Consider combustion within a closed chamber. There is no motion (convection) and consequently density remains constant...

 

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Consider combustion within a closed chamber. There is no motion (convection) and consequently density remains constant during the combustion process. Then the governing equations becomes dT dt dY A Po -=-T₁ = SA dt dYB Poc − (r₂^H₂ +r₂^H₂+r3^H₂) =- Po dt Po Po dYc =T₁-T₂=SB -=1₂-13 = Sc -=T3 = SD dt dYp dt where the initial density is 200 kg/m³. Y₁ is each species mass fraction. The rate of chemical reaction for each step of a combustible mixture is given by A→B: r₁ = A₁ exp(-E₁/RT) POYA BC: r₂ = A₂ exp(-E₂/RT) POYB CD: 13 = A3 exp(-E/RT) PoYc with YA+Y+Yc+Y₂ = 1, R₁ + R₂ + Rc+R₂=0 for satisfying the mass conservation law. Reaction 1 2 3 step C (J/kg °C) In A₁. 44s 40s-¹ 30cm³/s-g E. (KJ/gmole) 190 180 140 1200 (A, B) ΔΗ(J/g) 270 -800 -4000 2000 (C, D) Solve these system of equations using 1) explicit scheme and 2) linearized implicit scheme. Plot Temperature vs. time. Plot species A,B,C,D versus time. This is called constant volume combustion of multi-species chemical mixture. Consider combustion within a closed chamber. There is no motion (convection) and consequently density remains constant during the combustion process. Then the governing equations becomes dT dt dY A Po -=-T₁ = SA dt dYB Poc − (r₂^H₂ +r₂^H₂+r3^H₂) =- Po dt Po Po dYc =T₁-T₂=SB -=1₂-13 = Sc -=T3 = SD dt dYp dt where the initial density is 200 kg/m³. Y₁ is each species mass fraction. The rate of chemical reaction for each step of a combustible mixture is given by A→B: r₁ = A₁ exp(-E₁/RT) POYA BC: r₂ = A₂ exp(-E₂/RT) POYB CD: 13 = A3 exp(-E/RT) PoYc with YA+Y+Yc+Y₂ = 1, R₁ + R₂ + Rc+R₂=0 for satisfying the mass conservation law. Reaction 1 2 3 step C (J/kg °C) In A₁. 44s 40s-¹ 30cm³/s-g E. (KJ/gmole) 190 180 140 1200 (A, B) ΔΗ(J/g) 270 -800 -4000 2000 (C, D) Solve these system of equations using 1) explicit scheme and 2) linearized implicit scheme. Plot Temperature vs. time. Plot species A,B,C,D versus time. This is called constant volume combustion of multi-species chemical mixture.

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Explicit Scheme The explicit scheme is used to solve the system of equations of constant volume combustion of a multispecies chemical mixture The equations used are dTdt r1H1 r2H2 r3H3 P0 dYAdt r1YAP0... View the full answer