STUDIES ON PHASE SHIFTING MECHANISM IN A PULSE TUBE CRYOCOOLER (PTC) 26 th International Cryogenic Engineering Conference ICEC26 – ICMC O-1B-2 COMPRESSOR REGENERATOR DISPLACER STIRLING CRYOCOOLER COMPRESSOR REGENERATOR PT, IT, RESERVOIR PULSE TUBE CRYOCOOLER Padmanabhan Gurudath C S Srikanth Thota Basavaraj S A Dr.Ambirajan A Dinesh Kumar Prof. Venkatarathnam G

Table of Contents  INTRODUCTION  OBJECTIVE  THEORY  EXPERIMENTAL SET – UP  RESULTS AND DISCUSSION  CONCLUSION  FUTURE WORK

Cryocoolers : Devices that generate temperatures in the cryogenic range i.e. from near absolute zero to 120K. Broadly classified as - 1.Steady state type cryocoolers Flow is unidirectional Comparable to DC electrical systems Performance depends on properties of the working fluid 2. Periodic type cryocoolers Flow is oscillatory Comparable to AC electrical systems Performance depends upon the phase angle between Pressure pulse (voltage) and mass flow (current) Introduction 1 Pulse Tube Cryocoolers (PTC) are of the periodic flow type having different configurations of a passive cold head encompassing different types of phase shifting mechanisms to attain optimum performanceconfigurationsphase shifting mechanisms

2 Objective  To study the phase shifting characteristics of an Inertance type phase shifter on the performance of the PTC.  To obtain an optimum phase angle between the mass flow and dynamic pressure at the PT cold end that results in the largest possible heat lift from this unit.  Develop a Theoretical model using Phasor Analysis and Transmission Line Model (TLM) for different mass flow and arrive at values of optimum frequency and phase angles.  Compare the experimental data from the PTC for different configurations of the Inertance tube/reservoir at various frequencies and charge pressures.  These studies were carried out to characterise an existing cryocooler and design an optimised phase shifter with the aim of improving the performance with respect to specific power input.

PHASOR ANALYSIS  Phasor representation 3 Where Q c = Gross refrigerating power Governing equations – P = P 0 + P 1 cos (  t) T = T 0 + T 1 cos (  t). (Sinusoidal variation) Applying conservation of mass condition : Yields equation connecting the cold and hot end flows as – Thus, is given by the vectorial addition of the 1 st and 2 nd term which are at an angle of (  /2) to each other.

INERTANCE PULSE TUBE CRYOCOOLER (IPTC)  Using the Inertance tube both leading and lagging phase angle are obtained by varying the r, l & c of the Inertance tube and capacitance of the reservoir.  The Orifice PTC gives only lagging phase angles i.e. pressure lagging mass flow.  Pressure Phasor   Pressure phasor Compr Pulse Tube Res Reg Inertance tube Compr Pulse Tube Res Reg Orifice 4

Res Compr Pulse Tube Real axis P Inertance tube Imaginary axis  r,h  r,c  Phase angle is zero at the center of the regenerator Mass flow rate is minimum for a given heat load. Regenerator losses are at a minimum, resulting in maximum performance of the system. Obtaining maximum cooling for given flow rate is the prime objective of the phase shifting circuit. Inertance Pulse Tube Cryocooler (IPTC) Phasor 5

Electrical Parameter Resistance (r) Inductance (l) Capacitance (c) Capacitance (C r ) Reservoir Equivalent Fluid parameter (per unit length) TRANSMISSION LINE MODEL Governing Equations Electrical ParameterEquivalent Fluid parameter Impedance (Z) Z = E /I E = Voltage I = current Impedance (Z m ) = / = Pressure amplitude = mass flow rate 6 r cCrCr Z -INDUCTIVE Z - CAPACITIVE

Solution to this pair of simultaneous differential equation yields the complex impedance of a terminated transmission line of length Le Where, impedance of the compliant load ; characteristic impedance |Z m | is the amplitude of the complex impedance at the inlet to the Inertance tube i.e. at the Pulse Tube / Inertance tube interface. θ z is the angle by which leads. Resonance condition in the phase shifting circuit is defined as the frequency at which the imaginary part of the complex impedance goes to zero. 7

EXPERIMENTAL SET – UP SCHEMATIC OF EXPERIMENTAL SET-UP Cold Head Compressor Phase shifter Detector I/F 8

RESULTS AND DISCUSSIONS Length  0.6  1.0  1.5  Phase Angle variation with Inertance Tube Geometry – TLM model. Length  0.6  1.0  1.5  Test case -1 : m = 0.35 g/s Test case -2: m = 1.05 g/s  To achieve a phase angle of > 30 0 at inertance inlet, tube sizes with ID around 2mm are necessary, for mass flow in the range of 0.35 g/s to 0.5 g/s. 9

The primary data needed for constructing the phasor diagrams needed for arriving at the phase relationships, is the mass flow rate from the compressor and that at the inertance tube inlet. I. Mass flow rate measurements at compressor outlet Compressor Reservoir P1P1 P2P2 Schematic of mass flow measurement Uncertainty analysis show - 2.7% error for mass flow leaving the compressor and 1.4% error for mass flow entering the reservoir. 10 The mass flow into the Reservoir is given by where, = time derivative of pressure, V r = reservoir volume and T r = reservoir temperature

II. Performance of cryocooler with different Inertance tube configurationsconfigurations Sl. no Inertance tube Frequency -Hz Mass flow IT entry g/s Ph. Angle TLM ( deg) Pr. Ampl (bar) Temp (K) ID (mm)Length (m)Exptl OptTLM * * *  The lowest temperature achieved (at zero applied heat load): 151K to 98K.  Phase difference varies from to and mass flow from to g/s  The results clearly show that the performance of the refrigerator is critically dependent on the configuration of the inertance tube.  The lowest temperature achieved with all configurations is close to the natural frequencies calculated by the model. 11

II (a) Output plots from performance teststests The operating frequency of the compressor was varied from 44 to 76 Hz and pressure from 18 to 28 bar. Reservoir volume constant at 100 cm 3.  An optimum frequency (f o ) exists for each inertance tube/reservoir combination.  The cryotip temperature (at f o ) decreases with an increase in the natural frequency of the inertance tube/reservoir and increase in charge pressure Frequency and Temperature variationPressure and Temperature variation 12 Tube ID:  1.76mm

 Operating experimental frequency is the frequency at which lowest temperature is obtained for a given configuration  Operating frequency f o is always lower than the natural frequency  As the natural frequency increases, f o increases.increases. Calculated vs Optimum Experimental frequency. Correlation between Calculated and Optimum frequency II (b) Output plots from performance teststests 13 Tube ID  1.76mm

 An experimental approach to measure this natural frequency was explored.  There exists a clear minima in the piston amplitude for fixed inertance tube inlet pressure amplitude.  TLM predicts a natural frequency that is 10 Hz higher than the experimental value.  The TLM results are based on a constant mass flow rate whereas in reality the mass flow rate changes with the piston amplitude.  This requires further study. III. Natural frequency determination teststests 14

Conclusions The performance of a Pulse tube refrigerator is a strong function of the phase angle between the pressure and flow rate phasors The cooling capacity of the refrigerator is highest when the compressor frequency is close to the natural frequency of the inertance tube. Higher natural frequency of the inertance tube higher the cooling capacity or lower the temperature achieved. The minima in temperature obtained in the PTC with respect to frequency variation is directly correlated with the natural frequency, obtained from the mathematical model, of the PSM. Higher the average pressure higher the cooling capacity, however the highest pressure is limited by the presence of transition joints between dissimilar metals in the refrigerator. Importance of natural frequency and an experimental approach to determine the same. 15

FURTHER SCOPE OF WORK  Study for natural frequency determination of compound Inertance tubes and subsequent cooling performance of the PTC with these configurations to obtain lower temperatures.  As observed from the test results, improved performance is obtained at higher frequencies and pressures. Hence Design and realisation of a high frequency PTC is envisaged. 16

THANK YOU…. for your attention References [1]Ross, R.G., Jr and Green K.1997 Cryocoolers 9 Plenum Publishing pp [2]Chan CK, Ross RG Jr et al Cryocoolers 10 Plenum Publishing pp [3]Hoffman A. and Pan H Cryogenics 39 pp [4]Faculty, 2011 CEP Course Adv. in Cryocooler Tech., Dept of Mech. Engg IIT-B Ch.1-4. [5]Skilling, H.H., 1951 Electric Transmission Lines, McGraw-Hill, Chapter 1-4. [6]Radebaugh R, Lewis M, Luo E, et.al Adv. in Cryogenic Engg. 51 pp [7]Luo,E., Radebaugh R. and Lewis M., 2004 Adv. in Cryogenic Engg. 49 pp [8]Schunk L.A., Experimental investigation and modeling of inertance tubes, MS Dissertation, University of Wisconsin-Madison, 2004, Chapter 4. [9]Haizen Dang., 2012 Cryogenics 52 pp 205 –

Schematic of Pulse tube geometrygeometry

Compressor Pulse Tube CHXHHX Regenerator After cooler Orifice Reservoir Compressor Pulse Tube CHXHHX Regenerator After cooler Orifice Reservoir Double inlet valve Compressor Pulse Tube CHXHHX Regenerator After cooler Inertance tube Reservoir OPTC DIPTC IPTC PHASE SHIFTING MECHANISMS IN PULSE TUBE CRYOCOOLERSCRYOCOOLERS

Res Compr Pulse Tube Real axis P Inertance tube  r,h  r,c  Real axis Imaginary axis Phasor diagrams for two practical cases for the IPTCIPTC

P4 P1 P2 Compressor PTC Cold head Cryotip P3 T1 Inertance tube Reservoir Schematic of performance evaluation test set-upset-up

P3P3 P1P1 Compressor Reservoir P2P2 Inertance tube LVDT Schematic of set-up for Natural frequency determination of phase shift circuitcircuit

III (e) Effect of change in Reservoir volume on phase angle  An order of magnitude change in the reservoir volumes do not change the phase angles significantly.  The guideline for choosing the reservoir is that it should be at least 50 times the pulse tube volume to provide for sufficient capacitance.

II (c) Mathematical model results with frequency variation

Length = 4m  Higher diameter tubes have lower sensitivity to mass flow rate, reflected by the same resonant frequency irrespective of the mass flow rate.  Frictional “resistance” occurs on the inner surface of the tube. Clearly the ratio of perimeter to cross-sectional area decreases with an increase in diameter (i.e.  D/[  D 2 /4]=4/D).

 Phase angles (calculated using TLM) are plotted as a function of frequency.  Minima in temperature occur at the frequency near the knee of the phase shift curve, for a given inertance tube / reservoir combination.  This seems physically plausible as the highest cooling is obtained when the pressure leads the mass flow rate by app. 60 o III (c) Output plots from performance teststests  1.76mm; L =3.5m  1.76mm; L =2.75m