Consider the backend of a gas turbine engine which consists

Consider the back-end of a gas turbine engine which consists of a turbine and nozzle in series. Air flows steadily through a turbine and nozzle shown below with a mass flow rate of 2.23 kg/s. Air enters the poorly insulated turbine at 10 bar and 1400 K and its velocity is 50 m/s. Heat is lost from the turbine at the rate of 25 kW while it produces power at the rate of 250 kW. Air leaves the turbine at 2 bar and its velocity at turbine exit is 300 m/s. Air exiting the turbine enters a well-insulated nozzle and expands to 0.5 bar and 420 K. For part (a) of the problem, you must start with the full form of the basic equations before simplying them down using the assumptions you list. Be sure to list at least four assumptions for each component and clearly draw your systems showing all energy interactions. In part (b) you can carry forward some of your analysis from(a) as needed.

(a) You will analyze this configuration using two different methods. First taking into account variations of specific heat with temperature:

(i) Calculate the temperature of air at the turbine exit/nozzle inlet, in K

(ii) Determine the flow area at the nozzle exit, in cm2

(b) Repeat the analysis in (b) assuming that the specific heat of the air is constant with a specific heat ratio, k = 1.4.

(c) Compare the results from (a) and (b) and discuss which analysis is more accurate, and comment on which method is “easier”.

Solution

The exit temprarure of nozzle is 767k.

The flow area at nozzle exit is 23cm2.

The easier approach is second one because values are easy to find .