Intimate Thermodynamic Design of the Stirling Engine Gas Circuit without the Computer

Proceedings of the Institution of Mechanical Engineers, Part C:

1994

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An exact, general and algebraically simple solution is obtained to the classic model of the thermal regenerator-general in the sense of coveringflushing ratios, A, of any magnitude, including the small values of interest in the context of Stirling cycle machines, and of depicting start-up and cyclic steady state operation. Specimen solutions turn the conventional picture of regenerator performance on its head: for aJlushing ratio equal to or less than unity, for example, zero heat-transfer coeficient (NTU = 0) leads to a temperature recovery ratio of 100 per cent! At a thermal capacity ratio, N,, above a certain, minimal, value, the wall temperature distribution sits invariant between the extremes of gas temperature swing, and increased NTcR has no effect on temperature recovery ratio. Thefindings are sufjicient to explain reports of unexpectedly good performance of Stirling machines with regenerators of cotton wool or glass fibre. NOTATIONabbreviations for terms considered constant over an integration step (defined in the text) free-flow cross-sectional area (m') common specific heat (incompressible fluid) (J/kg K) specific heat at constant pressure/volume (J/kg K) diameter of wire regenerator gauze (m) mean mass velocity = pu (kg/mz s) coefficient of convective heat transfer enthalpy per blow (J) length (m) a reference length-may be Lreg (below) (m) overall physical length of regenerator packing (4 mesh number-number of wires/unit length (m-7 number of regenerator subdivisions cycles per second = w/2n (l/s) local, instantaneous Reynolds number = Stanton number = h/gc, characteristic temperature ratio, T,/T,. Note that this is the inverse of the traditional definition of the temperature ratio for Stirling cycle machines, but is consistent with more recent notation thermal capacity ratio = p , cJpc for incompressible fluid or T,,, pw cw/pref for compressible fluid. Respective numerical values differ by a factor of (y -l)/y number of transfer units = N,, x/rh, N,, Lreg/rh absolute pressure (Pa) reference pressure (Pa) wetted perimeter (m) gas constant for specific gas (J/kg K) hydraulic radius, free-flow arealwetted perimeter = A$P (m) time (s) (W/m2 K) P U d PThe MS was C09093 0 IMechE 1994 T,, TE constant, uniform temperatures of gas entering from the right and left extremities of regenerator respectively (K) normalized velocity = u/Lref n, U velocity (m/s) u X length coordinate (m)specific heat ratio = cJcU temperature recovery ratio, defined in text normalized length/distance = l/Lref, x/Lrer normalized hydraulic radius = r,JLref reduced length or 'flushing ratio' = (gas particle excursion amplitude)/L,,, density (kg/m3) crank angle-dimensionless time (rad) angular frequency = 2nn, (rad/s) volumetric porosity = void volume/total volume. For rectangular wire gauze this becomes 1 -tnm, d , Subscriptsg gas or fluid W wall, wire -(underscore) mean value during finite interval of a numerical integration step 1 BACKGROUNDThe theories of the thermal regenerator have been described, by Max Jakob (l), as 'among the mos...

Section: Defining Equationsmentioning

confidence: 99%

Solution of the Classic Thermal Regenerator Problem

Proceedings of the Institution of Mechanical Engineers, Part C:

1994

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“…Figure 1 is a map of fluid particle trajectories over a complete cycle computed for a planar equivalent of the Philips (1961) MP1002CA air engine. The map derives from a cycle simulation (3-conservation law (Organ 1991)) rather than from measurement. The trajectories are thus somewhat idealized, bu t sufficiently representative of reality for present purposes.…”

Section: Essential Features Of the Temperature Solutionsmentioning

confidence: 99%

Transient thermal performance of the stirling engine wire regenerator

1994

Proc. R. Soc. Lond. A

“…5, mass distribution is symmetrical, as required by equation (9). 4 Takase's isothermal optimization curves include the extreme case vD = 0, permitting interpretation of equation (9) in terms of the Schmidt model. K ,~~ for this hypothetical case (zero dead volume) % constant/N, The asymmetry of the ideal 'static' cycle for vd > 0 may reflect the fact that, with these realistic values of vD, compression and expansion no longer follow the law for the uniform, isothermal mass (3), that is pV # constant.…”

Section: Implications For Understanding the Ideal 'Static' Cyclementioning

confidence: 99%

‘Natural’ Coordinates for Analysis of the Practical Stirling Cycle

Proceedings of the Institution of Mechanical Engineers, Part C:

1992

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The appropriate choice of coordinate system so simplifies basic cycle analysis that computation of the ideal particle trajectory diagram reduces to a straightforward yraphical process. Ideal pressure, Reynolds number N,, , friction factor C, and heat-transfer parameters N,, and Nii3 follow in function of location and crank angle via a few steps on the hand calculator. A thermodynamic design parameter is identiJ5ed which has essentially the same numerical value for such diverse Stirling engines as Philips' MPI002CA, General Motors' G PU-3 and the turn-of-the-century Kyko hot-air engine. NOTATIONC04092 @ IMechE 1992