Page 132 - 48Fundamentals of Compressible Fluid Mechanics

94 CHAPTER 5. NORMAL SHOCK

is accelerated in very rapid way and air adjoint to piston is flowing in Mach number

% . Calculate what is the velocity of the shock created by the piston in the

length. Assume that there is no friction and Fanno flow model is not applicable.
air? Calculate the time the shock it take to reach to the end of the tube of
SOLUTION

5.4 Shock Tube
The Shock tube is a
5 expansion 4 3 2 1
study tool with very lit- front
tle practical purposes
which is used in many Diaphragm
t
cases to understand
certain phenomena. Other
situations can be ex- some where reflective
reflective wave shock
amined and extended wave
from this phenomena.
A cylinder with two
chambers connected by t 1 back Contact Surface
a diaphragm. In one front shock wave
side the pressure is
high while the pres-
sure in the other side
distance
is low. When the di-
aphragm is rupture the Fig. 5.10: The shock tube schematic with pressure ”diagram”
gas from the high pres-
sure is flowing into the low pressure section. When the pressure is high enough
shock is created that is travels to the low pressure chamber. This is the same
case as was study in suddenly open valve described before. In the back of the
shock expansion waves occur with reduction of the pressure. The temperature has
known to reach several thousands for very brief time. The high pressure chamber
referred in the literature as the driver section and the low section is referred as the
expansion section.
Initially the gas from the driver section is coalescing of small shock waves
into a large shock wave. In this analysis, it is assumed that this time is essentially
zero. Zone 1 is undisturbed gas and zone 2 is area where the shock already
passed. Due to the assumption that the shock is very sharp with zero width. On the
other side, the explanation waves are moving into the high pressure chamber i.e.
driver section. The shock is moving in supersonic speed (depend on the definition
i.e what reference temperature is used used) and the medium behind shock is
also moving but in velocity, which can be supersonic or subsonic in stationary
coordinates. The velocities in the expansion chamber are varied between three