Thermodynamic Models
The models described in this chapter are called thermodynamic models since they are based on the first law of thermodynamics and mass balances only. The principles of momentum conservation are not considered in this model type and spatial variations of co
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The models described in this chapter are called thermodynamic models since they are based on the first law of thermodynamics and mass balances only. The principIes of momentum conservation are not considered in this model type and spatial variations of composition and thermodynamic properties are neglected. Thus, the entire combustion chamber of an internal combustion engine is typically treated as a single, homogeneously mixed zone. These assumptions obviously represent a significant abstraction of the problem and prohibit the usage of thermodynamic models in order to study locally resolved subprocesses such as detailed spray processes or reaction chemistry. However, the great advantage of these models is that they are both easy to handle and computationally very efficient. Therefore, they are still widely used in applications where there is only interest in spatially and sometimes even temporally averaged information and where computational time is crucial.
2.1 Thermodynamic Fundamentals Generally, an open thermodynamic system with transient in- and outflows as shown in Fig. 2.1 can be described by mass and energy balances. The change of mass contained within the control volume is equal to the difference between all entering and exiting mass flows, mi and me respectively: dm cv " \ ' . " \ ' . --=L..Jm-L..Jm dt i' e e·
(2.1)
contral volume boundary
region e
Fig. 2.1. Schematic illustration of an open contra! vo!ume with transient in- and outflows
G. Stiesch, Modeling Engine Spray and Combustion Processes © Springer-Verlag Berlin Heidelberg 2003
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2 Thermodynamic Models
The energy balance (first law of thermodynamics) for the control volume becomes dEcv dt
=Q+~ + I(mihi )- I(mA), i
(2.2)
e
where ~ represents the rate of mechanical work and Q is the rate of heat transferred to the system. If changes in kinetic and gravitational potential energies of the mass contained in the system are neglected the change in total energy dEcv is equal to the change in internal energy dUcv and Eq. 2.2 can be written as (2.3) In order to correlate the above change in internal energy of the control volume dUcv to changes in temperature and pressure, that are usually of greater interest, an
equation of state is necessary in addition to the above mass and energy balances. For a pure substance i, the mass based specific internal energy Uj = U/rn is generally a function of temperature and pressure, (2.4)
but it reduces to a function of only temperature for ideal gases. This assumption usually represents a good approximation for combustion gases because of the high temperatures encountered. However, combustion products are not a pure substance but a mixture of various components such as C0 20 H20, N2, O2, etc .. Hence, the internal energy depends not only on temperature but also on the mixture composition, i.e. the mass fractions Yj of the each species i within the mixture: (ideal gas mixture) .
(2.5)
For a known gas composition, which in combustion engines could be approximated by the equivalence ratio -
0
co
Gi "0 "
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