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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
                               TECHNOLOGY 2, May-August (2012), © IAEME
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue(IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)                                                           IJMET
Volume 3, Issue 2, May-August (2012), pp. 633-642
© IAEME: www.iaeme.com/ijmet.html
Journal Impact Factor (2012): 3.8071 (Calculated by GISI)                      ©IAEME

                                    Z. Ahmed1, D. K. Mahanta2
          Royal School of Engineering& Technology, Gauhati University, Guwahati – 35,
                                         Assam, India
            Assam Engineering College, Gauhati University, Guwahati – 35, Assam, India

In this study, energy and exergy analysis are applied to the experimental data of a naturally
aspirated, direct injection, single cylinder, 4 stroke diesel engine. The data are collected using an
engine test unit which enables the measurement of fuel flow rate, air flow rate, engine load, in-
cylinder pressure and volume as a function of crank angle and all relevant temperatures. The
development of rate and cumulative in-cylinder exergy rate terms during an engine cycle are
shown in a diagram which identifies the processes in which exergy destruction due to
irreversibilties are involved. The energy and exergy efficiencies are calculated for different
loads and compared. It is found that combustion is the dominant irreversibility term and that it
decreases with increase in load.

Keywords: Second-law, Exergy, Compression Ignition Engine, Irreversibilities


           =                                                =      Entropy (J/K)
                    )gk/J( ygrexe cificepS
           =                                                       Heat rate (W)
                )J( ytilibaliava ro ygrexE
           =    Exergy rate (W)                                    Work rate (W)
           =    Specific energy (J/kg)                       =     Mass rate (kg/s)
           =    Energy or Heat (J)                         ℎ=      Specific enthalpy (J/K)
           =    Energy rate or heat rate (W)                =      Crank angle (deg)
           =    Internal energy (J)                         =      Torque (Nm)
           =    Pressure (N/m2)                              =     Specific heat (J/kg.K)
           =    Volume (m2)                                 =      Efficiency
           =    Temperature (K)                                  = Lower calorific value (J)
           =    Specific entropy (J/kg.K))

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME

     An exergy-based analysis is the analysis of a system based on the second law of thermodynamics
that overcomes the limit of an energy-based analysis. Exergy is defined as the maximum theoretical
useful work obtained as a system interacts with an equilibrium state. Exergy is generally not
conserved as energy but destroyed in the system. Exergy destruction is a measure of irreversibility
that is the source of performance loss. Therefore, an exergy analysis assessing the magnitude of
exergy destruction identifies the location, the magnitude and the source of thermodynamic
inefficiencies in a thermal system. This provides useful information to improve the overall efficiency
and cost effectiveness of a system and/or comparing the performance of the two systems [1, 2].
     Internal combustion engine simulation modeling has long been established as an effective tool
for studying engine performance and contributing to evaluation and new developments.
Thermodynamic models of the real engine cycle have served as effective tools for complete analysis
of engine performance and sensitivity to various operating parameters. On the other hand, it has long
been understood that traditional first-law analysis, which is needed for modeling the engine processes,
often fails to give the engineer the best insight into the engine’s operation. In order to analyze engine
performance—that is, evaluate the inefficiencies associated with the various processes—second-law
analysis must be applied. For second-law analysis, the key concept is or exergy.The exergy of a
material represents its potential to do useful work. Unlike energy, exergyis destroyed asa result of
such phenomena as combustion, friction, mixing and throttling. The destruction of exergy —often
termed irreversibility—is the source for the defective exploitation of fuel into useful mechanical work
in a compression or spark ignition engine. The reduction of irreversibilities can lead to better engine
performance through a more efficient exploitation of fuel. To reduce the irreversibilities, we need to
quantify them. That is we need to evaluate the availability destructions-we need the second-law
analysis.[3, 4, 5, 6]
     The objective of this study is to identify those processes in a compression engine in which
destruction or loss of exergy occurs and to define efficiencies that can be studied and compared for
possible improvements


2.1 Exergy of a system

     The exergy or availability of a system in a given state can bedefined as the maximum useful
work that can be produced through interaction of the system with itssurroundings, as it reaches
thermal, mechanical and chemical equilibrium. Usually, the terms with thermomechanical and
chemical equilibration aredifferentiated and calculated separately.
     For a closed system experiencing heat and workinteractions with the environment, the
followingequation holds, for the thermomechanical exergy [7].
                    =     −     )+        −   )−         −   )                                        (1)
where =          +       + with          the kinetic and     the potential energy,     and     are the
fixedpressure and temperature of the environment; and , and           are the internal energy, volume
and entropyof the contents were they brought to and .
        Exergy is an extensive property with a valuegreater than or equal to zero. Its value
dependsnot only on the state of the system, but also on theambient properties.[7]
     There is no exergy in a systemwhen thermal, mechanical and chemical equilibriumexists with the
environment. Thermal equilibrium isachieved when the temperature of the system is equal tothe
temperature of the surrounding environment. In thesame way, mechanical equilibrium is achieved
whenthere is no pressure difference between the workingmedium and the environment.

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME

2.2. Chemical equilibrium

     Chemical equilibrium is achieved only when there are no components of the working medium,
which could interact with those of the environment to produce work.
     In the case of engines, all the components of the working medium must be either oxidized (e.g.
fuel, CO, H), or reduced (e.g. NO, OH), in a reversible way as the system reaches the dead state (see
following section for deadstate definition). The only components of the system,which cannot react
chemically with the atmosphere and,therefore, constitute the components of the mixture atthe dead
state are O2, N2, CO2 and H2O.
     Chemical exergy take into account the capacity to produce work because of the difference
between the partial pressures of the components (when in thermal and mechanical equilibrium with
the environment) and the partial pressures of the same components in the atmosphere. [8]

2.3 Dead state

     The choice of a reference dead state is of paramount importance when dealing with exergy
calculations since this will determine what kind of equilibrium will be established with the
environment and consequently, the calculated values of exergy.[8]
         In general, a system is considered to be at the so called ‘restricted’ dead state when no work
potential exists between the system and the environment due to temperature or pressure differences.
This is the dead state reached when calculating the thermo-mechanical exergy. On the other hand, if
chemical equilibrium with the environment is of concern, then we refer to the ‘true’ or ‘unrestricted’
dead state, where the chemical potentials of the system also equal those of the environmentFor engine
applications the (environmental) pressure and temperature conditions of the dead state are usually
taken to be      = 1.01325 bar and       = 298.15 K, and if chemical availability is also taken into
account, then the molar composition of the environment is: 20.35% O2, 75.67% N2, 0.03% CO2,
3.03% H2O and 0.92% various other substances.Changes in the dead state conditions are reflected by
changes in the value of the system availability. [8]

2.4     General energy balance equation

For an open system experiencing mass exchange with the surrounding environment, the following
equation holds for the total energy on a time basis [8]:

                         =        −       +   .   −         .                                       2)

Where       represents the time rate of heat transfer at the boundary of the control volume. ;
    mechanical work transfer from control volume ; . − . are the energy terms associated
with inflow and outflow of masses, respectively. In particular, the terms and   refer to the flow or
energy of the incoming and the outgoing cylinder mass flow rates, respectively, given by = .
(neglecting kinetic and potential energy contribution):

2.5 General exergy balance equation
For an open system experiencing mass exchange with the surrounding environment, the following
equation holds for the total exergy on a time basis [8]:

                     =       1−       .   −       −     .       +     .
                                  −       .   −

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME

where:       is the time rate of change in the exergy of the control volume content (i.e. engine cylinder,
or exhaust manifold, etc.) ;         1−         .       is the exergy term for heat transfer, with    the
temperature at the boundary of the system, which in general, is different from the temperature level of
a process (although these two temperatures are the same when applying the most usual simulation
approach of internal combustionengines operation, i.e. single-zone modeling) ;        − .        is the
exergy term associated with (mechanical or electrical) work transfer ; .       denotes the dead state
work. ;           . −         . are the exergyterms associated with inflow and outflow
ofmasses,respectively. In particular, the terms   and in refer to the flow or stream exergy (or
exergy) of the incoming and the outgoing cylinder mass flow rates, respectively, given by (neglecting
kinetic and potential energy contribution):

                            =ℎ−ℎ −                  −   )                                              4)
with the entropy of (cylinder) flow rate were it brought to         and . Flow exergy is defined as the
maximum work output that can be obtained as thefluid passes reversibly from the given state to a dead
state, while exchanging heat solely with the environment ; is the rate of exergy destroyed due to
irreversibility production inside the control volume due to combustion, throttling, mixing, heat
transfer under finite temperature difference to cooler medium, etc.        = .      based on an entropy
balance, with       denoting the rate of entropy creation due to irreversibilities.


3.1 Engine Modeling of Compression ignition engines

     In a single-zone model the working fluid in the engine is assumed to be a thermodynamic system
that undergoes energy and mass exchange with the surroundings, where the energy released during the
combustion process is obtained by applying the first law of thermodynamics to the system.
     The heat release rate as a function of crank angle was deduced from experimentally obtained in-
cylinder pressure data, which was then used as an input to the in-cycle calculations.

3.2 Assumptions included while doing calculations

     a. Spatial homogeneity of pressure ,
     b. Spatial homogeneity of temperature (for the whole cylinder),
     c. Working fluid is considered an ideal gas,
     d. Gas properties (enthalpy, internal energy, etc.) are modeled using polynomial relations with
        temperature (and pressure),
     e. Heat released from combustion is distributed evenly throughout the cylinder,
     f. Blow-by losses are not taken into account,
     g. Enthalpy associated with pressure of injected fuel is usually not significant and hence ignored,
     h. No heat transfer occurs between burned and unburned zones,
     i. Work required to transfer fluid from the unburned zone to the burned zone is negligible.

3.3 Engine analysis

In the following subsections, the equations will be given that deal with the exergy balance applied to
the engine cylinder in order to evaluate the various processes irreversibilities.

3.3.1 Fuel exergy

          The chemical exergy of fuel of type            is approximated by:

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME

                   =        . 1.04224 + 0.011925. −                                                            5)

where LCV is the fuel lower calorific value.
       Table 1 gives a summary of the most usually applied values for approximation of the
chemical exergy of fuels with interest for internal combustion calculations.

            Table 1: Approximation of ratio of fuel chemical exergy to low calorific value
                                     = 1.01325 bar and = 298.15 K.

                                Fuel                                            Reference
                        n-Dodecane                      )           1.0645       Moran
                        Diesel fuel   .                 .   )       1.0599       Moran
                        Octane       )                              1.0638       Moran
                        Gasolene        )                           1.0652       Moran
3.3.2   Engine cylinder exergy balance

        For the engine cylinder, on crank angle basis, we have[8]:
                        .   −       .
                  =                         −           −           +     −                                    6)
where is the incoming flow rate form the inlet manifold and                      outgoing flow rate to the exhaust
  i.     is the exergy rate of work transfer, given by

                                    =           −           .                                                  7)

        where      is the instantaneous cylinder pressure ;
  ii.       is the exergy rate of the heat transfer to the cylinder walls, given by

                                    =        . 1−                                                              8)

        where      is the in cylinder temperature ;
 iii.       is the fuel exergy rate, given by

                                        =           .                                                          9)

        where         = 1.0599              for diesel fuel.
 iv.       is the rate exergy generation due to irreversibility production within the cylinder, which
       consists of combustion (dominant contribution), viscous dissipation, turbulence, inlet valve
       throttling and mixing of the incoming air or air– fuel mixture with the cylinder residuals.
And the term on the left hand side is expressed explicitly as,

                                =       +       .       −       .                                             10)

representing the rate of change in the total exergy of the cylinder contents.
        As regards cumulative terms, these are defined after integration of the respective rate terms
over an engine cycle. Especially, for steady-state operation, the cumulative value for the cylinder
exergy is

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME

                                       .    =0                                                      11)


4.1 Engine Setup

    Experiments were conducted on an existing test unit. The test unit was a Single Cylinder,
Naturally Aspirated, Direct Injection, Compression Engine using standard diesel fuel

                            Fig. 1: Schematic diagram of engine test unit.

                      Table. 2:        Measurement taken from engine test unit.
                                            ℎ                            )
                                  ℎ                                                  ℃)
                                  ℎ                                                  ℃)

     The set up enabled measurement of in-cylinder pressure and volume as a function of crank angle;
fuel rate, air flow rate, cooling water flow rates to engine and gas calorimeter, engine load; and inlet
and outlet temperatures for each stream and other parameters as shown on table 2. The experiment
was firstly carried out at 85% load and 1503 rpm so as to obtain exergy rate terms at different crank
angle. Secondly, experiment was carried out and data was recorded at 8%, 31%, 41% and 85% so as
to obtain energy and exergy terms at different loads. Energy and exergy analysis of the engine was
also done at different loads

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME


5.1 Development of rate and cumulative In-cylinder exergy during a cycle

    Experimental data were applied to equations (6) – (11) for engine cylinder and exergy rate
terms& cumulative exergyterms tabulated and plotted on an exergy rate versus crank angle graph as
depicted in Fig.2 & Fig.3.

                    In-cylinder Exergy rate Terms (Joules)







                                                                       0     60     120    180     240     300      360    420    480   540   600       660      720

                                                                                                             Crank angle

                                                                                           Cylinder exergy
                                                                                           Exhaust gas exergy
                                                                                           Work exergy
                                                                                           Heat loss Exergy
                                                                                           Fuel Exergy

                 Fig: 2 Development of the exergy terms during and engine cycle
                        (Naturally Aspirated, DI diesel engine at 1503 rpm and 85% load)

                                                                                                                                                              In-cylinder cumulative exergy rate terms (Joules)










                          0                                   60       120    180    240    300      360     420     480    540   600   660   720

                                                                                           Crank Angle (deg)

                                                                                                  Exhaust gas
                                                                                                  Heat Loss

            Fig: 3 Development of the cumulative exergy terms during an engine cycle
                   (Naturally Aspirated, DI diesel engine at 1503 rpm and 85% load)

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME

5.2 Energy and Exergy Balance at different loads
Table 3: Energy Balance at different loads                                                   Table 4: Energy breakdown at different loads

                                                                                                               Energy            Exhaust       Heat loss
 Load                                                                                  Load                   Efficiency         heat loss        %
            (kW)                      (kW)          (kW)         (kW)                             Energy
                                                                                                                  %                 %
  8%        6.26                      1.05          1.08         4.13                   8%         100            16.77           17.18         66.05
 31%        8.66                      1.49          1.59         5.58                  31%         100            17.22           18.32         64.46
 43%        9.36                      1.81          1.76         5.79                  43%         100            19.33           18.80         61.87
 85%       15.62                      4.25          3.00         8.37                  85%         100            27.21           19.22         53.57
                                                           =      +

Table 5: Exergy Balance at different loads                                                   Table 6: Exergy breakdown at different loads

Load                                                                                 Load        Fuel      Exergy     Exhaust          Heat        Exergy
        (kW)    (kW)                   (kW)         (kW)         (kW)                           Exergy      Eff.      Exergy           loss       destroyed
 8%     6.63       1.05                 0.20         0.03        5.35                             %          %          %             exergy          %
31%     9.18       1.49                 0.42         0.09        7.18                8%          100       15.82          3.00         0.44        80.74
43%     9.92       1.81                 0.55         0.15        7.43                31%         100       16.25          4.54         0.98        78.23
85%     16.56      4.25                 1.17         0.29        10.85               43%         100       18.23          5.51         1.49        74.77
                                                           =     +                   85%         100       25.67          7.06         1.75        65.52




                      % Fuel Exergy







                                               10           20           30   40        50         60        70           80

                                                                                   % Load

                                                                                   Exergy Efficiency
                                                                                   Exhaust Exergy %
                                                                                   Heat Loss Exergy %
                                                                                   Exergy Destroyed %

                                                           Fig 4: Exergy breakdown at different loads
5.3      Error Analysis:

        The error analysis is done on the measuring devices using ‘Data Sampling’ method. This is a
powerful methodof statistical error analysis applied to the analysis of precision errors. As shown in
figure 1, pressure transducer has been used as pressure sensor for cylinder pressure measurement and
thermocouples for various temperature measurements. The pressure sensors and thermocouples are

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME

connected to a signal conditioning unit that transforms the analog signal to a digital signal, which is
then transmitted to a PC.
        A set of 15 trails are taken while the engine is running at constant speed of 1561 rpm with
constant fuel supply rate and constant water flow rate. From the data sample the maximum value,
minimum value, range, average, standard deviation and standard error are determined for each
measuring device and compared with error specified by the manufacturer.
                                             Table 7: Error Analysis

It is observed from the Table 7 that standard error (precision error) is within the limits set by the manufacturer.


      From fig.2, it is observed that the exergy rate of the cylinder (control volume) increase until the
start of compression because of work offered by the piston during compression stroke. This is almost
equal to the exergy transfer rate through heat of the working mediumwhose temperature is increasing
because of compression and the irreversibility rate is almost zero.
      At the point the fuel injection starts, the fuel starts to ignite after a delay period. During this
period there is loss of heat of evaporation. This causes a small drop in the cylinder exergy rate.
      After the start of combustion, the burning of fuel causes a considerable increase in pressure and
temperature and, consequently, in cylinder exergy and heat loss. The irreversibility rate increases due
to combustion, mixing and heat transfer.
      During the expansion stroke, when the pressure and temperature begin to fall, there is also a
decrease in the cylinder exergy rate and it becomes negative. The available energy accumulated in the
cylinder contents during compression and mainly during combustion is being returned in the form of
(indicated) work production, which causes the decrease in the exergy of the working medium.
      After the opening of the exhaust valve, the exhaust gas leaving the cylinder during blow-down
period causes the cylinder exergy rate to drop to a second minimum. The cumulative exergy term
continues to decrease so that, at the end of the cycle, its value is zero again, as the working medium
has returned to its initial state.
      Figure 4 shows that the exergy terms as a percentage of fuel exergy. Exergy destruction
decreases, because combustion irreversibility decreases with increasing load. Greater load results in
less degradation of the fuel chemical exergy when transferred to the exhaust gases and also less
mixing of exhaust gases with the air.
      It is also observed that both the energy efficiency and the exergy efficiency increase with
increasing load. The exergy efficiency is lower than the energy efficiency for the same power output.
This is due to the fact that the chemical that the chemical availability or exergy of the fuel is slightly
higher than its input energy.


    First and second laws of thermodynamics are employedto analyze the quality and quantity of
energy in a diesel engine and the thermal energy storage system. The energy and exergy analyses
enable us to develop a systematic approach that can be used to identify the sites of real losses of

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 2, May-August (2012), © IAEME

valuable energy in thermal devices. The first law analysis shows that significant losses occur in the
exhaust gas and cooling water. However, when analyzed using the exergy method, it is found that the
actual exergy losses are insignificant compared to the irreversibility losses in the engine. By
identifying and quantifying the exergy destruction or irreversibilities for specific engine parameters
and parameters the engine performance can be improved. In the analysis it was shown that the exergy
degradation is due to dominant combustion irreversibilities term. This indicates that improving the
performance of the engine is of more importance than the recovery of low grade energy loss. The
reduction of combustion irreversibilities can be realized by all parameters which increase the level of
pressures and temperatures in the cylinder, i.e. fuel–air equivalence ratio, compression ratio, cylinder
wall insulation and turbocharging.
     At the moment, the heat transfer from the hot cylinder walls to the cooling water, being at a very
low temperature, destroys the greatest part of this available energy. The recoveryof energy streams, is
an important subject whoseexploitation needs to be established and implemented through the use of
heat recovery devices(eg. bottoming cycles) and storage devices (eg. phase change material).


    [1] C.D. Rakopoulus and E.G.Giakoumis (2005) Second-law analysis applied to internal
        combustion engine operation. Progress in Energy & Combustion Science 32 (2006) 2-47
    [2] C.D. Rakopoulus and E.G.Giakoumis (1996) Simulation and exergy analysis of transient
        diesel engine operation. Energy Vol.22 No.9 pp 875-885, 1997
    [3] Michael J. Moran, Thermal Design and Optimization, Chapter 6, Pg. 130-171 New York:
        Wiley, 1996
    [4] Bejan, A., Tsatsaronis, G. and Moran, M. (1996) Thermal Design and Optimization, New
        York: John Wiley and Sons Inc.
    [5] Caton, J.A. (2000) `On the destruction of availability (exergy) due to combustion processes ±
        with specific application to internal-combustion engines', Energy, Vol. 25, pp.1097±1117.
    [6] Dunbar, W.R. and Lior, N. (1994) `Sources of combustion irreversibility', Combust Sci.
        Technol., Vol. 103, pp.41±61.
    [7] Yunus A. Çengel and Michael A. Boles, Thermodynamics: An Engineering Approach, 5th
        edition, Chapter 8, Pg. 423-470, New York: McGraw-Hill, 2006
    [8] Moran MJ. Availability analysis: a guide to efficient energy use. New Jersey: Prentice-Hall;


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