The Brayton Cycle

The basic air-breathing (i.e., open) gas turbine cycle is shown schematically in Figure 1. The basic
cycle is often called the Brayton cycle, named for the American inventor George Brayton who
developed the power cycle in the 1870’s. The original Brayton cycle used reciprocating compression
and expansion processes rather than the rotary machines that are used in modern gas turbine cycles.
Outdoor air at state 1 is drawn into a compressor and compressed to a higher pressure at state 2. The
ratio of the pressure at state 2 to the pressure at state 1 is called the pressure ratio and it is an important
design parameter for this cycle. The compressed air at state 2 enters a combustion chamber where it is
mixed with fuel and combusted. The combustion process is assumed to occur at nearly constant
pressure. We assume that the energy provided by combustion of the fuel can be expressed in terms of
the heat of combustion of the fuel (HC) which is the energy released per unit mass of fuel. In this
chapter, we will further assume that the properties of the combustion products are the same as the
properties of pure air. The ratio of the mass flow rate of air to the mass flow rate of fuel is referred to as
the air-fuel ratio (AF). High air-fuel ratios are used in the combustion process (i.e., the combustion is
lean) in order to control the temperature of the combustion products entering the turbine at state 3 and
avoid damage to the blades. Higher turbine inlet temperatures lead to higher cycle efficiency. However
the fatigue strength of the turbine blades that are continuously exposed to the high temperature exhaust
products dictates a maximum temperature that is approximately 1200◦C. Special alloys and/or
enhanced turbine blade cooling methods may allow higher temperatures and a significant amount of
research is devoted to increasing the maximum turbine inlet temperature in a gas turbine power cycle.
The high pressure and high temperature combustion gas entering the turbine at state 3 expands in a
gasifier turbine that produces shaft power sufficient to drive the compressor. If the gas turbine power
cycle is operating correctly, it is not necessary to expand the gas to atmospheric pressure in the gasifier
turbine; that is, P4 > P1. Therefore, the gas can subsequently be expanded in a power turbine that
produces some net useful power. Depending on the application, the output power may be used to
provide mechanical power (e.g., to a helicopter rotor) or electrical power using a generator. In some
cases the gasifier and power turbines are collocated on the same shaft whereas in other cases it is useful
to separate these functions, allowing the gasifier turbine to operate at its optimal speed while the speed
of the power turbine varies in response to the mechanical load.

Figure 1
$UnitSystem SI Radian Mass J K Pa
$TabStops 0.2 3.5 in

"Input conditions"
T_amb=converttemp(C,K,20[C]) "ambient temperature"
P_atm=1 [atm]*convert(atm,Pa) "ambient pressure"
{AF= 70} "air to fuel ratio"
PR=25 [-] "pressure ratio"
HC=42e6 [J/kg] "heat of combustion of fuel"
T_t_in_C = 1300 [C]

"Performance parameters"
eta_gt=0.88 [-] "gasifier turbine efficiency"
eta_pt=0.82 [-] "power turbine efficiency"
eta_c=0.85 [-] "compressor efficiency"

"State 1"
T[1]=T_amb "temperature"
P[1]=P_atm "pressure"
s[1]=entropy(Air,T=T[1],P=P[1]) "entropy"
h[1]=enthalpy(Air,T=T[1]) "enthalpy"

"State 2"
P[2]=PR*P[1] "pressure"
s_s[2]=s[1] "entropy balance on reversible compressor"
h_s[2]=enthalpy(Air,s=s_s[2],P=P[2]) "enthalpy leaving reversible compressor"
W_s_c =h_s[2]-h[1] "work per mass required by reversible compressor"
W_a_c= h[2]-h[1] "work per mass required by actual compressor"
eta_c = (h_s[2]-h[1])/(h[2]-h[1]) "enthalpy leaving actual compressor"
s[2]=entropy(Air,h=h[2],P=P[2]) "entropy leaving actual compressor"
T[2]=temperature(Air,h=h[2]) "temperature leaving actual compressor"

"State 3"
h[2]+HC/AF=h[3]*(1+1/AF) "combustor energy balance"
P[3]=P[2] "no pressure loss"
T[3]=temperature(Air,h=h[3]) "temperature"
s[3]=entropy(Air,h=h[3],P=P[3]) "entropy"

"State 4"
{P[4]=(P[1]+P[2])/2} "guess for pressure leaving gasifier turbine"
s_s[4]=s[3] "entropy balance on reversible gasifier turbine"
h_s[4]=enthalpy(Air,s=s_s[4],P=P[4]) "enthalpy leaving reversible gasifier turbine"
W_s_gt =(h[3]-h_s[4])*(1+1/AF) "work per mass associated with reversible gasifier
turbine"
W_a_gt = (h[3]-h[4])*(1+1/AF) "work per mass associated with actual gasifier
turbine"
eta_gt = (h[3]-h[4])/(h[3]-h_s[4]) "enthalpy leaving actual gasifier turbine"
s[4]=entropy(Air,h=h[4],P=P[4]) "entropy leaving actual gasifier turbine"
T[4]=temperature(Air,h=h[4]) "temperature leaving actual gasifier turbine"
W_a_gt =W_a_c "power from gasifier turbine must equal power required by compressor"

"State 5"
P[5]=P_atm "exit pressure"
s_s[5]=s[4] "entropy balance on reversible power turbine"
h_s[5]=enthalpy(Air,s=s_s[5],P=P[5]) "enthalpy leaving reversible power turbine"
W_s_pt =(h[4]-h_s[5])*(1+1/AF) "work per mass associated with reversible power
turbine"
W_a_pt = (h[4]-h[5])*(1+1/AF) "work per mass associated with actual power turbine"
eta_pt = (h[4]-h[5])/(h[4]-h_s[5]) "enthalpy leaving actual power turbine"
s[5]=entropy(Air,h=h[5],P=P[5]) "entropy leaving actual power turbine"
T[5]=temperature(Air,h=h[5]) "temperature leaving actual power turbine"

T_t_in_C=converttemp(K,C,T[3]) "turbine inlet temperature, C"