ICEC 15 Proceedings ICEC 15 Proceedings LINEAR NETWORK ANALYSIS OF SPLIT-TYPE STIRLING REFRIGERATOR B.J. Huang and C.W. Lu Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan A 'linear network model is developed for split-type Stirling refrigerators. We obtain an equivalent network and two transfer-function functions from which the system performance can be evaluated. Implementation of the linear network model in the system design analysis of split-type StiFling refrigerator is shown sati;Jfactory. INTRODUCTION Stirling refrigerator operates at a cyclic state and the physical process is thus transient. The system design using conventional heat transfer analysis requires a sophisticated computing equipment and suffers from numerical instability and high computing cost. A linear network model is thus developed in the present study for the system design analysis of split-type Stirling refrigerator (Figure 1). EQUIVALENT NETWORI~ OF STIRLING REFRIGERATOR The linearly-perturbed models of the components can be derived from the governing equations and lin- earization method. Connecting the equivalent circuits of the components according to the process of Stirling refrigerator, we obtain the equivalent network as shownin Figure 2. Only block diagram can be drawn in Figure 2 for the connecting tube and regenerator since the distributed models are derived for them. TRANSFER FUNCTIONS OF STIRLING REFRIGERATOR where Solving the linear dynamics equations, we obtain two transfer functions for Stirling refrigerator: 1 .,oA. (1) co.(s) =- -:~°(s) x.(s) _{IG4(s)+G-~(s)G6(S)]l_G~(s) J ~as(s)+[Ph'm(s)+G2(s)G6(S)]l-as(s) ]} × [I~,,~)_: z,,(s)+i~(s)] spoA,, [ ~ + Z,,(s)/Zo(,) j × R--E-~ (2) as (s) + G7 (s)Zc, (s)tanh[r, (s)L,] Z.. (s) = aT(s) + [as (s)/zo, Cs)] tanh[r, (s) L,]' G,(s) = D,,w (s) + D,,,(s) . R,.,(s); G2(s) = D,,e(s). Rp.~(s); G3(s) = C, (s) + G2(s) . W,.,,(s)~, G,(s) = R~(.)+R,,..(,).Wm.(s); C~(.<) = C~(s).W,.,,(s);Co(s) = a,,.,(s)W,.<,(s); C~(s)~,o(S) = C,(s)~o(s); Wrap = -sVwo/(RTw); W.~. = -spoAd~/(RT~); Z,(s) = R¢~/(sV¢o); [ ~(_s) c0(.)] E,..(s)c2Cs) W~,,(s)G2(s)] _ E,...(s) ~..(s) + - • as(s) = R,,~,~(s) 1-~. i-SG~o(s) ] 1 - as(s) J i : ~ ' spoAp/(R~'~ f(p(s) m,,(s) = 1 + Z,,(s)/Zc(s) " Cryogenics-1994Vo134 ICEC Supplement 207