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

68The following is the derivative version of the equations modified based onKreiger and Borman [19] which using for determination of two-zone of burned zoneand water injection zone to analyze the rate of temperature, pressure and mass transferbased on equally volume of a spark ignition engine. Consider the schematic of anengine cylinder while combustion products are occurring in expansion strokeseparating the burned zone and the water zone as in figure B-1Q • mWP, V,mbbR , T , ub b bP , V,mWWR , T , uW W WΔQ • b( P + )WP dVbFIGURE B-1 Schematic of burned zone and water zone model based on equallyvolumeAssumptions:•• •1) Volume,V , in the burned and water zones is equal V = VW= V•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.B-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 Dalton’s law.P= Pb+ PW and m= mb+ m WEq.B-2From Eq.B-2 we can writeW1 W2b2• •mbm −Δ m= m and m −Δ m= m which leads to − mW=Eq.B-3b1The ideal gas law statesPV = mRTEq.B-4From which we can writemRTb b bmWRWTWV = P= bPEq.B-5WDifferentiating Eq.B-4 givesPdV + VdP = mRdT + mTdR + RTdmEq.B-6