Steam Nozzles Notes

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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.

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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:

1. Convergent Nozzle – Narrows down; increases velocity for subsonic flows.

2. Divergent Nozzle – Expands; used for supersonic flows.

3. Convergent-Divergent Nozzle – First narrows (throat), then expands; used in turbines.

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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).

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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.

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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).

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

To achieve maximum discharge, we calculate:

1. Throat Area (Aₜ) – Minimum area where the steam velocity reaches sonic speed.

2. 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.

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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.

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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.

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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:

1. High-pressure steam enters the injector and passes through a nozzle.

2. This creates a high-velocity jet that generates suction, pulling in feedwater.

3. The steam and water mix in a diffuser, where velocity decreases, and pressure increases.

4. The resulting high-pressure mixture is delivered to the boiler.

Applications:

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

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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.

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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.