Steam Turbines

Steam turbines convert thermal energy of steam into mechanical work by expansion through nozzles and blades. They are used in Rankine cycles for power generation. Main turbine types: impulse (all pressure drop in stationary nozzles; rotor mainly changes momentum) and reaction (continuous pressure drop across stator+rotor; both contribute to enthalpy drop). Key practical considerations: isentropic (ideal) vs actual expansion, stage design (single- vs multi-stage, impulse vs reaction stages), degree of reaction, blade/rotor speed and velocity triangles, nozzle and blade losses, moisture at exhaust (causes erosion and reduced efficiency), reheating and regeneration to improve cycle efficiency, and partial admission effects on unsteady loading. Engineering analysis uses enthalpy balances (h, kJ/kg), energy conversion to kinetic energy in nozzles, and the Euler turbine equation for rotor work.

Governing FormulaKey relations (SI units): - Turbine specific work (ideal or actual): w = h_in - h_out (kJ/kg) - Turbine power: P = m_dot * (h_in - h_out) (kW when h in kJ/kg and m_dot in kg/s) - Isentropic efficiency (turbine): eta_t = (h_in - h_out_actual) / (h_in - h_out_isentropic) (dimensionless) - Nozzle kinetic relation (neglecting losses): h_in - h_out = v^2 / 2 (J/kg) -> if h in kJ/kg multiply by 1000 - Euler turbine equation (specific work from rotor): w = U * (c_theta1 - c_theta2) (J/kg), where U = blade peripheral speed (m/s), c_theta = tangential component of absolute steam velocity (m/s) - Degree of reaction: R = (enthalpy drop in rotor) / (total enthalpy drop of stage) = (Delta h_rotor) / (Delta h_stage) (dimensionless) Notes: h is specific enthalpy (kJ/kg), v, U, c_theta in m/s, P in kW or W depending on units. State assumptions are provided in each question.

Knowledge Check

10 Questions

1.Which statement correctly distinguishes an impulse turbine from a reaction turbine?

2.A steam turbine inlet has specific enthalpy h1 = 3500 kJ/kg. The actual outlet enthalpy is h2_actual = 2800 kJ/kg. The isentropic (ideal) outlet enthalpy for the same inlet and outlet pressures would be h2s = 2700 kJ/kg. What is the isentropic efficiency of the turbine (in percent)?

3.Steam with h_in = 3200 kJ/kg expands in a turbine to h_out = 2400 kJ/kg. If the mass flow is 10.0 kg/s, what is the mechanical power output (neglecting auxiliary losses)?

4.A nozzle produces a specific enthalpy drop of 200 kJ/kg which is converted to kinetic energy at the nozzle exit (neglecting losses). What is the nozzle exit velocity (m/s)?

5.What does a degree of reaction R = 0.5 indicate for a turbine stage?

6.Which describes the principal effect of significant moisture (liquid droplets) in the low-pressure stages of a steam turbine exhaust?

7.What is the main thermodynamic benefit of regenerative feedwater heating in a Rankine cycle using steam turbines?

8.Using the Euler turbine equation, compute the specific work (kJ/kg) for a rotor with peripheral speed U = 300 m/s if the tangential component of absolute steam velocity at rotor inlet c_theta1 = 400 m/s and at rotor outlet c_theta2 = 100 m/s. Use w = U*(c_theta1 - c_theta2) and present answer in kJ/kg.

9.What is the primary effect of reheating steam between turbine stages in a multi-stage Rankine cycle?

10.What is meant by partial admission in a steam turbine stage, and what is a principal consequence?