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Department of Mechanical Engineering

MSc/PGDip/PGCert in Energy Systems and the Environment

Specialist Modules

Wednesday 17 January 2007 2.00pm – 5.00pm (3 hours)

Full-time MSc/PGDip/PGCert students should attempt ONE question from each module.

All other students (inc. part-time postgraduates and exchange)

should attempt ONE question per module for which they are registered. Time allocation is 1 hour per question.

Calculators must not be used to store text and/or formulae nor be capable of communication. Invigilators may require calculators to be reset.

The following will be supplied with this paper: Property tables Figures 4(a) & 4(b) Ammonia p-h chart

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16915 ENERGY RESOURCES AND POLICY

Q.1 (a) Which has the higher efficiency, a coal-fired electricity generating station or a nuclear power plant? Give reasons for your answer.

(4 marks)

(b) What could be done to utilise a greater proportion of the energy produced from coal or nuclear plants? Discuss briefly.

(8 marks)

(c) A site for a small hydro-electric plant provides a head of 42m. The supply pipeline is 0.3m in diameter and 310m long, with a friction factor estimated at 0.0055. At a design flow rate of 0.2m3/s, calculate the transmission efficiency and the power delivered to the turbine.

(10 marks)

(d) What is the maximum power that the system can produce? (8 marks)

(e) After constructing the power plant, it was found that the maximum power deliverable was only 62.5kW. Use this information to calculate the actual pipe friction factor, and thus calculate the power it will actually deliver at the design flow rate of 0.2m3/s.

(15 marks)

(f) Sketch the power / flow rate characteristics of the system as designed and as actually built, showing the maximum power points and the operating points at the design flow rate.

(5 marks)

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Q.2 (a) The power extracted by a wind turbine is given by [ ]2221

eVVAV −∞ρ ,

where ( )aVV −= ∞ 1 and ( )aVVe 21 −= ∞ . V∞ is the wind speed, ρ is the air density and A is the rotor swept area. Show that the maximum possible value of the turbine power coefficient is 16 / 27.

(12 marks)

(b) Why is this value so much less than 1? Explain briefly. (5 marks)

(c) “The average Scottish household consumes 3kW, so a 1kW rated wind turbine will provide one-third of its needs.” Briefly discuss the validity of this statement.

(8 marks)

(d) There is presently much talk in the UK about producing domestic houses which will produce zero net carbon emissions during their lifetimes, using a combination of demand-side and supply-side measures. How in practice might this be achieved? Make recommendations which are appropriate for the UK climate.

(25 marks)

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16916 ENERGY SYSTEMS ANALYSIS

Q.3 (a) The rate of radiation heat transfer between two surfaces can be expressed as:

( )

⎟⎟⎠

⎞⎜⎜⎝

⎛ −++

−−

=

2

2

2

1

121

1

42

411

111εε

εεσ

AA

F

TTAQ

Indicate the meaning of the terms in this equation, and show how it can be simplified for the case of a small surface-mounted heating panel in a large enclosure.

(5 marks)

(b) A heating panel 2m long by 1m high is fitted to the wall of a large room in which the air and surfaces are at 20oC. The surface of the panel is maintained at 84oC and its emissivity is 0.85. Using the tables provided, and the information given below, calculate the rate of heat emission from the panel. For convection, Nu = 0.13 (Gr Pr)0.33 Gr = βg (ΔT)l3 ρ2/μ2 For radiation, σ = 5.67× 10-8 W/m2K4

(12 marks)

(c) A house has a composite wall made up of 25mm thick plywood on the outside, 110mm thick glass fibre insulation and 15mm thick plasterboard on the inside. The thermal conductivities of plywood, glass fibre and plasterboard are 0.15, 0.04 and 0.20W/mK respectively. The inside air temperature is 22oC and the inside surface heat transfer coefficient is 8.0W/m2K. On a cold and windy winter day, the outside air temperature is -5oC with an outside surface heat transfer coefficient of 75W/m2K. The total surface area of the wall is 400m2. Calculate the rate of heat loss through the wall and the temperature at the mid-point of the insulation.

(13 marks)

(d) The relative humidity in the house in (c) above has been measured as 46.4%. Using the tables provided, determine the dew point temperature and moisture content. Barometric pressure = 100kPa

(5 marks)

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(e) A shell-and-tube heat exchanger with one shell pass and two tube passes is to be used to condense 1.5kg/s of saturated steam at 1bar to saturated liquid. Condensation occurs on the outer surface of the tubes and the corresponding convection heat transfer coefficient is 10,200W/m2K. Cooling water flows through the tubes. Each tube pass consists of 50 thin-walled tubes of 25mm internal diameter. The cooling water is supplied to the exchanger at 18oC and is to leave it at 32oC. Using the tables provided and the data given below, determine:

i) the overall heat transfer coefficient ii) the required tube length per pass.

For flow inside tubes, Nu = 0.023Re0.8Pr0.4

(15 marks)

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Q.4 (a) The layout of a gas turbine plant is shown in Figure 4(a). Two stages of compression are used, with intercooling between the compressors. There are two stages of expansion, with a reheat combustion chamber between the turbines. The HP turbine drives the HP compressor. The LP turbine drives the LP compressor and provides the power output from the plant. Air enters the LP compressor at 1bar and 18oC. The intercooling between the compressors is perfect and the pressure at entry to the HP turbine is 9bar. The temperature at entry to both turbines is 660oC. The pressure ratios of both compressors are equal. The isentropic efficiencies of the compressors and turbines are 0.8 and 0.85 respectively. Calculate:

i) the pressure at entry to the LP turbine ii) the power output from the plant for a flow rate of 100kg/s

iii) the thermal efficiency and work ratio of the plant

Assume air is the working fluid throughout, for which γ = 1.4 and Cp = 1.005kJ/kgK.

(25 marks)

(b) In an ammonia refrigeration system, one evaporator provides a refrigeration capacity of 150kW at a temperature of -10oC. A second evaporator provides a refrigeration capacity of 180kW at a temperature of 10oC. The system uses two compression stages with flash intercooling and is arranged as shown in Figure 4(b). The discharge pressure of the LP compressor and the suction pressure of the HP compressor are the same as the pressure in the 10oC evaporator. The ammonia leaves both evaporators as dry saturated vapour. The condensing pressure is 1500kN/m2 and the ammonia leaving the condenser is subcooled to 25oC. Both compressions can be taken as isentropic.

i) Draw the cycle on the pressure-enthalpy chart provided and evaluate the enthalpy value for each state point.

Also determine:

ii) the mass flow rate through each compressor

iii) the coefficient of performance of the plant

iv) the swept volume in m3/min of the HP compressor if the volumetric efficiency is 0.82.

(25 marks)

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16917 ELECTRICAL POWER SYSTEMS

Q.5 (a) You are asked to produce a preliminary design for an 80MW hydro power scheme in the North of Scotland.

i) What type of generator would you recommend for this scheme? (2 marks)

ii) Explain the reasons behind your recommendation.

(8 marks)

iii) Would your recommended generator be suitable for a steam turbine?

(2 marks)

(b) The transformer connecting the power station to the local transmission line is protected by a unit protection scheme; there is also a back-up non-unit protection scheme.

i) Briefly describe the difference between unit and non-unit protection schemes.

(8 marks) ii) Using a diagram if necessary, describe the main components

found in any protection scheme and explain their function. (12 marks)

(c) The per-phase equivalent circuit of a 3-phase synchronous generator feeding a resistive load is shown below.

i) For this phase, calculate the magnitude of the current, voltage V and the phase angle δ.

(12 marks)

ii) Calculate the total real, reactive and apparent power supplied by the generator to the load.

(6 marks)

44 Ω

j65 Ω

V∠0 4000∠δ

I

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Q.6 (a) With the aid of diagrams describe the basic components and operation of

a coal power station and a combined cycle gas turbine power (CCGT) station.

(12 marks)

(b) i) Discuss the economic and environmental benefits of the CCGT station compared to traditional coal stations.

(6 marks)

ii) For the UK, discuss some of the drawbacks of developing large numbers of CCGT stations.

(6 marks)

(c) The phasor voltage and current drawn by a single-phase load in a factory are as follows:

input voltage (50Hz):

007.229 ∠ input current (50Hz):

0404.40 −∠

For this machine calculate:

(i) the peak current flowing into the machine and peak voltage across the machine input terminals

(4 marks)

(ii) the apparent power consumption (4 marks)

(iii) the real power consumption

(4 marks)

(iv) the reactive power consumption (4 marks)

(v) the power factor of the machine.

(4 marks)

(d) Explain how the power factor could be improved and how this could

reduce the cost of running the machine. (6 marks)

END OF PAPER

(A D Grant, R C McLean, N Kelly)