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.
Understanding Steam Turbine Stages Reference
Velocity triangles are the main tool for seeing what the steam does at a blade row. Absolute velocity is the steam velocity seen by a stationary observer. Blade velocity is the speed of the moving blade.
Relative velocity is the steam velocity seen by someone travelling with that blade. These three velocities form a triangle at blade entry and another at blade exit. The whirl component points around the rotor and produces torque.
The flow component points through the passage between blades. Students should label every angle carefully and keep one direction convention throughout a calculation. A reversed outlet whirl component usually means more work is taken from the steam, but excessive turning can create losses.
The blade shape must guide steam smoothly. If steam strikes the leading edge at the wrong relative angle, it does not enter the passage cleanly. This is called incidence loss.
Friction along blade surfaces reduces relative velocity. Turbulence, leakage over blade tips, wet steam droplets, and mixing between flows remove more useful energy. These effects explain why an ideal velocity triangle gives a larger work value than a real stage produces.
In school problems, ideal flow is often assumed first. In practical engineering, designers allow for losses and choose blade angles that work well over the expected operating range.
A single stage cannot usually handle the full expansion from boiler pressure to condenser pressure efficiently. The steam velocity would become extremely high, requiring blades to turn the flow too sharply. Many stages divide the total enthalpy drop into smaller parts.
This keeps blade speeds and flow angles within workable limits. Some impulse turbines use velocity compounding, where several moving blade rows reduce one high steam velocity. Pressure compounding uses several nozzle and rotor sets, with a smaller pressure drop in each set.
Reaction turbines commonly use many similar stages. Their pressure change through moving passages means that clearances and seals matter greatly, since leakage bypasses blade passages and reduces output.
Steam turbines appear in thermal power stations, nuclear stations, marine propulsion systems, and some industrial plants that need both electricity and process steam. The early stages handle hot, high pressure steam and need strong materials. Later stages handle larger steam volumes because expansion lowers density.
Their blades therefore become longer. At the low pressure end, steam can become wet. Water droplets can erode blade edges over time.
When solving stage problems, begin by identifying the given velocities, angles, mass flow rate, and whether the values are absolute or relative. Then find the whirl components before calculating work.
Finally compare the actual work with the available enthalpy drop. This order helps prevent sign mistakes and makes the physical meaning of each result clearer.