1. Acoustic field modulation in a regenerator
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
Presenter：J. Y. Hu
International Cryogenic Engineering Conference
March 7-11, 2016, New Delhi, India
Good morning, ladies and gentlemen. I am Hu Jianying. The title of my paper is acoustic field modulation in a regenerator with two compressors. .

2. Acoustic field modulation
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions

3. Importance of acoustic field
Energy conversion efficiency and capacity are significantly influenced by the acoustic field
Theoretical results need to be verified by experiments
With some special acoustic field, how parameters influence the performance needs further to be studied
The energy conversion efficiency and capability of a regenerator are significantly affected by the acoustic field. Based on REGEN3.2, this figure shows the regenerator losses vary with the phase between the flow and the pressure. If the acoustic field is not appropriate, the regenerator will work bad. Although many theoretical studies about the influence have be done, the experimental verification is still not enough. The main difficulty lies in the modulation of the acoustic field.
Much effort has been paid to the modulation in regenerators and channels

4. Methods of acoustic field modulation
Method 1: needs long resonators, low power density
Method 2: generator parameters need to be adjusted to match different impedance
flow field imaging equipment
In the upper figure, two loudspeakers and two resonators are used to modulate the acoustic field. The resonators make system very big. High pressure amplitude can not be realized. In the middle figure, a compressor and alternator are used. The alternator absorbs the acoustic work coming out of the regenerator. For different acoustic field, the electrical resistance, capacity, piston mass in the alternator must be changed, which is very troublesome. We can also use inertance tube to modulate the acoustic field. But we must use some flow field imaging equipment to obtain the volume flow rate, which is very difficult. There are some other methods. The modulation is very limited. In this paper, we will introduce a new method.
Method 3: Needs flow field imaging equipment to measure the velocity
Other methods: acoustic field modulation is very limited

5. Acoustic field modulation
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions

6. Inspiration Question: Can we use two compressors to modulate?
Compresor1
Compressor2
The work from the regenerator will conflict with that from C2
This two figures inspired us to think of a question: Can we use two compressors to modulate the acoustic field. The answer is no. Because the work coming out of the regenerator will conflict with that from the right compressor. No one can dissipate or absorb the work. This is also the reason that an alternator is used in this figure. So we thought of using a RC load to dissipated the work after the double acting piston. It may work. But it is not convenient to produce a double acting compressor. Then, we thought of moving the RC load to the expansion chamber.
Compresor1
Compressor2
RC load
Double acting compressor is not easy to produce

7. New method of modulationP1 P2
Compresor1
Compresor2
LVDT
LVDT
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.
This is the final configuration for this new method. It is composed of two compressors and a RC load. The work from the regenerator and the compressor is dissipated by the orifice. By adjusting the pistons’ movement through the currents in the compressors, the acoustic field can be modulated. The pressure and volume flow rate can be obtained through some simple sensors.
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

8. Acoustic field modulation
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions

9. Relationship between Ucom and Uexp
Compressor 1
Compressor 2
Orifice
Reservoir
Pcom
Ucom
Pexp
Uexp
There is a transmission matrix correlating the pressures and volume flow rates:
For a regenerator, there is a transmission matrix correlating the pressures and volume flow rates at its two ends. From the matrix, we can obtain the expression for impedance Zcom and the relationship for the two volume flow rates. They are all functions of Zexp.
Then,

10. Expression for Ucom and Uexp
Compressor 1
Compressor 2
Orifice
Reservoir
Pcom
Ucom
Pexp
Uexp
For Compressor 1
For Compressor 2
For the two compressors, there are two force balance equations. Then we can obtain the expression for the two volume flow rates. Substitute them into the afore obtained equations, then we have this equation
Then,
Substitute them into the afore obtained equations, then we have:

11. Relationship between I1 and I2
For any acoustic field determined by Pexp and Zexp, it can be satisfied by adjusting the currents
This equation correlates the relationship between the currents in the two compressors. It is function of Pexp and Zexp . For any acoustic field which 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.
In experiment, the impedances can be easily calculated without any flow field imaging equipment

12. Acoustic field modulation
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions
Here ,we will present a design case to demonstrate the feasibility of this method.

13. Design of the two compressors
Orifice
Reservoir
Pcom
Ucom
Pexp
Uexp
Parameters
Value
Diameter and length of regenerator
Ø75 mm×L70 mm
Diameter and length of pulse tube
Ø37 mm×L150 mm
transduction coefficient
80 N/A
Mechanical resistance
50 N·m/s
Electrical resistance
0.5 Ω
Spring constant
5*104 N/m
This table presents the main parameters of a pulse tube cryocooler. If the Zexp is this and the pressure in the expansion chamber is 0.25 Mpa, according to some design principle, we can obtain the optimal piston diameter and resonant piston mass. Then the currents in the two compressors can be obtained.
If,
Diameter Dopt,1
85.3 mm
Diameter Dopt,2
88.1 mm
Mass Mpis,1
1.608 kg
4.857 kg
Current I1
21*(cos28°+i*sin28°)
Current I2
9.4*(cos62°+i*sin62°)
then,

14. Current in compressors
These two figures show the influence of the phase on the currents in the two compressors. The modulus of the currents do no vary much with the phase, which is very helpful for the designing of the compressors. If the currents increase too much, the wire diameter of the coils should be especially enlarged.
The modulus of the current doesn’t vary much with the phase, which is helpful for the compressor design

15. Influence of the phase
In this figure, we can see that the efficiency of C1 varies little. The efficiency of C2 drops a little bit fast, but its output acoustic work is small. The output acoustic work of C1 is much more if the phase is small. If higher pressure amplitude is wanted, C1 will output more acoustic work. So the power capacity of C1 should be big enough.
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

16. Influence of output work
Meanwhile, we can see that in this figure, it is always possible for C2 to work with relative small output work because the resistance of the orifice can be adjusted in the experiment. In the right figure, the phase of Zexp is set as 30°。We can see that the current varies little with the acoustic work when the pressure amplitude is relative big. So the current capacity of C2 should be big enough if the pressure amplitude will varies in a wide range.
C2 can always work with very small output work because the orifice can be adjusted.
The current in C1 cannot be very small because it doesn’t match with Zexp when the phase is small

17. Acoustic field modulation
OUTLINE
Acoustic field modulation
in a regenerator
Background
New modulation method
Theoretical analysis
Practical case study
Conclusions

18. 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 new method of modulating the acoustic field 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.
A practical design case was presented to show the characteristics of this new method

19. Thank you