De Naval Nozzle
Is it possible practiaclly to accelerate a flow from sonic to supersonic flow using Convergent divergent nozzel or De Naval Nozzle ? or is it just an idea? because in every experiment there will be some error ?

Your question is not clear. If you are asking whether De Laval nozzles are used to create supersonic flow, the answer is yes. Or are you asking something else?

next one is the question

According to the Euler's one dimensional compressible equation ..... Mach number has to be 1 exactly at the throat of the nozzle for subsonic flow to become supersonic...if it perturbs a little then the flow can not be supersonic ... Now the more realistic flow equation is compressible NS equation...... so euler's theory is insuffcient to explain how a flow can be converted to subsonic to supersonic using De Naval Nozzle.
I want to know the basic idea behind the design of the nozzle. 
Actually, most nozzle design makes use of the inviscid equations. If the throat of a nozzle is choked (the throat Mach number is 1) then the exit flow may still be subsonic. If it is, then a pressure variation at the nozzle exit can cause the throat to become subsonic, assuming fixed nozzle inlet conditions. If the exit flow is supersonic, then pressure fluctuations can't travel upstream, and the throat conditions depend on the upstream (inlet) conditions. Nozzle design begins by deciding on a pressure ratio Pexit/Pinlet and then creating an expansion region that will result in shockfree flow that yields a Mach number at the exit plane which matches the isentropic result from the 1D with area change result computed from the given pressure ratio. Viscous effects can be added in with a boundary layer thickness adjustment, usually in an iterative design process. The method of characteristics is still used quite heavily in nozzle design (at least in the area that I work in).

Zucrow is an old but still wellsuited book for the design based on Euler equations and the characteristic method. However, modern CFD techniques can now approach NS equations

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