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This book will explore all key mathematical methods that need to be learned in order to model a cryocooler with all its various aspects and physical phenomena. The cryocooler will be studied in terms of thermodynamics, harmonic approximations, nodal numerical modelling, 2D and 3D modelling, and hydrodynamic modelling. Furthermore, data analysis methods that employ more recently developed machine learning methods will be explored that improve multi-parameter optimisation methods, and introductory analysis methods for integrating cryocoolers into spacecraft systems will be presented.
Key Features:
- Presents key mathematical methods for modelling physical phenomena of cryocooler systems
- Includes introductory context and background information that enables a student at graduate level and upwards to get up to speed for the required modelling methodologies
- Includes helpful examples throughout each chapter to demonstrate how calculations and modelling can be performed
- Relates the theory and mathematics to practical examples that are relevant to current research in the field, referencing literature throughout the book
1. Cryocooler Fundamentals
a. Background
b. Types of cryocoolers
c. Scope of book: Addressing pulse tube and Stirling cryocoolers, but
methodologies can be applied to GM and many other types, as per
mentioned in section 1c
2. Mathematics Fundamentals
a. Complex numbers and euler-form
b. Expansion series
c. Differential equations
3. Thermodynamics
a. 1st and 2nd law
b. Thermodynamic cycles
c. P-V diagrams
d. Work, enthalpy, entropy
e. Entropy analyses
4. Numerical modelling
a. Key equations throughout cryocooler
b. Mathematical methods for 1D nodal modelling
c. Sage modelling & further methods
5. Harmonic approximations
a. Basics of sinusoidal waveforms
b. Harmonic oscillators
c. Further on normal modes maths
d. Phasor analysis & phase modulation
e. Phasor diagrams
6. Thermoacoustic Modelling
a. Acoustic waves
b. Rott’s acoustic approximations
c. Gas springs
d. Thermoacoustic power
7. Electrical analogy modelling
a. Electrical analogies
b. Transmission line modelling (TLM)
c. Component losses
8. Hydrodynamic modelling
a. CFD modelling
b. Fluids modelling for varied configurations
c. Regenerator modelling 9. Data analysis & optimisation methods
a. Signal processing in the Lab
b. Regression analyses
i. Data regression lines
ii. Waveform curve fitting
c. Parametric optimisation
d. Bayesian optimisation
10. Spacecraft integration
a. Integrating cryocoolers into spacecraft
b. Failure and fatigue analysis
c. Cost analyses
11. Conclusions
12. Appendices
a. Example calculations from various chapters
b. Example Python code from chapter 6