Solution Structure and Stability of Viscous Flow in Curved Square Ducts

[+] Author and Article Information
Tianliang Yang, Liqiu Wang

Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

J. Fluids Eng 123(4), 863-868 (Jun 05, 2001) (6 pages) doi:10.1115/1.1412457 History: Received February 09, 2000; Revised June 05, 2001
Copyright © 2001 by ASME
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Dean,  W. R., 1927, “The stream-line motion of a fluid in a curved pipe,” Philos. Mag., 5, pp. 673–695.
Stewartson,  K., Cebeci,  T., and Chang,  K. C., 1980, “A boundary-layer collision in a curved duct,” Q. J. Mech. Appl. Math., 33, pp. 59–75.
Berger,  S. A., Talbot,  L., and Yao,  L-S., 1983, “Flow in curved pipes,” Annu. Rev. Fluid Mech., 15, pp. 461–512.
Nandakumar, K., and Masliyah, J. H., 1986, “Swirling flow and heat transfer in coiled and twisted pipes,” Advances in Transport Processes, 4 , pp. 49–112.
Itō,  H., 1987, “Flow in curved pipes,” JSME Int. J., 30, pp. 543–552.
Berger, S. A., 1991, “Flow and heat transfer in curved pipes and tubes,” AIAA 91-0030, pp. 1–19.
Cheng,  K. C., and Akiyama,  M., 1970, “Laminar forced convection heat transfer in curved rectangular channels,” Int. J. Heat Mass Transf., 13, pp. 471–490.
Joseph,  B., Smith,  E. P., and Adler,  R. J., 1975, “Numerical treatment of laminar flow in helically coiled tubes of square cross section,” AIChE J., 21, pp. 965–974.
Masliyah,  J. H., 1980, “On laminar flow in curved semicircular ducts,” J. Fluid Mech., 99, pp. 469–479.
Nandakumar,  K., and Masliyah,  J. H., 1982, “Bifurcation in steady laminar flow through curved tubes,” J. Fluid Mech., 119, pp. 475–490.
Winters,  K. H., 1987, “A bifurcation study of laminar flow in a curved tube of rectangular cross-section,” J. Fluid Mech., 180, pp. 343–369.
Daskopoulos,  P., and Lenhoff,  A. M., 1989, “Flow in curved ducts: bifurcation structure for stationary ducts,” J. Fluid Mech., 203, pp. 125–148.
Cheng, K. C., Nakayama, J., and Akiyama, M., 1979, “Effect of finite and infinite aspect ratios on flow patterns in curved rectangular channels,”in Flow Visualization, Hemisphere.
Wang,  L., and Cheng,  K. C., 1996, “Flow transitions and combined free and forced convective heat transfer in rotating curved channels: The case of positive rotation,” Phys. Fluids A, 6, pp. 1553–1573.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, New York, pp. 28–30.
Rheinboldt,  W. C. 1980, “Solution fields of nonlinear equations and continuation methods,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 17, pp. 221–237.
Keller, H. B., 1977, “Numerical solution of Bifurcation and nonlinear eigenvalue problems,” Applications of Bifurcation Theory, Academic Press, New York, pp. 359–384.
Seydel,  R., 1983, “Branch switching in bifurcation problems for ordinary differential equations,” Numerical Mathematics, 41, pp. 91–116.
Seydel, R., 1994, From Equlibrium to Chaos, Practical Bifurcation and Stability Analysis, Elsevier Science Publishing, New York, pp. 109–304.
Yang, T. and Wang, L., 2000, “Solution structure and stability of viscous flow and heat transfer in curved channels,” The 34th National Heat Transfer Conference, Pittsburgh, PA.
Yang, T., 2001, “Multiplicity and stability of flow and heat transfer in rotating curved ducts,” Ph.D. thesis, The University of Hong Kong.
Pomeau,  Y., and Manneville,  P., 1980, “Intermittent transition to turbulence in dissipative dynamical systems,” Commun. Math. Phys., 74, pp. 189–197.


Grahic Jump Location
Typical time evolution process in 0≤Dk≤191.27 at σ=0.02, and Pr=0.7: dynamic response of solution on S1−2 at Dk=180 to finite random disturbances: evolution to stable steady 2-cell state on S1−1
Grahic Jump Location
Typical time evolution process in 191.27<Dk≤375 at σ=0.02, and Pr=0.7: dynamic response of solution at Dk=300 on A1−1 to finite random disturbances: periodic oscillation (period=0.159)
Grahic Jump Location
Typical time evolution process in 375<Dk≤620 at σ=0.02, and Pr=0.7: dynamic response of solution at Dk=550 on S2−1 to finite random disturbances: evolution to stable steady 2-cell state on S2−2
Grahic Jump Location
Typical time evolution process in 620<Dk≤650 at σ=0.02, and Pr=0.7: dynamic response of solution at Dk=630 on S2−1 to finite random disturbances: intermittency
Grahic Jump Location
Typical time evolution process in 650<Dk≤800: dynamic response of the solution at Dk=800,σ=0.02, and Pr=0.7 on A3−1 to finite random disturbances: chaotic oscillation
Grahic Jump Location
Physical problem and coordinate system
Grahic Jump Location
Solution branches and their connectivity for the flow through the stationary curved duct of square cross-section at σ=0.02,Pr=0.7 (dimensionless velocity in r direction at r=0.9,z=0.14 vs. Dk). (a) Connectivity between S1 and A1, (b) four limit points on A1, (c) connectivity between S2 and A2, (d) connectivity between S2 and A3, (e) connectivity between S2 and A4
Grahic Jump Location
The flow patterns at Dk=180/550,σ=0.02,Pr=0.7. (a) Dk=180 on S11,De=123.4, (b) Dk=550,De=274 on S1−3, (c) Dk=550,De=290 on A1−1, (d) Dk=550,De=279 on S2−1, (e) Dk=550,De=289 on S2−2, (f ) Dk=550,De=291 on S2−3 (g) Dk=550,De=288 on S2−4
Grahic Jump Location
The secondary flow patterns at Dk=700,σ=0.02,Pr=0.7. (a) Re=2328,De=329 on S1−3, (b) Re=2447,De=346 on A1−1, (c) Re=2345,De=332 on S2−1, (d) Re=2402,De=340 on S2−4, (e) Re=2400,De=339 on S2−5, (f ) Re=2410,De=341 on S2−6, (g) Re=2448,De=346 on A2−1, (h) Re=2399,De=339 on A4−1




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