Energy Systems LM

Politecnico di Milano

Department of Energy

School of Industrial and Information Engineering

Course Energy Systems LM

proff. S. CONSONNI, E. MARTELLI, M. ROMANO - Academic Year 2015/16

Written Exam 08 February 2016 - Problems - Time: 2 hours

PLEASE NOTICE

1) Exam is open book, but computers and cell phones are NOT allowed. Talking with colleagues and/or

copying will lead to the immediate cancellation of the exam.

2) Answer clearly ONLY to the questions posed by the problem sets. Even if correct, additional

considerations and/or calculations will NOT be considered.

3) Fill this sheet with your name and return it together with your solutions.

4) Mark each sheet of the solution with your name and page number.

5) The final grade is the sum of the points assigned to the solution of each problem plus a bonus of max

3 points. The bonus will be given based on whether the solution of each problem is complete, with

clear details and explanations.

FIRST NAME………………………......……..…FAMILY NAME………….…………………………..

Problem 1 (16 points) 1

A natural gas-fired boiler with combustion power 10 MW is fed with natural gas with the following molar

composition:

Methane (molecular mass 16 kg/kmol, LHV 50 MJ/kg): 88%

Ethane (molecular mass 30 kg/kmol, LHV 47.8 MJ/kg): 8%

Nitrogen (molecular mass 28 kg/kmol, LHV 0 MJ/kg): 4%

For the sake of simplicity, combustion air can be assumed a mixture of just nitrogen and oxygen, with a

molar ratio 3.76

1) Evaluate the mass flow rate of natural gas

At design conditions:

both air and natural gas are fed to the boiler at the reference temperature of 25°C;

combustion efficiency is 99.5% (i.e., unburned fuel losses = 0.5%);

heat losses from the boiler walls are negligible;

percentage excess air is 20%

temperature of combustion products discharged by the boiler is 110°C;

the boiler generates pressurized water at 10 bar, 140°C;

feedwater enters the boiler at 10 bar, 50°C

Assuming that the specific heat of combustion products can be considered constant and the ratio =c /c

p v

is 1.32, evaluate the following:

2) oxygen content in dry, combustion products;

3) boiler efficiency;

4) mass flow rate of water heated up by the boiler;

5) assuming that the combustor is adiabatic, determine the effectiveness of the heat exchanger that

transfers heat from the combustion products to the pressurized water;

6) calculate CO specific emissions [grams of CO per MJ of useful heat]

2 2

1 Combustion power = [fuel mass flow rate]*LHV

Energy Systems LM - written test of Feb 8th, 2016 page 1 of 3

Politecnico di Milano

Department of Energy

School of Industrial and Information Engineering

Course Energy Systems LM

proff. S. CONSONNI, E. MARTELLI, M. ROMANO - Academic Year 2015/16

Problem 2 (16 points)

In order to avoid the exposure to high-temperature corrosive gases, the reheater of the waste-to-energy

plant in Amsterdam is heated up by saturated steam extracted from the steam drum, like in the cycle

represented in Fig. 1. In such scheme the heat needed for steam reheating is released by saturated

steam (flow 14 of Fig. 1) taken from the steam drum; the saturated liquid left after condensation (flow 15 in

Fig. 1) is returned to the drum.

Assume that the steam cycle in Fig. 1 features the following parameters.

Condensation pressure 0.07 bar

De-aerator pressure 4 bar

Admission at HPT inlet (point 9): 150 ton/hour at 130 bar, 450°C

Admission at LPT inlet (point 11): 20 bar, 320°C

Turbogenerator efficiencies:

87% (isoentropic) for HPT;

92% (isoentropic) for the LPT expansion from inlet (point 11) to extraction (point 12);

90% (isoentropic) for the LPT expansion from inlet (point 11) to outlet (point 13);

98% mechanical

97% for electric generator

Efficiency of feedwater pumps:

90% hydraulic

97% mechanical

95% for electric motor

Boiler efficiency 87%

For the sake of simplicity, all pressure losses can be neglected.

1) Draw the T-Q diagram of the reheater.

Calculate the following:

2) mass flow of steam fed to the deaerator (point 12);

3) net power output;

4) thermal power supplied by the boiler to the steam cycle;

5) net plant efficiency. p T h s vap fract

state bar °C kJ/kg kJ/kg-K x

sat liq 0.07 39.0 163.38 0.559 0.000

sat liq 4.00 143.6 604.67 1.776 0.000

sh vap 130.00 450.0 3194.58 6.251 1.000

liq+vap 20.00 212.4 2755.45 6.251 0.978

sh vap 20.00 320.0 3071.16 6.849 1.000

liq+vap 4.00 143.6 2718.59 6.849 0.991

liq+vap 0.07 39.0 2126.82 6.849 0.815

sat vap 130.00 330.8 2666.98 5.441 1.000

Table 1. Properties of water and steam at selected conditions

Energy Systems LM - written test of Feb 8th, 2016 page 2 of 3

Politecnico di Milano

Department of Energy

School of Industrial and Information Engineering

Course Energy Systems LM

proff. S. CONSONNI, E. MARTELLI, M. ROMANO - Academic Year 2015/16

Figure 1. Configuration of steam cycle

Energy Systems LM - written test of Feb 8th, 2016 page 3 of 3

Politecnico di Milano

Department of Energy

School of Industrial and Information Engineering

Course Energy Systems LM

proff. S. CONSONNI, E. MARTELLI, M. ROMANO - Academic Year 2015/16

Written Exam 29 February 2016 - Problems - Time: 2 hours

PLEASE NOTICE

1) Exam is open book, but computers and cell phones are NOT allowed. Talking with colleagues and/or

copying will lead to the immediate cancellation of the exam.

2) Answer clearly ONLY to the questions posed by the problem sets. Even if correct, additional

considerations and/or calculations will NOT be considered.

3) Fill this sheet with your name and return it together with your solutions.

4) Mark each sheet of the solution with your name and page number.

5) The final grade is the sum of the points assigned to the solution of each problem plus a bonus of max

3 points. The bonus will be given based on whether the solution of each problem is complete, with

clear details and explanations.

FIRST NAME………………………......……..…FAMILY NAME………….…………………………..

Problem 1 (16 points)

A microturbine features a regenerative gas cycle with uncooled turbine (no cooling system) and the

following operating parameters:

- Turbine outlet temperature = 565 °C

- Compressor pressure ratio = 4

- Regenerator effectiveness = 80%

- Isentropic efficiency of turbine = 90%

- Isentropic efficiency of compressor = 75%

- Relative pressure drops of regenerator on air side and flue gas side = 1% of inlet pressure

- Relative pressure drop of combustor = 0.5% of inlet pressure

- Thermal losses and Losses for unburned fuel species are negligible

- Air properties: = 1.01 kJ/kg K, MM = 28.1 kg/kmol

molar composition: 21% O2, 79% N2, T = 15°C, c p

- Flue gas properties: c = 1.05 kJ/kg K, MM = 28.5 kg/kmol

p

- Mechanical efficiency of the shaft and power transmission system = 95%

- Electric efficiency of the generator = 94%

- Net electric power = 200 kW

- Fuel properties:

composition: pure CH , T = 25°C, MM = 16 kg/kmol, LHV = 50.1 MJ/kg

4

1. Draw the scheme of the cycle

Determine the following unknown parameters:

2. Turbine pressure ratio

3. Turbine inlet temperature

4. Temperature of preheated air at regenerator exit

5. Flue gas temperature at stack

6. Air mass flow rate

7. Net electric efficiency and net specific work

Energy Systems LM - written test of Feb 29th, 2016 page 1 of 3

Politecnico di Milano

Department of Energy

School of Industrial and Information Engineering

Course Energy Systems LM

proff. S. CONSONNI, E. MARTELLI, M. ROMANO - Academic Year 2015/16

Problem 2 (16 points)

A power plant is equipped with a closed-loop heat rejection system that discharges to ambient the heat

collected from electric generators and lubricating oil, using water as cooling medium (see figure below). At

design conditions, the system rejects a thermal power of 10 MW, with the water loop operating between

40 and 48°C and ambient temperature 30°C.

ELECTRIC

GENERATORS 48°C HEAT

REJECTION

40°C SYSTEM

LUBRICATING

OIL COOLERS

1) Calculate the mass flow rate of water circulating through the heat rejection system.

Two options are under consideration for the design of the heat rejection system.

The first design option features finned air-cooled heat exchangers where the ratio between the external,

finned surface (on the air-side) and the internal surface of the tubes that carry the water is 15.

The air-side heat transfer coefficient varies with air velocity according to the following equation:

0.4

h=50*u

2

where the air-side heat transfer coefficient h [W/m -K] is referred to the external heat transfer surface

ext

and u [m/s] is the air velocity through the heat exchanger. The internal, water-side heat transfer coefficient

2

is 2000 W/m -K, referred to the internal heat transfer surface.

int

At design conditions, ambient air enters the external, finned heat transfer surface at 30°C and exits at

40°C.

For this first design option calculate the following.

2) Internal and external heat transfer surface of the air cooled heat exchanger, considering that the heat

exchanger has a counter-flow arrangement and the design air velocity through the exchanger is 2 m/s

3) Expected water temperatures when the heat exchanger with the surfaces evaluated at point 2) is

2

subject to fouling, causing an additional thermal resistance of 0.0002 m -K/W, referred to the internal

heat transfer surface. Consider that in this case thermal power, water mass flow rate and air mass flow

rate are the same as the design conditions.

The second design option features a cooling tower where the water flowing in the loop is cooled by direct

contact with air. At the design point, ambient air at 30°C and 40% relative humidity entering the bottom of

the tower is heated and humidified to 30°C and saturated conditions (relative humidity=100%).

4) On the psychrometric chart on the next page show the air conditions at the inlet and outlet of the

cooling tower.

5) Calculate the air flow rate through the tower and the consumption of the induced draft fan placed at

the top of the tower, which handles the saturated air exiting the tower, Assume an air pressure drop

through the tower of 90 Pa and a total efficiency (isentropic, mechanical, electrical) of the fan of 60%.

6) Calculate the required water make up flow, considering that in order to avoid excessive accumulation

of salts in the water loop a purge flow of water equal to the flow of evaporated water must be discharged

from the loop.

Other data: c =4.186 kJ/kg-K; c =1 kJ/kg-K

p,water p,air

Energy Systems LM - wr