11.2 Turbines and Compressors

Types and Applications of Turbines and Compressors

Turbines and compressors sit on opposite sides of the same energy exchange. Turbines extract mechanical work from a flowing fluid, while compressors put mechanical work into a fluid to raise its pressure. Understanding both devices together makes sense because the thermodynamic analysis is nearly identical, just running in reverse directions.

Turbines

A turbine converts the energy of a moving, pressurized fluid into shaft work (rotation). There are three main types, classified by their working fluid:

• Gas turbines expand high-temperature, high-pressure combustion gases to produce shaft power. You'll find them in jet engines, natural gas power plants, and oil and gas facilities.
• Steam turbines expand high-pressure steam to produce shaft power. They're the workhorse of coal-fired and nuclear power plants, and they show up in chemical manufacturing for process heat recovery.
• Hydraulic turbines convert the kinetic and potential energy of flowing water into mechanical energy. These are the core of hydroelectric power generation at dams and run-of-river installations.

Compressors

A compressor does the opposite: it takes in low-pressure fluid and uses mechanical work to raise its pressure. Three major categories exist:

• Centrifugal compressors spin fluid outward through an impeller, converting kinetic energy into pressure rise. Common in natural gas processing, refrigeration systems, and HVAC.
• Axial compressors push fluid through a series of rotating and stationary blade rows, progressively compressing it along the axis of rotation. These are standard in gas turbines and jet engines where high flow rates are needed.
• Positive displacement compressors trap a fixed volume of fluid and physically reduce that volume to raise pressure. Used in household refrigerators, heat pumps, and pneumatic tool systems.

The key distinction between centrifugal/axial (dynamic) compressors and positive displacement compressors is how they raise pressure: dynamic compressors accelerate the fluid and then decelerate it to convert velocity into pressure, while positive displacement compressors directly reduce volume.

Thermodynamics and Performance Characteristics

Thermodynamics of turbines and compressors

Both turbines and compressors are analyzed using the steady-flow energy equation applied to an open system. The ideal benchmark for both is the isentropic process, where entropy remains constant (no friction, no heat loss, fully reversible).

Turbines undergo an expansion process. High-pressure, high-temperature fluid enters and low-pressure, lower-temperature fluid exits, with the energy difference extracted as work.

• In an isentropic expansion, the turbine produces the maximum possible work for a given pressure drop.
• In the actual expansion, irreversibilities (friction in blade passages, heat transfer to surroundings, flow separation) reduce the work output below the isentropic ideal.

Compressors undergo a compression process. Low-pressure fluid enters and high-pressure, higher-temperature fluid exits, requiring work input.

• In an isentropic compression, the compressor requires the minimum possible work for a given pressure rise.
• In the actual compression, the same types of irreversibilities mean you need to supply more work than the isentropic case.

Performance metrics

Power quantifies the rate of energy transfer. For both devices, apply the steady-flow energy equation assuming negligible changes in kinetic and potential energy:

• Turbine power output:

$\dot{W}_t = \dot{m}(h_1 - h_2)$

• Compressor power input:

$\dot{W}_c = \dot{m}(h_2 - h_1)$

where $\dot{m}$ is the mass flow rate, $h_1$ is the inlet specific enthalpy, and $h_2$ is the outlet specific enthalpy.

Isentropic efficiency measures how close the real device comes to the ideal. Notice the formulas are structured differently for turbines and compressors:

• Turbine isentropic efficiency:

$\eta_t = \frac{h_1 - h_2}{h_1 - h_{2s}}$

This is actual work out divided by ideal work out (always ≤ 1).

• Compressor isentropic efficiency:

$\eta_c = \frac{h_{2s} - h_1}{h_2 - h_1}$

This is ideal work in divided by actual work in (also always ≤ 1).

In both expressions, $h_{2s}$ is the specific enthalpy at the outlet if the process were isentropic (same inlet state, same exit pressure, but at constant entropy).

Pressure ratio is the ratio of outlet to inlet pressure ($P_2 / P_1$ for compressors, $P_1 / P_2$ for turbines as an expansion ratio). Higher pressure ratios generally increase the work per unit mass but also affect efficiency, component sizing, and material requirements.

Design Considerations and Operating Principles

Gas turbines and the Brayton cycle

Gas turbines operate on the Brayton cycle, which has four idealized steps:

1. Isentropic compression in the compressor: ambient air is compressed to high pressure.
2. Constant-pressure heat addition in the combustion chamber: fuel is mixed with compressed air and burned.
3. Isentropic expansion in the turbine: hot, high-pressure gases expand through the turbine, producing shaft work.
4. Constant-pressure heat rejection in the exhaust: spent gases are discharged to the atmosphere (open cycle) or cooled in a heat exchanger (closed cycle).

The three main components are the compressor (raises air pressure), the combustion chamber (adds thermal energy), and the turbine (extracts work). A significant portion of the turbine's output goes right back to driving the compressor, so the net power output is the turbine work minus the compressor work.

Design challenges for gas turbines include:

• High-temperature materials: turbine inlet temperatures can exceed 1500°C, requiring nickel-based superalloys and thermal barrier coatings.
• Blade cooling: internal cooling passages, film cooling, and transpiration cooling keep blade metal temperatures survivable.
• Emission control: technologies like dry low-NOx combustors reduce pollutant formation at the source.

Steam turbines and the Rankine cycle

Steam turbines operate on the Rankine cycle, which also has four idealized steps:

1. Isentropic compression in the pump: liquid water is pressurized.
2. Constant-pressure heat addition in the boiler: water is heated to high-pressure steam.
3. Isentropic expansion in the turbine: steam expands through the turbine, producing shaft work.
4. Constant-pressure heat rejection in the condenser: low-pressure steam is condensed back to liquid water.

The four main components are the pump, boiler, turbine, and condenser, forming a closed loop.

Design challenges for steam turbines include:

• Steam quality and moisture separation: as steam expands, it can partially condense. Water droplets erode turbine blades, so moisture separators are placed between turbine stages.
• Blade erosion prevention: special coatings and stellite shields on leading edges protect against droplet impact damage.
• Thermal efficiency improvements: regenerative feedwater heating (using bleed steam to preheat boiler feedwater) and reheat stages (returning partially expanded steam to the boiler for reheating before further expansion) both raise cycle efficiency. Modern plants commonly use multiple feedwater heaters and one or two reheat stages.