1. Novel Simulation Model for GM type Orifice Pulse Tube Cryocooler
P B Gujarati1, K P Desai1, H B Naik1 and M D Atrey2
1S V National Institute of Technology, Surat, Gujarat, India,
2Indian Institute of Technology Bombay, Mumbai, Maharashtra, India,
158-C1PoA
New Model Capabilities
Various analysis and Design models
Enthalpy Flow analysis
Phasor Analysis
Isothermal Model
Numerical Model
Finite Volume Method (Discretization)
Gauss Siedel Iterative Method
Pressure and Temperatures (Node of a cell )
Mass flow rate /Velocity (Face of a cell )
Second Order Upwind Scheme (Advection terms)
Assumptions in Numerical Model
1D flow of compressible helium gas
No axial conduction in solids
Pressure drop is neglected everywhere
Transient Numerical Model
Estimates the cool down behavior
Uses the Conservation laws
Higher accuracy in solution
Rotary valve is an integral part of the model
Model can calculate the pressure waveform
Model can predicts the change in pressure ratio
Energy Equation for Gas
Outlet mass flow rate:
Orifice
Energy Equation for Solid
Inlet mass flow rate:
Rotary Valve
For Pressurization
For P > Pr
Left end, Temperature boundary
Uses mass balance at a given instant of time to calculate the pressure
Temperature field is calculated from Energy equation of gas
Tb=Tin for ṁleft ≥ 0 (left to right flow)
Tb=Tgas for ṁleft < 0 (right to left flow)
For P < Pr
For Depressurization
Right end, Temperature boundary
Continuity Equation
Tb=Tgas for ṁright ≥ 0 (left to right flow)
Tb=Tr for ṁright < 0 (left to right flow)
INPUT DATA
Conclusion:
The novel simulation model of orifice pulse tube cryocooler is proposed. The unique feature of the proposed model is that instead of fixed pressure waveform as pressure input to the numerical model, the present model is capable of calculating the pressure waveform from flow area variation between stator and rotor. This makes the model capable of designing and simulating the complete GM type pulse tube cryocooler including rotary valve. The model also predicts the change in pressure ratio during the cooldown process. The change in pressure ratio can be prevented to some extent by changing the valve timing diagram by proving different intake time. Better cooling performance can be achieved by optimizing the rotor by simulating the effect of different intake time.
Stator - Rotor Geometry
Pressure Ratio Variation Vs Cooling Time
Refrigeration Power
Parameters
Value
Length of Regenerator
210 mm
ID of Regenerator
16.5 mm
Length of Pulse Tube
230 mm
ID of Pulse Tube
15 mm
Wall thickness (Pulse Tube & Regenerator)
0.5 mm
High Pressure
20 bar
Low Pressure
8 bar
Regenerator Mesh size
SS 200 #
Regenerator Porosity
0.68
Waveform
Comparison
% Change of Pressure Ratio
Area variation at Rotary valve
for different cases
Change in Waveform
Validation
Cycle No
Case-1
Case-2
Case-3 1
2.5
2.500
100
2.467
2.489
2.490
200
2.410
2.475
2.482
400
2.228
2.376
2.420
600
2.135
2.259
2.317
800
2.123
2.225
2.279
Steady State
2.120
2.226
2.276
% change
15.20
10.96
8.95
References:
[1] Gifford W E and Longsworth R C 1964 Pulse tube refrigeration Trans. ASME
[2] Mikulin E I, Tarasov A A and Shrebyonock M P 1984 Low temperature expansion pulse tube Adv. in Cryo. Engg. Plenum Press
[3] Zhu S, Wu P and Chen Z 1990 Double inlet pulse tube refrigerator-an important
improvement Cryogenics
[4] Wang C, Wu P Y and Chen Z Q 1992 Numerical modelling of an orifice pulse tube
refrigerator Cryogenics
[5] Wang C, Wu P Y and Chen Z Q 1994 Numerical analysis of double inlet pulse tube
refrigerator Cryogenics
[6] Wang C 1997 Numerical analysis of 4 K pulse tube coolers: part I. numerical simulation Cryogenics
[7] Desai K P 2003 Investigations of orifice pulse tube refrigerator SVNIT PhD thesis 91
[8] Gujarati P B, Desai K P, Naik H B and Atrey M D 2015 Transient analysis of single stage GM type double inlet pulse tube cryocooler IOP Conference Series: Materials Science and Engineering Volume 101 article id
Case:1 (‘D’) Case: 2 (‘1.5D’) Case: 3 (‘2D’)
Acknowledgement
Authors are thankful to the Department of Science and Technology (DST), Government of India, (No.SR/S3/MERC-008/2011(G)) for funding the research project under which present work is carried out.
Presented at CEC-ICMC 2017, Madison, USA – July, 2017