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

78The following is the derivative versions of the equations modified based on Kreigerand Borman [16] which using for determination two-zone of burned zone and waterinjection zone to analyze the rate of temperature, volume and mass transfer based onequally pressure in a spark ignition engine. Consider the schematic of an engine cylinderwhile combustion products are occurring in expansion stroke separating the burned zoneand the water zone as in figure.C-1Q • mWP, V , mbbR , T , ub b bPV , , mWWR , T , uW W WΔQ • bPd ( V + V )WbFIGURE C-1 Schematic of burned zone and water zone model based on equally pressureAssumptions:• •1) Pressure , P , in the burned and water zones is equal So, P= PW = P•b2) There is heat transfer between the burned and water zones.3) No chemical reactions take place in the water zone (zone is said to be frozen)∂xW ∂xW ∂MW ∂RW ∂MW ∂RW ∂uWi.e. = = 0⇒ = = = = = 0 Eq.C-1∂T ∂P ∂T ∂T ∂P ∂P ∂P4) The total cylinder volume and mass is taken up by the burned and watervolumes and masses only, Determining is defined from Amagat’s law.V = Vb+ VW and m= mb+ m WEq.C-2From Eq.C-2 we can writeW1 W2b2• •mbm −Δ m= m and m −Δ m= m which leads to − mW=Eq.C-3b1The ideal gas law statesPV = mRTEq.C-4From which we can writemRTb b bmWRWTWP = V= bVEq.C-5WDifferentiating Eq.C-4 givesPdV + VdP = mRdT + mTdR + RTdmEq.C-6