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Unsteady vortex pattern in a flow over a flat plate at zero angle of attack (two-dimensional problem). (English. Russian original) Zbl 1347.76021
Fluid Dyn. 51, No. 3, 343-359 (2016); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2016, No. 3, 48-65 (2016).
Summary: A technique of self-consistent analytical and numerical modeling of strongly and weakly (with the buoyancy frequency $$N=1.2$$ and $$0.02\text{s}^{-1}$$) stratified flows, as well as of almost and absolutely homogeneous flows (with $$N=10^{-5}$$ and $$0.0 \text{s}^{-1}$$), is developed using the fundamental system of equations without additional hypotheses or constants. Using an open-source software, the basic physical parameters (velocity, density, pressure) and their derivatives in the flow around a thick (0.5 cm) and a relatively thin (0.05 cm) rectangular plate 10 cm long are first calculated within the framework of a unique formulation over a wide range of velocities $$0<U<80$$ cm/s. A complex flow structure comprising leading disturbances, internal waves, vortices, and thin interlayers is visualized. The maximal gradients are observed near the leading edge. In the unsteady vortex regime the structural parameters vary due to the nonlinear interaction of the flow components with different scales. For the finite plate, the calculated friction differs substantially from the Blasius solution but, for a semi-infinite plate, agrees to the accuracy of 5%.

##### MSC:
 76D17 Viscous vortex flows 76D50 Stratification effects in viscous fluids
##### Software:
OpenFOAM; ParaView; SALOME
Full Text:
##### References:
 [1] O. Lilienthal, Die Flugapparate, Algemeine Gesichtspunkte bei deren Herstellung und Anwendung, (Mayer and Müller, Berlin, 1894). [2] W. Wright and O. Wright, “Pioneering Aviation Works of Wright Brothers,” http://www. paperlessarchives. com/wright brotherspapershtml [3] E Hanson, R.; Buckley, H. P.; Lavoie, P., Aerodynamic optimization of the flat plate leading edge for experimental studies of laminar and transitional boundary layers, Experiments in Fluids, 53, 863-871, (2012) [4] Liu, C.; Yan, Y.; Lu, P., Physics of turbulence generation and sustenance in a boundary layer, Computers and Fluids, 102, 353-384, (2014) [5] Prandtl, L., Über flüssigkeitsbewegung bei sehr kleiner reibung, 484-491, (1905) · JFM 36.0800.02 [6] H. Schlichting, Boundary Layer Theory (Mc-Graw Hill, New York, 1968). · Zbl 0096.20105 [7] Khapko, T.; Duguet, Y.; Kreilos, T.; etal., Complexity of localized coherent structures in a boundary-layer flow, Eur. Phys. J. E, 37, 1-12, (2014) [8] Goldstein, S., On laminar boundary-layer flow near a position of separation, Q. J. Mech. Appl. Math., 1, 43-69, (1948) · Zbl 0033.31701 [9] V. Ya. Neiland, V. V. Bogolepov, G. N. Dugin, and I. I. Lipatov, Asymptotic Theory of Supersonic Flows of Viscous Gas [in Russian] (Fizmatlit, Moscow, 2004). [10] Braun, S.; Scheichl, S., On recent developments in marginal separation theory, Phil. Trans. R. Soc., A372, 20130343, (2014) · Zbl 1353.76040 [11] Gaifullin, A. M.; Zubtsov, A. V., Flow past a plate with a moving surface, Fluid Dynamics, 44, 540-544, (2009) · Zbl 1213.76050 [12] Grek, G. R.; Kozlov, V. V.; Chernorai, V. G., Hydrodynamic instability of boundary layers and separated flows, Advances in Mechanics, 1, 52-89, (2006) [13] Sattarzadeh, S. S.; Fransson, J. H. M., Experimental investigation on the steady and unsteady disturbances in a flat plate boundary layer, Phys. Fluids, 26, 124103, (2014) [14] Chashechkin, Yu. D., Differential mechanics of fluids: self-consistent analytical, numerical, and laboratory models of stratified flows, Bulletin of N. E. Bauman MSTU, 6, 67-95, (2014) [15] Zagumennyi, Ya. V.; Chashechkin, Yu. D., Fine structure of an unsteady diffusion-induced flow over a fixed plate, Fluid Dynamics, 48, 374-388, (2013) · Zbl 1272.76249 [16] Chashechkin, Yu. D.; Mitkin, V. V., A visual study on flow pattern around the strip moving uniformly in a continuously stratified fluid, J. Visualiz., 7, 127-134, (2004) [17] Bardakov, R. N.; Chashechkin, Yu. D., Calculation and visualization of two-dimensional attached internal waves in an exponentially stratified viscous fluid, Izv. RAS, Fizika Atmos. Okeana, 40, 531-544, (2004) [18] Bardakov, R. N.; Mitkin, V. V.; Chashechkin, Yu. D., Fine structure of a stratified flow over a plate, Prikl. Mekh. Tekh. Fiz., 48, 77-91, (2007) · Zbl 1271.76081 [19] L. D. Landau and E. M. Lifshits, Theoretical Physics. V. 6. Hydromechanics (Pergamon Press, Oxford, 1987). · Zbl 0655.76001 [20] Open ComputationalResources, URLs: http://wwwopenfoamcom, http://wwwparavieworg, http://wwwsalomeplatformorg. · Zbl 1271.76081 [21] N. E. Kochin, I. A. Kibel’, and N. V. Roze, Theoretical Hydromechanics [in Russian] (GITTL, Moscow, 1955). · Zbl 0121.20301 [22] Prokhorov, V. E.; Chashechkin, Yu. D., Visualization and acoustic sounding of the fine structure of a stratified flow behind a vertical plate, Fluid Dynamics, 48, 722-733, (2013) · Zbl 1287.76023 [23] Chashechkin, Yu. D.; Zagumennyi, Ya. V., Pressure field structure on a plate in a transitional flow regime, Dokl. RAS, 461, 39-44, (2015)
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