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7.5.3 Wave Speed Measurements To test the capabilities of the measurement system, a shock in air is generated. The pressure in the CT is lowered to approximately 0.37 bar, while the LPP is kept at atmospheric pressure. The whole setup is at ambient temperature, equal to ≈ 18 oC. Upon opening of the FOV, a compression propa- gates into the charge tube, eventually forming a shock. The expected location of shock formation is estimated using the knowledge on the opening time of the FOV: with tFOV = 4.5 ms, the intersection of the first and last characteristic is expected to occur at ≈ 5.2 m from the FOV. Since partial shock formation speeds up the wave, it is expected that complete formation requires more length. It can indeed be seen that the shock has not yet formed at pressure transducer PT1 and PT2. The shock seems to have formed when it passes at PT3 and PT4, since the pressure is much steeper compared to the one given by PT1 and PT2. (a) (b) 1.2 1 0.8 0.6 0.4 0 2 4 6 8 10 t [s] 0.8 Figure 7.10: Pressure signals from a compression in air. 7.10: complete compression from below atmospheric up to ambient pressure conditions, the four signals are not distinguishable at this level of detail. 7.10b: detail of the very first compression phase, it is possible to distinguish the four signals, and the shock wave forming (1 − 2) and then bouncing back (3 − 4) in the tube. Since the shock has not formed yet at PT1 and PT2, the compression can be considered a simple compression wave, thus traveling with the speed of the characteristic. By solving the corresponding Riemann problem, values of 341 m s−1 before and 488 m s−1 after the compression are found as propagation speeds. By using the time-of-flight method, very similar values are found experimen- tally, as can be seen in Fig. 7.11. Once the shock has formed, it is expected to travel at a velocity of 422 m s−1, this value being in extremely good agreement with the experimental observation. It is demonstrated that the measurement equipment and the devised procedure are best suited to capture steep pressure variations, i.e. shock waves propagating in the CT, which is also the main objective of the setup. Weaker phenomena, such as those involved in speed of sound measurements, are also sensed in a fairly accurate way, but more sophisticated signal analysis techniques than the simple TOF method adopted here are necessary, as detailed also, e.g., in Ref. [50]. The expected pressure after the compression, as calculated by the exact solution of the Riemann problem, is 0.6 bar, which 1 0.6 PIT1 0.4 Commissioning of the FAST setup PIT3 PIT2 PIT4 P [bar] P [bar] 1234 2.2 2.21 2.22 2.23 2.24 2.25 t [s] 193PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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