Week 7 - Simulation of a 1D Super-sonic nozzle flow simulation using Macormack Method

from the above question we dervie the contious equation as follows as

this program i divided into three parts one is

1) main program where all the non conservative and conservative forms of plotting will be there

2)non conservative form for the programming in the form of function

3) conservative form of the programming in the form of function

we consider the isentropic flow from a convergent and divergent flow the flow of the inlet come from the nozzle as the pressure temperature,mach number and density of the liquid are taken into the consideration

po=pressure

vo=volume are stag nation values

and super sonic are denoted with the area sand the mach number

and at the throat the area of sub sonic will be calucated from their it moves to the end of the nozzle with the super sonic speed

pe,ve,me,de

the force is suppled by the pressure ratio po/pe

we assumed flow is constant at all the one direction we find the governing equation

as continutity equation

movementum equaton

energy equation in anatlical solution we find the values of the given function

as follows

A/A*=1/M^2[2/gamma+1(1+(gamma-1)/2*m^2]^(gamma+1)/(gamma-1)

NON-CONSERVATIVE -FORM

the continutivity equation is

dp/dt=-rho*dv/dx-rho*vd(loga)/dx-v*dp/dx

movemetum equation

dv/dt=-v*dv/dx-(i/gamma)(dt/dx+t/rho*dp/dx)

similary energy equation