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Lecture 14 example - jet engine with a regenerative heat exchangerTutorialCurrent spec2:218 min

ENGR5003 Lecture 14 example heat exchanger question (slides 5-11)

A jet engine is treated as a Brayton cycle with a pressure ratio of 8. The temperature and pressure of the inlet gases are 250 K and 50 kPa. The temperature after combustion is 1300 K, and you can assume $\gamma = 1.4$ and $c_p = 1.0045\ \mathrm{kJ/(kg\,K)}$ . For an ideal heat exchanger between the exhaust (state 4) and the compressed air (state 2), the Lecture 14 models are (Figure 1): cocurrent flow $T_2' = T_4' = \tfrac{1}{2}(T_2 + T_4)$ ; countercurrent flow $T_2' = T_4$ and $T_4' = T_2$ .

Figure 1: cocurrent flow (both streams leave near the mean temperature) and countercurrent flow (each stream can leave near the other's inlet temperature) (Lecture 14, slide 5).

Formulas you may need

Adiabatic (isentropic) ideal gas: $\dfrac{T_2}{T_1} = r_p^{(\gamma-1)/\gamma}$ (on the formula sheet)
Brayton efficiency: $\eta = 1 - \dfrac{T_1}{T_2}$ ; $\eta_{th} = 1 - \dfrac{q_{out}}{q_{in}}$ (on the formula sheet)
Isobaric heat: $q = c_p\Delta T$ (on the formula sheet)
Heat exchanger models: cocurrent $T_2' = T_4' = \tfrac{1}{2}(T_2 + T_4)$ ; countercurrent $T_2' = T_4$ , $T_4' = T_2$ (learn this, Lecture 14)

(a)
Determine the temperature at each stage of the cycle as well as the thermal efficiency. How much specific heat addition is required?
T2 =K
T4 =K
eta_th =
q_in =kJ/kg
(b)
A heat exchanger is now used to recycle some of the heat from the exhaust to the compressed air. Determine the thermal efficiency and the specific heat exchanged when the heat exchanger uses (i) cocurrent flow and (ii) countercurrent flow.
q_HX cocurrent =kJ/kg
eta cocurrent =
q_HX countercurrent =kJ/kg
eta countercurrent =
(c)
Find the maximum pressure ratio for which a heat exchanger would still be useful.
r_p,max =