Lesson test: The Brayton cycle

1.[2p]
An ideal Brayton cycle has a pressure ratio of $12$ and $k = 1.400$ . What is its thermal efficiency?

CorrectNot quite: 0.508

2.[2p]
Air enters that cycle at $300$ K. What is the compressor exit temperature, in kelvin?

CorrectNot quite: 610

3.[3p]
The ideal Brayton efficiency depends only on the pressure ratio. Why does that stop being true for a real machine?

The component losses are fixed fractions of work terms that scale differently with peak temperature

Correct

The pressure ratio changes during operation

The answer is: The component losses are fixed fractions of work terms that scale differently with peak temperature

Real gases do not obey the isentropic relation at all

The answer is: The component losses are fixed fractions of work terms that scale differently with peak temperature

The heat addition stops being at constant pressure

The answer is: The component losses are fixed fractions of work terms that scale differently with peak temperature

4.[2p]
With $η_{C} = 0.80$ and $η_{T} = 0.85$ , the same cycle at $T_{3} = 1400$ K gives $w_{c} = 389.7$ and $w_{t} = 608.0$ kJ/kg. What is the back work ratio?

CorrectNot quite: 0.641

5.[3p]
For that real cycle the heat input is $715.8$ kJ/kg. What is the thermal efficiency?

CorrectNot quite: 0.305

6.[2p]
A gas turbine's high back work ratio is why the concept is old but working machines are not.

True

Correct

False

The answer is: True

7.[3p]
A regenerator of effectiveness $0.80$ preheats air from $610.2$ K using exhaust at $688.3$ K. What temperature does the air reach, in kelvin?

CorrectNot quite: 673

8.[3p]
Above a pressure ratio of about $14.8$ in this cycle, a regenerator becomes useless. Why?

The compressor discharge is then hotter than the exhaust, so heat would have to flow the wrong way

Correct

The regenerator's effectiveness falls to zero at high pressure

The answer is: The compressor discharge is then hotter than the exhaust, so heat would have to flow the wrong way

The turbine exhaust becomes supersonic

The answer is: The compressor discharge is then hotter than the exhaust, so heat would have to flow the wrong way

The heat input is already at its maximum

The answer is: The compressor discharge is then hotter than the exhaust, so heat would have to flow the wrong way

9.[3p]
Which of these does the cold-air-standard analysis get wrong about a real gas turbine?

Select all that apply

It uses a specific heat too low for gas at $1400$ K

Correct

It ignores the mass of fuel added and the combustor pressure drop

Correct

It ignores the compressor air bled to cool the turbine blades

Correct

It assumes the compression and expansion are adiabatic

The answer is: It uses a specific heat too low for gas at $1400$ K, It ignores the mass of fuel added and the combustor pressure drop, It ignores the compressor air bled to cool the turbine blades

1.[2p] An ideal Brayton cycle has a pressure ratio of 12 and k=1.400. What is its thermal efficiency?

2.[2p] Air enters that cycle at 300 K. What is the compressor exit temperature, in kelvin?

3.[3p] The ideal Brayton efficiency depends only on the pressure ratio. Why does that stop being true for a real machine?

4.[2p] With ηC=0.80 and ηT=0.85, the same cycle at T3=1400 K gives wc=389.7 and wt=608.0 kJ/kg. What is the back work ratio?

5.[3p] For that real cycle the heat input is 715.8 kJ/kg. What is the thermal efficiency?

6.[2p] A gas turbine's high back work ratio is why the concept is old but working machines are not.

7.[3p] A regenerator of effectiveness 0.80 preheats air from 610.2 K using exhaust at 688.3 K. What temperature does the air reach, in kelvin?

8.[3p] Above a pressure ratio of about 14.8 in this cycle, a regenerator becomes useless. Why?

9.[3p] Which of these does the cold-air-standard analysis get wrong about a real gas turbine?

1.[2p]
An ideal Brayton cycle has a pressure ratio of $12$ and $k = 1.400$ . What is its thermal efficiency?

2.[2p]
Air enters that cycle at $300$ K. What is the compressor exit temperature, in kelvin?

3.[3p]
The ideal Brayton efficiency depends only on the pressure ratio. Why does that stop being true for a real machine?

4.[2p]
With $η_{C} = 0.80$ and $η_{T} = 0.85$ , the same cycle at $T_{3} = 1400$ K gives $w_{c} = 389.7$ and $w_{t} = 608.0$ kJ/kg. What is the back work ratio?

5.[3p]
For that real cycle the heat input is $715.8$ kJ/kg. What is the thermal efficiency?

6.[2p]
A gas turbine's high back work ratio is why the concept is old but working machines are not.

7.[3p]
A regenerator of effectiveness $0.80$ preheats air from $610.2$ K using exhaust at $688.3$ K. What temperature does the air reach, in kelvin?

8.[3p]
Above a pressure ratio of about $14.8$ in this cycle, a regenerator becomes useless. Why?

9.[3p]
Which of these does the cold-air-standard analysis get wrong about a real gas turbine?