Theory of Periodic Shocks and Large Amplitude Gas Oscillations in a Closed Tube
Alfred Saenger, G. Hudson
Jul 1, 1958
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Key Takeaway Key Takeaway: Periodic shocks and large amplitude gas oscillations in a closed tube can be predicted using a theory that considers wall friction and heat exchange, and allows for the presence of shocks.
Abstract
When a piston oscillating with a finite amplitude at one end of a closed tube drives the enclosed gas at a frequency near a natural acoustic frequency of the system, the pressure observed at various positions along the tube shows the presence of a shock wave moving periodically back and forth [G. E. Hudson and A. Saenger, Phys. Rev. 99, 633(A) (1955); G. E. Hudson, J. Acoust. Soc. Am. 28, 154(A) (1956)]. A theory of the gas motion has been developed which includes effects of wall friction and heat exchange, and allows for the presence of shocks. The theory includes a condition in the form of a relation between the driving frequency of the piston motion and its amplitude which specifies when shocks should first appear. An approximate solution of the equations of motion and shock conditions at resonance represents the motion as the sum of a forced continuous motion and a free discontinuous one. Conditions of periodicity and single valuedness applied to this solution and considerations of energy transfer thr...