Correlation between No-slip and Slip Boundary Conditions Associated with a Two-dimensional Navier-Stokes Flows in a Plane Diffuser
DOI:
https://doi.org/10.5890/JVTSD.2022.06.005Abstract
We examine the viscous effects of slip boundary conditions for the model describing two-dimensional Navier-Stokes flows in a plane diffuser. It is shown that the velocity profile is related to a half period shifted Weierstrass function with two parameters. This allows to approximate the explicit solution by a Taylor series expansion with two new micro-parameters, that can be measured in physical experiments. It is shown that the assumption for no-slip boundary conditions is stable in the sense that a small perturbation of the boundary values result in a small perturbation in the solutions.References
[1] Aidoun, Z., Ameur, K., Falsafioon, M., and Badache, M. (2019), Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 1: Single-Phase Ejectors, Inventions, 4, 15.
[2] Yapici, R., Ersoy, H.K., Aktoprakoglu, A., Halkaci, H.S., and Yigit, O. (2008), Experimental determination of the optimum performance of ejector refrigeration system depending on ejector area ratio, Int. J. Refrig., 31, 1183-1189.
[3] Eames, I.W., Ablwaifa, A.E., and Petrenko, V. (2007), Results of an experimental study of an advanced jet-pump refrigerator operating with R245fa, Appl. Therm. Eng., 27, 2833-2840.
[4] Ishizaka, K., Saitoh, K., Ito, E, Yuri, M., and Masada, J., Key Technologies for 1700 $^{circ}{rm C}$ Class Ultra High Temperature Gas Turbine, Mitsubishi Heavy Industries Technical Review, 54(3).
[5] Carlton FREng, J.S. (2019), in Marine Propellers and Propulsion (Fourth Edition).
[6] Lundgren, T.S., Sethna, P.R., and Bajaj, A.K. (1979), Stability boundaries for flow induced motions of tubes with an inclined terminal nozzle, Journal of Sound and Vibration, 64(4), 553-571.
[7] Zegenhagen, M.T. and Ziegler, F. (2015), A one-dimensional model of a jet-ejector in critical double choking operation with R134a as a refrigerant including real gas effects, Int. J. Refrig., 55, 72-84.
[8] Chandra, V.V. and Ahmed, M.R. (2014), Experimental and computational studies on a steam jet refrigeration system with constant area and variable area ejectors, Energy Convers. Manag., 79, 377-386.
[9] Wang, L., Cai, W., Zhao, H., Lin, C., and Yan, J. (2016), Experimentation and cycle performance prediction of hybrid A/C system using automobile exhaust waste heat, Appl. Therm. Eng., 94, 314-323.
[10] Desevaux, P., Lanzetta, F., and Bailly, Y. (2002), CFD modelling of shock train inside a supersonic ejector: Validation against flow visualizations and pressure measurements in the case of zero-secondary flow, In Proceedings of the 10th International Symposium on Flow Visualization, Kyoto, Japan, 26-29.
[11] Prandtl, L. (1938), Zur berechnung der grenzschichten, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik}, 18(1), 77-82.
[12] Struchtrup, H. and Torrilhon, M. Higher-order effects in rarefied channel flows, Physical Review E, 78(4 Pt 2), 046301.
[13] Stone, H., Stroock, A., and Ajdari, A. (2004), Engineering flows in small devices: Microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech., 36, 381-411.
[14] Tabeling P. (2004), Slip phenomena at liquid-solid interfaces, C. R. Physique, 5, 531-537.
[15] Shankar, P.N. and Deshpande, M.D. (2000), Fluid mechanics in the driven cavity, Annual Review of Fluid Mechanics, 32, 93-136.
[16] Iorio, C.S., Goncharova, O., and Kabov, O. (2011), Influence of boundaries on shear-driven flow of liquids in open cavities, Microgravity Science and Technology, 23(4), pp. 373-379.
[17] Neto, C., Evans, D.R., Bonaccurso, E., Butt, H., and Craig V. (2005), Boundary slip in Newtonian liquids: a review of experimental studies, Rep. Prog. Phys., 68, 2859-2897.
[18] Akhiezer, N.I. (1990), Elements of the Theory of Elliptic Functions, Translations of Mathematical Monographs, 79, American Mathematical Society, ISBN 0-8218-4532-2.
[19] Hawkins, J. and Koss, L. (2005), Connectivity properties of Julia sets of Weierstrass elliptic functions, Topology Appl., 152(1-2), 107, 137.
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