Advances in Cryogenic Engineering pp 1933-1940 | Cite as

# Interface Loss in the Small Amplitude Orifice Pulse Tube Model

## Abstract

Linearized analysis of the orifice pulse-tube refrigerator yields simple expressions and key concepts such as the enthalpy flux. However, except for the irreversibility that occurs at the orifice, the linear model is ideal, and it yields the theoretical Kittel coefficient of performance, equal to the temperature ratio. One of the major losses, and one of the least-well understood, that this device shares with Stirling refrigerators, is the interface loss. This loss is due to the abrupt transition between the cold end or freezer, which is an approximately isothermal space, and the tube, in which the flow is approximately isentropic. In the linearized analysis, the loss appears as a second order correction. It is found to be strongly dependent upon the pressure amplitude and of the cosine of the phase angle.

## Keywords

Phase Angle Mass Flow Rate Speed Ofsound Temperature Ratio Pulse Tube## Nomenclature

- A
cross-section

- Ḣ
enthalpy flux

- L
length of the tube

- R
tube radius

- Ṡ
entropy flux

- T
temperature, dimensionless

- X
rescaled coordinate

- a
speed of sound at T

_{ref}- i
\(\sqrt { - 1}\)

- p
pressure

- r
radial coordinate

- s
specific entropy

- t
time

- u
velocity

- x
longitudinal coordinate

- Ω
orifice resistance

- δ
= L/aτ

- ε
small dimensionless No., = ΔL

_{CP}/L- γ
ratio of specific heats, = c

_{p}/c_{v}- μ
dynamic viscosity

- φ
phase angle between u and p

- π
= 3.141596535....

- ρ
density of the cycle fluid

- τ
period

## Subscripts

- CP
compressor (piston)

- F
interface freezer/tube

- O
orifice

- T
reservoir

- 0, 1, 2
term of order 1, ε, ε

^{2}.etc.

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