Turbo Machinery:

Introduction to Turbo Machinery

• Turbo machine: ऐसी machine जिसमें rotating blades और flowing fluid के बीच energy transfer होता है.
• Energy transfer मुख्यतः change in angular momentum के कारण होता है.
• Hydraulic machines: Pumps and hydraulic turbines.
• Thermal turbo machines: Steam turbines, gas turbines, compressors.

Euler Turbomachine Equation

\[ \text{Work done per unit mass} = U_2 V_{w2} – U_1 V_{w1} \]

• \( U \) = Blade speed.
• \( V_w \) = Whirl/tangential component of absolute velocity.
• यह turbomachinery energy-transfer analysis का fundamental relation है.

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Reciprocating Pumps

• Positive displacement pump.
• Fluid को piston/plunger की reciprocating motion से deliver करता है.
• Low discharge + high head applications के लिए suitable.
• Main parts → Cylinder, piston/plunger, suction valve, delivery valve, crank and connecting rod.

Types

• Single-acting pump
• Double-acting pump

Theoretical Discharge

Single-acting:

\[ Q_{th} = \frac{ALN}{60} \]

Double-acting:

\[ Q_{th} \approx \frac{2ALN}{60} \]

• \( A \) = Piston area.
• \( L \) = Stroke length.
• \( N \) = rpm.

Slip

\[ \text{Slip} = Q_{th} – Q_{actual} \]

\[ \% \text{Slip} = \left[ \frac{Q_{th} – Q_{actual}}{Q_{th}} \right] \times 100 \]

• Negative slip may occur at high speeds under certain operating conditions.

Air Vessel

• Flow fluctuations कम करता है.
• Acceleration head और friction losses को reduce करने में मदद करता है.
• Pump operation को smoother बनाता है.

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Rotary Pumps

• Positive displacement pump.
• Rotating elements के द्वारा fluid को continuously displace करता है.
• Generally moderate discharge और high pressure applications में उपयोग.

Types

• Gear pump
• Vane pump
• Screw pump
• Lobe pump

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Hydraulic Turbines

• Hydraulic turbine water की hydraulic energy → mechanical energy में conversion करती है.
• Turbine shaft को generator से connect करके electrical energy produce की जा सकती है.

Main Classification

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Pelton Wheel

• Impulse turbine.
• High head + low discharge applications.
• Water jet nozzle से निकलकर buckets पर strike करता है.
• Runner पर pressure approximately atmospheric रहता है.
• Energy transfer mainly jet velocity के change से होता है.

Main Components

• Nozzle
• Runner
• Bucket
• Spear/needle
• Casing
• Brake nozzle

Important Facts

• Bucket का splitter incoming jet को approximately two streams में divide करता है.
• Jet direction लगभग 160°–170° तक deflect हो सकती है.
• Maximum power condition के लिए ideal simple analysis में bucket speed ≈ jet speed का आधा.

Power

\[ P = \rho Q (V_{w1} u_1 \pm V_{w2} u_2) \]

Sign convention velocity triangle के अनुसार लिया जाता है.

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Francis Turbine

• Reaction turbine.
• Medium head + medium discharge applications.
• Mixed-flow turbine.
• Water runner में radial component के साथ enter करता है और generally axial direction में exit करता है.

Main Components

• Spiral casing
• Stay vanes
• Guide vanes
• Runner
• Draft tube

Important Point

• Francis turbine में pressure change runner के अंदर भी होता है.
• Draft tube kinetic energy के कुछ हिस्से को pressure energy में recover करता है.

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Kaplan Turbine

• Reaction turbine.
• Low head + high discharge.
• Axial-flow turbine.
• Propeller-type runner.
• Runner blades adjustable pitch की हो सकती हैं.

Important Components

• Scroll/spiral casing
• Guide vanes
• Runner
• Draft tube

Pelton vs Francis vs Kaplan

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Impulse & Reaction Turbines

Impulse Turbine

• Pressure drop मुख्यतः nozzle में होता है.
• Runner के across pressure लगभग constant रहता है.
• Runner को high-velocity jet strike करता है.
• Example → Pelton wheel.

Reaction Turbine

• Pressure drop guide/runner passages में होता है.
• Runner में fluid pressure और velocity दोनों बदलते हैं.
• Runner fully/partially immersed flow passage में operate करता है.
• Examples → Francis, Kaplan.

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Velocity Diagrams

• Velocity triangles turbomachinery में fluid और blade velocities के vector relationship को show करते हैं.
• Absolute velocity (V): Stationary observer के relative fluid velocity.
• Blade velocity (U): Rotor के peripheral velocity.
• Relative velocity (\( V_r \)): Blade के relative fluid velocity.

Velocity Relation

\[ V = U + V_r \]

Components of Absolute Velocity

• \( V_w \) → Whirl/tangential component.
• \( V_f \) → Flow component.

\[ V^2 = V_w^2 + V_f^2 \]

Blade Speed

\[ U = \frac{\pi D N}{60} \]

• \( D \) = Rotor diameter.
• \( N \) = rpm.

Euler Turbine Equation

\[ \text{Work} = U_2 V_{w2} – U_1 V_{w1} \]

• Specific work sign depends on turbine/pump convention and velocity-triangle definition.

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Steam Turbines

• Steam की thermal energy → mechanical shaft work.
• Steam turbines are continuous-flow machines.
• Mainly power generation और industrial drives में use.

Types

• Impulse turbine
• Reaction turbine
• Condensing turbine
• Back-pressure turbine

Impulse Turbine

• Pressure drop nozzle में.
• Example → De Laval turbine.

Reaction Turbine

• Pressure drop stationary + moving blades दोनों में.
• Example → Parsons turbine.

Compounding

• High steam pressure को multiple stages में expand करके rotor speed को practical range में रखा जाता है.
• Velocity compounding: Pressure drop mainly first nozzle stage; velocity stages में energy extraction.
• Pressure compounding: Pressure drop multiple nozzle stages में divide.
• Pressure-velocity compounding: दोनों principles combined.

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Gas Turbines

• Continuous-flow combustion engine.
• Air compressor में compressed होता है → combustor में fuel burn → turbine में expansion.

Basic Brayton Cycle

Applications

• Aircraft propulsion
• Gas-turbine power plants
• Peak-load power generation
• Mechanical drives

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Jet Propulsion

• Jet propulsion Newton’s third law और momentum change के principle पर based है.
• High-velocity exhaust gases → forward thrust produce करते हैं.

Basic Thrust Relation

\[ F \approx \dot{m}(V_e – V_0) \]

Pressure thrust significant होने पर:

\[ F = \dot{m}(V_e – V_0) + (p_e – p_0)A_e \]

• \( \dot{m} \) = Mass flow rate.
• \( V_e \) = Exit velocity.
• \( V_0 \) = Flight/inlet velocity.

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Pulse Jet Engine

• Air-breathing jet engine.
• Combustion intermittent/pulsating होती है.
• Valves may be used in conventional valved pulse jets.
• Compressor turbine set की आवश्यकता नहीं होती.
• Simple construction but high noise and vibration are characteristic limitations.

Basic Sequence

• Air intake
• Fuel injection
• Combustion
• Pressure rise
• Exhaust through tail pipe
• Thrust generation

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Ram Jet Engine

• Air-breathing jet engine.
• Moving aircraft की high speed से inlet air compression होती है.
• No rotating compressor.
• Combustion continuous होती है.
• High-speed applications में suitable.

Working

• Air intake → Diffuser → Combustion chamber → Nozzle → High-speed exhaust.
• Diffuser inlet kinetic energy को pressure energy में convert करता है.

Pulse Jet vs Ram Jet

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Reciprocating Compressors

• Positive-displacement compressor.
• Piston की reciprocating motion से gas compress होती है.
• High pressure ratio और relatively low flow applications के लिए suitable.

Types

• Single-stage
• Multi-stage
• Single-acting
• Double-acting

Important Terms

• Clearance volume → piston और cylinder head के बीच remaining volume.
• Volumetric efficiency → actual intake volume / swept volume.

\[ \eta_v = \frac{\text{Actual suction volume}}{\text{Swept volume}} \]

Isothermal Compression Work

\[ W = mRT \ln\left(\frac{V_1}{V_2}\right) \]

Polytropic Compression

\[ pV^n = \text{constant} \]

Multi-stage Compression

• High pressure ratio के लिए multi-stage compression useful है.
• Stages के बीच intercooling work requirement को reduce करता है.
• Ideal intermediate pressure ratio के लिए stages में approximately equal pressure ratio रखा जाता है.

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Rotary Compressors

• Rotating elements द्वारा continuous compression.
• Generally high flow और continuous operation के लिए suitable.

Types

• Centrifugal compressor
• Axial-flow compressor
• Rotary vane compressor
• Screw compressor
• Roots blower

Centrifugal Compressor

• Radial-flow compressor.
• Impeller fluid को high velocity देता है.
• Diffuser velocity energy को pressure energy में convert करता है.

Axial Compressor

• Fluid predominantly axial direction में flow करता है.
• Multiple rotor-stator stages use किए जाते हैं.
• Gas-turbine engines में widely used.

Compressor Comparison

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Compressor Applications

• Gas turbines
• Refrigeration and air conditioning
• Pneumatic systems
• Industrial process plants
• Petrochemical industries
• Air tools
• Aircraft engines

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Pump & Turbine Key Performance Terms

Pump Head

\[ H = \text{Energy added per unit weight of fluid} \]

Hydraulic Power

\[ P = \rho g Q H \]

Overall Efficiency

\[ \eta = \frac{\text{Output Power}}{\text{Input Power}} \]

Specific Speed

Machine selection और performance comparison के लिए dimensionless/standardized specific-speed concepts उपयोग किए जाते हैं.

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High-Yield Exam Facts

• Pelton → impulse + high head + low discharge.
• Francis → reaction + medium head + mixed flow.
• Kaplan → reaction + low head + high discharge + axial flow.
• Pelton runner में pressure drop mainly nozzle में होता है.
• Reaction turbine में runner के अंदर भी pressure change होता है.
• Draft tube → reaction turbines में important; kinetic energy recovery में मदद करता है.
• Velocity triangle → V, U और \( V_r \) का relation बताता है.
• V = U + \( V_r \).
• U = πDN/60.
• Euler turbomachinery equation → angular momentum principle पर आधारित.
• Reciprocating pump → positive displacement pump.
• Reciprocating compressor → positive displacement compressor.
• Centrifugal compressor → dynamic compressor.
• Axial compressor → very high flow applications.
• Intercooling → multi-stage compressor में work requirement कम कर सकता है.
• Steam turbine → steam thermal energy to shaft work.
• Gas turbine → Brayton cycle से associated.
• Pulse jet → intermittent combustion.
• Ram jet → ram effect द्वारा air compression; mechanical compressor नहीं.
• Jet propulsion → momentum change + Newton’s third law.

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