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An experimental investigation of a wall jet in a torus

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Abstract

Results of an experimental investigation of the velocity profile of a turbulent gas injected in a toroidal configuration are presented. The measurements surprisingly show that it is possible to describe the radial distribution of the azimuthal velocity in terms of a plane wall jet discharging in an external stream.

The growth of the inner boundary layer, the width of the jet, and the velocity profile are in accordance with the known experimental data on this subject. A fundamentally different relation has been deduced for the decay of the maximum velocity. Up to now Sigalla's formula \(U_m /U_j \propto \sqrt {a/x}\) is generally accepted. Our data based on an essentially extended range of x/a, correlate with the exponential relation

$$U_m /U_j = exp\left[ { - 154(Re_x )^{ - 0.777} \frac{x}{a}} \right].$$

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Abbreviations

a :

width of entrance slit

M :

Mach number

P tot :

pressure at the stagnation point of the total pressure tube, measured in the entrance slit

P stat :

static pressure at the torus wall

r :

minor radius of the torus

R :

main radius of the torus

Re a :

Reynolds number with respect to a, U j a/ν

Re x :

Reynolds number with respect to x, U j x/ν

uφ:

fluctuation in the azimuthal velocity component

\(\overline {U_\phi ^2 }\) :

mean square of the fluctuation in the azimuthal velocity component

U :

azimuthal velocity

U j :

jet velocity

U m :

maximum azimuthal velocity at any station x

U ∞ :

velocity of external stream (defined as the azimuthal velocity at distance y=10δ 1)

x :

distance measured along wall from entrance slit

x 0 :

value of x where maximum velocity begins to decay

y :

distance perpendicular to wall

γ :

ratio of specific heat at constant pressure to specific heat at constant volume

δ 1 :

value of y where U=U m

δ 2 :

value of y farthest from wall, where U=1/2U m

ν :

kinematic viscosity of fluid

τ :

degree of turbulence

References

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Authors and Affiliations

  1. Association Euratom-FOM, FOM-Instituut voor Plasma-Fysica Rijnhuizen, Jutphaas, The Netherlands

    H. W. Piekaar & R. W. Polman

Authors
  1. H. W. Piekaar
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  2. R. W. Polman
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Piekaar, H.W., Polman, R.W. An experimental investigation of a wall jet in a torus. Appl. Sci. Res. 23, 393–406 (1971). https://doi.org/10.1007/BF00413213

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  • DOI: https://doi.org/10.1007/BF00413213

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