AAE 339 Aerospace Propulsion Summer 2023 Homework Assignment 1 Problems 1-4 Complete problems 1, 5, 7, 8 in Chapter 2 of Hill and Peterson. A scanned copy of these problems is shown below. 1 2 Hints: • Problem 1 is an application of the 1st Law of Thermodynamics (Eqn 2-5 in H&P). Note the problem stipulates adiabatic flow (Q_dot=0), meaning there is no heat flow into or out of the system or control volume so the change in energy must be equal to the amount of work done. Pay attention to the sign convention: work done by a system is positive and work done on a system is negative. For part b, calculate the change in entropy (see Eqn 2-17) and check it against the 2nd Law of Thermodynamics. For part c, use Eqn 2-18 to calculate T2, and then the conservation of energy (eg Eq 2-7) to calculate u2. • In Problem 5 apply the conservation of energy to calculate temperature of the mixed streams, and then calculate the entropy change in each stream as they go to the mixed state to check feasibility. • Problems 7 and 8 are applications of conservation of momentum. Remember that ∫𝜌𝑢⃗ ∙𝑛⃗ 𝑑𝐴 can be written as 𝑚̇ entering and exiting the control surface, with negative and positive signs, respectively, due to the dot product operation with the unit normal vector pointing outward from control surface. 3 Problem 5 Modern gas turbine engines operate at fuel-to-air ratios of about 0.02, pressure ratios (ratio of compressor exit pressure to inlet pressure) of nearly 40, and with a turbine inlet temperature (combustor exit temperature) of about 1800 K. At this condition, the gas mixture exiting the combustor comprises about 4% CO2, 4% H2O, 77% N2, and 15% O2 (in mole percentages). Calculate the average properties of the gas exiting the combustor, specifically molecular weight, M, density, , heat capacity, cp (see Appendix II), and sound speed, a. Since we often approximate this gas as heated air, compare these values with corresponding values for air at 1800 K. 4 Problems 6-7 Complete problems 13, 14 in Chapter 2 of Hill and Peterson. A scanned copy is shown below. 5
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