Athens, Ohio, is a hotbed of Stirling cycle machine activity, both engines and coolers, and includes three R&D and manufacturing companies as well as David Gedeon, an internationally recognized consultant in the area of Stirling cycle computer analysis. The parent company of this activity is Sunpower, Inc. It was formed by William Beale thirty years ago, mainly based on his invention of the free-piston Stirling engine. Sunpower have licensed their free-piston machines for manufacture throughout the world, and begun to manufacture free-piston Stirling cycle croygenic coolers for liquifying oxygen. Global Cooling is a licencee of Sunpower, mainly in order to develop free-piston Stirling cycle coolers for home refrigerator applications. These systems, apart from being significantly more efficient than regular vapor-compression refrigerators, have the added advantage of being compact, portable units using environmentally benign helium as the working fluid.
Some members of the ME321 (Thermodynamics) class had the unique experience of visiting Global Cooling on Wednesday (10/3/07) where we had a fascinating tour by Jesse Edwards. We were exposed to state-of-the-art Stirling machine development - low and high power (600W) coolers and engines, as well as the unique symbiotic Stirling/CO2 designs, for home, industrial and military use.
We are fortunate to have obtained two M100B state-of-the-art coolers from Global Cooling. The one is used as a demonstrator unit, and is shown in operation in the following photograph. The second unit is set up as a ME Senior Lab project in which we evaluate the performance of the machine under various specified loads and temperatures.
A schematic diagram of the cooler is shown
below.
Conceptually the cooler is an extremely simple device, consisting essentially of only two moving parts - a piston and a displacer. The displacer shuttles the working gas (helium) between the compression and expansion spaces. The phasing between the piston and displacer is such that when the most of the gas is in the ambient compression space then the piston compresses the gas while rejecting heat to the ambient. The displacer then displaces the gas through the regenerator to the cold expansion space, and then both displacer and piston allow the gas to expand in this space while absorbing heat at a low temperature. The complete cycle is demonstrated in a delightful animated schematic of the cooler by Global Cooling.
Unfortunately the analysis of actual Stirling cycle machines is extremely complex and requires sophisticated computer analysis. We will consider an idealised model of this cooler defined in terms of the P-V diagram shown below. In this quiz you will determine the ideal performance of the M100B under typical operating conditions from this ideal model.
The Ideal Stirling Cycle can be described with respect to the P-V diagram as follows: Process (1) - (2) is the isothermal compression process at temperature TC = 30°C, during which heat QC is rejected to the ambient. Process (2) - (3) is the constant volume displacement process during which heat QR is rejected to the regenerator matrix. Process (3) - (4) is the isothermal expansion process at temperature TE = -20°C, during which heat QE is absorbed from the freezer, and finally process (4) - (1) is the constant volume displacement process during which heat QR is absorbed from the regenerator matrix. Thus the ideal Stirling cycle consists of four distinct processes, each one of which can be separately analysed. State (1) is defined at a maximum volume of 35 cm3 and a pressure of 1.9 MPa, and State (2) is defined at a minimum volume of 30 cm3. (Note that the values presented here are not actual values of the M100B, however were devised by your instructor for purposes of this quiz only).
Note that the practical Stirling cycle has many losses associated with it and does not really involve isothermal processes, nor ideal regeneration. Furthermore since the Free Piston Stirling cooler involves sinusoidal motion, the P-V diagram has an oval shape, rather than the sharp edges defined in the above diagram. Nevertheless we use the ideal Stirling cycle to get an initial understanding and appreciation of the cycle performance.
1. Determine the heat absorbed in the expansion space QE during the expansion process (3) - (4) (Joules). Determine also the heat power absorbed (Q'E Watts). Note that the cycle frequency is the line frequency (f = 60 Hz), thus Q'E = f*QE.
2. Determine the net work done per cycle (Joules): Wnet = WE + WC (Note that the compression work WC is always negative). Determine also the power supplied to the linear electric motor (Watts).
3. Evaluate the Coefficient of Performance of the refrigerator defined as: COPR = QE / Wnet. (heat absorbed in the expansion space divided by the net work done).
4. Determine the amount of heat rejected by the working fluid QR as it passes through the regenerator matrix during process (2) - (3). If there were no regenerator present then this heat would need to be removed from the gas by the expansion process in order to reduce the temperature to the cold temperature of the freezer. How would this affect the performance of the cooler? Discuss the importance of an effective regenerator in the Stirling cycle cooler.
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Declaration of Honesty - I hereby declare that this take-home
quiz is my own work, and that I did not collaborate with or receive
help from anyone else while doing it.
(Signed)___________________________ (Date)______________________