# Bulletin of the American Physical Society

# 76th Annual Meeting of the Division of Fluid Dynamics

## Sunday–Tuesday, November 19–21, 2023; Washington, DC

### Session A13: Compressible Flows: General

8:00 AM–9:31 AM,
Sunday, November 19, 2023

Room: 143C

Chair: Kenneth Granlund, North Carolina State University

### Abstract: A13.00005 : The Piston Problem:sonic and supersonic velocities

8:52 AM–9:05 AM

#### Presenter:

David R Kassoy

(University of Colorado. Boulder (Ret.))

#### Authors:

David R Kassoy

(University of Colorado. Boulder (Ret.))

Adam Norris

(University of Colorado)

The objective of current model is to employ the Euler equations written in terms of the logarithms (

*ln)*of the thermodynamic variables to reveal the physics of the flow induced by a dimensional (') time-dependent piston velocity, u'

_{p}(t')= αa

_{0}f(t') whereα is a non-dimensional parameter and a'

_{0}

_{ }is the speed of sound in the undisturbed gas. The change in fluid particle density, pressure and temperature is caused directly by the spatial derivative of the induced fluid speed, u'

_{x}. The analysis is developed for subsonic, α<>O(1), pistons. The first reproduces the linear Kevorkian and Cole results. The sonic case is described by weakly nonlinear acoustic equations for the induced speed and the thermodynamic variables. The supersonic case utilizes an unusual asymptotic formalism facilitated, for example, by the nondimensional mass conservation equation, D(

*ln*ρ)/Dt=-αu

_{x}where the parameter can be removed from the equation with the non-linear variable transformation for the density, ρ=exp(αR), where R is the rescaled density. Ditto for T and p.

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