Turbomachinery: turbines, pumps and compressors

In short

A turbomachine transfers energy between a continuously flowing fluid and a rotating row of blades: a turbine takes energy out of the fluid, while a pump, fan or compressor puts energy in. All of them are analysed with the same two tools — the velocity triangle and the Euler turbomachine equation — so one set of ideas covers hydro turbines, pumps and dynamic compressors. The topic carries heavy weight in GATE (Fluid Machinery), ESE, state JE/AE and university "Fluid Machinery / Turbomachines" papers. It is bread-and-butter interview material at BHEL, NHPC, NTPC, Kirloskar Brothers, KSB, Grundfos, Shakti, Atlas Copco, Thermax, L&T and every process plant that runs rotating equipment.

Explained

What a turbomachine is, and how they are classified

• Defining feature: energy transfer happens through the dynamic action of a rotor (impeller/runner) on a steady flow — unlike positive-displacement machines (piston pump, gear pump, reciprocating compressor) that trap and squeeze a fixed volume.
• By energy direction: power-producing (hydraulic, steam, gas, wind turbines) and power-absorbing (pumps, fans, blowers, compressors).
• By flow path: radial (centrifugal pump, Francis runner), axial (Kaplan, propeller pump, axial fan/compressor), mixed flow (large irrigation pumps, high-specific-speed Francis).
• By fluid: incompressible machines (hydraulic turbines, pumps — density constant, work expressed as head in metres) and compressible machines (compressors, steam/gas turbines — work expressed as enthalpy change, kJ/kg).
• Impulse vs reaction: in an impulse machine all pressure drop occurs in the nozzle and the rotor sees constant pressure (Pelton); in a reaction machine pressure also falls across the moving blades (Francis, Kaplan, axial compressor stages).
• Open vs enclosed: wind turbines and propellers are unenclosed (actuator-disc theory, Betz limit 59.3%); pumps and turbines in casings are enclosed.

Velocity triangles and the Euler equation

• Three velocities at each station: U = blade speed (πDN/60), V = absolute fluid velocity, Vr = velocity relative to blade; V = U + Vr vectorially.
• Components of V: Vw (whirl/tangential, the component that does work) and Vf or Va (flow/axial-radial component, which carries the discharge).
• Angles: α = absolute flow angle (vane/nozzle angle), β = blade (relative) angle. Blades are shaped so Vr enters tangential to the blade — otherwise shock/incidence loss occurs off-design.
• Euler's equation comes from the moment-of-momentum (angular momentum) principle applied to a control volume around the rotor: torque = ṁ(r₂Vw₂ − r₁Vw₁), and power = torque × ω.
• For a pump/compressor: work input per kg = U₂Vw₂ − U₁Vw₁; for a turbine: work output = U₁Vw₁ − U₂Vw₂. Radial entry (Vw₁ = 0) is the usual design assumption for centrifugal pumps, so w = U₂Vw₂.
• The three energy terms of the Euler head show where head comes from: centrifugal effect (U₂²−U₁²)/2g, diffusion in the impeller passage (Vr₁²−Vr₂²)/2g, and kinetic energy at exit (V₂²−V₁²)/2g recovered in the volute/diffuser.
• Degree of reaction R = static head (or enthalpy) change in the rotor ÷ total change in the stage. R = 0 for an impulse stage; R = 0.5 (symmetric blading) is common in axial compressors because it splits the pressure rise and loading evenly between rotor and stator.
• Vane shape in a centrifugal impeller: backward-curved (β₂ < 90°) gives a drooping, stable head–flow curve and the best efficiency — standard practice; radial (β₂ = 90°) gives higher head; forward-curved (β₂ > 90°) gives the highest head but an unstable rising curve and is used only in small fans/blowers.

Hydraulic turbines

• Net (effective) head H = gross head − losses in penstock; power output P = ηₒρgQH. Overall efficiency of a large machine is 90–95%.
• Pelton wheel (impulse, tangential, high head): nozzle converts the whole head into a jet; split buckets turn the jet nearly back on itself (deflection ≈ 165–170°, i.e. bucket outlet angle β₂ ≈ 10–15° from the tangent, not a full 180°, to clear the incoming jet). Flow controlled by a spear/needle valve, with a jet deflector for quick load rejection so the penstock is not water-hammered. Maximum efficiency at U = V₁/2; jet ratio D/d usually 9–12; number of buckets ≈ 15 + D/2d.
• Francis (reaction, mixed flow, medium head): water enters radially through a spiral/scroll casing and adjustable wicket (guide) gates, leaves axially; the gates govern the flow and the swirl. Modern runners are mixed-flow and the machine is fully filled with water.
• Kaplan/propeller (reaction, axial, low head, large flow): few blades (3–6) on a hub; Kaplan blades are adjustable and are moved in step with the guide gates ("double regulation"), which keeps efficiency high down to about 40% load — a propeller turbine with fixed blades has a sharply peaked curve. Bulb/tubular variants are used for canal and run-of-river sites.
• Draft tube (reaction turbines only): a gradually expanding passage that recovers exit kinetic energy and allows the runner to be set above tailwater by converting the velocity head and creating a partial vacuum; types — straight conical, elbow, moody/spreading. A Pelton wheel discharges to atmosphere and has none.
• Governing: load changes are met by an oil-pressure governor whose actuator/servomotor moves the spear (Pelton) or guide vanes (Francis/Kaplan) to hold constant speed, i.e. constant frequency (50 Hz in India, so N = 120f/p for the generator pole count). Runaway speed (full load thrown off, no governing) is roughly 1.8× rated for Pelton and 2–2.8× for Kaplan — the shaft and generator must survive it.
• Surge tank / forebay absorbs pressure transients in a long pressure conduit; pumped storage units (Tehri, Purulia, Kadamparai, Sardar Sarovar reversible units) run as a pump-turbine in both directions.
• Selection is by specific speed, which follows from head and flow; model testing follows IEC 60193 (model acceptance tests) and field testing IEC 60041, with BIS equivalents in the IS 12800 series for selection of hydraulic turbines (check the current BIS edition — numbers are periodically revised).

Pumps

• Centrifugal pump parts: suction pipe with strainer and foot valve, impeller (closed for clean water, semi-open/open for slurries and sewage), casing (volute, vortex chamber, or vaned diffuser), delivery pipe with non-return and gate valve, stuffing box/mechanical seal, wear rings.
• Heads: static head = suction lift + delivery lift; manometric head Hm = static head + all friction losses + delivery velocity head = what the pump must actually generate.
• Priming: the casing must be filled with liquid before starting, because the head a centrifugal impeller generates is proportional to fluid density — pumping air generates almost no head and the pump cannot lift water. Self-priming pumps, foot valves or a vacuum pump do this. A positive-displacement pump does not need priming.
• Minimum starting speed: the pump delivers nothing until the centrifugal head (U₂²−U₁²)/2g exceeds Hm — this sets the minimum speed.
• Efficiencies: manometric ηmano = gHm/(U₂Vw₂) (how much Euler head survives as useful head), volumetric (leakage through clearances), mechanical (bearing, seal, disc friction); overall = product of the three, typically 60–85%.
• Series and parallel: stages in series (multistage pump) add head at the same flow; pumps in parallel add flow at the same head — used in water-supply pump houses for turndown.
• Duty point = intersection of the pump H–Q curve with the system curve (static head + kQ²). Flow is reduced either by throttling (wasteful — moves along the curve, adds loss) or by speed reduction with a VFD (power falls roughly with N³, large saving) or by impeller trimming.
• Cavitation: if local pressure anywhere (impeller eye, Kaplan blade tip, draft tube) falls to the liquid's vapour pressure, bubbles form and then collapse violently in the higher-pressure region, causing noise, vibration, pitting of metal, head/efficiency drop and eventual failure. Controls: keep suction lift small (ideally positive suction, flooded), short/large suction pipe, lower liquid temperature, reduce speed, use an inducer; for turbines, set the runner low enough relative to tailwater.
• NPSH: the available net positive suction head must exceed the pump's required NPSH (a test-measured property of the pump), with a margin of roughly 0.5–1 m or 10–30%. Thoma's cavitation factor σ = NPSH/H is the equivalent criterion for turbines.
• Reciprocating (positive-displacement) pump: plunger/piston in a cylinder with suction and delivery valves; single or double acting, single or multi-cylinder. Delivers almost constant flow against any head, is self-priming, but the flow pulsates — an air vessel on each side smooths it and reduces the acceleration head (which is what limits the speed and can cause separation in the suction pipe). Slip = (Qth − Qact)/Qth, usually small and occasionally negative (a long suction pipe at high speed opens the delivery valve before the suction stroke ends, so actual flow exceeds theoretical).
• Indian standards and labelling: IS 6595 (horizontal centrifugal pumps, clear cold water), IS 9079 (electric monoset pumps for agriculture), IS 8034 (submersible pumpsets), IS 9137 (acceptance test code, Class C); API 610/ISO 13709 for refinery and petrochemical pumps; BEE star labelling of agricultural and monoset pumps under the Energy Conservation Act 2001, and energy-efficient pumps mandated in schemes such as PM-KUSUM solar pumping and the Jal Jeevan Mission (check the latest BEE schedule, as ratings are revised).

Dynamic compressors and fans

• Centrifugal (radial) compressor: impeller with an inducer, usually radial-tipped blades, followed by a diffuser and volute. Work input = ψ·σs·U₂² approximately, where slip factor σs = Vw₂/U₂ (< 1 because the fluid cannot fully follow the blade — inertia/relative eddy) and the power input factor (1.03–1.05) accounts for disc friction and windage. High pressure ratio per stage (3–5), wide flow range, rugged.
• Axial compressor: many stages of rotor + stator blades, each giving a small pressure ratio (1.15–1.4) but high efficiency and high mass flow; stage work = λ·U·ΔVw, with work-done factor λ ≈ 0.85–0.98 falling along the machine because of boundary-layer growth.
• Surge: at low flow the blading stalls and flow reverses in violent cycles — it is a system-wide instability that can wreck a compressor; prevented by anti-surge (recycle/blow-off) valves, variable inlet guide vanes, bleed valves. Rotating stall is a localised cell of stalled flow travelling round the annulus. Choking is the maximum-flow limit when a passage reaches Mach 1.
• Fans/blowers are the low-pressure-rise end of the same family; the dividing line is conventionally about 1.1 pressure ratio for fans and 1.1–3 for blowers. (Reciprocating machines, multi-staging with intercooling and volumetric efficiency belong to the air-compressor topic.)

Similarity, specific speed and characteristics

• Dimensional analysis of a turbomachine gives flow coefficient Q/ND³, head coefficient gH/N²D², power coefficient P/ρN³D⁵, plus Reynolds number and (for compressors) Mach number. Two geometrically similar machines at the same coefficients are homologous — the basis of model testing.
• Affinity (similarity) laws follow directly: for the same machine, Q ∝ N, H ∝ N², P ∝ N³; for similar machines at the same speed, Q ∝ D³, H ∝ D², P ∝ D⁵.
• Specific speed is the shape parameter obtained by eliminating D: it identifies the *type* of machine, not its size. Low Ns → radial, low flow coefficient and high head coefficient; high Ns → axial. It is the single most-used selection number in practice.
• Unit quantities (unit speed, unit discharge, unit power) reduce a turbine's test data to 1 m head, so performance at any other head can be predicted.
• Characteristic curves: pumps are plotted as H, P, η vs Q at constant N (main characteristics) and as the family of curves/iso-efficiency "hill chart" when speed varies; turbines are plotted as η vs load/speed ratio, and Kaplan shows the flattest part-load curve, Pelton next, propeller and Francis the most peaked.
• Thrust and balance: a centrifugal impeller generates axial thrust — balanced by double-suction impellers, balance holes, back-to-back staging or a balance drum; thrust bearings carry the rest.

Key points

• Turbomachine – energy exchange with a continuously flowing fluid through a rotating blade row, no trapped volume.
• Euler equation – w = U₂Vw₂ − U₁Vw₁ (input machines), U₁Vw₁ − U₂Vw₂ (output machines); the whirl component alone does the work.
• Velocity triangle – V = U + Vr at inlet and outlet; blade angle must match the relative velocity, else incidence loss.
• Degree of reaction – share of the stage's static pressure change occurring in the rotor; 0 for impulse, 0.5 for symmetric axial stages.
• Pelton – impulse, high head, low flow, best at U = V₁/2, jet deflection ~165°, controlled by spear valve and deflector.
• Francis – reaction, mixed flow, medium head, guide-vane governed, needs a draft tube.
• Kaplan – reaction, axial, low head, huge flow, adjustable blades give flat part-load efficiency.
• Draft tube – recovers exit kinetic energy and permits the runner to be set above tailwater; absent in impulse turbines.
• Specific speed – N√Q/H^0.75 for pumps, N√P/H^1.25 for turbines; fixes the machine type, and its numerical value depends on the units used.
• Affinity laws – Q ∝ ND³, H ∝ N²D², P ∝ ρN³D⁵; speed control therefore saves power as N³.
• Manometric efficiency – gHm/(U₂Vw₂); overall efficiency = manometric × volumetric × mechanical.
• Priming – a centrifugal pump must be filled with liquid first because head ∝ density; positive-displacement pumps are self-priming.
• Cavitation / NPSH – vapour bubbles forming and collapsing; avoided by keeping NPSH available above NPSH required with a margin; σ = NPSH/H for turbines.
• Backward-curved vanes – stable drooping head curve and best efficiency; forward-curved give more head but unstable operation.
• Surge – low-flow flow reversal in a dynamic compressor, a system instability; rotating stall is localised, choking is the maximum-flow limit.
• Slip factor and work-done factor – corrections (<1) for fluid not fully following the blade in centrifugal and axial machines respectively.
• Duty point – where the pump curve meets the system curve; throttling wastes energy, a VFD does not.
• Series vs parallel – series/multistage adds head, parallel adds flow.

Formulas and examples

1. Centrifugal pump — Euler head, manometric head and power. D₂ = 0.40 m, B₂ = 25 mm, N = 1450 rpm, β₂ = 30°, Vf₂ = 2.5 m/s, radial entry, ηmano = 80%, ηₒ = 72%.

• U₂ = π × 0.40 × 1450/60 = 30.37 m/s
• Vw₂ = 30.37 − 2.5/tan30° = 30.37 − 4.33 = 26.04 m/s
• Euler head He = 30.37 × 26.04/9.81 = 790.8/9.81 = 80.6 m
• Manometric head Hm = 0.80 × 80.6 = 64.5 m (the rest is lost in the impeller and volute)
• Q = πD₂B₂Vf₂ = π × 0.40 × 0.025 × 2.5 = 0.0785 m³/s (78.5 L/s)
• Water power = 1000 × 9.81 × 0.0785 × 64.5 = 49.7 kW; shaft power = 49.7/0.72 = 69.0 kW (motor to be selected above this)

2. Pelton wheel — jet and wheel sizing. Net head 400 m, output 6 MW, Cv = 0.98, speed ratio φ = 0.46, ηₒ = 86%, N = 500 rpm.

• V₁ = 0.98 × √(2 × 9.81 × 400) = 0.98 × 88.59 = 86.82 m/s; U = 0.46 × 88.59 = 40.75 m/s
• Q = P/(ηₒρgH) = 6 000 000/(0.86 × 1000 × 9.81 × 400) = 1.778 m³/s
• Jet area a = Q/V₁ = 1.778/86.82 = 0.02048 m² → d = 161 mm
• D = 60U/(πN) = 60 × 40.75/(π × 500) = 1.556 m; jet ratio m = 1.556/0.161 = 9.7 (within the usual 9–12)
• Ns = 500 × √6000/400^1.25 = 500 × 77.46/1788.9 = 21.7 — squarely in the Pelton range

3. Affinity laws and specific speed. A pump gives Q = 0.05 m³/s at H = 30 m taking 18 kW at 1450 rpm. Find output at 1160 rpm.

• Speed ratio = 1160/1450 = 0.80 → Q′ = 0.05 × 0.80 = 0.040 m³/s; H′ = 30 × 0.80² = 19.2 m; P′ = 18 × 0.80³ = 9.2 kW
• Saving = 1 − 0.512 = 48.8% of shaft power for a 20% speed cut — the case for VFDs instead of throttle valves
• Ns = 1450 × √0.05/30^0.75 = 1450 × 0.2236/12.82 = 25.3 (rpm, m³/s, m) → radial/centrifugal impeller

4. NPSH check. Water at 30 °C (pv = 4.25 kPa), pump 4.0 m above sump level, suction friction + velocity losses 1.2 m, atmosphere 101.3 kPa, pump NPSHr = 3.5 m, rated head 40 m.

• (pa − pv)/ρg = (101 300 − 4250)/(1000 × 9.81) = 9.89 m
• NPSHa = 9.89 − 4.0 − 1.2 = 4.69 m > 3.5 m → margin 1.19 m, acceptable
• σ = 4.69/40 = 0.117. If the suction lift were raised to 6 m, NPSHa = 2.69 m < NPSHr → the pump would cavitate.

5. Axial compressor stage. U = 200 m/s, Va = 150 m/s constant, β₁ = 50°, β₂ = 25° (from axial), λ = 0.9, ηs = 0.88, T₀₁ = 288 K.

• Vrw₁ = 150 tan50° = 178.8 m/s; Vrw₂ = 150 tan25° = 69.9 m/s → ΔVw = 108.8 m/s
• w = 0.9 × 200 × 108.8 = 19.6 kJ/kg; ΔT₀ = 19 586/1005 = 19.5 K
• Pressure ratio = (1 + 0.88 × 19.5/288)^3.5 = (1.0596)^3.5 = 1.22
• R = (150/400)(tan50° + tan25°) = 0.375 × 1.658 = 0.62 (62%)

Where it is used

• Hydropower: NHPC, THDC, SJVN and state boards run Pelton/Francis/Kaplan sets built or refurbished by BHEL (Bhopal, Hardwar), Voith, Andritz and Toshiba — design, commissioning, governor and cavitation-repair roles.
• Water supply and irrigation: municipal pump houses, lift-irrigation schemes and the Jal Jeevan Mission; India has crores of agricultural pumpsets, so BEE star-rated monoset and submersible pumps (Kirloskar Brothers, KSB, Grundfos, Shakti, Crompton, Texmo) and PM-KUSUM solar pumps are a large employer base.
• Process, refinery and fertiliser plants: API 610 pumps and API 617 centrifugal compressors handling crude, ammonia, process gas — rotating-equipment and reliability engineers monitor vibration, seals and surge margin.
• Thermal and nuclear stations: boiler feed pumps, condensate extraction, circulating water pumps, ID/FD/PA fans — the plant's own largest auxiliary loads.
• HVAC, fire-fighting and building services: chilled-water pumps, cooling-tower and AHU fans, fire pumps to IS/NBC requirements; energy audits under the Energy Conservation Act target pump and fan systems first.
• Turbochargers, aero engines and gas pipelines: radial and axial compressors and turbines, and pipeline booster compressors (GAIL), plus wind turbines as the unenclosed branch of the family.

Interview questions

• Q: What does the Euler turbomachine equation tell you? A: That work per unit mass equals the change in the product of blade speed and whirl velocity, U₂Vw₂ − U₁Vw₁ — only the tangential component of absolute velocity contributes to energy transfer.
• Q: Why must a centrifugal pump be primed but not a reciprocating pump? A: The head a centrifugal impeller produces is proportional to fluid density, so filled with air it cannot generate enough suction; a reciprocating pump physically displaces air and draws liquid up.
• Q: What is cavitation and how do you prevent it? A: Vapour bubbles form where pressure falls to vapour pressure and collapse violently downstream, causing noise, pitting and loss of head; prevent it by reducing suction lift, enlarging/shortening the suction line, lowering speed or temperature, and keeping NPSHa above NPSHr with margin.
• Q: Why is maximum efficiency of a Pelton wheel at U = V₁/2? A: Work per kg is U(V₁−U)(1+k cos β₂); differentiating with respect to U gives V₁ − 2U = 0, so U = V₁/2, at which the water leaves with almost no absolute velocity.
• Q: Why is the jet deflection angle about 165° and not 180°? A: A full 180° reversal would throw the leaving water onto the back of the incoming jet and the following bucket, so a small angle is kept for clearance at a tiny loss of work.
• Q: Why does a Kaplan turbine keep high efficiency at part load but a propeller turbine does not? A: Kaplan blades are adjustable and move with the guide vanes, keeping the inlet angle shock-free at all loads; fixed propeller blades suffer incidence loss off-design.
• Q: What is the purpose of a draft tube? A: It recovers the kinetic energy at runner exit as useful head and lets the runner be set above tailwater by maintaining a sub-atmospheric pressure at its inlet.
• Q: Specific speed — why bother, when you already know head and flow? A: It is dimensionally independent of size and tells you the *type* of impeller or runner suited to that head–flow duty, which is the first step in selection.
• Q: If you halve pump speed, what happens to flow, head and power? A: Flow halves, head falls to one-quarter and power to one-eighth — hence the large savings from variable-speed drives.
• Q: What is surge, and how is it different from stall and choking? A: Surge is a violent system-level oscillation with flow reversal at low flow; rotating stall is a localised stalled cell travelling round the blade annulus; choking is the flow limit when a passage reaches sonic velocity.
• Q: Why are backward-curved vanes preferred in centrifugal pumps? A: They give a stable falling head–flow characteristic, a lower exit kinetic energy (so less diffuser loss) and the highest efficiency; forward-curved vanes give an unstable rising curve.
• Q: What is slip factor, and is it a loss? A: It is the ratio Vw₂/U₂, less than one because the fluid cannot fully follow the blade (relative eddy); it reduces the work transferred but is not itself a loss of efficiency — it simply means less work is put in than Euler predicts.

Common mistakes

• Using the absolute velocity instead of the whirl component in Euler's equation, or getting the sign/order of terms reversed between pump and turbine.
• Mixing up blade angle β with absolute (vane/nozzle) angle α while drawing the velocity triangle, and forgetting that Vr must be tangential to the blade.
• Quoting specific speed without stating the units — the same machine gives wildly different numbers for Q in m³/s, L/s or gpm, and for P in kW or hp.
• Confusing Euler head with manometric head, or multiplying by manometric efficiency twice when finding shaft power.
• Treating cavitation as "boiling due to heat" or as the same thing as water hammer, and ignoring the NPSH margin because NPSHa merely exceeds NPSHr.
• Applying the affinity laws across a changed impeller diameter *and* speed carelessly, or using them where efficiency changes substantially (large speed/size steps, viscous fluids).
• Forgetting that a Pelton wheel has no draft tube, or that a reaction turbine runs full of water at pressure while an impulse runner does not.

Related topics

Fluid mechanics: flow through pipes and losses · Steam turbines and nozzles · Gas turbines and jet propulsion · Air compressors · Boilers and steam power plants · Power cycles: Rankine, Otto, Diesel and Brayton