Summary
This paper describes results of measurements concerning the radial and axial distribution of time-mean values of velocity, temperature, and gas concentration in a turbulent jet issuing from a round orifice into quiescent ambient air. The results show that the rates of spreading of heat and matter are mutually equal but greater than that of velocity. A constant ratio between the coefficient of transfer of heat or matter and the coefficient of shearing stress does not seem to exist. The results have been subjected to a theoretical analysis.
The theory based on a constant coefficient of shearing stress across the jet gives the best agreement with measured radial velocity-distribution in a central zone of the jet.
The theory based on a constant coefficient of transfer of heat or matter gives results that cover the experimental results reasonably well, again for the central zone. A better agreement, however, is obtained if the coefficient of transfer of heat or matter is assumed to contain not only a constant part but also a part proportional to the local velocity. This assumption is in agreement with the variable ratio between this coefficient and that of shearing stress.
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Abbreviations
- x :
-
co-ordinate in axial direction; axial distance to orifice
- y :
-
co-ordinate in radial direction; radial distance to jet axis
- a :
-
distance of apparent aperture to orifice
- d :
-
diameter of orifice
- η:
-
radial distance ratioy/(x+a)
- U :
-
time-mean velocity component in axial direction
- u :
-
fluctuating part of axial velocity component
- V :
-
time-mean velocity component in radial direction
- v :
-
fluctuating part of radial velocity component
- Θ:
-
time-mean value of temperature difference with ambient air
- Ω:
-
time-mean value of concentration difference with ambient air
- ω:
-
fluctuating part of concentration difference
- Γ:
-
time-mean value of either temperature or concentration
- γ:
-
fluctuating part of Γ
- p :
-
static pressure
- Δp :
-
velocity pressure
- ϱ:
-
density
- ν:
-
kinematic viscosity
- εm :
-
coefficient of transfer of momentum; coefficient of shearing stress
- εv :
-
coefficient of transfer of vorticity
- εΓ:
-
coefficient of transfer of Γ
- l m :
-
mixing length for transfer of momentum
- l v :
-
mixing length for transfer of vorticity
- l Γ :
-
mixing length for transfer of Γ
- c m :
-
constant defined byl m/x
- c ν :
-
constant defined byl ν/x
- cΓ:
-
constant defined byl Γ/x
- λ:
-
scale of micro turbulence
- F :
-
function of η related to velocity-distribution
- G :
-
function of η related to Γ-distribution
- K u :
-
factor accounting for the deviation from the rectangular velocity distribution at the orifice
- K Ω :
-
factor accounting for the deviation from the rectangular concentration distribution at the orfice
- αi :
-
1, 2, 3,. ... constants
- βi :
-
1, 2, 3,. ... constants
- Re :
-
Reynolds' number=U 0d/v. The index 0 refers to values at the orifice. The indexm refers to values in the axis of the jet (maximum value over a cross-section), unless otherwise stated.
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Hinze, J.O., Van Der Hegge Zijnen, B.G. Transfer of heat and matter in the turbulent mixing zone of an axially symmetrical jet. Appl. Sci. Res. 1, 435 (1949). https://doi.org/10.1007/BF02120346
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DOI: https://doi.org/10.1007/BF02120346