Applied Thermodynamics Essentials

This cheat sheet summarizes key concepts in applied thermodynamics, covering cycles, efficiency, refrigeration, psychrometrics, nozzle flow, shock waves, compressors, and turbines, including essential derivations and numerical problem-solving approaches.

Core Principles

Stoichiometric air-fuel ratio and exhaust gas analysis.
Adiabatic flame temperature and influencing factors.
Rankine cycle analysis with reheat and regeneration.
Comparison of Otto, Diesel, and Dual cycles.
Brayton cycle enhancements (regeneration, intercooling, reheating).
Vapor compression refrigeration cycle and refrigerant properties.
Psychrometric properties (DBT, WBT, dew point, humidity).
Stagnation properties and choked flow in nozzles.
Normal shock wave relations.
Multi-stage compressor work and intercooling.
Effect of clearance volume on compressor volumetric efficiency.
Velocity and pressure compounding in turbines.
Numerical problem-solving for thermal efficiency, air requirements, and nozzle flow.

Action Steps

1. Understand fundamental thermodynamic cycles (Rankine, Otto, Diesel, Brayton).
2. Master efficiency derivations for each cycle.
3. Analyze refrigeration and psychrometric processes using diagrams.
4. Apply principles of fluid dynamics to nozzle and shock wave problems.
5. Solve numerical problems involving thermal efficiency, air-fuel ratios, and flow properties.
6. Differentiate between velocity and pressure compounding in turbines.
7. Identify and state desirable properties of refrigerants.
8. Explain the impact of process enhancements (reheat, regeneration, intercooling) on cycle performance.

Formulas

Thermal efficiency of Rankine cycle: $\eta_{th} = 1 - \frac{Q_{out}}{Q_{in}}$
Thermal efficiency of Otto cycle: $\eta_{th} = 1 - \frac{1}{r^{{\gamma}-1}}$
Thermal efficiency of Diesel cycle: $\eta_{th} = 1 - \frac{1}{{\gamma}r^{{\gamma}-1}} \frac{{\alpha}^{\gamma}-1}{{\alpha}-1}$
Thermal efficiency of Brayton cycle: $\eta_{th} = 1 - \frac{T_1}{T_2}$
Critical pressure ratio for isentropic flow: $\frac{P_0}{P^*} = \left(1 + \frac{{\gamma}-1}{2}M^{*2}\right)^{{\gamma}/({\gamma}-1)}$
Mach number relation across normal shock: $M_2^2 = \frac{1 + \frac{{\gamma}-1}{2}M_1^2}{{{\gamma}M_1^2} - \frac{{\gamma}-1}{2}}$

Key Terms

Stoichiometric Air-Fuel Ratio: The ideal air-fuel ratio where complete combustion occurs, with no excess air or unburnt fuel.
Adiabatic Flame Temperature: The theoretical maximum temperature reached during combustion assuming no heat loss.
Rankine Cycle: A thermodynamic cycle that converts heat into work, typically used in steam power plants.
Brayton Cycle: A thermodynamic cycle that describes the operation of gas turbine engines.
Psychrometrics: The study of the thermodynamic properties of moist air and the processes that affect them.
Choked Flow: The condition in fluid flow where the velocity reaches the speed of sound (Mach 1) at the narrowest point (throat).
Normal Shock Wave: A shock wave that stands perpendicular to the direction of fluid flow.
Volumetric Efficiency: The ratio of the actual volume of fluid drawn into a cylinder to the cylinder's swept volume.
Compounding (Turbine): A technique used in turbines to improve efficiency by dividing the pressure drop or velocity increase into multiple stages.