Day 3 - Brayton Cycle

Draw Brayton PV and TS Diagram

Equal Values

P1 = P4 ; P2 = P3 ; S1 = S2 ; S3 = S4

Process 1 - 2: Isentropic Compression

rk = V1/V2 = (P2/P1)^1/k = (T2/T1)^1/k-1

Process 1 - 2: Pressure Ratio

rp = P2/P1 = P3/P4

Process 1 - 2: Compressor Work

Wc = m cp (T2-T1) = h2 - h1

Process 2 - 3: Constant Pressure Process

P2 = P3

V3/V2 = T3/T2

Process 2 - 3: Heat Added

Qa = m cp (T3-T2) = h3 - h2

Process 3 - 4: Isentropic Expansion

re = V4/V3 = P3/P4^1/k = T3/T4^1/k-1

Expansion and Pressure Ratio

re = rp^1/k

Compression and Pressure Ratio

rp = rk^k

Process 3 - 4: Turbine Work

Wt = m cp (T3-T4) = h3 - h4

Process 3 - 4: Pressure Ratio

rp = P2/P1 = P3/P4

Process 4 - 1: Constant Pressure

P4 = P1

V4/V1 = T4/T1

Compression and Expansion Ratio Brayton

re = rk

Process 4 - 1: Heat Rejected

Qr = m cp (T4-T1) = h4 - h1

Net Turbine Work: Wn

Wnet = Wt - Wc

Cycle Efficiency

e = Wnet / Qa = Wt - Wc / Qa

e = 1 - 1/(rp^(k-1)/k)

e = 1- 1/(rk^(k-1))

Backwork Ratio

BW = Wc / Wt = (T2-T1) / (T3-T4) = h2 - h1 / h3 - h4

Max Net Work Relations

T2 = T4 = sqrt (T1 T3)

Max Net Work

Wmax = m cp (sqrt(T3) - sqrt (T1))²

Actual Net Work

Wna = Wta - Wtc

Turbine Efficiency

et = Wta / Wti

Compressor Efficiency

ec = Wti / Wta