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Subject - THERMAL ENGINEERING - II ME 4003
Branch - Mechanical Engineering
Semester - 4th Semester

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STEAM NOZZLES

A steam nozzle is a passage of varying cross-section through which steam flows to convert thermal energy into kinetic energy. Steam nozzles are commonly used in steam turbines, injectors, and other steam-powered devices where high-velocity steam is required.

4.1 Flow of Steam Through Nozzle

When steam enters a nozzle, it undergoes expansion due to a decrease in pressure. This expansion increases the velocity of the steam, converting heat energy into kinetic energy. The steam flow can be:

Subsonic Flow (Low velocity, before reaching the throat)
Sonic Flow (At the throat, when the velocity reaches the speed of sound)
Supersonic Flow (Beyond the throat, in a diverging section)

A nozzle can be of three types:

Convergent Nozzle – Narrows down; increases velocity for subsonic flows.
Divergent Nozzle – Expands; used for supersonic flows.
Convergent-Divergent Nozzle – First narrows (throat), then expands; used in turbines.

4.2 Velocity of Steam at Exit of Nozzle (Using Heat Drop & Mollier Chart)

The velocity of steam at the exit of a nozzle can be calculated using the first law of thermodynamics (Steady Flow Energy Equation - SFEE):

V_2 = \sqrt{2(h_1 - h_2)}

Where:

$V_2$ = Exit velocity of steam (m/s)
$h_1$ = Enthalpy of steam at inlet (kJ/kg)
$h_2$ = Enthalpy of steam at exit (kJ/kg)

The heat drop (h₁ - h₂) can be determined from steam tables or the Mollier chart (h-s diagram).

4.3 Discharge of Steam Through Nozzles

The mass flow rate of steam through the nozzle is given by:

m = A \cdot V \cdot \rho

Where:

$m$ = Mass flow rate (kg/s)
$A$ = Cross-sectional area (m²)
$V$ = Velocity of steam (m/s)
$\rho$ = Steam density (kg/m³)

At maximum discharge, steam reaches sonic velocity at the throat.

4.4 Critical Pressure Ratio

The critical pressure ratio (P₂/P₁) is the ratio of exit pressure ( $P_2$ ) to inlet pressure ( $P_1$ ) at which the mass flow rate is maximum. It is given by:

\left(\frac{P_2}{P_1}\right)_{\text{critical}} = \left(\frac{2}{n+1}\right)^{\frac{n}{n-1}}

Where:

$n$ = Expansion index (usually 1.3 for steam).

For steam, the approximate critical pressure ratio is 0.546 (i.e., the pressure at the throat is about 54.6% of inlet pressure for maximum discharge).

4.5 Calculation of Cross-Sectional Areas (Throat & Exit) for Maximum Discharge

To achieve maximum discharge, we calculate:

Throat Area (Aₜ) – Minimum area where the steam velocity reaches sonic speed.
Exit Area (Aₑ) – The final expanded area for maximum velocity.

The formula for throat area is:

A_t = \frac{m}{\rho_t V_t}

Where:

$\rho_t$ = Density of steam at throat.
$V_t$ = Velocity of steam at throat.

The exit area is calculated similarly using exit velocity and density.

4.6 Effect of Friction in Nozzles

Friction reduces kinetic energy by converting part of it into heat.
Due to friction, the actual velocity of steam is lower than the theoretical velocity.
The isentropic efficiency ( $\eta$ ) of the nozzle is given by:

\eta = \frac{\text{Actual K.E. at exit}}{\text{Theoretical K.E. at exit}}

Friction also increases steam entropy, affecting the enthalpy drop.

4.7 Super-Saturated Flow in Nozzles

In super-saturated flow, steam does not condense immediately even if it enters the wet region.
This happens when steam expands very quickly, preventing immediate droplet formation.
Effects of super-saturation:
- Increases velocity beyond normal dry-saturated expansion.
- Reduces heat drop because some energy remains in the vapor phase.
- Can cause shock waves in the nozzle.

4.8 Working of a Steam Jet Injector

A steam jet injector (or ejector) is a device that uses high-velocity steam to pump water or another fluid.

Working Principle:

High-pressure steam enters the injector and passes through a nozzle.
This creates a high-velocity jet that generates suction, pulling in feedwater.
The steam and water mix in a diffuser, where velocity decreases, and pressure increases.
The resulting high-pressure mixture is delivered to the boiler.

Applications:

Used in boiler feed systems to pump water without mechanical parts.

4.9 Simple Numerical Problems

Example 1: Velocity at Nozzle Exit

Given:

Inlet enthalpy, $h_1 = 2800$ kJ/kg
Exit enthalpy, $h_2 = 2500$ kJ/kg

Find exit velocity ( $V_2$ ):

V_2 = \sqrt{2 \times (h_1 - h_2)}

V_2 = \sqrt{2 \times (2800 - 2500)}

V_2 = \sqrt{600}

V_2 = 34.64 \times 10 = 346.4 \text{ m/s}

So, the exit velocity is 346.4 m/s.

Conclusion

Steam nozzles convert heat energy into kinetic energy, increasing steam velocity.
The critical pressure ratio ensures maximum mass flow rate.
Friction reduces efficiency, while super-saturation affects expansion behavior.
Steam jet injectors use high-velocity steam to pump fluids efficiently.