Interface Loss in the Small Amplitude Orifice Pulse Tube Model

  • Luc Bauwens
Part of the Advances in Cryogenic Engineering book series (ACRE, volume 43)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A

cross-section

enthalpy flux

L

length of the tube

R

tube radius

entropy flux

T

temperature, dimensionless

X

rescaled coordinate

a

speed of sound at Tref

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., = ΔLCP/L

γ

ratio of specific heats, = cp/cv

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, ε2.etc.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Luc Bauwens
    • 1
  1. 1.Department of Mechanical EngineeringThe University of CalgaryCalgaryCanada

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