SOLUSI NUMERIK UNTUK MENYELESAIKAN PERSAMAAN NAVIER-STOKES DALAM SILINDER SIRKULER

Muh. Fachrul Latief

Abstract


Telah dilakukan kajian studi numerik tentang aliran fluida mampat dua dimensi yang tunak melewati kaskade pada silinder sirkuler. Aliran fluida tersebut dideskripsikan oleh persamaan Navier-Stokes yang dituliskan dalam fungsi aliran dan vortisitas yang diselesaikan dengan metode kolokasi Chebychev dalam satu arah dan metode beda hingga (finite-difference) orde tinggi dalam arah lainnya. Selain itu, pemecahan langsung juga akan dikombinasikan dengan linearisasi Newton-Raphson untuk menyelesaikan persamaan diskrit. Solusi aliran diperoleh untuk bilangan Reynolds yang jauh lebih besar untuk berbagai lebar celah antara silinder. Solusi yang diperoleh adalah 3 jenis yang berbeda yang bergantung pada celahnya. Perbandingan dengan teoritis untuk berbagai besaran aliran menunjukkan hasil yang baik, terutama untuk kasus dengan lebar celahnya yang sempit.

Keywords


Solusi Numerik, Navier-Stokes, Slinder Sirkuler

Full Text:

PDF

References


Acrivos, A., Leal, L., Snowden, D. & Pan, F. 1968 Further experiments on steady separated flow past bluff objects. J. Fluid Mech. 34, 25–48

Acrivos, A., Snowden, D., Grove, A. & Petersen, E. 1965 The steady flow past a circular cylinder at large Reynolds numbers. J. Fluid Mech. 21, 737–760.

Batchelor, G. 1956 A proposal concerning laminar wakes behind bluff bodies at large Reynolds numbers. J. Fluid Mech. 1, 177–190.

Bhattacharya, S., Dennis, S. & Smith, F. 2001 Separating flow past a surface-mounted blunt obstacle. J. Engng Maths 39, 47–62.

Canuto, C., Hussaini, M. Y., Quaternoni, A. & Zang, T. 1987 Spectral Methods in Fluid Dynamics. Springer

Castro, I. 2002 Weakly stratifified laminar flow past normal flat plates. J. Fluid Mech. 454, 21–46 .

Chernyshenko, S. 1988 The asymptotic form of the stationary separated circumference of a body at high Reynolds numbers. Prikl. Matem. Mekh. 52, 958–966.

Chernyshenko, S. 1993 Stratifified flow in a channel. J. Fluid Mech. 250, 423–431

Chernyshenko, S. 1998 Asymptotic theory of global separation. Appl. Mech. Rev. 51, 523–535.

Chernyshenko, S. & Castro, I. 1993 High-Reynolds number asymptotics of the steady flow through a row of bluff bodies. J. Fluid Mech. 257, 421–449.

Chernyshenko, S. & Castro, I. 1996 High Reynolds number weakly stratifified flow past an obstacle. J. Fluid Mech. 317, 155–178.

Davies, C. & Carpenter, P. 1997 Numerical simulation of the evolution of Tollmien-Schlichting waves over fifinite compliant panels. J. Fluid Mech. 352, 205–243.

Ehrenstein, E. & Peyret, R. 1989 A chebychev collocation method for the Navier–Stokes equations with application to double-difusive convection. Intl J. Numer. Meth. Fluids 9, 427–452.

Fornberg, B. 1980 A numerical study of steady viscous flow past a circular cylinder. Intl J. Numer. Meth. Fluids 98, 819–855.

Fornberg, B. 1983 Steady viscous flow past a circular cylinder. NASA Conf Publ 2295, pp. 201–224.

Fornberg, B. 1985 Steady viscous flow past a cicular cylinder up to Reynolds number 600. J. Comput. Phys. 61, 297–320.

Fornberg, B. 1991 Steady incompressible flow past a row of circular cylinders. J. Fluid Mech. 225, 655–671.

Fornberg, B. 1998 A Practical Guide to Pseudospectral Methods. Cambridge University Press.

Ingham, D., Tang, T. & Morton, B. 1990 Steady two-dimensional flow through a row of normal flflat plates. J. Fluid Mech. 210, 281–302.

Kirchoff, G. 1869 Zur theorie freier-flussigkeits strahlen. J. Reine Angew Math Bd 70(H4), 289–298.

Milos, F. & Acrivos, A. 1986 Steady flow past sudden expansions at large Reynolds numbers Part i. Boundary layer solutions. Phys. Fluids 29, 1353–1359.

Milos, F. & Acrivos, A. 1987 Steady flow past sudden expansions at large Reynolds numbers. Part ii. Navier–Stokes solutions for the cascade expansion. Phys. Fluids 30, 7–18.

Natarajan, R., Fornberg, B. & Acrivos, A. 1993 Flow past a row of flat plates at large Reynolds numbers. Proc. R. Soc. Lond. A 441, 211–235.

Peregrine, H. 1985 A note on the steady high Reynolds number flow past a circular cylinder. J. Fluid Mech. 157, 493–500.

Sadovskii, V. 1970 A region of uniform vorticity in plane potential flow. Uch. Zap. TsAGI 1 (4), 1–9.

Sadovskii, V. 1971 On local properties of vortex flows. Uch. Zap. TsAGI 3 (4), 117–120.

Smith, F. 1979 Laminar flow of an incompressible fluid past a bluff body: The separation, reattachment, eddy properties and drag. J. Fluid Mech. 92, 171–205.

Smith, F. 1985a On large-scale eddy closure. J. Math. Phys. Sci. 19, 1–80.

Smith, F. 1985b A structure for laminar flow past a bluf body at large Reynolds numbers. J. Fluid Mech. 155, 175–191.

Sychev, V. 1967 On steady laminar flow behind a bluf body at high Reynolds numbers. In Proc. 8th Symposium on Current Problems of the Mechanics of Liquids and Gases. Tarda, Poland.

Sychev, V. 1982 Asymptotic theory of separated flows. Izv. AN SSSR, Mekh Zhidki 2, 20–30.

Taganov 1968 Contribution to the theory of stationary separation zones. Izv. AN SSSR Mekh Zhidki Gaza 5, 3–19.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.