Lecture-5-nozzles-and-diffs.pdf 334p3z

Adiabatic flow through nozzles

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But the actual process is irreversible adiabatic. Since the shaft work is absent the stagnation enthalpy remains constant (h01=h02).

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The actual velocity c2 is less tan than the isentropic velocity. Also irreversible adiabatic flow experiences an increase in entropy ∆s and decrease in the stagnation pressure ∆p0= p01 – p02

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Nozzle efficiency for large pressure ratio 

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The function of nozzle is to transform the energy of the expanding gas in to KE. Nozzle efficiency should be a measure of he energy transformation

We have

(7)

Nozzle Velocity coefficient 

Most of the applications the gas or steam enters the nozzle from a large space. So the enthalpy at the beginning of the process is considered as h01 instead of h1

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We have

Nozzle efficiency for small pressure ratio 

From eqn. (7) we have

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(h2-h2s) is the enthalpy loss due to irreversible flow For isentropic process we have

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=0

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If the change in pressure is small, the flow can be considered as incompressible (ρ = constant).

Adiabatic flow through diffs 

The transformation of KE of gases in to a static pressure rise takes place in a diff

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There is no change in entropy and loss in stagnation pressure during a reversible adiabatic pressure.

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But actual process is irreversible adiabatic, it must be accompanied by a stagnation pressure loss and increase in entropy. Final state after irreversible adiabatic process is represented by point 2. This is fixed by assuming same change in the KE.

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There will be a change in static pressure but the stagnation enthalpy remains the same

Diff efficiency for small pressure rise 

For small rise in static pressure, the flow in the diff can be considered as incompressible (ρ ≈ constant)

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Therefore the pressure rise is given by

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For the actual state point 2

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Therefore the pressure rise in actual process is given by

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But

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Thus we have

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Diff efficiency

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But we have

Diff efficiency for large pressure rise 

For large pressure rise through turbines, density change is appreciable and flow is compressible

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We have the energy equation for the processes

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Substituting this in to the efficiency equation we have

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For incompressible flow this expression can be reduced to expressions derived for small pressure rise. For example

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Therefore we have

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This is same as the expression that derived for small pressure rise.