Steam turbine stages convert the thermal energy of high-pressure steam into shaft work by expanding steam through nozzles and moving blade rows. This cheat sheet helps engineering students compare impulse and reaction stages, read basic velocity triangles, and connect pressure drop to useful turbine power. It is useful for design sketches, lab reports, and quick review before turbine performance problems.
The most important ideas are that nozzles increase steam velocity, blades change momentum, and each stage extracts only part of the total available energy. Impulse stages place most pressure drop in the fixed nozzles, while reaction stages share pressure drop between fixed and moving blades. Key formulas include blade speed U = piDN, power P = m dot times specific work, and efficiency = useful output divided by ideal energy input.
Key Facts
- A turbine stage usually contains one row of fixed blades or nozzles followed by one row of moving blades attached to the rotor.
- In an impulse stage, most of the pressure drop occurs in the fixed nozzles, and the moving blades mainly reduce steam velocity by changing its direction.
- In a reaction stage, pressure drops in both fixed and moving blades, so the moving blades act partly like nozzles.
- Blade speed is U = piDN, where U is rim speed, D is mean rotor diameter, and N is rotational speed in revolutions per second.
- Stage specific work can be estimated from Euler's turbine equation: w = U(Vw1 - Vw2), where Vw1 and Vw2 are inlet and outlet whirl velocity components.
- Turbine power is P = m dot w, where m dot is mass flow rate and w is specific work output.
- Stage efficiency is eta stage = actual work output / ideal isentropic enthalpy drop.
- The degree of reaction is R = enthalpy drop in moving blades / total stage enthalpy drop.
Vocabulary
- Stage
- A turbine stage is one energy-conversion unit made of fixed blades and moving blades.
- Impulse stage
- An impulse stage is a turbine stage where steam pressure drops mainly in the nozzles before striking the moving blades.
- Reaction stage
- A reaction stage is a turbine stage where steam expands and loses pressure in both fixed and moving blade passages.
- Velocity triangle
- A velocity triangle is a diagram that shows absolute steam velocity, blade velocity, and relative steam velocity at a blade row.
- Whirl velocity
- Whirl velocity is the tangential component of steam velocity that produces torque on the turbine rotor.
- Degree of reaction
- Degree of reaction is the fraction of total stage enthalpy drop that occurs in the moving blades.
Common Mistakes to Avoid
- Confusing impulse and reaction stages, because impulse stages have pressure drop mainly in nozzles while reaction stages have pressure drop in both fixed and moving blades.
- Using rpm directly in U = piDN, because N must be in revolutions per second unless the formula is adjusted for revolutions per minute.
- Ignoring whirl velocity direction, because Euler turbine work depends on Vw1 - Vw2 and a sign error can make turbine work appear too large or negative.
- Treating all enthalpy drop as useful work, because real turbines have losses from friction, leakage, moisture, and nonideal expansion.
- Drawing velocity triangles without consistent reference directions, because absolute velocity, relative velocity, and blade speed must share the same scale and sign convention.
Practice Questions
- 1 A turbine rotor has a mean diameter of 0.80 m and rotates at 3000 rpm. Calculate the blade speed U in m/s using U = piDN with N in revolutions per second.
- 2 A stage has U = 180 m/s, Vw1 = 420 m/s, and Vw2 = 80 m/s. Calculate the stage specific work using w = U(Vw1 - Vw2).
- 3 A steam turbine stage produces 210 kJ/kg of actual work from an ideal isentropic enthalpy drop of 250 kJ/kg. Calculate the stage efficiency.
- 4 Explain why a multistage turbine is usually preferred over extracting the full steam pressure drop in one single stage.