(a) To determine The thermal efficiency of the cycle. Explanation The figure below shows the T - s diagram of an air-standard regenerative cycle. Figure-(1) The process 1 - 2 s is an isentropic expansion process, 2-3 is an isobaric heat addition process, 3 - 4 s is an isentropic compression process and 4-1 is an isobaric heat rejection process. The process 1-2 is a compression process with losses and the process 3-4 is an expansion process with losses. The air in process 2 s − x is preheated through the exhaust air from 4 s - y . Write the expression for the temperature ratio for process 1 − 2 s . T 2 s T 1 = ( p 2 p 1 ) ( k − 1 k ) (I) Here, the temperature at state 2 s is T 2 s , the temperature at state 1 is T 1 , the pressure at state 2 is p 2 , the pressure at state 1 is p 1 and the adiabatic index is k . Write the expression for the isentropic efficiency of the compressor. η c = h 2 s − h 1 h 2 − h 1 (II) Here, the specific enthalpy at state 1 is h 1 , the specific enthalpy at state 2 is h 2 and the specific enthalpy at state 2 s is h 2 s . Write the expression for the change in enthalpy in process 1 - 2 s . h 2 s − h 1 = c p ( T 2 s − T 1 ) Here, the specific heat at constant pressure is c p . Write the expression for the change in enthalpy in process 1 - 2 . h 2 − h 1 = c p ( T 2 − T 1 ) Here, the temperature at state 2 is T 2 . Substitute c p ( T 2 − T 1 ) for h 2 − h 1 and c p ( T 2 s − T 1 ) for h 2 s − h 1 in Equation (II). η c = c p ( T 2 s − T 1 ) c p ( T 2 − T 1 ) = ( T 2 s − T 1 ) ( T 2 − T 1 ) T 2 = T 1 + ( T 2 s − T 1 ) η c (III) Write the expression for the temperature at state 4 s . T 4 s = T 3 ( p 4 p 3 ) ( k − 1 k ) (IV) Here, the pressure at state 4 is p 4 , the pressure at state 3 is p 3 and the temperature at state 3 is T 3 . Write the expression for the turbine efficiency. η t = h 3 − h 4 h 3 − h 4 s (V) Here, the specific enthalpy at state 3 is h 3 the specific enthalpy at state 4 is h 4 s and the specific enthalpy at state 4 s is h 4 s . Write the expression for the change in enthalpy in process 3 - 4 s . h 3 − h 4 s = c p ( T 3 − T 4 s ) Here, the specific heat at constant pressure is c p . Write the expression for the change in enthalpy in process 3 - 4 . h 3 − h 4 = c p ( T 3 − T 4 ) Here, the temperature at state 4 is T 4 . Substitute c p ( T 3 − T 4 ) for h 3 − h 4 and c p ( T 3 − T 4 s ) for h 3 − h 4 s in Equation (V). η t = c p ( T 3 − T 4 ) c p ( T 3 − T 4 s ) η t = ( T 3 − T 4 ) ( T 3 − T 4 s ) T 4 = T 3 − η t ( T 3 − T 4 s ) (VI) Write the expression for the efficiency of the regenerator. η r e g = T x − T 2 T 4 − T 2 T x = T 2 + η r e g ( T 4 − T 2 ) (VII) The heat lost by the exhaust gases is utilized by the regenerator. Write the expression for the heat energy in the regenerator. c p ( T y − T 4 ) = c p ( T x − T 2 ) T y − T 4 = T x − T 2 T y = T x − T 2 + T 4 (VIII) Write the expression for the heat added to the cycle. Q ˙ i n = m ˙ c p ( T 3 − T x ) Here, the mass flow rate of the gas is m ˙ (b) To determine The back work ratio of the cycle. (c) To determine The net work of the cycle. (d) To determine The rate of entropy produced within the regenerator.

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Question

Chapter 9.14, Problem 62P

(a)

To determine

The thermal efficiency of the cycle.

(b)

To determine

The back work ratio of the cycle.

(c)

To determine

The net work of the cycle.

(d)

To determine

The rate of entropy produced within the regenerator.

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Chapter 9.14, Problem 61P

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