The problem of separated flow in bends of arbitrary turning angles has been examined. The method of analysis is based on the inviscid flow theory coupled with Kirchhoff’s separation model. The physical flow problem is first transformed to the hodograph domain, and then into a rectangular computational region using properly selected flow parameters. The solution is first established in the hodograph plane. The final flow pattern including the inner and outer walls of the bend, the separation streamline, and other flow properties in the physical plane are subsequently obtained through direct integration. The results of the present analysis are compared with those of Lichtarowicz and Markland as well as Mankbadi and Zaki.
Issue Section:
Technical Papers
1.
Mankbadi
, R. R.
, and Zaki
, S. S.
, 1986
, “Computations of the Contraction Coefficient of Unsymmetrical Bends
,” AIAA J.
, 24
, pp. 1285
–1289
.2.
Lichtarowicz
, A.
, and Markland
, E.
, 1963
, “Calculation of Potential Flow With Separation in a Right-Angled Elbow With Unequal Branches
,” J. Fluid Mech.
, 17
, pp. 596
–606
.3.
Smith
, F. T.
, 1979
, “Laminar Flow of an Incompressible Fluid Past a Bluff Body: The Separation, Reattachment, Eddy Properties and Drag
,” J. Fluid Mech.
, 92
, Part 1, pp. 171
–205
.4.
Smith
, F. T.
, and Duck
, P. W.
, 1980
, “On the Severe Non-symmetric Constriction, Curving or Cornering of Channel Flows
,” J. Fluid Mech.
, 98
, Part 4, pp. 727
–753
.5.
Heskestad
, G.
, 1971
, “Two-Dimensional Miter-Bend Flow
,” ASME J. Basic Eng.
, 93
, pp. 433
–443
.6.
Roshko
, A.
, 1955
, “On the Wake and Drag of Bluff Bodies
,” J. Aeronaut. Sci.
, 22
, pp. 124
–132
.7.
Liu
, S. K.
, and Chow
, W. L.
, 1978
, “Numerical Solutions of the Compressible Hodograph Equation
,” AIAA J.
, 16
, pp. 188
–189
.8.
Chow
, W. L.
, and Han
, T.
, 1979
, “Inviscid Solution for the Problem of Free Overfall
,” ASME J. Appl. Mech.
, 46
, pp. 1
–5
.9.
Han
, T.
, and Chow
, W. L.
, 1981
, “The Study of Sluice Gate and Sharp Crested Weir Through Hodograph Transformation
,” ASME J. Appl. Mech.
, 48
, pp. 229
–238
.10.
Wu
, C.
, and Chow
, W. L.
, 1985
, “Study of an Asymmetric Flap Nozzle as a Vector-Thrust Device
,” AIAA J. Propul. Power
, 1
, pp. 286
–291
.11.
Chow
, W. L.
, Chow
, W. L.
, Alice
, A. L.
, and Tsai
, P. H.
, 1987
, “Discharge From a Vessel Through an Axisymmetric Control Valve
,” ASME J. Appl. Mech.
, 54
, pp. 447
–452
.12.
Weng
, Z. M.
, Weng
, Z. M.
, Alice
, A. L.
, and Chow
, W. L.
, 1987
, “Discharge of a Compressible Fluid Through a Control Valve
,” ASME J. Appl. Mech.
, 54
, pp. 955
–960
.13.
Chu
, S. S.
, Miller
, S. K.
, and Chow
, W. L.
, 1990
, “Quasi-Steady Discharge of Fluid From a Vessel Through a Poppet Valve
,” ASME J. Fluids Eng.
, 112
, pp. 437
–440
.14.
Chu
, S. S.
, and Chow
, W. L.
, 1992
, “A Hodograph-Based Method for the Solutions of Axisymmetric Orifice Flows
,” J. CSME
, 13
(2
), pp. 167
–170
.15.
Chu, S. S., and Wei, C. Y., 1996, “Study of the Jet-Plate Interaction Using the Method of Hodograph Transformation,” Proceedings of the 38th Conf. on Aeronautics and Astronautics, AASRC, Tainan, R.O.C., pp. 191–197.
16.
Chu
, S. S.
, and Chow
, W. L.
, 1997
, “Jet-Plate Interaction for Wedge-Shaped Plates of Arbitrary Angles
,” ASME J. Fluids Eng.
, 119
, pp. 929
–933
.17.
Chu, S. S., and Wu, C. C., 1997, “The Inviscid Interaction Between a Jet and a Flat Plate,” Proceedings of the 39th Conf. on Aeronautics and Astronautics, AASRC, Tainan, R.O.C., pp. 83–90.
18.
Kirchhoff
, G.
, 1869
, “Zur Theorie freir Flussigkeitsstrahlen
,” J. Reine Angew. Math.
, 70
, pp. 289
–298
.19.
Roshko, A., 1954, “A New Hodograph for Free Streamline Theory,” NACA Technical Note No. 3168.
20.
Birkhoff, A., 1950, Hydrodynamics, Dover, New York.
21.
Cooke, G. C., 1968, “Peripheral Jets and Plenum Chambers—An Exact Potential Flow Analysis,” TRAE 6811, Rensselaer Polytechnic Institute, Troy, NY.
22.
Shapiro, A. H., 1953, The Dynamics and Thermodynamics of Compressible Fluid Flow, The Ronald Press Company, New York.
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