Transfer function of small convergent–divergent (C–D) nozzles and opposite (D–C) devices filled with thermo-viscous fluid at rest

• An analytical description for the shapes of small acoustic elements is established.
• The shapes are more or less tapered, including zero and infinite slope at its ends.
• Transfer function and input impedance are calculated analytically and numerically.
• Experimental results obtained on prototypes are compared to the theoretical ones.
• The role the shapes play in an association of such small elements is emphasized.

An analytical representation, which involves single integrals, is established for describing the shape of small acoustic elements (slits or tubes) more or less tapered (the shape being governed by only one parameter). This representation includes the ability to create a zero slope (horizontal) at one end and an infinite one (vertical) at the other end, the limiting shapes being small cylindrical tubes or cavities. Then, the results obtained from the analytic procedure presented in a previous paper (Honzík et al., 2013), whereby one expresses the transfer function of such elements filled with a thermo-viscous fluid and, beyond, the transfer function of components obtained when connecting them continuously, are presented and compared to numerical and experimental results. Two prototype components gradually narrowing and widening, and conversely, are considered, namely a convergent–divergent nozzle which makes a symmetric hourglass-shape and the opposite divergent–convergent device, with different loads that end the device. The results show the potentialities of such small components when used in acoustic devices.

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