Consider a one-dimensional duct with a length of 200 m which initially contains stationary air. At one end of the duct (
Posted: Tue Jun 07, 2022 2:24 pm
Consider a one-dimensional duct with a length of 200 m which
initially contains stationary air. At one end of the duct (x = 0)
there is a piston which suddenly starts moving at a speed of up
m/s. This will lead to a shock wave which would move toward the
other end of the duct (x = 200 m) Assuming that the end of the duct
at x = 200 m is closed. Plot pressure on the surface of the piston
vs. time until the piston reaches x = 199 m for a) up = 150 m/s, b)
up = 1 m/s. Take initial pressure and temperature to be 1 atm and
300 K, respectively.
Consider the duct configuration given in the first problem. This
time the the end of the duct at x = 200 m is open to atmosphere
where atmospheric pressure and temperature are 1 atm and 300 K,
respectively. How long would it take the reflected head expansion
wave to reach the piston. At that time what wold be the positions
of the had wave (also the piston) and tail wave. Plot the variation
of pressure and temperature across the expansion wave at the time
the reflected head expansion wave to reach the piston. Take up =
150 m/s. Note that, the formulation given in the class for moving
expansion waves were derived for the case where the flow speed
upstream of the head wave was zero. In this case, the flow speed
upstream of reflected the head wave will not be zero. Therefore,
the formulations need to be updated accordingly.
initially contains stationary air. At one end of the duct (x = 0)
there is a piston which suddenly starts moving at a speed of up
m/s. This will lead to a shock wave which would move toward the
other end of the duct (x = 200 m) Assuming that the end of the duct
at x = 200 m is closed. Plot pressure on the surface of the piston
vs. time until the piston reaches x = 199 m for a) up = 150 m/s, b)
up = 1 m/s. Take initial pressure and temperature to be 1 atm and
300 K, respectively.
Consider the duct configuration given in the first problem. This
time the the end of the duct at x = 200 m is open to atmosphere
where atmospheric pressure and temperature are 1 atm and 300 K,
respectively. How long would it take the reflected head expansion
wave to reach the piston. At that time what wold be the positions
of the had wave (also the piston) and tail wave. Plot the variation
of pressure and temperature across the expansion wave at the time
the reflected head expansion wave to reach the piston. Take up =
150 m/s. Note that, the formulation given in the class for moving
expansion waves were derived for the case where the flow speed
upstream of the head wave was zero. In this case, the flow speed
upstream of reflected the head wave will not be zero. Therefore,
the formulations need to be updated accordingly.