Abstract
A detailed similarity analysis of the incompressible radial free, wall, and luquid jets with swirl is presented. The analysis aims at a determination of the space flow geometry of the given generally formulated problems. The derived space flow geometry implies that the transformed formulations of the given problems are formally identical to those without swirl. Unlike the free jet, the wall and liquid jets with swirl are treated only for a Newtonian fluid but in this case the similarity analysis also provides the interpretation of a virtual origin.
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Abbreviations
- A(x), B(x), E(x), T 1 (x), T 3 (x) :
-
positive similarity coefficients
- C, C 2,C 3,C 4,D :
-
constants
- K, l, m, R, S :
-
constants
- e :
-
swirl parameter
- f(η),h(η),T(η),T 2(η),T 4(η):
-
similarity functions
- L :
-
radius of a circumference-point-source
- M ∞,N, Q :
-
integral invariants
- q (q max):
-
(maximum) velocity component in ξ-direction
- u(u max):
-
(maximum) radial velocity component
- v :
-
axial velocity component
- w (w max):
-
(maximum) peripheral velocity component
- x :
-
radial coordinate
- y :
-
transverse coordinate
- β:
-
outflow angle
- δ:
-
characteristic jet width
- η(x,y) :
-
similarity variable (scaledx andy coordinate)
- ν:
-
molecular kinematic viscosity
- \(\xi ( = \sqrt {x^2 - e^2 } )\) :
-
tangential coordinate
- ρ:
-
fluid density
- τ:
-
shear stress in ξ-direction
- τ xy , τ ϕy :
-
shear stress tensor components
- ψ:
-
stream function
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Filip, P., Kolář, V. & Curev, A.G. Space flow geometry of the radial free, wall and liquid jets with swirl. Appl. Sci. Res. 42, 185–196 (1985). https://doi.org/10.1007/BF02421349
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DOI: https://doi.org/10.1007/BF02421349