In short
A steam nozzle converts the enthalpy (pressure energy) of steam into a high-velocity jet; a steam turbine then converts that jet's kinetic energy into shaft rotation through rows of moving blades. Together they are the expansion end of every thermal power station, and their analysis is pure applied thermodynamics plus velocity triangles. In India this is the working heart of NTPC, Tata Power, Adani Power and JSW stations, of BHEL's and Siemens Energy's turbine shops, of sugar, paper and refinery cogeneration sets, and of nuclear plants under NPCIL. Universities examine nozzle sizing, critical pressure ratio and blade-work derivations every year, and GATE ME regularly asks a numerical on optimum blade speed ratio or maximum blade efficiency.
Explained
Flow through a steam nozzle
- A nozzle is a duct of varying cross-section in which steam expands, dropping pressure and enthalpy while gaining velocity; a diffuser does the reverse.
- Flow is treated as steady, adiabatic and (ideally) frictionless, with negligible work and potential energy change. Steady-flow energy equation: h₁ + C₁²/2 = h₂ + C₂²/2.
- Hence C₂ = √(2(h₁ − h₂) + C₁²); with negligible inlet velocity, C₂ = √(2 Δh) = 44.72√(Δh) with Δh in kJ/kg.
- The enthalpy drop Δh is read as the vertical drop on the h-s (Mollier) chart between inlet pressure and exit pressure along an isentropic line - this is why steam-table and Mollier practice matters here.
- Area variation: a converging passage accelerates subsonic steam; once sonic velocity is reached the passage must diverge to accelerate further. So:
- Convergent nozzle - exit pressure ratio above critical; exit Mach number ≤ 1.
- Convergent-divergent (De Laval) nozzle - large pressure drop; throat is sonic, divergent part gives supersonic exit. Used in impulse turbine nozzle blocks and in steam ejectors.
- Throat: the minimum area section, where the mass flow per unit area is maximum and the velocity equals the local sonic velocity (M = 1) when the nozzle is choked.
- Choking: once the back pressure falls to the critical value, mass flow becomes maximum and further lowering of back pressure does not increase it - the throat "chokes". Flow is then fixed by inlet conditions and throat area.
- Critical pressure ratio p*/p₁ = [2/(n+1)]^{n/(n−1)}, using the expansion index n of the index law pvn = constant:
- superheated steam n ≈ 1.3 → p*/p₁ ≈ 0.546;
- dry saturated steam n ≈ 1.135 → p*/p₁ ≈ 0.577;
- wet steam n = 1.035 + 0.1x (Zeuner's relation, x = inlet dryness fraction).
- Off-design behaviour: if the back pressure is above design, the divergent part acts as a diffuser or a shock wave forms inside it (over-expansion/under-expansion losses); if below design, expansion continues outside the nozzle as oblique waves. Both reduce efficiency without changing the choked mass flow.
Nozzle efficiency, friction and supersaturated flow
- Friction appears mainly in the divergent portion (longer passage, supersonic flow, boundary-layer growth), so it is accounted for by an efficiency rather than modelled in detail.
- Nozzle efficiency η_N = actual enthalpy drop / isentropic enthalpy drop = (h₁ − h₂′)/(h₁ − h₂) = C_actual²/C_ideal². Typical values 0.90-0.95; the velocity coefficient (coefficient of velocity) = √η_N ≈ 0.95-0.97.
- Friction reheats the steam: the actual exit state lies to the right of the isentropic point on the h-s chart, so exit dryness fraction and specific volume are higher than the isentropic values. Exit area must be computed with the *actual* specific volume.
- Supersaturated (metastable) flow: steam expands so fast (of the order of milliseconds) that condensation lags behind - it continues as a dry vapour below its saturation temperature, i.e. undercooled, behaving like a perfect gas with γ = 1.3.
- Wilson line: the locus on the h-s chart (roughly 3-5% below the saturation line, about x ≈ 0.95-0.97) at which the metastable state collapses and condensation suddenly occurs.
- Effects of supersaturation: actual specific volume lower than equilibrium → higher mass flow for the same throat area; reduced enthalpy drop, so slightly lower exit velocity; higher dryness fraction; the degree of undercooling is the temperature difference below the saturation temperature at that pressure.
Impulse and reaction turbines
- Impulse turbine (De Laval, Curtis, Rateau type): the whole pressure drop occurs in the fixed nozzles; steam flows through the moving blades at constant pressure, only its direction changing. Blades are symmetrical, passages of constant area, and partial admission (only part of the periphery) is possible.
- Reaction turbine (Parsons type): pressure drops in both the fixed (nozzle) and moving blade rows; moving blade passages are convergent, so steam accelerates relative to the blade and leaves with a reactive thrust. Full peripheral admission is necessary, and axial thrust must be balanced (dummy pistons, double flow).
- Degree of reaction R = enthalpy drop in moving blades / enthalpy drop in the stage. R = 0 → pure impulse; R = 0.5 → Parsons stage, in which moving and fixed blades are mirror images and the velocity triangles are congruent.
- Impulse-reaction (modern practice): real large machines use an impulse (or low-reaction) control stage followed by reaction stages whose degree of reaction rises from root to tip of long LP blades (vortex/twisted blading).
- Comparison of typical practice: impulse stages tolerate large pressure drop per stage, allow nozzle governing and partial admission; reaction stages are more efficient per stage but need many more stages and tight tip clearances.
Velocity diagrams and blade work (single-stage impulse)
- Symbols: C = absolute steam velocity, C_w = its tangential (whirl) component, C_a = axial component, V (or C_r) = relative velocity, U = blade speed, α = nozzle angle, β = blade angle; subscripts 1 (inlet) and 2 (outlet).
- Construction: draw C₁ at α₁ to the tangential direction; subtract U vectorially to get V₁ at blade inlet angle β₁; at exit V₂ = K·V₁ where K = blade velocity coefficient (friction factor, 0.85-0.95); add U back to get C₂.
- Tangential force F_t = ṁ(C_w1 + C_w2) when the exit whirl is opposite in direction (the usual case); work W = F_t·U; power P = ṁ U ΔC_w.
- Axial thrust F_a = ṁ(C_a1 − C_a2) - carried by the thrust bearing.
- Blade (diagram) efficiency η_b = 2U ΔC_w / C₁²; stage efficiency = η_N × η_b; gross/overall stage efficiency also includes disc friction and windage.
- Optimum blade speed ratio (single-stage impulse): ρ = U/C₁ = cos α₁ / 2, giving η_b,max = (cos²α₁/2)(1 + K·cos β₂/cos β₁); for ideal symmetric, frictionless blades η_b,max = cos²α₁.
- For a two-row velocity-compounded (Curtis) stage, optimum ρ = cos α₁/4, and in general cos α₁/(2n) for n moving rows; the first row does the largest share of the work (for ideal two rows, 3:1).
- Reaction (Parsons, R = 0.5): optimum ρ = cos α₁ and η_b,max = 2cos²α₁/(1 + cos²α₁) - higher than the impulse value, which is why reaction blading dominates the HP/IP sections of large sets.
- Nozzle (blade) height: from continuity ṁ v = A C, with A = π D h × (fraction of periphery admitted) × (1 − blockage); blade heights increase stage by stage as specific volume rises.
Compounding, multi-stage machines and the reheat factor
- A single-stage impulse turbine using the full boiler-to-condenser drop would need a blade speed of several hundred m/s and rotor speeds of 30,000 rpm or more - unsafe centrifugal stress and poor efficiency. Compounding splits the drop into stages to bring blade speed down.
- Velocity compounding (Curtis): one set of nozzles expands all the way; the resulting high-velocity jet is absorbed in two or three moving rows separated by fixed guide blades that only redirect the steam. Pressure constant across all moving rows; cheap and compact, used as a control/first stage, but less efficient.
- Pressure compounding (Rateau): nozzle ring and moving row alternate; pressure falls in each nozzle ring while velocities stay moderate. More stages, more efficient, longer and costlier.
- Pressure-velocity compounding: a few Curtis wheels in series - large drop per wheel, shorter machine (older marine and some industrial sets).
- Reaction (Parsons) compounding: many stages of alternating fixed and moving blades, each taking a small drop.
- Reheat factor RF = Σ(isentropic stage enthalpy drops) / (overall isentropic drop from inlet to exhaust) > 1, because the constant-pressure lines on the h-s chart diverge, so each stage gets a slightly larger drop than the single-expansion line would give. Typical RF = 1.03-1.06.
- Internal (stage) efficiency = η_stage × RF; this "reheat gain" is a real benefit of multi-staging, distinct from the boiler reheat cycle.
- Classification of steam turbines: by flow direction (axial, radial - the Ljungström double-rotation radial turbine), by steam supply/exhaust (condensing, non-condensing/back-pressure, extraction-cum-condensing, mixed-pressure, reheat), by casing (single, double or triple cylinder; tandem-compound or cross-compound), by application (power generation at 3,000 rpm for India's 50 Hz grid, mechanical drive, marine).
Losses, governing, and plant practice in India
- Losses: nozzle friction; blade friction and profile loss; leakage past diaphragms, blade tips and glands; partial-admission and windage loss on idle blade arc; disc friction; residual (leaving/carry-over) velocity loss; wetness/erosion loss in LP stages; mechanical loss in bearings and the exhaust/hood loss.
- Moisture: wetness beyond about 10-12% erodes LP blades; controlled by cycle reheat, water-extraction grooves in casings, and stellite/erosion shields on blade leading edges.
- Governing (keeping speed within limits as load varies):
- Throttle governing - a servo-operated throttle valve reduces inlet pressure (constant-enthalpy throttling); simple and cheap, used in small sets, poorer part-load efficiency.
- Nozzle governing - nozzle groups of the first stage are cut out in sequence; keeps inlet pressure and hence efficiency high at part load; standard on large impulse-control-stage machines.
- By-pass governing - at overload, steam is by-passed from the first-stage exhaust to a later stage to gain extra output.
- Combination of nozzle and by-pass governing is common in utility sets.
- Protection: overspeed trip (typically about 110% of rated speed), low lube-oil pressure trip, high axial-displacement and vibration trips, low-vacuum trip, turning (barring) gear for cooldown.
- Condenser vacuum matters: every 10 mbar rise in back pressure costs roughly 0.5-1% heat rate in a large condensing set (value varies with design) - hence cooling-tower and air-ejector performance is monitored hourly.
- Indian practice and codes: BHEL supplies 210/250/500/600/660/800 MW sets; supercritical (about 242 bar / 247 kgf/cm², 537/565 °C) and ultra-supercritical units are the current new-build standard (NTPC's 660/800 MW units). Power steam piping is designed to ASME B31.1, with IBR 2026 (Indian Boiler Regulations, 2026, framed under the Boilers Act, 2025; they superseded IBR 1950 in October 2026) governing steam-side pressure parts up to the turbine stop valve, ASME PTC 6 for turbine performance testing and IEC 60045 / IS 14774 for steam turbine specification. Blade and rotor materials are covered by IS/ASTM grades; CEA (Central Electricity Authority) regulations and the Grid Code govern operation, with frequency held near 50 Hz. Figures of this kind are revised periodically - verify against the current edition before quoting in design work.
Key points
- Nozzle - duct that converts enthalpy to kinetic energy; C₂ = 44.72√Δh (Δh in kJ/kg) with negligible inlet velocity.
- Throat - minimum area; sonic (M = 1) when choked; sets the maximum mass flow.
- Critical pressure ratio - p*/p₁ ≈ 0.546 (superheated, n = 1.3), 0.577 (dry saturated, n = 1.135).
- Choked flow - lowering back pressure below critical cannot raise mass flow; raise inlet pressure or throat area instead.
- Convergent-divergent nozzle - needed only when the overall pressure ratio is below critical, i.e. for supersonic exit.
- Nozzle efficiency - 0.90-0.95; velocity coefficient = √η_N; friction raises exit dryness and specific volume.
- Supersaturated flow - condensation lags, steam undercooled, γ = 1.3; gives more mass flow but slightly less exit velocity; ends at the Wilson line (x ≈ 0.95-0.97).
- Impulse turbine - full pressure drop in nozzles, constant pressure across moving blades, symmetrical blades, partial admission possible.
- Reaction turbine - drop in both fixed and moving rows; converging moving passages; full admission; axial thrust significant.
- Degree of reaction - R = moving-blade drop / stage drop; R = 0.5 is the Parsons stage with congruent velocity triangles.
- Blade efficiency - η_b = 2UΔC_w/C₁²; stage efficiency = η_N × η_b.
- Optimum ρ = U/C₁ - cos α₁/2 (single impulse row), cos α₁/(2n) (n velocity-compounded rows), cos α₁ (50% reaction).
- Maximum blade efficiency - cos²α₁ (ideal impulse), 2cos²α₁/(1 + cos²α₁) (50% reaction).
- Blade velocity coefficient K - V₂/V₁, about 0.85-0.95; friction loss = ṁ(V₁² − V₂²)/2.
- Compounding - velocity (Curtis), pressure (Rateau), pressure-velocity, reaction; needed to cut blade speed and stress.
- Reheat factor - 1.03-1.06; sum of stage isentropic drops exceeds the single overall isentropic drop.
- Governing - throttle (simple, lossy), nozzle (efficient at part load), by-pass (overload); overspeed trip near 110%.
- Degradation watch-list - LP blade erosion above ~10-12% wetness, gland and tip leakage, falling condenser vacuum.
Formulas and examples
ṁ = A C / v [ṁ kg/s, A m², C m/s, v m³/kg - specific volume at that section]
p*/p₁ = [2/(n + 1)]^{n/(n−1)} ; n = 1.3 superheated, 1.135 dry saturated, n = 1.035 + 0.1x wet
ṁ_max = A_throat √{ n (p₁/v₁) [2/(n+1)]^{(n+1)/(n−1)} } (choked flow)
η_N = (h₁ − h₂′)/(h₁ − h₂) = (C_actual/C_ideal)² ; velocity coefficient k = C_actual/C_ideal = √η_N
ΔC_w = C_w1 + C_w2 = C₁cos α₁ + C₂cos α₂ (exit whirl opposing) ; axial thrust F_a = ṁ(C_a1 − C_a2)
Blade work W = ṁ U ΔC_w [W in watts if ṁ kg/s, U m/s, ΔC_w m/s] ; blade efficiency η_b = 2 U ΔC_w / C₁²
Impulse: ρ_opt = cos α₁/2, η_b,max = (cos²α₁/2)(1 + K C) where C = cos β₂/cos β₁ ; ideal η_b,max = cos²α₁
n moving rows (velocity compounded): ρ_opt = cos α₁/(2n) ; work in rows ratio 3:1 for ideal 2 rows
50% reaction: ρ_opt = cos α₁, η_b,max = 2cos²α₁/(1 + cos²α₁) ; ΔC_w = 2C₁cos α₁ − U
Blade friction loss = ṁ (V₁² − V₂²)/2 ; Reheat factor RF = Σ Δh_s,stage / Δh_s,overall
Nozzle/blade height: ṁ v = π D h ε C_a , ε = fraction of periphery admitted
Example 1 - Critical pressure, throat area and exit area of a convergent-divergent nozzle. Steam at 10 bar, dry saturated (h₁ = 2,778 kJ/kg) expands to 1.5 bar; ṁ = 0.5 kg/s; inlet velocity negligible; nozzle efficiency 100% up to the throat and 90% for the divergent part (isentropic drops from steam tables/Mollier chart).
- n = 1.135 → critical ratio = 0.577 → p\* = 5.77 bar.
- Isentropic drop to throat ≈ 103 kJ/kg → C_t = 44.72√103 ≈ 454 m/s; at the throat v ≈ 0.317 m³/kg, x ≈ 0.962.
- A_throat = ṁ v / C = 0.5 × 0.317 / 454 = 3.49 × 10⁻⁴ m² = 3.49 cm² → throat diameter = √(4 × 3.49/π) ≈ 2.1 cm.
- Isentropic drop 10 bar → 1.5 bar ≈ 330 kJ/kg, so the divergent part's isentropic share is 330 − 103 = 227 kJ/kg, of which 0.9 × 227 = 204 kJ/kg is realised; total actual drop = 103 + 204 = 307 kJ/kg → C₂ = 44.72√307 ≈ 784 m/s.
- Actual exit state: x₂ ≈ 0.90 at 1.5 bar (friction reheat raises it) → v₂ ≈ 0.90 × 1.159 ≈ 1.043 m³/kg.
- A₂ = 0.5 × 1.043 / 784 = 6.65 × 10⁻⁴ m² = 6.65 cm² → exit diameter ≈ 2.9 cm. (Divergence check: A₂/A_t ≈ 1.9.)
Example 2 - Single-stage impulse turbine, full velocity diagram. Nozzle angle α₁ = 20°, C₁ = 600 m/s, U = 250 m/s, blade exit angle β₂ = 25°, K = V₂/V₁ = 0.9, ṁ = 5 kg/s.
- C_w1 = 600 cos 20° = 600 × 0.9397 = 563.8 m/s; C_a1 = 600 sin 20° = 600 × 0.3420 = 205.2 m/s.
- Relative inlet: V_w1 = 563.8 − 250 = 313.8 m/s → V₁ = √(313.8² + 205.2²) = √(98,470 + 42,107) = √140,577 ≈ 374.9 m/s; β₁ = tan⁻¹(205.2/313.8) = 33.2°.
- V₂ = 0.9 × 374.9 = 337.4 m/s; V_w2 = 337.4 cos 25° = 337.4 × 0.9063 = 305.8 m/s; C_a2 = 337.4 sin 25° = 142.6 m/s.
- ΔC_w = V_w1 + V_w2 = 313.8 + 305.8 = 619.6 m/s (equivalently C_w1 + C_w2 with C_w2 = 305.8 − 250 = 55.8 m/s → 563.8 + 55.8 = 619.6 m/s ✓).
- Power = ṁ U ΔC_w = 5 × 250 × 619.6 = 774,500 W ≈ 774.5 kW.
- η_b = 2UΔC_w/C₁² = 2 × 250 × 619.6/600² = 309,800/360,000 = 86.1%.
- Axial thrust = 5 × (205.2 − 142.6) = 313 N. Blade friction loss = 5 × (374.9² − 337.4²)/2 = 5 × (140,577 − 113,839)/2 ≈ 66.8 kW.
Example 3 - Optimum blade speed ratio and maximum efficiency. For the same blading (α₁ = 20°, β₂ = 25°, β₁ = 33.2°, K = 0.9):
- ρ_opt = cos 20°/2 = 0.9397/2 = 0.470 → for C₁ = 600 m/s the best blade speed is U = 281.9 m/s (the 250 m/s above is slightly below optimum).
- C = cos β₂/cos β₁ = 0.9063/0.8368 = 1.083 → η_b,max = (cos²20°/2)(1 + 0.9 × 1.083) = (0.8830/2)(1.9747) = 0.4415 × 1.9747 = 87.2%.
- Ideal symmetric frictionless limit = cos²20° = 88.3% - so friction costs only about 1 percentage point here.
- If the same jet drove a two-row Curtis stage, ρ_opt = cos 20°/4 = 0.235 → U ≈ 141 m/s, i.e. half the rotor speed for the same jet.
Example 4 - 50% reaction (Parsons) stage. Fixed and moving blades identical, α₁ = 20°, blade mean diameter 1.2 m, rotor speed 3,000 rpm, ṁ = 12 kg/s, stage working at the optimum ratio.
- U = πDN/60 = π × 1.2 × 3,000/60 = 188.5 m/s.
- ρ_opt = cos 20° = 0.9397 → C₁ = U/0.9397 = 200.6 m/s.
- ΔC_w = 2C₁cos α₁ − U = 2 × 200.6 × 0.9397 − 188.5 = 376.9 − 188.5 = 188.4 m/s.
- Power = 12 × 188.5 × 188.4 = 426,100 W ≈ 426 kW per stage.
- η_b,max = 2cos²20°/(1 + cos²20°) = 2 × 0.8830/1.8830 = 1.7660/1.8830 = 93.8%.
- Stage isentropic drop needed: work/kg = UΔC_w = 188.5 × 188.4 = 35,520 J/kg ≈ 35.5 kJ/kg → with 93.8% blade efficiency and 95% nozzle efficiency the stage needs about 39.9 kJ/kg of isentropic drop, hence the large number of stages in a reaction machine.
Example 5 - Reheat factor and internal efficiency. A turbine expands from 40 bar, 400 °C to 0.1 bar in four stages; the stage isentropic drops are 265, 272, 279 and 285 kJ/kg; the overall isentropic drop (single expansion line) is 1,069 kJ/kg; stage efficiency 0.85.
- Σ stage drops = 265 + 272 + 279 + 285 = 1,101 kJ/kg.
- RF = 1,101/1,069 = 1.030.
- Internal (turbine) efficiency = 0.85 × 1.030 = 0.876 → 87.6%.
- Actual work = 0.876 × 1,069 = 936 kJ/kg; at ṁ = 100 kg/s, output ≈ 93.6 MW.
| Feature | Impulse stage | 50% reaction stage |
|---|---|---|
| Pressure drop | Only in nozzles | In fixed and moving rows |
| Pressure on moving blades | Constant | Falls |
| Blade shape | Symmetrical, constant area | Aerofoil, converging passage |
| Admission | Partial possible | Must be full |
| Optimum U/C₁ | cos α₁/2 | cos α₁ |
| Max blade efficiency | cos²α₁ | 2cos²α₁/(1 + cos²α₁) |
| Stages for a given drop | Fewer | Many more |
| Axial thrust | Small | Large - needs balancing |
| Typical use | Control/first stage, small sets | HP and IP sections of large sets |
| Compounding | Pressure drop | Velocity level | Note |
|---|---|---|---|
| Velocity (Curtis) | One nozzle set, all at once | Very high jet, absorbed in 2-3 rows | Compact, cheaper, lower efficiency |
| Pressure (Rateau) | In each nozzle ring | Moderate throughout | Efficient, long machine |
| Pressure-velocity | Large per wheel | High per wheel | Shorter than Rateau |
| Reaction (Parsons) | Small, in every row | Low | Highest stage efficiency, most stages |
Where it is used
- Utility power generation: NTPC, NLC, Tata Power, Adani, JSW and state gencos run condensing reheat sets of 210-800 MW at 3,000 rpm; BHEL Hyderabad/Haridwar and Siemens Energy, Toshiba JSW and GE Power India build and service the rotors, nozzle blocks and blading.
- Captive and cogeneration plants: back-pressure and extraction-cum-condensing turbines in sugar mills (Maharashtra, UP, Karnataka), paper, textile, cement, fertiliser and refinery complexes - process steam plus power; Triveni Turbine and Siemens supply much of the 1-100 MW industrial range.
- Nuclear and solar thermal: NPCIL's PHWR/VVER units use large wet-steam LP turbines with moisture separators and reheaters; CSP plants use small steam turbines.
- Marine and defence: steam turbine propulsion and turbo-generators in naval vessels; nozzle theory also underpins steam ejectors, air ejectors for condenser vacuum, injectors and de-superheaters.
- Job roles: turbine design and blade aero engineer, performance/heat-rate engineer (ASME PTC 6 tests), O&M and shift engineer at a power station, erection and commissioning engineer, overhaul/retrofit engineer and NDT/blade-inspection roles; the GATE-ME and ESE syllabi feed PSU recruitment (NTPC, BHEL, NPCIL, SAIL, IOCL).
- Exam and testing use: nozzle calibration and turbine-performance experiments in the thermal engineering laboratory; Mollier-chart expansion and blade velocity diagrams are routine viva questions.
Interview questions
- Q: Why does a steam nozzle need a divergent portion? A: Once the steam reaches sonic velocity at the throat, further acceleration requires increasing area; a convergent passage alone can only reach Mach 1 at exit.
- Q: What is the critical pressure ratio and its value for steam? A: The exit-to-inlet pressure ratio at which the throat velocity becomes sonic and the mass flow is maximum - about 0.546 for superheated steam (n = 1.3) and 0.577 for dry saturated steam (n = 1.135).
- Q: What happens if the back pressure is lowered below the design value of a choked nozzle? A: The mass flow stays unchanged; the extra expansion happens outside the nozzle as expansion waves, so only efficiency and thrust direction are affected.
- Q: What is supersaturated flow and why does it matter? A: Expansion is so rapid that condensation lags and the steam stays metastably dry below its saturation temperature; the lower specific volume raises mass flow for the same throat area, the enthalpy drop and exit velocity fall slightly, and the state collapses at the Wilson line.
- Q: Where does most nozzle friction occur, and what does it do to the exit state? A: In the divergent portion; it reduces the enthalpy drop and velocity and reheats the steam, so exit dryness fraction and specific volume are higher than the isentropic values.
- Q: Distinguish impulse from reaction turbines in one sentence. A: In an impulse turbine the entire pressure drop occurs in the nozzles and the moving blades only change the steam's direction at constant pressure; in a reaction turbine pressure also falls in the converging moving-blade passages.
- Q: Why is compounding necessary? A: Expanding the whole boiler-to-condenser drop in one stage would need blade speeds and rotor speeds far above safe centrifugal stress limits and would waste most of the jet energy as leaving loss.
- Q: Why is the optimum blade speed ratio cos α₁/2 for an impulse stage but cos α₁ for a 50% reaction stage? A: In a reaction stage the moving blades themselves accelerate the steam, so the work per unit jet velocity peaks at twice the blade speed ratio of an impulse stage.
- Q: What is the reheat factor and why is it greater than one? A: It is the ratio of the sum of stage isentropic drops to the overall isentropic drop; constant-pressure lines diverge on the h-s chart, so each successive stage gets a slightly larger isentropic drop.
- Q: Compare throttle and nozzle governing. A: Throttle governing reduces inlet pressure at constant enthalpy and is simple but inefficient at part load; nozzle governing shuts off groups of first-stage nozzles, keeping pressure and efficiency high, and is used on large sets.
- Q: Why is partial admission possible in an impulse stage but not in a reaction stage? A: Impulse blades run at constant pressure, so inactive arcs cause only windage; in a reaction stage a pressure difference exists across the moving row, and an open arc would simply leak steam past the blades.
- Q: Why does LP blade erosion occur and how is it controlled? A: Water droplets in wet steam strike the blades at high relative velocity; it is limited by cycle reheat, moisture-extraction grooves, and stellite shielding of leading edges, keeping wetness below roughly 10-12%.
- Q: Why does falling condenser vacuum hurt output? A: It raises turbine exhaust pressure, cutting the available enthalpy drop and so the work per kg of steam - a typical large set loses of the order of 0.5-1% in heat rate for a 10 mbar rise.
Common mistakes
- Using C = 44.72√Δh with Δh in J/kg instead of kJ/kg, or forgetting the inlet velocity term when it is significant.
- Computing exit area with the isentropic specific volume instead of the actual (friction-reheated) value - the area comes out too small.
- Applying a convergent-divergent shape when the pressure ratio is above critical, or sizing the throat with exit (rather than throat) properties.
- Thinking a lower back pressure increases the mass flow of a choked nozzle.
- Assuming supersaturation raises the exit velocity - it raises mass flow and dryness, but the enthalpy drop and velocity fall slightly.
- Taking ΔC_w as the difference of the whirl components when the exit whirl is opposite in direction - it must then be added; always read the sign off the velocity diagram.
- Mixing up ρ_opt = cos α₁/2 (impulse) with cos α₁ (50% reaction), or forgetting the 1/(2n) rule for velocity-compounded rows.
- Confusing the reheat factor of a multi-stage turbine with the reheat cycle of a boiler - the first is a chart geometry effect, the second a cycle modification.
- Quoting nozzle efficiency as the ratio of velocities rather than of enthalpy drops (velocity coefficient = √η_N).
Related topics
- Properties of steam and steam tables · Power cycles: Rankine, Otto, Diesel and Brayton · Boilers and steam power plants · Turbomachinery: turbines, pumps and compressors · Gas turbines and jet propulsion · Second law, entropy and availability