## THERMAL SCIENCE

International Scientific Journal

### OPTIMAL PATHS OF PISTON MOTION OF IRREVERSIBLE DIESEL CYCLE FOR MINIMUM ENTROPY GENERATION

**ABSTRACT**

A Diesel cycle heat engine with internal and external irreversibility’s of heat transfer and friction, in which the finite rate of combustion is considered and the heat transfer between the working fluid and the environment obeys Newton’s heat transfer law [q≈ Δ(T)], is studied in this paper. Optimal piston motion trajectories for minimizing entropy generation per cycle are derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston motion trajectories for the cases of with piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments, respectively. Numerical examples for optimal configurations are provided, and the results obtained are compared with those obtained when maximizing the work output with Newton’s heat transfer law. The results also show that optimizing the piston motion trajectories could reduce engine entropy generation by more than 20%. This is primarily due to the decrease in entropy generation caused by heat transfer loss on the initial portion of the power stroke.

**KEYWORDS**

PAPER SUBMITTED: 2011-07-20

PAPER REVISED: 2011-09-14

PAPER ACCEPTED: 2011-09-16

**THERMAL SCIENCE** YEAR

**2011**, VOLUME

**15**, ISSUE

**4**, PAGES [975 - 993]

- Curzon, F. L., Ahlborn, B., Efficiency of a Carnot engine at maximum power output, Am. J. Phys., 43(1975), 1, pp. 22-24
- Andresen, B., et al., Thermodynamics for processes in finite time, Acc. Chem. Res., 17(1984), 8, pp. 266-271
- Bejan A., Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes, J. Appl. Phys., 79(1996), 3, pp. 1191-1218
- Berry, R. S., et al., Thermodynamic Optimization of Finite Time Processes, Wiley, Chichester, 1999
- Chen, L., Wu, C., Sun, F., Finite time thermodynamic optimization or entropy generation minimization of energy systems, J. Non-Equilib. Thermodyn., 24(1999), 4, pp. 327-359
- Sieniutycz, S., Hamilton-Jacobi-Bellman framework for optimal control in multistage energy systems, Phys. Rep., 326(2000), 4, pp. 165-285
- Salamon, P., et al., Principles of control thermodynamics, Energy, The Int. J., 26(2001), 3, pp. 307-319
- Hoffman, K. H., et al., Optimal process paths for endoreversible systems, J. Non-Equilib. Thermodyn., 28(2003), 3, pp. 233-268
- Chen, L., Sun, F., Advances in Finite Time Thermodynamics: Analysis and Optimization,: Nova Science, New York, USA, 2004
- hen, L., Finite Time Thermodynamics Analysis of Irreversible Progresses and Cycles (in Chinese), High Education Press, Beijing, 2005
- Sieniutycz, S., Jezowski, J., Energy Optimization in Process Systems, Elsevier, Oxford, UK, 2009
- Feidt, M., Thermodynamics applied to reverse cycle machines, a review, Int. J. Refrig., 33(2010), 7, pp. 1327-1342
- Andresen, B., Current trends in finite-time thermodynamics, Angew. Chem. Int. Edit., 50(2011), 12, pp. 2690-2704
- Radcenco, V., Vasilescu, E. E., Feidt, R., Thermodynamic optimization of direct cycles, Thermotehnica, (2003), 1-2, pp. 26-31
- Mozurkewich, M., Berry, R. S., Finite-time thermodynamics: Engine performance improved by optimized piston motion, Proc. Natl. Acad. Sci. U.S.A., 78(1981), 4, pp. 1986-1988
- Mozurkewich, M., Berry, R. S., Optimal paths for thermodynamic systems: The ideal Otto cycle, J. Appl. Phys., 53(1982), 1, pp. 34-42
- Hoffman, K. H., Berry, R. S., Optimal paths for thermodynamic systems: The ideal Diesel cycle, J. Appl. Phys., 58(1985), 6, pp. 2125-2134
- Blaudeck, P., Hoffman, K. H., Optimization of the power output for the compression and power stroke of the Diesel engine, Proc. Int. Conf. ECOS'95, Volume 2: 754, Istanbul, Turkey, 1995
- Teh, K. Y., Edwards, C. F., Optimizing piston velocity profile for maximum work output from an IC engine, Proc. IMECE2006, IMECE2006-13622, 2006 ASME Int. Mech. Engng. Congress and Exposition, November 5-10, Chicago, Illinois, USA, 2006
- Teh, K. Y., Miller, S. L., Edwards, C. F., Thermodynamic requirements for maximum internal combustion engine cycle efficiency Part 1: Optimal combustion strategy, Int. J. Engine Res., 9(2008), 6, pp. 449-465
- Teh, K. Y., Miller, S. L., Edwards, C. F., Thermodynamic requirements for maximum internal combustion engine cycle efficiency Part 2: Work extraction and reactant preparation strategies, Int. J. Engine Res., 9(2008), 6, pp. 467-481
- Teh, K. Y., Edwards, C. F., An optimal control approach to minimizing entropy generation in an adiabatic internal combustion engine, Trans. ASME J. Dyn. Sys., Meas., Contr., 130(2008), 4, pp. 041008
- Teh, K. Y., Edwards, C. F., An optimal control approach to minimizing entropy generation in an adiabatic IC engine with fixed compression ratio, Proc. IMECE2006, IMECE2006-13581, 2006 ASME Int. Mech. Engng. Congress and Exposition, November 5-10, Chicago, Illinois, USA, 2006
- Ge, Y., Chen, L., Sun, F., Optimal paths of piston motion of irreversible Otto cycle heat engines for minimum entropy generation (in Chinese), Sci. China: Phys., Mech., Astron., 40(2010), 9, pp. 1115-1129
- Band, Y. B., Kafri, O., Salamon, P., Maximum work production from a heated gas in a cylinder with piston, Chem. Phys. Lett., 72(1980), 1, pp. 127-130
- Band, Y. B., Kafri, O., Salamon, P., Finite time thermodynamics: Optimal expansion of a heated working fluid, J. Appl. Phys., 53(1982), 1, pp. 8-28
- Salamon, P., Band, Y. B., Kafri, O., Maximum power from a cycling working fluid, J. Appl. Phys., 53(1982), 1, pp. 197-202
- Aizenbud, B. M., Band, Y. B., Power considerations in the operation of a piston fitted inside a cylinder containing a dynamically heated working fluid, J. Appl. Phys., 52(1981), 6, pp. 3742-3744
- Aizenbud, B. M., Band, Y. B., Kafri, O., Optimization of a model internal combustion engine, J. Appl. Phys., 53(1982), 3, pp. 1277-1282
- Band, Y. B., Kafri, O., Salamon, P., Optimization of a model external combustion engine, J. Appl. Phys., 53(1982), 1, pp. 29-33
- Burzler, J. M., Hoffman, K. H., Optimal piston paths for Diesel engines. Chapter 7 ‘Thermodynamics of energy conversion and transport', Sienuitycz S and De vos A, eds., Springer, New York, 2000
- Burzler, J. M., Performance Optimal for Endoreversible Systems, Ph. D. Thesis, University of Chemnitz, Germany, 2002, pp. 73-88
- Xia, S., Chen, L., Sun, F., Maximum power output of a class of irreversible non-regeneration heat engines with a non-uniform working fluid and linear phenomenological heat transfer law, Sci. China Ser. G: Phys., Mech., Astron., 52(2009), 5, pp. 708-719
- Ge, Y., Chen, L., Sun, F., The optimal path of piston motion of irreversible Otto cycle for minimum entropy generation with radiative heat transfer law, Submitted to J. Energy Inst.
- Chen, L., Sun, F., Wu, C., Optimal expansion of a heated working fluid with phenomenological heat transfer, Energy Convers. Manage., 39(1998), 3/4, pp. 149-156
- Song, H., Chen, L., Sun, F., Optimization of a model external combustion engine with linear phenomenological heat transfer law, J. Energy Inst., 82(2009), 3, pp. 180-183
- Chen, L., et al., Optimization of a model internal combustion engine with linear phenomenological heat transfer law, Int. J. Ambient Energy, 31(2010), 1, pp. 13-22
- Song, H., Chen, L., Sun, F., Optimal expansion of a heated working fluid for maximum work output with generalized radiative heat transfer law, J. Appl. Phys., 102(2007), 9, pp. 94901
- Ma, K., Chen, L., Sun, F., Optimal expansion of a heated gas under Dulong-Petit heat transfer law (in Chinese), J. Eng. Therm. Energy Pow., 24(2009), 4, pp. 447-451
- Chen, L., et al., Optimal expansion of a heated working fluid with convective-radiative heat transfer law, Int. J. Ambient Energy, 31(2010), 2, pp. 81-90
- Ma, K., Optimal Configurations of Engine Piston Motions and Forced Cool-down Processes, Ph. D. Thesis, Naval University of Engineering, China, 2010
- Ma, K., Chen, L., Sun, F., A new solving method for optimal expansion of a heated working fluid with generalized radiative heat transfer law (in Chinese), Chin. J. Mech. Eng., 46(2010), 6, pp. 149-157
- Ma, K., Chen, L., Sun, F., Optimization of a model external combustion engine for maximum work output with generalized radiative heat transfer law, J. Energy Inst., in press
- Chen, L., Ma, K., Sun, F., Optimal expansion of a heated working fluid for maximum work output with time-dependent heat conductance and generalized radiative heat transfer law, J. Non-Equilib. Thermodyn., 36(2011), 2, pp.99-122
- Taylor, C. F., The Internal Combustion Engine in Theory and Practice, Volumes 1 and 2, MA, Cambridge, 1977
- Biezeno, C. B., Grammel, R., Engineering Dynamics, Blackie, London, 1955, 4, pp. 2-5
- Andresen, B., Rubin, M. H., Berry, R. S., Availability for finite-time processes. General theory and a model, J. Chem. Phys., 87(1983), 15, pp. 2704-2713
- Shen, W., Jiang, Z., Tong, J., Engineering Thermodynamics (in Chinese), High Education Press, Beijing, 2001
- Radcenco V., et al., New approach to thermal power plants operation regimes maximum power versus maximum efficiency. Int. J. Therm. Sci., 46(2007), 12, pp. 1259-1266
- Sieniutycz S., Salamon P., Advances in Thermodynamics. Volume 4: Finite Time Thermodynamics and Thermoeconomics, Taylor & Francis, New York, 1990.