Journal Paper Format - International Journal of Mechatronics

International Journal of Mechatronics, Electrical and Computer Technology Vol. 4(12), J ul, 2 0 1 4, pp. 1 1 7 5-1191, ISSN: 2 3 0 5-0543

Available online at: http://www.aeuso.org © A ustrian E-Journals of Universal Scientif ic Organization

--------------------------------------------------Performance Evaluation of an Air-Standard Miller Cycle with Consideration of Heat Losses A. Mousapour 1 2

1*

and M.M. Rashidi

2,3

Young Researchers and Elite Club, Karaj Branch, Islamic Azad University, Karaj, Iran.

Mechanical Engineering Department, University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, Peoples Republic of China.

3

Mechanical Engineering Department, Engineering Faculty of Bu -Ali Sina University, Hamedan, Iran. *Corresponding Author's E-mail: [email protected]

Abstract There are heat losses during the cycle of an actual engine, which are neglected, in the airstandard analysis. In this paper, performance of an air-standard Miller cycle with consideration of heat losses is evaluated, assuming that the heat loss through the cylinder wall only occurs during combustion and that to be proportional to the average temperature of both the working fluid and cylinder wall. In addition, effects of various design parameters, such as the compression ratio, the supplementary compression ratio, the initial temperature of the working fluid and the constants related to combustion and heat transfer through the cylinder wall on the net work output, the thermal efficiency, the maximum work output and the corresponding compression ratio and thermal efficiency at maximum work output are investigated. Miller cycle now is widely used in the automotive industry and the results obtained in this paper will provide some theoretical guidance for the design optimization of the Miller cycle. Keywords: Air-standard cycle, Miller cycle, Combustion, Working fluid, Combustion, Heat transfer, Compression ratio, Net work output, Thermal efficiency, Maximum work output.

1. Introduction The Miller cycle, named after R. H. Miller (1890 - 1967), is a modern modification of the Atkinson cycle and has an expansion ratio greater than the compression ratio. This is

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--------------------------------------------------accomplished, however, in a much different way. Whereas an engine designed to operate on the Atkinson cycle needed a complicated mechanical linkage system of some kind, a Miller cycle engine uses unique valve timing to obtain the same desired results. The cycle experienced in the cylinder of an internal combustion engine is very complex; to make the analysis of an engine cycle much more manageable, the real cycle is approximated with an ideal air-standard cycle, which differs from the actual by some aspects. In practice, the airstandard analysis is quite useful for illustrating the thermodynamic aspects of an engine operation cycle. Additionally, it can provide approximate estimates of trends as the major engine operating variables change. For the air-standard analysis, air (as an ideal gas with constant specific heats) is treated as the fluid flow through the entire engine, and property values of air are used in the analysis. The real open cycle is changed into a closed cycle by assuming that the amount of mass remains constant; combustion and exhaust strokes are replaced with the heat addition and heat rejection processes, respectively; and actual engine processes are approximated with ideal processes [1-4]. There are heat losses during the cycle of a real engine that strongly affect the engine performance, but they are neglected in ideal air-standard analysis. In recent years, much attention has been paid to effect of the heat transfer on performance of internal combustion engines for different cycles. Klein [5] examined the effect of heat transfer through a cylinder wall on the work outputs of the Otto and Diesel cycles. Chen et al. [6,7], Akash [8] and Hou [9] studied the effect of heat transfer through a cylinder wall during combustion on the net work output and the thermal efficiency of the air-standard Otto, Diesel and Dual cycles. Hou [10] also applied to performance analysis and comparison of the air-standard Otto and Atkinson cycles with heat transfer consideration. Ge et al. [11,12], Chen et al. [13], Al-Sarkhi et al. [14] investigated the effects of heat transfer, friction and variable specific heats of the working fluid on the performance of the Atkinson, Diesel, Dual and Miller cycles, respectively. The effects of heat loss as percentage of fuel’s energy, friction and variable specific heats of the working fluid on the performance of the Otto, Atkinson, Miller and Diesel cycles have been analyzed by Lin and Hou [15-18]. This paper will

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--------------------------------------------------investigate the performance of an air-standard Miller cycle with consideration of heat transfer through a cylinder wall during combustion.

Figure 1: The P-v and T-s diagrams for an air-standard Miller cycle.

2. Thermodynamic analysis Since thermodynamic analysis of internal combustion engines in practical conditions is too complicated, for this reason the real cycles are approximated with ideal air-standard cycles by applying a number of assumptions. The P – v and the T – s diagrams of an airstandard Miller cycle are shown in Fig. 1. It can be seen that Process 1→2 is reversible adiabatic compression. Process 2→3 is isochoric heat addition. Process 3→4 is reversible adiabatic expansion and processes 4→5 and 5→1 are isochoric and isobaric heat rejection, respectively. Assuming that the working fluid is an ideal gas with constant specific heats, the net work output per unit mass of the working fluid of the cycle can be written in the form:

wnet  q23   q45  q15   CV T3  T2   CV T4  T5   CP T5  T1  ,

(1)

where, q23 is the heat added to the working fluid per unit mass during the process 2→3. q45 and q51 are the heats rejected by the working fluid per unit mass during the processes

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--------------------------------------------------4→5 and 5→1. C P and C V are the constant-pressure and constant-volume specific heats of the working fluid, and T1 , T2 , T3 , T4 and T5 are the absolute temperatures at states 1, 2, 3, 4 and 5, respectively. Equation describing entropy change for a reversible process is, as follow:

 Ti   Vi    R ln   .  Tj   Vj 

si  s j  CV ln 

(2)

Using Eq. (2), for the isentropic processes (1→2) and (3→4), we will have T2  T1rc k 1 ,

(3)

and

T4  T3  r rc 

1k

(4)

,

where, k is the specific heat ratio  CP CV  , while rc and r are the compression ratio and the supplementary compression ratio, that are defined as: rc 

V1

(5)

,

V2

and r

V5 V1

(6)

.

Thus, for the adiabatic process (5→1) we have T5  T1r .

(7)

The heat added per unit mass of the working fluid of the cycle during the constantvolume process (2→3) is represented by the following equation: qin  q23  CV T3  T2  .

(8)

The temperatures within the combustion chamber of an internal combustion engine reach values on the order of 2700 (K) and up. Materials in the engine cannot tolerate this kind of temperature and would quickly fail if proper heat transfer did not occur. Thus, because of keeping an engine and engine lubricant from thermal failure, the interior maximum

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--------------------------------------------------temperature of the combustion chamber must be limited to much lower values by heat fluxes through the cylinder wall during the combustion period. Since, during the other processes of the operating cycle, the heat flux is essentially quite small and negligible due to the very short time involved for the processes, it is assumed that the heat loss through the cylinder wall occurs only during combustion. The calculation of actual heat transfer through the cylinder wall occurring during combustion is quite complicated, so it is approximately assumed to be proportional to the average temperature of both the working fluid and cylinder wall and that, during the operation, the wall temperature remains approximately invariant. The heat added per unit mass of the working fluid of the cycle by combustion is given by the following linear relation [5]: qin  A  B T2  T3  ,

(9)

Where, A and B are constants related to combustion and heat transfer, respectively. Combining Eqs. (8) and (9) yields T3 

A   CV  B  T2

 CV  B 

.

(10)

Substituting Eq. (3) into Eq. (10) gives

 A   CV  B  T1rc k 1  T3   .  CV  B 

(11)

Substitution of Eq. (11) into Eq. (4) gives

 Ar1 k rc1 k   CV  B  T1r1 k  T4   .  CV  B 

(12)

By combining results obtained from Eqs. (3), (7), (11) and (12) into Eq. (1), the net work output per unit mass of the working fluid of the cycle can be expressed as:

  A 1  r 1 k rc1 k   2 BT1rc k 1   CV  B  T1r 1 k   CV  B  T1r   wnet  CV    CPT1  r  1 . (13)    CV  B    Similarly, by combining Eqs. (3) and (11) into Eq. (8), for the heat added per unit mass of the working fluid of the cycle, we have

1179



--------------------------------------------------  A  2 BT1rc k 1   qin  CV  .   CV  B    

(14)

Dividing Eq. (13) by Eq. (14) gives the indicated thermal efficiency of the cycle

  Ar 1 k rc1 k   CV  B  T1r 1 k   CV  B  T1r  k  CV  B  T1  r  1    th   1   . (15) k 1  qin   A  2 BT r 1 c     wnet

Maximizing the net work output with respect to compression ratio, by setting wnet rc

0

(16)

We finally get Ar 1 k  2 BT1rc 2 k  2  0.

(17)

Solving Eq. (17), gives the corresponding compression ratio at maximum work output, rcm , so we will have 1

 Ar1k  2 k 1 rcm   .   2BT1 

(18)

Hence, the maximum work output, wmax , and the corresponding thermal efficiency at maximum work output,  m , can be obtained by substituting rc  rcm into Eqs. (13) and (15) as the following equations:

wmax

1  1 k 2 A  2 2 ABT r  1    CV  B  T1r1k   CV  B  T1r       C T r 1 ,  CV    P 1    CV  B     

and

1180

(19)



--------------------------------------------------1   1 k 2 2 ABT r   CV  B  T1r 1 k   CV  B  T1r  k  CV  B  T1  r  1     1   . m  1    1     1 k 2    A   2 ABT1r      

(20)

3. Numerical calculations and results The following constants and parameters have been used in the calculations: A  2500 – 4000  kJ kg  ,

B  0.5  1.2  kJ kg .K  ,

Tmin  280  320  K  ,

CP  0.9728  kJ kg .K  , CV  0.6858  kJ kg .K  , r  1.2  1.8.

Substituting above constants and parameters into obtained equations and then choosing a suitable range for the parameter rc , we can get temperature ranges of different states, the heat added, the heat rejected, the net work output, the thermal efficiency, the maximum work output and corresponding compression ratio and thermal efficiency at maximum work output in the specified range. Figs. 2–5 show the effects of parameters r , Tmin , A and B on characteristic curves of the net work output versus the thermal efficiency, respectively. Apparently, the curves of the net work output versus the thermal efficiency are loop-shaped except for the special case of r  1. Note that for this value according to Eq. (7), the thermodynamic states 1 and 5 overlap and thus the Miller cycle will be converted to the Otto cycle. It can be found that for given values of r , Tmin , A and B, the maximum amounts of both the net work output and the thermal efficiency do not occur at similar compression ratios. The maximum work output and the maximum thermal efficiency increase with increasing A and decreasing Tmin and B. On the other hand, with increasing r , the maximum work output increases,

whereas the maximum thermal efficiency decreases. Figs. 6-8 depict the influences of parameters r , Tmin and A on the maximum work output for different values of B, respectively. It can be seen that with increasing B that corresponds to enlarging heat loss and thus, decreasing the net amount of heat added to the

1181



--------------------------------------------------working fluid, the maximum work output decreases. This figures also illustrate that the maximum value of net work output increases with a rise in r and A , and a fall in Tmin , for a given B. Figs. 9-11 indicate the effects of parameters r , Tmin and A on the corresponding compression ratio at maximum work output for different values of B, respectively. It is found that an increasing in B leads to a decrease of rcm . Furthermore, this figures reveal that the maximum value of net work output occurs at smaller compression ratios with increasing r and Tmin , and decreasing A , for a given B. Figs. 12-14 illustrate the effects of parameters r , Tmin and A on the corresponding thermal efficiency at maximum work output for different values of B, respectively. According to these figures, the corresponding thermal efficiency at the maximum work output increases with the increase of r and A , and the decrease of Tmin and B. 600

Tmin = 300 [K] A = 3000 [kJ/kg]

500

Net work output, wnet (kJ/kg)

r= r= r= r=

B = 1 [kJ/kg.K]

1 1.2 1.5 1.8

Cp = 0.9728 [kJ/kg.K]

400

Cv = 0.6858 [kJ/kg.K] 300

200

100

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Thermal efficiency, th Figure 2: Effect of r on curve of the net work output versus the thermal efficiency.

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--------------------------------------------------600


500

r = 1.5

Tmin = 280 [K]

A = 3000 [kJ/kg]

Tmin = 300 [K]

B = 1 [kJ/kg.K]

Tmin = 320 [K]

Cp = 0.9728 [kJ/kg.K]

400

Cv = 0.6858 [kJ/kg.K] 300

200

100

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Thermal efficiency, th

Figure 3: Effect of Tmin on curve of the net work output versus the thermal efficiency.

900 A A A A

Tmin = 300 [K]

800


r = 1.5 700

B = 1 [kJ/kg.K] Cp = 0.9728 [kJ/kg.K]

600

= = = =

2500 [kJ/kg] 3000 [kJ/kg] 3500 [kJ/kg] 4000 [kJ/kg]

Cv = 0.6858 [kJ/kg.K]

500 400 300 200 100 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Figure 4: Effect of A on curve of the net work output versus the thermal efficiency.

1183



--------------------------------------------------1200 B B B B

Tmin = 300 [K] r = 1.5


1000

A = 3000 [kJ/kg] Cp = 0.9728 [kJ/kg.K]

800

= = = =

0.5 [kJ/kg.K] 0.7165 [kJ/kg.K] 1 [kJ/kg.K] 1.2 [kJ/kg.K]

Cv = 0.6858 [kJ/kg.K] 600

400

200

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Figure 5: Effect of B on curve of the net work output versus the thermal efficiency. 1000 r= r= r= r=

Maximum work output, wmax (kJ/kg)

900 800

1 1.2 1.5 1.8

700 600 500

Tmin = 300 [K]

400

A = 3000 [kJ/kg] B = 1 [kJ/kg.K]

300 200

Cp = 0.9728 [kJ/kg.K] Cv = 0.6858 [kJ/kg.K]

100 0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K)

Figure 6: Effect of r on curve of the maximum work output versus B.

1184



--------------------------------------------------1000 Tmin = 280 [K]


900

Tmin = 300 [K]

800

Tmin = 320 [K]

700 600 500

r = 1.5

400

A = 3000 [kJ/kg] B = 1 [kJ/kg.K]

300

Cp = 0.9728 [kJ/kg.K]

200

Cv = 0.6858 [kJ/kg.K]

100 0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K) Figure 7: Effect of Tmin on curve of the maximum work output versus B.

1600


Tmin = 300 [K] 1400

r = 1.5

1200

B = 1 [kJ/kg.K] Cp = 0.9728 [kJ/kg.K]

1000

Cv = 0.6858 [kJ/kg.K]

A A A A

= = = =


800 600 400 200 0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K)

Figure 8: Effect of A on curve of the maximum work output versus B.

1185



--------------------------------------------------Compression ratio at maximum work output, r cm

30 r= r= r= r=

Tmin = 300 [K] 25

A = 3000 [kJ/kg]

1 1.2 1.5 1.8

B = 1 [kJ/kg.K] 20

Cp = 0.9728 [kJ/kg.K] Cv = 0.6858 [kJ/kg.K]

15

10

5

0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K)

Figure 9: Effect of r on curve of the compression ratio at maximum work output versus B.

Compression ratio at maximum work output, r cm

30 Tmin = 280 [K]

r = 1.5 25

Tmin = 300 [K]

A = 3000 [kJ/kg]

Tmin = 320 [K]

B = 1 [kJ/kg.K] 20

Cp = 0.9728 [kJ/kg.K] Cv = 0.6858 [kJ/kg.K]

15

10

5

0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K)

Figure 10: Effect of Tmin on curve of the compression ratio at maximum work output versus B.

1186



--------------------------------------------------Compression ratio at maximum work output, r cm

30 A A A A

Tmin = 300 [K] 25

r = 1.5

= = = =


B = 1 [kJ/kg.K] 20

Cp = 0.9728 [kJ/kg.K] Cv = 0.6858 [kJ/kg.K]

15

10

5

0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K)

Figure 11: Effect of A on curve of the compression ratio at maximum work output versus B.

Thermal efficiency at maximum work output, m

1 r= r= r= r=

0.9 0.8

1 1.2 1.5 1.8

0.7 0.6 0.5

Tmin = 300 [K]

0.4

A = 3000 [kJ/kg] B = 1 [kJ/kg.K]

0.3 0.2

Cp = 0.9728 [kJ/kg.K] Cv = 0.6858 [kJ/kg.K]

0.1 0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K)

Figure 12: Effect of r on curve of the thermal efficiency at maximum work output versus B.

1187



---------------------------------------------------


1 Tmin = 280 [K]

0.9

Tmin = 300 [K]

0.8

Tmin = 320 [K]

0.7 0.6 0.5

r = 1.5

0.4

A = 3000 [kJ/kg] B = 1 [kJ/kg.K]

0.3 0.2

Cp = 0.9728 [kJ/kg.K] Cv = 0.6858 [kJ/kg.K]

0.1 0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K)

Figure 13: Effect of Tmin on curve of the thermal efficiency at maximum work output versus B.


1 A A A A

0.9 0.8

= = = =


0.7 0.6 0.5

Tmin = 300 [K]

0.4

r = 1.5 B = 1 [kJ/kg.K]

0.3 0.2

Cp = 0.9728 [kJ/kg.K] Cv = 0.6858 [kJ/kg.K]

0.1 0 0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

B (kJ/kg.K)

Figure 14: Effect of A on curve of the thermal efficiency at maximum work output versus B.

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--------------------------------------------------Conclusions In this manuscript, the performance of an air-standard Miller cycle with consideration of losses due to heat transfer through the cylinder wall during combustion has been investigated. In addition, the influences of some relevant design parameters such as the compression ratio, supplementary compression ratio, the initial temperature of the working fluid and the combustion and heat transfer constants on the net work output, the thermal efficiency, the maximum work output, the corresponding compression ratio at maximum work output and the corresponding thermal efficiency at maximum work output has been discussed, numerically. The obtained results show that the effects of these parameters on the performance of the Miller cycle are non-negligible and should be considered in practical Miller engines.

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--------------------------------------------------Authors Ashkan Mousapour (A. Mousapour) is born in A hvaz, Iran in 1987. H e received his B.Sc. degree in M echanical Engineering from Is lamic Azad University of K araj and received his M .Sc. degree in M echanical Engineering from Science and Res e arch Branch of Islamic Az ad U nivers ity. His current res earch interest includes T hermodynamics and Energy . He published 2 journal papers ( both are in Scopus). H e is a member of Young Res earchers and Elite Club of K araj Branch, Is lamic Az ad University, Karaj, Iran. E-mail: [email protected]

Moh ammad Meh di Rashi di (M.M. Rashi di) is born in H amedan, Iran in 1972. H e received his B.Sc. degree in Bu-A li Sina U nivers ity, Hamedan, Iran in 1995. He als o received his M .Sc. and Ph.D. degrees from T arbiat M odares U nivers ity, Tehran, Iran in 1997 and 2002, respect ively. His res earch focus es on H eat and M ass T ransfer, Thermodynamics, Comput ational F luid Dynamics (CFD ), Nonlinear Analysis, Engineering M athemat ics, Exergy and Second Law Analysis, Numerical and Experiment al Invest igations of N anofluids F l ow for Increasing H eat Trans fer and Study of M agnetohydrodynamic Vis cous F low. H e is a professor (full) of M echanical Engineering at the Bu -A li Sina University, Hamedan, Iran. Now H e is w orking on some research projects at univers ity of M ichigan-Shanghai Jiao Tong university, J oint Inst itute. H is works have been published in the journal of Energy , Computers and Fluids, Communicat ions in Nonlinear Science and Numerical Simulation and s everal other peer-review ed int ernat ional journals . He has published two books : A dvanced Engineering M athematics w ith Applied Examples of M ATHEM ATICA Software (2007) (320 pages) (in Pers ian), and M athemat ical M odelling of Nonlinear F lows of M icropolar Fluids (Germany, Lambert Academic Press , 2011). H e has publis hed over 165 (100 of them are in Scopus ) journal art icles and 43 conference p apers . D r. Ras hidi is a review er of several journals (over 110 refereed journals) s uch as Applied M athemat ical M odelling, Computers and F luids , Energy, Computers and M athemat ics w ith Applications , International J ournal of H eat and M ass Trans fer, International journal of thermal s cience, M athemat ical and Computer M odelling, etc. H e w as an invit ed profess or in Génie M écanique, Univers ité de Sherbrooke, Sherbrooke, QC, Canada J1K 2R (From Sep 2010 -Feb 2012), U nivers ité Paris Ouest, F rance (F or Sep 2011) and Univers ity of the Witwat ers rand, J ohannes burg, South A frica (For A ug 2012). H e is the editor of F orty four (44) Int ernat ional Journals, s ome of them are as follow: Caspian Journal of Applied Sciences Research (ISI), Ass ociate Editor of J ournal of K ing Saud Univers ity-Engineering Sciences (Els evier), Scientific Res earch and Ess ays (indexed in SCOPU S), Walailak Journal of Science and T echnology (indexed in SCOPU S) and M odern Applied Science (indexed in SCOPUS). E-mail: mm_rashidi@s jtu.edu.cn , [email protected]

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