Career Episode 2: CFD Simulation of Stirling Cryocooler
2.1 Introduction
2.1.1 I got to study advanced Machine Design and Drawing concepts in my 2 nd and 3rd year of the
course. As a part of this, I learnt design and simulation tools like AutoCAD, Fluent, Pro
Engineer and more. This opened up a lot of avenues and possibilities for me and I learnt that
modern engineering depends a lot on running simulations for various designs and then find
the optimum values for the design. As part of an assignment for Machine Design subject, my
subject faculty asked everyone in the class to design and run simulations on a topic of our
choice. The outcome can be an optimal design for the required functional requirement or
study of effect of a particular concept/component in different conditions to find out optimal
control parameters. Around this time, I had also studied different types of engine cycles
(Petrol engine cycle and diesel engine cycle). I decided to use this learning of
thermodynamics and design and run simulations on such a system for my assignment.
2.1.2 I did this project while studying in my 6 th semester while doing my Bachelor of Technology in
Mechanical Engineering course from Global Institute of Engineering & Technology as
affiliated with JNTU, Hyderabad, India. My subject faculty was Prof. XXXX and he approved
the topic of designing and running simulations for a Stirling Cryocooler engine. This was an
individual assignment and I worked on it from from XXXX to XXXX for a period of 2 weeks.
2.2 Background
Nature of the project
2.2.1 My college boasted of a faculty with a lot of industry experience. The management in my
college had intentionally done this as they wanted to impart a sense of practical knowledge
oriented engineering graduates from my college. Due to this, many a times, our professors
would come up with novel type of assignments instead of the typical assignments and other
academic deliverable that our course prescribed. These type of application oriented
assignments forced their students to think how different subjects are intertwined together.
In a similar vein, my faculty for Engineering Drawing and machine design gave the students
an assignment similar to aforementioned.
2.2.2 They outline for the assignment was to study or design a system and then apply the
knowledge of design and simulation software to come up with an analytical study and
validate the understanding using the same as well. I picked up thermodynamics related
concepts of different types of engine cycles for my focus analysis. I picked a Cryocooler
based Stirling Engine for my analysis. There were a couple of reasons for this. Undertaking
this study, I would also learn how a cryocooler engine would be different than a typical
engine, learn its performance objectives, control parameters and their optimum output
values.
Scope of the project
2.2.3 Based on this idea, I proposed the below scope for the project and my faculty approved it:
Understand what is a cryocooler & its types
Understand the PV Diagram and different stages of the Stirling Cryocooler cycle
Study the working of a Stirling Cryocooler
Identify key components
Understand the governing equations of the cycle
Design a Stirling Cryocooler using GAMBIT
Run Simulations for key control variables on FLUENT
Study the results of the simulations
Conclusion
2.2.4 This project would help me apply the below technical concepts:
Thermodynamics
Engineering Drawing
Machine Design
Advanced Mathematics
GAMBIT & FLUENT
Stirling Cycle
Design & Simulation
Organization Structure
2.2.5 Below was the structure of the project team:
Prof. XXXX (HOD
Mechanical Engineering
Dept)
Prof. XXXX (Academic
Guide)
Mr. Mirza Humaid Baig
2.3 Personal Engineering Activity
Application of Engineering Knowledge
2.3.1 My first step was to understand the system in hand. I wanted to understand in detail what a
Cryocooler is, what are its applications. I found out that a cryocooler is basically a
refrigeration machine capable of reaching temperatures as low as 0-150K. This capability has
resulted in extensive application of cryocoolers in defence, environmental studies, medicine,
transport and logistics and more domains. Medical and medicine applications remain the
pinnacle of the application capability for cryocoolers.
2.3.2 So, I started exploring different types of cryocoolers to find out that there are open cycle
cryocoolers and closed cycle cryocoolers. Open cycle coolers make use of cryogens working
in a Joule Thomson expansion valve. The closed cycle coolers operate by rejection of heat at
very high temperatures. It makes use of Stirling cycle or Brayton cycle for this. I decided to
study a Stirling cycle powered Cryocooler as this’d also help me in understanding a Petrol
Engine cycle which has a wider range of application in the current environment.
2.3.3 Now principally, these cryocoolers are heat exchangers capable of rejecting heat from an
isolated system. So basically, if we’re able to pump in a lot of heat and energy, then
subsequently this system is capable of rejecting a lot of heat as well. If we’re able to change
the location of heat rejection so that one part only rejects heat whereas the other one
always accepts heat, we’ll get a cool and hot section. This is the working philosophy of heat
exchangers. I studied recuperative and regenerative heat exchangers for this.
2.3.4 With this background, I started by studying Stirling Cryocoolers which make use of a
regenerative heat exchanger and works on a Stirling Cycle. The best point to start studying
any such cycle (I believe) is the PV Diagram. In a typical Stirling cycle, the pressure is first
increased within an isolated system which compresses (reduced volume) the air inside. This
causes the pressure to increase a bit further. Once the max pressure and minimum volume is
reached, the pressure drops and this causes expansion of gas which causes heat rejection.
These 4 stages of Stirling Cycle consist of isothermal expansion, isochoric heat addition,
isothermal compression and lastly isochoric heat rejection.
2.3.5 Now to gain these stages of a Stirling cycle, I studied the design of the engine which makes
this happen. A typical Stirling Cryocooler consists of a compressor consisting of a piston and
aftercooler. A transfer line connects the regenerator which has a hot space, cold space and a
regenerator piston. The 2 pistons in both sections are connected and compressor side piston
movement gets controlled by controlled expansion of fuel. I studied different stages of this
piston position in both sections and understood that the 4 stages of my Stirling cycle
corresponds to the piston position of the regenerator and the hot space and cool space can
be considered as isolated heat rejection and heat acceptance chamber of the system.
2.3.6 Now the main reason to dive in this deep into the working of the cycle was to understand
and come up with the governing equations of this system. The philosophy of simulation
software is to first identify the governing equation for the whole system. Then this system
undergoes something called as meshing. Here, the system is broken down into numerous
same size components and each component is subjected to these governing equations. This
would mean that we’ll be able to analyse every component of this system and study the
effect of its operation. Now the governing equations to be applied depends on the metrics I
want to test/analyse. In this case, I wanted to understand the energy dynamics to study the
temperature variance across the system, the momentum caused due to the medium being
pushed around and lastly the effect on medium (mass). So I studied the governing equation
of mass transport, momentum and energy equation. I would use this to outline the
boundary conditions.
Tasks undertaken
2.3.7 Now with the theory understood, I started designing the system on my design software
(Gambit). I was able to define the edges, faces and dimensions of the system. I had to design
each and every component of a Stirling cycle which included pistons, compressor,
aftercooler, transfer line, hot and cold space, regenerator and displacer. The design model I
created was as below:
2.3.8 These dimensions were taken from the library present in the software. Using this library, I
did not have to manually design every component in as much detail and helped me get
accurate design of a standard design. Once I had the design, I meshed it to break down the
system into smaller components.
2.3.9 Next I exported this file and opened it in FLUENT which is a simulation software. The
boundary conditions I put in the solver were energy equations, mass movement, pressure
calculations and temperature calculations. I selected other conditions as per the standard
engine like piston being adiabatic, compressor was steel and adiabatic. Again, the library I
was using had these options default marked/configured.
2.3.10 Now with the design ready, I wanted to run simulations by keeping some control variables
constant, vary some and study the effect of the same. I decided to go for a no load condition
with a vibrating frequency of 20Hz to 50 Hz (10 Hz increment). I found out that for no load
case at 30 Hz, the cool space temperature varied sinusoidally and kept dipping. The pressure
was also sinusoidal, but more or less remained constant. If I studied the temperature dip
over a period of time, I noticed that initially the heat rejection was rapid, but slowly it
stabilised. The graph felt a lot like a reverse exponential curve. The temperature stabilised
around 172 sec in the simulation. I studied the temperature contour of the system to see
that highest temperature is at the compressor where load is applied. Then in the
regenerator, as expected, the hot side had higher temperature and as we went towards the
cooler section, the temperature dropped.
2.3.11 Since the temperature on the cool side stabilised at 172 sec, I drew a temperature plot of
different positions on the system to get the below graph. It showed the temperature
variation across the whole system and its components.
2.3.12 I ran a similar configuration of control variables with a load of 0.5 W. But I found out that the
temperature delta was the same, but the starting point of heat rejection was higher. So even
though the performance was the same, the lowest temperature achieved was higher than
the no load condition.
2.3.13 To understand the optimum frequency, I ran simulations for aforementioned control
variables at 20Hz, 30Hz, 40Hz & 50 Hz. I found out that the minimum temperature achieved
was at 30 Hz. I also concluded that adding any load to the system was not helping the lowest
temperature achieved. The lowest temperature I achieved was around 72K.
2.4 Summary
2.4.1 This analysis study helped me understand the theory of a Stirling cycle, also seethe effect of
operation of this cycle at various operation point. This helped me see the effect and
operation of various stages of the cycle in action. My conclusions from this simulation study
validated the hypothesis of various studies done and I came out better equipped with this
topic. My guide was happy with this exercise and approved my assignment.
