Experiment 1 - Part 2

Q1: Why is the shock Mach number not directly calculated but taken from a chart?

The shock Mach number depends on the pressure ratio p4/p1 and is not analytically trivial to compute due to nonlinear equations.
Charts or iterative tables are commonly used because they provide accurate values from experimental or numerical solutions. It simplifies the process while maintaining accuracy.

Q2: Why does increasing diaphragm thickness result in higher shock speed?

A thicker diaphragm requires higher pressure to rupture, so the pressure ratio p4/p1​​ at the moment of burst is greater.
According to shock tube theory, higher pressure ratio → higher shock Mach number → faster shock wave. This is confirmed in our data:

• 0.05 mm foil shows shorter Δt, meaning higher speed (506.2 m/s) than 0.03 mm cases.

Q3: Why does Channel 2 show no signal in all configurations?

Possible reasons include:

• Faulty or disconnected sensor or cable.

• Poor sensitivity or gain settings on that channel.

• It could also be a deliberate blank (e.g., non-functional port) for validation.

• Since all 3 test cases show this, it's likely instrumentation-related, not flow-related.

Q4: Why is Channel 4’s amplitude higher than Channel 1, even though it’s farther from the rupture point?

Likely due to constructive wave interference or reflection effects:

• In half-open setups, reflections from the closed end superimpose with the incoming wave.

• Channel 4 is located near that closed end → pressure wave reflections amplify the local signal.

• Additionally, some sensor-specific gain/sensitivity could also play a role.

Q5: What does the damping rate of the waveforms tell you about the system?

A slow damping (especially in fully open cases) suggests:

• Low energy loss → fewer reflections or smoother boundaries.

• Low internal resistance in the pneumatic cavity.

• If damping were fast, it might indicate friction, leakages, or energy absorbed by cavity walls.

The 0.05 mm test shows symmetric waves with high amplitude and slow decay, indicating a clean, high-energy shock.

Q6: Why does the measured peak pressure (~170 kPa) differ from the theoretical (~150 kPa)?

Several real-world effects can explain this ~13% difference:

• Non-ideal rupture behavior (membrane doesn’t burst instantaneously).

• Friction or turbulence in the tube slows the shock less than expected.

• Sensor delay or overshoot, especially with pneumatic cavities.

• Calibration limits (errors in voltage-to-pressure conversion).
  Still, this deviation is within the accepted range for shock tube experiments (±10–20%).

Q7: What advantages does a fully open tube offer over a half-open one in shock tube calibration?

Fully open tubes:

• Minimize wave reflection, giving cleaner, one-way shock profiles.

• Produce symmetric waveforms better suited for dynamic calibration.

• Improve frequency analysis (e.g., FFT), since reflections don’t interfere with the signal.
  In contrast, half-open tubes show interference and bouncing waves, which are more complex to interpret.

Q8: How did you calculate shock speed and why is Channel 1–4 used?

Speed is calculated from:

v=Δx/Δt

where Δx=4 m between Channel 1 and 4.

These are used because:

• Channel 1 sees the shock first → best reference point.

• Channel 4 is far enough to give a clear time difference.

• Other channels (like Ch. 5) may have cavity delay or weaker signal.

Q9: Why might Channel 5 be less suitable for theoretical comparison?

Because Channel 5 is connected to the probe with a small pneumatic cavity:

• Cavity adds a low-pass filtering effect → delays response and reduces amplitude.

• The signal includes sensor and cavity dynamics, not just raw shock impact.

• Therefore, it's ideal for dynamic analysis, but not for clean shock speed or pressure comparisons.

Q10: What causes the oscillations after the shock front in the plots (Figures 3.2–3.4)?

These are due to:

• Natural frequencies of the sensor membrane and cavity (resonance).

• Reflected waves in the tube (especially in half-open setup).

• Sensor or signal conditioning system might also have electronic ringing.
  The symmetry and frequency content of these oscillations help in FFT analysis and transfer function estimation.