The Stirling Engine: The Heat Engine

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1 Memoril University of Newfounln Deprtment of Physis n Physil Oenogrphy Physis 2053 Lortory he Stirling Engine: he Het Engine Do not ttempt to operte the engine without supervision. Introution Het engines re generlly esrie in terms of yli proesses in whih gs sors het t high temperture, releses het t lower temperture, n performs n mount of work W. he effiieny of het engine is given y η = W, however, even for n iel (reversile) yle in whih there is no frition, effiieny is limite y the seon lw of thermoynmis. p v W Figure 1: he Crnot Cyle: the reversile yle for n engine operting etween two infinite het ths. Crnot, in the 1820s, showe tht the mximum theoretil effiieny ville from reversile het engine epens only on the temperture hnge in the yle. he Crnot yle is the reversile yle whih opertes etween two onstnt temperture ths. he 1

2 pressure-volume igrm for the yle is shown in Fig (1). Het is sore n relese s the gs is expne or ompresse long the isotherms n. During steps n, the gs is thermlly isolte n hnges temperture s it expns or is ompresse. he effiieny for this yle is η 1 where the equl sign pplies only for reversile (fritionless) yle n the inequlity pplies for rel engine. For ll het engines, the work one y the gs in one yle is given y the re enlose in pressure-volume igrm. he Crnot yle is iffiult to relize in prtie n proues reltively smll mount of work per yle. he Stirling yle uses more thn two therml reservoirs ut hs the sme mximum effiieny s the Crnot yle n, for given pir of tempertures n volume hnge, proues more work per yle. Roert Stirling ( ) took out ptent for his engine in Unlike stem engines, it h no high pressure oiler n ws thus somewht sfer. Its mehnil omplexity limite the prtil size n it ws only use for smll pplitions, primrily in frming, n only until the 1920s when the more powerful internl omustion engines eme more populr. he Stirling engine ontinues to ttrt ttention s more fuel effiient n potentilly lener engine for some pplitions. Currently, the primry pplition of Stirling engines is in refrigertion. he Stirling Cyle he pv igrm for n iel Stirling yle is shown in Fig (2). In our setup two pistons move in the yliner, shown shemtilly in Fig (3); the top region of the yliner is hete y n eletri heter n the lower wlls of the yliner re oole y flowing wter. he volume of the ir is hnge y the movement of the lower piston. he upper piston moves the ir from the hete region of the yliner to the ooler region through entrl hole whih is fille with opper wool n is lle the regenertor. When ir psses from the hete region, through the regenertor, to the oole region, it releses het to the opper wool n is oole. When the gs psses in the other iretion, it retrieves this het n is wrme. his shuttling of het in n out of the regenertor is lele R in Figs 2 n 3. he regenertor n e thought of s thir, finite, therml reservoir. he yle is s follows: 2

3 p R R v Figure 2: he Stirling Cyle operting etween the sme temperture n volume limits s ove. his yle requires more thn two therml reservoirs. []he volume is minimum n most of the gs is in the hete prt of the yliner. he gs is t temperture. [ ] he gs sors het from the heter n expns t onstnt temperture. [] he gs is t its mximum volume n still t temperture. [ ] he upper piston moves up foring the gs through the regenertor n extrting het R to leve the gs t temperture. [] he gs is still t its mximum volume, t temperture, n in ontt with the oole region of the yliner. [ ] he gs is ompresse t onstnt temperture n releses het to the ooling wter. [] he gs is t its minimum volume n still t temperture. [ ] he upper piston moves own n fores the gs through the regenertor where it resors het R n wrms to. he theoretil effiieny of Stirling yle operting etween n is the sme s for the Crnot yle. In rel engine, frition n the trnsfer of het ross finite temperture grients reue the tul effiieny. 3

4 R R Figure 3: Digrm to show the reltive positions of the pistons uring opertion of the Stirling engine. Using the Pso SieneWorkshop Interfe 1. Chek tht the Rotry Motion Sensor is plugge into hnnel 1 (yellow) n hnnel 2 (lk), n the ifferentil pressure sensor is plugge into hnnel. 2. Strt the DtStuio progrm. Clik on Crete Experiment Selet Rotry motion sensor n Pressure Sensor (Differentil). 3. Clik on the Rotry motion sensor ion to open up the Sensor Properties winow. Uner the Generl t, set the smple rte to 200 Hz; uner Mesurement, selet ngulr Position (mesure in egrees sine we nnot mesure volume iretly). Repet for the pressure sensor, seleting pressure in kp. 4

5 4. o isply grph of pressure versus volume: Doule-lik on Grph (on the Displys menu). Selet Pressure s the t soure. set of xes will pper with pressure on the vertil xis n time on the horizontl xis. Clik on the xis lel ime n selet ngulr Position from the rop-own list. Clik Strt to egin olleting t.urn the engine slowly y hn for few turns. Clik on Stop, expn the sle if neessry n esrie the orresponene etween the position of the pistons n the resulting tre. Opertion of the Stirling Engine s Het Engine Otin your rw t s quikly s you n to prevent overheting of the onneting wires ue to high urrents. 1. Strt with oil urrent of out 8. he engine is unlikely to strt t lower urrents. When the engine spee hs stilize, etermine the rte of rottion of the flywheel using the ounter. (Mesuring the numer of rottions in 30 seons is suggeste). Clik on Strt to otin new tre. t the sme time lulte the eletril power supplie to the heter oil. 2. Repet the ove steps, inresing the urrent y out 1 eh time. Do not let the oil urrent exee 13. urn off the Engine y swithing off the heter urrent. nlysis 1. Sve your pressure-volume t for eh run. Give set meningful nme. File - Export. Ensure tht you sve eh set s.sv file (spresheet formt). 2. Import your rw t into spresheet. You nee pirs of (x, y) vlues orresponing to one omplete loop only s shown in Fig 4. Remove exess points. Note tht the ngulr Position xis represents the volume hnge tht ours insie the yliner so tht the istne etween mximum n minimum vlues on the horizontl xis of the grph orrespons to volume hnge of 150 m 3. 5

6 Pressure (kp) Series ngulr position Figure 4: ypil output for one omplete yle from Stirling Engine experiment 3. he work one y the engine is otine from the re of eh loop. It n e shown tht the re of polygon with n verties n e foun from the Guss-Green formul, n i=1 (y i + y i+1 ) (x i x i+1 ) 2 he urve nees to e single loop tht oesn t interset itself. he first n lst points must e the sme. If neessry opy the first point to the en of the t list. 4. Now use the spresheet to lulte the re of the loop n the work one y the gs per yle. Clulte lso the power output n, y ompring with the eletril power supplie, lulte the effiieny of the engine. 5. Summrize your results y plotting effiieny versus pplie urrent, n isuss how your results emonstrte the preitions of the Seon Lw. How muh work is one in overoming frition n other imperfetions in the Engine? Referene: C. G. Deon, R. Gouling, C. Hriss n. e Young, Demonstrtion Experiments with Stirling Engine, Physis Eution 29, (1994) 6

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