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Shock waves produced by Reddy TubeTRANSCRIPT
Studies on Shock Waves Produced by Reddy Tube
ABSTRACT
Shock tubes are usually used to produce shockwaves in the laboratory.
Reddy tube is a hand operated device capable of producing shockwaves exceeding
Mach number 1.5. The shockwaves generated by Reddy tube have many scientific
application. Since this shock tube is hand operated, these waves are of low
strength. In order to increase the strength of the shock waves it is necessary to
focus the shock waves.
In this project we study the shock waves and increase their intensity by
focusing with mechanical lenses. Computational Fluid Dynamics will be used to
arrive at optimum configurations for focusing shock waves and the best
configuration will then be experimentally tested.
INTRODUCTION
FLOW REGIMES AND SHOCK WAVES
The ratio of velocity of a flow in still air to that of the local speed of sound in
that medium gives rise to one of the most important dimensionless quantities in
the field of aero dynamics. This ratio is called the Mach number, generally denoted
by M, named after noted physicist Ernst Mach.
M=u/a
Where,
M is the Mach number,
u is the velocity of flow,
a is the speed of sound in the medium.
If the Mach number is less than 0.8, it is known as subsonic flow.
If the Mach number is between 0.8 and 1.2, it is known as transonic flow.
If the Mach number is greater than 1.2, it is known as supersonic flow.
If the Mach number is greater than 5, it is known as hypersonic flow.
Shock waves are mechanical waves of finite amplitudes and arise when
matter is subjected to rapid compression. These are produced by sudden release
of energy (like in explosions or volcanic eruptions) by bodies moving at supersonic
speeds or by impact of high speed projectiles or by laser ablations. Like an ordinary
wave, a shock wave carries energy and can propagate through a medium. It is
characterized by abrupt change in pressure, temperature and density of medium.
A shock tube is a simple device that is used to generate a shock wave in a
controlled environment. It basically consists of two long tubes separated by a solid
metal diaphragm. On one side of this diaphragm, a gas is filled to a pressure high
enough to rupture the metal diaphragm and the pressure in the other tube is
reduced to a value lower than the atmospheric pressure. The former side is
termed as the driver side and the latter side termed as the driven side.
EXPERIMENTAL SETUP
Fig 01: a. Schematic diagram of the 29mm diameter Reddy tube indicating the locations of pressure
sensors. b. Photograph of fully assembled, modified Reddy tube with pressure gauges mounted for
measuring the shock speed and the diaphragm rupture pressure.
The Reddy tube consists of a 29mm inner diameter stainless steel shock
tube divided into a 490mm long driver tube and 500mm long driven tube
separated by a 0.1mm thick aluminum diaphragm. A long driver tube ensures late
arrival of the expansion fan, which enables achieving a test time longer than 500
micro seconds.
The diaphragm rupture pressure in the driver section is generated manually
by pushing a 29mm diameter piston. This rupture pressure is monitored using a
digital pressure gauge mounted close to the diaphragm station. The speed of the
shock wave inside the driven tube and the pressure jump between the primary and
reflected shock waves are measured using two piezoelectric pressure gauges.
The shock waves are passed through either an aluminum mirror or through
struts which are placed at the end of the driven section of the shock tube. At the
converging point, the pressure is measured using a set of piezoelectric transducers.
VISUALIZATION
Fig 02: Schematic of the experimental arrangement for the schlieren visualization of flow field.
Shock waves are characterized by a considerable change of density of the
fluid as it crosses the features. A method of flow visualization known as schlieren is
adopted to be used in conditions characterized by density gradients. The word
‘schliere’ means ‘streak’ in German.
The experimental setup uses a concave mirror to render parallel light from a
point source by keeping the point source at the focal length of the mirror. This
parallel light is refocused to a point using a similar concave mirror, where the
image is captured using a high speed camera. A sharp blockage, termed as the
knife edge, is kept at this focal point so that it cuts about half the intensity of the
light forming the image.
FOCUSING OF SHOCK WAVES
The Reddy tube is an easy and safe way to produce shock waves. From
previous literatures of K P J Reddy, the intensities of shock wave produced by hand
operated shock tubes are low. It is possible to increase this intensity by focusing
the shock waves using aluminum mirrors or struts [1]. In this project we propose to
enhance the strength of shock wave produced by the Reddy tube. Schlieren and
pressure probes are used to measure the shock waves.
The first study on focusing of shock waves was done by Guderley in 1942 [2].
Later, Perry and Kantrowitz conducted experiments in order to study the
convergence of cylindrical shock waves by using a tear drop shock tube [3].
Fig 03: Schematic representation of a Tear Drop Shock Tube for focusing a shock wave.
Sturtevant and Kulkarny, in 1976, used a parabolic reflector to study the
complex behavior of shock waves in a focal region. In this intensive experimental
study, shock waves were bought to a focal region by reflecting a plane shock wave
from the surface of a reflector [4].
Takayama and Watanabe, in 1989, studied the convergence of cylindrical
shock waves in shock tubes with an annular section. One of the most interesting
observations of this study was the formation of square shock waves in the final
stages of convergence process [5].
COMPUTATIONAL FLUID DYNAMICS
Computational Fluid Dynamics (CFD) has emerged as a complementary tool
for studying fluid flows, wherein the governing equations of fluid dynamics are
solved using numerical techniques typically with a computer program. In this study
a commercial code ANSYS‐CFX will be used. The first step in CFD is to generate the
geometry of the flow domain model. Then, the domain is divided into a number
small volumes (called “Mesh”). The initial and boundary conditions are setup and
the governing equations are solved. ANSYS‐CFX uses a coupled multigrid algorithm
for solving the discretized fluid flow equations which are important to get stable
solutions for complex flows such as the ones generated in the shock tube. The CFD
code will first be validated for predicting the flow in the Reddy tube.
Configurations to focus the shock wave will be devised and these
configurations will first be studied using CFD and the best of these configurations
will be experimentally tested in the Reddy tube.
CONCLUSION
The shock waves generated by the Reddy tube will be studied closely and
configurations to intensify the generated shock waves will be analyzed using CFD
simulations, following which they will be experimentally tested.
BIBILOGRAPHY
[1] Reddy K P J ‐ Experiments on shock tube using Reddy tube.
[2] Reddy K P J and Sharath N ‐ Manually Operated Piston‐Driven Shock Tube P.172, Current Science, Vol. 104, No. 2.
[3] Perry R W and Kantrowitz A – 1951 ‐ The Production and Stability of Converging Shock Waves. Pg. 878‐886.
[4] Sturtevant B and Kulkarny V A ‐ The focusing of Shock Waves, Fluid Mech. Pg. 651‐671, 1976.
[5] Takayama K – 1989 – International Workshop on Shock Waves Focusing, Tohoku University Shock Wave Research Center, Sendai.