A De Laval turbine is a single-stage impulse turbine. A fixed converging-diverging nozzle directs a high-speed steam jet onto curved blades around one rotor. The flow passes through the blade row, changing its tangential momentum and transferring work to the wheel.
De Laval Steam Turbine Interactive Calculator
Explore a single impulse rotor fed by a fixed expanding nozzle. Compare blade speed with jet speed and nozzle angle using an ideal frictionless, symmetric-blade velocity model.
Equation Used
- Steady axial throughflow and symmetric frictionless blade turning.
- Nozzle angle is measured from the tangential direction of blade travel.
- No mass-flow, rotor diameter, stress, bearing-loss or steam-state calculation.
- Ideal maximum blade utilization is cos²α, not 100% for a finite nozzle angle.
Utilization is the ideal fraction of nozzle-exit kinetic energy transferred to the rotor, not overall steam-plant efficiency. Negative values indicate a non-extracting operating point in this ideal velocity model.
A fixed nozzle and one moving blade row
The illustration separates the stationary nozzle from the rotating wheel. Steam enters at an angle to the direction of blade travel and crosses the wheel axially. The peripheral blades turn the relative flow. A separate velocity diagram shows why jet speed and blade speed must be distinguished.
The wheel and flow indicators are intentionally slowed. They explain direction and component placement, not actual particle transit or rotor speed. Blade count, thickness and casing proportions are schematic.
Explore the blade-speed ratio
The calculator compares blade speed U with absolute nozzle-exit speed V. Nozzle angle α determines how much of V lies in the direction of wheel motion. The simple half-jet-speed optimum is recovered only in the limiting zero-angle model.
The displayed ideal utilization is not a complete turbine or plant efficiency. Steam-state changes, nozzle losses, bearings, leakage, disc friction and exhaust losses are not calculated.
Frictionless symmetric-blade model
The inlet tangential component is Vw1=V cos α. Relative inlet tangential velocity is Vw1−U. For ideal symmetric turning, its tangential sign reverses at exit while the axial component remains V sin α. Adding blade speed back gives Vw2=2U−V cos α.
Specific rotor work is U(Vw1−Vw2). Dividing by inlet kinetic energy V²/2 gives ηb=4(U/V)(cos α−U/V). Differentiating with respect to U gives Uopt=V cos α/2 and maximum ηb=cos²α.
If U exceeds V cos α, this ideal expression becomes negative. The result is shown rather than clipped into a misleading positive efficiency. A real fixed blade row also incurs off-design incidence losses absent from this model.
A 1000 m/s jet at 20 degrees
At U=400 m/s, the speed ratio is 0.4. Inlet tangential velocity is 939.69 m/s and ideal exit tangential velocity is −139.69 m/s. The ideal utilization is 86.35%.
The ideal optimum is 469.85 m/s, with maximum blade utilization 88.30%. The selected 400 m/s is 14.87% below that optimum. These figures are not steam-plant efficiency or an allowable mechanical rotor speed.
Limits of the ideal comparison
The model assumes matched symmetric blade turning at each selected condition. Actual blade metal angles are fixed, so changing wheel or jet speed changes incidence and losses. The illustration’s blade outline does not serve as a manufactured blade profile.
A rotor-strength check needs dimensions, materials, temperature and stress analysis. No permissible speed, service interval or power output is inferred from this velocity comparison.
Impulse turbine questions
Why is optimum speed below half the jet speed?
Only the tangential jet component V cos α enters this optimum-speed expression.
What does negative outlet tangential velocity mean?
The exhaust swirl is opposite the direction of wheel travel in the fixed frame. The axial component can still carry flow through the rotor.
Is 90% utilization 90% thermal efficiency?
No. This denominator is nozzle-exit jet kinetic energy, not fuel heat or total steam-cycle input.
References
NPTEL Fluid Machinery, lecture 22, single-stage impulse turbine and velocity components. Lecture 23, optimum speed ratio and ideal blade utilization. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), printed page 99, movements 369–370, nozzle and peripheral bucket arrangement.
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