Acquisition procedure and data reduction

Steady state operating fbw conditions were set up by adjusting the inlet to­tal pressure, inlet total temperature, and outlet static pressure. Both stagnation pressure and temperature were measured in the settling chamber using a total pressure probe and a T-type thermocouple which gave an accuracy of ±0.7K on the temperature reading. The outlet static pressure was measured using a pressure tap located on the upper and side walls at x=290mm. Unsteady op­erating flow conditions were thereafter estimated by measuring the change in back pressure between the extreme positions (vertical and horizontal) of the downstream rod and then setting the averaged value order to match the steady state operating point. The experimental operating conditions are summarized in table 1.

Once the operating conditions were set up, the acquisition procedure for unsteady pressure measurements basically consisted in sliding the 2D bump throughout the width of the channel and record the transducer output voltage together with TTL reference signal for each of the operating conditions sum­marized in table 1. Schlieren visualizations were performed at the very same operating conditions. As the resolution of the CCD camera decreases with the frame rate, a translation device was used in order to focus the image onto the region of interest in the test section. As a result, shock motion were recorded throughout the whole channel’s height.

The data reduction for unsteady pressure measurements consisted of, first, converting the output voltages from the transducers into pressure signals using the coefficients obtained during the static calibration. An ensemble average (EA) of the time-serie data was then performed for each channel using the ref­erence TTL signal from the motor. The obtained single unsteady cycle hence represents an average of all unsteady cycles. Thereafter, a Discrete Fourier Serie Decomposition (DFSD) was performed on the EA signal computed pre­viously and the amplitude and phase angle of the few first harmonics were evaluated. Additionally, a Fast Fourier Transform (FFT) was performed on the entire time fhctuating signal to evaluate all frequency components. At this point, the transfer function (TF) throughout each capillarity tube was evaluated depending on the respective amplitude of the fundamental and finally, both the DFSD components (amplitude and phase of all harmonics) as well as the FFT signal (amplitude only) were corrected using the damping and phase lag values evaluated at the corresponding frequency.

The data reduction procedure for high speed Schlieren visualizations con­sisted in extracting the instantaneous shock position at different location of the channel’s height, perform an EA to obtain a single unsteady cycle and conduct an harmonic analysis on the resulting time-serie signal.

Finally, all data was made dimensionless by dividing the amplitude of each harmonic of the DFSD on pressure by the amplitude of the fundamental at the outlet, and subtracting the phase angle of the outlet pressure signal for each harmonic respectively. As a result, the data issued from harmonic analysis presented in this paper actually corresponds to the pressure amplification and phase lag relative to a reference at the outlet.