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Deficiency-surplus transition function (DeSuTra) in semi-empirical formulas for tumbling of freely falling card

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new phenomenological method for composing analytical formulae to describe dynamic systems using the DeSuTra function as a building block is introduced. Based on heuristic considerations, it is possible to write a correct formula with several unknown coefficients. Next, these coefficients are tuned such a way that the result coincides with the experimental data. To illustrate the viability of such a method, a simple but not trivial aerodynamic system was chosen: the autorotation of a rectangular piece of paper that falls in air. Three correction coefficients (diminishers) were introduced to calculate its rotation frequency Then a simple expression for the Magnus effect and drag force was used. All the obtained formulae were experimentally proved and the coefficients calculated. The conclusions drawn confirm the usefulness of the presented calculation procedure for the design of composites with chaotically distributed reinforcements.
Rocznik
Strony
92--98
Opis fizyczny
Bibliogr. 33 poz., rys., tab.
Twórcy
  • Riga Technical University, Riga Institute of Aeronautics, Faculty of Mechanical Engineering, Transport and Aeronautics, 6B Ķīpsalas St., Kurzemes rajons, LV-1048, Riga, Latvia
  • Riga Technical University, Riga Institute of Aeronautics, Faculty of Mechanical Engineering, Transport and Aeronautics, 6B Ķīpsalas St., Kurzemes rajons, LV-1048, Riga, Latvia
Bibliografia
  • [1] Zeeman E.C., Catastrophe Theory – Selected Papers 1972-1977, Addison-Wesley, Reading, MA 1977.
  • [2] Kozioł M., Effect of thread tension on mechanical performance of stitched glass fibre-reinforced polymer laminates – experimental study, Journal of Composite Materials 2013, 47, 16, 1919-1930, DOI: 10.1177/0021998312452179.
  • [3] Jones M.A., Shelley M.J., Falling cards, J. Fluid Mech. 2005, 540, 393-425 DOI: 10.1017/S0022112005005859.
  • [4] Mittal R., Seshadri V., Udaykumar H.S., Flutter, tumble and vortex induced autorotation, Theor. Comput. Fluid Dyn. 2004, 17(3), 165-170, DOI: 10.1007/s00162-003-0101-5.
  • [5] Smith A.M.O., On the motion of a tumbling body, Journal of the Aeronautical Sciences 1953, 20, 2, 73-84.
  • [6] Smith E.H., Autorotating wings: An experimental investigation, J. Fluid Mech. 1971, 50, 513-534, DOI: 10.1017/s0022112071002738.
  • [7] Wang W.B., Hu R.F., Xu S.J., Wu Z.N., Influence of aspect ratio on tumbling plates, Journal of Fluid Mechanics 2013, DOI: 10.1017/jfm.2013.461.
  • [8] Wang Y., Shu C., Teo C.J., Yang L.M., Numerical study on the freely falling plate: Effects of density ratio and thickness-to-length ratio editors-pick, Physics of Fluids 2016, 28, 103603, DOI: 10.1063/1.4963242.
  • [9] Heisinger L., Coins falling in water 2013, https://arxiv.org/pdf/1312.2278.pdf.
  • [10] Assemat P., Fabre D., Magnaudet J., The onset of unsteadiness of two-dimensional bodies falling or rising in a viscous fluid: A linear study, J. Fluid Mech. 2012, 690, 173-202, DOI: 10.1017/jfm.2011.419.
  • [11] Auguste F., Magnaudet J., Fabre D., Falling styles of disks, J. Fluid Mech. 2013, 719, 388-405, DOI: 10.1017/jfm.2012.602.
  • [12] Chrust M., Bouchet G., Dušek J., Numerical simulation of the dynamics of freely falling discs, Phys. Fluids 2013, 25(4), 044102, DOI: 10.1063/1.4799179.
  • [13] Lee C.B., Su Z., Zhong H.J., Chen S.Y., Zhou M.D., Wu J.Z., Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral, J. Fluid Mech. 2013, 732, 77-104, DOI: 10.1017/jfm.2013.390.
  • [14] Field S.B.M., Klaus M., Moore G., Nori F., Chaotic dynamics of falling disks, Letters of Nature 1997, http://www.nature.com/nature/journal/v388/n6639/full/3882
  • 52a0.html.
  • [15] Vincent L., Shambaugh W.S., Kanso E., Holes stabilize freely falling coins, J. Fluid Mech. 2016, 801, 250-259, DOI: 10.1017/jfm.2016.432.
  • [16] Fernando V., Caetano R., Calculation of dynamic behaviour of falling disc or plate in fluid 2010, https://fenix.tecnico. ulisboa.pt/downloadFile/395142133553/resumo.pdf.
  • [17] Zhong H.J., Lee C.B., Su Z., Chen S.Y., Zhou M.D., Wu J.Z., Experimental investigation of freely falling thin disks. I. The flow structures and Reynolds number effects on the zigzag motion, J. Fluid Mech. 2013, 716, 228-250, DOI: 10.1017/jfm.2012.543.
  • [18] Zhong H., Chen S.Y., Lee C., Experimental study of freely falling thin disks: Transition from planar zigzag to spiral, Phys. Fluids 2011, 23, 011702, DOI: 10.1063/1.3541844.
  • [19] Chatys R., Application of the Markov chain theory in estimating the strength of fiber-layered composite structures with regard to manufacturing aspects, Advances in Science and Technology Research Journal 2020, 14 (40), 1-8.
  • [20] Iversen J.D., Autorotation flat-plate wings: The effect of the moment of inertia, geometry and Reynolds number, J. Fluid Mech. 1979, 92, 327-348, DOI: 10.1017/s0022112079000641.
  • [21] Andersen A., Pesavento U., Wang Z.J., Analysis of transitions between fluttering, tumbling and steady descent of falling cards, J. Fluid Mech. 2005, 541, 91-104, DOI: 10.1017/S0022112005005847.
  • [22] Andersen A., Pesavento U., Wang Z. J., Unsteady aerodynamics of fluttering and tumbling plates, J. Fluid Mech. 2005, 541, 65-90, DOI: 10.1017/S002211200500594X.
  • [23] Belmonte A., Eisenberg H., Moses E., From flutter to tumble: Inertial drag and froude similarity in falling paper, Phys. Rev. Lett. 1998, 81(2), 345-348, DOI: 10.1103/physrevlett.81.345.
  • [24] Changqui J., Numerical study of unsteady aerodynamic of falling plate, http://www.math.ust.hk/~makxu/PAPER/CiCP-Jin-Xu.pdf.
  • [25] Bonisch S., Heuveline V., On the numerical simulation of the unsteady free fall of a solid in fluid. I. The Newtonian case, Comput. Fluids 2007, 36(9), 1434-1445, DOI: 10.1016/j.compfluid.2007.01.010.
  • [26] Ern P., Risso F., Fabre, D., Magnaudet J., Wake-induced oscillatory paths of bodies freely rising or falling in fluids, Annu. Rev. Fluid Mech. 2012, 44(44), 97-121, DOI: 10.1146/annurev-fluid-120710-101250.
  • [27] Maxwell J.C., Niven W.D., Maxwell J.C., On a particular case of the descent of a heavy body in a resisting medium, Cambridge University Press, 1853.
  • [28] Pesavento U., Wang Z.J., Falling Paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation, Phys. Rev. Lett. 2004, 93(14), 144501, DOI: 10.1103/physrevlett.93.144501.
  • [29] Field S.B., Klaus M., Moore M.G., Nori F., Chaotic dynamics of falling disks, Nature 1997, 388(6639), 252-254 DOI: 10.1038/40817.
  • [30] Mahadevan L., Tumbling cards, Physics Fluid 1999, https://www.seas.harvard.edu/softmat/downloads/pre2000-05.pdf.
  • [31] Toroń B., Szperlich P., Kozioł M., SbSI composites based on epoxy resin and cellulose for energy harvesting and sensors – the influence of SBSI nanowires conglomeration on piezoelectric properties, Materials 2020, 13(4), 902, DOI: 10.3390/ma13040902.
  • [32] Chatys, R., Orzechowski, T., Surface extension in layered structures with the use of metal meshes for heat-transfer enhancement, Mechanics of Composite Materials 2004, 40(2), 159-168.
  • [33] Olesik P., Godzierz M., Kozioł M., Preliminary characterization of movel LDPE-Based wear-resistant composite suitable for FDM 3D printing, Materials 2019, 12, 2520, DOI: 10.3390/ma12162520.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5f424456-5f8e-4b14-8653-a9d851e8b11f
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