Question

Derive the formula of Wnetmax in an air standard Brayton Cycle by maximizing the formula of Wnet in terms of T2 and using the relationship T1/T2=T4/T3 . Your answer should be as a function of m, Cp, T1, T2 and T3 only. Using the derived formula, find Wnetmax when T1= 300C, T3=1000C and T2=500C in kJ/kg.

Answer 1

Solution-

Assumption-

• Kinetic and potential energies across turbine and compressor neglected.
• Steady state operation
• Air Standard assumptions valid.

Let us consider a brayton cycle with 1-2 as Isentropic compression .2-3 Heat addition in combustion chamber , 3-4 Isentropic expansion in turbine , 4-1 Heat rejection to atmosphere at constant pressure.

Analysis-

1 Qin Wt. 4 like Qout. L S We = (kl) comp E During process Ito 2 Compression vosk input. inco (T2-T) kJ. Buring process ? toh Tsentropic expansion in turbine Wq = (1) tor inco (T3-T4) KI Whet = WT-Wc Whet mcp (T3-14 - Tz +To) kJ. using Relation given given in Question, Tu (7) Wnet = nice [13 - T (7) -T2 +T). Whet wit Tz for max. Wark. i Ty To a Ta T3 Differenting

2 dlwhet) - mico micg {0+ m2 -1 +0] =- d (T2) Tits = 12 T2 = √ToT3. using Relationship in equation @ Tu Tito o for max Work net obtained from above system, T2 = T4 = to. Tz (Wnet )max = hicp [T3-T2 -12 +T] (Wlmet) max inco [Tz +11 - 2To], kw. Using Data Data Ti= 300c or 573k. Tz=100oc on 1273k T2 = 500'c or 773k. maxa (almet) max (Winet)max, loos (1273+573- 26773 kalny = 301.5

Result-

From the above relationship for (W _net)_max is a function of T₃ = T _max temperature which is constraint by material properties of gas turbine . T₁ = T _min which is constraint by atmosphere(ambient temperature and pressure).

Condition for (W _net)_max

$\small T_{2}=T_{4}= \sqrt{T_{1}*T_{3}}$