analysis of water injection into high-temperature mixture of ...

101 dV VCA = (m dθ+ ω) Eq.3-4dV VC( + )vb ln vb 1/2 Tb Tw vu ln vu 1/2 Tb TwB h dθω⎡ ⎤∂ − ∂−= x + ( 1−x )ωm ⎢cPb ∂lnTb Tb cPu ∂lnTu T ⎥⎣b ⎦2dx ∂ln vb hu−h⎡bdx ( x−x ) C ⎤C= −( vb−vu)−vb−dθ ∂ lnTb cPbT ⎢bdθ ω ⎥⎣ ⎦Eq.3-5Eq.3-6⎡22⎤vb ln vb vblnD x ⎛ ⎞∂∂ vb= +⎥ cPb T ⎜bln T ⎟⎢ ⎜∂ ⎝ b ⎠ P ∂lnP⎣⎥⎦⎡22⎤vu ln vu vulnE ( 1 x ⎛ ⎞)∂∂ vu= − +⎥ cPu T ⎜uln T ⎟⎢ ⎜∂ ⎝ u ⎠ P ∂lnP⎣⎥⎦Eq.3-7Eq.3-8Following defined pressure and burned temperature as the function of the crank angle.3.1.2 Derivation of Slider-Crank ModelThe cylinder volumes are known from compression ratio ( r), volume at TDCV , and half of connecting rod length ratio ( ε = S/2l) where ( S ) is stroke ( l)is rod( ) 0length. Action of Eq.3-1 and Eq.3-3 represent the remaining parameter, whichrequired determine the pressure, temperature and constant values. The derivative formof the slider-crank model is given as a non-dimensional relationship is described asfollowing equation Ferguson [6].⎡ r −1⎧1⎡V = V 01+ ⎪1− cosθ+ 1− 1−ε sin θ⎢⎨⎢⎣ 2 ⎪⎩ε ⎣2 2( ) 1/2⎤⎫⎤⎪⎥⎬⎦⎪⎭⎥⎦Eq.3-9dV V ( 1) 2 21/20r− ⎡ ε− ⎤= sinθ sin 2θ(1 ε sin θdθ2 ⎢+ − )⎣ 2⎥Eq.3-10⎦There parameters define the basic geometry of an internal combustion engine, whichcan be solved into section 3.1.1.3.1.3 Thermodynamic Properties of Various Ideal Gases Mixtures and FuelsThermodynamic properties of various ideal gas mixtures are required by thetwo-zone heat releases which predict the model for both burned and unburned zones.In order to do this, the properties of the individual species are proposed as an ideal gasmixture and the gas properties can then be found using the appropriate relationshipsfrom Cengel and Lewis and Randall [10, 11]. Thermodynamic data for elements aredescried to be 11 products as CO , H O, N , O , CO, H , H,O, OH, NO and N to2 2 2 2 2