ICEC 26
Acoustic field modulation in a regenerator
J. Y. Hu, W. Wang, E. C. Luo, Y. Y. Chen
Technical Institute of Physics and Chemistry, CAS, Beijing 100190
Presenter：J. Y. Hu
International Cryogenic Engineering Conference
March 7-11, 2016, New Delhi, India
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions
Importance of acoustic field
Energy conversion efficiency and capacity are significantly
influenced by the acoustic field
2.5
Theoretical results need to be
verified by experiments
2.0
.
.
S loss /Sc
With some special acoustic
field, how parameters influence
the performance needs further
to be studied
Th = 300 K
T c = 80 K
P 0 = 2.0 MPa
P r = 1.40
f
= 45 Hz
Vrg /Ve = 5.7
1.5
OPTR
1.0
.
Sre g
.
Sc
.
Stot
.
Sc
.
SP
.
Sc
DIPTR
BPTR
Stirling
0.5
Much effort has been paid to
the modulation in regenerators
and channels
0
-60
-40
-20
0
20
40
.
PHASE ANGLE, m c- P, (degrees)
60
Icc7c.cdr
Methods of acoustic field modulation
Method 1: needs long resonators,
low power density
Method 2: generator parameters
need to be adjusted to match
flow field imaging equipment
different impedance
Method 3: Needs flow field
imaging equipment to measure
the velocity
Other methods: acoustic field modulation is very limited
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions
Inspiration
Question: Can we use two compressors to modulate?
Compresor1
Compressor2
The work from the regenerator
will conflict with that from C2
Compresor1
Compressor2
RC load
Double acting compressor is not easy to produce
New method of modulation
P1
P2
Compresor2
LVDT
LVDT
Compresor1
RC load
P3
It is composed of two linear compressors and a RC load. The work
from the regenerator and C2 is dissipated by the orifice.
By adjusting the pistons’ movement through the currents in the two
compressors, the acoustic field can be modulated
The pressure and volume flow rate can be obtained through some
simple sensors
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions
Relationship between Ucom and Uexp
Compressor 1
Compressor 2
Pcom
Ucom
Pexp
Uexp
Orifice
There is a transmission matrix correlating
the pressures and volume flow rates:
Reservoir
 pexp  T1 T2   pcom 


 U 
T
T
U
 exp   3 4   com 
Then,
Z com 
pcom T2  T4 Z exp

U com T3Z exp  T1
U exp
U com
 T3
T2  T4 Z exp
T3Z exp  T1
 T4
Expression for Ucom and Uexp
Compressor 2
Compressor 1
Pcom
Ucom
Pexp
Uexp
Orifice
For Compressor 1
For Compressor 2
Reservoir
 pcom A1   1 I1  Z mech ,1v1

v1 A1  U com
Then,
U com
 pexp A2   2 I 2  Z mech ,2v2

v2 A2  pexp Z ori  U exp
I1 1 A1

Z com A12  Z mech ,1
U exp 
 2 I 2 A2  Z mech ,2 pexp Z ori
Z exp A22  Z mech ,2
Substitute them into the afore obtained equations, then we have:
Relationship between I1 and I2
I 2 2 A2  Z mech ,2 pexp Z ori
Z exp A  Z mech ,2
2
2

 T2  T4 Z exp

 T4 
 T3

T3Z exp  T1
2


A2  Z mech ,1
I1 1 A1
T2  T4 Z exp
T3Z exp  T1
For any acoustic field determined by Pexp and Zexp, it can be
satisfied by adjusting the currents
In experiment, the impedances can be easily calculated without
any flow field imaging equipment
Z ori 
pexp
U exp

i pexp Pa
 presVres
Z acou ,2 
pexp
U2

i pexp Pa
 pbackVback
Zexp
1

1 Zori  1 Z acou ,2
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions
Design of the two compressors
Compressor 2
Compressor 1
Pcom
Ucom
Parameters
Diameter and length of regenerator
Diameter and length of pulse tube
transduction coefficient
Mechanical resistance
Electrical resistance
Spring constant
If,
then,
Pexp
Uexp
Value
Ø75 mm×L70 mm
Ø37 mm×L150 mm
80 N/A
50 N·m/s
0.5 Ω
5*104 N/m
Z exp =4.4  107   cos 60  i sin 60

Orifice
Reservoir
pexp  0.25 MPa
Diameter Dopt,1 85.3 mm
Diameter Dopt,2 88.1 mm
Mass Mpis,1
1.608 kg
Mass Mpis,1
Current I1
21*(cos28°+i*sin28°) Current I2
4.857 kg
9.4*(cos62°+i*sin62°)
Current in compressors
28
24
20
16
Phase of current /°
Modulus of currents /A
80
|Pexp|=0.25 MPa
Re(Zori)=4.41*107
In C1
In C2
12
8
70
60
|Pexp|=0.25 MPa
Re(Zori)=4.41*107
In C1
In C2
50
40
30
20
10
30
40
50
60
70
Phase of Zexp /°
80
30
40
50
60
70
Phase of Zexp /°
The modulus of the current doesn’t vary much with the phase,
which is helpful for the compressor design
80
Influence of the phase
0.90
Output acoustic work /W
4000
Efficiency
0.87
0.84
0.81
|Pexp|=0.25 MPa
Re(Zori)=4.41*107
C1
C2
0.78
0.75
0.72
30
40
50
60
Phase of Zexp /°
70
80
|Pexp|=0.25 MPa
Re(Zori)=4.41*107
C1
C2
3500
3000
2500
2000
1500
1000
500
0
30
40
50
60
70
Phase of Zexp /°
The efficiency of C2 drops a little bit fast, but its output acoustic
work is small. The power capacity of C1 should be big enough
80
16
16
14
Output work of C2
with 100 W
with 350 W
with 600 W
12
10
8
6
|Pexp|=0.25 MPa
4
30
40
50
60
70
80
Phase of Zexp /°
C2 can always work with very small
output work because the orifice can
be adjusted.
Modulus of current /A
Modulus of current in C2
Influence of output work
14
12
10
8
Phase of Zori is 30°
Pexp=0.1 Mpa
Pexp=0.25 Mpa
Pexp=0.4 Mpa
6
4
0
50
100
150
200
250
Output acoustic work of C2 /W
The current in C1 cannot be very
small because it doesn’t match with
Zexp when the phase is small
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions
Conclusions
A new method of modulating the acoustic field in a regenerator with
two compressors and RC load is presented
Theoretical analysis shows that any acoustic field can be satisfied by
adjusting the current in the two compressors and the RC load
A practical design case was presented to show the characteristics of this
new method
Thank you