MAE 115 – Applied Engineering Thermodynamics Examination #2

Conceptual Short Answer (20 points):

1.   Answer the following questions:

a)   List the “Air Standard Assumptions” and discuss why it is useful to use them for studying gas cycles?

b)   Demonstrate that for the same compression ratio (with r≠1) ηth,otto  > ηth,Diesel

Vapor cycles (25 points):

2.    Superheated steam enters in a steam turbine at 400°C and 30 bar, at a rate of 10 kg/s. The output pressure is 1 bar. Assuming that the turbine operates in steady state conditions and with an isentropic efficiency of 85%, determine:

a.   The mechanical power produced

b.   The vapor quality at the turbine outlet

Use vapor and liquid tables or computational methods to determine the thermodynamic properties of superheated and saturated fluids.

Steam properties at 400°C and 30 bar: h = 3232 kg/kJ, s  = 6.922 kg-k/kJ

Gas turbine cycles (30 points):

3.    Consider an ideal simple Joule-Brayton cycle that works with air at 30°C and 1 atm. The maximum temperature of the cycle is 1000°C and the compression ratio is 4.

Determine the following:

(a) All state points for the ideal cycle (temperatures and pressures). Assume air as an ideal diatomic gas with constant specific heat capacities

(b) The first law efficiency of the ideal cycle

(c) Assuming an isentropic efficiency for the compressor and turbine of 90% and 92% respectively, determine the states of the real cycle

(d) Determine the first law efficiency of the real cycle

(e) In the real cycle case, is it possible to use a recuperator? If so, determine the first law

efficiency of the recuperative cycle, assuming an effectiveness of the heat exchanger of 100%

For extra credit, estimate the speed of a fluid leaving a simple gas turbine (no recuperation) with the same properties as the engine above. Assume the engine is operating at take-off (i.e., inlet fluid speed = 0 m/s)