Abstract
Experiments were performed on laminar, vertical, annular, liquid curtains to study the dynamics of steady curtains, and the onset and frequency of oscillating curtains. The experiments were conducted to observe the effects of inertia and pressure on liquid curtains with different surface tensions. For steady curtains, convergence lengths were measured as functions of Froude number and pressure differential for three different surface tensions. The factors causing the onset of oscillations in a pressurized curtain were observed and the frequency of the internal pressure fluctuations were measured for various Froude numbers and two surface tensions.
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Abbreviations
- b :
-
local thickness of curtain sheet
- b 0 :
-
initial thickness of curtain or nozzle gap thickness (0.5 mm)
- C P :
-
pressure coefficient \(\left( {Fr^2 \frac{{\Delta P}}{{\rho V_0^2 }}} \right)\)
- Fr :
-
Froude number (V 20 /g R 0)
- g :
-
gravitational acceleration
- g :
-
gravitational acceleration
- L :
-
convergence length of curtain
- L * :
-
dimensionless convergence length (L/R 0)
- N c :
-
convergence number (g 2 R 20 b 0 ϱ/2v 20 σ)
- P e :
-
pressure outside the curtain (ambient)
- P i :
-
pressure inside the curtain
- ΔP :
-
pressure differential (P i– P e)
- ΔP cr :
-
pressure differential at which curtain begins to oscillate
- R :
-
local radius of curvature in the horizontal plane
- R 0 :
-
initial curtain radius or radius of nozzle exit (50 mm)
- r v :
-
local radius of curvature in the vertical plane
- V :
-
local liquid velocity
- V 0 :
-
initial liquid velocity
- V * :
-
dimensionless local liquid velocity (V/V 0)
- z :
-
axial distance from the nozzle
- z * :
-
dimensionless axial distance from the nozzel (z/R 0)
- δs :
-
differential length of curtain
- δφ :
-
differential angle in the horizontal plane
- α :
-
angle between the direction of the surface tension force in the vertical plane and the direction of r v
- β:
-
deangle between the direction of the surface tension force in the horizontal plane and the direction of R
- θ:
-
angle between r vand R in the vertical plane
- θ0 :
-
nozzle exit angle (zero degrees)
- σ:
-
surface tension of liquid
- ϱ:
-
liquid density (1.0 gm/cm3)
References
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Kelly-Zion, P., Chigier, N. Experimental investigations of steady and oscillating annular liquid curtains with different surface tensions. Experiments in Fluids 10, 168–175 (1990). https://doi.org/10.1007/BF00215026
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DOI: https://doi.org/10.1007/BF00215026