A study is made of the flow normal to the mainstream direction (cross flow) that takes place in three-dimensional ‘bounded’ turbulent boundary layers near a wall, i.e. boundary layers restricted by the presence of bounding surfaces normal to that wall. Such boundary layers are present in the flow through rows of blades in a turbo machine.
Analytical expressions for the cross-flow velocity profiles are derived for these ‘bounded’ boundary layers and are compared with experimental data.
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References
1.
JohnstonJ. P. ‘On the three-dimensional turbulent boundary layers generated by secondary flow’, J. bas. Engng, Trans. Am. Soc. mech. Engrs196082, 233.
2.
HoadleyD. ‘Boundary layer development in an annular diffuser’, Proc. Symp. Internal Flows1971 (Institution of Mechanical Engineers, London).
3.
LewkowiczA. K.Two- and three-dimensional incompressible turbulent boundary layers Ph. D. Thesis, University of Liverpool, 1965.
4.
CookeJ. C.HallM. G. ‘Boundary layers in three dimensions’, Progress in aeronautical sciences21962 (Pergamon Press, Oxford).
5.
JoubertP. N.PerryA. E.BrownK. C. ‘Critical review and current developments in three-dimensional turbulent boundary layers’, Fluid mechanics of internal flow, SovranG., 1967 (Elsevier, Amsterdam).
6.
HorlockJ. H.NorburyJ. F.CookeJ. C. ‘Three-dimensional turbulent boundary layers: A report on Euromech 2’, J. Fluid Mech.196727, 369.
7.
CumpstyN. ‘A critical examination of the use of a two-dimensional turbulent profile family to represent three-dimensional boundary layers’, A. R. C. Current Paper No. 10681970.
8.
CumpstyN. ‘Cross-flow in turbulent boundary layers’, A. R. C. Current Paper 10671970.
9.
CumpstyN.HeadM. R. ‘The calculation of three-dimensional turbulent boundary layers (I)’, Aeronaut. Q.196718, 55–84.
10.
NashJ. F. ‘The calculation of three-dimensional turbulent boundary layers in incompressible flow’, J. Fluid Mech.196937, 625–642.
11.
BradshawP. ‘Calculation of three-dimensional turbulent boundary layers’, J. Fluid Mech.197146, 417–445.
12.
HorlockJ. H.HoadleyD. ‘Calculation of the annulus wall boundary layers in axial flow turbomachines’, A. R. C. Current Paper No. 11961972.
13.
StratfordB. S. ‘The use of boundary layer techniques to calculate the blockage from the annulus boundary layers in a compressor’, A. S. M. E. Paper 67-WA/GT-7, 1967.
14.
HorlockJ. H. ‘Boundary layer problems in axial turbo-machines’, Flow research on blading, DzungL. S., 1969 (Elsevier, Amsterdam).
15.
HorlockJ. H.MarshH. ‘Flow models for turbo-machines’, J. mech. Engng Sci.197113 (No. 5), 358–368.
16.
HawthorneW. R. ‘Some formulae for the calculation of secondary flow in cascades’, A. R. C. rept No. 175191955.
17.
ColesD. ‘The law of the wake in the turbulent boundary layer’, J. Fluid Mech.19561, 191–226.
18.
ThompsonB. G. J. ‘A critical review of existing methods of calculating the turbulent boundary layer’, A. R. C. rept Memor. No. 34471964.
19.
EastL. F. ‘Measurement of skin friction at low subsonic speed by the razor blade technique’, A. R. C. rept Memor. No. 35251968.
20.
GruschwitzE. ‘Turbulente Reibungsschichten mit Sekundäströmung’, Ing. Arch.1935vi, 355.
21.
EichelbrennerE. A. ‘Theoretical investigation and control by measuring tests on the behaviour of the three-dimensional turbulent boundary layer on an annular wing at various incidences’, Bureau of Technology Zborowski Report for ONR, Air Progress Branch, 1963.
22.
MerringtonG. L.A study of the hub boundary layer in an axial flow compressor Ph. D. Thesis, University of Tasmania, 1970.
23.
SharnbrookJ. R.HatchD. E. ‘A family of hodograph models for the cross-flow velocity component of three-dimensional turbulent boundary layers’, A. S. M. E. Paper No. 71-FE-1, 1971.
24.
PerryA. E.JoubertP. N. ‘A three-dimensional turbulent boundary layer’, J. Fluid Mech.196522, 285–304.
25.
PerryA. E.BellJ. B.JoubertP. N. ‘Velocity and temperature profiles in adverse pressure-gradient turbulent boundary layers’, J. Fluid Mech.196623, 299–320.
26.
BradshawP. ‘Prediction of turbulent shear layers in turbomachines’, Proc. Conf. Fluid Mechanics Design Turbo-machines NASA STP 304, 1970.
27.
MagerA. ‘Generalization of boundary layer momentum integral equations to three-dimensional flow including those of rotating systems’, NASA Rept No. 10671952.
28.
SmithL. H. ‘Secondary flow in axial flow turbomachinery’, Trans. Am. Soc. mech. Engrs195577, 1065–1076.
29.
SquireH. B.WinterK. G. ‘The secondary flow in a cascade of aerofoils in a non-uniform stream’, J. aeronaut. Sci.195118, 271–277.
30.
HawthorneW. R. ‘Secondary circulation in fluid flow’, Proc. R. Soc.1951A206, 374–387.
31.
LouisJ. F.Stalling phenomena in axial-flow compressors Ph. D. Thesis, University of Liverpool, 1957.
32.
MellorG. L.WoodG. M. ‘An axial compressor end wall boundary layer theory’, A. S. M. E. Paper No. 70-GT-80, 1970.
33.
RottaJ.Progress in aeronautical sciences 21962 (Pergamon Press, Oxford).
34.
TownsendA. A.The structure of turbulent shear flow1956 (Cambridge University Press, London).
35.
TownsendA. A. ‘Equilibrium layers and wall turbulence’, J. Fluid Mech.196111, 97–120.
36.
HorlockJ. H. ‘Annulus wall boundary layers in axial flow compressor stages’, J. bas. Engng, Trans. Am. Soc. mech. Engrs196385, 55.
37.
DaneshyarM.Private communication, 1971.
38.
VermeulenA.Measurements of three-dimensional turbulent boundary layers Ph. D. Thesis, University of Cambridge, 1971.