Pistonphone - an overview | ScienceDirect Topics (2023)

The electrostatic actuator is a flat metallic electrode positioned at a nominal distance d₁ from the microphone membrane. A voltage applied between the electrode and membrane produces a uniform electrostatic pressure on the membrane. If an ac voltage υ_a is superimposed upon a high dc polarization voltage V_a, then the applied ac voltage and resulting electrostatic pressure have the same frequency. The membrane responds to the electrostatic pressure as it would to a sound pressure. The electrode is slotted to relieve acoustic loading between the electrode and membrane. The electrostatic pressure exciting the membrane is

(14)$\text{p}={\epsilon }_0{\text{V}}_{\text{a}}{\upsilon }_{\text{a}}/{\text{d}}_1^2$

With typical values V_a=800V, υ_a=30V rms, and d₁=0.0005m, the rms pressure is 0.85Pa, or 93 dB. The technique is excellent for obtaining frequency response but is not suitable for absolute calibration because of a twofold uncertainty in the distance d₁. First, the slots in the electrode necessitate a theoretically derived correction and, second, the polarization voltage shifts the equilibrium position of the membrane toward the actuator electrode.

The essential parts of a pistonphone are a coupler, into which the microphone cartridge is inserted and sealed, usually with an O-ring, and a vibrating piston of known displacement. The piston may be driven by a cam having a sinusoidal contour, generating a pure tone, or by a crankshaft, which in addition produces considerable second-harmonic distortion. The frequency is controlled through the speed of the cam or crankshaft. The pressure generated in the coupler is

(15)$\text{p}=\gamma {\text{P}}_0{\text{S}}_{\text{p}}\text{d}/\text{V}$

where S_p is the piston area, d the rms stroke, and V the volume of the coupler (including the equivalent volume of the microphone). With typical values of γ=1.4, P₀=10⁵N/m² (1atm), S_p=10⁻⁵m³, d=1.4×10⁻⁴m, and V=2×10⁻⁵m³, the rms pressure is 9.8Pa, or 114dB. At audio frequencies, a precision of a couple of tenths of a decibel is attainable. At low frequencies a correction is needed for nonadiabatic compression. In the form of a portable, battery-operated device, it is ideally suited for quick calibration of microphones in the field. Two limitations are fixed amplitude and relatively low operating frequency (several hundred hertz maximum). Devices using moving-coil drivers (without servo control) are not true pistonphones, for the generated volume velocity depends on the acoustic impedance of the load.

The reciprocity procedure is based on the following electromechanical principle. When a reversible transducer is operated as a receiver, the ratio of open-circuit output voltage υ to applied acoustic pressure p will equal some constant A. Then, when it is operated as a transmitter, the ratio of the generated volume velocity U to the input current I will equal the same constant A, if the acoustic load Z_r is small (see Fig. 2a.a, b). According to this procedure, three transducers are placed pairwise in an acoustic coupler—a transmitter T, a reversible transducer R, and the test microphone M. In test 1, transmitter T generates a sound pressure P_T to excite receiver R, resulting in an open-circuit voltage υ_R=A_RP_T. In test 2, test microphone M replaces transducer R to yield υ_M=A_MP_T. These lead to the relationship:

(16)${\text{A}}_{\text{M}}={\text{A}}_{\text{R}}{\nu }_{\text{M}}/{\nu }_{\text{R}}$

In test 3, transducer R, as transmitter, excites test microphone M, resulting in υ′_M=A_MP_R. However, the above-stated reciprocity property, U_R=A_RI_R, and the known acoustic impedance of the coupler, Z_C=P_R/U_R, lead to the relationship:

(17)${\text{A}}_{\text{R}}=\frac{{\text{U}}_{\text{R}}}{{\text{I}}_{\text{R}}}=\frac{{\text{P}}_{\text{R}}}{{\text{Z}}_{\text{C}}{\text{I}}_{\text{R}}}=\frac{{\upsilon }_{\text{M}}^{\prime }}{{\text{A}}_{\text{M}}{\text{Z}}_{\text{C}}{\text{I}}_{\text{R}}}$

Substitution of Eq. (17) into (16) yields:

(18)${\text{A}}_{\text{M}}={({\upsilon }_{\text{M}}{\upsilon }_{\text{M}}^{\prime }/{\text{Z}}_{\text{C}}{\upsilon }_{\text{R}}{\text{I}}_{\text{R}})}^{1/2}$

Thus, the microphone sensitivity depends only on electrical quantities, which are measurable to high precision, and a readily determinable acoustic impedance. The reciprocity method, the most precise of all known methods, can achieve absolute precisions of the order of hundredths of a decibel. A free-field variation of the procedure is similar but is beset with practical difficulties.

Experimental studies are conducted on a well-designed T-shaped combustion system to measure the growth rate G ≡ α/ω of combustion-driven oscillations normalized by its frequency. This test rig is a spin-off of classical Rijke-type combustor [18,19]. The schematic of the experimental setup is shown in Fig. 1.29. The bottom stem of the T-combustor is 30cm long and has an inner diameter of 50mm. The bifurcating branches sharing the same inner diameter of 45mm and the same axial length of 50cm. A perforated pipe made of acrylic materials is attached to the T-shaped combustor. To protect the perforated pipe with an axial length of 15cm and inner diameter of 45mm, a centrifugal pump is implemented. It pumps ambient air through the perforated pipe joining the combustion flow and flowing out through the right-hand-side horizontal branch of the T-combustor. The cooling flow rate is in the range of 0–0.1074m³/s. The perforated pipe involves with 112 circle-shaped orifices with a diameter of 3mm. these orifices are distributed equally in space along the pipe surface. Acoustic pressure measurements are conducted by using 2 arrays of B& K 4957 microphones with a sensitivity of 11.2mV/Pa. The microphones are calibrated with B&K Pistonphone (124dB @250Hz, Type 4228). A premixed conical-shaped flame is confined at 13.5cm away from the bottom open inlet.

The measured combustion-driven oscillations from the 4 pressure sensors are shown in Fig. 1.30. It shows the time evolution of the phase diagram/plot between the pressure p′(t) (Pa) and its gradient dp′(t)/dt (Pa/s). The combustion-driven oscillations are limit cycles initially at t≤20s, as revealed by the circle-shaped phase plot. This is known as Rijke-type thermoacoustic phenomena as discussed by Feldman JR [18]. However, as the cooling flow rate is increased to 5.5m/s, the oscillations are attenuated (see 30s≤t≤60s). At t=60s, the cooling flow rate is suddenly reduced to 0m/s. The combustion-driven oscillations quickly grow into limit cycles.

Time evolution of the local peaks/amplitude of the experimentally measured acoustic pressure fluctuations [18,19] is shown in Fig. 1.31. Fig. 1.31A and B illustrates the two sensors measurements on left- and right-hand-side bifurcating branches respectively. The growth rate α is determined by fitting the linear equation (denoted by the dash line). The frequency of the measured acoustic fluctuations is shown in Fig. 1.31C in the pressure spectrum. It is approximately 215Hz. There are harmonic peaks in the spectrum. However, these peaks magnitudes are at least 1 order lower than the dominant peak at 215Hz. With the dominant oscillation frequency determined, the mode-shape as experimentally measured is shown in Fig. 1.31D. The combustion system is a standing-wave one [87,136]. This confirms that the acoustic frequency is intrinsically selected according to the longitudinal resonance nature of the combustor. In practice, such self-sustained limit cycle oscillations [144,157–176] are desirable in thermoacoustic Stirling engines [144] and refridges [148].

Instrumentation microphones designed for scientific work are often the most expensive but can provide well-defined, accurately documented, and stable characteristics. Examples are the 1/2-in. diameter B&K 4190 illustrated in Fig. 10.26A and the 1/4-in. G.R.A.S. 40-PH-S5-1 shown in Fig. 10.26B. Microphones of this type may be provided with documentation of their frequency response when exposed to plane sound waves parallel to the diaphragm, as well as deviations from that response for off-axis sound (e.g., Fig. 10.27). Within its operating range (6.3Hz–20kHz for the B&K 4190) this type of microphone will generally have an almost constant amplitude response to sources ahead of the diaphragm so that in this range only a single value of the microphone sensitivity is needed to make a quantitative sound measurement. Precise measurement of this sensitivity (to account for environmental conditions at the time of a measurement) can be made using a pistonphone. This is a handheld device produces pressure fluctuations of known amplitude by using the mechanical motion of a vibrating piston at a fixed frequency to simulate a sound wave by compressing a fixed volume of air to which the microphone diaphragm is exposed.

The placement and mounting of microphones outside of the test flow involves a number of considerations. It is usually desirable for the microphone to be as close as possible to the source to maximize signal-to-noise ratio. At the same time, keeping the microphone in the acoustic far field (at least one wavelength from the source) is often desirable to simplify the interpretation of the measurement. Also, placing the microphone too close to the free jet or acoustic window can result in contamination by near-field pressure fluctuations associated with the turbulent shear layer. It is usual to orient the microphone to point as directly as possible at the source. This aligns the wavefronts parallel to the diaphragm and makes use of the most favorable microphone response. To exploit the best characteristics of the anechoic chamber, microphones are usually placed at least a quarter wavelength away from the walls, defined by the wedge tips. To avoid unpredictable scattering effects microphones should either use slender mounts and be held from behind or be mounted on a solid surface designed to cleanly reflect the incoming acoustic waves (in which case the measured sound pressure amplitude is doubled because of the addition of the incident and reflected waves). Fig. 10.28 shows single microphones mounted with these considerations in mind in an open-jet wind tunnel. Note that acoustic foam is wrapped around the support beams of the microphone gantry in order to reduce acoustic reflections. Two different mounting strategies for a microphone array are shown in Figs. 10.29 and 10.30. In Fig. 10.29 the microphones are mounted flush in the face of a circular carbon fiber disk designed to reflect the sound, and in Fig. 10.30 the microphones are supported from behind using an open lattice designed to transmit the sound at wavelengths of interest.

It is often of interest to obtain sound measurements at angles that require placing microphones inside the flow. A good example here is rotor testing, where sound radiated on or near the rotor axis is of particular scientific interest. When a microphone is placed directly in the flow its signal will be contaminated with turbulent and sound pressure fluctuations resulting from the interaction of the microphone and its support with the flow. To minimize the contamination an aerodynamic fore-body is used with the microphone, and a streamlined fairing is placed over the supporting strut. The typical microphone fairing shown in Fig. 10.31 is a 1/2-in. diameter B&K model UA 0386 nose cone. This consists of a bullet-shaped housing with a circumferential opening covered by a porous screen. When mounted to the front of a microphone the space interior to the screen forms a cylindrical cavity with one face formed by the microphone diaphragm. Regardless of the orientation of the acoustic source of interest, the microphone is mounted with the nose-cone facing directly into the flow. In this position its streamlined shape minimizes the generation of turbulence, and the screen keeps any flow generated pressure fluctuations separated from the diaphragm. Furthermore, the screen tends to average out turbulent pressure fluctuations that are incoherent around its circumference. The principal drawback of this arrangement is that the nose cone changes the response of the microphone to sound at wavelengths of comparable size. Fig. 10.27 shows the effect of this nose cone on the free-field response of the 1/2-in. B&K 4190 microphone. For sound waves directed roughly at the face of the microphone θ=0degrees and 30degrees the nose cone considerably attenuates the intensity of the sound measured at frequencies above about 15kHz. The forebody actually amplifies sound coming from the side and behind in this frequency range. Obviously, these effects need to be corrected if sound at these frequencies is to be measured accurately. Note that other longer forebody designs can further reduce flow noise contamination [15].

The design of the strut supporting the microphone in the flow is equally critical. Even as a streamlined airfoil, the strut will be an acoustic source that competes with the sound produced by the model under test. Making the strut as quiet as possible, maximizing the distance of the microphone from the strut (by using a long sting support) can be simple and effective measures. (Note that Fig. 10.31 shows a microphone being used to measure relatively intense sound from a rotor system, and thus a short microphone sting was adequate in this case.) Ideally, the airfoil section chosen for the strut needs to be quiet. In particular, it must not generate vortex shedding tones while being thick enough to provide rigid structural support for the microphone. The McMasters-Henderson airfoil [16], a symmetric 28% thick section illustrated in Fig. 10.32, works well in this role [15].