Expansion waves, Rayleigh and Fanno Flow:

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Design of a Supersonic Nozzle using Method of Characteristics:

General Theory of Method of Characteristics:

Characteristics are ‘lines’ in a supersonic flow oriented in specific directions along which disturbances (pressure waves) are propagated. The Method of Characteristics (MOC) is a numerical procedure appropriate for solving, among other things, two-dimensional compressible flow problems. By using this technique, flow properties such as direction and velocity, can be calculated at distinct points throughout a flow field.

The three properties of characteristics are as follows:
Property 1: A characteristic in a two dimensional supersonic flow is a curve or line along which physical disturbances are propagated at the local speed of sound relative to the gas.
Property 2: A characteristic is a curve across which flow properties are continuous, although they may have discontinuous first derivatives, and along
which the derivatives are indeterminate.
Property 3: A characteristic is a curve along which the governing partial differential equations may be manipulated into an ordinary differential equation.

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FANNO FLOW:

clip_image004[8] discussed above .it was proved by equation above that at the maximum entropy point F on the Fanno line the gas had sonic velocity.

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