Secondary Diaphragm Thickness Effects and Improved Pressure Measurements in an Expansion Tube

T HE aim of this Technical Note is to present practical considerations for measuring pressure in an expansion-tube flow facility; some aspects of this work can be applied to pressure measurement strategies in other impulse (e.g., reflected shock tunnel) or continuous flow facilities that may suffer from similar issues. We assume that the reader is familiar with the terminology and general operating principles regarding expansion tubes; formore information regarding expansion tubes, please refer to the seminal work of Trimpi [1]. In many studies relevant to aerospace engineering, propulsion, and fluid mechanics, pressure measurement is often a diagnostic of primary interest [2–7], but obtaining high-quality (i.e., high signalto-noise, or SNR) pressure measurements can be a challenge in expansion-tube facilities (or other impulse facilities). Because of the short test times in impulse facilities, high-bandwidth pressure transducers are necessary to capture transients of interest, but as we show in this work, certain transducer architectures are more susceptible to noise than others. Analog or digital signal processing can be used to filter some noise from the measurements, but at the expense of measurement bandwidth or accuracy; thus, the engineer must compromise between bandwidth and SNR to acquire reliable pressure measurements. Practical information regarding the acquisition of optimal (i.e., high SNR) pressure measurements in impulse facilities is sparse; however, some articles do provide useful details of implementation, for example Dufrene et al. [8] present specifics of pressure instrumentation in an expansion-tube facility, and Beresh et al. [9] report on the response characteristics of a variety of pressure transducers. Expansion-tube facilities also produce a contaminated freestream flow due to the presence of the secondary diaphragm; the primary shock wave may reflect off the secondary diaphragm [10], and secondary diaphragm fragments of a broad range of sizes are entrained in the test gas [11]. We have found that diaphragm fragments impacting the structure in which pressure transducers are mounted can have a significant, adverse effect on pressure measurement quality. An example of this effect is presented in Fig. 1, which shows a pressure time history alongwith a schlieren image taken at the instant in time when a diaphragm fragment impacts the model that houses the pressure transducers. The shadowed shape in the schlieren image is a flat platewith a pitot-pressure transducer (PCB113A26)mounted above the plate in a conical housing; directly below the pitot opening, a wall-mounted transducer (PCB 112A22) simultaneously measures the wall static pressure. (We will interpret these pressure traces in Sec. III.A, but for now, we only demonstrate the level of noise in the two traces.) The displayed still schlieren image is taken from a high-speed schlieren video that captures the full event during a test. A diaphragm fragment can be seen impacting the top of the model, at which time both pressure traces become extremely noisy. We have also observed the spontaneous eruption of noise in pressure time histories in many other tests, and generally, the time at which the pressure traces become noisy varies from shot to shot, and the onset of noise never occurs before the arrival of the test gas. These introductory observations suggest that diaphragm fragments impacting the model are a major source of noise in these pressure measurements. To test the hypothesis that diaphragm fragment impacts are a source of noise in pressure measurements, we make pressure measurements as a function of secondary diaphragm thickness, expecting thinner diaphragms (and less massive fragments) to cause less noise. Two types of pressure transducers are also tested, two different piezoelectric sensors and two different piezoresistive sensors, and the noise characteristics of each sensor are compared. As a secondary objective, we also test whether the secondary diaphragm thickness affects test-gas conditions as inferred from shock speed measurements. Last, a practical solution for minimizing noise in piezoelectric transducers is provided.