Chapter 11
Completing the Picture


The new approach has made short work of the ‘traditional’ regenerator problem. However, in the Stirling engine flow is not uniform between switching and pressure is far from constant. On the other hand, convective heat transfer still depends on local, instantaneous temperature difference, ΔT, and acts on fluid particles in motion. The extra features are thus readily added to the formulation. All that is required is a representative map of fluid particle motion to replace the idealized picture of Fig. 8.1. How this is done will be outlined later.

Appropriately coded for computer, the comprehensive approach yields (Organ 1997a) the optimum regenerator — the combination of volumetric porosity, hydraulic radius, etc. for which the combined losses due to hydrodynamic pumping and imperfect heat exchange at given operating conditions (NT, NMA, NSG, etc.) are a minimum. A computer-coded search for the optimum is not the same as an explicit optimum — a traditional, symbolic algebraic formula expressing ideal flow passage geometry in terms of the parameters of engine operation.

However, it is sometimes the case that, when the appropriate approach to a problem has been identified (in this instance, formulation in terms of ΔT), further simplification follows. Used in conjunction with the concept of NTU (Number of Transfer Units) and with insights from temperature solutions yielded by the computer-coded implementation, the ΔT formulation allows just this explicit algebraic statement of the optimum. Results can be displayed in the form of charts, bringing design of the optimum regenerator within reach of anyone who can use a hand calculator. To this extent, regenerator analysis has now taken a form of which Robert Stirling himself might have approved. Indeed, it can be convincingly argued (Chapter 12) that the 1818 engine could not have functioned at all — let alone pumped water — had Stirling not predetermined the wire diameter and winding pitch of the regenerator, possibly along the lines of the material of this chapter. The account is taken largely from the author's paper (2000b) with the permission of the Council of the Institution of Mechanical Engineers.

  • 11.1 Regenerator analysis further simplified
  • 11.2 Some background
  • 11.3 Flush ratio
  • 11.4 Algebraic development
  • 11.4.1 Temperature profile
  • 11.4.2 The ‘flush’ phase in perspective
  • 11.4.3 Temperature recovery ratio
  • 11.4.4 Matrix temperature swing
  • 11.5 Common denominator for losses
  • 11.5.1 Heat transfer and flow friction correlations
  • 11.5.2 Heat transfer loss
  • 11.6 Hydrodynamic pumping loss
  • 11.7 Matrix temperature variation again
  • 11.8 Optimum NTU
  • 11.9 Inference of NTU actually achieved
  • 11.9.1 From temperature recovery ratio, ηT
  • 11.9.2 NTU from mean cycle Nre
  • 11.10 Evaluation of optimum NTU
  • 11.11 Implications
  • 11.12 Complete temperature solutions
  • 11.13 Thermodynamic study of the 1818 engine (continued)
  • 11.14 Interim deductions

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