Week 6 - Multivariate Newton Rhapson Solver

Aim: To, Write a code that takes all the reactions from the GRI mechanism and calculates 10 most sensitive reactions The sensitivity parameter should be with respect to the Temperature Given: Initial temeprature= 1500K & Pressure=1 atm Theory: Sensitivity analysis provides us with insight into the relationship between…

Aim: 1. To calculate the auto-ignition delay for Methane using Cantera for varying pressure between 1-5 atm at constant tempertaure=1250K 2.To calculate the auto-ignition delay for Methane using Cantera for varying temperatures between 950-1450 Kelvin at a constant pressure=5 atm 3. To print the rate of change of molar…

Aim: To solve the set of non-linear differential equations using Multivariate Newton Rhapson method Given:   Equations:   Initial condition: y1=y2=y3=0 Numerical Analysis: To solve using the Backward difference method & Jacobian method Solver: Newton Rhapson Method is used to iteratively approximate the roots…

1. When does a ODE become unstable? To answer this question it is essential to undertsand the type of numerical schemes available to solve and ODE. Solving an ODE analytically could be tedious. However, numerical methods for ODE prove to be efficient while dealing with more than one parameters. The numerical approximation/computation…

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Aim : comparing the effect of pre-heated oxidizer on AFT           comparing the effect of pre-heating oxidizer on combustion efficiency Given: Fuel - CH4 , constant pressure heat exchange system -Recuperator, LHV=50MJ/Kg           …

The stoichiometric equation for CH4-Methane comnustion is CH4+2(O2 +3.76N2) ---> CO2+ 2H2O +7.52N2   1. Using "moles" method requires us to input the mass fractions of the air (0.21 oxygen + 0.79 nitrogen) at STP. to arrive at the correct no. of moles of air mass fraction, o2 = Moles, o2/( Moles, air)                       …

Theory: 1. ATF Vs equivalence ratio in Constant Volume condition. The Stoichiometric general equation for the combustion of methane is given as follows CxHy + a(O2 +3.76N2) = b(xCO2) + c((y/2)H2O) + 3.76a N2 + d(O2) + e(CO) For phi<1, the coefficient for CO(product), i.e, e=0, This is known a lean combustion For phi<1,…