bose gas and, in particular the relationship to the theory of the homogeneous two-dimensional gas and the Berezinskii-Kosterlitz-Thouless phase. We obtain a phase diagram for the trapped two-dimensional gas, finding a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose-Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose-Einstein condensate, a vortex pair plasma with fluctuating condensate phase and a thermal Bose gas. The thermal activation of vortex-antivortex pair formation is confirmed using finite-temperature classical field simulations.
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25

Orlishausen, M., L. Butzhammer, D. Schlotbohm, D. Zapf, and W. Köhler. "Particle accumulation and depletion in a microfluidic Marangoni flow." Soft Matter 13, no. 39 (2017): 7053–60. http://dx.doi.org/10.1039/c7sm00954b.

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26

Rahman, O. "Nonlinear propagation of dust-ion-acoustic solitary waves in an unmagnetized dusty plasma with trapped particle distribution." Modern Physics Letters A 30, no. 40 (December 28, 2015): 1550216. http://dx.doi.org/10.1142/s0217732315502168.

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The nonlinear propagation of dust-ion-acoustic (DIA) solitary waves (SWs) in an unmagnetized four-component dusty plasma containing electrons and negative ions obeying vortex-like (trapped) velocity distribution, cold mobile positive ions and arbitrarily charged stationary dust has been theoretically investigated. The properties of small but finite amplitude DIASWs are studied by employing the reductive perturbation technique. It has been found that owing to the departure from the Maxwellian electron and Maxwellian negative ion distribution to a vortex-like one, the dynamics of such DIASWs is governed by a modified Korteweg–de Vries (mKdV) equation which admits SW solution under certain conditions. The basic properties (speed, amplitude, width, etc.) of such DIASWs are found to be significantly modified by the presence of trapped electron and trapped negative ions. The implications of our results to space and laboratory dusty electronegative plasmas (DENPs) are briefly discussed.
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27

Chen, Song, Randy S. M. Chue, Jörg Schlüter, Tue T. Q. Nguyen, and Simon C. M. Yu. "Numerical Investigation of a Trapped Vortex Miniature Ramjet Combustor." Journal of Propulsion and Power 31, no. 3 (May 2015): 872–82. http://dx.doi.org/10.2514/1.b35602.

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28

Singhal, Atul, and R. V. Ravikrishna. "Single Cavity Trapped Vortex Combustor Dynamics – Part-1: Experiments." International Journal of Spray and Combustion Dynamics 3, no. 1 (March 2011): 23–44. http://dx.doi.org/10.1260/1756-8277.3.1.23.

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29

Singhal, Atul, and R. V. Ravikrishna. "Single Cavity Trapped Vortex Combustor Dynamics – Part-2: Simulations." International Journal of Spray and Combustion Dynamics 3, no. 1 (March 2011): 45–62. http://dx.doi.org/10.1260/1756-8277.3.1.45.

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30

Chen, Mingzhou, Michael Mazilu, Yoshihiko Arita, Ewan M. Wright, and Kishan Dholakia. "Dynamics of microparticles trapped in a perfect vortex beam." Optics Letters 38, no. 22 (November 15, 2013): 4919. http://dx.doi.org/10.1364/ol.38.004919.

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31

Katta, V. R., and W. M. Roquemore. "Numerical Studies on Trapped-Vortex Concepts for Stable Combustion." Journal of Engineering for Gas Turbines and Power 120, no. 1 (January 1, 1998): 60–68. http://dx.doi.org/10.1115/1.2818088.

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Spatially locked vortices in the cavities of a combustor aid in stabilizing the flames. On the other hand, these stationary vortices also restrict the entrainment of the main air into the cavity. For obtaining good performance characteristics in a trapped-vortex combustor, a sufficient amount of fuel and air must be injected directly into the cavity. This paper describes a numerical investigation performed to understand better the entrainment and residence-time characteristics of cavity flows for different cavity and spindle sizes. A third-order-accurate time-dependent Computational Fluid Dynamics with Chemistry (CFDC) code was used for simulating the dynamic flows associated with forebody-spindle-disk geometry. It was found from the nonreacting flow simulations that the drag coefficient decreases with cavity length and that an optimum size exists for achieving a minimum value. These observations support the earlier experimental findings of Little and Whipkey (1979). At the optimum disk location, the vortices inside the cavity and behind the disk are spatially locked. It was also found that for cavity sizes slightly larger than the optimum, even though the vortices are spatially locked, the drag coefficient increases significantly. Entrainment of the main flow was observed to be greater into the smaller-than-optimum cavities. The reacting-flow calculations indicate that the dynamic vortices developed inside the cavity with the injection of fuel and air do not shed, even though the cavity size was determined based on cold-flow conditions.
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32

Tao, Xu, and Zhang Sheng-Li. "Bifurcation of Vortex Density Current in Trapped Bose Condensates." Communications in Theoretical Physics 37, no. 6 (June 15, 2002): 682–84. http://dx.doi.org/10.1088/0253-6102/37/6/682.

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33

JIN, Yi, Xiaomin HE, Bo JIANG, Zejun WU, and Guoyu DING. "Design and Performance of an Improved Trapped Vortex Combustor." Chinese Journal of Aeronautics 25, no. 6 (December 2012): 864–70. http://dx.doi.org/10.1016/s1000-9361(11)60456-1.

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34

Lundh, E. "Hydrodynamic approach to vortex stability in trapped Bose condensates." Physica B: Condensed Matter 284-288 (July 2000): 19–20. http://dx.doi.org/10.1016/s0921-4526(99)01953-5.

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35

Wu, Zejun, Xiaomin He, Bo Jiang, and Yi Jin. "Experimental investigation on a single-cavity trapped vortex combustor." International Communications in Heat and Mass Transfer 68 (November 2015): 8–13. http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.003.

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36

Kumar, P. K. Ezhil, and D. P. Mishra. "Flame Stability Characteristics of Two-Dimensional Trapped Vortex Combustor." Combustion Science and Technology 188, no. 8 (May 24, 2016): 1283–302. http://dx.doi.org/10.1080/00102202.2016.1190343.

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37

Rokhsar, D. S. "Vortex Stability and Persistent Currents in Trapped Bose Gases." Physical Review Letters 79, no. 12 (September 22, 1997): 2164–67. http://dx.doi.org/10.1103/physrevlett.79.2164.

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38

Wu, Hui, Qin Chen, Weiwei Shao, Yongliang Zhang, Yue Wang, and Yunhan Xiao. "Combustion of hydrogen in an experimental trapped vortex combustor." Journal of Thermal Science 18, no. 3 (September 2009): 256–61. http://dx.doi.org/10.1007/s11630-009-0256-5.

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39

Selvaganesh, P., and S. Vengadesan. "Cold flow analysis of trapped vortex combustor using two equation turbulence models." Aeronautical Journal 112, no. 1136 (October 2008): 569–80. http://dx.doi.org/10.1017/s0001924000002530.

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Abstract A new combustor concept referred as the trapped vortex combustor (TVC) employs a vortex that is trapped inside a cavity to stabilise the flame. The cavity is formed between two axisymmetric disks mounted in tandem. TVC offers many advantages when compared to conventional swirl stabilisers. In the present work, numerical investigation of cold flow (non-reacting) through trapped vortex combustor is performed. The numerical simulation involves passive flow through TVC to obtain an optimum cavity size to trap stable vortices inside the cavity and to observe the important characteristics of TVC. One of the main objectives is to evaluate various two equation turbulence models for the aerodynamic predictions of TVC. Commercial CFD software Fluent is used for the present study. In addition to many models available, Non-linear k-ω and modified k-ω models are incorporated through user defined functions. Results obtained include streamlines, residence time and entrainments for all models. The reattachment length obtained by non-linear k-ω model closely matches with that obtained by DNS in the case of forebody-spindle alone. Non-linear k-ω model alone captures the corner vortices while all the other models failed to capture. From the entrainment characteristics study, it is inferred that the primary air needs to be injected for accommodating the decrease in oxidizer inside the cavity to obtain better performance from the TVC.
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40

Lamb, V. R., and G. S. Janowitz. "Shallow rotating flow over an isolated obstacle." Journal of Fluid Mechanics 158 (September 1985): 1–22. http://dx.doi.org/10.1017/s002211208500252x.

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The deflection of flow around an isolated obstacle in a rotating homogeneous fluid is investigated. Criteria for the onset of closed streamlines over an isolated obstacle are reviewed. In the flow regime where no closed streamlines exist, steady solutions for the stream function are obtained for both quasigeostrophic and finite-Rossby-number flows. A measure is proposed to allow quantitative evaluation of the flow patterns, and the dependence of deflection on obstacle volume and aspect ratio is examined. In the regime where closed streamlines can exist, the presence of a trapped vortex to the right (looking downstream) of the obstacle is investigated by means of time integration of the shallow-water equations. The significance of the trapped vortex for a real fluid is then tested through the addition of the frictional effect of Eckman pumping.
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41

Wang, Zhang Jun, Zhuo Xiong Zeng, and Guo Hui Tu. "Study of Turbulence Characteristics in Different Advanced Vortex Combustor Structure." Applied Mechanics and Materials 387 (August 2013): 345–49. http://dx.doi.org/10.4028/www.scientific.net/amm.387.345.

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Based on the idea of single cavity trapped vortex combustor, a advanced vortex combustor which is constitute by three blunt bodies and double concave cavity is proposed. And the interior combustor flow characteristics are analyzed. The results shows that the flow field characteristics changed a lot before and after combustor modification, and D2=20mm, D3=4mm are respectively the best modification scheme on the second and third blunt body.
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42

Rossow, Vernon J. "Aerodynamics of airfoils with vortex trapped by two spanwise fences." Journal of Aircraft 31, no. 1 (January 1994): 146–53. http://dx.doi.org/10.2514/3.46467.

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43

Duarte, Rui, Xavier Carton, Xavier Capet, and Laurent Chérubin. "Trapped instability and vortex formation by an unstable coastal current." Regular and Chaotic Dynamics 16, no. 6 (December 2011): 577–601. http://dx.doi.org/10.1134/s1560354711060037.

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44

Adhikari, S. K. "Stable controllable giant vortex in a trapped Bose–Einstein condensate." Laser Physics Letters 16, no. 8 (July 12, 2019): 085501. http://dx.doi.org/10.1088/1612-202x/ab2d2c.

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45

Lee, W. M., V. Garcés-Chávez, and K. Dholakia. "Interference from multiple trapped colloids in an optical vortex beam." Optics Express 14, no. 16 (2006): 7436. http://dx.doi.org/10.1364/oe.14.007436.

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46

Yip, S. K. "Internal Vortex Structure of a Trapped Spinor Bose-Einstein Condensate." Physical Review Letters 83, no. 23 (December 6, 1999): 4677–81. http://dx.doi.org/10.1103/physrevlett.83.4677.

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47

Caradoc-Davies, B. M., R. J. Ballagh, and K. Burnett. "Coherent Dynamics of Vortex Formation in Trapped Bose-Einstein Condensates." Physical Review Letters 83, no. 5 (August 2, 1999): 895–98. http://dx.doi.org/10.1103/physrevlett.83.895.

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48

Komineas, S. "Vortex rings and solitary waves in trapped Bose–Einstein condensates." European Physical Journal Special Topics 147, no. 1 (August 2007): 133–52. http://dx.doi.org/10.1140/epjst/e2007-00206-8.

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49

Lam, Simon K. H., and Sabaratnasingam Gnanarajan. "Hysteretic behaviour of nanoSQUIDs—prospective application as trapped-vortex memory." Superconductor Science and Technology 22, no. 6 (May 14, 2009): 064005. http://dx.doi.org/10.1088/0953-2048/22/6/064005.

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50

Svidzinsky, Anatoly A., and Alexander L. Fetter. "Stability of a Vortex in a Trapped Bose-Einstein Condensate." Physical Review Letters 84, no. 26 (June 26, 2000): 5919–23. http://dx.doi.org/10.1103/physrevlett.84.5919.

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