UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING

FINAL EXAMINATION, APRIL-2017

MIE 311 Hi S - THERMAL ENERGY CONVERSION

Exam Type: X

Examiner: J.S. Wallace

You may use your copy of the course textbook by Moran and Shapiro, your lab manual,

class notes or study notes prepared by you personally, returned problem sets, material

distributed in class and any printed/written material posted on the Winter 2017 MIE 311

course Blackboard. Calculators will be non-printing, non-communicating, silent & self-

powered. Show your work on your exam booklet.

1.(20%) Air enters a window air conditioner at I atm (101.325 kPa), 32°C and 70%

relative humidity at a volumetric flow rate of 3 m3/min (state 1). It leaves as

saturated air at 12°C (state 3). Any

moisture condensed from the air leaves 41, . 4 at 12°C (state 2). Cp,air = 1.005 kJ/kg-K

and Rar= 0.287 kJ/kg-K. /-

Using analytical methods (not the

psychrometric chart),

Calculate the rate of moisture removal

(kg/mm) from the air.

Calculate the rate of cooling (kW)

required.

2. (20%) A four-stroke diesel engine operating on the air standard Limited Pressure

(Dual) cycle has a nominal (geometric) compression ratio of 17.3:1. This four-cylinder

engine has a bore and stroke of 102 mm and 120 mm respectively fora total displacement

of 3.9 litres. The displaced volume for one cylinder is 9.806 x iO m3 and the clearance

volume is 6.016 x 10 m3. Intake air temperature and pressure are 175 kPa and 87°C

respectively. The maximum pressure achieved during the cycle is Pmax = 12 MPa and the

total heat input to a cycle is 1300 kJ/kg. Due to the large temperature range involved,

the variation of specific heat with temperature cannot be neglected so the Air Tables

must be used. Rair = 0.287 kJ/kg-K

Calculate the mass of air (kg) in the cylinder.

Calculate the temperature (K) and pressure (kPa) at the end of each process.

Calculate the net work output, Wnet (kJ), and the thermal efficiency for the cycle

Calculate the mean effective pressure (kPa) for the cycle.

Calculate the power output (kW) of this engine running at 1800 rpm at the operating

conditions used in (a) through (d).

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3. (20%) A mixture consists of 2.7 Ibm of helium and 3.0 Ibm of nitrogen at 10 psia, 80°F. The mixture is compressed isentropically to 100 psia. Assuming ideal gas behavior:

Calculate the mass fractions of the two components in the mixture Calculate the final temperature of the mixture (°F) Calculate the work (BTU) required for compression Calculate the entropy change (BTU/R) for each of the two components during this

process.

Useful data: RHe = 0.4961 BTU/Ibm-R, RN2 = 0.0709 BTU/lbm-R

For helium: cpHe = 1.24 BTU/Ibm-R, Cv,He = 0.744 BTU/lbm-R Note that, as a monatomic gas, there is no variation of Cp, cv with temperature for Helium.

For nitrogen: Temperature (°F) cp (BTU/lbm-R) CV (BTU/lbm-R)

40 0.248 0.177

100 0.248 0.178

200 0.249 0.178

300 0.250 0.179

400 0.251 0.180

500 0.254 0.183

600 0.256 0.185

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4. (25%). Consider an ideal dual-loop heat-powered refrigeration cycle utilizing R134a

as the working fluid. The cycle is shown in the figure below. Saturated vapor at 80°C

leaves the boiler and expands in the turbine to the condenser pressure. Saturated vapor

at -18°C leaves the evaporator and is compressed to the condenser pressure. The ratio

of mass flows through the two loops is such that the turbine produces just enough power

to drive the compressor. The two exiting streaming mix together and enter the condenser,

which operates at a pressure of 7bar. Saturated liquid leaves the condenser and is split

into two streams in the necessary proportions.

bine omresso [j

I, — -

r

j

coier Power Refrigeration [1- 1001) loop €vaporato

Condenser -j-.-. Qc0d

Pump J—

Expansion valve

Assuming that the turbine and compressor are each 75% efficient and that the pump is

100% efficient, calculate:

The ratio of mass flow rate through the power loop to that through the refrigerant loop (ñi1/ñi7 )?

If the refrigeration capacity is 6 tons, what is the mass flow rate of R-1 34a required in

the refrigerant loop, rn7 (kg/s)?

What rate of heat input H (kW) is required to operate the system to produce 6 tons of refrigeration?

The performance of the cycle, in terms of the ratio 6iAH.

At what rate is heat rejected from the condenser e2conctenser (kW)?

Sketch the process on a T-s diagram.

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5. (15%). Distillation of water boiling and then condensing the vapor in a different

container is a classic method of water purification but it is a very energy intensive process.

Compression-distillation technology offers some advantages compared to distillation. A

simplified flow diagram of a very basic compression distillation system is shown below.

Ki

A steady flow of impure water at 14.696 and 60°F (state 1) enters a heat exchanger in

which it is evaporated. The purified saturated vapor water (state 2) is compressed and

then fed back to the other side of the heat exchanger (state 3) where it provides the heat

input Q to evaporate the water. The heat exchanger tube or plate wall prevents any direct

contact between the impure water (process 1-2) and the pure water (process 3-4).

Assuming that the compressor efficiency is 0.7 and that the purified water emerges (state

4) at 212°F, 60 psia,

What is the state of the water at state 1 (Neglect the effect of any impurities on the

properties of water) and its enthalpy hi (BTU/lbm)?.

What is the state of the water at state 4 and its enthalpy h4?

What is the state of the water at state 3 and its enthalpy h3?

What is the work input to the compressor per Ibm of distilled water?

Sketch the process on a T-s diagram.

A conventional distillation process effectively involves just the change of state from 1

to 2. What is the heat input required per unit mass of water for the process 1 to 2?

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