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 100190 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. .

Acoustic field modulation 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 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

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

Acoustic field modulation 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 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

New method of modulation P1 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

Acoustic field modulation 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 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,

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:

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

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.

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,

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

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

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

Acoustic field modulation 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 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

Thank you