WATER JET CONFERENCE - Waterjet Technology Association

or, in dimensionless form
t * ( X * ) =
X *
dy *
∫ *
V 0 p
where time has been nondimensionalized by the parameter
[ S3 Ap E ]
1
2
105
(25)
The elapsed time can be evaluated numerically more easily than in closed form.
ANALYTICAL RESULTS
The purpose of the analysis is to provide detailed understanding of the operation
of a pulsed extrusion device. The analytical results are also very useful for designing the
experimental apparatus. A typical design case of interest in the current project is as
follows.
CASE I
E = 1000 ft-lbf = 1360 joules
M p = 66.25 lbm = 30 kg
ρ=62.4 lbm/ft 3 =1.0gm/cc
L c= 2.5 in = 6.35 cm
L n= 2.0 in = 5.08 cm
S= 0.793 in = 2.01 cm
D p= 0.513 in = 1.30 cm
A p= 0.207 in 2 = 1.34 cm 2
D j= 0.0198 in = 0.5 mm
R= 670
λ= 0.02
The nozzle for this described by (0≤ Z ≤ L n )
−Z ln R
D(Z ) = Dpesp[ 2Ln and the fluid is water.
The piston mass is large to simulate the driver mass of a commercially available
hydraulically-cocked gas spring. Analytical results for the chamber pressure at the piston
face, the jet exit velocity, cumulative jet energy and elapsed time are shown in Figures 3
through 6. Inviscid results ( λ = 0) for Case I are also presented in these figures.
Quasi-steady flow has been achieved when the pressure history "tracks" the driving force
per unit piston area (F/A p ). Figure 3 shows that quasi-steady flow is achieved for Case I
at about X*=0.1.