EXAMINATION PAPER: ACADEMIC SESSION 2020/2021

University of Greenwich

Campus Medway

Faculty Engineering & Science

Level 7

Exam Session April/May 2021

MODULE CODE GEEN 1121

MODULE TITLE Advanced Thermo-fluidApplicationExamType Online Exam

Exam Duration 2 hours

Instructions to Candidates

AnswerAllQuestionsinPartA.AnswerOne QuestioninPartBAll questions carry equal marks. Calculators may be used.

A formula sheet is appended.

Students will be required to achieve an overall grade of 50% to achieve a pass grade

PARTA

Q1

1. In a heat transfer relation 𝑄^̇ = 𝑈𝐴_𝑠𝜃_𝑚for heat exchanger, what is

𝜃_𝑚called? How is it calculated for parallel-flow and counter-flow heat exchanger?

[5 marks]

2. List five of the common approximations made in the analysis of heat exchangers.

[5 marks]

3. An exhaust pipe of 75 mm outside diameter is cooled by surrounding it by an annular space containing water in a parallel flow arrangement. The exhaust gas enters the exhaust pipe at 350^oC, and the water enters from the mains at 10^oC. The heat transfer coefficients for the gases and water may be taken as 0.3 and 1.5 kW/m²-K, and the pipe thickness may be negligible. The gasses are required to be cooled to 100^oC and the mean specific heat capacity at constant pressure is 1.13 kJ/kg-K. The gas flow rate is 200 kg/h and the water flow rate is 1400 kg/h. Take specific heat capacity of water as 4.19 kJ/kg-K. For this system described
   1. Calculate the heat transfer.

[3 marks]

1. Determine the overall heat transfer coefficient.

[3 marks]

1. Calculate the required pipe length for parallel flow.

[5 marks]

1. Calculate the required pipe length for counter flow.

[4 marks]

[Total marks: 25]

Q2

1. What is the physical meaning of the vorticity, 𝜉, in fluid flows? How you would work it out if the velocity field, 𝑉, is known?

[4 marks]

2. An ideal fluid flows between the inclined walls of a two-dimensional channel into a line sink located at the origin, as shown in Figure Q2. The velocity potential for this flow field is given by the expression ∅ =

𝑚 𝐿𝑛⁽𝑟⁾, where 𝑚 is a constant.

1. Find expressions for the radial (𝑣_𝑟) and tangential ((𝑣_𝜃) velocity components.

[4 marks]

1. Determine the corresponding stream function. Note that the value

of the stream function along the 𝑂𝐴 (i.e

𝜃 =

𝜋₎ 3

is zero.

[12 marks]

1. Find the value of the constant 𝑚 if the value of the stream function at point 𝐵 located at (𝑥 = 1 , 𝑦 = 4) is 𝜓_𝐵 = −0.71.

[5 marks]

[Total: 25 marks]

Figure Q2

Q3

(a) A vapour compression refrigeration plant using R134a operates with a compression suction pressure of 2 bar and a temperature and -10.09^oC. The condenser pressure is 8 bar and there is no undercooling of the condensate. Compression takes place in two stages, and the condensate is throttled into a flash chamber at 4 bar from which dry saturated vapour is drawn to mix with the refrigerant from the Low- pressure (LP) compressor before entering into the High-pressure (HP)

compressor. The liquid from the flash chamber is throttled into the evaporator. If each compressor operates isentropically and the refrigerant capacity is 10 tons.

1. Show the block diagram and the corresponding Temperature- entropy (T-s) diagram.

[6 marks]

2. Find the enthalpy at each point in the cycle.

[8 marks]

3. Determine the mass flow of the refrigerant for the lower and upper cycle.

[6 marks]

4. Calculate the power input to each compressor.

[3 marks]

5. Determine the coefficient of performance (COP) of the plant.

[2 marks]

[Total: 25 marks]

END of PART A

PARTB

Q4

NB:thisishalfthermoquestionandhalffromfluidaswehave5questiononly.

1. When is a heat exchanger classified as being compact?

[2 marks]

2. Do you think a double-pipe heat exchanger can be classified as a compact heat exchanger?

[2 marks]

3. How does a cross-flow heat exchanger differs from a counter-flow one?

[2 marks]

4. What is the difference between mixed and unmixed fluids in cross- flow?

[1 marks]

5. What is the role of the baffles in a shell-and-tube heat exchanger? How does the presence of baffles affect the heat transfer and the pumping power requirements? Explain.

[5 marks]

6. Give a critical appraisal of the HAWT and VAWT technologies and considering recent advancements in control systems and constructions materials present, with justification, whether or not, for some applications, the VAWT technology is likely to be as successful as the HAWT.

[13 marks]

[Total: 25 marks]

Q5

1. Consider an ideal Assume a Horizontal Axis Wind Turbine (HAWT) having an infinite number of blades for the rotor to be considered an actuator. Also assume the air to be homogeneous, steady, non- compressible and with a non-rotating wake.

Show that the velocity, 𝒖, at the rotor is the average of the upstream velocity 𝑼_𝒐 and the downstream velocity 𝒖_𝟏. You can apply Bernoulli’s equation to the regions upstream and downstream of the rotor to obtain the thrust on the rotor and combine with the rate of change of axial momentum of the wind through the rotor.

[12 marks]

2. Calculate the axial wind velocity 𝒖 at the rotor if the upstream wind velocity is 𝑼_𝒐 = 𝟏𝟐𝒎𝒔^−𝟏 and the axial induction factor is 𝒂 = 𝟎. 𝟐𝟏.

[4 marks]

3. Calculate the wind velocity 𝒖_𝟏 far downstream of the rotor when the ^{pressure is restored to the level of the upstream pressure 𝑷𝒐}.

[6 marks]

4. Calculate the thrust on the rotor if the blades have a span of 𝟔𝒎. Take the air density 𝝆 = 𝟏. 𝟐𝒌𝒈𝒎^−𝟑 and neglect the diameter of the hub.

[3 marks]

[Total: 25 marks]

END OF PART B END OF PAPER

FormulaSheet

Conditions for irrotational flow:

𝜕𝑤

𝜕𝑦

𝜕𝑣

= ,

𝜕𝑧

𝜕𝑢

𝜕𝑧

𝜕𝑤

=

𝜕𝑥

𝑎𝑛𝑑

𝜕𝑣

𝜕𝑥

𝜕𝑢

=

𝜕𝑦

Continuity equation:

𝜕𝑢 𝜕𝑣 𝜕𝑤

+ + = 0

𝜕𝑥 𝜕𝑦 𝜕𝑧

1 𝜕𝑤 𝜕𝑣 1

Rotation in a fluid: 𝜔 = ( − ) 𝑖̂ +

𝜕𝑢 𝜕𝑤 1 𝜕𝑣 𝜕𝑢

₋ ̂ ( ) 𝑗̂ + ( − )𝑘

2 𝜕𝑦

𝜕𝑧

2 𝜕𝑧

𝜕𝑥

2 𝜕𝑥

𝜕𝑦

Shear strain in a fluid:

𝑟_𝑥𝑦 =

1 𝜕𝑣 [

2 𝜕𝑥

𝜕𝑢

+

𝜕𝑦

] , 𝑟_𝑦𝑧 =

1 𝜕𝑣 [

2 𝜕𝑧

𝜕𝑤

+

𝜕𝑦

] , 𝑟_𝑥𝑧 =

1 𝜕𝑢 [

2 𝜕𝑧

𝜕𝑤

+ ]

𝜕𝑥

Axial induction factor

𝑈_𝑜 − 𝑢

𝑎 =

𝑈_𝑜

Wind velocity far downstream a wind turbine’s rotor:

𝑢₁ = 𝑈_𝑜(1 − 2𝑎)

Elementary flow rate per unit length

𝑑𝑞 = 𝑢𝑑𝑥

Definition of stream function

1 𝜕𝜓

𝜕∅

𝜕𝜓

1 𝜕∅

𝑣_𝑟 = _{𝑟 𝜕𝜃} = _𝜕𝑟 𝑎𝑛𝑑 𝑣_𝜃 = − _𝜕𝑟 = _{𝑟 𝜕𝜃}

Definition of velocity potential

𝑢 =

𝜕𝜙

𝜕𝑥

𝑎𝑛𝑑 𝑣 = −

𝜕𝜙

𝜕𝑦

Bernoulli’s equation

𝑃 +

1

𝜌𝑢²

2

= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

Thrust on a rotor.

𝑇 = 𝑚̇ (𝑈₀ − 𝑢₁)

𝑚̇ = 𝜌𝑢𝐴

𝑟 = ^√𝑥² + 𝑦²

𝜃 = tan⁻¹(^𝑦)

𝑥

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