Warianty tytułu
Języki publikacji
Abstrakty
In this article, a numerical study was carried out to study the dynamic adaptive grid method, based on the concept of the equidistribution method. The article explores a method for adapting the computational grid to solving two-dimensional Navier-Stokes differential equations, which describe the physical processes of gas dynamics specifically for the problem of a two-dimensional channel with an expansion coefficient (H/h) = 2. Different flow characteristics were calculated at different Reynolds numbers Re = from 100 to 1000, to get the actual thread behavior. Calculations are performed for laminar flow mode. The results of the longitudinal velocity profiles in different sections of the channel and the length of the primary and secondary vortices are obtained with a change in the Reynolds number after the ledge. For the numerical solution of this problem, a second-order accuracy McCormack scheme was used. To confirm the adequacy and reliability of the numerical results, a careful comparison was made with the experimental data of Armaly V.F. et al., taken from the literature. It is also shown that as a result of using this method of adaptive grids, it is possible to improve the numerical accuracy obtained for a given number of node points. It is shown that the existing method of multiple 2D adaptive meshes makes it easier to concentrate meshes in the required areas. This method should prove useful for many Navier-Stokes flow calculations.
Rocznik
Tom
Strony
47--68
Opis fizyczny
Bibliogr. 49 poz., rys., tab., wykr.
Twórcy
autor
- Information System and Mathematical Sciences, Plekhanov Russian University of Economics, UZBEKISTAN, bakhodir.kholboev@gmail.com
autor
- Fergana Polytechnic Institute, UZBEKISTAN
autor
- Institute of Mechanics and Seismic Stability of Structures named after M.T.Urazbaev Academy of Sciences of the Republic of Uzbekistan, UZBEKISTAN
autor
- Information System and Mathematical Sciences, Plekhanov Russian University of Economics, UZBEKISTAN
autor
- Information System and Mathematical Sciences, Plekhanov Russian University of Economics, UZBEKISTAN
Bibliografia
- [1] Blasius Н. (1910): Laminare stromung in kanalen wechselnder breite.– Zeitschrift fur Math. und Phys., vol.58, No.10,pp.225-233.
- [2] Honji H (1975): The starting flow down a step.– J. Fluid Mech., vol.69, No.2, pp.229-240. DOI:https://doi.org/10.1017/S0022112075001413.
- [3] Sinha S.P., Gupta A.K. and Oberai M.M. (1981): Laminar separation flow around benches and caverns. Part 1. Flowbehind the ledge.– Rocketry and Cosmonautics, vol.19, No.12, pp.33-37.
- [4] Armaly В.F., Durst F., Pereira J.C.F. and Schonung B. (1983): Experimental and theoretical investigation ofbackward-facing step flow.– J. Fluid Mech., vol.127, pp.473-496, DOI:https://doi.org/10.1017/S0022112083002839.
- [5] Zheng P. (1972): Separated Flows.– Mir, p.354.
- [6] Gogish L.V. and Stepanov G.Yu. (1982): Turbulent separation flows.– Fluid Dynamics, vol.17, pp.188-202.
- [7] Le H., Moin P. and Kim J. (1997): Direct numerical simulation of turbulent flow over a backward-facing step.– J.Fluid Mech., vol.330, pp.349-374, DOI: https://doi.org/10.1017/S0022112096003941.
- [8] Durst F., Melling A. and Whitelow J.H. (1974): Low Reynolds number flow over a plane symmetric suddenexpansion.– J. Fluid Mech., vol.64, No.1, pp.111-118, DOI: https://doi.org/10.1017/S0022112074002035.
- [9] Cherdron W., Durst F. and Whitelow J.H. (1978): Asymmetric flows and instabilities in symmetric ducts with suddenexpansions.– J. Fluid Mech., vol.84, No.1, pp.13-31, DOI: https://doi.org/10.1017/S0022112078000026.
- [10] Macadno E.O., and Hung Т.-K. (1967): Computational and experimental study of a captive annular eddy.– J. FluidMech., vol.28, No.1, pp.43-64, DOI: https://doi.org/10.1017/S0022112067001892.
- [11] Kumar A. and Yajnik K.S. (1980): Internal separated flows at large Reynolds number.– J. Fluid Mech., vol.97, No.1,pp.27-51, DOI: https://doi.org/10.1017/S0022112080002418.
- [12] Plotkin A. (1983): Spectral method calculations of some separated laminar flows in channels.– Aerospacetechnology, No.7, pp.75-85.
- [13] Acrivos A. and Schrader М.L. (1982): Steady flow in a sudden expansion at high Reynolds numbers.– Phys. Fluids,vol.25, No.6, pp.923-930, DOI: https://doi.org/10.1063/1.863844.
- [14] Kuon O., Pletcher R. and Lewis J. (1984): Calculation of sudden expansion flows using boundary layer equations.–Theor. Fundamentals of Engineering Calculations, vol.106, No.3, pp.116-123.
- [15] Lewis J.P. and Pletcher R.H. (1986): Limits of applicability of boundary layer equations for calculating laminarflows with symmetric sudden expansion.– Theor. Fundamentals of Engineering Calculation, No.2, pp.284-294.
- [16] Malikov Z.M. and Madaliev M.E. (2021): Numerical simulation of flow in a flat suddenly expanding channel basedon a new two-fluid turbulence model.– Bulletin of MSTU im. N.E. Bauman. Ser. Natural Sciences, vol.97, No.4,pp.24-39, DOI: https://doi.org/10.18698/1812-3368-2021-4-24-39.
- [17] Malikov Z.M. and Madaliev M.E. (2022): Numerical simulation of turbulent flows based on modern turbulencemodels.– Computational Mathematics and Mathematical Physics, vol.62, No.10, pp.1707-1722.
- [18] Mirzoev A.A. Madaliev M., Sultanbayevich D.Y. and Habibullo ugli A.U. (2020): Numerical modeling of non-stationary turbulent flow with double barrier based on two liquid turbulence model.– 2020 International Conferenceon Information Science and Communications Technologies (ICISCT), IEEE, pp.1-7.
- [19] Lee Y.S. and Smith L.C. (1986): Analysis of Power-Law Viscous Materials Using Complex Stream, Potential andStress Functions.– in Encyclopedia of Fluid Mechanics, vol.1, Flow Phenomena and Measurement, ed. N.P.Cheremisinoff, pp.1105-1154.
- [20] Roache P.J. (1972): Computational Fluid Dynamics.– Hermosa, New Mexico, pp.139-173.
- [21] Taylor T.D. and Ndefo E. (1971): Computation of viscous flow in a channel by the method of splitting.– Proc. of theSecond Int. Conf. on Num. Methods in Fluid Dynamics, Lecture Notes in Physics, vol.8, pp.356-364, SpringerVerlag, New York.
- [22] Durst F. and Peireira J.C.F. (1988): Time-dependent laminar backward facing step flow in a two-dimensional duct.–ASME J. Fluids Eng., vol.110, pp.289-296.
- [23] Alleborn N., Nandakumar K., Raszillier H. and Durst F. (1997): Further contributions on the two-dimensional flowin a sudden expansion.– J. Fluid Mech., vol.330, pp.169-188.
- [24] Brandt A., Dendy J.E. and Ruppel H. (1980): The multigrid method for semi-implicit hydrodynamic codes.– J.Comput. Phys., vol.34, pp.348-370.
- [25] Hackbusch W. (1985): Multigrid Methods for Applications.– Springer, Berlin.
- [26] Lange C.F., Schäfer M. and Durst F. (2002): Local block refinement with a multigrid flow solver.– Int. J. Numer.Methods Fluids, vol.38, pp.21-41.
- [27] Kim J. and Moin P. (1985): Application of a fractional-step method to incompressible Navier-Stokes equations.– J.Comput. Phys., vol.59, pp.308-323.
- [28] Durst F., Peireira J.C.F. and Tropea C. (1993): The plane symmetric sudden-expansion flow at low Reynoldsnumbers.– J. Fluid Mech., vol.248, pp.567-581.
- [29] Kaiktsis L., Karniadakis G.E. and Orszag S.A. (1996): Unsteadiness and convective instabilities in a two-dimensionalflow over a backward-facing step.– J. Fluid Mech., vol.321, pp.157-187.
- [30] Baines M.J. (1994): Moving finite elements.– Clarendon Press Oxford.
- [31] Huang W. and Russell R.D. (2010): Adaptive Moving Mesh Methods.– vol.174, Springer Science & Business Media.
- [32] Hawken D.F., Gottlieb J.J. and Hansen J.S. (1991): Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations.– Journal of Computational Physics, vol.95,No.2, pp.254-302.
- [33] Tang T. (2005): Moving mesh methods for computational fluid dynamics.– Contemporary Mathematics, vol.383,No.8, pp.141-173, DOI:10.1090/conm/383/07162.
- [34] MacCormack R.W. (1969): The Effect of Viscosity in Hypervelocity Impact Cratering.– AIAA Paper, pp.69-354,Cincinnati, Ohio, https://doi.org/10.1007/BFb0021338.
- [35] Loytsyansky L.G. (1987): Mechanics of liquid and gas.– Maskva. Science, pp.678.
- [36] Sommer A.F.and Shokina N.Yu. (2012): On some problems of designing difference schemes on two-dimensionalmoving grids.– Computational Technologies, vol.17, No.4, pp.88-108.
- [37] Khakimzyanov G.S. and Shokina N.Yu. (1998): Equidistribution method for constructing adaptive grids.–Computational technologies. vol.3, No.6. pp.63-81.
- [38] Shyy W. (1986): An adaptive grid method for Navier-Stokes flow computation II: Grid addition.– Applied numericalmathematics, vol.2, No.1, pp.9-19.
- [39] Shyy W., Tong S.S. and Correa S.M. (1985): Numerical recirculating flow calculation using a body-fitted coordinatesystem.– Numerical Heat Transfer. vol.8, No.1, pp.99-113.
- [40] Basile F., Chapelier J.-B., de La Llave Plata M., Laraufie R. and Frey P. (2021): A high-order h-adaptivediscontinuous Galerkin method for unstructured grids based on a posteriori error estimation.– AIAA Scitech 2021Forum, p.1696.
- [41] Huang W. and Zhan X. (2005): Adaptive moving mesh modeling for two-dimensional groundwater flow andtransport.– Contemporary Mathematics, vol.383, pp.239-252.
- [42] Ou K., Liang C. and Jameson A. (2010): High-order spectral difference method for the Navier-Stokes equation onunstructured moving deformable grid.– 48th AIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition, p.541.
- [43] Patankar S.V. (1980): Numerical Heat Transfer and Fluid Flow.– Taylor & Francis, ISBN 978-0-89116-522-4.
- [44] Erkinjon Son M.M. (2021): Numerical calculation of an air centrifugal separator based on the SARC turbulencemodel.– J. Appl. Comput. Mech., vol.6, pp.1133-1140, https://doi.org/10.22055/JACM.2020.31423.1871.
- [45] Madaliev E., Madaliev M., Adilov K. and Pulatov T. (2021) Comparison of turbulence models for two-phase flowin a centrifugal separator.– in E3S Web of Conferences, vol.264, p.1009,https://doi.org/10.1051/e3sconf/202126401009.
- [46] Volk B.L., Lagoudas D.C., Chen Y.C. and Whitley K.S. (2010): Analysis of the finite deformation response of shapememory polymers: I. Thermomechanical characterization.– Smart Materials and Structures, vol.19, No.7, p.10,DOI: 10.1088/0964-1726/19/7/075005.
- [47] Ratajczak M., Ptak M., Chybowski L., Gawdzińska K. and Będziński R. (2019): Material and structural modelingaspects of brain tissue deformation under dynamic loads.– Materials, MDPI, vol.12, No.2, Article number 271, p.13,doi: 10.3390/ma120271.
- [48] Reparaz J.S., Pereira da Silva K., Romero A.H., Serrano J., Wagner M.R., Callsen G., Choi S.J., Speck J.S. and GoñiA.R. (2018): Comparative study of the pressure dependence of optical-phonon transverse-effective charges andlinewidths in wurtzite.– In N. Phys., Rev.B, vol.98, Article number 165204, DOI:https://doi.org/10.1103/PhysRevB.98.165204.
- [49] Kholboev B.M., Navruzov D.P., Asrakulova D.S., Engalicheva N.R. and Turemuratova A.A. (2022): Comparisonof the results for calculation of vortex currents after sudden expansion of the pipe with different diameters.– Int. J.of Applied Mechanics and Engineering, vol.27, No.2, pp.115-123. https://doi.org/10.2478/ijame-2022-0023.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-89515a5d-e9f0-409b-9490-23097eb409be