Gas and Steam Turbines
Comprehensive university textbook unit covering fundamental principles, governing relationships, and engineering applications of Gas and Steam Turbines.
§5.1 Gas turbine specific work and power
**Outcome.** Use conservation laws and appropriate reference stations to analyze **gas turbine specific work and power**; solve a traceable numerical example; expose model limitations; and justify a provisional engineering choice. This is Unit 05, **Gas and Steam Turbines**.
§5.2 Turbine isentropic efficiency
**Outcome.** Use conservation laws and appropriate reference stations to analyze **turbine isentropic efficiency**; solve a traceable numerical example; expose model limitations; and justify a provisional engineering choice. This is Unit 05, **Gas and Steam Turbines**.
§5.3 Impulse, reaction and stage velocity triangles
**Outcome.** Use conservation laws and appropriate reference stations to analyze **impulse, reaction and stage velocity triangles**; solve a traceable numerical example; expose model limitations; and justify a provisional engineering choice. This is Unit 05, **Gas and Steam Turbines**.
§5.4 Steam expansion, quality and moisture
**Outcome.** Use conservation laws and appropriate reference stations to analyze **steam expansion, quality and moisture**; solve a traceable numerical example; expose model limitations; and justify a provisional engineering choice. This is Unit 05, **Gas and Steam Turbines**.
§5.5 Turbine cooling and net cycle balance
**Outcome.** Use conservation laws and appropriate reference stations to analyze **turbine cooling and net cycle balance**; solve a traceable numerical example; expose model limitations; and justify a provisional engineering choice. This is Unit 05, **Gas and Steam Turbines**.
Step-by-Step Turbomachinery Solutions
Three original questions connect calculations, definitions and interpretation. Open each solution to follow the reasoning.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Gas turbine specific work and power** under steady operational loading.
Worked Engineering Derivation:
**Teaching case:** Gas with m_dot=18 kg/s, cp=1.15 kJ/(kg K) and a 210 K total-temperature drop develops about 4.35 MW fluid power. **Explicit substitution:** P=18×1.15×210; therefore **4347 kW = 4.347 MW**. The cp is a given mean value over the temperature interval. Check arithmetic independently. Then perturb one input by 10%: linear, quadratic and cubic factors become 1.1, 1.21 and 1.331, respectively. Recompute nonlinear property relationships. An algebraic change is not evidence of a new real-machine operating point.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Turbine isentropic efficiency** under steady operational loading.
Worked Engineering Derivation:
**Teaching case:** With T01=1100 K, T02=900 K and ideal T02s=865 K, turbine efficiency is about 0.851. **Explicit substitution:** eta_t=(1100−900)/(1100−865)=200/235; therefore **0.8511**. For a turbine the actual enthalpy drop is less than ideal. Check arithmetic independently. Then perturb one input by 10%: linear, quadratic and cubic factors become 1.1, 1.21 and 1.331, respectively. Recompute nonlinear property relationships. An algebraic change is not evidence of a new real-machine operating point.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Impulse, reaction and stage velocity triangles** under steady operational loading.
Worked Engineering Derivation:
**Teaching case:** At constant U=240 m/s, inlet whirl=160 m/s and exit whirl=-40 m/s, extraction is 48 kJ/kg. **Explicit substitution:** w=240×160−240×(−40); therefore **48,000 J/kg**. Rotor extracts power; outlet counter-swirl increases extracted work. Check arithmetic independently. Then perturb one input by 10%: linear, quadratic and cubic factors become 1.1, 1.21 and 1.331, respectively. Recompute nonlinear property relationships. An algebraic change is not evidence of a new real-machine operating point.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Steam expansion, quality and moisture** under steady operational loading.
Worked Engineering Derivation:
**Teaching case:** At x=0.90, hg=2600 kJ/kg and hf=200 kJ/kg, mixture enthalpy is 2360 kJ/kg. **Explicit substitution:** h=0.90×2600+0.10×200; therefore **2360 kJ/kg**. Saturation quality is mass fraction of vapor. Check arithmetic independently. Then perturb one input by 10%: linear, quadratic and cubic factors become 1.1, 1.21 and 1.331, respectively. Recompute nonlinear property relationships. An algebraic change is not evidence of a new real-machine operating point.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Turbine cooling and net cycle balance** under steady operational loading.
Worked Engineering Derivation:
**Teaching case:** A 12 MW turbine driving a 7.5 MW compressor and 0.4 MW auxiliaries leaves 4.1 MW net before electrical losses. **Explicit substitution:** P_net=12−7.5−0.4; therefore **4.1 MW**. Generator and other downstream electrical losses not included. Check arithmetic independently. Then perturb one input by 10%: linear, quadratic and cubic factors become 1.1, 1.21 and 1.331, respectively. Recompute nonlinear property relationships. An algebraic change is not evidence of a new real-machine operating point.