GRAPHO-ANALYTICAL METHOD FOR CALCULLATING IRREVERSIBILITY PROCESSES WITH FINITE SPEED

Transcription

1 GRAPHO-ANALYTICAL METHOD FOR CALCULLATING IRREVERSIBILITY PROCESSES WITH FINITE SPEED Prof.Eng. Traian FLOREA PhD 1 Lecturer.mat. Ligia-Adriana SPORIȘ PhD 1 Assist.prof.Eng. Corneliu MOROIANU PhD 1 Eng. Traian Vasile FLOREA Ph.D 2 Prof.Eng. Anastase PRUIU PhD 1 1 Mircea cel Batran Naval Academy of Constanta ROMANIA 2 A.P.M. Agigea of Constanta ROMANIA Abstract: A technique for calculating the efficiency and power of Stirling machines is presented. This technique is based on the First Law of Thermodynamics for processes with finite Speed. A new and novel pv/px diagram is presented that shows the effects of pressure losses due to friction finite speed and throttling processes in the regenerator of the Stirling engine. The method used for the analysis of this irreversible cycle with finite speed involves the direct integration of equations based on the First Law for processes with finite speed to directly obtain the cycle efficiency and power. This technique is termed the Direct Method. The results predicted by this analysis were in good agreement with the actual engine performance data of twelve different Stirling engines over a range of output from economy to maximum power. This provides a solid verification that this analysis can accurately predict actual Stirling engine performance particularly with regard to efficiently and output power. Keywords: power finire speed analysis 1. INTRODUCTION A new technique for calculating the efficiency and power of actual operating Stirling machines is presented. This technique is based on the First Law of Thermodynamics for processes with finite speed [1 14] and a new method for determining the imperfect regeneration coefficient [15]. The analytical results depend upon inclusion of two calibration coefficients (y and z) based on experimental data to accurately predict performance. The thermal efficiency is expressed as a product of the Carnot cycle efficiency and second law efficiency [ ] as has been suggested by Bejan [23]: SE CC II irrev T L T L 1 1 TH S TH S 1 CC II irrev T X 1 T L / TH S 3 Pi 1 1 1ln P1 TH S / TL ln II irrevx II irrev Pi with 1 T L / T H S II irrev X 1 (1) 157

2 11/ 3 The pressure losses and their effect on efficiency and power of the engine depend on the piston speed and hence the speed of the engine. The power output of the engine is: Power mrt ln w/ S (2) SE SE H g 2 The speed for maximum power may be determined since the power output is also a function of the engine speed. Therefore the operating speed of a particular Stirling engine can be selected for either maximum economy or for maximum power. Also knowledge of the nature of these losses can be effectively used in engine design. A major loss in Stirling engines is caused by incomplete regeneration. This is expressed by the coefficient of regenerative losses X. An analysis for determining this loss has been made by Petrescu et al. and Florea [15 33]: 1 1 2M e 21 M mgcv g M m X 1 y X 2 1 y 1 TL / TH S R / c T ln II irrev X (3) v X B 1 B M R C R 1 B M e X 2 (4-5) 1 M har S 1 (6-7) m c w g v g P / RT w c T vt 0395 m L g P m m h (8) / Pr 4 / 1 DR b d where y is one of the adjusting coefficients of the method with the value of One objective of this paper is to make a more realistic analysis of the pressure losses through use of a pv/px diagram as will be described below and by Petrescu et al. [14]. Finally the technique for calculating the efficiency and power of Stirling engines is presented and the results predicted by this analysis are compared with performance data taken on twelve actual Stirling engines over a range of operating conditions [ ]. 2. THE METHOD OF DETERMINING THE PERFORMANCE OF THE STIRLING ENGINE Computation of pressure losses work losses efficiency and power for the processes shown on the new pv/px diagrams [14 15] are made using the first law of thermodynamics for processes with finite speed [1-13]. The first law written to specifically include these conditions is:

3 aw b P f Pf thrott du Q Pm i 1 dv c 2Pmi P (9) mi The irreversible work is: aw b P Pf thrott Wirrev Pmi 1 dv (10) c 2Pmi P mi when applied to processes with finite speed as shown on the pv/px diagram. Computing and summing all pressure losses of the Stirling engine cycle presented above the term from eq. (1) becomes [ ]: II irrev Pi w ln 5 N w w 10 w w S L S L 44 II irrev Pi 1 (11) ln ln The heat input during the expansion process is also irreversible due to finite speed. In order to take account of this influence an calibration coefficient z is introduced: Q z mrt ln (12) 34 H g Finally the real power output of the engine eq. (2) becomes: Power zmrt ln w / 2S (13) SEirrev SE H g where the value of z was evaluated at 08 by comparison with available experimental data for twelve Stirling engines [24-28]. 3. DISCUSSIONS The variation of the coefficient of regenerative losses X with the piston speed for several values of the gas average pressure is shown in Fig. 2. It is an example of the results obtained from the sensitivity study [15] for X. It shows an important increase of the regenerative losses with the gas average pressure. Then the results of computations based on this analysis are compared to performance data taken from a number of operating Stirling engines in Figs. 3-5 and Table I. The high degree of correlation between the analytic and the operational data shown in these figures indicate that the analysis is capable of accurately predicting Stirling engine performance under a wide range of conditions. This capability should be of considerable value in Stirling engine design and in predicting the performance of a particular Stirling engine over a range of operating speed

4 Stirling Engine Actual Power [kw] Calculat ed Power [kw] Actual Efficienc y Calculat ed Efficienc y Table I. Comparison between analytical results and actual engine performance data [24-29] NS-03M regime (economy) NS-03M regime 1 (max power) NS-03T regime (economy) NS-03T regime 1 (max power) NS-30A regime (economy) NS-30A regime 1 (max power) NS-30S regime (economy) NS-30S regime 1 (max power) STM V MKII GPU MP1002 CA Free Piston Stirling Engine 200 W W RE Fig.1. The pv/px diagram for description of the Stirling cycle processes 160

5 4. CONCLUSION The objective of this approach was to closely simulate the operation of actual Stirling engines without losing insight to the mechanisms that generate the irreversibilities. Pressure and work losses generated by finite speed of the actual processes were computed as were the power and efficiency of engines. The first law of thermodynamics for processes with finite speed was used to compute the power losses generated by the pressure losses. The analysis presented was applied to specific operating Stirling cycle engines and results were compared to the measured performance of the engines. The strong correlation between the analytical results and actual engine performance data indicates that the Direct Method of using the First Law for Finite Speed is a valid method of analysis for irreversible cycles. Fig. 2. Coefficient of regenerative losses versus the piston speed for several values of the average pressure of the working gas (D C = 60 mm b/d = 1.5 τ = 2 N = 700) Fig. 3. Comparison of the analysis results with actual performance data for the NS-30S Stirling engine 161

6 Fig. 4. Comparison of the analysis results Fig. 5. Comparison of the analysis with actual performance data for the results with actual performance Stirling engine data for the Free Piston Stirling engine REFERENCES: [1] Stoicescu L. Petrescu S. 1964a The First Law of Thermodynamics for Processes with Finite Speed in Closed Systems (German language) Bulletin of Polytechnic Institute of Bucharest Vol. XXVI No. 5; [2] Stoicescu L. Petrescu S. 1964b Thermodynamic Processes Developing with Constant Finite Speed (German language) Bulletin of Polytechnic Institute of Bucharest Vol. XXVII No. 6; [3] Stoicescu L. Petrescu S. 1965a Thermodynamic Processes Developing with Variable Finite Speed (German language) Bulletin of Polytechnic Institute of Bucharest Vol. XXVII No. 1; [4] Stoicescu L. Petrescu S. 1965b Experimental Verification of the Processes with Finite Speed (German language) Bulletin of Polytechnic Institute of Bucharest Vol. XXVII No. 2; [5] Stoicescu L. Petrescu S. 1965c Cycles with Finite Speed (German language) Bulletin of Polytechnic Institute of Bucharest Vol. XXVII No. 2; [6] Petrescu S. 1969a Contribution to the Study of Interactions and Processes of nonequilibrium in Thermal Machines Ph.D. Thesis Polytechnic Institute of Bucharest Romania; [7] Petrescu S. 1969b The Determination of the Expression of the Work in a Process with Finite Speed using the Phenomenological Thermodynamics of Reversible Processes Studii şi Cercetări de Energetică şi electrotehnică Romanian Academy Vol. 19 No. 2; 162

7 [8] Petrescu S Kinetically Considerations Regarding the Pressure on a Piston Moving with Finite Speed Studii şi Cercetări de Energetică şi Electrotehnică Romanian Academy Vol. 1 No. 11; [9] Petrescu S Experimental Study of the Gas-Piston Interaction with Finite Speed in the Case of an Open System Studii şi cercetări de Mecanică Aplicată Romanian Academy Vol. 31 No. 5; [10] Petrescu S Lectures on New Sources of Energy Helsinki University of Technology Finland; [11] Petrescu S. Stanescu G. Iordache R. Dobrovicescu A The First Law of Thermodynamics for Closed Systems Considering the Irreversibility Generated by the Friction Piston-Cylinder the Throttling of the Working Medium and Finite Speed of the Mechanical Interaction Proc. of the Inter. Conf. on Efficiency Costs Optimization and Simulation of Energy Systems ECOS 92 Zaragoza Spain edited by A. Valero and G. Tsatsaronis ASME pp ; [12] Petrescu S. Harman C. Florea T The Connection between the First and Second Law of Thermodynamics for Processes with Finite Speed. A Direct Method for Approaching and Optimization of Irreversible Processes Journal of The Heat Transfer Society of Japan Vol. 33 No. 128; [13] Petrescu S. Zaiser J. Valeria Petrescu Florea T Lectures on Advanced Energy Conversion Bucknell University Lewisburg PA USA; [14] Petrescu S. Harman Florea T. C. Costea M. 2000a Determination of the Pressure Losses in a Stirling Cycle through Use of a PV/Px Diagram paper accepted to the Inter. Conf. on Efficiency Costs Optimization and Simulation of Energy Systems ECOS 2000 Entschede Netherlands July 5-7; [15] Petrescu S. Harman C. Florea T. Costea M. 2000b A Method for Calculating the Coefficient for the Regenerative Losses in Stirling Machines Proc. of 5 th European Stirling Forum 2000 Ösnabruck Germany February 22-24; [16] Petrescu S. Stanescu G A Direct Method of the Study of Irreversible Processes which are Developing with Finite Speed in Closed Systems (Romanian Language) Termotehnica No. 1 Editura Tehnica Bucharest; [17] Petrescu S. Stanescu G. Florea T. Costea M. 1993a The study of the optimisation of the Carnot cycle which develops with finite speed Proc. of the Inter. Conf. on Energy Systems and Ecology Cracow Poland edited by J. Szargut Z. Kolenda G. Tsatsaronis anda. Ziebik pp ; [18] Petrescu S. Stanescu G. Costea M. Florea T. 1993b A Direct Method for the Optimization of Irreversible Cycles using a New Expression for the First Law of Thermodynamics for Processes with Finite Speed Proc. of the 1 st Conference on Energy ITEC 93 Marrakesh Morocco pp ; [19] Petrescu S. Petrescu V. Florea T. Stanescu G. Costea M. 1993c A Comparison between Optimization of Thermal Machines and Fuel Cells based on New Expression of the First Law of Thermodynamics for Processes with Finite Speed Proc. of the 1 st Conference on Energy ITEC 93 Marrakesh Morocco pp ; 163

8 [20] Petrescu S. Harman C. Bejan A. Florea T The Carnot Cycle with External and Internal Irreversibility Proc. of FLOWERS 94 Symposium Energy for The 21 st Century: Conversion Utilization and Enviromental Quality Florence Italy; [21] Petrescu S. Harman C Stirling Cycle Optimization Including the Effects of Finite Speed Operation Proc. of the Inter. Conf. on Efficiency Costs Optimization Simulation and Enviromental Aspects of Energy Systems ECOS 96 Stockolm Sweden edited by P. Alvfors L. Edensten G. Svedberg and J. Yan pp ; [22] Costea M. Petrescu S. Harman C. Florea T The Effect of Irreversibility s on Solar Stirling Engine Cycle Performance Proc. of the Inter. Conf. on Efficiency Costs Optimization Simulation and Environmental Aspects of Energy Systems ECOS 98 Nancy France edited by A. Bejan M. Feidt M.J. Moran and G. Tsatsaronis Nancy France p ; [23] Bejan A Advanced Engineering Thermodynamics Wiley New York; [24] Fujii I From Solar Energy to Mechanical Power Harwood Academic Publishers New York; [25] Allen D.I. Tomazic W.A ot Piston Ring Tests NASA TM ; [26] Geng S.M Calibration and Comparison of the NASA Lewis Free-Piston Stirling Engine Model Prediction with RE-1000 Test Data NASA TM-89853; [27] Stine W.B. Diver R.B A Compendium of Solar Dish / Stirling Technology Sandia Laboratories Report; [28] Farell R.A. et al Automotive Stirling Engine Development Program NASA CR ; [29] Organ J.A Thermodynamics and Gas Dynamics of Stirling Cycle Machine Cambridge University Press Cambridge; [30] Walker G Cry coolers Part 1: Fundamentals Plenum Press New York; [31] Costea M. Petrescu S. Harman C The Effect of Irreversibility on Solar Stirling Engines Cycle Performance Energy Conversion & Management Vol. 40 pp ; [32] Costea M Improvement of heat exchangers performance in view of the thermodynamic optimisation of Stirling machine; Unsteady-state heat transfer in porous media Ph.D. Thesis P. U. Bucharest & U.H.P. Nancy 1; [33] Florea T Grapho-Analytical Method for the Study of Irreversible Processes in Stirling Engines Ph.D. Thesis Polytechnic University of Bucharest; 164