Haug-Warberg TMT4140 (Control volumes)

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Applied thermodynamics TMT4140 Lecture 9 Open
(dynamic) CV Tore Haug-Warberg Department of
Chemical Engineering Spring semester 2007
Haug-Warberg TMT4140 (Control volumes)
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Open (dynamic) system
An open control volume has at least one port that
lets matter flow in and out. The result is a
quite general description of numerous practical
devices. The rocket is one example
Note that a control volume of this type has to be
dynamic unless it has reached a dead state (which
in effect behaves like a static, closed system).
Haug-Warberg TMT4140 (Control volumes)
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Discharging a tank
Energy and mass balance
Tk-v Tut T
Ideal gas
Combine equations
Total differential
Haug-Warberg TMT4140 (Control volumes)
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Filling a tank
Energy and mass balance
Ideal gas
Combine equations
T Tk-v gt Tinn To
Haug-Warberg TMT4140 (Control volumes)
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Filling a tank with Helium
Note asymptote
where
Discharging means expansion (cooling) of the gas,
while filling means compression (heating) of the
gas!
Haug-Warberg TMT4140 (Control volumes)
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Joules experiment
Discharge a small pressurized tank into a larger
evacuated one
Energy balances
Quasi-stationary valve
Haug-Warberg TMT4140 (Control volumes)
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Joules experiment (contd)
Smaller tank gets cold
Bigger tank gets hot
However, the energy is constant
Haug-Warberg TMT4140 (Control volumes)
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Helmholtz resonator
Bypassing stream of air
Uniformity assumption The control volume is
small compared to the wavelength of sound.
Oscillating air piston
Cavity Isentropic compression.
Neck Incompressible gas (piston).
Resonance cavity
Linearization
Haug-Warberg TMT4140 (Control volumes)
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Helmholtz resonator (contd)
Solving the 2nd order differential equation gives
the resonance frequency
Signal-frequency diagram measured for a 100ml
laboratory flask shown to the right
Haug-Warberg TMT4140 (Control volumes)