A Study on Design Parameters of Stirling Engines for Buildings 1

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1 ESL-IC ICEBO006, Shenzhen, China A Study on Deign arameter of Stirling Engine for Building Guozhong Ding Suyi Huang Chunping Zhang Xinghua Hu Xiaoqing Zhang Fangzhong Guo School of Energy and ower Engineering,Huazhong Univerity of Science and Technology,Wuhan,Hubei,430074,.R.China Ding_guo_zhong@63.com Abtract:One of the mot promiing project in the application of combined heat and power(ch) lie in energy production for building. Stirling engine are very applicable to reidential building, epecially becaue of the higher electricity/heat efficiency. A literature review on tirling engine i firt provided and a number of reearch work on the development and application of Stirling engine are dicued. Then according to building energy conumption, relevant output of power denity of Stirling engine i etimated. From the reult, the deign parameter of Stirling engine are derived and the temperature difference on frequency and performance of Stirling engine i alo dicued. Key word: Stirling engine; frequency band; building. INTRODUCTION Solar energy i one of the more attractive renewable energy ource that can be ued a an input energy ource for heat engine. Green building are a key iue for all over the world. In fact, any heat energy ource can be ued with the Stirling engine. The olar radiation can be focued onto the diplacer hot-end of the Stirling engine, thereby creating a olar-powered prime mover. The direct converion of olar power into mechanical power reduce both the cot and complexity of the prime mover. In theory, the principal advantage of Stirling engine are their ue of an external heat ource and their high efficiency. Stirling engine are able to ue olar energy that i a cheap ource of energy. Since during two-third of the day, olar energy i not available, olar/fuel hybrid are needed. For olar electric generation in the range of -00Kw, the Stirling engine wa conidered to be the cheapet []. Stirling engine are very applicable to reidential building, epecially becaue the higher electricity/heat efficiency. Commercially, mall-cale fuel cell are in a development phae, whilt a mall number of tirling engine unit have been deployed on a demontration bai and developer are preparing to manufacture the product on a larger cale. Electrical efficiency i roughly 5% at the deign point, and decreae a power output decreae. The objective of thi article i to provide a baic review of exiting literature on Stirling engine and low temperature differential Stirling engine technology. According to building energy conume, relevant output of power denity of Stirling engine i etimated. From the reult, the deign parameter of Stirling engine i derived and the temperature difference on frequency and performance of Stirling engine i alo dicued. Dih-Stirling ytem track the un and focu olar energy into a cavity receiver where it i aborbed and tranferred to a heat engine/generator. Figure i a repreentation of a Dih Stirling Sytem with the major ytem component, the dih, the power converion unit(cu), etc. identified. Stirling engine are preferred for thee ytem becaue of their high efficiencie (thermal-to-mechanical efficiencie in exce of 40% have been reported), high power denity (40 70 kw/liter for olar engine),and potential for long-term, low-maintenance operation. Dih-Stirling ytem are modular, i.e., each ytem i a elf-contained power generator, allowing their aembly into plant ranging in ize from a few kilowatt to ten of megawatt. Supported by National Natural Science Foundation of China( ) roceeding of the Sixth International Conference for Enhanced Building Operation, Shenzhen, China, November 6-9, 006

2 ESL-IC ICEBO006, Shenzhen, China application.k.bancha and W. Somchai [7] propoed a review of olar-powered Stirling engine and low temperature differential Stiling engine.. CONCETUAL DESIGN AND OWER CALCULATION OF STIRLING ENGINE FOR BUILDINGS Fig. Dih Stirling ytem component In 99, Cummin ower Generation, tarted development of two Dih-Stirling ytem a 7-kW ytem for remote application and a 5-kW ytem for grid-connected power generation [,3]. Cummin wa innovative in it Dih-Stirling ytem, incorporating a lot of advanced technologie into the deign, including a olar concentrator with a polar-axi drive and polymer, tretched-membrane facet, heat-pipe receiver, and free-piton Stirling engine. The heat-pipe receiver tranfer the aborbed olar heat to the engine by evaporating odium and condening it on the tube of the engine heater head. The receiver erve a a thermal buffer between the concentrator and the engine, and becaue it tranfer heat to the engine by condenation, it allow the engine to operate at a high average temperature and efficiency [4,5]. Dih-Stirling ytem have demontrated that they are capable of producing electricity for the grid and for remote power application. Technology development need are for low-cot component and ytem that can operate unattended at very high level of reliability. Current effort are focued on etablihing reliability and, through break-and-repair approache, identifying the component that require improvement, redeign, and replacement. In a parallel approach, advanced component, uch a heat-pipe receiver, control, and optical urface, that promie higher reliability and lower cot are being deigned and teted. low temperature Stirling engine are not a ucceful a their high temperature counterpart.s.abdullah et al [6] propoed a conceptual deign of low temperature differential double-acting Stirling engine for olar. Conceptual Deign Schematic diagram of a gamma-configuration Stirling engine are hown in Fig.. According to the mechanical configuration of Stirling engine, which are claified into the alpha-, beta-, and gamma-configuration, light difference in their p v diagram reult in the cycle net work not being the ame. The Schmidt or Wet formula can be ued to make a calculation of engine haft power. Fig. Schematic diagram of a gamma configuration Stirling engine The Stirling engine need a complete deign analyi,it can be ubdivided into four tage: the analyi of wept volume and dead volume; the analyi of heater and cooler parameter; the analyi of regenerator; and, finally, the optimiation the critical engine parameter.. ower Calculation of Stirling Engine Schmidt [8] howed a mathematically exact expreion for determining the indicated work per cycle of a Stirling engine. The Schmidt formula may be hown in variou form depending on the notation ued. Becaue of it complexity, it take time to verify the calculation [9]. The calculation for gamma configuration Stirling engine i a follow [0] : roceeding of the Sixth International Conference for Enhanced Building Operation, Shenzhen, China, November 6-9, 006

3 ESL-IC ICEBO006, Shenzhen, China k inα Y X W π ( τ) pmaxv D () Y + Y X Y + X Where k / V VD D AD LD V V A L X α + ( τ ) ( τ ) k co k τ 4k τ Y τ k τ T T C H V k V D inuoidal motion compared to the exact olution from Eq. (6). However, it i more popular becaue of it implicity. Beale [] noted that the power output of everal Stirling engine oberved could be calculated approximately from the equation: 0. 05p fv m (5) where i the engine power output in Watt, p m Where W i the indicated work per cycle in N m, p max the maximum preure attained during cycle in N/m, k the wept volume ratio, k the dead pace volume ratio, VD the diplacer wept volume in m 3, V the power piton wept volume in m3, VS the dead pace volume in m 3, AD the diplacer cylinder cro-ection area in m, A the power cylinder cro-ection area in m, LD the diplacer troke in m, L the power piton troke in m, a the phae angle lead of the diplacer over the power piton in degree, and t i the temperature ratio. Becaue it i more convenient to ue the mean or average cycle preure, maximum cycle preure, p m p max, intead of the, the maximum preure under the Schmidt aumption i related to the average cycle preure [9]. It i a follow: p p Y + X Y X max m () Subtituting Eq. () into Eq. () give the impler form of the Schmidt formula for determining the indicated cyclic work of the gamma-configuration Stirling engine: k inα W π ( τ ) pmvd (3) Y + Y X Wet [9] propoed a impler formula to determine indicated work a follow: πpm VDV TH TC W inα VD + 0.5V + V TH + T (4) C Eq. (4) give an error of the indicated work for the mean cycle preure in bar, f the cycle frequency in Hz, and V i diplacement of power piton in cm 3. The Beale formula can be ued for all configuration and for variou ize of Stirling engine. Eq. (4) may be written in a general form a follow: /( p fv ) con tan t (6) m The reulting dimenionle parameter /( p fv ) m i called the Beale number. It i clear that the Beale number i a function of both ource and ink temperature. The olid line in Fig. 6 indicate the relationhip between the Beale number and ource temperature. The upper bound repreent the high efficiency, well-deigned engine with low ink temperature, while the lower bound repreent the moderate efficiency, le well-deigned engine with high ink temperature []. The Beale number correlation wa modified by Walker [3], Wet [4], Thi correlation i ued to determine the Stirling engine haft power output a follow: T T H C Fpm fv (7) TH + TC Eq. (7) i a powerful tool in the firt tep of the deign. Senft [9] and Wet [4] decribed that an F value of may be ued for practical ue. The preure ratio and heat tranfer of the heater and cooler are howed a follow [0] : γ p p ( + δ ) ( δ ) (8) max min πpmveδ inθ Q E πpmve Δinθ (9) + δ roceeding of the Sixth International Conference for Enhanced Building Operation, Shenzhen, China, November 6-9, 006

4 ESL-IC ICEBO006, Shenzhen, China πp V κδ in( θ α) m E Q C (0) Where A + δ ( τ + τκ coα + κ ) B τ + κ + δ A B.3 The Frequency Band Under Different ower Denity of Building F Meillaud [5] gave a evaluation of a building 3MJ/y,,Uually building have m then,the requirement of energy i.47kw~47kw.from Eq.(5),it i howed that the frequency band under different denity of building a Fig.3: peed (N), the maximum preure of the working fluid ( p max ) and the ize of the engine, which i expreed in term of the wept volume. However, the direct effect of the dead volume and wept volume to the engine power hould be detailed. Fig. 4 illutrate the variation of the power a a function of the wept volume, which wa calculated on the dead volume of 500 and 5000cm 3 under the fixed temperature difference of 50. It i hown that the power increae when the wept volume increae. Alo, it i noticeable that the peed increae with the increae in power. Thee two remark imply that the wept volume i proportional to the engine power for everal peed. The variation of the engine power a a function of dead volume i calculated and the reult are hown in Fig.5 for the engine peed of 00 rpm. It i hown that the power decreae when the dead volume increae and decreae with the decreae in wept volume. Fig.3 Relationhip between power and working frequency 3.RESULTS AND DISCUSSION It i obviou from Schmidt-cycle equation that the net cycle power and the thermal load on the heat exchanger are direct linear function of the engine Fig.4 Influence of wept volume on engine power(dead volume of 500cm 3 ) Tab. optimization of frequency band SAIC/STM SB SES WAG(Mod) WAG(Mod) Sytem Sytem Sytem ADDA Sytem Remote Sytem Aperture Dia.(cm) No. of Cylinder 4 4 Diplacement(cc) Operate Speed(rpm) Working Fluid hydrogen helium hydrogen hydrogen hydrogen Ann Efficiency Net 4.50% 5.70% 4.60% 8.90% 8% roceeding of the Sixth International Conference for Enhanced Building Operation, Shenzhen, China, November 6-9, 006

5 ESL-IC ICEBO006, Shenzhen, China Fig.5 Influence of dead volume on engine power(engine peed of 00 rpm). Influence of ome other parameter on Stirling engine i howed a Fig.6. γ Q E Q C W t γ Q E Q C W t toke limit L max (m) Fig.6 Influence of troke of piton on preure ratio γ,expanion heat heat Q C Q E and cycle outpower W,compreion It i een that the troke of piton ha a ignificant influence on the heat tranfer of expanion pace and compreion pace, a optimized troke of piton and correponding wept volume and dead volume are needed. 4 CONCLUSION In thi paper, a number of technical parameter in deigning a Stirling engine have been propoed. Thee relationhip of ome parameter have been etablihed through the ue of the Schmidt analyi and have later been optimied.the tudy can provide a bai of a novel energy production for building by applying Stirling engine. REFERENCES [] Stine WB. Stirling engine. In: Kreith F, editor. The CRC handbook of mechanical engineer. Boca Raton: CRC re; 998. p [] Gallup, D., and Mancini, T.. The Utility-Scale Joint-Venture rogram.roc. of 9th IECEC[C]. Monterey, CA, (ISBN ), 994,pp [3]Bean, J. R., and Diver, R. B.. Technical Statu of the Dih/Stirling Joint Venture rogram. roc. of 30th IECEC[C], Orlando, FL, 995, pp [4] Andraka, C., Diver, R., Adkin, D., Rawlinon, S., Cordeiro,., Dudley, V.,and Mo, T.. Teting of Stirling Engine Solar Reflux Heat-ipe Receiver.roc. of 8th Interociety Energy Converion Conf. (IECEC)[C], Atlanta,GA, (ISBN ), 993, pp [5] Andraka, C., Adkin, D., Mo, T., Cole, H., and Andrea, N.. Felt-Metal-Wick. Heat-ipe Receiver. Solar Engineering roc. of ASME/JSME/JSES Int. Solar Energy Conf.[C], Maui, HI, (ISBN ), 995,pp [6] S.Abdullah et al.deign conideration of low temperature differential double-acting Stirling engine for olar application[j].renewable energy,005,30: [7]Bancha K,Somchai W. A review of olar-powered Stirling engine and low temperature differential Stirling engine[j].renewable and Sutainable energy review,003,7:3-54. [8] Schmidt G. Theorie der Lehmannchen calorichen machine. Zeit[J]. De Vereine deutch Ing 87;5(-):97. [9] Senft JR. Ringbom Stirling engine[m]. New York: Oxford Univerity re, 993. [0] Martini WR. Stirling engine deign manual[m]. nd ed. NASA CR-68088; 983. [] Wet CD. rinciple and application of Stirling engine[m]. New York: Van Notrand Reinhold, 986. [] Walker G. Stirling engine[m]. Oxford: Clarendon re, 980. [3] Walker G. Elementary deign guideline for Stirling engine. In: roceeding of the 4th Interociety Energy Converion Engineerng Conference, aper 79930[C]. Boton: American Chemical Society; roceeding of the Sixth International Conference for Enhanced Building Operation, Shenzhen, China, November 6-9, 006

6 ESL-IC ICEBO006, Shenzhen, China 979. [4] Wet CD. Theoretical bai for the Beale number. In: roceeding of the 6th Interociety Energy Converion Engineering Conference, aper 89787[C]. Atlanta: American Society of Mechanical Engineer; 98. [5] F Meillaud, J Gay. Evaluation of a building uing the emergy method[j]. Solar energy,005,79:04-. roceeding of the Sixth International Conference for Enhanced Building Operation, Shenzhen, China, November 6-9, 006