Mechanics of transition in an axisymmetric laminar boundary layer on a circular cylinder

  • G. N. V. Rao
Original Papers

Abstract

Measurements of the growth of artificially generated turbulent spots and intermittency distribution in the transition region on a circular cylinder in axial flow show that the instability Reynolds number of 11,000 has a marked effect on the properties. In particular, it is found that the spot production in the initial region when a single turbulent spot has not yet wrapped around the cylinder and the propagation is essentially two-dimensional, is significantly altered. But the transition in the downstream or latter region, where most of the turbulent spots propagate onedimensionally (like the turbulent plugs in a pipe), is not affected. When the radius Reynolds number is more than 11,000, the intermittency law in the initial region is essentially the same as in twodimensional flow on a flat plate and in the latter region it is the one-dimensional flow in a pipe, the demarcation between the two regions being quite sharp.

Symbols

a

radius of the circular cylinder

d

2a

g

spot production function defined as the number of spots produced per unit area in unit time

l

total distance from the leading edge of the cylinder

N

number of turbulent spots produced at a point in unit time

Ra

Reynolds number defined as (Uoa/v)

Rd

Reynolds number defined as (Uod/v)

Rt

Reynolds number defined as (Uoxt/v)

Reynolds number defined as (Uoλ/v)

Rδ

Reynolds number defined as (Uoδ/v)

Uo

Freestream velocity

x

distance from the leading edge of the cylinder

xt

the distance to the beginning of transition from the leading edge of the cylinder

γ

Intermittency in the transition region defined as the fraction of the time that the flow is turbulent at a point

δ

boundary layer thickness at a point

λ

the distance in the transition region between the point where γ=0.25 and the point where γ=0.75

σ

spot propagation parameter defined by Emmons

kinematic viscosity of the fluid

ζ

(x-xt)/λ

Zusammenfassung

Die Entwicklung von künstlich erzeugten Turbulenzflecken und die Intermittenzverteilung im Umschlaggebiet an einem Kreiszylinder wurden gemessen. Die Messungen zeigen, daß die Instabilitäts-Reynolds-Zahl von 11,000 einen ausgeprägten Einfluß auf diese Eigenschaften hat. Im einzelnen zeigt sich, daß die Fleckenbildung im Anfangsgebiet, wo sich noch kein einziger Turbulenzfleck um den Zylinder gewickelt hat und die Fortpflanzung im wesentlichen zweidimensional ist, sich erheblich ändert. Dagegen wird der Umschlag im stromabwärts gelegenen Gebeit, wo die meisten Turbulenzflecke (wie die Turbulenzstöpsel in Rohren) sich eindimensional fortpflanzen, nicht beeinflußt. Wenn die Radius-Reynolds-Zahl größer als 11,000 ist, ist das Intermittenzgesetz im Anfangsgebiet im wesentlichen identisch mit dem in der zweidimensionalen Strömung auf einer ebenen Platte, und das im strömabwärts gelegenen Gebiet ist identisch mit der eindimensionalen Strömung in einem Rohr, wobei die Abgrenzung zwischen den beiden Gebieten ziemlich scharf ist.

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References

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Copyright information

© Birkhäuser Verlag 1974

Authors and Affiliations

  • G. N. V. Rao
    • 1
  1. 1.Department of Aeronautical EngineeringIndian Institute of ScienceBangalore-12India

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