The Egyptian International Journal of
Engineering Sciences and Technology
Vol. 19 No. 2 (2016-Special Issue) 282–296
http://www.eijest.zu.edu.eg
A Comparative Study of Supercavitation Phenomena on
Different Projectiles Shapes in Transient Flow by CFD
Mohsen Y. Mansour1*, Mohamed H. Mansour2, Nabil H. Mostafa3 and Magdy Abu
Rayan2
1
Aeronautical Eng., Mansoura University, Egypt
2
Mechanical Power Department, Mansoura University, Egypt
3
Mechanical Power Department, Zagazig University, Zagazig, P.O. 44519, Egypt
ARTICLE INFO ABSTRACT
Article history: Body shape of high-speed underwater vehicles has a great effect on the
Received 13 May 2016
Received in revised form Supercavitation behaviour. The transient flow around either partially cavitating or
7 June 2016 supercavitating body affects the trajectory of high-speed underwater vehicles.
Accepted 14 June 2016 Commercial code (ESI-CFD ACE+, V 2010) was used to simulate the
Available online 1 July 2014
supercavitation around two different shapes of a projectile with their noses of
hemispherical shape and telescopic shape. Also, conical and blunt projectile shapes
Keywords:
Supercavitation; were considered. Also, a comparison between two different designs of grid was
Structured grid; performed numerically. Grid designs were structured and unstructured grids.
Unstructured grid; Navier-Stokes equations were used as governing equations for simulating
ESI-CFD; supercavitation. Cavity shape was determined over projectile body and around
Hydrofoil;
Projectile; wake. Also, two-dimensional flow field around the cavitating body was determined.
Shape optimization. Projectile body has a diameter about 0.4 times its length (0.4L). In the case of the
Blunt end there is a strong wake effect. The ESI-CFD code (2010) is valid for
observing the supercavitation phenomena. Unstructured grid is more accurate than
structured one in simulating supercavitation.
speeds, a vortex ring is situated over the bubble
1. Introduction boundary.
High-speed underwater vehicles have many The flow around either partially cavitating or
advantages and disadvantages. So, many researchers supercavitating hydrofoils are treated by Kinnas et al.
simulate is behaviour and try to control is trajectory. (1994) with a viscous/ inviscid interactive method.
Mostafa et al. (2001) study experimentally the flow Owis and Nayfeh (2003) compute the compressible
around a hemisphere cylinder by shooting a projectile Multiphase Flow Over the cavitating high-speed
and employing Particle Image Velocimetry (PIV) to torpedo. The cavitating flow over hemispherical and
measure the velocity field. A doublet is generated conical bodies indicate that the preconditioned
between the projectile nose and its rear end. At high system of equations converges rapidly to the required
solution at very low speeds.
* Corresponding author. Tel.: +201009387559.
E-mail address: mohsen_mansour@hotmail.com.
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To improve the understanding of the unsteady the mixture density Kg/m3
behaviour of supercavitating flows, Mostafa (2005) effective exchange coefficient
used a three-dimensional Navier-Stokes code to Suffixes
model the two-phase flow field around a hemisphere c bubble reduction and collapse
cylinder. The governing equations are discretized on e bubble generation and expansion
a structured grid using an upwind difference scheme. gas, G gas phases
L liquid phases
Supercavitating vehicles exploit supercavitation as V vapor phases
a means to reduce drag and achieve an extremely
high underwater speed. Supercavitation is achieved
when a body moves through water at sufficient speed, Theory Background
so that the fluid pressure drops to the water vapor
pressure. In supercavitating flows, a low-density
The calculation of cavitation phenomena in this paper
gaseous cavity entirely envelops the vehicle and the
is based on solving Navier-Stokes equations through
skin drag of the vehicle is almost negligible. Hence,
cavitation module of ESI - CFD 2010 and K-
the vehicle can move at extremely high speed in a
turbulence model. A numerical model previously
two-phase medium, Ahn (2007). So, A
developed by ESI-CFD to solve (Navier- Stokes)
supercavitating torpedo is a complex high speed
equations (Sighal, 1999).
undersea weapon that is exposed to extreme
As we know in cavitational flow as 2D flow, the
operating conditions due to the weapon’s speed.
Alyanak et al. (2006) formulates an optimize this mixture mass density () is function of vapour mass
problem to determines the general shape of the fraction (f), water density and vapour density. The -
torpedo in order to satisfy the required performance f relationship is:
1 f 1 f (1)
v
criteria function of speed. Kamada (2005).
The object of this work is to study the transit flow
1
The previous equation can be written by using vapour
around either partially cavitating or supercavitating
volume fraction. Therefore, it is deduced from f as
body affecting the high-speed underwater vehicles,
follows:
which have different body shapes and cavitation
f
(2)
numbers. Calculation will use structured grids and
un-structured grids Structure v
The transport equation for vapor is written as
Nomenclature follows:
Ce , Cc phase change rate coefficients
D projectile diameter m ( f )V (Vf )V (f )R R (3)
f vapor mass fraction t e c
L Projectile length m
turbulence kinetic energy m2/s2 The expressions of Re and Rc have been derived from
P fluid static pressure N/m2 the reduced form of the Rayleigh-Plesset equation
psat saturation pressure N/m2 (Hammitt, 1980), which describes the dynamics of
P’turb magnitude of pressure fluctuations N/m2 single bubble in an infinite liquid domain. The
Pt total pressure N/m2 expressions for Re and Rc are:
R universal gas constant Nm/Kg.k
V p p
Re Ce ch v 2 sat
R the rate of phase change (4)
(1 f )
Ren Renold number l 3 l
T fluid temperature K
∆t physical time step second V p p
Rc Cc ch v 2 sat f
(5)
velocity in x, y, w respectively
u,v,w m/s
V velocity vector l 3 l
Vch characteristic velocity Vch =√
W molecular weight kg/kg-mol As we know that cavitation occurs in flow areas
where flow velocity is very high or flow pressure is
Greek letters very low and approach to the water vapour pressure.
vapor volume fraction The magnitude of pressure fluctuations is estimated
cavitation number ((p-pv)/(1/2lu2)) N/m
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EIJEST Vol. 19 No. 2 (2016-Special Issue) 282–296
by using the following empirical correlation (Hinze, projectile is projected horizontally by speed 60 m/s in
1975): water. All present figures are according the projectile
is moved from right to left except figure 21 which
P’turb= 0.39 k (6)
depend on moving the projectile from left to right.
The phase-change threshold pressure value is as:
Also, the projectile dimensions are related to D/L=
0.4. Comparison between two grids is performed.
pv psat 0.5 p ' (7)
Table 1 shows the data of each grid. The table
turb
illustrates the number of cells, number of nodes,
In this model due to low flow pressure, we put the number of zones, and the time consumed to solve one
dissolved (non condensable) gases in cavitation time-step for each case.
calculations. However, the corresponding density
(and hence volume fraction) varies significantly with
Table 1: Comparison between the two grids in mesh specifications
local pressure. The perfect gas law is used to account for both projectiles.
for the expansion (or compressibility) of gas; i.e.,
Hemisphere projectile Telescopic projectile
WP
gas (8) Structured Unstructured Structured Unstructured
RT Cells 25,043 28,768 28,089 26,222
nodes 25,440 14,615 28,990 13,337
The calculation of mixture density (equation 1) is zones 3 1 6 1
time 0.5 0.1 2.5 2
modified as: (min)
1 f v f g 1 f v f g
(9)
v g The used computer for simulation the present
l
study for both cases is a workstation with
We have the following expression for the volume specifications:
fractions of vapor (v) and gas (g):
Processor: double Intel Xeon CPU E5-2620
v2 @ 2.10 GHz
v f v
(10)
Memory: 16 GB
v
g f g
(11)
The transient cavitation flow analysis is computed
g for cavitation number of 0.0555. Used time-step
and, interval is 1x10-5 sec.
1v g (12)
l 3.1 hemisphere projectile
The combined volume fraction of vapor and gas (i.e.,
v g) is referred to as the Void Fraction (). In Hemisphere projectile is hemispherical projectile
practical applications, for qualitative assessment of on two sides. The structured grid for this projectile is
the extent and location of cavitation, contour maps of used as shown in figure 1a. The structure grids are
void fraction () are important. divided into three zones.
Unstructured grid of the projectile, shown in
Results and Discussion figure 1b, is performed in one zone domain. The
grids are clustered near the body to solve the
In present research, supercavitation around projectile boundary layer. The physical time step is taken to be
is simulated for two different projectile shapes. 1x10-5 second for the unsteady flow computations in
Hemisphere projectile has a hemispherical shape order to resolve accurately the transients of the
from both sides. Telescopic projectile is a telescopic supercavitating flow.
shape at nose and flat shape at tail. Both shapes are
modelled by use two different grid designs, Figures 5 and 6 display the iso-density contours
structured and unstructured. The used grids are for cavitating flow over both grids of hemispherical
structured mesh and unstructured mesh grids. The
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Mansour et al./ A Comparative Study of Supercavitation Phenomena on Different Projectiles Shapes in Transient Flow by CFD
body in a time sequence of the bubble shape. This for cavitating flow over both grids of hemispherical
hemisphere projectile has half spheres from both body in a time sequence of the bubble shape. This
sides at diameter 0.4 L. The cavitation number is hemisphere projectile has half spheres from both
=0.0555 at speed of u= 60 m/s. It is demonstrated sides at diameter 0.4 L. The cavitation number is
that the cavity formation has five stages. First, a =0.0555 at speed of u= 60 m/s. It is demonstrated
cavity starts to grow at the wake of the body only due that the cavity formation has five stages. First, a
to its low pressure. At the second stage, another cavity starts to grow at the wake of the body only due
cavity grows beside the nose while the cavity at the to its low pressure. At the second stage, another
body wake continues to grow. The cavity beside the cavity grows beside the nose while the cavity at the
nose grows enough to affect the pressure at the body body wake continues to grow. The cavity beside the
wake, so, the cavity at the body wake starts to nose grows enough to affect the pressure at the body
collapse at the third stage. In the fourth stage, the wake, so, the cavity at the body wake starts to
cavity beside the nose grows enough to merge with collapse at the third stage. In the fourth stage, the
the cavity at the body wake. Finally, that cavity starts cavity beside the nose grows enough to merge with
to have a fluctuation around the final shape. the cavity at the body wake forming a large one.
Finally, that cavity starts to have a fluctuation around
Figures 13 and 14 represent the distribution of the final shape.
void fraction, total pressure, static pressure and
velocity magnitude. The void fraction contour is Figures 15 and 16 represent the distribution of
approximately similar to the iso-density contours as void fraction, total pressure, pressure and velocity
well as the iso-total pressure contours. There is a magnitude. Also, void fraction contour is
reverse flow in the horizontal velocity component at approximately similar to the iso-density contours as
the cavities region near to the body and in the body well as the iso-total pressure contours. There is a
wake. The maximum vertical velocity component is reverse flow in the horizontal velocity component at
concentrated around the front nose. In this case, the the cavities region near to the body and in the body
maximum turbulence kinetic energy is around the wake. The maximum vertical velocity component is
front nose similar to the iso-pressure contour. concentrated around the front nose. In this case, the
maximum turbulence kinetic energy is around the
Figures show observation which is finding a front nose similar to the iso-pressure contour.
vortex in the nose area by using unstructured grid of
telescopic projectile. This vortex is in agreement with 3.3 blunt projectile
actual (experimental) case of Mostafa et al. (2001).
The results by structured grid did not show this Blunt projectile is flat-nose projectile and flat at
vortex. tail. The structured grid for this projectile is used as
shown in figure 3a. Structured mesh is refined but by
3.2 telescopic projectile
dividing the domain to 3 zones.
Telescopic projectile is telescopic-nose projectile
and flat at tail. The structured grid for this projectile In present case of structured grid blunt projectile is
is used as shown in figure 2a. Structured mesh is used as shown in figure 3a. The structure grids are
refined but by dividing the domain to 3 zones. divided into three zones.
In present case of structured grid telescopic Unstructured grid of the projectile, shown in
projectile is used as shown in figure 2a. The figure 3b, is performed in one zone domain. The
structure grids are divided into three zones. grids are clustered near the body to solve the
Unstructured grid of the projectile, shown in boundary layer. The physical time step is taken to be
figure 2b, is performed in one zone domain. The 1x10-5 second for the unsteady flow computations in
grids are clustered near the body to solve the order to resolve accurately the transients of the
boundary layer. The physical time step is taken to be supercavitating flow.
1x10-5 second for the unsteady flow computations in
order to resolve accurately the transients of the Figures 9 and 10 display the iso-density contours
supercavitating flow. for cavitating flow over both grids of blunt body in a
time sequence of the bubble shape. This hemisphere
Figures 7 and 8 display the iso-density contours projectile has half spheres from both sides at
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EIJEST Vol. 19 No. 2 (2016-Special Issue) 282–296
diameter 0.4 L. The cavitation number is =0.0555 beside the nose while the cavity at the body wake
at speed of u= 60 m/s. It is demonstrated that the continues to grow. The cavity beside the nose grows
cavity formation has five stages. First, a cavity starts enough to affect the pressure at the body wake, so,
to grow at the wake of the body only due to its low the cavity at the body wake starts to collapse at the
pressure. At the second stage, another cavity grows third stage. In the fourth stage, the cavity beside the
beside the nose while the cavity at the body wake nose grows enough to merge with the cavity at the
continues to grow. The cavity beside the nose grows body wake forming a large one. Finally, that cavity
enough to affect the pressure at the body wake, so, starts to have a fluctuation around the final shape.
the cavity at the body wake starts to collapse at the
third stage. In the fourth stage, the cavity beside the Figures 19 and 20 represent the distribution of
nose grows enough to merge with the cavity at the void fraction, total pressure, pressure and velocity
body wake forming a large one. Finally, that cavity magnitude. Also, void fraction contour is
starts to have a fluctuation around the final shape. approximately similar to the iso-density contours as
well as the iso-total pressure contours. There is a
Figures 17 and 18 represent the distribution of reverse flow in the horizontal velocity component at
void fraction, total pressure, pressure and velocity the cavities region near to the body and in the body
magnitude. Also, void fraction contour is wake. The maximum vertical velocity component is
approximately similar to the iso-density contours as concentrated around the front nose. In this case, the
well as the iso-total pressure contours. There is a maximum turbulence kinetic energy is around the
reverse flow in the horizontal velocity component at front nose similar to the iso-pressure contour.
the cavities region near to the body and in the body
3.5 comparisons and observations
wake. The maximum vertical velocity component is
concentrated around the front nose. In this case, the Mostafa et al. (2001) illustrate the formation of
maximum turbulence kinetic energy is around the cavity during supercavitation around a projectile.
front nose similar to the iso-pressure contour. Figure 21 shows their experimental results that
confirmed existence of two types of vortices. First
3.4 conical projectiles
type is at projectile nose. Second one is at projectile
Conical projectile is conical-nose projectile and tail.
flat at tail. The structured grid for this projectile is
used as shown in figure 4a. Structured mesh is Figures show a new note is observed which
refined but by dividing the domain to 3 zones. existence of a vortex in the nose area is by using
unstructured grid of telescopic projectile. This vortex
In present case of structured grid conical projectile is in agreement with actual (experimental) case of
is used as shown in figure 4a. The structure grids are Mostafa et al. (2001) as in figure 21. The results by
divided into three zones. structured grid did not show this vortex.
Unstructured grid of the projectile, shown in 4 Summary and Conclusions
figure 4b, is performed in one zone domain. The
grids are clustered near the body to solve the The unsteady flow around either partially
boundary layer. The physical time step is taken to be cavitating or supercavitating high-speed underwater
1x10-5 second for the unsteady flow computations in vehicles is simulated. Also, the accuracy of results is
order to resolve accurately the transients of the affected by grid design.
supercavitating flow.
Cavity formation five stages goes through First, a
cavity starts to grow at the wake of the body only due
Figures 11 and 12 display the iso-density contours
its low pressure. At the second stage, another cavity
for cavitating flow over both grids of conical body in
grows beside the nose while the cavity at the body
a time sequence of the bubble shape. This conical
wake continues to grow. The cavity beside the nose
projectile has half spheres from both sides at
grows enough to affect the pressure at the body wake,
diameter 0.4 L. The cavitation number is =0.0555
so, the cavity at the body wake starts to collapse at
at speed of u= 60 m/s. It is demonstrated that the
the third stage. In the fourth stage, the cavity beside
cavity formation has five stages. First, a cavity starts
the nose grows enough to merge with the cavity at
to grow at the wake of the body only due to its low
the body wake forming a large one. Finally, that
pressure. At the second stage, another cavity grows
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Mansour et al./ A Comparative Study of Supercavitation Phenomena on Different Projectiles Shapes in Transient Flow by CFD
cavity starts to fluctuate around the final shape. results by structured grid did not show this vortex.
Using unstructured grid is better than structured
There is a reverse flow in the horizontal velocity
one for water-flow simulation of supercavitation for a
component at the cavities region near to the body and
hemispherical projectile.
in the body wake. The maximum vertical velocity
component is concentrated around the front nose. Using ESI-CFD commercial code is valid for
simulating supercavitation around projectiles in
New note is observed which is finding a vortex in
water.
the nose area by using unstructured grid of telescopic
projectile. This vortex is in agreement with actual
(experimental) case of Mostafa et al. (2001). The
a) structured mesh b) unstructured mesh
Fig. (1) Grid over hemisphere projectile.
a) structured mesh b) unstructured mesh
Fig. (2) Grid over telescopic projectile.
a) structured mesh b) unstructured mesh
Fig. (3) Grid over blunt projectile.
a) structured mesh b) unstructured mesh
Fig. (4) Grid over conical projectile.
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EIJEST Vol. 19 No. 2 (2016-Special Issue) 282–296
a) Density distribution at t=50x10-5 sec a) Density distribution at t=50x10-5 sec
b) Density distribution at t=100x10-5 sec b) Density distribution at t=100x10-5 sec
c) Density distribution at t=300x10-5 sec c) Density distribution at t=300x10-5 sec
d) Density distribution at t=500x10-5 sec d) Density distribution at t=500x10-5 sec
e) Density distribution at t=800x10-5 sec e) Density distribution at t=800x10-5 sec
f) Density distribution at t=1000x10-5 sec f) Density distribution at t=1000x10-5 sec
g) Density distribution at t=1100x10-5 sec g) Density distribution at t=1100x10-5 sec
h) Density distribution at t=1200x10-5 sec h) Density distribution at t=1200x10-5 sec
i) Density distribution at t=1400x10-5 sec i) Density distribution at t=1400x10-5 sec
Fig. (5) Supercavitating cavities formation upon Fig. (6) Supercavitating cavities formation upon
hemisphere projectile at speed 60 m/s, using hemisphere projectile at speed 60 m/s, using
structured mesh domain. unstructured mesh domain.
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Mansour et al./ A Comparative Study of Supercavitation Phenomena on Different Projectiles Shapes in Transient Flow by CFD
a) Density distribution at t=50x10-5 sec a) Density distribution at t=50x10-5 sec
b) Density distribution at t=200x10-5 sec b) Density distribution at t=100x10-5 sec
c) Density distribution at t=300x10-5 sec c) Density distribution at t=300x10-5 sec
d) Density distribution at t=400x10-5 sec d) Density distribution at t=500x10-5 sec
e) Density distribution at t=500x10-5 sec e) Density distribution at t=800x10-5 sec
f) Density distribution at t=1000x10-5 sec f) Density distribution at t=1000x10-5 sec
g) Density distribution at t=1100x10-5 sec g) Density distribution at t=1100x10-5 sec
h) Density distribution at t=1200x10-5 sec h) Density distribution at t=1200x10-5 sec
i) Density distribution at t=1400x10-5 sec i) Density distribution at t=1400x10-5 sec
Fig. (7) Supercavitating cavities formation upon Fig. (8) Supercavitating cavities formation upon
telescopic projectile at speed 60 m/s, using telescopic projectile at speed 60 m/s, using
structured mesh domain. unstructured mesh domain.
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EIJEST Vol. 19 No. 2 (2016-Special Issue) 282–296
a) Density distribution at t=1x10-5 sec a) Density distribution at t=1x10-5 sec
b) Density distribution at t=50x10-5 sec b) Density distribution at t=50x10-5 sec
c) Density distribution at t=100x10-5 sec c) Density distribution at t=100x10-5 sec
d) Density distribution at t=300x10-5 sec d) Density distribution at t=300x10-5 sec
e) Density distribution at t=500x10-5 sec e) Density distribution at t=500x10-5 sec
f) Density distribution at t=800x10-5 sec f) Density distribution at t=800x10-5 sec
g) Density distribution at t=1000x10-5 sec g) Density distribution at t=1000x10-5 sec
h) Density distribution at t=1100x10-5 sec h) Density distribution at t=1100x10-5 sec
i) Density distribution at t=1200x10-5 sec i) Density distribution at t=1200x10-5 sec
j) Density distribution at t=1400x10-5 sec j) Density distribution at t=1400x10-5 sec
Fig. (9) Supercavitating cavities formation upon Fig. (10) Supercavitating cavities formation upon
blunt projectile at speed 60 m/s, using structured blunt projectile at speed 60 m/s, using
mesh domain. unstructured mesh domain.
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Mansour et al./ A Comparative Study of Supercavitation Phenomena on Different Projectiles Shapes in Transient Flow by CFD
a) Density distribution at t=1x10-5 sec a) Density distribution at t=1x10-5 sec
b) Density distribution at t=50x10-5 sec b) Density distribution at t=50x10-5 sec
c) Density distribution at t=100x10-5 sec c) Density distribution at t=100x10-5 sec
d) Density distribution at t=300x10-5 sec d) Density distribution at t=300x10-5 sec
e) Density distribution at t=500x10-5 sec e) Density distribution at t=500x10-5 sec
f) Density distribution at t=800x10-5 sec f) Density distribution at t=800x10-5 sec
g) Density distribution at t=1000x10-5 sec g) Density distribution at t=1000x10-5 sec
h) Density distribution at t=1100x10-5 sec h) Density distribution at t=1100x10-5 sec
i) Density distribution at t=1200x10-5 sec i) Density distribution at t=1200x10-5 sec
j) Density distribution at t=1400x10-5 sec j) Density distribution at t=1400x10-5 sec
Fig. (11) Supercavitating cavities formation upon Fig. (12) Supercavitating cavities formation upon
conical projectile at speed 60 m/s, using structured conical projectile at speed 60 m/s, using
mesh domain. unstructured mesh domain.
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EIJEST Vol. 19 No. 2 (2016-Special Issue) 282–296
a) velocity distribution a) velocity distribution
b) Static-pressure distribution b) Static-pressure distribution
c) Total-pressure distribution c) Total-pressure distribution
d) void-fraction distribution d) void-fraction distribution
e) Total-void fraction distribution e) Total-void fraction distribution
Fig. (13) Flow condition around hemisphere Fig. (14) Flow condition around hemisphere
projectile using structured grid at projectile using unstructured grid at
supercavitating condition: =0.0555, u= 60 supercavitating condition: =0.0555, u= 60 m/s,
m/s, Ren=306 x106, and t= 0.014 sec. Ren=306 x106, and t= 0.014 sec.
a) velocity distribution a) velocity distribution
b) Static-pressure distribution b) Static-pressure distribution
c) Total-pressure distribution c) Total-pressure distribution
d) void-fraction distribution d) void-fraction distribution
e) Total-void fraction distribution e) Total-void fraction distribution
Fig. (15) Flow condition around telescopic Fig. (16) Flow condition around telescopic
projectile using structured grid at projectile using unstructured grid at
supercavitating condition: =0.0555, u= 60 m/s, supercavitating condition: =0.0555, u= 60 m/s,
Ren=306 x106, and t= 0.014 sec. Ren=306 x106, and t= 0.014 sec.
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Mansour et al./ A Comparative Study of Supercavitation Phenomena on Different Projectiles Shapes in Transient Flow by CFD
a) velocity distribution a) velocity distribution
b) Static-pressure distribution b) Static-pressure distribution
c) Total-pressure distribution c) Total-pressure distribution
d) void-fraction distribution d) void-fraction distribution
e) Total-void fraction distribution e) Total-void fraction distribution
Fig. (17) Flow condition around blunt projectile Fig. (18) Flow condition around blunt projectile
using structured grid at supercavitating condition: using unstructured grid at supercavitating
=0.0555, u= 60 m/s, Ren=306 x106, and t= 0.014 condition: =0.0555, u= 60 m/s, Ren=306 x106,
sec. and t= 0.014 sec.
a) velocity distribution a) velocity distribution
b) Static-pressure distribution b) Static-pressure distribution
c) Total-pressure distribution c) Total-pressure distribution
d) void-fraction distribution d) void-fraction distribution
e) Total-void fraction distribution e) Total-void fraction distribution
Fig. (19) Flow condition around conical projectile Fig. (20) Flow condition around conical projectile
using structured grid at supercavitating condition: using unstructured grid at supercavitating
=0.0555, u= 60 m/s, Ren=306 x106, and t= 0.014 condition: =0.0555, u= 60 m/s, Ren=306 x106,
sec. and t= 0.014 sec.
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EIJEST Vol. 19 No. 2 (2016-Special Issue) 282–296
Fig. (21) Formation of cavitating vortex ring,( Mostafa et al. 2001).
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Mansour et al./ A Comparative Study of Supercavitation Phenomena on Different Projectiles Shapes in Transient Flow by CFD
a) Structured Grid
b) Unstructured Grid
Figure (22) velocity vectors for hemispherical projectile using structured grid at supercavitating
condition: =0.0555, u= 60 m/s, Ren=306 x106, and t= 0.014 sec.
a) Structured Grid
b) Unstructured Grid
Figure (23) velocity vectors for telescopic projectile using structured grid at supercavitating
condition: =0.0555, u= 60 m/s, Ren=306 x106, and t= 0.014 sec.
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EIJEST Vol. 19 No. 2 (2016-Special Issue) 282–296
a) Structured Grid
.
b) Unstructured Grid
Figure (24) velocity vectors for blunt projectile using structured grid at supercavitating condition:
=0.0555, u= 60 m/s, Ren=306 x106, and t= 0.014 sec.
a) Structured Grid
b) Unstructured Grid
Figure (25) velocity vectors for conical projectile using structured grid at supercavitating condition:
=0.0555, u= 60 m/s, Ren=306 x106, and t= 0.014 sec.
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