, légèrement inférieure à celle prévue ce qui, tel quel, modifie l'équilibre mécanique de la partie Stirling à piston libre. Mais il est très facile de réduire légèrement la valeur de la résistance de façon à

A. J. Organ, Stirling cycle engines -inner workings and design. 1 ère Edition, vol.296, pp.978-1118818435, 2014.

G. Walker, , vol.554, pp.978-0198562092, 1980.

T. Finkelstein and A. J. Organ, , pp.287-978, 2001.

G. Walker and J. R. Senft, Free piston Stirling engines, Lecture notes in engineering, vol.268, pp.978-3540154952, 1985.

I. Kolin, Historische Stirlingmotoren : 1815 -1990. Edition Oberursel : Schmidt, vol.16, 1991.

B. Kongtragool and S. Wongwises, A review of solar-powered stirling engines and low temperature differential stirling engines, Renewable and Sustainable Energy Reviews, vol.7, pp.131-154, 2003.

F. Lanzetta, J. Boucher, and P. Nika, Journée SFT : Machines thermiques exotiques, 2004.

J. E. Cairelli, L. G. Thieme, and R. J. Walter, Initial test results with a single-cylinder rhombic drive Stirling engine, vol.42, 1978.

L. G. Thieme and R. C. Tew, Baseline performance of the GPU 3 Stirling engine. NASA-LRC. TM-79038, vol.13, 1978.

L. G. Thieme, High-power baseline and motoring test results for the GPU-3 Stirling engine. NASA-LRC. TM-82646, vol.41, 1981.

J. Schreiber, Test Results and description of a 1 kW free-piston Stirling engine with a dashpot load, NASA-LRC, vol.24, 1983.

J. Schreiber, Testing and performance characteristics of a 1 kW free-piston Stirling engine. NASA-LRC. TM-82999, vol.50, 1983.

R. C. Tew, Comparaison of free-piston Stirling engine model predictions with RE1000 engine test data. NASA-LRC. TM-83650, vol.28, 1984.

A. Mathieu, Contribution à la conception et à l'optimisation thermodynamique d'une microcentrale solaire thermo-électrique, 2012.

D. M. Berchowitz, M. Richter, and D. Shade, , 1987.

, Inc. 22nd Intersociety Energy Conversion Engineering Conference, pp.1834-1840

D. Gedeon and J. G. Wood, Oscillating flow regenerator test rig : Hardware and theory with derived correlations for screens and felts, vol.50, 1996.

R. Gheith, Etude expérimentale et théorique des moteurs Stirling à apport de chaleur externe : application aux machines de types Beta et Gamma, 2011.

H. Lemrani and P. Stouffs, Dynamic simulation of kinematics Stirling engines applied to power control, 1994.

G. Benvenuto, F. De-monte, and F. Farina, Dynamic Behaviour prediction of free piston Stirling engines, Energy Conversion Engineering Conference. Proceedings of the 25th Intersociety, pp.346-351, 1990.

W. R. Martini, Stirling engine design Manual. 2 nd Edition, NASA-LRC -CR 168088, vol.410, 1983.

D. Sauzade, G. Imbert, and J. Mollard, The supporting technologies and sea trials of a long range autonomous civilian submarine. Marine, Technology Society Journal, vol.25, pp.3-13, 1991.

C. D. West, A Fluidyne Stirling engine. Harwell university, report no, 1981.

D. G. Thombare and S. K. Verma, Technological development in the Stirling cycle engines, Renewable & Sustainable Energy Reviews, vol.12, pp.1-38, 2008.

I. Urieli and D. M. Berchowitz, Stirling cycle engine analyses. A. Hilger, vol.256, 1984.

I. Urieli and C. J. Rallis, , p.18, 1975.

G. Popescu, C. Radcenco, M. Costea, and M. Feidt, Optimisation thermodynamique en temps fini du moteur de Stirling endo-et exo-irréversible, Rev. Génie Thermique, pp.656-661, 1996.

F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, American Journal of Physics, vol.43, pp.22-24, 1975.

D. A. Blank, Universal power optimized work for reciprocating internally reversible Stirling-like heat engine cycles with regeneration and linear external heat transfer, Journal of Applied Physics, vol.84, pp.2385-2392, 1998.

S. C. Kaushik and S. Kumar, Finite time thermodynamic evaluation of irreversible Ericsson and Stirling heat engines, Energy Conversion & Management, vol.42, pp.295-312, 2001.

M. Costea and M. Feidt, The effect of the overall heat transfer coefficient variation on the optimal distribution of the heat transfer surface conductance or area in a Stirling engine, Energy Conversion & Management, vol.39, pp.1753-1761, 1998.

S. K. Tyagi, S. C. Kaushik, and R. Salhotra, Ecological optimization and performance study of irreversible Stirling and Ericsson heat engines, Journal of Physics D : Applied Physics, vol.35, pp.2668-2675, 2002.

M. H. Ahmadi, A. H. Mohammadi, and S. M. Pourkiaei, Optimisation of the thermodynamic performance of the Stirling engine, International Journal of Ambient Energy, 2014.

N. C. Chen, F. P. Griffin, and C. D. West, Linear harmonic analysis of Stirling engine thermodynamics. Oak Ridge National Laboratory / CON-155, vol.134, 1984.

N. C. Chen and F. P. Griffin, Linear harmonic analyses of free-piston Stirling engines. Oak Ridge National Laboratory / CON-172, vol.106, 1986.

P. A. Rios, An approximate solution to the shuttle heat-transfer losses in a reciprocating machine, Journal of Engineering for Power, pp.177-182, 1971.

T. S. Zhao and P. Cheng, Heat transfer in oscillatory flows, Annual Review of Heat Transfer, vol.9, pp.359-420, 1998.

S. Uchida, Pulsating viscous flow superposed on the steady laminar motion, ZAMP, vol.17, pp.403-422, 1956.

D. Gedeon, Mean parameter modeling of Oscillating flow, Journal of Heat Transfer, vol.108, pp.513-518, 1986.

P. Nika, Y. Bailly, and F. Lanzetta, Transferts thermiques en écoulements oscillants laminaires incompressibles, International Journal of Refrigeration, vol.28, pp.353-367, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00325190

N. Kwanwoo and J. Sangkwon, Experimental study on the regenerator under actual operating conditions, Advances in Cryogenic Engineering, vol.47, pp.977-984, 2002.

W. M. Kays and K. L. London, Compact heat exchangers. 3 nd Edition, vol.352, 1998.

Q. Q. Shen and Y. L. Ju, A new correlation of friction factor for oscillating flow regenerator operating at high frequencies, Advances in Cryogenic Engineering, vol.53, pp.267-274, 2008.

H. Miyabe, S. Takahashi, and K. Hamaguchi, An approach to the design of Stirling engine regenerator matrix using packs of wire gauzes, Proc. IECEC, vol.17, pp.1983-1844, 1982.

P. H. Chen, Z. C. Chang, and B. J. Huang, Effect of oversize in wire-creen matrix to the matrix holding tube on regenerator thermal performance, Cryogenics, vol.36, issue.5, pp.365-372, 1996.

I. Garaway and G. Grossman, Studies in high frequency oscillating compressible flow for application in a micro regenerative cryocooler, Advances in Cryogenic Engineering, vol.51, pp.1588-1595, 2006.

T. S. Zhao and P. Cheng, Oscillatory pressure drops through a woven-screen packed column subjected to a cyclic flow, Cryogenics, vol.36, pp.333-341, 1996.

C. Sungryel, N. Kwanwoo, and J. Sangkwon, Investigation on the pressure drop characteristics of cryocooler regenerators under oscillating flow and pulsating pressure conditions, Cruogenics, vol.44, pp.203-210, 2004.

M. Tanaka, I. Yamashita, and F. Chisaka, Flow and heat transfer characteristics of the Stirling engine regenerator in an oscillating flow, Japanese Society of Mechanical Engineering JSME, vol.33, issue.2, pp.283-289, 1990.

T. S. Zhao and P. Cheng, Experimental studies on the onset of turbulence and frictional losses in an oscillatory turbulent pipe flow, Journal of Heat and Fluid Flow, vol.17, pp.356-362, 1996.

H. Snyman, T. M. Harms, and J. M. Strauss, Design Analysis methods for Stirling engines, Journal of Energy in Southern Africa, vol.19, pp.4-19, 2008.

W. Arias, H. I. Velasquez, and D. Florez, Thermodynamic analysis, performance numerical simulation and losses analysis of a low cost Stirling engine V-Type, and its impact on social development in remote areas, ECOS, pp.3767-3778, 2011.

M. Abbas, N. Said, and B. Boumeddane, Optimisation d'un moteur Stirling de type gamma, 2010.

M. Abbas, N. Said, and B. Boumeddane, Thermal analysis of a Gamma type Stirling engine in non-ideal conditions, Revue des Energies Renouvelables, vol.11, pp.503-514, 2008.

H. Jiale, L. Mianli, and J. Tao, A comprehensive empirical correlation for finned heat exchangers with parallel plates working in oscillating flow, MDPI : Applied Science, p.117, 2017.

P. D. Richardson, Effects of sound and vibration on heat transfer, Applied Mechanics Review, vol.20, pp.201-217, 1967.

C. Yanyan, L. Ercang, and D. Wei, Heat transfer characteristics of oscillating flow regenerator filled with circular tubes or parallel plates, Cryogenics, vol.47, pp.40-48, 2007.

P. Nika, Y. Bailly, and F. Guermeur, Thermoacoustics and related oscillatory heat and fluid flows in micro heat exchangers, Journal Heat Mass Transfer, vol.18, pp.3773-3792, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00325184

P. Nika, Y. Bailly, and F. Lanzetta, Particularites des transferts thermiques en écoulements alternés à vitesse moyenne nulle. Termotechnica, vol.7, p.p, 2004.

P. Nika, Y. Bailly, and F. Lanzetta, Transfert thermiques en écoulement oscillants laminaires incompressibles, International Journal of Refrigeration, vol.28, pp.353-367, 2004.

T. Zhao and P. Cheng, Oscillatory heat transfer in a pipe subjected to a laminar reciprocating flow, ASME Journal of Heat Transfer, vol.118, pp.592-598, 1996.

E. C. Nsofor, S. Celik, and X. D. Wang, Experiment study on the heat transfer at the exchanger of the thermoacoustic refrigerating system, Applied Thermal Energy, vol.27, pp.2435-2442, 2007.

W. Kamsanam, X. N. Mao, and A. J. Jaworski, Thermal performance of finned tube thermoacoustic heat exchangers in oscillatory flow conditions, Journal of Thermal Science, vol.101, pp.169-180, 2016.

X. Tang and P. Cheng, Correlations of the cycle averaged Nusselt number in a periodically reversing pipe flow, International Communications in Heat and Mass Transfer, vol.20, pp.161-172, 1993.

A. Piccolo and G. Pistone, Estimation of heat transfer coefficient in oscillating flows : The thermoacoustic case, International Journal of Heat and Mass Transfer, vol.49, pp.1631-1642, 2006.

K. Tang, J. Yu, and Y. P. Wang, Heat transfer of laminar oscillating flow in finned heat exchanger of pulse tube refrigerator, International Journal of Heat and Mass Transfer, vol.70, pp.811-818, 2014.

G. Xiao, C. Chen, and B. Shi, Experimental study on heat transfer of oscillating flow of a tubular Stirling engine heater, International Journal of Heat and Mass Transfer, vol.71, pp.1-7, 2014.

E. C. Nsofor, S. Celik, and X. Wang, Experimental study on the heat transfer at the heat exchanger of the thermoacoustic refrigerating system, Applied Thermal Engineering, vol.27, pp.2435-2442, 2007.

C. G. Scheck, Thermal hysteresis loss in gas springs. These de doctorat to the faculty of the college of engineering and technology, 1988.

S. Begot, G. Layes, and F. , Modèle pour conception/ optimisation d'un moteur Stirling à pistons libres « mécaniques, p.6

E. D. Rogdakis, N. A. Bormpilas, and I. K. Koniakos, A thermodynamic study for the optimization of stable operation of free piston Stirling engines, Energy Conversion & Management, vol.45, pp.575-593, 2004.

J. Boucher, P. Nika, and F. Lanzetta, Modélisation thermomécanique d'un moteur Stirling à pistons libres. VIIème Colloque interuniversitaire Franco-Québécois sur la thermique des systèmes, 2005.

J. Boucher, P. Nika, and F. Lanzetta, Optimization of a dual free piston Stirling engine, Applied thermal Engineering, vol.27, pp.802-811, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00140568

T. T. Dang, Optimisation de l'ensemble convertisseur-générateur-commande intégré à un système de micro-cogénération thermo-mécano-électrique, 2013.

F. Formosa and G. Despesse, Analytical model for Stirling cycle machine design, Energy Conversion and Management, vol.51, pp.1855-1863, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00633043

J. Bert, Contribution à l'étude de la valorisation des rejets thermiques. Etudes et optimisation de moteurs Stirling, 2012.

J. Chen, Z. Yan, G. Lin, and &. B. Andersen, On the Curzon-Ahlborn efficiency and its connection with the efficiencies of real heat engines, Energy Conversion and Management, vol.42, pp.173-181, 2001.

F. Nepveu, Production décentralisée d'électricité et de chaleur par système Parabole/Stirling : Application au système EURODISH, 2008.

S. Harmim, Etude analytique de machines synchrones à aimants permanents, 1993.
URL : https://hal.archives-ouvertes.fr/tel-02007123

P. Ragot, Modélisation analytique multiphysique pour la conception optimale de moteurs synchrones à aimants permanents, 2008.

F. W. Carter, Air-gap Induction, Electrical World and Engineer, vol.38, pp.884-888, 1901.

B. Heller and V. Hamata, Harmonic field effects in induction machines, 1977.

M. B. Ibrahim, M. Wang, and D. Gedeon, Experimental investigation of oscillatory flow pressure and pressure drop through complex geometries. 2 nd International Energy Conversion Engineering Conference, 2004.

R. Pendyala, S. Jayanti, and A. R. Balakrishnan, Flow and pressure drop fluctuations in a vertical tube subject to low frequency oscillations, Nuclear Engineering and Design, vol.238, pp.178-187, 2007.

F. A. Saat and A. J. Jaworski, Friction factor correlation for regenerator working in a travelling wave thermoacoustic system, Applied Science, vol.7, issue.3, 2017.

M. S. Kahaleras, F. Lanzetta, G. Layes, and P. Nika, Caractérisation expérimentale d'un régénérateur en fonctionnement dynamique

P. Nika, F. Lanzetta, J. Boucher, E. Gavignet, and J. E. Raktoniaina, Aspects dynamiques et thermiques de l'écoulement oscillant dans la matrice poreuse d'un régénérateur de machine Stirling, Congrès Français de Thermique, pp.825-830, 2004.

Y. Ju, Y. Jiang, and Y. Zhou, Experimental study of the oscillating flow characteristics for a regenerator in a pulse tube cryocooler, Cryogénics, elsevier, vol.38, pp.649-656, 1998.

T. S. Zhao and P. Cheng, Experimental studies on the onset of turbulence and frictional losses in an oscillatory turbulent pipe flow, International Journal of Heat and Fluid flow, vol.12, pp.356-362, 1995.

P. Bouvier, P. Stouffs, and J. Bardon, Experimental study of heat transfer in oscillating flow, International Journal of Heat and Fluid flow, vol.48, pp.2473-2482, 2005.

Z. Yu, X. Mao, and A. J. Jaworski, Heat transfer in an oscillatory gas flow inside a parallel-plate channel with imposed axial temperature gradient, International Journal of Heat and Mass Transfer, vol.77, pp.1023-1032, 2014.

J. Batina, R. Creff, and Y. Lecointe, Résultats numériques relatifs aux transferts thermiques convectifs instationnaires en écoulement compressible pulsé laminaire et turbulent. Revue générale de Thermique, vol.35, pp.580-591, 1996.

X. Wang and N. Zhang, Numerical analysis of heat transfer in pulsating turbulent flow in a pipe, International Journal of Heat and Mass Transfer, vol.48, pp.3957-3970, 2005.

H. N. Hemida, M. N. Sabry, A. Abdel-rahim, and H. Mansour, Theoretical analysis of heat transfer in laminar pulsating flow, International Journal of Heat and Mass Transfer, vol.45, pp.1767-1780, 2002.

M. J. Cheadle, G. F. Nellis, and S. A. Klein, Regenerator friction factor and Nusslet number information derived from CFD Analysis. International Cryocooler Conference, pp.397-404, 2011.

B. Thomas and D. Pittman, Update on the evaluation of different correlations for the flow friction factor and heat transfer of Stirling engine regenerators, American Institute of Aeronautics & Astronautics, pp.76-84, 2000.

F. De-monte, G. Galli, and F. Marcotullio, An analytical oscillating flow thermal analysis of the heat exchangers and regnerator in Stirling machines, 1996.

S. C. Costa, M. Tutar, I. Barreno, H. Barrutia, and J. I. Prieto, Experimental and numerical flow investigation of Stirling engine regenerator, Energy, vol.72, pp.800-812, 2014.

A. Kardas, On a problem in thetheory of the unidirectional regenerator, International Journal of Heat and Mass Transfer, vol.9, pp.567-579, 1965.

D. C. Swanepoel and D. G. Kröger, Rotary regenerator design theory and optimisation, R&D Journal, vol.12, issue.3, pp.90-97, 1996.

A. J. Organ, Transient thermal performance of the Stirling engine wire regenerator, pp.53-72, 1994.

G. W. Swift and W. C. Ward, Simple harmonic analysis of regenerators, Journal of Thermophysics and Heat Transfer, vol.10, issue.4, pp.652-662, 1996.

H. E. Hassani, N. Boutammachte, J. Knorr, and L. E. Hannaoui, Study of a low temperature Stirling engine driven by a rhombic drive mechanism, International Journal of Energy and Environmental Engineering, vol.4, 2013.

B. Kongtragool and S. Wongwises, Thermodynamic analysis of a Stirling engine including dead volumes of hot space, cold space and regenerator, vol.31, pp.345-359, 2006.

P. Puech and V. Tishkova, Thermodynamic analysis of a Stirling engine including regenerator dead volume, Renewable Energy, elsevier, vol.36, pp.872-878, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01895327

L. Grosu and P. Rochelle, Application de la méthode de Schmidt avec régénération imparfaite aux 3 types de moteur Stirling

N. Parlak, A. Wagner, M. Elsner, and H. S. Soyhan, Thermodynamic analysis of a gamma type Stirling engine in non-ideal adiabatic condition, vol.34, pp.266-273, 2008.

M. Abbas, N. Said, and B. Boumeddane, Optimisation d'un moteur Stirling de type Gamma, Revue des Energies Renouvelables, vol.13, pp.1-12, 2010.

Y. Timouni, I. Tlili, and S. B. Nasrallah, Performance optimization of Stirling engines, Renewable Energy, vol.33, pp.2134-2144, 2008.

F. Wu, L. Chen, C. Wu, and F. Sun, Optimum performance of irreversible Stirling engine with imperfect regeneration, Energy Conversion Management, vol.39, issue.8, pp.727-732, 1998.

S. M. Geng, Calibration and Comparison of the NASA Lewis Free-Pisston Stirling engine model predictions with RE-1000 Test data, vol.23, 1987.

R. C. Tew, Progress of Stirling cycle analysis and loss mechanism characterization. NASA-LRC. TM-88891, vol.19, 1986.

L. B. Gordon, Loss Terms in free-piston Stirling. NASA-LRC. CR-69259, vol.17, 1992.

J. A. Riofrio, K. Al-dakkan, M. E. Hofacker, and E. J. Barth, Control-based deisgn of freepiston Stirling engines, pp.1533-1538, 2008.

H. Karabulut, Dynamic analysis of a free piston Stirling engine working with closed and open thermodynamic cycles, vol.36, pp.1704-1709, 2011.

B. Nedjar, Modélisation basée sur la méthode des réseaux de perméances en vue de l'optimisation de machines synchrones à simple et à double excitation, 2012.

D. L. Trumper, Design and Analyses Framework for Linear Permanent-Magnet Machines, Institute of Electrical and Electronics Engineers, vol.32, issue.2, pp.371-379, 1996.

Q. Gu and H. Gao, Effect of slotting in PM electrical machines, Electrical Machines Power System, vol.11, issue.2, pp.376-380, 1986.

Q. Gu and H. Gao, The frigging effect in PM electric machines, Electrical Machines Power System, vol.11, issue.2, pp.159-169, 1986.

J. Wang, G. W. Jewell, and D. Howe, A general framework for the analysis and design of tubular linear permanent magnet machines, Institue of Electrical and Electronics Engineers, vol.35, issue.3, 1999.

T. T. Dang, P. François, L. Prévond, and H. B. Ahmed, Theoretical and experimental results of tubular linear induction generator for Stirling cogenerator System, XIX International Conference on Electrical Machines. RD-015407, 2010.

P. Francois, I. G. Burrel, H. B. Ahmed, L. Prévond, and B. Multon, 3D analytical model for a tubular linear induction generator in a Stirling cogeneration system, Institue of Electrical and Electronics Engineers, p.16195, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00676232

S. A. Evans, Design and optimization of a permanent magnet linear reluctance motor for reciprocating electromechanical systems, 1996.

, Modélisation des actionneurs électromagnétiques par réseaux de réluctances. Création d'un outil métier dédié au pré-dimensionnement par optimisation, 2006.

T. P. Do, Simulation dynamique des actionneur et capteurs électromagnétiques par réseaux de réluctances : modèles, méthodes et outils, 2010.

P. Enciu, Dérivation automatique pour le calcul des sensibilités appliqué au dimensionnement en génie électrique, 2009.

S. Bégot, G. Layes, F. Lanzetta, and P. Nika, Stability analysis of free piston Stirling engines, The European Physical Journal -Applied Physics, pp.1-16, 2013.

F. Nepveu, Production décentralisée d'électricité et de chaleur par système Parabole/Stirling : Application au système EURODISH, 2008.

B. Andlauer, Optimisation systémique de micro-cogénérateurs intégrés au batiment, vol.2, 2014.

I. Urieli, A computer simulation of Stirling cycle machines. Thesis submitted to the faculty of Engineering, 1977.

S. Bonnet, Moteurs thermiques à apport de chaleur externe : étude d'un moteur Stirling et d'un moteur Ericsson, 2006.

D. Gedeon, Sage : Object Oriented Software for Stirling Machine Design, pp.1902-1907, 1994.

D. Haywood, Investigation of Stirling-type Heat-pump and Refrigerator Systems using Air as the Refrigerant. These submitted for the Degree of Doctor of Philosophy, Mechanical Engineering, 2004.

B. Hoegel, Thermodynamics-Based Design of Stirling engines for Low-Temperature Heat Source. These submitted for the Degree of Doctor of Philosophy, Mechanical Engineering, 2014.

D. Gedeon, Sage user's guide, Gedeon Asociate, 2010.

R. Stirling--wikipédia and . Disponible,

. Tout, S. Le-moteur, and . Disponible,

, Thermodynamics Graphical homepage

, Sage user's guide -Gedeon Associates, 2010.

, Le débit est toujours déterminé par récurrence à partir de la chambre d'expansion

, A partir du débit on détermine la chute de pression avec une liste de coefficients d'irréversibilités k

, Conservation de l'énergie dans l'ensemble des volumes de contrôles

E. Dans and L. Régénérateur, différents : Bien que ce soit difficile de représenter le profil de température dans l'espace et dans le temps en même temps, on peut remarquer le profil exponentiel de la température dans les échangeurs en fonction du sens du fluide

, On se concentre maintenant sur l'échangeur chaud dans lequel le débit est plus important que dans l'échangeur froid. Les effets de la vitesse sur la température du fluide sont donc plus visibles