Unit 6: Elementary Turbine Design - Subjective Questions

A gas turbine is a continuous-flow heat engine in which high-temperature, high-pressure gas expands through turbine stages to produce shaft work.

The turbine section performs the following functions:

• Energy conversion: It converts the thermal and pressure energy of combustion gases into mechanical energy.
• Compressor drive: A major portion of turbine work drives the compressor.
• Accessory drive: It may power fuel pumps, generators and other accessories.
• Useful output: The remaining work produces shaft power or contributes to jet thrust.

A turbine stage generally consists of:

1. A stator or nozzle row, which accelerates and directs the gas.
2. A rotor blade row, which extracts energy from the gas and produces torque.

The specific work produced by a turbine is governed by the change in whirl velocity:

where is the blade speed and and are the inlet and outlet whirl components of absolute velocity.

The main differences are:

In practice, both types experience aerodynamic losses. The distinction is based on where the static enthalpy drop occurs within the stage.

A velocity triangle represents the vector relationship among:

• Absolute gas velocity,
• Blade velocity,
• Relative gas velocity,

These are related by:

Inlet triangle:

• Draw the blade velocity in the tangential direction.
• Draw the absolute inlet velocity at the stator exit angle .
• The vector joining the end of to the end of gives .
• Resolve into axial and whirl components:

when is measured from the wheel direction.

Outlet triangle:

• Draw the relative outlet velocity at rotor exit angle .
• Add vectorially to obtain .
• Resolve into and .

The change determines turbine work, while the axial component determines the mass-flow capacity.

Consider a mass flow rate passing through a rotor at mean radius . The angular-momentum equation gives the torque:

The rotor power is:

Since and ,

Therefore, the specific turbine work is:

For an axial turbine operating at approximately constant mean radius, , so:

For an adiabatic rotor, this work equals the stagnation-enthalpy drop:

Thus, turbine work is produced by reducing the whirl component of absolute velocity. A larger positive change in whirl velocity generally produces greater torque and work.

Blade or diagram efficiency is the ratio of work transferred to the rotor to the kinetic energy supplied at rotor inlet. For an impulse stage:

It evaluates the effectiveness of the rotor velocity diagram.

Total-to-total stage efficiency compares the actual stagnation-enthalpy drop with the isentropic stagnation-enthalpy drop:

It is appropriate when the exit kinetic energy can be utilized by a subsequent stage.

Total-to-static stage efficiency compares actual work with the isentropic enthalpy drop to the actual exit static pressure:

It treats the rotor-exit kinetic energy as unavailable and is useful for the final turbine stage. These efficiencies differ because they account for exit kinetic energy in different ways.

For an ideal impulse rotor, assume:

• No relative-velocity loss, so
• Symmetrical blades, so
• Constant blade speed

Let the nozzle velocity be and the inlet angle measured from the wheel direction be . Define the speed ratio:

For an ideal symmetrical impulse rotor, the blade efficiency becomes:

For maximum efficiency:

Therefore,

Substitution gives:

At this condition, the outlet whirl component is zero, so the gas leaves the rotor axially. Actual turbines have a lower optimum efficiency because of blade friction, leakage and non-ideal flow.

The degree of reaction, , is the ratio of the static enthalpy drop in the rotor to the static enthalpy drop in the complete stage:

Its physical significance is:

• : all ideal static enthalpy drop occurs in the stator; the stage is an impulse stage.
• : the static enthalpy drop is shared equally between stator and rotor.
• : the ideal static enthalpy drop occurs entirely in the rotor.

For an adiabatic rotor at constant blade speed, conservation of relative stagnation enthalpy gives:

For a repeating stage with equal stage inlet and exit absolute velocities, the stage static enthalpy drop equals the Euler work. Hence:

Reaction influences blade shape, pressure distribution, axial thrust, leakage, efficiency and the velocity triangles.

A Parsons stage has a degree of reaction:

Therefore, half of the stage static enthalpy drop occurs in the stator and half in the rotor.

For an ideal repeating stage with constant axial velocity:

• The stator and rotor blade passages have similar aerodynamic duties.
• The velocity triangles are approximately symmetrical.
• The absolute velocity leaving the stator is related geometrically to the relative velocity leaving the rotor.
• Stator and rotor blade profiles may be geometrically similar when viewed in opposite directions.

Advantages:

• Balanced diffusion and acceleration in the blade rows
• Good stage efficiency
• Moderate aerodynamic loading per blade row
• Convenient design for multistage axial turbines
• Reduced risk of excessive velocity in a single blade row

Limitations:

• Pressure drop in the rotor increases tip-leakage sensitivity.
• It produces greater axial thrust than a pure impulse stage.
• Effective sealing and accurate tip-clearance control are necessary.

A large pressure or enthalpy drop in a single impulse stage produces very high nozzle velocity. For maximum efficiency, the rotor would then require an impractically high blade speed. Excessive speed causes high centrifugal stress, vibration, bearing problems and mechanical failure.

Compounding divides the total energy conversion among multiple blade rows or stages so that rotor speed remains practical.

The principal methods are:

1. Velocity compounding: The pressure drop occurs mainly in one nozzle row, while the resulting high velocity is absorbed through two or more moving-blade rows separated by guide blades.
2. Pressure compounding: The total pressure drop is divided among several stages, each containing a nozzle row and a moving row.
3. Pressure-velocity compounding: The pressure drop is divided into groups, and each pressure group contains multiple velocity-compounded moving rows.

Compounding reduces blade speed and stress, but additional blade rows can increase friction, leakage, weight and manufacturing complexity.

In a velocity-compounded turbine, also called a Curtis stage, the entire stage pressure drop occurs mainly in the first nozzle row. The high-velocity jet then passes through multiple moving-blade rows.

Working sequence:

1. The nozzle converts pressure energy into kinetic energy.
2. The first rotor row extracts part of the kinetic energy.
3. A fixed guide-blade row redirects the flow without an intentional pressure drop.
4. The next rotor row extracts additional kinetic energy.
5. The process may be repeated through further guide and rotor rows.

The absolute velocity decreases progressively through successive moving rows, while pressure remains approximately constant after the nozzle.

Advantages:

• Large pressure drop can be handled at moderate shaft speed.
• Fewer pressure stages and casing partitions are required.
• The arrangement is compact.

Limitations:

• Guide and rotor friction losses accumulate.
• Later rotor rows operate with lower velocity and produce less work.
• Efficiency is generally lower than pressure compounding.
• Flow turning and secondary-flow losses can be significant.

In pressure compounding, the total turbine pressure drop is divided among several stages. Each stage contains a stator nozzle row followed by a rotor row. The gas is accelerated in every nozzle row and transfers work in the following rotor.

Pressure compounding is preferred when high overall efficiency is important. Its disadvantages are increased stage count, turbine length, casing complexity, leakage paths and manufacturing cost.

Pressure-velocity compounding combines pressure compounding and velocity compounding.

• The total pressure drop is first divided among several pressure stages or groups.
• Each pressure group contains a nozzle row followed by two or more moving rows.
• Fixed guide blades between the moving rows redirect the gas for the next rotor row.
• Pressure falls mainly in the nozzle at the beginning of each group.
• Velocity is reduced successively across the moving rows within that group.

Advantages:

• Lower shaft speed than a simple turbine
• Fewer pressure stages than a purely pressure-compounded turbine
• More manageable nozzle velocities than a single velocity-compounded stage
• A compromise between compactness and efficiency

Disadvantages:

• More complex velocity diagrams
• Losses in intermediate guide rows
• Unequal work distribution among rotor rows
• More complicated blade design and matching

It is useful where space, cost and permissible rotational speed require fewer pressure stages, but a single Curtis stage would have excessive aerodynamic losses.

Multistaging divides a large total turbine enthalpy drop among several stator-rotor stage pairs.

It is used because it:

• Limits blade speed and centrifugal stress.
• Prevents excessive Mach number and shock losses.
• Maintains acceptable blade loading and flow turning.
• Improves efficiency by avoiding extreme diffusion or acceleration.
• Permits controlled area variation as gas density decreases.
• Allows cooling and materials to be selected according to local temperature.

For stages, the total specific work is:

If the stages are similar and equally loaded, the approximate work per stage is:

In practice, work is not always distributed equally. Front stages face the highest temperature and may be limited by cooling and stress, while rear stages handle a larger volume flow and may be limited by blade height, annulus area and exhaust losses.

The stage loading coefficient is the nondimensional work output:

It indicates how much stagnation enthalpy is extracted relative to blade-speed energy. A very high requires strong flow turning and can cause separation, high losses and poor efficiency.

The flow coefficient is:

where is the axial velocity. It relates through-flow velocity to blade speed and influences annulus area, blade angles and stage mass-flow capacity.

Their importance includes:

• Determining the shapes of velocity triangles
• Controlling blade inlet and outlet angles
• Indicating aerodynamic loading and turning
• Supporting comparison between geometrically different turbines
• Helping select the number of stages
• Influencing efficiency, Mach number and blade height

Efficient turbines operate within suitable ranges of both coefficients rather than maximizing either coefficient independently.

Important stage-performance parameters include:

• Specific work:

• Stage loading coefficient:

• Flow coefficient:

• Degree of reaction: It specifies how the static enthalpy drop is divided between rotor and stator.
• Total-to-total efficiency: It is appropriate when exit kinetic energy is recovered in another stage.
• Total-to-static efficiency: It is important for the final stage when exhaust kinetic energy is not recovered.
• Mass-flow parameter: It describes corrected flow capacity and is commonly related to .
• Pressure ratio: It indicates the expansion achieved by the stage.

Performance is also assessed using exit swirl, Mach number, incidence, deviation, Reynolds number and loss coefficients. A satisfactory stage must provide the required work and flow while maintaining acceptable efficiency, stress and operating range.

Major turbine losses include:

Aerodynamic losses:

• Profile loss: Boundary-layer friction and separation on blade surfaces.
• Secondary-flow loss: Passage vortices generated by end-wall boundary layers and turning.
• Tip-leakage loss: Flow through the rotor tip clearance bypasses the blade passage.
• Trailing-edge loss: Mixing occurs behind finite-thickness trailing edges.
• Shock loss: Supersonic or transonic flow creates shocks and total-pressure loss.
• Incidence loss: Flow entering at an angle different from the design blade angle separates or turns abruptly.
• Exit kinetic-energy loss: Residual velocity at turbine discharge remains unused.
• Cooling-mixing loss: Cooling air mixes irreversibly with the hot gas.

Mechanical and other losses:

• Disc windage and bearing friction
• Seal leakage
• Heat transfer to the casing and cooling system
• Partial-admission losses where applicable

These losses increase entropy, reduce stagnation-pressure recovery and lower both stage efficiency and useful shaft power.

Turbine design is limited by interacting thermal, aerodynamic, mechanical and operational constraints.

• Turbine inlet temperature: Limited by blade material strength, oxidation, creep and available cooling.
• Centrifugal stress: Approximately increases with material density and , restricting blade speed and diameter.
• Gas bending force: Aerodynamic loading produces bending and torsional stresses.
• Creep and fatigue: High temperature causes time-dependent deformation, while start-stop cycles cause thermal fatigue.
• Vibration: Blade natural frequencies must avoid engine-order excitations and flutter.
• Mach number: Excessive relative or absolute Mach number causes shocks and high losses.
• Blade loading and diffusion: Excessive pressure gradients can cause boundary-layer separation.
• Tip clearance: Small clearance improves efficiency but increases rubbing risk.
• Annulus geometry: Hub-to-tip ratio and blade height must accommodate expanding flow.
• Cooling-air requirement: More cooling protects blades but reduces cycle efficiency.
• Manufacturing and cost: Thin walls, internal passages and coatings add complexity.

A successful design is therefore an optimization rather than the maximization of a single performance parameter.

Modern turbine inlet temperatures can exceed the permissible metal temperature of blade alloys. Cooling is required to keep the blade below limits imposed by creep, oxidation, corrosion and thermal fatigue.

Benefits of cooling:

• Increases blade creep life
• Reduces oxidation and hot corrosion
• Permits a higher turbine inlet temperature
• Improves possible cycle specific work and thermal efficiency
• Protects blade roots, platforms and trailing edges

Performance penalties:

• Compressor bleed air used for cooling does not fully participate in combustion.
• Cooling air requires compression work.
• Mixing between coolant and hot gas causes entropy generation.
• Film injection disturbs the main-flow boundary layer.
• Internal passages increase pressure loss.

The designer must therefore use the minimum coolant flow that maintains an acceptable metal temperature. Blade life depends not only on average temperature but also on temperature gradients, local hot spots, stress concentration and thermal cycling.

The principal blade-cooling methods are:

1. Internal convection cooling: Compressor bleed air flows through radial or serpentine internal passages. Ribs and pin fins increase heat transfer. It is reliable but causes internal pressure loss.

2. Impingement cooling: Coolant jets strike the inner blade wall, producing high local heat-transfer coefficients. It is commonly used near the leading edge.

3. Film cooling: Air exits through small holes and forms a protective layer over the blade surface. It directly reduces hot-gas contact but creates mixing losses.

4. Effusion cooling: A large number of closely spaced holes distribute coolant over the surface. It provides more uniform protection but is difficult to manufacture.

5. Transpiration cooling: Coolant passes through a porous wall to form a continuous protective film. It can be highly effective but has durability and blockage concerns.

6. Trailing-edge cooling: Coolant passes through narrow slots, often with pin fins, to cool the thin trailing edge.

Practical blades combine internal convection, leading-edge impingement and external film cooling, together with thermal-barrier coatings.

The inlet whirl component is:

Because the gas leaves axially:

Using the Euler turbine equation:

Therefore:

The kinetic energy supplied at rotor inlet is:

Hence the diagram efficiency is:

The turbine power is:

This result neglects nozzle, blade, leakage and mechanical losses.